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, relation or similiar object is created from scratch,
569 the space in which it lives needs to be specified using an C<isl_space>.
570 Each space involves zero or more parameters and zero, one or two
571 tuples of set or input/output dimensions. The parameters and dimensions
572 are identified by an C<isl_dim_type> and a position.
573 The type C<isl_dim_param> refers to parameters,
574 the type C<isl_dim_set> refers to set dimensions (for spaces
575 with a single tuple of dimensions) and the types C<isl_dim_in>
576 and C<isl_dim_out> refer to input and output dimensions
577 (for spaces with two tuples of dimensions).
578 Local spaces (see L</"Local Spaces">) also contain dimensions
579 of type C<isl_dim_div>.
580 Note that parameters are only identified by their position within
581 a given object. Across different objects, parameters are (usually)
582 identified by their names or identifiers. Only unnamed parameters
583 are identified by their positions across objects. The use of unnamed
584 parameters is discouraged.
586 #include <isl/space.h>
587 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
588 unsigned nparam, unsigned n_in, unsigned n_out);
589 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
591 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
592 unsigned nparam, unsigned dim);
593 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
594 void isl_space_free(__isl_take isl_space *space);
595 unsigned isl_space_dim(__isl_keep isl_space *space,
596 enum isl_dim_type type);
598 The space used for creating a parameter domain
599 needs to be created using C<isl_space_params_alloc>.
600 For other sets, the space
601 needs to be created using C<isl_space_set_alloc>, while
602 for a relation, the space
603 needs to be created using C<isl_space_alloc>.
604 C<isl_space_dim> can be used
605 to find out the number of dimensions of each type in
606 a space, where type may be
607 C<isl_dim_param>, C<isl_dim_in> (only for relations),
608 C<isl_dim_out> (only for relations), C<isl_dim_set>
609 (only for sets) or C<isl_dim_all>.
611 To check whether a given space is that of a set or a map
612 or whether it is a parameter space, use these functions:
614 #include <isl/space.h>
615 int isl_space_is_params(__isl_keep isl_space *space);
616 int isl_space_is_set(__isl_keep isl_space *space);
617 int isl_space_is_map(__isl_keep isl_space *space);
619 Spaces can be compared using the following function:
621 #include <isl/space.h>
622 int isl_space_is_equal(__isl_keep isl_space *space1,
623 __isl_keep isl_space *space2);
625 It is often useful to create objects that live in the
626 same space as some other object. This can be accomplished
627 by creating the new objects
628 (see L<Creating New Sets and Relations> or
629 L<Creating New (Piecewise) Quasipolynomials>) based on the space
630 of the original object.
633 __isl_give isl_space *isl_basic_set_get_space(
634 __isl_keep isl_basic_set *bset);
635 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
637 #include <isl/union_set.h>
638 __isl_give isl_space *isl_union_set_get_space(
639 __isl_keep isl_union_set *uset);
642 __isl_give isl_space *isl_basic_map_get_space(
643 __isl_keep isl_basic_map *bmap);
644 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
646 #include <isl/union_map.h>
647 __isl_give isl_space *isl_union_map_get_space(
648 __isl_keep isl_union_map *umap);
650 #include <isl/constraint.h>
651 __isl_give isl_space *isl_constraint_get_space(
652 __isl_keep isl_constraint *constraint);
654 #include <isl/polynomial.h>
655 __isl_give isl_space *isl_qpolynomial_get_domain_space(
656 __isl_keep isl_qpolynomial *qp);
657 __isl_give isl_space *isl_qpolynomial_get_space(
658 __isl_keep isl_qpolynomial *qp);
659 __isl_give isl_space *isl_qpolynomial_fold_get_space(
660 __isl_keep isl_qpolynomial_fold *fold);
661 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
662 __isl_keep isl_pw_qpolynomial *pwqp);
663 __isl_give isl_space *isl_pw_qpolynomial_get_space(
664 __isl_keep isl_pw_qpolynomial *pwqp);
665 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
666 __isl_keep isl_pw_qpolynomial_fold *pwf);
667 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
668 __isl_keep isl_pw_qpolynomial_fold *pwf);
669 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
670 __isl_keep isl_union_pw_qpolynomial *upwqp);
671 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
672 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
675 __isl_give isl_space *isl_aff_get_domain_space(
676 __isl_keep isl_aff *aff);
677 __isl_give isl_space *isl_aff_get_space(
678 __isl_keep isl_aff *aff);
679 __isl_give isl_space *isl_pw_aff_get_domain_space(
680 __isl_keep isl_pw_aff *pwaff);
681 __isl_give isl_space *isl_pw_aff_get_space(
682 __isl_keep isl_pw_aff *pwaff);
683 __isl_give isl_space *isl_multi_aff_get_domain_space(
684 __isl_keep isl_multi_aff *maff);
685 __isl_give isl_space *isl_multi_aff_get_space(
686 __isl_keep isl_multi_aff *maff);
687 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
688 __isl_keep isl_pw_multi_aff *pma);
689 __isl_give isl_space *isl_pw_multi_aff_get_space(
690 __isl_keep isl_pw_multi_aff *pma);
691 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
692 __isl_keep isl_union_pw_multi_aff *upma);
694 #include <isl/point.h>
695 __isl_give isl_space *isl_point_get_space(
696 __isl_keep isl_point *pnt);
698 The identifiers or names of the individual dimensions may be set or read off
699 using the following functions.
701 #include <isl/space.h>
702 __isl_give isl_space *isl_space_set_dim_id(
703 __isl_take isl_space *space,
704 enum isl_dim_type type, unsigned pos,
705 __isl_take isl_id *id);
706 int isl_space_has_dim_id(__isl_keep isl_space *space,
707 enum isl_dim_type type, unsigned pos);
708 __isl_give isl_id *isl_space_get_dim_id(
709 __isl_keep isl_space *space,
710 enum isl_dim_type type, unsigned pos);
711 __isl_give isl_space *isl_space_set_dim_name(
712 __isl_take isl_space *space,
713 enum isl_dim_type type, unsigned pos,
714 __isl_keep const char *name);
715 int isl_space_has_dim_name(__isl_keep isl_space *space,
716 enum isl_dim_type type, unsigned pos);
717 __isl_keep const char *isl_space_get_dim_name(
718 __isl_keep isl_space *space,
719 enum isl_dim_type type, unsigned pos);
721 Note that C<isl_space_get_name> returns a pointer to some internal
722 data structure, so the result can only be used while the
723 corresponding C<isl_space> is alive.
724 Also note that every function that operates on two sets or relations
725 requires that both arguments have the same parameters. This also
726 means that if one of the arguments has named parameters, then the
727 other needs to have named parameters too and the names need to match.
728 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
729 arguments may have different parameters (as long as they are named),
730 in which case the result will have as parameters the union of the parameters of
733 Given the identifier or name of a dimension (typically a parameter),
734 its position can be obtained from the following function.
736 #include <isl/space.h>
737 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
738 enum isl_dim_type type, __isl_keep isl_id *id);
739 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
740 enum isl_dim_type type, const char *name);
742 The identifiers or names of entire spaces may be set or read off
743 using the following functions.
745 #include <isl/space.h>
746 __isl_give isl_space *isl_space_set_tuple_id(
747 __isl_take isl_space *space,
748 enum isl_dim_type type, __isl_take isl_id *id);
749 __isl_give isl_space *isl_space_reset_tuple_id(
750 __isl_take isl_space *space, enum isl_dim_type type);
751 int isl_space_has_tuple_id(__isl_keep isl_space *space,
752 enum isl_dim_type type);
753 __isl_give isl_id *isl_space_get_tuple_id(
754 __isl_keep isl_space *space, enum isl_dim_type type);
755 __isl_give isl_space *isl_space_set_tuple_name(
756 __isl_take isl_space *space,
757 enum isl_dim_type type, const char *s);
758 int isl_space_has_tuple_name(__isl_keep isl_space *space,
759 enum isl_dim_type type);
760 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
761 enum isl_dim_type type);
763 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
764 or C<isl_dim_set>. As with C<isl_space_get_name>,
765 the C<isl_space_get_tuple_name> function returns a pointer to some internal
767 Binary operations require the corresponding spaces of their arguments
768 to have the same name.
770 Spaces can be nested. In particular, the domain of a set or
771 the domain or range of a relation can be a nested relation.
772 The following functions can be used to construct and deconstruct
775 #include <isl/space.h>
776 int isl_space_is_wrapping(__isl_keep isl_space *space);
777 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
778 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
780 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
781 be the space of a set, while that of
782 C<isl_space_wrap> should be the space of a relation.
783 Conversely, the output of C<isl_space_unwrap> is the space
784 of a relation, while that of C<isl_space_wrap> is the space of a set.
786 Spaces can be created from other spaces
787 using the following functions.
789 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
790 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
791 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
792 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
793 __isl_give isl_space *isl_space_params(
794 __isl_take isl_space *space);
795 __isl_give isl_space *isl_space_set_from_params(
796 __isl_take isl_space *space);
797 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
798 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
799 __isl_take isl_space *right);
800 __isl_give isl_space *isl_space_align_params(
801 __isl_take isl_space *space1, __isl_take isl_space *space2)
802 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
803 enum isl_dim_type type, unsigned pos, unsigned n);
804 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
805 enum isl_dim_type type, unsigned n);
806 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
807 enum isl_dim_type type, unsigned first, unsigned n);
808 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
809 enum isl_dim_type dst_type, unsigned dst_pos,
810 enum isl_dim_type src_type, unsigned src_pos,
812 __isl_give isl_space *isl_space_map_from_set(
813 __isl_take isl_space *space);
814 __isl_give isl_space *isl_space_map_from_domain_and_range(
815 __isl_take isl_space *domain,
816 __isl_take isl_space *range);
817 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
818 __isl_give isl_space *isl_space_curry(
819 __isl_take isl_space *space);
821 Note that if dimensions are added or removed from a space, then
822 the name and the internal structure are lost.
826 A local space is essentially a space with
827 zero or more existentially quantified variables.
828 The local space of a (constraint of a) basic set or relation can be obtained
829 using the following functions.
831 #include <isl/constraint.h>
832 __isl_give isl_local_space *isl_constraint_get_local_space(
833 __isl_keep isl_constraint *constraint);
836 __isl_give isl_local_space *isl_basic_set_get_local_space(
837 __isl_keep isl_basic_set *bset);
840 __isl_give isl_local_space *isl_basic_map_get_local_space(
841 __isl_keep isl_basic_map *bmap);
843 A new local space can be created from a space using
845 #include <isl/local_space.h>
846 __isl_give isl_local_space *isl_local_space_from_space(
847 __isl_take isl_space *space);
849 They can be inspected, modified, copied and freed using the following functions.
851 #include <isl/local_space.h>
852 isl_ctx *isl_local_space_get_ctx(
853 __isl_keep isl_local_space *ls);
854 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
855 int isl_local_space_dim(__isl_keep isl_local_space *ls,
856 enum isl_dim_type type);
857 int isl_local_space_has_dim_id(
858 __isl_keep isl_local_space *ls,
859 enum isl_dim_type type, unsigned pos);
860 __isl_give isl_id *isl_local_space_get_dim_id(
861 __isl_keep isl_local_space *ls,
862 enum isl_dim_type type, unsigned pos);
863 int isl_local_space_has_dim_name(
864 __isl_keep isl_local_space *ls,
865 enum isl_dim_type type, unsigned pos)
866 const char *isl_local_space_get_dim_name(
867 __isl_keep isl_local_space *ls,
868 enum isl_dim_type type, unsigned pos);
869 __isl_give isl_local_space *isl_local_space_set_dim_name(
870 __isl_take isl_local_space *ls,
871 enum isl_dim_type type, unsigned pos, const char *s);
872 __isl_give isl_local_space *isl_local_space_set_dim_id(
873 __isl_take isl_local_space *ls,
874 enum isl_dim_type type, unsigned pos,
875 __isl_take isl_id *id);
876 __isl_give isl_space *isl_local_space_get_space(
877 __isl_keep isl_local_space *ls);
878 __isl_give isl_aff *isl_local_space_get_div(
879 __isl_keep isl_local_space *ls, int pos);
880 __isl_give isl_local_space *isl_local_space_copy(
881 __isl_keep isl_local_space *ls);
882 void *isl_local_space_free(__isl_take isl_local_space *ls);
884 Two local spaces can be compared using
886 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
887 __isl_keep isl_local_space *ls2);
889 Local spaces can be created from other local spaces
890 using the following functions.
892 __isl_give isl_local_space *isl_local_space_domain(
893 __isl_take isl_local_space *ls);
894 __isl_give isl_local_space *isl_local_space_range(
895 __isl_take isl_local_space *ls);
896 __isl_give isl_local_space *isl_local_space_from_domain(
897 __isl_take isl_local_space *ls);
898 __isl_give isl_local_space *isl_local_space_intersect(
899 __isl_take isl_local_space *ls1,
900 __isl_take isl_local_space *ls2);
901 __isl_give isl_local_space *isl_local_space_add_dims(
902 __isl_take isl_local_space *ls,
903 enum isl_dim_type type, unsigned n);
904 __isl_give isl_local_space *isl_local_space_insert_dims(
905 __isl_take isl_local_space *ls,
906 enum isl_dim_type type, unsigned first, unsigned n);
907 __isl_give isl_local_space *isl_local_space_drop_dims(
908 __isl_take isl_local_space *ls,
909 enum isl_dim_type type, unsigned first, unsigned n);
911 =head2 Input and Output
913 C<isl> supports its own input/output format, which is similar
914 to the C<Omega> format, but also supports the C<PolyLib> format
919 The C<isl> format is similar to that of C<Omega>, but has a different
920 syntax for describing the parameters and allows for the definition
921 of an existentially quantified variable as the integer division
922 of an affine expression.
923 For example, the set of integers C<i> between C<0> and C<n>
924 such that C<i % 10 <= 6> can be described as
926 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
929 A set or relation can have several disjuncts, separated
930 by the keyword C<or>. Each disjunct is either a conjunction
931 of constraints or a projection (C<exists>) of a conjunction
932 of constraints. The constraints are separated by the keyword
935 =head3 C<PolyLib> format
937 If the represented set is a union, then the first line
938 contains a single number representing the number of disjuncts.
939 Otherwise, a line containing the number C<1> is optional.
941 Each disjunct is represented by a matrix of constraints.
942 The first line contains two numbers representing
943 the number of rows and columns,
944 where the number of rows is equal to the number of constraints
945 and the number of columns is equal to two plus the number of variables.
946 The following lines contain the actual rows of the constraint matrix.
947 In each row, the first column indicates whether the constraint
948 is an equality (C<0>) or inequality (C<1>). The final column
949 corresponds to the constant term.
951 If the set is parametric, then the coefficients of the parameters
952 appear in the last columns before the constant column.
953 The coefficients of any existentially quantified variables appear
954 between those of the set variables and those of the parameters.
956 =head3 Extended C<PolyLib> format
958 The extended C<PolyLib> format is nearly identical to the
959 C<PolyLib> format. The only difference is that the line
960 containing the number of rows and columns of a constraint matrix
961 also contains four additional numbers:
962 the number of output dimensions, the number of input dimensions,
963 the number of local dimensions (i.e., the number of existentially
964 quantified variables) and the number of parameters.
965 For sets, the number of ``output'' dimensions is equal
966 to the number of set dimensions, while the number of ``input''
972 __isl_give isl_basic_set *isl_basic_set_read_from_file(
973 isl_ctx *ctx, FILE *input);
974 __isl_give isl_basic_set *isl_basic_set_read_from_str(
975 isl_ctx *ctx, const char *str);
976 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
978 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
982 __isl_give isl_basic_map *isl_basic_map_read_from_file(
983 isl_ctx *ctx, FILE *input);
984 __isl_give isl_basic_map *isl_basic_map_read_from_str(
985 isl_ctx *ctx, const char *str);
986 __isl_give isl_map *isl_map_read_from_file(
987 isl_ctx *ctx, FILE *input);
988 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
991 #include <isl/union_set.h>
992 __isl_give isl_union_set *isl_union_set_read_from_file(
993 isl_ctx *ctx, FILE *input);
994 __isl_give isl_union_set *isl_union_set_read_from_str(
995 isl_ctx *ctx, const char *str);
997 #include <isl/union_map.h>
998 __isl_give isl_union_map *isl_union_map_read_from_file(
999 isl_ctx *ctx, FILE *input);
1000 __isl_give isl_union_map *isl_union_map_read_from_str(
1001 isl_ctx *ctx, const char *str);
1003 The input format is autodetected and may be either the C<PolyLib> format
1004 or the C<isl> format.
1008 Before anything can be printed, an C<isl_printer> needs to
1011 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1013 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1014 void *isl_printer_free(__isl_take isl_printer *printer);
1015 __isl_give char *isl_printer_get_str(
1016 __isl_keep isl_printer *printer);
1018 The printer can be inspected using the following functions.
1020 FILE *isl_printer_get_file(
1021 __isl_keep isl_printer *printer);
1022 int isl_printer_get_output_format(
1023 __isl_keep isl_printer *p);
1025 The behavior of the printer can be modified in various ways
1027 __isl_give isl_printer *isl_printer_set_output_format(
1028 __isl_take isl_printer *p, int output_format);
1029 __isl_give isl_printer *isl_printer_set_indent(
1030 __isl_take isl_printer *p, int indent);
1031 __isl_give isl_printer *isl_printer_indent(
1032 __isl_take isl_printer *p, int indent);
1033 __isl_give isl_printer *isl_printer_set_prefix(
1034 __isl_take isl_printer *p, const char *prefix);
1035 __isl_give isl_printer *isl_printer_set_suffix(
1036 __isl_take isl_printer *p, const char *suffix);
1038 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1039 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1040 and defaults to C<ISL_FORMAT_ISL>.
1041 Each line in the output is indented by C<indent> (set by
1042 C<isl_printer_set_indent>) spaces
1043 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1044 In the C<PolyLib> format output,
1045 the coefficients of the existentially quantified variables
1046 appear between those of the set variables and those
1048 The function C<isl_printer_indent> increases the indentation
1049 by the specified amount (which may be negative).
1051 To actually print something, use
1053 #include <isl/printer.h>
1054 __isl_give isl_printer *isl_printer_print_double(
1055 __isl_take isl_printer *p, double d);
1057 #include <isl/set.h>
1058 __isl_give isl_printer *isl_printer_print_basic_set(
1059 __isl_take isl_printer *printer,
1060 __isl_keep isl_basic_set *bset);
1061 __isl_give isl_printer *isl_printer_print_set(
1062 __isl_take isl_printer *printer,
1063 __isl_keep isl_set *set);
1065 #include <isl/map.h>
1066 __isl_give isl_printer *isl_printer_print_basic_map(
1067 __isl_take isl_printer *printer,
1068 __isl_keep isl_basic_map *bmap);
1069 __isl_give isl_printer *isl_printer_print_map(
1070 __isl_take isl_printer *printer,
1071 __isl_keep isl_map *map);
1073 #include <isl/union_set.h>
1074 __isl_give isl_printer *isl_printer_print_union_set(
1075 __isl_take isl_printer *p,
1076 __isl_keep isl_union_set *uset);
1078 #include <isl/union_map.h>
1079 __isl_give isl_printer *isl_printer_print_union_map(
1080 __isl_take isl_printer *p,
1081 __isl_keep isl_union_map *umap);
1083 When called on a file printer, the following function flushes
1084 the file. When called on a string printer, the buffer is cleared.
1086 __isl_give isl_printer *isl_printer_flush(
1087 __isl_take isl_printer *p);
1089 =head2 Creating New Sets and Relations
1091 C<isl> has functions for creating some standard sets and relations.
1095 =item * Empty sets and relations
1097 __isl_give isl_basic_set *isl_basic_set_empty(
1098 __isl_take isl_space *space);
1099 __isl_give isl_basic_map *isl_basic_map_empty(
1100 __isl_take isl_space *space);
1101 __isl_give isl_set *isl_set_empty(
1102 __isl_take isl_space *space);
1103 __isl_give isl_map *isl_map_empty(
1104 __isl_take isl_space *space);
1105 __isl_give isl_union_set *isl_union_set_empty(
1106 __isl_take isl_space *space);
1107 __isl_give isl_union_map *isl_union_map_empty(
1108 __isl_take isl_space *space);
1110 For C<isl_union_set>s and C<isl_union_map>s, the space
1111 is only used to specify the parameters.
1113 =item * Universe sets and relations
1115 __isl_give isl_basic_set *isl_basic_set_universe(
1116 __isl_take isl_space *space);
1117 __isl_give isl_basic_map *isl_basic_map_universe(
1118 __isl_take isl_space *space);
1119 __isl_give isl_set *isl_set_universe(
1120 __isl_take isl_space *space);
1121 __isl_give isl_map *isl_map_universe(
1122 __isl_take isl_space *space);
1123 __isl_give isl_union_set *isl_union_set_universe(
1124 __isl_take isl_union_set *uset);
1125 __isl_give isl_union_map *isl_union_map_universe(
1126 __isl_take isl_union_map *umap);
1128 The sets and relations constructed by the functions above
1129 contain all integer values, while those constructed by the
1130 functions below only contain non-negative values.
1132 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1133 __isl_take isl_space *space);
1134 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1135 __isl_take isl_space *space);
1136 __isl_give isl_set *isl_set_nat_universe(
1137 __isl_take isl_space *space);
1138 __isl_give isl_map *isl_map_nat_universe(
1139 __isl_take isl_space *space);
1141 =item * Identity relations
1143 __isl_give isl_basic_map *isl_basic_map_identity(
1144 __isl_take isl_space *space);
1145 __isl_give isl_map *isl_map_identity(
1146 __isl_take isl_space *space);
1148 The number of input and output dimensions in C<space> needs
1151 =item * Lexicographic order
1153 __isl_give isl_map *isl_map_lex_lt(
1154 __isl_take isl_space *set_space);
1155 __isl_give isl_map *isl_map_lex_le(
1156 __isl_take isl_space *set_space);
1157 __isl_give isl_map *isl_map_lex_gt(
1158 __isl_take isl_space *set_space);
1159 __isl_give isl_map *isl_map_lex_ge(
1160 __isl_take isl_space *set_space);
1161 __isl_give isl_map *isl_map_lex_lt_first(
1162 __isl_take isl_space *space, unsigned n);
1163 __isl_give isl_map *isl_map_lex_le_first(
1164 __isl_take isl_space *space, unsigned n);
1165 __isl_give isl_map *isl_map_lex_gt_first(
1166 __isl_take isl_space *space, unsigned n);
1167 __isl_give isl_map *isl_map_lex_ge_first(
1168 __isl_take isl_space *space, unsigned n);
1170 The first four functions take a space for a B<set>
1171 and return relations that express that the elements in the domain
1172 are lexicographically less
1173 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1174 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1175 than the elements in the range.
1176 The last four functions take a space for a map
1177 and return relations that express that the first C<n> dimensions
1178 in the domain are lexicographically less
1179 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1180 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1181 than the first C<n> dimensions in the range.
1185 A basic set or relation can be converted to a set or relation
1186 using the following functions.
1188 __isl_give isl_set *isl_set_from_basic_set(
1189 __isl_take isl_basic_set *bset);
1190 __isl_give isl_map *isl_map_from_basic_map(
1191 __isl_take isl_basic_map *bmap);
1193 Sets and relations can be converted to union sets and relations
1194 using the following functions.
1196 __isl_give isl_union_set *isl_union_set_from_basic_set(
1197 __isl_take isl_basic_set *bset);
1198 __isl_give isl_union_map *isl_union_map_from_basic_map(
1199 __isl_take isl_basic_map *bmap);
1200 __isl_give isl_union_set *isl_union_set_from_set(
1201 __isl_take isl_set *set);
1202 __isl_give isl_union_map *isl_union_map_from_map(
1203 __isl_take isl_map *map);
1205 The inverse conversions below can only be used if the input
1206 union set or relation is known to contain elements in exactly one
1209 __isl_give isl_set *isl_set_from_union_set(
1210 __isl_take isl_union_set *uset);
1211 __isl_give isl_map *isl_map_from_union_map(
1212 __isl_take isl_union_map *umap);
1214 A zero-dimensional set can be constructed on a given parameter domain
1215 using the following function.
1217 __isl_give isl_set *isl_set_from_params(
1218 __isl_take isl_set *set);
1220 Sets and relations can be copied and freed again using the following
1223 __isl_give isl_basic_set *isl_basic_set_copy(
1224 __isl_keep isl_basic_set *bset);
1225 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1226 __isl_give isl_union_set *isl_union_set_copy(
1227 __isl_keep isl_union_set *uset);
1228 __isl_give isl_basic_map *isl_basic_map_copy(
1229 __isl_keep isl_basic_map *bmap);
1230 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1231 __isl_give isl_union_map *isl_union_map_copy(
1232 __isl_keep isl_union_map *umap);
1233 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1234 void *isl_set_free(__isl_take isl_set *set);
1235 void *isl_union_set_free(__isl_take isl_union_set *uset);
1236 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1237 void isl_map_free(__isl_take isl_map *map);
1238 void *isl_union_map_free(__isl_take isl_union_map *umap);
1240 Other sets and relations can be constructed by starting
1241 from a universe set or relation, adding equality and/or
1242 inequality constraints and then projecting out the
1243 existentially quantified variables, if any.
1244 Constraints can be constructed, manipulated and
1245 added to (or removed from) (basic) sets and relations
1246 using the following functions.
1248 #include <isl/constraint.h>
1249 __isl_give isl_constraint *isl_equality_alloc(
1250 __isl_take isl_local_space *ls);
1251 __isl_give isl_constraint *isl_inequality_alloc(
1252 __isl_take isl_local_space *ls);
1253 __isl_give isl_constraint *isl_constraint_set_constant(
1254 __isl_take isl_constraint *constraint, isl_int v);
1255 __isl_give isl_constraint *isl_constraint_set_constant_si(
1256 __isl_take isl_constraint *constraint, int v);
1257 __isl_give isl_constraint *isl_constraint_set_coefficient(
1258 __isl_take isl_constraint *constraint,
1259 enum isl_dim_type type, int pos, isl_int v);
1260 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1261 __isl_take isl_constraint *constraint,
1262 enum isl_dim_type type, int pos, int v);
1263 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1264 __isl_take isl_basic_map *bmap,
1265 __isl_take isl_constraint *constraint);
1266 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1267 __isl_take isl_basic_set *bset,
1268 __isl_take isl_constraint *constraint);
1269 __isl_give isl_map *isl_map_add_constraint(
1270 __isl_take isl_map *map,
1271 __isl_take isl_constraint *constraint);
1272 __isl_give isl_set *isl_set_add_constraint(
1273 __isl_take isl_set *set,
1274 __isl_take isl_constraint *constraint);
1275 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1276 __isl_take isl_basic_set *bset,
1277 __isl_take isl_constraint *constraint);
1279 For example, to create a set containing the even integers
1280 between 10 and 42, you would use the following code.
1283 isl_local_space *ls;
1285 isl_basic_set *bset;
1287 space = isl_space_set_alloc(ctx, 0, 2);
1288 bset = isl_basic_set_universe(isl_space_copy(space));
1289 ls = isl_local_space_from_space(space);
1291 c = isl_equality_alloc(isl_local_space_copy(ls));
1292 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1293 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1294 bset = isl_basic_set_add_constraint(bset, c);
1296 c = isl_inequality_alloc(isl_local_space_copy(ls));
1297 c = isl_constraint_set_constant_si(c, -10);
1298 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1299 bset = isl_basic_set_add_constraint(bset, c);
1301 c = isl_inequality_alloc(ls);
1302 c = isl_constraint_set_constant_si(c, 42);
1303 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1304 bset = isl_basic_set_add_constraint(bset, c);
1306 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1310 isl_basic_set *bset;
1311 bset = isl_basic_set_read_from_str(ctx,
1312 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1314 A basic set or relation can also be constructed from two matrices
1315 describing the equalities and the inequalities.
1317 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1318 __isl_take isl_space *space,
1319 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1320 enum isl_dim_type c1,
1321 enum isl_dim_type c2, enum isl_dim_type c3,
1322 enum isl_dim_type c4);
1323 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1324 __isl_take isl_space *space,
1325 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1326 enum isl_dim_type c1,
1327 enum isl_dim_type c2, enum isl_dim_type c3,
1328 enum isl_dim_type c4, enum isl_dim_type c5);
1330 The C<isl_dim_type> arguments indicate the order in which
1331 different kinds of variables appear in the input matrices
1332 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1333 C<isl_dim_set> and C<isl_dim_div> for sets and
1334 of C<isl_dim_cst>, C<isl_dim_param>,
1335 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1337 A (basic or union) set or relation can also be constructed from a
1338 (union) (piecewise) (multiple) affine expression
1339 or a list of affine expressions
1340 (See L<"Piecewise Quasi Affine Expressions"> and
1341 L<"Piecewise Multiple Quasi Affine Expressions">).
1343 __isl_give isl_basic_map *isl_basic_map_from_aff(
1344 __isl_take isl_aff *aff);
1345 __isl_give isl_map *isl_map_from_aff(
1346 __isl_take isl_aff *aff);
1347 __isl_give isl_set *isl_set_from_pw_aff(
1348 __isl_take isl_pw_aff *pwaff);
1349 __isl_give isl_map *isl_map_from_pw_aff(
1350 __isl_take isl_pw_aff *pwaff);
1351 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1352 __isl_take isl_space *domain_space,
1353 __isl_take isl_aff_list *list);
1354 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1355 __isl_take isl_multi_aff *maff)
1356 __isl_give isl_map *isl_map_from_multi_aff(
1357 __isl_take isl_multi_aff *maff)
1358 __isl_give isl_set *isl_set_from_pw_multi_aff(
1359 __isl_take isl_pw_multi_aff *pma);
1360 __isl_give isl_map *isl_map_from_pw_multi_aff(
1361 __isl_take isl_pw_multi_aff *pma);
1362 __isl_give isl_union_map *
1363 isl_union_map_from_union_pw_multi_aff(
1364 __isl_take isl_union_pw_multi_aff *upma);
1366 The C<domain_dim> argument describes the domain of the resulting
1367 basic relation. It is required because the C<list> may consist
1368 of zero affine expressions.
1370 =head2 Inspecting Sets and Relations
1372 Usually, the user should not have to care about the actual constraints
1373 of the sets and maps, but should instead apply the abstract operations
1374 explained in the following sections.
1375 Occasionally, however, it may be required to inspect the individual
1376 coefficients of the constraints. This section explains how to do so.
1377 In these cases, it may also be useful to have C<isl> compute
1378 an explicit representation of the existentially quantified variables.
1380 __isl_give isl_set *isl_set_compute_divs(
1381 __isl_take isl_set *set);
1382 __isl_give isl_map *isl_map_compute_divs(
1383 __isl_take isl_map *map);
1384 __isl_give isl_union_set *isl_union_set_compute_divs(
1385 __isl_take isl_union_set *uset);
1386 __isl_give isl_union_map *isl_union_map_compute_divs(
1387 __isl_take isl_union_map *umap);
1389 This explicit representation defines the existentially quantified
1390 variables as integer divisions of the other variables, possibly
1391 including earlier existentially quantified variables.
1392 An explicitly represented existentially quantified variable therefore
1393 has a unique value when the values of the other variables are known.
1394 If, furthermore, the same existentials, i.e., existentials
1395 with the same explicit representations, should appear in the
1396 same order in each of the disjuncts of a set or map, then the user should call
1397 either of the following functions.
1399 __isl_give isl_set *isl_set_align_divs(
1400 __isl_take isl_set *set);
1401 __isl_give isl_map *isl_map_align_divs(
1402 __isl_take isl_map *map);
1404 Alternatively, the existentially quantified variables can be removed
1405 using the following functions, which compute an overapproximation.
1407 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1408 __isl_take isl_basic_set *bset);
1409 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1410 __isl_take isl_basic_map *bmap);
1411 __isl_give isl_set *isl_set_remove_divs(
1412 __isl_take isl_set *set);
1413 __isl_give isl_map *isl_map_remove_divs(
1414 __isl_take isl_map *map);
1416 It is also possible to only remove those divs that are defined
1417 in terms of a given range of dimensions or only those for which
1418 no explicit representation is known.
1420 __isl_give isl_basic_set *
1421 isl_basic_set_remove_divs_involving_dims(
1422 __isl_take isl_basic_set *bset,
1423 enum isl_dim_type type,
1424 unsigned first, unsigned n);
1425 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1426 __isl_take isl_set *set, enum isl_dim_type type,
1427 unsigned first, unsigned n);
1428 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1429 __isl_take isl_map *map, enum isl_dim_type type,
1430 unsigned first, unsigned n);
1432 __isl_give isl_set *isl_set_remove_unknown_divs(
1433 __isl_take isl_set *set);
1434 __isl_give isl_map *isl_map_remove_unknown_divs(
1435 __isl_take isl_map *map);
1437 To iterate over all the sets or maps in a union set or map, use
1439 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1440 int (*fn)(__isl_take isl_set *set, void *user),
1442 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1443 int (*fn)(__isl_take isl_map *map, void *user),
1446 The number of sets or maps in a union set or map can be obtained
1449 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1450 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1452 To extract the set or map in a given space from a union, use
1454 __isl_give isl_set *isl_union_set_extract_set(
1455 __isl_keep isl_union_set *uset,
1456 __isl_take isl_space *space);
1457 __isl_give isl_map *isl_union_map_extract_map(
1458 __isl_keep isl_union_map *umap,
1459 __isl_take isl_space *space);
1461 To iterate over all the basic sets or maps in a set or map, use
1463 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1464 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1466 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1467 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1470 The callback function C<fn> should return 0 if successful and
1471 -1 if an error occurs. In the latter case, or if any other error
1472 occurs, the above functions will return -1.
1474 It should be noted that C<isl> does not guarantee that
1475 the basic sets or maps passed to C<fn> are disjoint.
1476 If this is required, then the user should call one of
1477 the following functions first.
1479 __isl_give isl_set *isl_set_make_disjoint(
1480 __isl_take isl_set *set);
1481 __isl_give isl_map *isl_map_make_disjoint(
1482 __isl_take isl_map *map);
1484 The number of basic sets in a set can be obtained
1487 int isl_set_n_basic_set(__isl_keep isl_set *set);
1489 To iterate over the constraints of a basic set or map, use
1491 #include <isl/constraint.h>
1493 int isl_basic_set_n_constraint(
1494 __isl_keep isl_basic_set *bset);
1495 int isl_basic_set_foreach_constraint(
1496 __isl_keep isl_basic_set *bset,
1497 int (*fn)(__isl_take isl_constraint *c, void *user),
1499 int isl_basic_map_foreach_constraint(
1500 __isl_keep isl_basic_map *bmap,
1501 int (*fn)(__isl_take isl_constraint *c, void *user),
1503 void *isl_constraint_free(__isl_take isl_constraint *c);
1505 Again, the callback function C<fn> should return 0 if successful and
1506 -1 if an error occurs. In the latter case, or if any other error
1507 occurs, the above functions will return -1.
1508 The constraint C<c> represents either an equality or an inequality.
1509 Use the following function to find out whether a constraint
1510 represents an equality. If not, it represents an inequality.
1512 int isl_constraint_is_equality(
1513 __isl_keep isl_constraint *constraint);
1515 The coefficients of the constraints can be inspected using
1516 the following functions.
1518 int isl_constraint_is_lower_bound(
1519 __isl_keep isl_constraint *constraint,
1520 enum isl_dim_type type, unsigned pos);
1521 int isl_constraint_is_upper_bound(
1522 __isl_keep isl_constraint *constraint,
1523 enum isl_dim_type type, unsigned pos);
1524 void isl_constraint_get_constant(
1525 __isl_keep isl_constraint *constraint, isl_int *v);
1526 void isl_constraint_get_coefficient(
1527 __isl_keep isl_constraint *constraint,
1528 enum isl_dim_type type, int pos, isl_int *v);
1529 int isl_constraint_involves_dims(
1530 __isl_keep isl_constraint *constraint,
1531 enum isl_dim_type type, unsigned first, unsigned n);
1533 The explicit representations of the existentially quantified
1534 variables can be inspected using the following function.
1535 Note that the user is only allowed to use this function
1536 if the inspected set or map is the result of a call
1537 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1538 The existentially quantified variable is equal to the floor
1539 of the returned affine expression. The affine expression
1540 itself can be inspected using the functions in
1541 L<"Piecewise Quasi Affine Expressions">.
1543 __isl_give isl_aff *isl_constraint_get_div(
1544 __isl_keep isl_constraint *constraint, int pos);
1546 To obtain the constraints of a basic set or map in matrix
1547 form, use the following functions.
1549 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1550 __isl_keep isl_basic_set *bset,
1551 enum isl_dim_type c1, enum isl_dim_type c2,
1552 enum isl_dim_type c3, enum isl_dim_type c4);
1553 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1554 __isl_keep isl_basic_set *bset,
1555 enum isl_dim_type c1, enum isl_dim_type c2,
1556 enum isl_dim_type c3, enum isl_dim_type c4);
1557 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1558 __isl_keep isl_basic_map *bmap,
1559 enum isl_dim_type c1,
1560 enum isl_dim_type c2, enum isl_dim_type c3,
1561 enum isl_dim_type c4, enum isl_dim_type c5);
1562 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1563 __isl_keep isl_basic_map *bmap,
1564 enum isl_dim_type c1,
1565 enum isl_dim_type c2, enum isl_dim_type c3,
1566 enum isl_dim_type c4, enum isl_dim_type c5);
1568 The C<isl_dim_type> arguments dictate the order in which
1569 different kinds of variables appear in the resulting matrix
1570 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1571 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1573 The number of parameters, input, output or set dimensions can
1574 be obtained using the following functions.
1576 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1577 enum isl_dim_type type);
1578 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1579 enum isl_dim_type type);
1580 unsigned isl_set_dim(__isl_keep isl_set *set,
1581 enum isl_dim_type type);
1582 unsigned isl_map_dim(__isl_keep isl_map *map,
1583 enum isl_dim_type type);
1585 To check whether the description of a set or relation depends
1586 on one or more given dimensions, it is not necessary to iterate over all
1587 constraints. Instead the following functions can be used.
1589 int isl_basic_set_involves_dims(
1590 __isl_keep isl_basic_set *bset,
1591 enum isl_dim_type type, unsigned first, unsigned n);
1592 int isl_set_involves_dims(__isl_keep isl_set *set,
1593 enum isl_dim_type type, unsigned first, unsigned n);
1594 int isl_basic_map_involves_dims(
1595 __isl_keep isl_basic_map *bmap,
1596 enum isl_dim_type type, unsigned first, unsigned n);
1597 int isl_map_involves_dims(__isl_keep isl_map *map,
1598 enum isl_dim_type type, unsigned first, unsigned n);
1600 Similarly, the following functions can be used to check whether
1601 a given dimension is involved in any lower or upper bound.
1603 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1604 enum isl_dim_type type, unsigned pos);
1605 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1606 enum isl_dim_type type, unsigned pos);
1608 The identifiers or names of the domain and range spaces of a set
1609 or relation can be read off or set using the following functions.
1611 __isl_give isl_set *isl_set_set_tuple_id(
1612 __isl_take isl_set *set, __isl_take isl_id *id);
1613 __isl_give isl_set *isl_set_reset_tuple_id(
1614 __isl_take isl_set *set);
1615 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1616 __isl_give isl_id *isl_set_get_tuple_id(
1617 __isl_keep isl_set *set);
1618 __isl_give isl_map *isl_map_set_tuple_id(
1619 __isl_take isl_map *map, enum isl_dim_type type,
1620 __isl_take isl_id *id);
1621 __isl_give isl_map *isl_map_reset_tuple_id(
1622 __isl_take isl_map *map, enum isl_dim_type type);
1623 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1624 enum isl_dim_type type);
1625 __isl_give isl_id *isl_map_get_tuple_id(
1626 __isl_keep isl_map *map, enum isl_dim_type type);
1628 const char *isl_basic_set_get_tuple_name(
1629 __isl_keep isl_basic_set *bset);
1630 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1631 __isl_take isl_basic_set *set, const char *s);
1632 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1633 const char *isl_set_get_tuple_name(
1634 __isl_keep isl_set *set);
1635 const char *isl_basic_map_get_tuple_name(
1636 __isl_keep isl_basic_map *bmap,
1637 enum isl_dim_type type);
1638 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1639 __isl_take isl_basic_map *bmap,
1640 enum isl_dim_type type, const char *s);
1641 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1642 enum isl_dim_type type);
1643 const char *isl_map_get_tuple_name(
1644 __isl_keep isl_map *map,
1645 enum isl_dim_type type);
1647 As with C<isl_space_get_tuple_name>, the value returned points to
1648 an internal data structure.
1649 The identifiers, positions or names of individual dimensions can be
1650 read off using the following functions.
1652 __isl_give isl_id *isl_basic_set_get_dim_id(
1653 __isl_keep isl_basic_set *bset,
1654 enum isl_dim_type type, unsigned pos);
1655 __isl_give isl_set *isl_set_set_dim_id(
1656 __isl_take isl_set *set, enum isl_dim_type type,
1657 unsigned pos, __isl_take isl_id *id);
1658 int isl_set_has_dim_id(__isl_keep isl_set *set,
1659 enum isl_dim_type type, unsigned pos);
1660 __isl_give isl_id *isl_set_get_dim_id(
1661 __isl_keep isl_set *set, enum isl_dim_type type,
1663 int isl_basic_map_has_dim_id(
1664 __isl_keep isl_basic_map *bmap,
1665 enum isl_dim_type type, unsigned pos);
1666 __isl_give isl_map *isl_map_set_dim_id(
1667 __isl_take isl_map *map, enum isl_dim_type type,
1668 unsigned pos, __isl_take isl_id *id);
1669 int isl_map_has_dim_id(__isl_keep isl_map *map,
1670 enum isl_dim_type type, unsigned pos);
1671 __isl_give isl_id *isl_map_get_dim_id(
1672 __isl_keep isl_map *map, enum isl_dim_type type,
1675 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1676 enum isl_dim_type type, __isl_keep isl_id *id);
1677 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1678 enum isl_dim_type type, __isl_keep isl_id *id);
1679 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1680 enum isl_dim_type type, const char *name);
1681 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1682 enum isl_dim_type type, const char *name);
1684 const char *isl_constraint_get_dim_name(
1685 __isl_keep isl_constraint *constraint,
1686 enum isl_dim_type type, unsigned pos);
1687 const char *isl_basic_set_get_dim_name(
1688 __isl_keep isl_basic_set *bset,
1689 enum isl_dim_type type, unsigned pos);
1690 int isl_set_has_dim_name(__isl_keep isl_set *set,
1691 enum isl_dim_type type, unsigned pos);
1692 const char *isl_set_get_dim_name(
1693 __isl_keep isl_set *set,
1694 enum isl_dim_type type, unsigned pos);
1695 const char *isl_basic_map_get_dim_name(
1696 __isl_keep isl_basic_map *bmap,
1697 enum isl_dim_type type, unsigned pos);
1698 int isl_map_has_dim_name(__isl_keep isl_map *map,
1699 enum isl_dim_type type, unsigned pos);
1700 const char *isl_map_get_dim_name(
1701 __isl_keep isl_map *map,
1702 enum isl_dim_type type, unsigned pos);
1704 These functions are mostly useful to obtain the identifiers, positions
1705 or names of the parameters. Identifiers of individual dimensions are
1706 essentially only useful for printing. They are ignored by all other
1707 operations and may not be preserved across those operations.
1711 =head3 Unary Properties
1717 The following functions test whether the given set or relation
1718 contains any integer points. The ``plain'' variants do not perform
1719 any computations, but simply check if the given set or relation
1720 is already known to be empty.
1722 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1723 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1724 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1725 int isl_set_is_empty(__isl_keep isl_set *set);
1726 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1727 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1728 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1729 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1730 int isl_map_is_empty(__isl_keep isl_map *map);
1731 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1733 =item * Universality
1735 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1736 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1737 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1739 =item * Single-valuedness
1741 int isl_basic_map_is_single_valued(
1742 __isl_keep isl_basic_map *bmap);
1743 int isl_map_plain_is_single_valued(
1744 __isl_keep isl_map *map);
1745 int isl_map_is_single_valued(__isl_keep isl_map *map);
1746 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1750 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1751 int isl_map_is_injective(__isl_keep isl_map *map);
1752 int isl_union_map_plain_is_injective(
1753 __isl_keep isl_union_map *umap);
1754 int isl_union_map_is_injective(
1755 __isl_keep isl_union_map *umap);
1759 int isl_map_is_bijective(__isl_keep isl_map *map);
1760 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1764 int isl_basic_map_plain_is_fixed(
1765 __isl_keep isl_basic_map *bmap,
1766 enum isl_dim_type type, unsigned pos,
1768 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1769 enum isl_dim_type type, unsigned pos,
1771 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1772 enum isl_dim_type type, unsigned pos,
1775 Check if the relation obviously lies on a hyperplane where the given dimension
1776 has a fixed value and if so, return that value in C<*val>.
1780 To check whether a set is a parameter domain, use this function:
1782 int isl_set_is_params(__isl_keep isl_set *set);
1783 int isl_union_set_is_params(
1784 __isl_keep isl_union_set *uset);
1788 The following functions check whether the domain of the given
1789 (basic) set is a wrapped relation.
1791 int isl_basic_set_is_wrapping(
1792 __isl_keep isl_basic_set *bset);
1793 int isl_set_is_wrapping(__isl_keep isl_set *set);
1795 =item * Internal Product
1797 int isl_basic_map_can_zip(
1798 __isl_keep isl_basic_map *bmap);
1799 int isl_map_can_zip(__isl_keep isl_map *map);
1801 Check whether the product of domain and range of the given relation
1803 i.e., whether both domain and range are nested relations.
1807 int isl_basic_map_can_curry(
1808 __isl_keep isl_basic_map *bmap);
1809 int isl_map_can_curry(__isl_keep isl_map *map);
1811 Check whether the domain of the (basic) relation is a wrapped relation.
1815 =head3 Binary Properties
1821 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1822 __isl_keep isl_set *set2);
1823 int isl_set_is_equal(__isl_keep isl_set *set1,
1824 __isl_keep isl_set *set2);
1825 int isl_union_set_is_equal(
1826 __isl_keep isl_union_set *uset1,
1827 __isl_keep isl_union_set *uset2);
1828 int isl_basic_map_is_equal(
1829 __isl_keep isl_basic_map *bmap1,
1830 __isl_keep isl_basic_map *bmap2);
1831 int isl_map_is_equal(__isl_keep isl_map *map1,
1832 __isl_keep isl_map *map2);
1833 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1834 __isl_keep isl_map *map2);
1835 int isl_union_map_is_equal(
1836 __isl_keep isl_union_map *umap1,
1837 __isl_keep isl_union_map *umap2);
1839 =item * Disjointness
1841 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1842 __isl_keep isl_set *set2);
1846 int isl_basic_set_is_subset(
1847 __isl_keep isl_basic_set *bset1,
1848 __isl_keep isl_basic_set *bset2);
1849 int isl_set_is_subset(__isl_keep isl_set *set1,
1850 __isl_keep isl_set *set2);
1851 int isl_set_is_strict_subset(
1852 __isl_keep isl_set *set1,
1853 __isl_keep isl_set *set2);
1854 int isl_union_set_is_subset(
1855 __isl_keep isl_union_set *uset1,
1856 __isl_keep isl_union_set *uset2);
1857 int isl_union_set_is_strict_subset(
1858 __isl_keep isl_union_set *uset1,
1859 __isl_keep isl_union_set *uset2);
1860 int isl_basic_map_is_subset(
1861 __isl_keep isl_basic_map *bmap1,
1862 __isl_keep isl_basic_map *bmap2);
1863 int isl_basic_map_is_strict_subset(
1864 __isl_keep isl_basic_map *bmap1,
1865 __isl_keep isl_basic_map *bmap2);
1866 int isl_map_is_subset(
1867 __isl_keep isl_map *map1,
1868 __isl_keep isl_map *map2);
1869 int isl_map_is_strict_subset(
1870 __isl_keep isl_map *map1,
1871 __isl_keep isl_map *map2);
1872 int isl_union_map_is_subset(
1873 __isl_keep isl_union_map *umap1,
1874 __isl_keep isl_union_map *umap2);
1875 int isl_union_map_is_strict_subset(
1876 __isl_keep isl_union_map *umap1,
1877 __isl_keep isl_union_map *umap2);
1879 Check whether the first argument is a (strict) subset of the
1884 =head2 Unary Operations
1890 __isl_give isl_set *isl_set_complement(
1891 __isl_take isl_set *set);
1892 __isl_give isl_map *isl_map_complement(
1893 __isl_take isl_map *map);
1897 __isl_give isl_basic_map *isl_basic_map_reverse(
1898 __isl_take isl_basic_map *bmap);
1899 __isl_give isl_map *isl_map_reverse(
1900 __isl_take isl_map *map);
1901 __isl_give isl_union_map *isl_union_map_reverse(
1902 __isl_take isl_union_map *umap);
1906 __isl_give isl_basic_set *isl_basic_set_project_out(
1907 __isl_take isl_basic_set *bset,
1908 enum isl_dim_type type, unsigned first, unsigned n);
1909 __isl_give isl_basic_map *isl_basic_map_project_out(
1910 __isl_take isl_basic_map *bmap,
1911 enum isl_dim_type type, unsigned first, unsigned n);
1912 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1913 enum isl_dim_type type, unsigned first, unsigned n);
1914 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1915 enum isl_dim_type type, unsigned first, unsigned n);
1916 __isl_give isl_basic_set *isl_basic_set_params(
1917 __isl_take isl_basic_set *bset);
1918 __isl_give isl_basic_set *isl_basic_map_domain(
1919 __isl_take isl_basic_map *bmap);
1920 __isl_give isl_basic_set *isl_basic_map_range(
1921 __isl_take isl_basic_map *bmap);
1922 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1923 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1924 __isl_give isl_set *isl_map_domain(
1925 __isl_take isl_map *bmap);
1926 __isl_give isl_set *isl_map_range(
1927 __isl_take isl_map *map);
1928 __isl_give isl_set *isl_union_set_params(
1929 __isl_take isl_union_set *uset);
1930 __isl_give isl_set *isl_union_map_params(
1931 __isl_take isl_union_map *umap);
1932 __isl_give isl_union_set *isl_union_map_domain(
1933 __isl_take isl_union_map *umap);
1934 __isl_give isl_union_set *isl_union_map_range(
1935 __isl_take isl_union_map *umap);
1937 __isl_give isl_basic_map *isl_basic_map_domain_map(
1938 __isl_take isl_basic_map *bmap);
1939 __isl_give isl_basic_map *isl_basic_map_range_map(
1940 __isl_take isl_basic_map *bmap);
1941 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1942 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1943 __isl_give isl_union_map *isl_union_map_domain_map(
1944 __isl_take isl_union_map *umap);
1945 __isl_give isl_union_map *isl_union_map_range_map(
1946 __isl_take isl_union_map *umap);
1948 The functions above construct a (basic, regular or union) relation
1949 that maps (a wrapped version of) the input relation to its domain or range.
1953 __isl_give isl_basic_set *isl_basic_set_eliminate(
1954 __isl_take isl_basic_set *bset,
1955 enum isl_dim_type type,
1956 unsigned first, unsigned n);
1957 __isl_give isl_set *isl_set_eliminate(
1958 __isl_take isl_set *set, enum isl_dim_type type,
1959 unsigned first, unsigned n);
1960 __isl_give isl_basic_map *isl_basic_map_eliminate(
1961 __isl_take isl_basic_map *bmap,
1962 enum isl_dim_type type,
1963 unsigned first, unsigned n);
1964 __isl_give isl_map *isl_map_eliminate(
1965 __isl_take isl_map *map, enum isl_dim_type type,
1966 unsigned first, unsigned n);
1968 Eliminate the coefficients for the given dimensions from the constraints,
1969 without removing the dimensions.
1973 __isl_give isl_basic_set *isl_basic_set_fix(
1974 __isl_take isl_basic_set *bset,
1975 enum isl_dim_type type, unsigned pos,
1977 __isl_give isl_basic_set *isl_basic_set_fix_si(
1978 __isl_take isl_basic_set *bset,
1979 enum isl_dim_type type, unsigned pos, int value);
1980 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1981 enum isl_dim_type type, unsigned pos,
1983 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1984 enum isl_dim_type type, unsigned pos, int value);
1985 __isl_give isl_basic_map *isl_basic_map_fix_si(
1986 __isl_take isl_basic_map *bmap,
1987 enum isl_dim_type type, unsigned pos, int value);
1988 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1989 enum isl_dim_type type, unsigned pos, int value);
1991 Intersect the set or relation with the hyperplane where the given
1992 dimension has the fixed given value.
1994 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1995 __isl_take isl_basic_map *bmap,
1996 enum isl_dim_type type, unsigned pos, int value);
1997 __isl_give isl_set *isl_set_lower_bound(
1998 __isl_take isl_set *set,
1999 enum isl_dim_type type, unsigned pos,
2001 __isl_give isl_set *isl_set_lower_bound_si(
2002 __isl_take isl_set *set,
2003 enum isl_dim_type type, unsigned pos, int value);
2004 __isl_give isl_map *isl_map_lower_bound_si(
2005 __isl_take isl_map *map,
2006 enum isl_dim_type type, unsigned pos, int value);
2007 __isl_give isl_set *isl_set_upper_bound(
2008 __isl_take isl_set *set,
2009 enum isl_dim_type type, unsigned pos,
2011 __isl_give isl_set *isl_set_upper_bound_si(
2012 __isl_take isl_set *set,
2013 enum isl_dim_type type, unsigned pos, int value);
2014 __isl_give isl_map *isl_map_upper_bound_si(
2015 __isl_take isl_map *map,
2016 enum isl_dim_type type, unsigned pos, int value);
2018 Intersect the set or relation with the half-space where the given
2019 dimension has a value bounded by the fixed given value.
2021 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2022 enum isl_dim_type type1, int pos1,
2023 enum isl_dim_type type2, int pos2);
2024 __isl_give isl_basic_map *isl_basic_map_equate(
2025 __isl_take isl_basic_map *bmap,
2026 enum isl_dim_type type1, int pos1,
2027 enum isl_dim_type type2, int pos2);
2028 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2029 enum isl_dim_type type1, int pos1,
2030 enum isl_dim_type type2, int pos2);
2032 Intersect the set or relation with the hyperplane where the given
2033 dimensions are equal to each other.
2035 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2036 enum isl_dim_type type1, int pos1,
2037 enum isl_dim_type type2, int pos2);
2039 Intersect the relation with the hyperplane where the given
2040 dimensions have opposite values.
2042 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2043 enum isl_dim_type type1, int pos1,
2044 enum isl_dim_type type2, int pos2);
2045 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2046 enum isl_dim_type type1, int pos1,
2047 enum isl_dim_type type2, int pos2);
2049 Intersect the relation with the half-space where the given
2050 dimensions satisfy the given ordering.
2054 __isl_give isl_map *isl_set_identity(
2055 __isl_take isl_set *set);
2056 __isl_give isl_union_map *isl_union_set_identity(
2057 __isl_take isl_union_set *uset);
2059 Construct an identity relation on the given (union) set.
2063 __isl_give isl_basic_set *isl_basic_map_deltas(
2064 __isl_take isl_basic_map *bmap);
2065 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2066 __isl_give isl_union_set *isl_union_map_deltas(
2067 __isl_take isl_union_map *umap);
2069 These functions return a (basic) set containing the differences
2070 between image elements and corresponding domain elements in the input.
2072 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2073 __isl_take isl_basic_map *bmap);
2074 __isl_give isl_map *isl_map_deltas_map(
2075 __isl_take isl_map *map);
2076 __isl_give isl_union_map *isl_union_map_deltas_map(
2077 __isl_take isl_union_map *umap);
2079 The functions above construct a (basic, regular or union) relation
2080 that maps (a wrapped version of) the input relation to its delta set.
2084 Simplify the representation of a set or relation by trying
2085 to combine pairs of basic sets or relations into a single
2086 basic set or relation.
2088 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2089 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2090 __isl_give isl_union_set *isl_union_set_coalesce(
2091 __isl_take isl_union_set *uset);
2092 __isl_give isl_union_map *isl_union_map_coalesce(
2093 __isl_take isl_union_map *umap);
2095 One of the methods for combining pairs of basic sets or relations
2096 can result in coefficients that are much larger than those that appear
2097 in the constraints of the input. By default, the coefficients are
2098 not allowed to grow larger, but this can be changed by unsetting
2099 the following option.
2101 int isl_options_set_coalesce_bounded_wrapping(
2102 isl_ctx *ctx, int val);
2103 int isl_options_get_coalesce_bounded_wrapping(
2106 =item * Detecting equalities
2108 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2109 __isl_take isl_basic_set *bset);
2110 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2111 __isl_take isl_basic_map *bmap);
2112 __isl_give isl_set *isl_set_detect_equalities(
2113 __isl_take isl_set *set);
2114 __isl_give isl_map *isl_map_detect_equalities(
2115 __isl_take isl_map *map);
2116 __isl_give isl_union_set *isl_union_set_detect_equalities(
2117 __isl_take isl_union_set *uset);
2118 __isl_give isl_union_map *isl_union_map_detect_equalities(
2119 __isl_take isl_union_map *umap);
2121 Simplify the representation of a set or relation by detecting implicit
2124 =item * Removing redundant constraints
2126 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2127 __isl_take isl_basic_set *bset);
2128 __isl_give isl_set *isl_set_remove_redundancies(
2129 __isl_take isl_set *set);
2130 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2131 __isl_take isl_basic_map *bmap);
2132 __isl_give isl_map *isl_map_remove_redundancies(
2133 __isl_take isl_map *map);
2137 __isl_give isl_basic_set *isl_set_convex_hull(
2138 __isl_take isl_set *set);
2139 __isl_give isl_basic_map *isl_map_convex_hull(
2140 __isl_take isl_map *map);
2142 If the input set or relation has any existentially quantified
2143 variables, then the result of these operations is currently undefined.
2147 __isl_give isl_basic_set *isl_set_simple_hull(
2148 __isl_take isl_set *set);
2149 __isl_give isl_basic_map *isl_map_simple_hull(
2150 __isl_take isl_map *map);
2151 __isl_give isl_union_map *isl_union_map_simple_hull(
2152 __isl_take isl_union_map *umap);
2154 These functions compute a single basic set or relation
2155 that contains the whole input set or relation.
2156 In particular, the output is described by translates
2157 of the constraints describing the basic sets or relations in the input.
2161 (See \autoref{s:simple hull}.)
2167 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2168 __isl_take isl_basic_set *bset);
2169 __isl_give isl_basic_set *isl_set_affine_hull(
2170 __isl_take isl_set *set);
2171 __isl_give isl_union_set *isl_union_set_affine_hull(
2172 __isl_take isl_union_set *uset);
2173 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2174 __isl_take isl_basic_map *bmap);
2175 __isl_give isl_basic_map *isl_map_affine_hull(
2176 __isl_take isl_map *map);
2177 __isl_give isl_union_map *isl_union_map_affine_hull(
2178 __isl_take isl_union_map *umap);
2180 In case of union sets and relations, the affine hull is computed
2183 =item * Polyhedral hull
2185 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2186 __isl_take isl_set *set);
2187 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2188 __isl_take isl_map *map);
2189 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2190 __isl_take isl_union_set *uset);
2191 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2192 __isl_take isl_union_map *umap);
2194 These functions compute a single basic set or relation
2195 not involving any existentially quantified variables
2196 that contains the whole input set or relation.
2197 In case of union sets and relations, the polyhedral hull is computed
2202 __isl_give isl_basic_set *isl_basic_set_sample(
2203 __isl_take isl_basic_set *bset);
2204 __isl_give isl_basic_set *isl_set_sample(
2205 __isl_take isl_set *set);
2206 __isl_give isl_basic_map *isl_basic_map_sample(
2207 __isl_take isl_basic_map *bmap);
2208 __isl_give isl_basic_map *isl_map_sample(
2209 __isl_take isl_map *map);
2211 If the input (basic) set or relation is non-empty, then return
2212 a singleton subset of the input. Otherwise, return an empty set.
2214 =item * Optimization
2216 #include <isl/ilp.h>
2217 enum isl_lp_result isl_basic_set_max(
2218 __isl_keep isl_basic_set *bset,
2219 __isl_keep isl_aff *obj, isl_int *opt)
2220 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2221 __isl_keep isl_aff *obj, isl_int *opt);
2222 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2223 __isl_keep isl_aff *obj, isl_int *opt);
2225 Compute the minimum or maximum of the integer affine expression C<obj>
2226 over the points in C<set>, returning the result in C<opt>.
2227 The return value may be one of C<isl_lp_error>,
2228 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2230 =item * Parametric optimization
2232 __isl_give isl_pw_aff *isl_set_dim_min(
2233 __isl_take isl_set *set, int pos);
2234 __isl_give isl_pw_aff *isl_set_dim_max(
2235 __isl_take isl_set *set, int pos);
2236 __isl_give isl_pw_aff *isl_map_dim_max(
2237 __isl_take isl_map *map, int pos);
2239 Compute the minimum or maximum of the given set or output dimension
2240 as a function of the parameters (and input dimensions), but independently
2241 of the other set or output dimensions.
2242 For lexicographic optimization, see L<"Lexicographic Optimization">.
2246 The following functions compute either the set of (rational) coefficient
2247 values of valid constraints for the given set or the set of (rational)
2248 values satisfying the constraints with coefficients from the given set.
2249 Internally, these two sets of functions perform essentially the
2250 same operations, except that the set of coefficients is assumed to
2251 be a cone, while the set of values may be any polyhedron.
2252 The current implementation is based on the Farkas lemma and
2253 Fourier-Motzkin elimination, but this may change or be made optional
2254 in future. In particular, future implementations may use different
2255 dualization algorithms or skip the elimination step.
2257 __isl_give isl_basic_set *isl_basic_set_coefficients(
2258 __isl_take isl_basic_set *bset);
2259 __isl_give isl_basic_set *isl_set_coefficients(
2260 __isl_take isl_set *set);
2261 __isl_give isl_union_set *isl_union_set_coefficients(
2262 __isl_take isl_union_set *bset);
2263 __isl_give isl_basic_set *isl_basic_set_solutions(
2264 __isl_take isl_basic_set *bset);
2265 __isl_give isl_basic_set *isl_set_solutions(
2266 __isl_take isl_set *set);
2267 __isl_give isl_union_set *isl_union_set_solutions(
2268 __isl_take isl_union_set *bset);
2272 __isl_give isl_map *isl_map_fixed_power(
2273 __isl_take isl_map *map, isl_int exp);
2274 __isl_give isl_union_map *isl_union_map_fixed_power(
2275 __isl_take isl_union_map *umap, isl_int exp);
2277 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2278 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2279 of C<map> is computed.
2281 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2283 __isl_give isl_union_map *isl_union_map_power(
2284 __isl_take isl_union_map *umap, int *exact);
2286 Compute a parametric representation for all positive powers I<k> of C<map>.
2287 The result maps I<k> to a nested relation corresponding to the
2288 I<k>th power of C<map>.
2289 The result may be an overapproximation. If the result is known to be exact,
2290 then C<*exact> is set to C<1>.
2292 =item * Transitive closure
2294 __isl_give isl_map *isl_map_transitive_closure(
2295 __isl_take isl_map *map, int *exact);
2296 __isl_give isl_union_map *isl_union_map_transitive_closure(
2297 __isl_take isl_union_map *umap, int *exact);
2299 Compute the transitive closure of C<map>.
2300 The result may be an overapproximation. If the result is known to be exact,
2301 then C<*exact> is set to C<1>.
2303 =item * Reaching path lengths
2305 __isl_give isl_map *isl_map_reaching_path_lengths(
2306 __isl_take isl_map *map, int *exact);
2308 Compute a relation that maps each element in the range of C<map>
2309 to the lengths of all paths composed of edges in C<map> that
2310 end up in the given element.
2311 The result may be an overapproximation. If the result is known to be exact,
2312 then C<*exact> is set to C<1>.
2313 To compute the I<maximal> path length, the resulting relation
2314 should be postprocessed by C<isl_map_lexmax>.
2315 In particular, if the input relation is a dependence relation
2316 (mapping sources to sinks), then the maximal path length corresponds
2317 to the free schedule.
2318 Note, however, that C<isl_map_lexmax> expects the maximum to be
2319 finite, so if the path lengths are unbounded (possibly due to
2320 the overapproximation), then you will get an error message.
2324 __isl_give isl_basic_set *isl_basic_map_wrap(
2325 __isl_take isl_basic_map *bmap);
2326 __isl_give isl_set *isl_map_wrap(
2327 __isl_take isl_map *map);
2328 __isl_give isl_union_set *isl_union_map_wrap(
2329 __isl_take isl_union_map *umap);
2330 __isl_give isl_basic_map *isl_basic_set_unwrap(
2331 __isl_take isl_basic_set *bset);
2332 __isl_give isl_map *isl_set_unwrap(
2333 __isl_take isl_set *set);
2334 __isl_give isl_union_map *isl_union_set_unwrap(
2335 __isl_take isl_union_set *uset);
2339 Remove any internal structure of domain (and range) of the given
2340 set or relation. If there is any such internal structure in the input,
2341 then the name of the space is also removed.
2343 __isl_give isl_basic_set *isl_basic_set_flatten(
2344 __isl_take isl_basic_set *bset);
2345 __isl_give isl_set *isl_set_flatten(
2346 __isl_take isl_set *set);
2347 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2348 __isl_take isl_basic_map *bmap);
2349 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2350 __isl_take isl_basic_map *bmap);
2351 __isl_give isl_map *isl_map_flatten_range(
2352 __isl_take isl_map *map);
2353 __isl_give isl_map *isl_map_flatten_domain(
2354 __isl_take isl_map *map);
2355 __isl_give isl_basic_map *isl_basic_map_flatten(
2356 __isl_take isl_basic_map *bmap);
2357 __isl_give isl_map *isl_map_flatten(
2358 __isl_take isl_map *map);
2360 __isl_give isl_map *isl_set_flatten_map(
2361 __isl_take isl_set *set);
2363 The function above constructs a relation
2364 that maps the input set to a flattened version of the set.
2368 Lift the input set to a space with extra dimensions corresponding
2369 to the existentially quantified variables in the input.
2370 In particular, the result lives in a wrapped map where the domain
2371 is the original space and the range corresponds to the original
2372 existentially quantified variables.
2374 __isl_give isl_basic_set *isl_basic_set_lift(
2375 __isl_take isl_basic_set *bset);
2376 __isl_give isl_set *isl_set_lift(
2377 __isl_take isl_set *set);
2378 __isl_give isl_union_set *isl_union_set_lift(
2379 __isl_take isl_union_set *uset);
2381 Given a local space that contains the existentially quantified
2382 variables of a set, a basic relation that, when applied to
2383 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2384 can be constructed using the following function.
2386 #include <isl/local_space.h>
2387 __isl_give isl_basic_map *isl_local_space_lifting(
2388 __isl_take isl_local_space *ls);
2390 =item * Internal Product
2392 __isl_give isl_basic_map *isl_basic_map_zip(
2393 __isl_take isl_basic_map *bmap);
2394 __isl_give isl_map *isl_map_zip(
2395 __isl_take isl_map *map);
2396 __isl_give isl_union_map *isl_union_map_zip(
2397 __isl_take isl_union_map *umap);
2399 Given a relation with nested relations for domain and range,
2400 interchange the range of the domain with the domain of the range.
2404 __isl_give isl_basic_map *isl_basic_map_curry(
2405 __isl_take isl_basic_map *bmap);
2406 __isl_give isl_map *isl_map_curry(
2407 __isl_take isl_map *map);
2408 __isl_give isl_union_map *isl_union_map_curry(
2409 __isl_take isl_union_map *umap);
2411 Given a relation with a nested relation for domain,
2412 move the range of the nested relation out of the domain
2413 and use it as the domain of a nested relation in the range,
2414 with the original range as range of this nested relation.
2416 =item * Aligning parameters
2418 __isl_give isl_basic_set *isl_basic_set_align_params(
2419 __isl_take isl_basic_set *bset,
2420 __isl_take isl_space *model);
2421 __isl_give isl_set *isl_set_align_params(
2422 __isl_take isl_set *set,
2423 __isl_take isl_space *model);
2424 __isl_give isl_basic_map *isl_basic_map_align_params(
2425 __isl_take isl_basic_map *bmap,
2426 __isl_take isl_space *model);
2427 __isl_give isl_map *isl_map_align_params(
2428 __isl_take isl_map *map,
2429 __isl_take isl_space *model);
2431 Change the order of the parameters of the given set or relation
2432 such that the first parameters match those of C<model>.
2433 This may involve the introduction of extra parameters.
2434 All parameters need to be named.
2436 =item * Dimension manipulation
2438 __isl_give isl_set *isl_set_add_dims(
2439 __isl_take isl_set *set,
2440 enum isl_dim_type type, unsigned n);
2441 __isl_give isl_map *isl_map_add_dims(
2442 __isl_take isl_map *map,
2443 enum isl_dim_type type, unsigned n);
2444 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2445 __isl_take isl_basic_set *bset,
2446 enum isl_dim_type type, unsigned pos,
2448 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2449 __isl_take isl_basic_map *bmap,
2450 enum isl_dim_type type, unsigned pos,
2452 __isl_give isl_set *isl_set_insert_dims(
2453 __isl_take isl_set *set,
2454 enum isl_dim_type type, unsigned pos, unsigned n);
2455 __isl_give isl_map *isl_map_insert_dims(
2456 __isl_take isl_map *map,
2457 enum isl_dim_type type, unsigned pos, unsigned n);
2458 __isl_give isl_basic_set *isl_basic_set_move_dims(
2459 __isl_take isl_basic_set *bset,
2460 enum isl_dim_type dst_type, unsigned dst_pos,
2461 enum isl_dim_type src_type, unsigned src_pos,
2463 __isl_give isl_basic_map *isl_basic_map_move_dims(
2464 __isl_take isl_basic_map *bmap,
2465 enum isl_dim_type dst_type, unsigned dst_pos,
2466 enum isl_dim_type src_type, unsigned src_pos,
2468 __isl_give isl_set *isl_set_move_dims(
2469 __isl_take isl_set *set,
2470 enum isl_dim_type dst_type, unsigned dst_pos,
2471 enum isl_dim_type src_type, unsigned src_pos,
2473 __isl_give isl_map *isl_map_move_dims(
2474 __isl_take isl_map *map,
2475 enum isl_dim_type dst_type, unsigned dst_pos,
2476 enum isl_dim_type src_type, unsigned src_pos,
2479 It is usually not advisable to directly change the (input or output)
2480 space of a set or a relation as this removes the name and the internal
2481 structure of the space. However, the above functions can be useful
2482 to add new parameters, assuming
2483 C<isl_set_align_params> and C<isl_map_align_params>
2488 =head2 Binary Operations
2490 The two arguments of a binary operation not only need to live
2491 in the same C<isl_ctx>, they currently also need to have
2492 the same (number of) parameters.
2494 =head3 Basic Operations
2498 =item * Intersection
2500 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2501 __isl_take isl_basic_set *bset1,
2502 __isl_take isl_basic_set *bset2);
2503 __isl_give isl_basic_set *isl_basic_set_intersect(
2504 __isl_take isl_basic_set *bset1,
2505 __isl_take isl_basic_set *bset2);
2506 __isl_give isl_set *isl_set_intersect_params(
2507 __isl_take isl_set *set,
2508 __isl_take isl_set *params);
2509 __isl_give isl_set *isl_set_intersect(
2510 __isl_take isl_set *set1,
2511 __isl_take isl_set *set2);
2512 __isl_give isl_union_set *isl_union_set_intersect_params(
2513 __isl_take isl_union_set *uset,
2514 __isl_take isl_set *set);
2515 __isl_give isl_union_map *isl_union_map_intersect_params(
2516 __isl_take isl_union_map *umap,
2517 __isl_take isl_set *set);
2518 __isl_give isl_union_set *isl_union_set_intersect(
2519 __isl_take isl_union_set *uset1,
2520 __isl_take isl_union_set *uset2);
2521 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2522 __isl_take isl_basic_map *bmap,
2523 __isl_take isl_basic_set *bset);
2524 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2525 __isl_take isl_basic_map *bmap,
2526 __isl_take isl_basic_set *bset);
2527 __isl_give isl_basic_map *isl_basic_map_intersect(
2528 __isl_take isl_basic_map *bmap1,
2529 __isl_take isl_basic_map *bmap2);
2530 __isl_give isl_map *isl_map_intersect_params(
2531 __isl_take isl_map *map,
2532 __isl_take isl_set *params);
2533 __isl_give isl_map *isl_map_intersect_domain(
2534 __isl_take isl_map *map,
2535 __isl_take isl_set *set);
2536 __isl_give isl_map *isl_map_intersect_range(
2537 __isl_take isl_map *map,
2538 __isl_take isl_set *set);
2539 __isl_give isl_map *isl_map_intersect(
2540 __isl_take isl_map *map1,
2541 __isl_take isl_map *map2);
2542 __isl_give isl_union_map *isl_union_map_intersect_domain(
2543 __isl_take isl_union_map *umap,
2544 __isl_take isl_union_set *uset);
2545 __isl_give isl_union_map *isl_union_map_intersect_range(
2546 __isl_take isl_union_map *umap,
2547 __isl_take isl_union_set *uset);
2548 __isl_give isl_union_map *isl_union_map_intersect(
2549 __isl_take isl_union_map *umap1,
2550 __isl_take isl_union_map *umap2);
2552 The second argument to the C<_params> functions needs to be
2553 a parametric (basic) set. For the other functions, a parametric set
2554 for either argument is only allowed if the other argument is
2555 a parametric set as well.
2559 __isl_give isl_set *isl_basic_set_union(
2560 __isl_take isl_basic_set *bset1,
2561 __isl_take isl_basic_set *bset2);
2562 __isl_give isl_map *isl_basic_map_union(
2563 __isl_take isl_basic_map *bmap1,
2564 __isl_take isl_basic_map *bmap2);
2565 __isl_give isl_set *isl_set_union(
2566 __isl_take isl_set *set1,
2567 __isl_take isl_set *set2);
2568 __isl_give isl_map *isl_map_union(
2569 __isl_take isl_map *map1,
2570 __isl_take isl_map *map2);
2571 __isl_give isl_union_set *isl_union_set_union(
2572 __isl_take isl_union_set *uset1,
2573 __isl_take isl_union_set *uset2);
2574 __isl_give isl_union_map *isl_union_map_union(
2575 __isl_take isl_union_map *umap1,
2576 __isl_take isl_union_map *umap2);
2578 =item * Set difference
2580 __isl_give isl_set *isl_set_subtract(
2581 __isl_take isl_set *set1,
2582 __isl_take isl_set *set2);
2583 __isl_give isl_map *isl_map_subtract(
2584 __isl_take isl_map *map1,
2585 __isl_take isl_map *map2);
2586 __isl_give isl_map *isl_map_subtract_domain(
2587 __isl_take isl_map *map,
2588 __isl_take isl_set *dom);
2589 __isl_give isl_map *isl_map_subtract_range(
2590 __isl_take isl_map *map,
2591 __isl_take isl_set *dom);
2592 __isl_give isl_union_set *isl_union_set_subtract(
2593 __isl_take isl_union_set *uset1,
2594 __isl_take isl_union_set *uset2);
2595 __isl_give isl_union_map *isl_union_map_subtract(
2596 __isl_take isl_union_map *umap1,
2597 __isl_take isl_union_map *umap2);
2601 __isl_give isl_basic_set *isl_basic_set_apply(
2602 __isl_take isl_basic_set *bset,
2603 __isl_take isl_basic_map *bmap);
2604 __isl_give isl_set *isl_set_apply(
2605 __isl_take isl_set *set,
2606 __isl_take isl_map *map);
2607 __isl_give isl_union_set *isl_union_set_apply(
2608 __isl_take isl_union_set *uset,
2609 __isl_take isl_union_map *umap);
2610 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2611 __isl_take isl_basic_map *bmap1,
2612 __isl_take isl_basic_map *bmap2);
2613 __isl_give isl_basic_map *isl_basic_map_apply_range(
2614 __isl_take isl_basic_map *bmap1,
2615 __isl_take isl_basic_map *bmap2);
2616 __isl_give isl_map *isl_map_apply_domain(
2617 __isl_take isl_map *map1,
2618 __isl_take isl_map *map2);
2619 __isl_give isl_union_map *isl_union_map_apply_domain(
2620 __isl_take isl_union_map *umap1,
2621 __isl_take isl_union_map *umap2);
2622 __isl_give isl_map *isl_map_apply_range(
2623 __isl_take isl_map *map1,
2624 __isl_take isl_map *map2);
2625 __isl_give isl_union_map *isl_union_map_apply_range(
2626 __isl_take isl_union_map *umap1,
2627 __isl_take isl_union_map *umap2);
2629 =item * Cartesian Product
2631 __isl_give isl_set *isl_set_product(
2632 __isl_take isl_set *set1,
2633 __isl_take isl_set *set2);
2634 __isl_give isl_union_set *isl_union_set_product(
2635 __isl_take isl_union_set *uset1,
2636 __isl_take isl_union_set *uset2);
2637 __isl_give isl_basic_map *isl_basic_map_domain_product(
2638 __isl_take isl_basic_map *bmap1,
2639 __isl_take isl_basic_map *bmap2);
2640 __isl_give isl_basic_map *isl_basic_map_range_product(
2641 __isl_take isl_basic_map *bmap1,
2642 __isl_take isl_basic_map *bmap2);
2643 __isl_give isl_basic_map *isl_basic_map_product(
2644 __isl_take isl_basic_map *bmap1,
2645 __isl_take isl_basic_map *bmap2);
2646 __isl_give isl_map *isl_map_domain_product(
2647 __isl_take isl_map *map1,
2648 __isl_take isl_map *map2);
2649 __isl_give isl_map *isl_map_range_product(
2650 __isl_take isl_map *map1,
2651 __isl_take isl_map *map2);
2652 __isl_give isl_union_map *isl_union_map_domain_product(
2653 __isl_take isl_union_map *umap1,
2654 __isl_take isl_union_map *umap2);
2655 __isl_give isl_union_map *isl_union_map_range_product(
2656 __isl_take isl_union_map *umap1,
2657 __isl_take isl_union_map *umap2);
2658 __isl_give isl_map *isl_map_product(
2659 __isl_take isl_map *map1,
2660 __isl_take isl_map *map2);
2661 __isl_give isl_union_map *isl_union_map_product(
2662 __isl_take isl_union_map *umap1,
2663 __isl_take isl_union_map *umap2);
2665 The above functions compute the cross product of the given
2666 sets or relations. The domains and ranges of the results
2667 are wrapped maps between domains and ranges of the inputs.
2668 To obtain a ``flat'' product, use the following functions
2671 __isl_give isl_basic_set *isl_basic_set_flat_product(
2672 __isl_take isl_basic_set *bset1,
2673 __isl_take isl_basic_set *bset2);
2674 __isl_give isl_set *isl_set_flat_product(
2675 __isl_take isl_set *set1,
2676 __isl_take isl_set *set2);
2677 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2678 __isl_take isl_basic_map *bmap1,
2679 __isl_take isl_basic_map *bmap2);
2680 __isl_give isl_map *isl_map_flat_domain_product(
2681 __isl_take isl_map *map1,
2682 __isl_take isl_map *map2);
2683 __isl_give isl_map *isl_map_flat_range_product(
2684 __isl_take isl_map *map1,
2685 __isl_take isl_map *map2);
2686 __isl_give isl_union_map *isl_union_map_flat_range_product(
2687 __isl_take isl_union_map *umap1,
2688 __isl_take isl_union_map *umap2);
2689 __isl_give isl_basic_map *isl_basic_map_flat_product(
2690 __isl_take isl_basic_map *bmap1,
2691 __isl_take isl_basic_map *bmap2);
2692 __isl_give isl_map *isl_map_flat_product(
2693 __isl_take isl_map *map1,
2694 __isl_take isl_map *map2);
2696 =item * Simplification
2698 __isl_give isl_basic_set *isl_basic_set_gist(
2699 __isl_take isl_basic_set *bset,
2700 __isl_take isl_basic_set *context);
2701 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2702 __isl_take isl_set *context);
2703 __isl_give isl_set *isl_set_gist_params(
2704 __isl_take isl_set *set,
2705 __isl_take isl_set *context);
2706 __isl_give isl_union_set *isl_union_set_gist(
2707 __isl_take isl_union_set *uset,
2708 __isl_take isl_union_set *context);
2709 __isl_give isl_union_set *isl_union_set_gist_params(
2710 __isl_take isl_union_set *uset,
2711 __isl_take isl_set *set);
2712 __isl_give isl_basic_map *isl_basic_map_gist(
2713 __isl_take isl_basic_map *bmap,
2714 __isl_take isl_basic_map *context);
2715 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2716 __isl_take isl_map *context);
2717 __isl_give isl_map *isl_map_gist_params(
2718 __isl_take isl_map *map,
2719 __isl_take isl_set *context);
2720 __isl_give isl_map *isl_map_gist_domain(
2721 __isl_take isl_map *map,
2722 __isl_take isl_set *context);
2723 __isl_give isl_map *isl_map_gist_range(
2724 __isl_take isl_map *map,
2725 __isl_take isl_set *context);
2726 __isl_give isl_union_map *isl_union_map_gist(
2727 __isl_take isl_union_map *umap,
2728 __isl_take isl_union_map *context);
2729 __isl_give isl_union_map *isl_union_map_gist_params(
2730 __isl_take isl_union_map *umap,
2731 __isl_take isl_set *set);
2732 __isl_give isl_union_map *isl_union_map_gist_domain(
2733 __isl_take isl_union_map *umap,
2734 __isl_take isl_union_set *uset);
2735 __isl_give isl_union_map *isl_union_map_gist_range(
2736 __isl_take isl_union_map *umap,
2737 __isl_take isl_union_set *uset);
2739 The gist operation returns a set or relation that has the
2740 same intersection with the context as the input set or relation.
2741 Any implicit equality in the intersection is made explicit in the result,
2742 while all inequalities that are redundant with respect to the intersection
2744 In case of union sets and relations, the gist operation is performed
2749 =head3 Lexicographic Optimization
2751 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2752 the following functions
2753 compute a set that contains the lexicographic minimum or maximum
2754 of the elements in C<set> (or C<bset>) for those values of the parameters
2755 that satisfy C<dom>.
2756 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2757 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2759 In other words, the union of the parameter values
2760 for which the result is non-empty and of C<*empty>
2763 __isl_give isl_set *isl_basic_set_partial_lexmin(
2764 __isl_take isl_basic_set *bset,
2765 __isl_take isl_basic_set *dom,
2766 __isl_give isl_set **empty);
2767 __isl_give isl_set *isl_basic_set_partial_lexmax(
2768 __isl_take isl_basic_set *bset,
2769 __isl_take isl_basic_set *dom,
2770 __isl_give isl_set **empty);
2771 __isl_give isl_set *isl_set_partial_lexmin(
2772 __isl_take isl_set *set, __isl_take isl_set *dom,
2773 __isl_give isl_set **empty);
2774 __isl_give isl_set *isl_set_partial_lexmax(
2775 __isl_take isl_set *set, __isl_take isl_set *dom,
2776 __isl_give isl_set **empty);
2778 Given a (basic) set C<set> (or C<bset>), the following functions simply
2779 return a set containing the lexicographic minimum or maximum
2780 of the elements in C<set> (or C<bset>).
2781 In case of union sets, the optimum is computed per space.
2783 __isl_give isl_set *isl_basic_set_lexmin(
2784 __isl_take isl_basic_set *bset);
2785 __isl_give isl_set *isl_basic_set_lexmax(
2786 __isl_take isl_basic_set *bset);
2787 __isl_give isl_set *isl_set_lexmin(
2788 __isl_take isl_set *set);
2789 __isl_give isl_set *isl_set_lexmax(
2790 __isl_take isl_set *set);
2791 __isl_give isl_union_set *isl_union_set_lexmin(
2792 __isl_take isl_union_set *uset);
2793 __isl_give isl_union_set *isl_union_set_lexmax(
2794 __isl_take isl_union_set *uset);
2796 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2797 the following functions
2798 compute a relation that maps each element of C<dom>
2799 to the single lexicographic minimum or maximum
2800 of the elements that are associated to that same
2801 element in C<map> (or C<bmap>).
2802 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2803 that contains the elements in C<dom> that do not map
2804 to any elements in C<map> (or C<bmap>).
2805 In other words, the union of the domain of the result and of C<*empty>
2808 __isl_give isl_map *isl_basic_map_partial_lexmax(
2809 __isl_take isl_basic_map *bmap,
2810 __isl_take isl_basic_set *dom,
2811 __isl_give isl_set **empty);
2812 __isl_give isl_map *isl_basic_map_partial_lexmin(
2813 __isl_take isl_basic_map *bmap,
2814 __isl_take isl_basic_set *dom,
2815 __isl_give isl_set **empty);
2816 __isl_give isl_map *isl_map_partial_lexmax(
2817 __isl_take isl_map *map, __isl_take isl_set *dom,
2818 __isl_give isl_set **empty);
2819 __isl_give isl_map *isl_map_partial_lexmin(
2820 __isl_take isl_map *map, __isl_take isl_set *dom,
2821 __isl_give isl_set **empty);
2823 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2824 return a map mapping each element in the domain of
2825 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2826 of all elements associated to that element.
2827 In case of union relations, the optimum is computed per space.
2829 __isl_give isl_map *isl_basic_map_lexmin(
2830 __isl_take isl_basic_map *bmap);
2831 __isl_give isl_map *isl_basic_map_lexmax(
2832 __isl_take isl_basic_map *bmap);
2833 __isl_give isl_map *isl_map_lexmin(
2834 __isl_take isl_map *map);
2835 __isl_give isl_map *isl_map_lexmax(
2836 __isl_take isl_map *map);
2837 __isl_give isl_union_map *isl_union_map_lexmin(
2838 __isl_take isl_union_map *umap);
2839 __isl_give isl_union_map *isl_union_map_lexmax(
2840 __isl_take isl_union_map *umap);
2842 The following functions return their result in the form of
2843 a piecewise multi-affine expression
2844 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2845 but are otherwise equivalent to the corresponding functions
2846 returning a basic set or relation.
2848 __isl_give isl_pw_multi_aff *
2849 isl_basic_map_lexmin_pw_multi_aff(
2850 __isl_take isl_basic_map *bmap);
2851 __isl_give isl_pw_multi_aff *
2852 isl_basic_set_partial_lexmin_pw_multi_aff(
2853 __isl_take isl_basic_set *bset,
2854 __isl_take isl_basic_set *dom,
2855 __isl_give isl_set **empty);
2856 __isl_give isl_pw_multi_aff *
2857 isl_basic_set_partial_lexmax_pw_multi_aff(
2858 __isl_take isl_basic_set *bset,
2859 __isl_take isl_basic_set *dom,
2860 __isl_give isl_set **empty);
2861 __isl_give isl_pw_multi_aff *
2862 isl_basic_map_partial_lexmin_pw_multi_aff(
2863 __isl_take isl_basic_map *bmap,
2864 __isl_take isl_basic_set *dom,
2865 __isl_give isl_set **empty);
2866 __isl_give isl_pw_multi_aff *
2867 isl_basic_map_partial_lexmax_pw_multi_aff(
2868 __isl_take isl_basic_map *bmap,
2869 __isl_take isl_basic_set *dom,
2870 __isl_give isl_set **empty);
2871 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
2872 __isl_take isl_map *map);
2873 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
2874 __isl_take isl_map *map);
2878 Lists are defined over several element types, including
2879 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2880 Here we take lists of C<isl_set>s as an example.
2881 Lists can be created, copied, modified and freed using the following functions.
2883 #include <isl/list.h>
2884 __isl_give isl_set_list *isl_set_list_from_set(
2885 __isl_take isl_set *el);
2886 __isl_give isl_set_list *isl_set_list_alloc(
2887 isl_ctx *ctx, int n);
2888 __isl_give isl_set_list *isl_set_list_copy(
2889 __isl_keep isl_set_list *list);
2890 __isl_give isl_set_list *isl_set_list_add(
2891 __isl_take isl_set_list *list,
2892 __isl_take isl_set *el);
2893 __isl_give isl_set_list *isl_set_list_set_set(
2894 __isl_take isl_set_list *list, int index,
2895 __isl_take isl_set *set);
2896 __isl_give isl_set_list *isl_set_list_concat(
2897 __isl_take isl_set_list *list1,
2898 __isl_take isl_set_list *list2);
2899 void *isl_set_list_free(__isl_take isl_set_list *list);
2901 C<isl_set_list_alloc> creates an empty list with a capacity for
2902 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2905 Lists can be inspected using the following functions.
2907 #include <isl/list.h>
2908 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2909 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2910 __isl_give isl_set *isl_set_list_get_set(
2911 __isl_keep isl_set_list *list, int index);
2912 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2913 int (*fn)(__isl_take isl_set *el, void *user),
2916 Lists can be printed using
2918 #include <isl/list.h>
2919 __isl_give isl_printer *isl_printer_print_set_list(
2920 __isl_take isl_printer *p,
2921 __isl_keep isl_set_list *list);
2925 Vectors can be created, copied and freed using the following functions.
2927 #include <isl/vec.h>
2928 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2930 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2931 void isl_vec_free(__isl_take isl_vec *vec);
2933 Note that the elements of a newly created vector may have arbitrary values.
2934 The elements can be changed and inspected using the following functions.
2936 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2937 int isl_vec_size(__isl_keep isl_vec *vec);
2938 int isl_vec_get_element(__isl_keep isl_vec *vec,
2939 int pos, isl_int *v);
2940 __isl_give isl_vec *isl_vec_set_element(
2941 __isl_take isl_vec *vec, int pos, isl_int v);
2942 __isl_give isl_vec *isl_vec_set_element_si(
2943 __isl_take isl_vec *vec, int pos, int v);
2944 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2946 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2949 C<isl_vec_get_element> will return a negative value if anything went wrong.
2950 In that case, the value of C<*v> is undefined.
2954 Matrices can be created, copied and freed using the following functions.
2956 #include <isl/mat.h>
2957 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2958 unsigned n_row, unsigned n_col);
2959 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2960 void isl_mat_free(__isl_take isl_mat *mat);
2962 Note that the elements of a newly created matrix may have arbitrary values.
2963 The elements can be changed and inspected using the following functions.
2965 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2966 int isl_mat_rows(__isl_keep isl_mat *mat);
2967 int isl_mat_cols(__isl_keep isl_mat *mat);
2968 int isl_mat_get_element(__isl_keep isl_mat *mat,
2969 int row, int col, isl_int *v);
2970 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2971 int row, int col, isl_int v);
2972 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2973 int row, int col, int v);
2975 C<isl_mat_get_element> will return a negative value if anything went wrong.
2976 In that case, the value of C<*v> is undefined.
2978 The following function can be used to compute the (right) inverse
2979 of a matrix, i.e., a matrix such that the product of the original
2980 and the inverse (in that order) is a multiple of the identity matrix.
2981 The input matrix is assumed to be of full row-rank.
2983 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2985 The following function can be used to compute the (right) kernel
2986 (or null space) of a matrix, i.e., a matrix such that the product of
2987 the original and the kernel (in that order) is the zero matrix.
2989 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2991 =head2 Piecewise Quasi Affine Expressions
2993 The zero quasi affine expression on a given domain can be created using
2995 __isl_give isl_aff *isl_aff_zero_on_domain(
2996 __isl_take isl_local_space *ls);
2998 Note that the space in which the resulting object lives is a map space
2999 with the given space as domain and a one-dimensional range.
3001 An empty piecewise quasi affine expression (one with no cells)
3002 or a piecewise quasi affine expression with a single cell can
3003 be created using the following functions.
3005 #include <isl/aff.h>
3006 __isl_give isl_pw_aff *isl_pw_aff_empty(
3007 __isl_take isl_space *space);
3008 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3009 __isl_take isl_set *set, __isl_take isl_aff *aff);
3010 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3011 __isl_take isl_aff *aff);
3013 A piecewise quasi affine expression that is equal to 1 on a set
3014 and 0 outside the set can be created using the following function.
3016 #include <isl/aff.h>
3017 __isl_give isl_pw_aff *isl_set_indicator_function(
3018 __isl_take isl_set *set);
3020 Quasi affine expressions can be copied and freed using
3022 #include <isl/aff.h>
3023 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3024 void *isl_aff_free(__isl_take isl_aff *aff);
3026 __isl_give isl_pw_aff *isl_pw_aff_copy(
3027 __isl_keep isl_pw_aff *pwaff);
3028 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3030 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3031 using the following function. The constraint is required to have
3032 a non-zero coefficient for the specified dimension.
3034 #include <isl/constraint.h>
3035 __isl_give isl_aff *isl_constraint_get_bound(
3036 __isl_keep isl_constraint *constraint,
3037 enum isl_dim_type type, int pos);
3039 The entire affine expression of the constraint can also be extracted
3040 using the following function.
3042 #include <isl/constraint.h>
3043 __isl_give isl_aff *isl_constraint_get_aff(
3044 __isl_keep isl_constraint *constraint);
3046 Conversely, an equality constraint equating
3047 the affine expression to zero or an inequality constraint enforcing
3048 the affine expression to be non-negative, can be constructed using
3050 __isl_give isl_constraint *isl_equality_from_aff(
3051 __isl_take isl_aff *aff);
3052 __isl_give isl_constraint *isl_inequality_from_aff(
3053 __isl_take isl_aff *aff);
3055 The expression can be inspected using
3057 #include <isl/aff.h>
3058 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3059 int isl_aff_dim(__isl_keep isl_aff *aff,
3060 enum isl_dim_type type);
3061 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3062 __isl_keep isl_aff *aff);
3063 __isl_give isl_local_space *isl_aff_get_local_space(
3064 __isl_keep isl_aff *aff);
3065 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3066 enum isl_dim_type type, unsigned pos);
3067 const char *isl_pw_aff_get_dim_name(
3068 __isl_keep isl_pw_aff *pa,
3069 enum isl_dim_type type, unsigned pos);
3070 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3071 enum isl_dim_type type, unsigned pos);
3072 __isl_give isl_id *isl_pw_aff_get_dim_id(
3073 __isl_keep isl_pw_aff *pa,
3074 enum isl_dim_type type, unsigned pos);
3075 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3076 __isl_keep isl_pw_aff *pa,
3077 enum isl_dim_type type);
3078 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3080 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3081 enum isl_dim_type type, int pos, isl_int *v);
3082 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3084 __isl_give isl_aff *isl_aff_get_div(
3085 __isl_keep isl_aff *aff, int pos);
3087 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3088 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3089 int (*fn)(__isl_take isl_set *set,
3090 __isl_take isl_aff *aff,
3091 void *user), void *user);
3093 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3094 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3096 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3097 enum isl_dim_type type, unsigned first, unsigned n);
3098 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3099 enum isl_dim_type type, unsigned first, unsigned n);
3101 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3102 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3103 enum isl_dim_type type);
3104 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3106 It can be modified using
3108 #include <isl/aff.h>
3109 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3110 __isl_take isl_pw_aff *pwaff,
3111 enum isl_dim_type type, __isl_take isl_id *id);
3112 __isl_give isl_aff *isl_aff_set_dim_name(
3113 __isl_take isl_aff *aff, enum isl_dim_type type,
3114 unsigned pos, const char *s);
3115 __isl_give isl_aff *isl_aff_set_dim_id(
3116 __isl_take isl_aff *aff, enum isl_dim_type type,
3117 unsigned pos, __isl_take isl_id *id);
3118 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3119 __isl_take isl_pw_aff *pma,
3120 enum isl_dim_type type, unsigned pos,
3121 __isl_take isl_id *id);
3122 __isl_give isl_aff *isl_aff_set_constant(
3123 __isl_take isl_aff *aff, isl_int v);
3124 __isl_give isl_aff *isl_aff_set_constant_si(
3125 __isl_take isl_aff *aff, int v);
3126 __isl_give isl_aff *isl_aff_set_coefficient(
3127 __isl_take isl_aff *aff,
3128 enum isl_dim_type type, int pos, isl_int v);
3129 __isl_give isl_aff *isl_aff_set_coefficient_si(
3130 __isl_take isl_aff *aff,
3131 enum isl_dim_type type, int pos, int v);
3132 __isl_give isl_aff *isl_aff_set_denominator(
3133 __isl_take isl_aff *aff, isl_int v);
3135 __isl_give isl_aff *isl_aff_add_constant(
3136 __isl_take isl_aff *aff, isl_int v);
3137 __isl_give isl_aff *isl_aff_add_constant_si(
3138 __isl_take isl_aff *aff, int v);
3139 __isl_give isl_aff *isl_aff_add_constant_num(
3140 __isl_take isl_aff *aff, isl_int v);
3141 __isl_give isl_aff *isl_aff_add_constant_num_si(
3142 __isl_take isl_aff *aff, int v);
3143 __isl_give isl_aff *isl_aff_add_coefficient(
3144 __isl_take isl_aff *aff,
3145 enum isl_dim_type type, int pos, isl_int v);
3146 __isl_give isl_aff *isl_aff_add_coefficient_si(
3147 __isl_take isl_aff *aff,
3148 enum isl_dim_type type, int pos, int v);
3150 __isl_give isl_aff *isl_aff_insert_dims(
3151 __isl_take isl_aff *aff,
3152 enum isl_dim_type type, unsigned first, unsigned n);
3153 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3154 __isl_take isl_pw_aff *pwaff,
3155 enum isl_dim_type type, unsigned first, unsigned n);
3156 __isl_give isl_aff *isl_aff_add_dims(
3157 __isl_take isl_aff *aff,
3158 enum isl_dim_type type, unsigned n);
3159 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3160 __isl_take isl_pw_aff *pwaff,
3161 enum isl_dim_type type, unsigned n);
3162 __isl_give isl_aff *isl_aff_drop_dims(
3163 __isl_take isl_aff *aff,
3164 enum isl_dim_type type, unsigned first, unsigned n);
3165 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3166 __isl_take isl_pw_aff *pwaff,
3167 enum isl_dim_type type, unsigned first, unsigned n);
3169 Note that the C<set_constant> and C<set_coefficient> functions
3170 set the I<numerator> of the constant or coefficient, while
3171 C<add_constant> and C<add_coefficient> add an integer value to
3172 the possibly rational constant or coefficient.
3173 The C<add_constant_num> functions add an integer value to
3176 To check whether an affine expressions is obviously zero
3177 or obviously equal to some other affine expression, use
3179 #include <isl/aff.h>
3180 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3181 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3182 __isl_keep isl_aff *aff2);
3183 int isl_pw_aff_plain_is_equal(
3184 __isl_keep isl_pw_aff *pwaff1,
3185 __isl_keep isl_pw_aff *pwaff2);
3189 #include <isl/aff.h>
3190 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3191 __isl_take isl_aff *aff2);
3192 __isl_give isl_pw_aff *isl_pw_aff_add(
3193 __isl_take isl_pw_aff *pwaff1,
3194 __isl_take isl_pw_aff *pwaff2);
3195 __isl_give isl_pw_aff *isl_pw_aff_min(
3196 __isl_take isl_pw_aff *pwaff1,
3197 __isl_take isl_pw_aff *pwaff2);
3198 __isl_give isl_pw_aff *isl_pw_aff_max(
3199 __isl_take isl_pw_aff *pwaff1,
3200 __isl_take isl_pw_aff *pwaff2);
3201 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3202 __isl_take isl_aff *aff2);
3203 __isl_give isl_pw_aff *isl_pw_aff_sub(
3204 __isl_take isl_pw_aff *pwaff1,
3205 __isl_take isl_pw_aff *pwaff2);
3206 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3207 __isl_give isl_pw_aff *isl_pw_aff_neg(
3208 __isl_take isl_pw_aff *pwaff);
3209 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3210 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3211 __isl_take isl_pw_aff *pwaff);
3212 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3213 __isl_give isl_pw_aff *isl_pw_aff_floor(
3214 __isl_take isl_pw_aff *pwaff);
3215 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3217 __isl_give isl_pw_aff *isl_pw_aff_mod(
3218 __isl_take isl_pw_aff *pwaff, isl_int mod);
3219 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3221 __isl_give isl_pw_aff *isl_pw_aff_scale(
3222 __isl_take isl_pw_aff *pwaff, isl_int f);
3223 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3225 __isl_give isl_aff *isl_aff_scale_down_ui(
3226 __isl_take isl_aff *aff, unsigned f);
3227 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3228 __isl_take isl_pw_aff *pwaff, isl_int f);
3230 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3231 __isl_take isl_pw_aff_list *list);
3232 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3233 __isl_take isl_pw_aff_list *list);
3235 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3236 __isl_take isl_pw_aff *pwqp);
3238 __isl_give isl_aff *isl_aff_align_params(
3239 __isl_take isl_aff *aff,
3240 __isl_take isl_space *model);
3241 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3242 __isl_take isl_pw_aff *pwaff,
3243 __isl_take isl_space *model);
3245 __isl_give isl_aff *isl_aff_project_domain_on_params(
3246 __isl_take isl_aff *aff);
3248 __isl_give isl_aff *isl_aff_gist_params(
3249 __isl_take isl_aff *aff,
3250 __isl_take isl_set *context);
3251 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3252 __isl_take isl_set *context);
3253 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3254 __isl_take isl_pw_aff *pwaff,
3255 __isl_take isl_set *context);
3256 __isl_give isl_pw_aff *isl_pw_aff_gist(
3257 __isl_take isl_pw_aff *pwaff,
3258 __isl_take isl_set *context);
3260 __isl_give isl_set *isl_pw_aff_domain(
3261 __isl_take isl_pw_aff *pwaff);
3262 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3263 __isl_take isl_pw_aff *pa,
3264 __isl_take isl_set *set);
3265 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3266 __isl_take isl_pw_aff *pa,
3267 __isl_take isl_set *set);
3269 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3270 __isl_take isl_aff *aff2);
3271 __isl_give isl_pw_aff *isl_pw_aff_mul(
3272 __isl_take isl_pw_aff *pwaff1,
3273 __isl_take isl_pw_aff *pwaff2);
3275 When multiplying two affine expressions, at least one of the two needs
3278 #include <isl/aff.h>
3279 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3280 __isl_take isl_aff *aff);
3281 __isl_give isl_basic_set *isl_aff_le_basic_set(
3282 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3283 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3284 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3285 __isl_give isl_set *isl_pw_aff_eq_set(
3286 __isl_take isl_pw_aff *pwaff1,
3287 __isl_take isl_pw_aff *pwaff2);
3288 __isl_give isl_set *isl_pw_aff_ne_set(
3289 __isl_take isl_pw_aff *pwaff1,
3290 __isl_take isl_pw_aff *pwaff2);
3291 __isl_give isl_set *isl_pw_aff_le_set(
3292 __isl_take isl_pw_aff *pwaff1,
3293 __isl_take isl_pw_aff *pwaff2);
3294 __isl_give isl_set *isl_pw_aff_lt_set(
3295 __isl_take isl_pw_aff *pwaff1,
3296 __isl_take isl_pw_aff *pwaff2);
3297 __isl_give isl_set *isl_pw_aff_ge_set(
3298 __isl_take isl_pw_aff *pwaff1,
3299 __isl_take isl_pw_aff *pwaff2);
3300 __isl_give isl_set *isl_pw_aff_gt_set(
3301 __isl_take isl_pw_aff *pwaff1,
3302 __isl_take isl_pw_aff *pwaff2);
3304 __isl_give isl_set *isl_pw_aff_list_eq_set(
3305 __isl_take isl_pw_aff_list *list1,
3306 __isl_take isl_pw_aff_list *list2);
3307 __isl_give isl_set *isl_pw_aff_list_ne_set(
3308 __isl_take isl_pw_aff_list *list1,
3309 __isl_take isl_pw_aff_list *list2);
3310 __isl_give isl_set *isl_pw_aff_list_le_set(
3311 __isl_take isl_pw_aff_list *list1,
3312 __isl_take isl_pw_aff_list *list2);
3313 __isl_give isl_set *isl_pw_aff_list_lt_set(
3314 __isl_take isl_pw_aff_list *list1,
3315 __isl_take isl_pw_aff_list *list2);
3316 __isl_give isl_set *isl_pw_aff_list_ge_set(
3317 __isl_take isl_pw_aff_list *list1,
3318 __isl_take isl_pw_aff_list *list2);
3319 __isl_give isl_set *isl_pw_aff_list_gt_set(
3320 __isl_take isl_pw_aff_list *list1,
3321 __isl_take isl_pw_aff_list *list2);
3323 The function C<isl_aff_neg_basic_set> returns a basic set
3324 containing those elements in the domain space
3325 of C<aff> where C<aff> is negative.
3326 The function C<isl_aff_ge_basic_set> returns a basic set
3327 containing those elements in the shared space
3328 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3329 The function C<isl_pw_aff_ge_set> returns a set
3330 containing those elements in the shared domain
3331 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3332 The functions operating on C<isl_pw_aff_list> apply the corresponding
3333 C<isl_pw_aff> function to each pair of elements in the two lists.
3335 #include <isl/aff.h>
3336 __isl_give isl_set *isl_pw_aff_nonneg_set(
3337 __isl_take isl_pw_aff *pwaff);
3338 __isl_give isl_set *isl_pw_aff_zero_set(
3339 __isl_take isl_pw_aff *pwaff);
3340 __isl_give isl_set *isl_pw_aff_non_zero_set(
3341 __isl_take isl_pw_aff *pwaff);
3343 The function C<isl_pw_aff_nonneg_set> returns a set
3344 containing those elements in the domain
3345 of C<pwaff> where C<pwaff> is non-negative.
3347 #include <isl/aff.h>
3348 __isl_give isl_pw_aff *isl_pw_aff_cond(
3349 __isl_take isl_pw_aff *cond,
3350 __isl_take isl_pw_aff *pwaff_true,
3351 __isl_take isl_pw_aff *pwaff_false);
3353 The function C<isl_pw_aff_cond> performs a conditional operator
3354 and returns an expression that is equal to C<pwaff_true>
3355 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3356 where C<cond> is zero.
3358 #include <isl/aff.h>
3359 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3360 __isl_take isl_pw_aff *pwaff1,
3361 __isl_take isl_pw_aff *pwaff2);
3362 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3363 __isl_take isl_pw_aff *pwaff1,
3364 __isl_take isl_pw_aff *pwaff2);
3365 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3366 __isl_take isl_pw_aff *pwaff1,
3367 __isl_take isl_pw_aff *pwaff2);
3369 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3370 expression with a domain that is the union of those of C<pwaff1> and
3371 C<pwaff2> and such that on each cell, the quasi-affine expression is
3372 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3373 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3374 associated expression is the defined one.
3376 An expression can be read from input using
3378 #include <isl/aff.h>
3379 __isl_give isl_aff *isl_aff_read_from_str(
3380 isl_ctx *ctx, const char *str);
3381 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3382 isl_ctx *ctx, const char *str);
3384 An expression can be printed using
3386 #include <isl/aff.h>
3387 __isl_give isl_printer *isl_printer_print_aff(
3388 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3390 __isl_give isl_printer *isl_printer_print_pw_aff(
3391 __isl_take isl_printer *p,
3392 __isl_keep isl_pw_aff *pwaff);
3394 =head2 Piecewise Multiple Quasi Affine Expressions
3396 An C<isl_multi_aff> object represents a sequence of
3397 zero or more affine expressions, all defined on the same domain space.
3399 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3402 #include <isl/aff.h>
3403 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3404 __isl_take isl_space *space,
3405 __isl_take isl_aff_list *list);
3407 An empty piecewise multiple quasi affine expression (one with no cells),
3408 the zero piecewise multiple quasi affine expression (with value zero
3409 for each output dimension),
3410 a piecewise multiple quasi affine expression with a single cell (with
3411 either a universe or a specified domain) or
3412 a zero-dimensional piecewise multiple quasi affine expression
3414 can be created using the following functions.
3416 #include <isl/aff.h>
3417 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3418 __isl_take isl_space *space);
3419 __isl_give isl_multi_aff *isl_multi_aff_zero(
3420 __isl_take isl_space *space);
3421 __isl_give isl_multi_aff *isl_multi_aff_identity(
3422 __isl_take isl_space *space);
3423 __isl_give isl_pw_multi_aff *
3424 isl_pw_multi_aff_from_multi_aff(
3425 __isl_take isl_multi_aff *ma);
3426 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3427 __isl_take isl_set *set,
3428 __isl_take isl_multi_aff *maff);
3429 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3430 __isl_take isl_set *set);
3432 __isl_give isl_union_pw_multi_aff *
3433 isl_union_pw_multi_aff_empty(
3434 __isl_take isl_space *space);
3435 __isl_give isl_union_pw_multi_aff *
3436 isl_union_pw_multi_aff_add_pw_multi_aff(
3437 __isl_take isl_union_pw_multi_aff *upma,
3438 __isl_take isl_pw_multi_aff *pma);
3439 __isl_give isl_union_pw_multi_aff *
3440 isl_union_pw_multi_aff_from_domain(
3441 __isl_take isl_union_set *uset);
3443 A piecewise multiple quasi affine expression can also be initialized
3444 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3445 and the C<isl_map> is single-valued.
3447 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3448 __isl_take isl_set *set);
3449 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3450 __isl_take isl_map *map);
3452 Multiple quasi affine expressions can be copied and freed using
3454 #include <isl/aff.h>
3455 __isl_give isl_multi_aff *isl_multi_aff_copy(
3456 __isl_keep isl_multi_aff *maff);
3457 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3459 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3460 __isl_keep isl_pw_multi_aff *pma);
3461 void *isl_pw_multi_aff_free(
3462 __isl_take isl_pw_multi_aff *pma);
3464 __isl_give isl_union_pw_multi_aff *
3465 isl_union_pw_multi_aff_copy(
3466 __isl_keep isl_union_pw_multi_aff *upma);
3467 void *isl_union_pw_multi_aff_free(
3468 __isl_take isl_union_pw_multi_aff *upma);
3470 The expression can be inspected using
3472 #include <isl/aff.h>
3473 isl_ctx *isl_multi_aff_get_ctx(
3474 __isl_keep isl_multi_aff *maff);
3475 isl_ctx *isl_pw_multi_aff_get_ctx(
3476 __isl_keep isl_pw_multi_aff *pma);
3477 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3478 __isl_keep isl_union_pw_multi_aff *upma);
3479 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3480 enum isl_dim_type type);
3481 unsigned isl_pw_multi_aff_dim(
3482 __isl_keep isl_pw_multi_aff *pma,
3483 enum isl_dim_type type);
3484 __isl_give isl_aff *isl_multi_aff_get_aff(
3485 __isl_keep isl_multi_aff *multi, int pos);
3486 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3487 __isl_keep isl_pw_multi_aff *pma, int pos);
3488 const char *isl_pw_multi_aff_get_dim_name(
3489 __isl_keep isl_pw_multi_aff *pma,
3490 enum isl_dim_type type, unsigned pos);
3491 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3492 __isl_keep isl_pw_multi_aff *pma,
3493 enum isl_dim_type type, unsigned pos);
3494 const char *isl_multi_aff_get_tuple_name(
3495 __isl_keep isl_multi_aff *multi,
3496 enum isl_dim_type type);
3497 int isl_pw_multi_aff_has_tuple_name(
3498 __isl_keep isl_pw_multi_aff *pma,
3499 enum isl_dim_type type);
3500 const char *isl_pw_multi_aff_get_tuple_name(
3501 __isl_keep isl_pw_multi_aff *pma,
3502 enum isl_dim_type type);
3503 int isl_pw_multi_aff_has_tuple_id(
3504 __isl_keep isl_pw_multi_aff *pma,
3505 enum isl_dim_type type);
3506 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3507 __isl_keep isl_pw_multi_aff *pma,
3508 enum isl_dim_type type);
3510 int isl_pw_multi_aff_foreach_piece(
3511 __isl_keep isl_pw_multi_aff *pma,
3512 int (*fn)(__isl_take isl_set *set,
3513 __isl_take isl_multi_aff *maff,
3514 void *user), void *user);
3516 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3517 __isl_keep isl_union_pw_multi_aff *upma,
3518 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3519 void *user), void *user);
3521 It can be modified using
3523 #include <isl/aff.h>
3524 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3525 __isl_take isl_multi_aff *multi, int pos,
3526 __isl_take isl_aff *aff);
3527 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3528 __isl_take isl_multi_aff *maff,
3529 enum isl_dim_type type, unsigned pos, const char *s);
3530 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3531 __isl_take isl_multi_aff *maff,
3532 enum isl_dim_type type, __isl_take isl_id *id);
3533 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3534 __isl_take isl_pw_multi_aff *pma,
3535 enum isl_dim_type type, __isl_take isl_id *id);
3537 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3538 __isl_take isl_multi_aff *maff,
3539 enum isl_dim_type type, unsigned first, unsigned n);
3540 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
3541 __isl_take isl_pw_multi_aff *pma,
3542 enum isl_dim_type type, unsigned first, unsigned n);
3544 To check whether two multiple affine expressions are
3545 obviously equal to each other, use
3547 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3548 __isl_keep isl_multi_aff *maff2);
3549 int isl_pw_multi_aff_plain_is_equal(
3550 __isl_keep isl_pw_multi_aff *pma1,
3551 __isl_keep isl_pw_multi_aff *pma2);
3555 #include <isl/aff.h>
3556 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3557 __isl_take isl_pw_multi_aff *pma1,
3558 __isl_take isl_pw_multi_aff *pma2);
3559 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3560 __isl_take isl_pw_multi_aff *pma1,
3561 __isl_take isl_pw_multi_aff *pma2);
3562 __isl_give isl_multi_aff *isl_multi_aff_add(
3563 __isl_take isl_multi_aff *maff1,
3564 __isl_take isl_multi_aff *maff2);
3565 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3566 __isl_take isl_pw_multi_aff *pma1,
3567 __isl_take isl_pw_multi_aff *pma2);
3568 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3569 __isl_take isl_union_pw_multi_aff *upma1,
3570 __isl_take isl_union_pw_multi_aff *upma2);
3571 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3572 __isl_take isl_pw_multi_aff *pma1,
3573 __isl_take isl_pw_multi_aff *pma2);
3574 __isl_give isl_multi_aff *isl_multi_aff_scale(
3575 __isl_take isl_multi_aff *maff,
3577 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3578 __isl_take isl_pw_multi_aff *pma,
3579 __isl_take isl_set *set);
3580 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3581 __isl_take isl_pw_multi_aff *pma,
3582 __isl_take isl_set *set);
3583 __isl_give isl_multi_aff *isl_multi_aff_lift(
3584 __isl_take isl_multi_aff *maff,
3585 __isl_give isl_local_space **ls);
3586 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3587 __isl_take isl_pw_multi_aff *pma);
3588 __isl_give isl_multi_aff *isl_multi_aff_align_params(
3589 __isl_take isl_multi_aff *multi,
3590 __isl_take isl_space *model);
3591 __isl_give isl_pw_multi_aff *
3592 isl_pw_multi_aff_project_domain_on_params(
3593 __isl_take isl_pw_multi_aff *pma);
3594 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3595 __isl_take isl_multi_aff *maff,
3596 __isl_take isl_set *context);
3597 __isl_give isl_multi_aff *isl_multi_aff_gist(
3598 __isl_take isl_multi_aff *maff,
3599 __isl_take isl_set *context);
3600 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3601 __isl_take isl_pw_multi_aff *pma,
3602 __isl_take isl_set *set);
3603 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3604 __isl_take isl_pw_multi_aff *pma,
3605 __isl_take isl_set *set);
3606 __isl_give isl_set *isl_pw_multi_aff_domain(
3607 __isl_take isl_pw_multi_aff *pma);
3608 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3609 __isl_take isl_union_pw_multi_aff *upma);
3610 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3611 __isl_take isl_multi_aff *ma1,
3612 __isl_take isl_multi_aff *ma2);
3613 __isl_give isl_multi_aff *isl_multi_aff_product(
3614 __isl_take isl_multi_aff *ma1,
3615 __isl_take isl_multi_aff *ma2);
3616 __isl_give isl_pw_multi_aff *
3617 isl_pw_multi_aff_flat_range_product(
3618 __isl_take isl_pw_multi_aff *pma1,
3619 __isl_take isl_pw_multi_aff *pma2);
3620 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3621 __isl_take isl_pw_multi_aff *pma1,
3622 __isl_take isl_pw_multi_aff *pma2);
3623 __isl_give isl_union_pw_multi_aff *
3624 isl_union_pw_multi_aff_flat_range_product(
3625 __isl_take isl_union_pw_multi_aff *upma1,
3626 __isl_take isl_union_pw_multi_aff *upma2);
3628 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3629 then it is assigned the local space that lies at the basis of
3630 the lifting applied.
3632 __isl_give isl_set *isl_multi_aff_lex_le_set(
3633 __isl_take isl_multi_aff *ma1,
3634 __isl_take isl_multi_aff *ma2);
3635 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3636 __isl_take isl_multi_aff *ma1,
3637 __isl_take isl_multi_aff *ma2);
3639 The function C<isl_multi_aff_lex_le_set> returns a set
3640 containing those elements in the shared domain space
3641 where C<ma1> is lexicographically smaller than or
3644 An expression can be read from input using
3646 #include <isl/aff.h>
3647 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3648 isl_ctx *ctx, const char *str);
3649 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3650 isl_ctx *ctx, const char *str);
3652 An expression can be printed using
3654 #include <isl/aff.h>
3655 __isl_give isl_printer *isl_printer_print_multi_aff(
3656 __isl_take isl_printer *p,
3657 __isl_keep isl_multi_aff *maff);
3658 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3659 __isl_take isl_printer *p,
3660 __isl_keep isl_pw_multi_aff *pma);
3661 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3662 __isl_take isl_printer *p,
3663 __isl_keep isl_union_pw_multi_aff *upma);
3667 Points are elements of a set. They can be used to construct
3668 simple sets (boxes) or they can be used to represent the
3669 individual elements of a set.
3670 The zero point (the origin) can be created using
3672 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3674 The coordinates of a point can be inspected, set and changed
3677 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3678 enum isl_dim_type type, int pos, isl_int *v);
3679 __isl_give isl_point *isl_point_set_coordinate(
3680 __isl_take isl_point *pnt,
3681 enum isl_dim_type type, int pos, isl_int v);
3683 __isl_give isl_point *isl_point_add_ui(
3684 __isl_take isl_point *pnt,
3685 enum isl_dim_type type, int pos, unsigned val);
3686 __isl_give isl_point *isl_point_sub_ui(
3687 __isl_take isl_point *pnt,
3688 enum isl_dim_type type, int pos, unsigned val);
3690 Other properties can be obtained using
3692 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3694 Points can be copied or freed using
3696 __isl_give isl_point *isl_point_copy(
3697 __isl_keep isl_point *pnt);
3698 void isl_point_free(__isl_take isl_point *pnt);
3700 A singleton set can be created from a point using
3702 __isl_give isl_basic_set *isl_basic_set_from_point(
3703 __isl_take isl_point *pnt);
3704 __isl_give isl_set *isl_set_from_point(
3705 __isl_take isl_point *pnt);
3707 and a box can be created from two opposite extremal points using
3709 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3710 __isl_take isl_point *pnt1,
3711 __isl_take isl_point *pnt2);
3712 __isl_give isl_set *isl_set_box_from_points(
3713 __isl_take isl_point *pnt1,
3714 __isl_take isl_point *pnt2);
3716 All elements of a B<bounded> (union) set can be enumerated using
3717 the following functions.
3719 int isl_set_foreach_point(__isl_keep isl_set *set,
3720 int (*fn)(__isl_take isl_point *pnt, void *user),
3722 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3723 int (*fn)(__isl_take isl_point *pnt, void *user),
3726 The function C<fn> is called for each integer point in
3727 C<set> with as second argument the last argument of
3728 the C<isl_set_foreach_point> call. The function C<fn>
3729 should return C<0> on success and C<-1> on failure.
3730 In the latter case, C<isl_set_foreach_point> will stop
3731 enumerating and return C<-1> as well.
3732 If the enumeration is performed successfully and to completion,
3733 then C<isl_set_foreach_point> returns C<0>.
3735 To obtain a single point of a (basic) set, use
3737 __isl_give isl_point *isl_basic_set_sample_point(
3738 __isl_take isl_basic_set *bset);
3739 __isl_give isl_point *isl_set_sample_point(
3740 __isl_take isl_set *set);
3742 If C<set> does not contain any (integer) points, then the
3743 resulting point will be ``void'', a property that can be
3746 int isl_point_is_void(__isl_keep isl_point *pnt);
3748 =head2 Piecewise Quasipolynomials
3750 A piecewise quasipolynomial is a particular kind of function that maps
3751 a parametric point to a rational value.
3752 More specifically, a quasipolynomial is a polynomial expression in greatest
3753 integer parts of affine expressions of parameters and variables.
3754 A piecewise quasipolynomial is a subdivision of a given parametric
3755 domain into disjoint cells with a quasipolynomial associated to
3756 each cell. The value of the piecewise quasipolynomial at a given
3757 point is the value of the quasipolynomial associated to the cell
3758 that contains the point. Outside of the union of cells,
3759 the value is assumed to be zero.
3760 For example, the piecewise quasipolynomial
3762 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3764 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3765 A given piecewise quasipolynomial has a fixed domain dimension.
3766 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3767 defined over different domains.
3768 Piecewise quasipolynomials are mainly used by the C<barvinok>
3769 library for representing the number of elements in a parametric set or map.
3770 For example, the piecewise quasipolynomial above represents
3771 the number of points in the map
3773 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3775 =head3 Input and Output
3777 Piecewise quasipolynomials can be read from input using
3779 __isl_give isl_union_pw_qpolynomial *
3780 isl_union_pw_qpolynomial_read_from_str(
3781 isl_ctx *ctx, const char *str);
3783 Quasipolynomials and piecewise quasipolynomials can be printed
3784 using the following functions.
3786 __isl_give isl_printer *isl_printer_print_qpolynomial(
3787 __isl_take isl_printer *p,
3788 __isl_keep isl_qpolynomial *qp);
3790 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3791 __isl_take isl_printer *p,
3792 __isl_keep isl_pw_qpolynomial *pwqp);
3794 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3795 __isl_take isl_printer *p,
3796 __isl_keep isl_union_pw_qpolynomial *upwqp);
3798 The output format of the printer
3799 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3800 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3802 In case of printing in C<ISL_FORMAT_C>, the user may want
3803 to set the names of all dimensions
3805 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3806 __isl_take isl_qpolynomial *qp,
3807 enum isl_dim_type type, unsigned pos,
3809 __isl_give isl_pw_qpolynomial *
3810 isl_pw_qpolynomial_set_dim_name(
3811 __isl_take isl_pw_qpolynomial *pwqp,
3812 enum isl_dim_type type, unsigned pos,
3815 =head3 Creating New (Piecewise) Quasipolynomials
3817 Some simple quasipolynomials can be created using the following functions.
3818 More complicated quasipolynomials can be created by applying
3819 operations such as addition and multiplication
3820 on the resulting quasipolynomials
3822 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3823 __isl_take isl_space *domain);
3824 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3825 __isl_take isl_space *domain);
3826 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3827 __isl_take isl_space *domain);
3828 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3829 __isl_take isl_space *domain);
3830 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3831 __isl_take isl_space *domain);
3832 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3833 __isl_take isl_space *domain,
3834 const isl_int n, const isl_int d);
3835 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3836 __isl_take isl_space *domain,
3837 enum isl_dim_type type, unsigned pos);
3838 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3839 __isl_take isl_aff *aff);
3841 Note that the space in which a quasipolynomial lives is a map space
3842 with a one-dimensional range. The C<domain> argument in some of
3843 the functions above corresponds to the domain of this map space.
3845 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3846 with a single cell can be created using the following functions.
3847 Multiple of these single cell piecewise quasipolynomials can
3848 be combined to create more complicated piecewise quasipolynomials.
3850 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3851 __isl_take isl_space *space);
3852 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3853 __isl_take isl_set *set,
3854 __isl_take isl_qpolynomial *qp);
3855 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3856 __isl_take isl_qpolynomial *qp);
3857 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3858 __isl_take isl_pw_aff *pwaff);
3860 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3861 __isl_take isl_space *space);
3862 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3863 __isl_take isl_pw_qpolynomial *pwqp);
3864 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3865 __isl_take isl_union_pw_qpolynomial *upwqp,
3866 __isl_take isl_pw_qpolynomial *pwqp);
3868 Quasipolynomials can be copied and freed again using the following
3871 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3872 __isl_keep isl_qpolynomial *qp);
3873 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3875 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3876 __isl_keep isl_pw_qpolynomial *pwqp);
3877 void *isl_pw_qpolynomial_free(
3878 __isl_take isl_pw_qpolynomial *pwqp);
3880 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3881 __isl_keep isl_union_pw_qpolynomial *upwqp);
3882 void *isl_union_pw_qpolynomial_free(
3883 __isl_take isl_union_pw_qpolynomial *upwqp);
3885 =head3 Inspecting (Piecewise) Quasipolynomials
3887 To iterate over all piecewise quasipolynomials in a union
3888 piecewise quasipolynomial, use the following function
3890 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3891 __isl_keep isl_union_pw_qpolynomial *upwqp,
3892 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3895 To extract the piecewise quasipolynomial in a given space from a union, use
3897 __isl_give isl_pw_qpolynomial *
3898 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3899 __isl_keep isl_union_pw_qpolynomial *upwqp,
3900 __isl_take isl_space *space);
3902 To iterate over the cells in a piecewise quasipolynomial,
3903 use either of the following two functions
3905 int isl_pw_qpolynomial_foreach_piece(
3906 __isl_keep isl_pw_qpolynomial *pwqp,
3907 int (*fn)(__isl_take isl_set *set,
3908 __isl_take isl_qpolynomial *qp,
3909 void *user), void *user);
3910 int isl_pw_qpolynomial_foreach_lifted_piece(
3911 __isl_keep isl_pw_qpolynomial *pwqp,
3912 int (*fn)(__isl_take isl_set *set,
3913 __isl_take isl_qpolynomial *qp,
3914 void *user), void *user);
3916 As usual, the function C<fn> should return C<0> on success
3917 and C<-1> on failure. The difference between
3918 C<isl_pw_qpolynomial_foreach_piece> and
3919 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3920 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3921 compute unique representations for all existentially quantified
3922 variables and then turn these existentially quantified variables
3923 into extra set variables, adapting the associated quasipolynomial
3924 accordingly. This means that the C<set> passed to C<fn>
3925 will not have any existentially quantified variables, but that
3926 the dimensions of the sets may be different for different
3927 invocations of C<fn>.
3929 To iterate over all terms in a quasipolynomial,
3932 int isl_qpolynomial_foreach_term(
3933 __isl_keep isl_qpolynomial *qp,
3934 int (*fn)(__isl_take isl_term *term,
3935 void *user), void *user);
3937 The terms themselves can be inspected and freed using
3940 unsigned isl_term_dim(__isl_keep isl_term *term,
3941 enum isl_dim_type type);
3942 void isl_term_get_num(__isl_keep isl_term *term,
3944 void isl_term_get_den(__isl_keep isl_term *term,
3946 int isl_term_get_exp(__isl_keep isl_term *term,
3947 enum isl_dim_type type, unsigned pos);
3948 __isl_give isl_aff *isl_term_get_div(
3949 __isl_keep isl_term *term, unsigned pos);
3950 void isl_term_free(__isl_take isl_term *term);
3952 Each term is a product of parameters, set variables and
3953 integer divisions. The function C<isl_term_get_exp>
3954 returns the exponent of a given dimensions in the given term.
3955 The C<isl_int>s in the arguments of C<isl_term_get_num>
3956 and C<isl_term_get_den> need to have been initialized
3957 using C<isl_int_init> before calling these functions.
3959 =head3 Properties of (Piecewise) Quasipolynomials
3961 To check whether a quasipolynomial is actually a constant,
3962 use the following function.
3964 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3965 isl_int *n, isl_int *d);
3967 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3968 then the numerator and denominator of the constant
3969 are returned in C<*n> and C<*d>, respectively.
3971 To check whether two union piecewise quasipolynomials are
3972 obviously equal, use
3974 int isl_union_pw_qpolynomial_plain_is_equal(
3975 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3976 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3978 =head3 Operations on (Piecewise) Quasipolynomials
3980 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3981 __isl_take isl_qpolynomial *qp, isl_int v);
3982 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3983 __isl_take isl_qpolynomial *qp);
3984 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3985 __isl_take isl_qpolynomial *qp1,
3986 __isl_take isl_qpolynomial *qp2);
3987 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3988 __isl_take isl_qpolynomial *qp1,
3989 __isl_take isl_qpolynomial *qp2);
3990 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3991 __isl_take isl_qpolynomial *qp1,
3992 __isl_take isl_qpolynomial *qp2);
3993 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3994 __isl_take isl_qpolynomial *qp, unsigned exponent);
3996 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3997 __isl_take isl_pw_qpolynomial *pwqp1,
3998 __isl_take isl_pw_qpolynomial *pwqp2);
3999 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4000 __isl_take isl_pw_qpolynomial *pwqp1,
4001 __isl_take isl_pw_qpolynomial *pwqp2);
4002 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4003 __isl_take isl_pw_qpolynomial *pwqp1,
4004 __isl_take isl_pw_qpolynomial *pwqp2);
4005 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4006 __isl_take isl_pw_qpolynomial *pwqp);
4007 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4008 __isl_take isl_pw_qpolynomial *pwqp1,
4009 __isl_take isl_pw_qpolynomial *pwqp2);
4010 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4011 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4013 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4014 __isl_take isl_union_pw_qpolynomial *upwqp1,
4015 __isl_take isl_union_pw_qpolynomial *upwqp2);
4016 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4017 __isl_take isl_union_pw_qpolynomial *upwqp1,
4018 __isl_take isl_union_pw_qpolynomial *upwqp2);
4019 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4020 __isl_take isl_union_pw_qpolynomial *upwqp1,
4021 __isl_take isl_union_pw_qpolynomial *upwqp2);
4023 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4024 __isl_take isl_pw_qpolynomial *pwqp,
4025 __isl_take isl_point *pnt);
4027 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4028 __isl_take isl_union_pw_qpolynomial *upwqp,
4029 __isl_take isl_point *pnt);
4031 __isl_give isl_set *isl_pw_qpolynomial_domain(
4032 __isl_take isl_pw_qpolynomial *pwqp);
4033 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4034 __isl_take isl_pw_qpolynomial *pwpq,
4035 __isl_take isl_set *set);
4036 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4037 __isl_take isl_pw_qpolynomial *pwpq,
4038 __isl_take isl_set *set);
4040 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4041 __isl_take isl_union_pw_qpolynomial *upwqp);
4042 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4043 __isl_take isl_union_pw_qpolynomial *upwpq,
4044 __isl_take isl_union_set *uset);
4045 __isl_give isl_union_pw_qpolynomial *
4046 isl_union_pw_qpolynomial_intersect_params(
4047 __isl_take isl_union_pw_qpolynomial *upwpq,
4048 __isl_take isl_set *set);
4050 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4051 __isl_take isl_qpolynomial *qp,
4052 __isl_take isl_space *model);
4054 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4055 __isl_take isl_qpolynomial *qp);
4056 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4057 __isl_take isl_pw_qpolynomial *pwqp);
4059 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4060 __isl_take isl_union_pw_qpolynomial *upwqp);
4062 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4063 __isl_take isl_qpolynomial *qp,
4064 __isl_take isl_set *context);
4065 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4066 __isl_take isl_qpolynomial *qp,
4067 __isl_take isl_set *context);
4069 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4070 __isl_take isl_pw_qpolynomial *pwqp,
4071 __isl_take isl_set *context);
4072 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4073 __isl_take isl_pw_qpolynomial *pwqp,
4074 __isl_take isl_set *context);
4076 __isl_give isl_union_pw_qpolynomial *
4077 isl_union_pw_qpolynomial_gist_params(
4078 __isl_take isl_union_pw_qpolynomial *upwqp,
4079 __isl_take isl_set *context);
4080 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4081 __isl_take isl_union_pw_qpolynomial *upwqp,
4082 __isl_take isl_union_set *context);
4084 The gist operation applies the gist operation to each of
4085 the cells in the domain of the input piecewise quasipolynomial.
4086 The context is also exploited
4087 to simplify the quasipolynomials associated to each cell.
4089 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4090 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4091 __isl_give isl_union_pw_qpolynomial *
4092 isl_union_pw_qpolynomial_to_polynomial(
4093 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4095 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4096 the polynomial will be an overapproximation. If C<sign> is negative,
4097 it will be an underapproximation. If C<sign> is zero, the approximation
4098 will lie somewhere in between.
4100 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4102 A piecewise quasipolynomial reduction is a piecewise
4103 reduction (or fold) of quasipolynomials.
4104 In particular, the reduction can be maximum or a minimum.
4105 The objects are mainly used to represent the result of
4106 an upper or lower bound on a quasipolynomial over its domain,
4107 i.e., as the result of the following function.
4109 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4110 __isl_take isl_pw_qpolynomial *pwqp,
4111 enum isl_fold type, int *tight);
4113 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4114 __isl_take isl_union_pw_qpolynomial *upwqp,
4115 enum isl_fold type, int *tight);
4117 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4118 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4119 is the returned bound is known be tight, i.e., for each value
4120 of the parameters there is at least
4121 one element in the domain that reaches the bound.
4122 If the domain of C<pwqp> is not wrapping, then the bound is computed
4123 over all elements in that domain and the result has a purely parametric
4124 domain. If the domain of C<pwqp> is wrapping, then the bound is
4125 computed over the range of the wrapped relation. The domain of the
4126 wrapped relation becomes the domain of the result.
4128 A (piecewise) quasipolynomial reduction can be copied or freed using the
4129 following functions.
4131 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4132 __isl_keep isl_qpolynomial_fold *fold);
4133 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4134 __isl_keep isl_pw_qpolynomial_fold *pwf);
4135 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4136 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4137 void isl_qpolynomial_fold_free(
4138 __isl_take isl_qpolynomial_fold *fold);
4139 void *isl_pw_qpolynomial_fold_free(
4140 __isl_take isl_pw_qpolynomial_fold *pwf);
4141 void *isl_union_pw_qpolynomial_fold_free(
4142 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4144 =head3 Printing Piecewise Quasipolynomial Reductions
4146 Piecewise quasipolynomial reductions can be printed
4147 using the following function.
4149 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4150 __isl_take isl_printer *p,
4151 __isl_keep isl_pw_qpolynomial_fold *pwf);
4152 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4153 __isl_take isl_printer *p,
4154 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4156 For C<isl_printer_print_pw_qpolynomial_fold>,
4157 output format of the printer
4158 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4159 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4160 output format of the printer
4161 needs to be set to C<ISL_FORMAT_ISL>.
4162 In case of printing in C<ISL_FORMAT_C>, the user may want
4163 to set the names of all dimensions
4165 __isl_give isl_pw_qpolynomial_fold *
4166 isl_pw_qpolynomial_fold_set_dim_name(
4167 __isl_take isl_pw_qpolynomial_fold *pwf,
4168 enum isl_dim_type type, unsigned pos,
4171 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4173 To iterate over all piecewise quasipolynomial reductions in a union
4174 piecewise quasipolynomial reduction, use the following function
4176 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4177 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4178 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4179 void *user), void *user);
4181 To iterate over the cells in a piecewise quasipolynomial reduction,
4182 use either of the following two functions
4184 int isl_pw_qpolynomial_fold_foreach_piece(
4185 __isl_keep isl_pw_qpolynomial_fold *pwf,
4186 int (*fn)(__isl_take isl_set *set,
4187 __isl_take isl_qpolynomial_fold *fold,
4188 void *user), void *user);
4189 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4190 __isl_keep isl_pw_qpolynomial_fold *pwf,
4191 int (*fn)(__isl_take isl_set *set,
4192 __isl_take isl_qpolynomial_fold *fold,
4193 void *user), void *user);
4195 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4196 of the difference between these two functions.
4198 To iterate over all quasipolynomials in a reduction, use
4200 int isl_qpolynomial_fold_foreach_qpolynomial(
4201 __isl_keep isl_qpolynomial_fold *fold,
4202 int (*fn)(__isl_take isl_qpolynomial *qp,
4203 void *user), void *user);
4205 =head3 Properties of Piecewise Quasipolynomial Reductions
4207 To check whether two union piecewise quasipolynomial reductions are
4208 obviously equal, use
4210 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4211 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4212 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4214 =head3 Operations on Piecewise Quasipolynomial Reductions
4216 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4217 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4219 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4220 __isl_take isl_pw_qpolynomial_fold *pwf1,
4221 __isl_take isl_pw_qpolynomial_fold *pwf2);
4223 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4224 __isl_take isl_pw_qpolynomial_fold *pwf1,
4225 __isl_take isl_pw_qpolynomial_fold *pwf2);
4227 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4228 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4229 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4231 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4232 __isl_take isl_pw_qpolynomial_fold *pwf,
4233 __isl_take isl_point *pnt);
4235 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4236 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4237 __isl_take isl_point *pnt);
4239 __isl_give isl_pw_qpolynomial_fold *
4240 isl_pw_qpolynomial_fold_intersect_params(
4241 __isl_take isl_pw_qpolynomial_fold *pwf,
4242 __isl_take isl_set *set);
4244 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4245 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4246 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4247 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4248 __isl_take isl_union_set *uset);
4249 __isl_give isl_union_pw_qpolynomial_fold *
4250 isl_union_pw_qpolynomial_fold_intersect_params(
4251 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4252 __isl_take isl_set *set);
4254 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4255 __isl_take isl_pw_qpolynomial_fold *pwf);
4257 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4258 __isl_take isl_pw_qpolynomial_fold *pwf);
4260 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4261 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4263 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4264 __isl_take isl_qpolynomial_fold *fold,
4265 __isl_take isl_set *context);
4266 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4267 __isl_take isl_qpolynomial_fold *fold,
4268 __isl_take isl_set *context);
4270 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4271 __isl_take isl_pw_qpolynomial_fold *pwf,
4272 __isl_take isl_set *context);
4273 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4274 __isl_take isl_pw_qpolynomial_fold *pwf,
4275 __isl_take isl_set *context);
4277 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4278 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4279 __isl_take isl_union_set *context);
4280 __isl_give isl_union_pw_qpolynomial_fold *
4281 isl_union_pw_qpolynomial_fold_gist_params(
4282 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4283 __isl_take isl_set *context);
4285 The gist operation applies the gist operation to each of
4286 the cells in the domain of the input piecewise quasipolynomial reduction.
4287 In future, the operation will also exploit the context
4288 to simplify the quasipolynomial reductions associated to each cell.
4290 __isl_give isl_pw_qpolynomial_fold *
4291 isl_set_apply_pw_qpolynomial_fold(
4292 __isl_take isl_set *set,
4293 __isl_take isl_pw_qpolynomial_fold *pwf,
4295 __isl_give isl_pw_qpolynomial_fold *
4296 isl_map_apply_pw_qpolynomial_fold(
4297 __isl_take isl_map *map,
4298 __isl_take isl_pw_qpolynomial_fold *pwf,
4300 __isl_give isl_union_pw_qpolynomial_fold *
4301 isl_union_set_apply_union_pw_qpolynomial_fold(
4302 __isl_take isl_union_set *uset,
4303 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4305 __isl_give isl_union_pw_qpolynomial_fold *
4306 isl_union_map_apply_union_pw_qpolynomial_fold(
4307 __isl_take isl_union_map *umap,
4308 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4311 The functions taking a map
4312 compose the given map with the given piecewise quasipolynomial reduction.
4313 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4314 over all elements in the intersection of the range of the map
4315 and the domain of the piecewise quasipolynomial reduction
4316 as a function of an element in the domain of the map.
4317 The functions taking a set compute a bound over all elements in the
4318 intersection of the set and the domain of the
4319 piecewise quasipolynomial reduction.
4321 =head2 Dependence Analysis
4323 C<isl> contains specialized functionality for performing
4324 array dataflow analysis. That is, given a I<sink> access relation
4325 and a collection of possible I<source> access relations,
4326 C<isl> can compute relations that describe
4327 for each iteration of the sink access, which iteration
4328 of which of the source access relations was the last
4329 to access the same data element before the given iteration
4331 The resulting dependence relations map source iterations
4332 to the corresponding sink iterations.
4333 To compute standard flow dependences, the sink should be
4334 a read, while the sources should be writes.
4335 If any of the source accesses are marked as being I<may>
4336 accesses, then there will be a dependence from the last
4337 I<must> access B<and> from any I<may> access that follows
4338 this last I<must> access.
4339 In particular, if I<all> sources are I<may> accesses,
4340 then memory based dependence analysis is performed.
4341 If, on the other hand, all sources are I<must> accesses,
4342 then value based dependence analysis is performed.
4344 #include <isl/flow.h>
4346 typedef int (*isl_access_level_before)(void *first, void *second);
4348 __isl_give isl_access_info *isl_access_info_alloc(
4349 __isl_take isl_map *sink,
4350 void *sink_user, isl_access_level_before fn,
4352 __isl_give isl_access_info *isl_access_info_add_source(
4353 __isl_take isl_access_info *acc,
4354 __isl_take isl_map *source, int must,
4356 void *isl_access_info_free(__isl_take isl_access_info *acc);
4358 __isl_give isl_flow *isl_access_info_compute_flow(
4359 __isl_take isl_access_info *acc);
4361 int isl_flow_foreach(__isl_keep isl_flow *deps,
4362 int (*fn)(__isl_take isl_map *dep, int must,
4363 void *dep_user, void *user),
4365 __isl_give isl_map *isl_flow_get_no_source(
4366 __isl_keep isl_flow *deps, int must);
4367 void isl_flow_free(__isl_take isl_flow *deps);
4369 The function C<isl_access_info_compute_flow> performs the actual
4370 dependence analysis. The other functions are used to construct
4371 the input for this function or to read off the output.
4373 The input is collected in an C<isl_access_info>, which can
4374 be created through a call to C<isl_access_info_alloc>.
4375 The arguments to this functions are the sink access relation
4376 C<sink>, a token C<sink_user> used to identify the sink
4377 access to the user, a callback function for specifying the
4378 relative order of source and sink accesses, and the number
4379 of source access relations that will be added.
4380 The callback function has type C<int (*)(void *first, void *second)>.
4381 The function is called with two user supplied tokens identifying
4382 either a source or the sink and it should return the shared nesting
4383 level and the relative order of the two accesses.
4384 In particular, let I<n> be the number of loops shared by
4385 the two accesses. If C<first> precedes C<second> textually,
4386 then the function should return I<2 * n + 1>; otherwise,
4387 it should return I<2 * n>.
4388 The sources can be added to the C<isl_access_info> by performing
4389 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4390 C<must> indicates whether the source is a I<must> access
4391 or a I<may> access. Note that a multi-valued access relation
4392 should only be marked I<must> if every iteration in the domain
4393 of the relation accesses I<all> elements in its image.
4394 The C<source_user> token is again used to identify
4395 the source access. The range of the source access relation
4396 C<source> should have the same dimension as the range
4397 of the sink access relation.
4398 The C<isl_access_info_free> function should usually not be
4399 called explicitly, because it is called implicitly by
4400 C<isl_access_info_compute_flow>.
4402 The result of the dependence analysis is collected in an
4403 C<isl_flow>. There may be elements of
4404 the sink access for which no preceding source access could be
4405 found or for which all preceding sources are I<may> accesses.
4406 The relations containing these elements can be obtained through
4407 calls to C<isl_flow_get_no_source>, the first with C<must> set
4408 and the second with C<must> unset.
4409 In the case of standard flow dependence analysis,
4410 with the sink a read and the sources I<must> writes,
4411 the first relation corresponds to the reads from uninitialized
4412 array elements and the second relation is empty.
4413 The actual flow dependences can be extracted using
4414 C<isl_flow_foreach>. This function will call the user-specified
4415 callback function C<fn> for each B<non-empty> dependence between
4416 a source and the sink. The callback function is called
4417 with four arguments, the actual flow dependence relation
4418 mapping source iterations to sink iterations, a boolean that
4419 indicates whether it is a I<must> or I<may> dependence, a token
4420 identifying the source and an additional C<void *> with value
4421 equal to the third argument of the C<isl_flow_foreach> call.
4422 A dependence is marked I<must> if it originates from a I<must>
4423 source and if it is not followed by any I<may> sources.
4425 After finishing with an C<isl_flow>, the user should call
4426 C<isl_flow_free> to free all associated memory.
4428 A higher-level interface to dependence analysis is provided
4429 by the following function.
4431 #include <isl/flow.h>
4433 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4434 __isl_take isl_union_map *must_source,
4435 __isl_take isl_union_map *may_source,
4436 __isl_take isl_union_map *schedule,
4437 __isl_give isl_union_map **must_dep,
4438 __isl_give isl_union_map **may_dep,
4439 __isl_give isl_union_map **must_no_source,
4440 __isl_give isl_union_map **may_no_source);
4442 The arrays are identified by the tuple names of the ranges
4443 of the accesses. The iteration domains by the tuple names
4444 of the domains of the accesses and of the schedule.
4445 The relative order of the iteration domains is given by the
4446 schedule. The relations returned through C<must_no_source>
4447 and C<may_no_source> are subsets of C<sink>.
4448 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4449 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4450 any of the other arguments is treated as an error.
4452 =head3 Interaction with Dependence Analysis
4454 During the dependence analysis, we frequently need to perform
4455 the following operation. Given a relation between sink iterations
4456 and potential source iterations from a particular source domain,
4457 what is the last potential source iteration corresponding to each
4458 sink iteration. It can sometimes be convenient to adjust
4459 the set of potential source iterations before or after each such operation.
4460 The prototypical example is fuzzy array dataflow analysis,
4461 where we need to analyze if, based on data-dependent constraints,
4462 the sink iteration can ever be executed without one or more of
4463 the corresponding potential source iterations being executed.
4464 If so, we can introduce extra parameters and select an unknown
4465 but fixed source iteration from the potential source iterations.
4466 To be able to perform such manipulations, C<isl> provides the following
4469 #include <isl/flow.h>
4471 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4472 __isl_keep isl_map *source_map,
4473 __isl_keep isl_set *sink, void *source_user,
4475 __isl_give isl_access_info *isl_access_info_set_restrict(
4476 __isl_take isl_access_info *acc,
4477 isl_access_restrict fn, void *user);
4479 The function C<isl_access_info_set_restrict> should be called
4480 before calling C<isl_access_info_compute_flow> and registers a callback function
4481 that will be called any time C<isl> is about to compute the last
4482 potential source. The first argument is the (reverse) proto-dependence,
4483 mapping sink iterations to potential source iterations.
4484 The second argument represents the sink iterations for which
4485 we want to compute the last source iteration.
4486 The third argument is the token corresponding to the source
4487 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4488 The callback is expected to return a restriction on either the input or
4489 the output of the operation computing the last potential source.
4490 If the input needs to be restricted then restrictions are needed
4491 for both the source and the sink iterations. The sink iterations
4492 and the potential source iterations will be intersected with these sets.
4493 If the output needs to be restricted then only a restriction on the source
4494 iterations is required.
4495 If any error occurs, the callback should return C<NULL>.
4496 An C<isl_restriction> object can be created, freed and inspected
4497 using the following functions.
4499 #include <isl/flow.h>
4501 __isl_give isl_restriction *isl_restriction_input(
4502 __isl_take isl_set *source_restr,
4503 __isl_take isl_set *sink_restr);
4504 __isl_give isl_restriction *isl_restriction_output(
4505 __isl_take isl_set *source_restr);
4506 __isl_give isl_restriction *isl_restriction_none(
4507 __isl_take isl_map *source_map);
4508 __isl_give isl_restriction *isl_restriction_empty(
4509 __isl_take isl_map *source_map);
4510 void *isl_restriction_free(
4511 __isl_take isl_restriction *restr);
4512 isl_ctx *isl_restriction_get_ctx(
4513 __isl_keep isl_restriction *restr);
4515 C<isl_restriction_none> and C<isl_restriction_empty> are special
4516 cases of C<isl_restriction_input>. C<isl_restriction_none>
4517 is essentially equivalent to
4519 isl_restriction_input(isl_set_universe(
4520 isl_space_range(isl_map_get_space(source_map))),
4522 isl_space_domain(isl_map_get_space(source_map))));
4524 whereas C<isl_restriction_empty> is essentially equivalent to
4526 isl_restriction_input(isl_set_empty(
4527 isl_space_range(isl_map_get_space(source_map))),
4529 isl_space_domain(isl_map_get_space(source_map))));
4533 B<The functionality described in this section is fairly new
4534 and may be subject to change.>
4536 The following function can be used to compute a schedule
4537 for a union of domains.
4538 By default, the algorithm used to construct the schedule is similar
4539 to that of C<Pluto>.
4540 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4542 The generated schedule respects all C<validity> dependences.
4543 That is, all dependence distances over these dependences in the
4544 scheduled space are lexicographically positive.
4545 The default algorithm tries to minimize the dependence distances over
4546 C<proximity> dependences.
4547 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4548 for groups of domains where the dependence distances have only
4549 non-negative values.
4550 When using Feautrier's algorithm, the C<proximity> dependence
4551 distances are only minimized during the extension to a
4552 full-dimensional schedule.
4554 #include <isl/schedule.h>
4555 __isl_give isl_schedule *isl_union_set_compute_schedule(
4556 __isl_take isl_union_set *domain,
4557 __isl_take isl_union_map *validity,
4558 __isl_take isl_union_map *proximity);
4559 void *isl_schedule_free(__isl_take isl_schedule *sched);
4561 A mapping from the domains to the scheduled space can be obtained
4562 from an C<isl_schedule> using the following function.
4564 __isl_give isl_union_map *isl_schedule_get_map(
4565 __isl_keep isl_schedule *sched);
4567 A representation of the schedule can be printed using
4569 __isl_give isl_printer *isl_printer_print_schedule(
4570 __isl_take isl_printer *p,
4571 __isl_keep isl_schedule *schedule);
4573 A representation of the schedule as a forest of bands can be obtained
4574 using the following function.
4576 __isl_give isl_band_list *isl_schedule_get_band_forest(
4577 __isl_keep isl_schedule *schedule);
4579 The individual bands can be visited in depth-first post-order
4580 using the following function.
4582 #include <isl/schedule.h>
4583 int isl_schedule_foreach_band(
4584 __isl_keep isl_schedule *sched,
4585 int (*fn)(__isl_keep isl_band *band, void *user),
4588 The list can be manipulated as explained in L<"Lists">.
4589 The bands inside the list can be copied and freed using the following
4592 #include <isl/band.h>
4593 __isl_give isl_band *isl_band_copy(
4594 __isl_keep isl_band *band);
4595 void *isl_band_free(__isl_take isl_band *band);
4597 Each band contains zero or more scheduling dimensions.
4598 These are referred to as the members of the band.
4599 The section of the schedule that corresponds to the band is
4600 referred to as the partial schedule of the band.
4601 For those nodes that participate in a band, the outer scheduling
4602 dimensions form the prefix schedule, while the inner scheduling
4603 dimensions form the suffix schedule.
4604 That is, if we take a cut of the band forest, then the union of
4605 the concatenations of the prefix, partial and suffix schedules of
4606 each band in the cut is equal to the entire schedule (modulo
4607 some possible padding at the end with zero scheduling dimensions).
4608 The properties of a band can be inspected using the following functions.
4610 #include <isl/band.h>
4611 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4613 int isl_band_has_children(__isl_keep isl_band *band);
4614 __isl_give isl_band_list *isl_band_get_children(
4615 __isl_keep isl_band *band);
4617 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4618 __isl_keep isl_band *band);
4619 __isl_give isl_union_map *isl_band_get_partial_schedule(
4620 __isl_keep isl_band *band);
4621 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4622 __isl_keep isl_band *band);
4624 int isl_band_n_member(__isl_keep isl_band *band);
4625 int isl_band_member_is_zero_distance(
4626 __isl_keep isl_band *band, int pos);
4628 int isl_band_list_foreach_band(
4629 __isl_keep isl_band_list *list,
4630 int (*fn)(__isl_keep isl_band *band, void *user),
4633 Note that a scheduling dimension is considered to be ``zero
4634 distance'' if it does not carry any proximity dependences
4636 That is, if the dependence distances of the proximity
4637 dependences are all zero in that direction (for fixed
4638 iterations of outer bands).
4639 Like C<isl_schedule_foreach_band>,
4640 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4641 in depth-first post-order.
4643 A band can be tiled using the following function.
4645 #include <isl/band.h>
4646 int isl_band_tile(__isl_keep isl_band *band,
4647 __isl_take isl_vec *sizes);
4649 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4651 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4653 The C<isl_band_tile> function tiles the band using the given tile sizes
4654 inside its schedule.
4655 A new child band is created to represent the point loops and it is
4656 inserted between the modified band and its children.
4657 The C<tile_scale_tile_loops> option specifies whether the tile
4658 loops iterators should be scaled by the tile sizes.
4660 A representation of the band can be printed using
4662 #include <isl/band.h>
4663 __isl_give isl_printer *isl_printer_print_band(
4664 __isl_take isl_printer *p,
4665 __isl_keep isl_band *band);
4669 #include <isl/schedule.h>
4670 int isl_options_set_schedule_max_coefficient(
4671 isl_ctx *ctx, int val);
4672 int isl_options_get_schedule_max_coefficient(
4674 int isl_options_set_schedule_max_constant_term(
4675 isl_ctx *ctx, int val);
4676 int isl_options_get_schedule_max_constant_term(
4678 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4679 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4680 int isl_options_set_schedule_maximize_band_depth(
4681 isl_ctx *ctx, int val);
4682 int isl_options_get_schedule_maximize_band_depth(
4684 int isl_options_set_schedule_outer_zero_distance(
4685 isl_ctx *ctx, int val);
4686 int isl_options_get_schedule_outer_zero_distance(
4688 int isl_options_set_schedule_split_scaled(
4689 isl_ctx *ctx, int val);
4690 int isl_options_get_schedule_split_scaled(
4692 int isl_options_set_schedule_algorithm(
4693 isl_ctx *ctx, int val);
4694 int isl_options_get_schedule_algorithm(
4696 int isl_options_set_schedule_separate_components(
4697 isl_ctx *ctx, int val);
4698 int isl_options_get_schedule_separate_components(
4703 =item * schedule_max_coefficient
4705 This option enforces that the coefficients for variable and parameter
4706 dimensions in the calculated schedule are not larger than the specified value.
4707 This option can significantly increase the speed of the scheduling calculation
4708 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4709 this option does not introduce bounds on the variable or parameter
4712 =item * schedule_max_constant_term
4714 This option enforces that the constant coefficients in the calculated schedule
4715 are not larger than the maximal constant term. This option can significantly
4716 increase the speed of the scheduling calculation and may also prevent fusing of
4717 unrelated dimensions. A value of -1 means that this option does not introduce
4718 bounds on the constant coefficients.
4720 =item * schedule_fuse
4722 This option controls the level of fusion.
4723 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
4724 resulting schedule will be distributed as much as possible.
4725 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
4726 try to fuse loops in the resulting schedule.
4728 =item * schedule_maximize_band_depth
4730 If this option is set, we do not split bands at the point
4731 where we detect splitting is necessary. Instead, we
4732 backtrack and split bands as early as possible. This
4733 reduces the number of splits and maximizes the width of
4734 the bands. Wider bands give more possibilities for tiling.
4735 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
4736 then bands will be split as early as possible, even if there is no need.
4737 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
4739 =item * schedule_outer_zero_distance
4741 If this option is set, then we try to construct schedules
4742 where the outermost scheduling dimension in each band
4743 results in a zero dependence distance over the proximity
4746 =item * schedule_split_scaled
4748 If this option is set, then we try to construct schedules in which the
4749 constant term is split off from the linear part if the linear parts of
4750 the scheduling rows for all nodes in the graphs have a common non-trivial
4752 The constant term is then placed in a separate band and the linear
4755 =item * schedule_algorithm
4757 Selects the scheduling algorithm to be used.
4758 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4759 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4761 =item * schedule_separate_components
4763 If at any point the dependence graph contains any (weakly connected) components,
4764 then these components are scheduled separately.
4765 If this option is not set, then some iterations of the domains
4766 in these components may be scheduled together.
4767 If this option is set, then the components are given consecutive
4772 =head2 Parametric Vertex Enumeration
4774 The parametric vertex enumeration described in this section
4775 is mainly intended to be used internally and by the C<barvinok>
4778 #include <isl/vertices.h>
4779 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4780 __isl_keep isl_basic_set *bset);
4782 The function C<isl_basic_set_compute_vertices> performs the
4783 actual computation of the parametric vertices and the chamber
4784 decomposition and store the result in an C<isl_vertices> object.
4785 This information can be queried by either iterating over all
4786 the vertices or iterating over all the chambers or cells
4787 and then iterating over all vertices that are active on the chamber.
4789 int isl_vertices_foreach_vertex(
4790 __isl_keep isl_vertices *vertices,
4791 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4794 int isl_vertices_foreach_cell(
4795 __isl_keep isl_vertices *vertices,
4796 int (*fn)(__isl_take isl_cell *cell, void *user),
4798 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4799 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4802 Other operations that can be performed on an C<isl_vertices> object are
4805 isl_ctx *isl_vertices_get_ctx(
4806 __isl_keep isl_vertices *vertices);
4807 int isl_vertices_get_n_vertices(
4808 __isl_keep isl_vertices *vertices);
4809 void isl_vertices_free(__isl_take isl_vertices *vertices);
4811 Vertices can be inspected and destroyed using the following functions.
4813 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4814 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4815 __isl_give isl_basic_set *isl_vertex_get_domain(
4816 __isl_keep isl_vertex *vertex);
4817 __isl_give isl_basic_set *isl_vertex_get_expr(
4818 __isl_keep isl_vertex *vertex);
4819 void isl_vertex_free(__isl_take isl_vertex *vertex);
4821 C<isl_vertex_get_expr> returns a singleton parametric set describing
4822 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4824 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4825 B<rational> basic sets, so they should mainly be used for inspection
4826 and should not be mixed with integer sets.
4828 Chambers can be inspected and destroyed using the following functions.
4830 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4831 __isl_give isl_basic_set *isl_cell_get_domain(
4832 __isl_keep isl_cell *cell);
4833 void isl_cell_free(__isl_take isl_cell *cell);
4837 Although C<isl> is mainly meant to be used as a library,
4838 it also contains some basic applications that use some
4839 of the functionality of C<isl>.
4840 The input may be specified in either the L<isl format>
4841 or the L<PolyLib format>.
4843 =head2 C<isl_polyhedron_sample>
4845 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4846 an integer element of the polyhedron, if there is any.
4847 The first column in the output is the denominator and is always
4848 equal to 1. If the polyhedron contains no integer points,
4849 then a vector of length zero is printed.
4853 C<isl_pip> takes the same input as the C<example> program
4854 from the C<piplib> distribution, i.e., a set of constraints
4855 on the parameters, a line containing only -1 and finally a set
4856 of constraints on a parametric polyhedron.
4857 The coefficients of the parameters appear in the last columns
4858 (but before the final constant column).
4859 The output is the lexicographic minimum of the parametric polyhedron.
4860 As C<isl> currently does not have its own output format, the output
4861 is just a dump of the internal state.
4863 =head2 C<isl_polyhedron_minimize>
4865 C<isl_polyhedron_minimize> computes the minimum of some linear
4866 or affine objective function over the integer points in a polyhedron.
4867 If an affine objective function
4868 is given, then the constant should appear in the last column.
4870 =head2 C<isl_polytope_scan>
4872 Given a polytope, C<isl_polytope_scan> prints
4873 all integer points in the polytope.