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 functions:
621 #include <isl/space.h>
622 int isl_space_is_equal(__isl_keep isl_space *space1,
623 __isl_keep isl_space *space2);
624 int isl_space_is_domain(__isl_keep isl_space *space1,
625 __isl_keep isl_space *space2);
627 C<isl_space_is_domain> checks whether the first argument is equal
628 to the domain of the second argument. This requires in particular that
629 the first argument is a set space and that the second argument
632 It is often useful to create objects that live in the
633 same space as some other object. This can be accomplished
634 by creating the new objects
635 (see L<Creating New Sets and Relations> or
636 L<Creating New (Piecewise) Quasipolynomials>) based on the space
637 of the original object.
640 __isl_give isl_space *isl_basic_set_get_space(
641 __isl_keep isl_basic_set *bset);
642 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
644 #include <isl/union_set.h>
645 __isl_give isl_space *isl_union_set_get_space(
646 __isl_keep isl_union_set *uset);
649 __isl_give isl_space *isl_basic_map_get_space(
650 __isl_keep isl_basic_map *bmap);
651 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
653 #include <isl/union_map.h>
654 __isl_give isl_space *isl_union_map_get_space(
655 __isl_keep isl_union_map *umap);
657 #include <isl/constraint.h>
658 __isl_give isl_space *isl_constraint_get_space(
659 __isl_keep isl_constraint *constraint);
661 #include <isl/polynomial.h>
662 __isl_give isl_space *isl_qpolynomial_get_domain_space(
663 __isl_keep isl_qpolynomial *qp);
664 __isl_give isl_space *isl_qpolynomial_get_space(
665 __isl_keep isl_qpolynomial *qp);
666 __isl_give isl_space *isl_qpolynomial_fold_get_space(
667 __isl_keep isl_qpolynomial_fold *fold);
668 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
669 __isl_keep isl_pw_qpolynomial *pwqp);
670 __isl_give isl_space *isl_pw_qpolynomial_get_space(
671 __isl_keep isl_pw_qpolynomial *pwqp);
672 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
673 __isl_keep isl_pw_qpolynomial_fold *pwf);
674 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
675 __isl_keep isl_pw_qpolynomial_fold *pwf);
676 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
677 __isl_keep isl_union_pw_qpolynomial *upwqp);
678 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
679 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
682 __isl_give isl_space *isl_aff_get_domain_space(
683 __isl_keep isl_aff *aff);
684 __isl_give isl_space *isl_aff_get_space(
685 __isl_keep isl_aff *aff);
686 __isl_give isl_space *isl_pw_aff_get_domain_space(
687 __isl_keep isl_pw_aff *pwaff);
688 __isl_give isl_space *isl_pw_aff_get_space(
689 __isl_keep isl_pw_aff *pwaff);
690 __isl_give isl_space *isl_multi_aff_get_domain_space(
691 __isl_keep isl_multi_aff *maff);
692 __isl_give isl_space *isl_multi_aff_get_space(
693 __isl_keep isl_multi_aff *maff);
694 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
695 __isl_keep isl_pw_multi_aff *pma);
696 __isl_give isl_space *isl_pw_multi_aff_get_space(
697 __isl_keep isl_pw_multi_aff *pma);
698 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
699 __isl_keep isl_union_pw_multi_aff *upma);
701 #include <isl/point.h>
702 __isl_give isl_space *isl_point_get_space(
703 __isl_keep isl_point *pnt);
705 The identifiers or names of the individual dimensions may be set or read off
706 using the following functions.
708 #include <isl/space.h>
709 __isl_give isl_space *isl_space_set_dim_id(
710 __isl_take isl_space *space,
711 enum isl_dim_type type, unsigned pos,
712 __isl_take isl_id *id);
713 int isl_space_has_dim_id(__isl_keep isl_space *space,
714 enum isl_dim_type type, unsigned pos);
715 __isl_give isl_id *isl_space_get_dim_id(
716 __isl_keep isl_space *space,
717 enum isl_dim_type type, unsigned pos);
718 __isl_give isl_space *isl_space_set_dim_name(
719 __isl_take isl_space *space,
720 enum isl_dim_type type, unsigned pos,
721 __isl_keep const char *name);
722 int isl_space_has_dim_name(__isl_keep isl_space *space,
723 enum isl_dim_type type, unsigned pos);
724 __isl_keep const char *isl_space_get_dim_name(
725 __isl_keep isl_space *space,
726 enum isl_dim_type type, unsigned pos);
728 Note that C<isl_space_get_name> returns a pointer to some internal
729 data structure, so the result can only be used while the
730 corresponding C<isl_space> is alive.
731 Also note that every function that operates on two sets or relations
732 requires that both arguments have the same parameters. This also
733 means that if one of the arguments has named parameters, then the
734 other needs to have named parameters too and the names need to match.
735 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
736 arguments may have different parameters (as long as they are named),
737 in which case the result will have as parameters the union of the parameters of
740 Given the identifier or name of a dimension (typically a parameter),
741 its position can be obtained from the following function.
743 #include <isl/space.h>
744 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
745 enum isl_dim_type type, __isl_keep isl_id *id);
746 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
747 enum isl_dim_type type, const char *name);
749 The identifiers or names of entire spaces may be set or read off
750 using the following functions.
752 #include <isl/space.h>
753 __isl_give isl_space *isl_space_set_tuple_id(
754 __isl_take isl_space *space,
755 enum isl_dim_type type, __isl_take isl_id *id);
756 __isl_give isl_space *isl_space_reset_tuple_id(
757 __isl_take isl_space *space, enum isl_dim_type type);
758 int isl_space_has_tuple_id(__isl_keep isl_space *space,
759 enum isl_dim_type type);
760 __isl_give isl_id *isl_space_get_tuple_id(
761 __isl_keep isl_space *space, enum isl_dim_type type);
762 __isl_give isl_space *isl_space_set_tuple_name(
763 __isl_take isl_space *space,
764 enum isl_dim_type type, const char *s);
765 int isl_space_has_tuple_name(__isl_keep isl_space *space,
766 enum isl_dim_type type);
767 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
768 enum isl_dim_type type);
770 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
771 or C<isl_dim_set>. As with C<isl_space_get_name>,
772 the C<isl_space_get_tuple_name> function returns a pointer to some internal
774 Binary operations require the corresponding spaces of their arguments
775 to have the same name.
777 Spaces can be nested. In particular, the domain of a set or
778 the domain or range of a relation can be a nested relation.
779 The following functions can be used to construct and deconstruct
782 #include <isl/space.h>
783 int isl_space_is_wrapping(__isl_keep isl_space *space);
784 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
785 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
787 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
788 be the space of a set, while that of
789 C<isl_space_wrap> should be the space of a relation.
790 Conversely, the output of C<isl_space_unwrap> is the space
791 of a relation, while that of C<isl_space_wrap> is the space of a set.
793 Spaces can be created from other spaces
794 using the following functions.
796 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
797 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
798 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
799 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
800 __isl_give isl_space *isl_space_params(
801 __isl_take isl_space *space);
802 __isl_give isl_space *isl_space_set_from_params(
803 __isl_take isl_space *space);
804 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
805 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
806 __isl_take isl_space *right);
807 __isl_give isl_space *isl_space_align_params(
808 __isl_take isl_space *space1, __isl_take isl_space *space2)
809 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
810 enum isl_dim_type type, unsigned pos, unsigned n);
811 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
812 enum isl_dim_type type, unsigned n);
813 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
814 enum isl_dim_type type, unsigned first, unsigned n);
815 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
816 enum isl_dim_type dst_type, unsigned dst_pos,
817 enum isl_dim_type src_type, unsigned src_pos,
819 __isl_give isl_space *isl_space_map_from_set(
820 __isl_take isl_space *space);
821 __isl_give isl_space *isl_space_map_from_domain_and_range(
822 __isl_take isl_space *domain,
823 __isl_take isl_space *range);
824 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
825 __isl_give isl_space *isl_space_curry(
826 __isl_take isl_space *space);
828 Note that if dimensions are added or removed from a space, then
829 the name and the internal structure are lost.
833 A local space is essentially a space with
834 zero or more existentially quantified variables.
835 The local space of a (constraint of a) basic set or relation can be obtained
836 using the following functions.
838 #include <isl/constraint.h>
839 __isl_give isl_local_space *isl_constraint_get_local_space(
840 __isl_keep isl_constraint *constraint);
843 __isl_give isl_local_space *isl_basic_set_get_local_space(
844 __isl_keep isl_basic_set *bset);
847 __isl_give isl_local_space *isl_basic_map_get_local_space(
848 __isl_keep isl_basic_map *bmap);
850 A new local space can be created from a space using
852 #include <isl/local_space.h>
853 __isl_give isl_local_space *isl_local_space_from_space(
854 __isl_take isl_space *space);
856 They can be inspected, modified, copied and freed using the following functions.
858 #include <isl/local_space.h>
859 isl_ctx *isl_local_space_get_ctx(
860 __isl_keep isl_local_space *ls);
861 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
862 int isl_local_space_dim(__isl_keep isl_local_space *ls,
863 enum isl_dim_type type);
864 int isl_local_space_has_dim_id(
865 __isl_keep isl_local_space *ls,
866 enum isl_dim_type type, unsigned pos);
867 __isl_give isl_id *isl_local_space_get_dim_id(
868 __isl_keep isl_local_space *ls,
869 enum isl_dim_type type, unsigned pos);
870 int isl_local_space_has_dim_name(
871 __isl_keep isl_local_space *ls,
872 enum isl_dim_type type, unsigned pos)
873 const char *isl_local_space_get_dim_name(
874 __isl_keep isl_local_space *ls,
875 enum isl_dim_type type, unsigned pos);
876 __isl_give isl_local_space *isl_local_space_set_dim_name(
877 __isl_take isl_local_space *ls,
878 enum isl_dim_type type, unsigned pos, const char *s);
879 __isl_give isl_local_space *isl_local_space_set_dim_id(
880 __isl_take isl_local_space *ls,
881 enum isl_dim_type type, unsigned pos,
882 __isl_take isl_id *id);
883 __isl_give isl_space *isl_local_space_get_space(
884 __isl_keep isl_local_space *ls);
885 __isl_give isl_aff *isl_local_space_get_div(
886 __isl_keep isl_local_space *ls, int pos);
887 __isl_give isl_local_space *isl_local_space_copy(
888 __isl_keep isl_local_space *ls);
889 void *isl_local_space_free(__isl_take isl_local_space *ls);
891 Two local spaces can be compared using
893 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
894 __isl_keep isl_local_space *ls2);
896 Local spaces can be created from other local spaces
897 using the following functions.
899 __isl_give isl_local_space *isl_local_space_domain(
900 __isl_take isl_local_space *ls);
901 __isl_give isl_local_space *isl_local_space_range(
902 __isl_take isl_local_space *ls);
903 __isl_give isl_local_space *isl_local_space_from_domain(
904 __isl_take isl_local_space *ls);
905 __isl_give isl_local_space *isl_local_space_intersect(
906 __isl_take isl_local_space *ls1,
907 __isl_take isl_local_space *ls2);
908 __isl_give isl_local_space *isl_local_space_add_dims(
909 __isl_take isl_local_space *ls,
910 enum isl_dim_type type, unsigned n);
911 __isl_give isl_local_space *isl_local_space_insert_dims(
912 __isl_take isl_local_space *ls,
913 enum isl_dim_type type, unsigned first, unsigned n);
914 __isl_give isl_local_space *isl_local_space_drop_dims(
915 __isl_take isl_local_space *ls,
916 enum isl_dim_type type, unsigned first, unsigned n);
918 =head2 Input and Output
920 C<isl> supports its own input/output format, which is similar
921 to the C<Omega> format, but also supports the C<PolyLib> format
926 The C<isl> format is similar to that of C<Omega>, but has a different
927 syntax for describing the parameters and allows for the definition
928 of an existentially quantified variable as the integer division
929 of an affine expression.
930 For example, the set of integers C<i> between C<0> and C<n>
931 such that C<i % 10 <= 6> can be described as
933 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
936 A set or relation can have several disjuncts, separated
937 by the keyword C<or>. Each disjunct is either a conjunction
938 of constraints or a projection (C<exists>) of a conjunction
939 of constraints. The constraints are separated by the keyword
942 =head3 C<PolyLib> format
944 If the represented set is a union, then the first line
945 contains a single number representing the number of disjuncts.
946 Otherwise, a line containing the number C<1> is optional.
948 Each disjunct is represented by a matrix of constraints.
949 The first line contains two numbers representing
950 the number of rows and columns,
951 where the number of rows is equal to the number of constraints
952 and the number of columns is equal to two plus the number of variables.
953 The following lines contain the actual rows of the constraint matrix.
954 In each row, the first column indicates whether the constraint
955 is an equality (C<0>) or inequality (C<1>). The final column
956 corresponds to the constant term.
958 If the set is parametric, then the coefficients of the parameters
959 appear in the last columns before the constant column.
960 The coefficients of any existentially quantified variables appear
961 between those of the set variables and those of the parameters.
963 =head3 Extended C<PolyLib> format
965 The extended C<PolyLib> format is nearly identical to the
966 C<PolyLib> format. The only difference is that the line
967 containing the number of rows and columns of a constraint matrix
968 also contains four additional numbers:
969 the number of output dimensions, the number of input dimensions,
970 the number of local dimensions (i.e., the number of existentially
971 quantified variables) and the number of parameters.
972 For sets, the number of ``output'' dimensions is equal
973 to the number of set dimensions, while the number of ``input''
979 __isl_give isl_basic_set *isl_basic_set_read_from_file(
980 isl_ctx *ctx, FILE *input);
981 __isl_give isl_basic_set *isl_basic_set_read_from_str(
982 isl_ctx *ctx, const char *str);
983 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
985 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
989 __isl_give isl_basic_map *isl_basic_map_read_from_file(
990 isl_ctx *ctx, FILE *input);
991 __isl_give isl_basic_map *isl_basic_map_read_from_str(
992 isl_ctx *ctx, const char *str);
993 __isl_give isl_map *isl_map_read_from_file(
994 isl_ctx *ctx, FILE *input);
995 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
998 #include <isl/union_set.h>
999 __isl_give isl_union_set *isl_union_set_read_from_file(
1000 isl_ctx *ctx, FILE *input);
1001 __isl_give isl_union_set *isl_union_set_read_from_str(
1002 isl_ctx *ctx, const char *str);
1004 #include <isl/union_map.h>
1005 __isl_give isl_union_map *isl_union_map_read_from_file(
1006 isl_ctx *ctx, FILE *input);
1007 __isl_give isl_union_map *isl_union_map_read_from_str(
1008 isl_ctx *ctx, const char *str);
1010 The input format is autodetected and may be either the C<PolyLib> format
1011 or the C<isl> format.
1015 Before anything can be printed, an C<isl_printer> needs to
1018 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1020 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1021 void *isl_printer_free(__isl_take isl_printer *printer);
1022 __isl_give char *isl_printer_get_str(
1023 __isl_keep isl_printer *printer);
1025 The printer can be inspected using the following functions.
1027 FILE *isl_printer_get_file(
1028 __isl_keep isl_printer *printer);
1029 int isl_printer_get_output_format(
1030 __isl_keep isl_printer *p);
1032 The behavior of the printer can be modified in various ways
1034 __isl_give isl_printer *isl_printer_set_output_format(
1035 __isl_take isl_printer *p, int output_format);
1036 __isl_give isl_printer *isl_printer_set_indent(
1037 __isl_take isl_printer *p, int indent);
1038 __isl_give isl_printer *isl_printer_indent(
1039 __isl_take isl_printer *p, int indent);
1040 __isl_give isl_printer *isl_printer_set_prefix(
1041 __isl_take isl_printer *p, const char *prefix);
1042 __isl_give isl_printer *isl_printer_set_suffix(
1043 __isl_take isl_printer *p, const char *suffix);
1045 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1046 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1047 and defaults to C<ISL_FORMAT_ISL>.
1048 Each line in the output is indented by C<indent> (set by
1049 C<isl_printer_set_indent>) spaces
1050 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1051 In the C<PolyLib> format output,
1052 the coefficients of the existentially quantified variables
1053 appear between those of the set variables and those
1055 The function C<isl_printer_indent> increases the indentation
1056 by the specified amount (which may be negative).
1058 To actually print something, use
1060 #include <isl/printer.h>
1061 __isl_give isl_printer *isl_printer_print_double(
1062 __isl_take isl_printer *p, double d);
1064 #include <isl/set.h>
1065 __isl_give isl_printer *isl_printer_print_basic_set(
1066 __isl_take isl_printer *printer,
1067 __isl_keep isl_basic_set *bset);
1068 __isl_give isl_printer *isl_printer_print_set(
1069 __isl_take isl_printer *printer,
1070 __isl_keep isl_set *set);
1072 #include <isl/map.h>
1073 __isl_give isl_printer *isl_printer_print_basic_map(
1074 __isl_take isl_printer *printer,
1075 __isl_keep isl_basic_map *bmap);
1076 __isl_give isl_printer *isl_printer_print_map(
1077 __isl_take isl_printer *printer,
1078 __isl_keep isl_map *map);
1080 #include <isl/union_set.h>
1081 __isl_give isl_printer *isl_printer_print_union_set(
1082 __isl_take isl_printer *p,
1083 __isl_keep isl_union_set *uset);
1085 #include <isl/union_map.h>
1086 __isl_give isl_printer *isl_printer_print_union_map(
1087 __isl_take isl_printer *p,
1088 __isl_keep isl_union_map *umap);
1090 When called on a file printer, the following function flushes
1091 the file. When called on a string printer, the buffer is cleared.
1093 __isl_give isl_printer *isl_printer_flush(
1094 __isl_take isl_printer *p);
1096 =head2 Creating New Sets and Relations
1098 C<isl> has functions for creating some standard sets and relations.
1102 =item * Empty sets and relations
1104 __isl_give isl_basic_set *isl_basic_set_empty(
1105 __isl_take isl_space *space);
1106 __isl_give isl_basic_map *isl_basic_map_empty(
1107 __isl_take isl_space *space);
1108 __isl_give isl_set *isl_set_empty(
1109 __isl_take isl_space *space);
1110 __isl_give isl_map *isl_map_empty(
1111 __isl_take isl_space *space);
1112 __isl_give isl_union_set *isl_union_set_empty(
1113 __isl_take isl_space *space);
1114 __isl_give isl_union_map *isl_union_map_empty(
1115 __isl_take isl_space *space);
1117 For C<isl_union_set>s and C<isl_union_map>s, the space
1118 is only used to specify the parameters.
1120 =item * Universe sets and relations
1122 __isl_give isl_basic_set *isl_basic_set_universe(
1123 __isl_take isl_space *space);
1124 __isl_give isl_basic_map *isl_basic_map_universe(
1125 __isl_take isl_space *space);
1126 __isl_give isl_set *isl_set_universe(
1127 __isl_take isl_space *space);
1128 __isl_give isl_map *isl_map_universe(
1129 __isl_take isl_space *space);
1130 __isl_give isl_union_set *isl_union_set_universe(
1131 __isl_take isl_union_set *uset);
1132 __isl_give isl_union_map *isl_union_map_universe(
1133 __isl_take isl_union_map *umap);
1135 The sets and relations constructed by the functions above
1136 contain all integer values, while those constructed by the
1137 functions below only contain non-negative values.
1139 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1140 __isl_take isl_space *space);
1141 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1142 __isl_take isl_space *space);
1143 __isl_give isl_set *isl_set_nat_universe(
1144 __isl_take isl_space *space);
1145 __isl_give isl_map *isl_map_nat_universe(
1146 __isl_take isl_space *space);
1148 =item * Identity relations
1150 __isl_give isl_basic_map *isl_basic_map_identity(
1151 __isl_take isl_space *space);
1152 __isl_give isl_map *isl_map_identity(
1153 __isl_take isl_space *space);
1155 The number of input and output dimensions in C<space> needs
1158 =item * Lexicographic order
1160 __isl_give isl_map *isl_map_lex_lt(
1161 __isl_take isl_space *set_space);
1162 __isl_give isl_map *isl_map_lex_le(
1163 __isl_take isl_space *set_space);
1164 __isl_give isl_map *isl_map_lex_gt(
1165 __isl_take isl_space *set_space);
1166 __isl_give isl_map *isl_map_lex_ge(
1167 __isl_take isl_space *set_space);
1168 __isl_give isl_map *isl_map_lex_lt_first(
1169 __isl_take isl_space *space, unsigned n);
1170 __isl_give isl_map *isl_map_lex_le_first(
1171 __isl_take isl_space *space, unsigned n);
1172 __isl_give isl_map *isl_map_lex_gt_first(
1173 __isl_take isl_space *space, unsigned n);
1174 __isl_give isl_map *isl_map_lex_ge_first(
1175 __isl_take isl_space *space, unsigned n);
1177 The first four functions take a space for a B<set>
1178 and return relations that express that the elements in the domain
1179 are lexicographically less
1180 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1181 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1182 than the elements in the range.
1183 The last four functions take a space for a map
1184 and return relations that express that the first C<n> dimensions
1185 in the domain are lexicographically less
1186 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1187 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1188 than the first C<n> dimensions in the range.
1192 A basic set or relation can be converted to a set or relation
1193 using the following functions.
1195 __isl_give isl_set *isl_set_from_basic_set(
1196 __isl_take isl_basic_set *bset);
1197 __isl_give isl_map *isl_map_from_basic_map(
1198 __isl_take isl_basic_map *bmap);
1200 Sets and relations can be converted to union sets and relations
1201 using the following functions.
1203 __isl_give isl_union_set *isl_union_set_from_basic_set(
1204 __isl_take isl_basic_set *bset);
1205 __isl_give isl_union_map *isl_union_map_from_basic_map(
1206 __isl_take isl_basic_map *bmap);
1207 __isl_give isl_union_set *isl_union_set_from_set(
1208 __isl_take isl_set *set);
1209 __isl_give isl_union_map *isl_union_map_from_map(
1210 __isl_take isl_map *map);
1212 The inverse conversions below can only be used if the input
1213 union set or relation is known to contain elements in exactly one
1216 __isl_give isl_set *isl_set_from_union_set(
1217 __isl_take isl_union_set *uset);
1218 __isl_give isl_map *isl_map_from_union_map(
1219 __isl_take isl_union_map *umap);
1221 A zero-dimensional set can be constructed on a given parameter domain
1222 using the following function.
1224 __isl_give isl_set *isl_set_from_params(
1225 __isl_take isl_set *set);
1227 Sets and relations can be copied and freed again using the following
1230 __isl_give isl_basic_set *isl_basic_set_copy(
1231 __isl_keep isl_basic_set *bset);
1232 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1233 __isl_give isl_union_set *isl_union_set_copy(
1234 __isl_keep isl_union_set *uset);
1235 __isl_give isl_basic_map *isl_basic_map_copy(
1236 __isl_keep isl_basic_map *bmap);
1237 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1238 __isl_give isl_union_map *isl_union_map_copy(
1239 __isl_keep isl_union_map *umap);
1240 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1241 void *isl_set_free(__isl_take isl_set *set);
1242 void *isl_union_set_free(__isl_take isl_union_set *uset);
1243 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1244 void isl_map_free(__isl_take isl_map *map);
1245 void *isl_union_map_free(__isl_take isl_union_map *umap);
1247 Other sets and relations can be constructed by starting
1248 from a universe set or relation, adding equality and/or
1249 inequality constraints and then projecting out the
1250 existentially quantified variables, if any.
1251 Constraints can be constructed, manipulated and
1252 added to (or removed from) (basic) sets and relations
1253 using the following functions.
1255 #include <isl/constraint.h>
1256 __isl_give isl_constraint *isl_equality_alloc(
1257 __isl_take isl_local_space *ls);
1258 __isl_give isl_constraint *isl_inequality_alloc(
1259 __isl_take isl_local_space *ls);
1260 __isl_give isl_constraint *isl_constraint_set_constant(
1261 __isl_take isl_constraint *constraint, isl_int v);
1262 __isl_give isl_constraint *isl_constraint_set_constant_si(
1263 __isl_take isl_constraint *constraint, int v);
1264 __isl_give isl_constraint *isl_constraint_set_coefficient(
1265 __isl_take isl_constraint *constraint,
1266 enum isl_dim_type type, int pos, isl_int v);
1267 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1268 __isl_take isl_constraint *constraint,
1269 enum isl_dim_type type, int pos, int v);
1270 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1271 __isl_take isl_basic_map *bmap,
1272 __isl_take isl_constraint *constraint);
1273 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1274 __isl_take isl_basic_set *bset,
1275 __isl_take isl_constraint *constraint);
1276 __isl_give isl_map *isl_map_add_constraint(
1277 __isl_take isl_map *map,
1278 __isl_take isl_constraint *constraint);
1279 __isl_give isl_set *isl_set_add_constraint(
1280 __isl_take isl_set *set,
1281 __isl_take isl_constraint *constraint);
1282 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1283 __isl_take isl_basic_set *bset,
1284 __isl_take isl_constraint *constraint);
1286 For example, to create a set containing the even integers
1287 between 10 and 42, you would use the following code.
1290 isl_local_space *ls;
1292 isl_basic_set *bset;
1294 space = isl_space_set_alloc(ctx, 0, 2);
1295 bset = isl_basic_set_universe(isl_space_copy(space));
1296 ls = isl_local_space_from_space(space);
1298 c = isl_equality_alloc(isl_local_space_copy(ls));
1299 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1300 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1301 bset = isl_basic_set_add_constraint(bset, c);
1303 c = isl_inequality_alloc(isl_local_space_copy(ls));
1304 c = isl_constraint_set_constant_si(c, -10);
1305 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1306 bset = isl_basic_set_add_constraint(bset, c);
1308 c = isl_inequality_alloc(ls);
1309 c = isl_constraint_set_constant_si(c, 42);
1310 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1311 bset = isl_basic_set_add_constraint(bset, c);
1313 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1317 isl_basic_set *bset;
1318 bset = isl_basic_set_read_from_str(ctx,
1319 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1321 A basic set or relation can also be constructed from two matrices
1322 describing the equalities and the inequalities.
1324 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1325 __isl_take isl_space *space,
1326 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1327 enum isl_dim_type c1,
1328 enum isl_dim_type c2, enum isl_dim_type c3,
1329 enum isl_dim_type c4);
1330 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1331 __isl_take isl_space *space,
1332 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1333 enum isl_dim_type c1,
1334 enum isl_dim_type c2, enum isl_dim_type c3,
1335 enum isl_dim_type c4, enum isl_dim_type c5);
1337 The C<isl_dim_type> arguments indicate the order in which
1338 different kinds of variables appear in the input matrices
1339 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1340 C<isl_dim_set> and C<isl_dim_div> for sets and
1341 of C<isl_dim_cst>, C<isl_dim_param>,
1342 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1344 A (basic or union) set or relation can also be constructed from a
1345 (union) (piecewise) (multiple) affine expression
1346 or a list of affine expressions
1347 (See L<"Piecewise Quasi Affine Expressions"> and
1348 L<"Piecewise Multiple Quasi Affine Expressions">).
1350 __isl_give isl_basic_map *isl_basic_map_from_aff(
1351 __isl_take isl_aff *aff);
1352 __isl_give isl_map *isl_map_from_aff(
1353 __isl_take isl_aff *aff);
1354 __isl_give isl_set *isl_set_from_pw_aff(
1355 __isl_take isl_pw_aff *pwaff);
1356 __isl_give isl_map *isl_map_from_pw_aff(
1357 __isl_take isl_pw_aff *pwaff);
1358 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1359 __isl_take isl_space *domain_space,
1360 __isl_take isl_aff_list *list);
1361 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1362 __isl_take isl_multi_aff *maff)
1363 __isl_give isl_map *isl_map_from_multi_aff(
1364 __isl_take isl_multi_aff *maff)
1365 __isl_give isl_set *isl_set_from_pw_multi_aff(
1366 __isl_take isl_pw_multi_aff *pma);
1367 __isl_give isl_map *isl_map_from_pw_multi_aff(
1368 __isl_take isl_pw_multi_aff *pma);
1369 __isl_give isl_union_map *
1370 isl_union_map_from_union_pw_multi_aff(
1371 __isl_take isl_union_pw_multi_aff *upma);
1373 The C<domain_dim> argument describes the domain of the resulting
1374 basic relation. It is required because the C<list> may consist
1375 of zero affine expressions.
1377 =head2 Inspecting Sets and Relations
1379 Usually, the user should not have to care about the actual constraints
1380 of the sets and maps, but should instead apply the abstract operations
1381 explained in the following sections.
1382 Occasionally, however, it may be required to inspect the individual
1383 coefficients of the constraints. This section explains how to do so.
1384 In these cases, it may also be useful to have C<isl> compute
1385 an explicit representation of the existentially quantified variables.
1387 __isl_give isl_set *isl_set_compute_divs(
1388 __isl_take isl_set *set);
1389 __isl_give isl_map *isl_map_compute_divs(
1390 __isl_take isl_map *map);
1391 __isl_give isl_union_set *isl_union_set_compute_divs(
1392 __isl_take isl_union_set *uset);
1393 __isl_give isl_union_map *isl_union_map_compute_divs(
1394 __isl_take isl_union_map *umap);
1396 This explicit representation defines the existentially quantified
1397 variables as integer divisions of the other variables, possibly
1398 including earlier existentially quantified variables.
1399 An explicitly represented existentially quantified variable therefore
1400 has a unique value when the values of the other variables are known.
1401 If, furthermore, the same existentials, i.e., existentials
1402 with the same explicit representations, should appear in the
1403 same order in each of the disjuncts of a set or map, then the user should call
1404 either of the following functions.
1406 __isl_give isl_set *isl_set_align_divs(
1407 __isl_take isl_set *set);
1408 __isl_give isl_map *isl_map_align_divs(
1409 __isl_take isl_map *map);
1411 Alternatively, the existentially quantified variables can be removed
1412 using the following functions, which compute an overapproximation.
1414 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1415 __isl_take isl_basic_set *bset);
1416 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1417 __isl_take isl_basic_map *bmap);
1418 __isl_give isl_set *isl_set_remove_divs(
1419 __isl_take isl_set *set);
1420 __isl_give isl_map *isl_map_remove_divs(
1421 __isl_take isl_map *map);
1423 It is also possible to only remove those divs that are defined
1424 in terms of a given range of dimensions or only those for which
1425 no explicit representation is known.
1427 __isl_give isl_basic_set *
1428 isl_basic_set_remove_divs_involving_dims(
1429 __isl_take isl_basic_set *bset,
1430 enum isl_dim_type type,
1431 unsigned first, unsigned n);
1432 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1433 __isl_take isl_set *set, enum isl_dim_type type,
1434 unsigned first, unsigned n);
1435 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1436 __isl_take isl_map *map, enum isl_dim_type type,
1437 unsigned first, unsigned n);
1439 __isl_give isl_set *isl_set_remove_unknown_divs(
1440 __isl_take isl_set *set);
1441 __isl_give isl_map *isl_map_remove_unknown_divs(
1442 __isl_take isl_map *map);
1444 To iterate over all the sets or maps in a union set or map, use
1446 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1447 int (*fn)(__isl_take isl_set *set, void *user),
1449 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1450 int (*fn)(__isl_take isl_map *map, void *user),
1453 The number of sets or maps in a union set or map can be obtained
1456 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1457 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1459 To extract the set or map in a given space from a union, use
1461 __isl_give isl_set *isl_union_set_extract_set(
1462 __isl_keep isl_union_set *uset,
1463 __isl_take isl_space *space);
1464 __isl_give isl_map *isl_union_map_extract_map(
1465 __isl_keep isl_union_map *umap,
1466 __isl_take isl_space *space);
1468 To iterate over all the basic sets or maps in a set or map, use
1470 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1471 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1473 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1474 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1477 The callback function C<fn> should return 0 if successful and
1478 -1 if an error occurs. In the latter case, or if any other error
1479 occurs, the above functions will return -1.
1481 It should be noted that C<isl> does not guarantee that
1482 the basic sets or maps passed to C<fn> are disjoint.
1483 If this is required, then the user should call one of
1484 the following functions first.
1486 __isl_give isl_set *isl_set_make_disjoint(
1487 __isl_take isl_set *set);
1488 __isl_give isl_map *isl_map_make_disjoint(
1489 __isl_take isl_map *map);
1491 The number of basic sets in a set can be obtained
1494 int isl_set_n_basic_set(__isl_keep isl_set *set);
1496 To iterate over the constraints of a basic set or map, use
1498 #include <isl/constraint.h>
1500 int isl_basic_set_n_constraint(
1501 __isl_keep isl_basic_set *bset);
1502 int isl_basic_set_foreach_constraint(
1503 __isl_keep isl_basic_set *bset,
1504 int (*fn)(__isl_take isl_constraint *c, void *user),
1506 int isl_basic_map_foreach_constraint(
1507 __isl_keep isl_basic_map *bmap,
1508 int (*fn)(__isl_take isl_constraint *c, void *user),
1510 void *isl_constraint_free(__isl_take isl_constraint *c);
1512 Again, the callback function C<fn> should return 0 if successful and
1513 -1 if an error occurs. In the latter case, or if any other error
1514 occurs, the above functions will return -1.
1515 The constraint C<c> represents either an equality or an inequality.
1516 Use the following function to find out whether a constraint
1517 represents an equality. If not, it represents an inequality.
1519 int isl_constraint_is_equality(
1520 __isl_keep isl_constraint *constraint);
1522 The coefficients of the constraints can be inspected using
1523 the following functions.
1525 int isl_constraint_is_lower_bound(
1526 __isl_keep isl_constraint *constraint,
1527 enum isl_dim_type type, unsigned pos);
1528 int isl_constraint_is_upper_bound(
1529 __isl_keep isl_constraint *constraint,
1530 enum isl_dim_type type, unsigned pos);
1531 void isl_constraint_get_constant(
1532 __isl_keep isl_constraint *constraint, isl_int *v);
1533 void isl_constraint_get_coefficient(
1534 __isl_keep isl_constraint *constraint,
1535 enum isl_dim_type type, int pos, isl_int *v);
1536 int isl_constraint_involves_dims(
1537 __isl_keep isl_constraint *constraint,
1538 enum isl_dim_type type, unsigned first, unsigned n);
1540 The explicit representations of the existentially quantified
1541 variables can be inspected using the following function.
1542 Note that the user is only allowed to use this function
1543 if the inspected set or map is the result of a call
1544 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1545 The existentially quantified variable is equal to the floor
1546 of the returned affine expression. The affine expression
1547 itself can be inspected using the functions in
1548 L<"Piecewise Quasi Affine Expressions">.
1550 __isl_give isl_aff *isl_constraint_get_div(
1551 __isl_keep isl_constraint *constraint, int pos);
1553 To obtain the constraints of a basic set or map in matrix
1554 form, use the following functions.
1556 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1557 __isl_keep isl_basic_set *bset,
1558 enum isl_dim_type c1, enum isl_dim_type c2,
1559 enum isl_dim_type c3, enum isl_dim_type c4);
1560 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1561 __isl_keep isl_basic_set *bset,
1562 enum isl_dim_type c1, enum isl_dim_type c2,
1563 enum isl_dim_type c3, enum isl_dim_type c4);
1564 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1565 __isl_keep isl_basic_map *bmap,
1566 enum isl_dim_type c1,
1567 enum isl_dim_type c2, enum isl_dim_type c3,
1568 enum isl_dim_type c4, enum isl_dim_type c5);
1569 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1570 __isl_keep isl_basic_map *bmap,
1571 enum isl_dim_type c1,
1572 enum isl_dim_type c2, enum isl_dim_type c3,
1573 enum isl_dim_type c4, enum isl_dim_type c5);
1575 The C<isl_dim_type> arguments dictate the order in which
1576 different kinds of variables appear in the resulting matrix
1577 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1578 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1580 The number of parameters, input, output or set dimensions can
1581 be obtained using the following functions.
1583 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1584 enum isl_dim_type type);
1585 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1586 enum isl_dim_type type);
1587 unsigned isl_set_dim(__isl_keep isl_set *set,
1588 enum isl_dim_type type);
1589 unsigned isl_map_dim(__isl_keep isl_map *map,
1590 enum isl_dim_type type);
1592 To check whether the description of a set or relation depends
1593 on one or more given dimensions, it is not necessary to iterate over all
1594 constraints. Instead the following functions can be used.
1596 int isl_basic_set_involves_dims(
1597 __isl_keep isl_basic_set *bset,
1598 enum isl_dim_type type, unsigned first, unsigned n);
1599 int isl_set_involves_dims(__isl_keep isl_set *set,
1600 enum isl_dim_type type, unsigned first, unsigned n);
1601 int isl_basic_map_involves_dims(
1602 __isl_keep isl_basic_map *bmap,
1603 enum isl_dim_type type, unsigned first, unsigned n);
1604 int isl_map_involves_dims(__isl_keep isl_map *map,
1605 enum isl_dim_type type, unsigned first, unsigned n);
1607 Similarly, the following functions can be used to check whether
1608 a given dimension is involved in any lower or upper bound.
1610 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1611 enum isl_dim_type type, unsigned pos);
1612 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1613 enum isl_dim_type type, unsigned pos);
1615 The identifiers or names of the domain and range spaces of a set
1616 or relation can be read off or set using the following functions.
1618 __isl_give isl_set *isl_set_set_tuple_id(
1619 __isl_take isl_set *set, __isl_take isl_id *id);
1620 __isl_give isl_set *isl_set_reset_tuple_id(
1621 __isl_take isl_set *set);
1622 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1623 __isl_give isl_id *isl_set_get_tuple_id(
1624 __isl_keep isl_set *set);
1625 __isl_give isl_map *isl_map_set_tuple_id(
1626 __isl_take isl_map *map, enum isl_dim_type type,
1627 __isl_take isl_id *id);
1628 __isl_give isl_map *isl_map_reset_tuple_id(
1629 __isl_take isl_map *map, enum isl_dim_type type);
1630 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1631 enum isl_dim_type type);
1632 __isl_give isl_id *isl_map_get_tuple_id(
1633 __isl_keep isl_map *map, enum isl_dim_type type);
1635 const char *isl_basic_set_get_tuple_name(
1636 __isl_keep isl_basic_set *bset);
1637 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1638 __isl_take isl_basic_set *set, const char *s);
1639 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1640 const char *isl_set_get_tuple_name(
1641 __isl_keep isl_set *set);
1642 const char *isl_basic_map_get_tuple_name(
1643 __isl_keep isl_basic_map *bmap,
1644 enum isl_dim_type type);
1645 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1646 __isl_take isl_basic_map *bmap,
1647 enum isl_dim_type type, const char *s);
1648 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1649 enum isl_dim_type type);
1650 const char *isl_map_get_tuple_name(
1651 __isl_keep isl_map *map,
1652 enum isl_dim_type type);
1654 As with C<isl_space_get_tuple_name>, the value returned points to
1655 an internal data structure.
1656 The identifiers, positions or names of individual dimensions can be
1657 read off using the following functions.
1659 __isl_give isl_id *isl_basic_set_get_dim_id(
1660 __isl_keep isl_basic_set *bset,
1661 enum isl_dim_type type, unsigned pos);
1662 __isl_give isl_set *isl_set_set_dim_id(
1663 __isl_take isl_set *set, enum isl_dim_type type,
1664 unsigned pos, __isl_take isl_id *id);
1665 int isl_set_has_dim_id(__isl_keep isl_set *set,
1666 enum isl_dim_type type, unsigned pos);
1667 __isl_give isl_id *isl_set_get_dim_id(
1668 __isl_keep isl_set *set, enum isl_dim_type type,
1670 int isl_basic_map_has_dim_id(
1671 __isl_keep isl_basic_map *bmap,
1672 enum isl_dim_type type, unsigned pos);
1673 __isl_give isl_map *isl_map_set_dim_id(
1674 __isl_take isl_map *map, enum isl_dim_type type,
1675 unsigned pos, __isl_take isl_id *id);
1676 int isl_map_has_dim_id(__isl_keep isl_map *map,
1677 enum isl_dim_type type, unsigned pos);
1678 __isl_give isl_id *isl_map_get_dim_id(
1679 __isl_keep isl_map *map, enum isl_dim_type type,
1682 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1683 enum isl_dim_type type, __isl_keep isl_id *id);
1684 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1685 enum isl_dim_type type, __isl_keep isl_id *id);
1686 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1687 enum isl_dim_type type, const char *name);
1688 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1689 enum isl_dim_type type, const char *name);
1691 const char *isl_constraint_get_dim_name(
1692 __isl_keep isl_constraint *constraint,
1693 enum isl_dim_type type, unsigned pos);
1694 const char *isl_basic_set_get_dim_name(
1695 __isl_keep isl_basic_set *bset,
1696 enum isl_dim_type type, unsigned pos);
1697 int isl_set_has_dim_name(__isl_keep isl_set *set,
1698 enum isl_dim_type type, unsigned pos);
1699 const char *isl_set_get_dim_name(
1700 __isl_keep isl_set *set,
1701 enum isl_dim_type type, unsigned pos);
1702 const char *isl_basic_map_get_dim_name(
1703 __isl_keep isl_basic_map *bmap,
1704 enum isl_dim_type type, unsigned pos);
1705 int isl_map_has_dim_name(__isl_keep isl_map *map,
1706 enum isl_dim_type type, unsigned pos);
1707 const char *isl_map_get_dim_name(
1708 __isl_keep isl_map *map,
1709 enum isl_dim_type type, unsigned pos);
1711 These functions are mostly useful to obtain the identifiers, positions
1712 or names of the parameters. Identifiers of individual dimensions are
1713 essentially only useful for printing. They are ignored by all other
1714 operations and may not be preserved across those operations.
1718 =head3 Unary Properties
1724 The following functions test whether the given set or relation
1725 contains any integer points. The ``plain'' variants do not perform
1726 any computations, but simply check if the given set or relation
1727 is already known to be empty.
1729 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1730 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1731 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1732 int isl_set_is_empty(__isl_keep isl_set *set);
1733 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1734 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1735 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1736 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1737 int isl_map_is_empty(__isl_keep isl_map *map);
1738 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1740 =item * Universality
1742 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1743 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1744 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1746 =item * Single-valuedness
1748 int isl_basic_map_is_single_valued(
1749 __isl_keep isl_basic_map *bmap);
1750 int isl_map_plain_is_single_valued(
1751 __isl_keep isl_map *map);
1752 int isl_map_is_single_valued(__isl_keep isl_map *map);
1753 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1757 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1758 int isl_map_is_injective(__isl_keep isl_map *map);
1759 int isl_union_map_plain_is_injective(
1760 __isl_keep isl_union_map *umap);
1761 int isl_union_map_is_injective(
1762 __isl_keep isl_union_map *umap);
1766 int isl_map_is_bijective(__isl_keep isl_map *map);
1767 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1771 int isl_basic_map_plain_is_fixed(
1772 __isl_keep isl_basic_map *bmap,
1773 enum isl_dim_type type, unsigned pos,
1775 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1776 enum isl_dim_type type, unsigned pos,
1778 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1779 enum isl_dim_type type, unsigned pos,
1782 Check if the relation obviously lies on a hyperplane where the given dimension
1783 has a fixed value and if so, return that value in C<*val>.
1787 To check whether a set is a parameter domain, use this function:
1789 int isl_set_is_params(__isl_keep isl_set *set);
1790 int isl_union_set_is_params(
1791 __isl_keep isl_union_set *uset);
1795 The following functions check whether the domain of the given
1796 (basic) set is a wrapped relation.
1798 int isl_basic_set_is_wrapping(
1799 __isl_keep isl_basic_set *bset);
1800 int isl_set_is_wrapping(__isl_keep isl_set *set);
1802 =item * Internal Product
1804 int isl_basic_map_can_zip(
1805 __isl_keep isl_basic_map *bmap);
1806 int isl_map_can_zip(__isl_keep isl_map *map);
1808 Check whether the product of domain and range of the given relation
1810 i.e., whether both domain and range are nested relations.
1814 int isl_basic_map_can_curry(
1815 __isl_keep isl_basic_map *bmap);
1816 int isl_map_can_curry(__isl_keep isl_map *map);
1818 Check whether the domain of the (basic) relation is a wrapped relation.
1822 =head3 Binary Properties
1828 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1829 __isl_keep isl_set *set2);
1830 int isl_set_is_equal(__isl_keep isl_set *set1,
1831 __isl_keep isl_set *set2);
1832 int isl_union_set_is_equal(
1833 __isl_keep isl_union_set *uset1,
1834 __isl_keep isl_union_set *uset2);
1835 int isl_basic_map_is_equal(
1836 __isl_keep isl_basic_map *bmap1,
1837 __isl_keep isl_basic_map *bmap2);
1838 int isl_map_is_equal(__isl_keep isl_map *map1,
1839 __isl_keep isl_map *map2);
1840 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1841 __isl_keep isl_map *map2);
1842 int isl_union_map_is_equal(
1843 __isl_keep isl_union_map *umap1,
1844 __isl_keep isl_union_map *umap2);
1846 =item * Disjointness
1848 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1849 __isl_keep isl_set *set2);
1853 int isl_basic_set_is_subset(
1854 __isl_keep isl_basic_set *bset1,
1855 __isl_keep isl_basic_set *bset2);
1856 int isl_set_is_subset(__isl_keep isl_set *set1,
1857 __isl_keep isl_set *set2);
1858 int isl_set_is_strict_subset(
1859 __isl_keep isl_set *set1,
1860 __isl_keep isl_set *set2);
1861 int isl_union_set_is_subset(
1862 __isl_keep isl_union_set *uset1,
1863 __isl_keep isl_union_set *uset2);
1864 int isl_union_set_is_strict_subset(
1865 __isl_keep isl_union_set *uset1,
1866 __isl_keep isl_union_set *uset2);
1867 int isl_basic_map_is_subset(
1868 __isl_keep isl_basic_map *bmap1,
1869 __isl_keep isl_basic_map *bmap2);
1870 int isl_basic_map_is_strict_subset(
1871 __isl_keep isl_basic_map *bmap1,
1872 __isl_keep isl_basic_map *bmap2);
1873 int isl_map_is_subset(
1874 __isl_keep isl_map *map1,
1875 __isl_keep isl_map *map2);
1876 int isl_map_is_strict_subset(
1877 __isl_keep isl_map *map1,
1878 __isl_keep isl_map *map2);
1879 int isl_union_map_is_subset(
1880 __isl_keep isl_union_map *umap1,
1881 __isl_keep isl_union_map *umap2);
1882 int isl_union_map_is_strict_subset(
1883 __isl_keep isl_union_map *umap1,
1884 __isl_keep isl_union_map *umap2);
1886 Check whether the first argument is a (strict) subset of the
1891 =head2 Unary Operations
1897 __isl_give isl_set *isl_set_complement(
1898 __isl_take isl_set *set);
1899 __isl_give isl_map *isl_map_complement(
1900 __isl_take isl_map *map);
1904 __isl_give isl_basic_map *isl_basic_map_reverse(
1905 __isl_take isl_basic_map *bmap);
1906 __isl_give isl_map *isl_map_reverse(
1907 __isl_take isl_map *map);
1908 __isl_give isl_union_map *isl_union_map_reverse(
1909 __isl_take isl_union_map *umap);
1913 __isl_give isl_basic_set *isl_basic_set_project_out(
1914 __isl_take isl_basic_set *bset,
1915 enum isl_dim_type type, unsigned first, unsigned n);
1916 __isl_give isl_basic_map *isl_basic_map_project_out(
1917 __isl_take isl_basic_map *bmap,
1918 enum isl_dim_type type, unsigned first, unsigned n);
1919 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1920 enum isl_dim_type type, unsigned first, unsigned n);
1921 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1922 enum isl_dim_type type, unsigned first, unsigned n);
1923 __isl_give isl_basic_set *isl_basic_set_params(
1924 __isl_take isl_basic_set *bset);
1925 __isl_give isl_basic_set *isl_basic_map_domain(
1926 __isl_take isl_basic_map *bmap);
1927 __isl_give isl_basic_set *isl_basic_map_range(
1928 __isl_take isl_basic_map *bmap);
1929 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1930 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1931 __isl_give isl_set *isl_map_domain(
1932 __isl_take isl_map *bmap);
1933 __isl_give isl_set *isl_map_range(
1934 __isl_take isl_map *map);
1935 __isl_give isl_set *isl_union_set_params(
1936 __isl_take isl_union_set *uset);
1937 __isl_give isl_set *isl_union_map_params(
1938 __isl_take isl_union_map *umap);
1939 __isl_give isl_union_set *isl_union_map_domain(
1940 __isl_take isl_union_map *umap);
1941 __isl_give isl_union_set *isl_union_map_range(
1942 __isl_take isl_union_map *umap);
1944 __isl_give isl_basic_map *isl_basic_map_domain_map(
1945 __isl_take isl_basic_map *bmap);
1946 __isl_give isl_basic_map *isl_basic_map_range_map(
1947 __isl_take isl_basic_map *bmap);
1948 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1949 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1950 __isl_give isl_union_map *isl_union_map_domain_map(
1951 __isl_take isl_union_map *umap);
1952 __isl_give isl_union_map *isl_union_map_range_map(
1953 __isl_take isl_union_map *umap);
1955 The functions above construct a (basic, regular or union) relation
1956 that maps (a wrapped version of) the input relation to its domain or range.
1960 __isl_give isl_basic_set *isl_basic_set_eliminate(
1961 __isl_take isl_basic_set *bset,
1962 enum isl_dim_type type,
1963 unsigned first, unsigned n);
1964 __isl_give isl_set *isl_set_eliminate(
1965 __isl_take isl_set *set, enum isl_dim_type type,
1966 unsigned first, unsigned n);
1967 __isl_give isl_basic_map *isl_basic_map_eliminate(
1968 __isl_take isl_basic_map *bmap,
1969 enum isl_dim_type type,
1970 unsigned first, unsigned n);
1971 __isl_give isl_map *isl_map_eliminate(
1972 __isl_take isl_map *map, enum isl_dim_type type,
1973 unsigned first, unsigned n);
1975 Eliminate the coefficients for the given dimensions from the constraints,
1976 without removing the dimensions.
1980 __isl_give isl_basic_set *isl_basic_set_fix(
1981 __isl_take isl_basic_set *bset,
1982 enum isl_dim_type type, unsigned pos,
1984 __isl_give isl_basic_set *isl_basic_set_fix_si(
1985 __isl_take isl_basic_set *bset,
1986 enum isl_dim_type type, unsigned pos, int value);
1987 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1988 enum isl_dim_type type, unsigned pos,
1990 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1991 enum isl_dim_type type, unsigned pos, int value);
1992 __isl_give isl_basic_map *isl_basic_map_fix_si(
1993 __isl_take isl_basic_map *bmap,
1994 enum isl_dim_type type, unsigned pos, int value);
1995 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1996 enum isl_dim_type type, unsigned pos, int value);
1998 Intersect the set or relation with the hyperplane where the given
1999 dimension has the fixed given value.
2001 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2002 __isl_take isl_basic_map *bmap,
2003 enum isl_dim_type type, unsigned pos, int value);
2004 __isl_give isl_set *isl_set_lower_bound(
2005 __isl_take isl_set *set,
2006 enum isl_dim_type type, unsigned pos,
2008 __isl_give isl_set *isl_set_lower_bound_si(
2009 __isl_take isl_set *set,
2010 enum isl_dim_type type, unsigned pos, int value);
2011 __isl_give isl_map *isl_map_lower_bound_si(
2012 __isl_take isl_map *map,
2013 enum isl_dim_type type, unsigned pos, int value);
2014 __isl_give isl_set *isl_set_upper_bound(
2015 __isl_take isl_set *set,
2016 enum isl_dim_type type, unsigned pos,
2018 __isl_give isl_set *isl_set_upper_bound_si(
2019 __isl_take isl_set *set,
2020 enum isl_dim_type type, unsigned pos, int value);
2021 __isl_give isl_map *isl_map_upper_bound_si(
2022 __isl_take isl_map *map,
2023 enum isl_dim_type type, unsigned pos, int value);
2025 Intersect the set or relation with the half-space where the given
2026 dimension has a value bounded by the fixed given value.
2028 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2029 enum isl_dim_type type1, int pos1,
2030 enum isl_dim_type type2, int pos2);
2031 __isl_give isl_basic_map *isl_basic_map_equate(
2032 __isl_take isl_basic_map *bmap,
2033 enum isl_dim_type type1, int pos1,
2034 enum isl_dim_type type2, int pos2);
2035 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2036 enum isl_dim_type type1, int pos1,
2037 enum isl_dim_type type2, int pos2);
2039 Intersect the set or relation with the hyperplane where the given
2040 dimensions are equal to each other.
2042 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2043 enum isl_dim_type type1, int pos1,
2044 enum isl_dim_type type2, int pos2);
2046 Intersect the relation with the hyperplane where the given
2047 dimensions have opposite values.
2049 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2050 enum isl_dim_type type1, int pos1,
2051 enum isl_dim_type type2, int pos2);
2052 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2053 enum isl_dim_type type1, int pos1,
2054 enum isl_dim_type type2, int pos2);
2056 Intersect the relation with the half-space where the given
2057 dimensions satisfy the given ordering.
2061 __isl_give isl_map *isl_set_identity(
2062 __isl_take isl_set *set);
2063 __isl_give isl_union_map *isl_union_set_identity(
2064 __isl_take isl_union_set *uset);
2066 Construct an identity relation on the given (union) set.
2070 __isl_give isl_basic_set *isl_basic_map_deltas(
2071 __isl_take isl_basic_map *bmap);
2072 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2073 __isl_give isl_union_set *isl_union_map_deltas(
2074 __isl_take isl_union_map *umap);
2076 These functions return a (basic) set containing the differences
2077 between image elements and corresponding domain elements in the input.
2079 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2080 __isl_take isl_basic_map *bmap);
2081 __isl_give isl_map *isl_map_deltas_map(
2082 __isl_take isl_map *map);
2083 __isl_give isl_union_map *isl_union_map_deltas_map(
2084 __isl_take isl_union_map *umap);
2086 The functions above construct a (basic, regular or union) relation
2087 that maps (a wrapped version of) the input relation to its delta set.
2091 Simplify the representation of a set or relation by trying
2092 to combine pairs of basic sets or relations into a single
2093 basic set or relation.
2095 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2096 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2097 __isl_give isl_union_set *isl_union_set_coalesce(
2098 __isl_take isl_union_set *uset);
2099 __isl_give isl_union_map *isl_union_map_coalesce(
2100 __isl_take isl_union_map *umap);
2102 One of the methods for combining pairs of basic sets or relations
2103 can result in coefficients that are much larger than those that appear
2104 in the constraints of the input. By default, the coefficients are
2105 not allowed to grow larger, but this can be changed by unsetting
2106 the following option.
2108 int isl_options_set_coalesce_bounded_wrapping(
2109 isl_ctx *ctx, int val);
2110 int isl_options_get_coalesce_bounded_wrapping(
2113 =item * Detecting equalities
2115 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2116 __isl_take isl_basic_set *bset);
2117 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2118 __isl_take isl_basic_map *bmap);
2119 __isl_give isl_set *isl_set_detect_equalities(
2120 __isl_take isl_set *set);
2121 __isl_give isl_map *isl_map_detect_equalities(
2122 __isl_take isl_map *map);
2123 __isl_give isl_union_set *isl_union_set_detect_equalities(
2124 __isl_take isl_union_set *uset);
2125 __isl_give isl_union_map *isl_union_map_detect_equalities(
2126 __isl_take isl_union_map *umap);
2128 Simplify the representation of a set or relation by detecting implicit
2131 =item * Removing redundant constraints
2133 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2134 __isl_take isl_basic_set *bset);
2135 __isl_give isl_set *isl_set_remove_redundancies(
2136 __isl_take isl_set *set);
2137 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2138 __isl_take isl_basic_map *bmap);
2139 __isl_give isl_map *isl_map_remove_redundancies(
2140 __isl_take isl_map *map);
2144 __isl_give isl_basic_set *isl_set_convex_hull(
2145 __isl_take isl_set *set);
2146 __isl_give isl_basic_map *isl_map_convex_hull(
2147 __isl_take isl_map *map);
2149 If the input set or relation has any existentially quantified
2150 variables, then the result of these operations is currently undefined.
2154 __isl_give isl_basic_set *isl_set_simple_hull(
2155 __isl_take isl_set *set);
2156 __isl_give isl_basic_map *isl_map_simple_hull(
2157 __isl_take isl_map *map);
2158 __isl_give isl_union_map *isl_union_map_simple_hull(
2159 __isl_take isl_union_map *umap);
2161 These functions compute a single basic set or relation
2162 that contains the whole input set or relation.
2163 In particular, the output is described by translates
2164 of the constraints describing the basic sets or relations in the input.
2168 (See \autoref{s:simple hull}.)
2174 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2175 __isl_take isl_basic_set *bset);
2176 __isl_give isl_basic_set *isl_set_affine_hull(
2177 __isl_take isl_set *set);
2178 __isl_give isl_union_set *isl_union_set_affine_hull(
2179 __isl_take isl_union_set *uset);
2180 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2181 __isl_take isl_basic_map *bmap);
2182 __isl_give isl_basic_map *isl_map_affine_hull(
2183 __isl_take isl_map *map);
2184 __isl_give isl_union_map *isl_union_map_affine_hull(
2185 __isl_take isl_union_map *umap);
2187 In case of union sets and relations, the affine hull is computed
2190 =item * Polyhedral hull
2192 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2193 __isl_take isl_set *set);
2194 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2195 __isl_take isl_map *map);
2196 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2197 __isl_take isl_union_set *uset);
2198 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2199 __isl_take isl_union_map *umap);
2201 These functions compute a single basic set or relation
2202 not involving any existentially quantified variables
2203 that contains the whole input set or relation.
2204 In case of union sets and relations, the polyhedral hull is computed
2209 __isl_give isl_basic_set *isl_basic_set_sample(
2210 __isl_take isl_basic_set *bset);
2211 __isl_give isl_basic_set *isl_set_sample(
2212 __isl_take isl_set *set);
2213 __isl_give isl_basic_map *isl_basic_map_sample(
2214 __isl_take isl_basic_map *bmap);
2215 __isl_give isl_basic_map *isl_map_sample(
2216 __isl_take isl_map *map);
2218 If the input (basic) set or relation is non-empty, then return
2219 a singleton subset of the input. Otherwise, return an empty set.
2221 =item * Optimization
2223 #include <isl/ilp.h>
2224 enum isl_lp_result isl_basic_set_max(
2225 __isl_keep isl_basic_set *bset,
2226 __isl_keep isl_aff *obj, isl_int *opt)
2227 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2228 __isl_keep isl_aff *obj, isl_int *opt);
2229 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2230 __isl_keep isl_aff *obj, isl_int *opt);
2232 Compute the minimum or maximum of the integer affine expression C<obj>
2233 over the points in C<set>, returning the result in C<opt>.
2234 The return value may be one of C<isl_lp_error>,
2235 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2237 =item * Parametric optimization
2239 __isl_give isl_pw_aff *isl_set_dim_min(
2240 __isl_take isl_set *set, int pos);
2241 __isl_give isl_pw_aff *isl_set_dim_max(
2242 __isl_take isl_set *set, int pos);
2243 __isl_give isl_pw_aff *isl_map_dim_max(
2244 __isl_take isl_map *map, int pos);
2246 Compute the minimum or maximum of the given set or output dimension
2247 as a function of the parameters (and input dimensions), but independently
2248 of the other set or output dimensions.
2249 For lexicographic optimization, see L<"Lexicographic Optimization">.
2253 The following functions compute either the set of (rational) coefficient
2254 values of valid constraints for the given set or the set of (rational)
2255 values satisfying the constraints with coefficients from the given set.
2256 Internally, these two sets of functions perform essentially the
2257 same operations, except that the set of coefficients is assumed to
2258 be a cone, while the set of values may be any polyhedron.
2259 The current implementation is based on the Farkas lemma and
2260 Fourier-Motzkin elimination, but this may change or be made optional
2261 in future. In particular, future implementations may use different
2262 dualization algorithms or skip the elimination step.
2264 __isl_give isl_basic_set *isl_basic_set_coefficients(
2265 __isl_take isl_basic_set *bset);
2266 __isl_give isl_basic_set *isl_set_coefficients(
2267 __isl_take isl_set *set);
2268 __isl_give isl_union_set *isl_union_set_coefficients(
2269 __isl_take isl_union_set *bset);
2270 __isl_give isl_basic_set *isl_basic_set_solutions(
2271 __isl_take isl_basic_set *bset);
2272 __isl_give isl_basic_set *isl_set_solutions(
2273 __isl_take isl_set *set);
2274 __isl_give isl_union_set *isl_union_set_solutions(
2275 __isl_take isl_union_set *bset);
2279 __isl_give isl_map *isl_map_fixed_power(
2280 __isl_take isl_map *map, isl_int exp);
2281 __isl_give isl_union_map *isl_union_map_fixed_power(
2282 __isl_take isl_union_map *umap, isl_int exp);
2284 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2285 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2286 of C<map> is computed.
2288 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2290 __isl_give isl_union_map *isl_union_map_power(
2291 __isl_take isl_union_map *umap, int *exact);
2293 Compute a parametric representation for all positive powers I<k> of C<map>.
2294 The result maps I<k> to a nested relation corresponding to the
2295 I<k>th power of C<map>.
2296 The result may be an overapproximation. If the result is known to be exact,
2297 then C<*exact> is set to C<1>.
2299 =item * Transitive closure
2301 __isl_give isl_map *isl_map_transitive_closure(
2302 __isl_take isl_map *map, int *exact);
2303 __isl_give isl_union_map *isl_union_map_transitive_closure(
2304 __isl_take isl_union_map *umap, int *exact);
2306 Compute the transitive closure of C<map>.
2307 The result may be an overapproximation. If the result is known to be exact,
2308 then C<*exact> is set to C<1>.
2310 =item * Reaching path lengths
2312 __isl_give isl_map *isl_map_reaching_path_lengths(
2313 __isl_take isl_map *map, int *exact);
2315 Compute a relation that maps each element in the range of C<map>
2316 to the lengths of all paths composed of edges in C<map> that
2317 end up in the given element.
2318 The result may be an overapproximation. If the result is known to be exact,
2319 then C<*exact> is set to C<1>.
2320 To compute the I<maximal> path length, the resulting relation
2321 should be postprocessed by C<isl_map_lexmax>.
2322 In particular, if the input relation is a dependence relation
2323 (mapping sources to sinks), then the maximal path length corresponds
2324 to the free schedule.
2325 Note, however, that C<isl_map_lexmax> expects the maximum to be
2326 finite, so if the path lengths are unbounded (possibly due to
2327 the overapproximation), then you will get an error message.
2331 __isl_give isl_basic_set *isl_basic_map_wrap(
2332 __isl_take isl_basic_map *bmap);
2333 __isl_give isl_set *isl_map_wrap(
2334 __isl_take isl_map *map);
2335 __isl_give isl_union_set *isl_union_map_wrap(
2336 __isl_take isl_union_map *umap);
2337 __isl_give isl_basic_map *isl_basic_set_unwrap(
2338 __isl_take isl_basic_set *bset);
2339 __isl_give isl_map *isl_set_unwrap(
2340 __isl_take isl_set *set);
2341 __isl_give isl_union_map *isl_union_set_unwrap(
2342 __isl_take isl_union_set *uset);
2346 Remove any internal structure of domain (and range) of the given
2347 set or relation. If there is any such internal structure in the input,
2348 then the name of the space is also removed.
2350 __isl_give isl_basic_set *isl_basic_set_flatten(
2351 __isl_take isl_basic_set *bset);
2352 __isl_give isl_set *isl_set_flatten(
2353 __isl_take isl_set *set);
2354 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2355 __isl_take isl_basic_map *bmap);
2356 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2357 __isl_take isl_basic_map *bmap);
2358 __isl_give isl_map *isl_map_flatten_range(
2359 __isl_take isl_map *map);
2360 __isl_give isl_map *isl_map_flatten_domain(
2361 __isl_take isl_map *map);
2362 __isl_give isl_basic_map *isl_basic_map_flatten(
2363 __isl_take isl_basic_map *bmap);
2364 __isl_give isl_map *isl_map_flatten(
2365 __isl_take isl_map *map);
2367 __isl_give isl_map *isl_set_flatten_map(
2368 __isl_take isl_set *set);
2370 The function above constructs a relation
2371 that maps the input set to a flattened version of the set.
2375 Lift the input set to a space with extra dimensions corresponding
2376 to the existentially quantified variables in the input.
2377 In particular, the result lives in a wrapped map where the domain
2378 is the original space and the range corresponds to the original
2379 existentially quantified variables.
2381 __isl_give isl_basic_set *isl_basic_set_lift(
2382 __isl_take isl_basic_set *bset);
2383 __isl_give isl_set *isl_set_lift(
2384 __isl_take isl_set *set);
2385 __isl_give isl_union_set *isl_union_set_lift(
2386 __isl_take isl_union_set *uset);
2388 Given a local space that contains the existentially quantified
2389 variables of a set, a basic relation that, when applied to
2390 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2391 can be constructed using the following function.
2393 #include <isl/local_space.h>
2394 __isl_give isl_basic_map *isl_local_space_lifting(
2395 __isl_take isl_local_space *ls);
2397 =item * Internal Product
2399 __isl_give isl_basic_map *isl_basic_map_zip(
2400 __isl_take isl_basic_map *bmap);
2401 __isl_give isl_map *isl_map_zip(
2402 __isl_take isl_map *map);
2403 __isl_give isl_union_map *isl_union_map_zip(
2404 __isl_take isl_union_map *umap);
2406 Given a relation with nested relations for domain and range,
2407 interchange the range of the domain with the domain of the range.
2411 __isl_give isl_basic_map *isl_basic_map_curry(
2412 __isl_take isl_basic_map *bmap);
2413 __isl_give isl_map *isl_map_curry(
2414 __isl_take isl_map *map);
2415 __isl_give isl_union_map *isl_union_map_curry(
2416 __isl_take isl_union_map *umap);
2418 Given a relation with a nested relation for domain,
2419 move the range of the nested relation out of the domain
2420 and use it as the domain of a nested relation in the range,
2421 with the original range as range of this nested relation.
2423 =item * Aligning parameters
2425 __isl_give isl_basic_set *isl_basic_set_align_params(
2426 __isl_take isl_basic_set *bset,
2427 __isl_take isl_space *model);
2428 __isl_give isl_set *isl_set_align_params(
2429 __isl_take isl_set *set,
2430 __isl_take isl_space *model);
2431 __isl_give isl_basic_map *isl_basic_map_align_params(
2432 __isl_take isl_basic_map *bmap,
2433 __isl_take isl_space *model);
2434 __isl_give isl_map *isl_map_align_params(
2435 __isl_take isl_map *map,
2436 __isl_take isl_space *model);
2438 Change the order of the parameters of the given set or relation
2439 such that the first parameters match those of C<model>.
2440 This may involve the introduction of extra parameters.
2441 All parameters need to be named.
2443 =item * Dimension manipulation
2445 __isl_give isl_set *isl_set_add_dims(
2446 __isl_take isl_set *set,
2447 enum isl_dim_type type, unsigned n);
2448 __isl_give isl_map *isl_map_add_dims(
2449 __isl_take isl_map *map,
2450 enum isl_dim_type type, unsigned n);
2451 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2452 __isl_take isl_basic_set *bset,
2453 enum isl_dim_type type, unsigned pos,
2455 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2456 __isl_take isl_basic_map *bmap,
2457 enum isl_dim_type type, unsigned pos,
2459 __isl_give isl_set *isl_set_insert_dims(
2460 __isl_take isl_set *set,
2461 enum isl_dim_type type, unsigned pos, unsigned n);
2462 __isl_give isl_map *isl_map_insert_dims(
2463 __isl_take isl_map *map,
2464 enum isl_dim_type type, unsigned pos, unsigned n);
2465 __isl_give isl_basic_set *isl_basic_set_move_dims(
2466 __isl_take isl_basic_set *bset,
2467 enum isl_dim_type dst_type, unsigned dst_pos,
2468 enum isl_dim_type src_type, unsigned src_pos,
2470 __isl_give isl_basic_map *isl_basic_map_move_dims(
2471 __isl_take isl_basic_map *bmap,
2472 enum isl_dim_type dst_type, unsigned dst_pos,
2473 enum isl_dim_type src_type, unsigned src_pos,
2475 __isl_give isl_set *isl_set_move_dims(
2476 __isl_take isl_set *set,
2477 enum isl_dim_type dst_type, unsigned dst_pos,
2478 enum isl_dim_type src_type, unsigned src_pos,
2480 __isl_give isl_map *isl_map_move_dims(
2481 __isl_take isl_map *map,
2482 enum isl_dim_type dst_type, unsigned dst_pos,
2483 enum isl_dim_type src_type, unsigned src_pos,
2486 It is usually not advisable to directly change the (input or output)
2487 space of a set or a relation as this removes the name and the internal
2488 structure of the space. However, the above functions can be useful
2489 to add new parameters, assuming
2490 C<isl_set_align_params> and C<isl_map_align_params>
2495 =head2 Binary Operations
2497 The two arguments of a binary operation not only need to live
2498 in the same C<isl_ctx>, they currently also need to have
2499 the same (number of) parameters.
2501 =head3 Basic Operations
2505 =item * Intersection
2507 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2508 __isl_take isl_basic_set *bset1,
2509 __isl_take isl_basic_set *bset2);
2510 __isl_give isl_basic_set *isl_basic_set_intersect(
2511 __isl_take isl_basic_set *bset1,
2512 __isl_take isl_basic_set *bset2);
2513 __isl_give isl_set *isl_set_intersect_params(
2514 __isl_take isl_set *set,
2515 __isl_take isl_set *params);
2516 __isl_give isl_set *isl_set_intersect(
2517 __isl_take isl_set *set1,
2518 __isl_take isl_set *set2);
2519 __isl_give isl_union_set *isl_union_set_intersect_params(
2520 __isl_take isl_union_set *uset,
2521 __isl_take isl_set *set);
2522 __isl_give isl_union_map *isl_union_map_intersect_params(
2523 __isl_take isl_union_map *umap,
2524 __isl_take isl_set *set);
2525 __isl_give isl_union_set *isl_union_set_intersect(
2526 __isl_take isl_union_set *uset1,
2527 __isl_take isl_union_set *uset2);
2528 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2529 __isl_take isl_basic_map *bmap,
2530 __isl_take isl_basic_set *bset);
2531 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2532 __isl_take isl_basic_map *bmap,
2533 __isl_take isl_basic_set *bset);
2534 __isl_give isl_basic_map *isl_basic_map_intersect(
2535 __isl_take isl_basic_map *bmap1,
2536 __isl_take isl_basic_map *bmap2);
2537 __isl_give isl_map *isl_map_intersect_params(
2538 __isl_take isl_map *map,
2539 __isl_take isl_set *params);
2540 __isl_give isl_map *isl_map_intersect_domain(
2541 __isl_take isl_map *map,
2542 __isl_take isl_set *set);
2543 __isl_give isl_map *isl_map_intersect_range(
2544 __isl_take isl_map *map,
2545 __isl_take isl_set *set);
2546 __isl_give isl_map *isl_map_intersect(
2547 __isl_take isl_map *map1,
2548 __isl_take isl_map *map2);
2549 __isl_give isl_union_map *isl_union_map_intersect_domain(
2550 __isl_take isl_union_map *umap,
2551 __isl_take isl_union_set *uset);
2552 __isl_give isl_union_map *isl_union_map_intersect_range(
2553 __isl_take isl_union_map *umap,
2554 __isl_take isl_union_set *uset);
2555 __isl_give isl_union_map *isl_union_map_intersect(
2556 __isl_take isl_union_map *umap1,
2557 __isl_take isl_union_map *umap2);
2559 The second argument to the C<_params> functions needs to be
2560 a parametric (basic) set. For the other functions, a parametric set
2561 for either argument is only allowed if the other argument is
2562 a parametric set as well.
2566 __isl_give isl_set *isl_basic_set_union(
2567 __isl_take isl_basic_set *bset1,
2568 __isl_take isl_basic_set *bset2);
2569 __isl_give isl_map *isl_basic_map_union(
2570 __isl_take isl_basic_map *bmap1,
2571 __isl_take isl_basic_map *bmap2);
2572 __isl_give isl_set *isl_set_union(
2573 __isl_take isl_set *set1,
2574 __isl_take isl_set *set2);
2575 __isl_give isl_map *isl_map_union(
2576 __isl_take isl_map *map1,
2577 __isl_take isl_map *map2);
2578 __isl_give isl_union_set *isl_union_set_union(
2579 __isl_take isl_union_set *uset1,
2580 __isl_take isl_union_set *uset2);
2581 __isl_give isl_union_map *isl_union_map_union(
2582 __isl_take isl_union_map *umap1,
2583 __isl_take isl_union_map *umap2);
2585 =item * Set difference
2587 __isl_give isl_set *isl_set_subtract(
2588 __isl_take isl_set *set1,
2589 __isl_take isl_set *set2);
2590 __isl_give isl_map *isl_map_subtract(
2591 __isl_take isl_map *map1,
2592 __isl_take isl_map *map2);
2593 __isl_give isl_map *isl_map_subtract_domain(
2594 __isl_take isl_map *map,
2595 __isl_take isl_set *dom);
2596 __isl_give isl_map *isl_map_subtract_range(
2597 __isl_take isl_map *map,
2598 __isl_take isl_set *dom);
2599 __isl_give isl_union_set *isl_union_set_subtract(
2600 __isl_take isl_union_set *uset1,
2601 __isl_take isl_union_set *uset2);
2602 __isl_give isl_union_map *isl_union_map_subtract(
2603 __isl_take isl_union_map *umap1,
2604 __isl_take isl_union_map *umap2);
2608 __isl_give isl_basic_set *isl_basic_set_apply(
2609 __isl_take isl_basic_set *bset,
2610 __isl_take isl_basic_map *bmap);
2611 __isl_give isl_set *isl_set_apply(
2612 __isl_take isl_set *set,
2613 __isl_take isl_map *map);
2614 __isl_give isl_union_set *isl_union_set_apply(
2615 __isl_take isl_union_set *uset,
2616 __isl_take isl_union_map *umap);
2617 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2618 __isl_take isl_basic_map *bmap1,
2619 __isl_take isl_basic_map *bmap2);
2620 __isl_give isl_basic_map *isl_basic_map_apply_range(
2621 __isl_take isl_basic_map *bmap1,
2622 __isl_take isl_basic_map *bmap2);
2623 __isl_give isl_map *isl_map_apply_domain(
2624 __isl_take isl_map *map1,
2625 __isl_take isl_map *map2);
2626 __isl_give isl_union_map *isl_union_map_apply_domain(
2627 __isl_take isl_union_map *umap1,
2628 __isl_take isl_union_map *umap2);
2629 __isl_give isl_map *isl_map_apply_range(
2630 __isl_take isl_map *map1,
2631 __isl_take isl_map *map2);
2632 __isl_give isl_union_map *isl_union_map_apply_range(
2633 __isl_take isl_union_map *umap1,
2634 __isl_take isl_union_map *umap2);
2636 =item * Cartesian Product
2638 __isl_give isl_set *isl_set_product(
2639 __isl_take isl_set *set1,
2640 __isl_take isl_set *set2);
2641 __isl_give isl_union_set *isl_union_set_product(
2642 __isl_take isl_union_set *uset1,
2643 __isl_take isl_union_set *uset2);
2644 __isl_give isl_basic_map *isl_basic_map_domain_product(
2645 __isl_take isl_basic_map *bmap1,
2646 __isl_take isl_basic_map *bmap2);
2647 __isl_give isl_basic_map *isl_basic_map_range_product(
2648 __isl_take isl_basic_map *bmap1,
2649 __isl_take isl_basic_map *bmap2);
2650 __isl_give isl_basic_map *isl_basic_map_product(
2651 __isl_take isl_basic_map *bmap1,
2652 __isl_take isl_basic_map *bmap2);
2653 __isl_give isl_map *isl_map_domain_product(
2654 __isl_take isl_map *map1,
2655 __isl_take isl_map *map2);
2656 __isl_give isl_map *isl_map_range_product(
2657 __isl_take isl_map *map1,
2658 __isl_take isl_map *map2);
2659 __isl_give isl_union_map *isl_union_map_domain_product(
2660 __isl_take isl_union_map *umap1,
2661 __isl_take isl_union_map *umap2);
2662 __isl_give isl_union_map *isl_union_map_range_product(
2663 __isl_take isl_union_map *umap1,
2664 __isl_take isl_union_map *umap2);
2665 __isl_give isl_map *isl_map_product(
2666 __isl_take isl_map *map1,
2667 __isl_take isl_map *map2);
2668 __isl_give isl_union_map *isl_union_map_product(
2669 __isl_take isl_union_map *umap1,
2670 __isl_take isl_union_map *umap2);
2672 The above functions compute the cross product of the given
2673 sets or relations. The domains and ranges of the results
2674 are wrapped maps between domains and ranges of the inputs.
2675 To obtain a ``flat'' product, use the following functions
2678 __isl_give isl_basic_set *isl_basic_set_flat_product(
2679 __isl_take isl_basic_set *bset1,
2680 __isl_take isl_basic_set *bset2);
2681 __isl_give isl_set *isl_set_flat_product(
2682 __isl_take isl_set *set1,
2683 __isl_take isl_set *set2);
2684 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2685 __isl_take isl_basic_map *bmap1,
2686 __isl_take isl_basic_map *bmap2);
2687 __isl_give isl_map *isl_map_flat_domain_product(
2688 __isl_take isl_map *map1,
2689 __isl_take isl_map *map2);
2690 __isl_give isl_map *isl_map_flat_range_product(
2691 __isl_take isl_map *map1,
2692 __isl_take isl_map *map2);
2693 __isl_give isl_union_map *isl_union_map_flat_range_product(
2694 __isl_take isl_union_map *umap1,
2695 __isl_take isl_union_map *umap2);
2696 __isl_give isl_basic_map *isl_basic_map_flat_product(
2697 __isl_take isl_basic_map *bmap1,
2698 __isl_take isl_basic_map *bmap2);
2699 __isl_give isl_map *isl_map_flat_product(
2700 __isl_take isl_map *map1,
2701 __isl_take isl_map *map2);
2703 =item * Simplification
2705 __isl_give isl_basic_set *isl_basic_set_gist(
2706 __isl_take isl_basic_set *bset,
2707 __isl_take isl_basic_set *context);
2708 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2709 __isl_take isl_set *context);
2710 __isl_give isl_set *isl_set_gist_params(
2711 __isl_take isl_set *set,
2712 __isl_take isl_set *context);
2713 __isl_give isl_union_set *isl_union_set_gist(
2714 __isl_take isl_union_set *uset,
2715 __isl_take isl_union_set *context);
2716 __isl_give isl_union_set *isl_union_set_gist_params(
2717 __isl_take isl_union_set *uset,
2718 __isl_take isl_set *set);
2719 __isl_give isl_basic_map *isl_basic_map_gist(
2720 __isl_take isl_basic_map *bmap,
2721 __isl_take isl_basic_map *context);
2722 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2723 __isl_take isl_map *context);
2724 __isl_give isl_map *isl_map_gist_params(
2725 __isl_take isl_map *map,
2726 __isl_take isl_set *context);
2727 __isl_give isl_map *isl_map_gist_domain(
2728 __isl_take isl_map *map,
2729 __isl_take isl_set *context);
2730 __isl_give isl_map *isl_map_gist_range(
2731 __isl_take isl_map *map,
2732 __isl_take isl_set *context);
2733 __isl_give isl_union_map *isl_union_map_gist(
2734 __isl_take isl_union_map *umap,
2735 __isl_take isl_union_map *context);
2736 __isl_give isl_union_map *isl_union_map_gist_params(
2737 __isl_take isl_union_map *umap,
2738 __isl_take isl_set *set);
2739 __isl_give isl_union_map *isl_union_map_gist_domain(
2740 __isl_take isl_union_map *umap,
2741 __isl_take isl_union_set *uset);
2742 __isl_give isl_union_map *isl_union_map_gist_range(
2743 __isl_take isl_union_map *umap,
2744 __isl_take isl_union_set *uset);
2746 The gist operation returns a set or relation that has the
2747 same intersection with the context as the input set or relation.
2748 Any implicit equality in the intersection is made explicit in the result,
2749 while all inequalities that are redundant with respect to the intersection
2751 In case of union sets and relations, the gist operation is performed
2756 =head3 Lexicographic Optimization
2758 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2759 the following functions
2760 compute a set that contains the lexicographic minimum or maximum
2761 of the elements in C<set> (or C<bset>) for those values of the parameters
2762 that satisfy C<dom>.
2763 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2764 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2766 In other words, the union of the parameter values
2767 for which the result is non-empty and of C<*empty>
2770 __isl_give isl_set *isl_basic_set_partial_lexmin(
2771 __isl_take isl_basic_set *bset,
2772 __isl_take isl_basic_set *dom,
2773 __isl_give isl_set **empty);
2774 __isl_give isl_set *isl_basic_set_partial_lexmax(
2775 __isl_take isl_basic_set *bset,
2776 __isl_take isl_basic_set *dom,
2777 __isl_give isl_set **empty);
2778 __isl_give isl_set *isl_set_partial_lexmin(
2779 __isl_take isl_set *set, __isl_take isl_set *dom,
2780 __isl_give isl_set **empty);
2781 __isl_give isl_set *isl_set_partial_lexmax(
2782 __isl_take isl_set *set, __isl_take isl_set *dom,
2783 __isl_give isl_set **empty);
2785 Given a (basic) set C<set> (or C<bset>), the following functions simply
2786 return a set containing the lexicographic minimum or maximum
2787 of the elements in C<set> (or C<bset>).
2788 In case of union sets, the optimum is computed per space.
2790 __isl_give isl_set *isl_basic_set_lexmin(
2791 __isl_take isl_basic_set *bset);
2792 __isl_give isl_set *isl_basic_set_lexmax(
2793 __isl_take isl_basic_set *bset);
2794 __isl_give isl_set *isl_set_lexmin(
2795 __isl_take isl_set *set);
2796 __isl_give isl_set *isl_set_lexmax(
2797 __isl_take isl_set *set);
2798 __isl_give isl_union_set *isl_union_set_lexmin(
2799 __isl_take isl_union_set *uset);
2800 __isl_give isl_union_set *isl_union_set_lexmax(
2801 __isl_take isl_union_set *uset);
2803 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2804 the following functions
2805 compute a relation that maps each element of C<dom>
2806 to the single lexicographic minimum or maximum
2807 of the elements that are associated to that same
2808 element in C<map> (or C<bmap>).
2809 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2810 that contains the elements in C<dom> that do not map
2811 to any elements in C<map> (or C<bmap>).
2812 In other words, the union of the domain of the result and of C<*empty>
2815 __isl_give isl_map *isl_basic_map_partial_lexmax(
2816 __isl_take isl_basic_map *bmap,
2817 __isl_take isl_basic_set *dom,
2818 __isl_give isl_set **empty);
2819 __isl_give isl_map *isl_basic_map_partial_lexmin(
2820 __isl_take isl_basic_map *bmap,
2821 __isl_take isl_basic_set *dom,
2822 __isl_give isl_set **empty);
2823 __isl_give isl_map *isl_map_partial_lexmax(
2824 __isl_take isl_map *map, __isl_take isl_set *dom,
2825 __isl_give isl_set **empty);
2826 __isl_give isl_map *isl_map_partial_lexmin(
2827 __isl_take isl_map *map, __isl_take isl_set *dom,
2828 __isl_give isl_set **empty);
2830 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2831 return a map mapping each element in the domain of
2832 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2833 of all elements associated to that element.
2834 In case of union relations, the optimum is computed per space.
2836 __isl_give isl_map *isl_basic_map_lexmin(
2837 __isl_take isl_basic_map *bmap);
2838 __isl_give isl_map *isl_basic_map_lexmax(
2839 __isl_take isl_basic_map *bmap);
2840 __isl_give isl_map *isl_map_lexmin(
2841 __isl_take isl_map *map);
2842 __isl_give isl_map *isl_map_lexmax(
2843 __isl_take isl_map *map);
2844 __isl_give isl_union_map *isl_union_map_lexmin(
2845 __isl_take isl_union_map *umap);
2846 __isl_give isl_union_map *isl_union_map_lexmax(
2847 __isl_take isl_union_map *umap);
2849 The following functions return their result in the form of
2850 a piecewise multi-affine expression
2851 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2852 but are otherwise equivalent to the corresponding functions
2853 returning a basic set or relation.
2855 __isl_give isl_pw_multi_aff *
2856 isl_basic_map_lexmin_pw_multi_aff(
2857 __isl_take isl_basic_map *bmap);
2858 __isl_give isl_pw_multi_aff *
2859 isl_basic_set_partial_lexmin_pw_multi_aff(
2860 __isl_take isl_basic_set *bset,
2861 __isl_take isl_basic_set *dom,
2862 __isl_give isl_set **empty);
2863 __isl_give isl_pw_multi_aff *
2864 isl_basic_set_partial_lexmax_pw_multi_aff(
2865 __isl_take isl_basic_set *bset,
2866 __isl_take isl_basic_set *dom,
2867 __isl_give isl_set **empty);
2868 __isl_give isl_pw_multi_aff *
2869 isl_basic_map_partial_lexmin_pw_multi_aff(
2870 __isl_take isl_basic_map *bmap,
2871 __isl_take isl_basic_set *dom,
2872 __isl_give isl_set **empty);
2873 __isl_give isl_pw_multi_aff *
2874 isl_basic_map_partial_lexmax_pw_multi_aff(
2875 __isl_take isl_basic_map *bmap,
2876 __isl_take isl_basic_set *dom,
2877 __isl_give isl_set **empty);
2878 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
2879 __isl_take isl_map *map);
2880 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
2881 __isl_take isl_map *map);
2885 Lists are defined over several element types, including
2886 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2887 Here we take lists of C<isl_set>s as an example.
2888 Lists can be created, copied, modified and freed using the following functions.
2890 #include <isl/list.h>
2891 __isl_give isl_set_list *isl_set_list_from_set(
2892 __isl_take isl_set *el);
2893 __isl_give isl_set_list *isl_set_list_alloc(
2894 isl_ctx *ctx, int n);
2895 __isl_give isl_set_list *isl_set_list_copy(
2896 __isl_keep isl_set_list *list);
2897 __isl_give isl_set_list *isl_set_list_add(
2898 __isl_take isl_set_list *list,
2899 __isl_take isl_set *el);
2900 __isl_give isl_set_list *isl_set_list_set_set(
2901 __isl_take isl_set_list *list, int index,
2902 __isl_take isl_set *set);
2903 __isl_give isl_set_list *isl_set_list_concat(
2904 __isl_take isl_set_list *list1,
2905 __isl_take isl_set_list *list2);
2906 void *isl_set_list_free(__isl_take isl_set_list *list);
2908 C<isl_set_list_alloc> creates an empty list with a capacity for
2909 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2912 Lists can be inspected using the following functions.
2914 #include <isl/list.h>
2915 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2916 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2917 __isl_give isl_set *isl_set_list_get_set(
2918 __isl_keep isl_set_list *list, int index);
2919 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2920 int (*fn)(__isl_take isl_set *el, void *user),
2923 Lists can be printed using
2925 #include <isl/list.h>
2926 __isl_give isl_printer *isl_printer_print_set_list(
2927 __isl_take isl_printer *p,
2928 __isl_keep isl_set_list *list);
2932 Vectors can be created, copied and freed using the following functions.
2934 #include <isl/vec.h>
2935 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2937 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2938 void isl_vec_free(__isl_take isl_vec *vec);
2940 Note that the elements of a newly created vector may have arbitrary values.
2941 The elements can be changed and inspected using the following functions.
2943 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2944 int isl_vec_size(__isl_keep isl_vec *vec);
2945 int isl_vec_get_element(__isl_keep isl_vec *vec,
2946 int pos, isl_int *v);
2947 __isl_give isl_vec *isl_vec_set_element(
2948 __isl_take isl_vec *vec, int pos, isl_int v);
2949 __isl_give isl_vec *isl_vec_set_element_si(
2950 __isl_take isl_vec *vec, int pos, int v);
2951 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2953 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2956 C<isl_vec_get_element> will return a negative value if anything went wrong.
2957 In that case, the value of C<*v> is undefined.
2961 Matrices can be created, copied and freed using the following functions.
2963 #include <isl/mat.h>
2964 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2965 unsigned n_row, unsigned n_col);
2966 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2967 void isl_mat_free(__isl_take isl_mat *mat);
2969 Note that the elements of a newly created matrix may have arbitrary values.
2970 The elements can be changed and inspected using the following functions.
2972 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2973 int isl_mat_rows(__isl_keep isl_mat *mat);
2974 int isl_mat_cols(__isl_keep isl_mat *mat);
2975 int isl_mat_get_element(__isl_keep isl_mat *mat,
2976 int row, int col, isl_int *v);
2977 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2978 int row, int col, isl_int v);
2979 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2980 int row, int col, int v);
2982 C<isl_mat_get_element> will return a negative value if anything went wrong.
2983 In that case, the value of C<*v> is undefined.
2985 The following function can be used to compute the (right) inverse
2986 of a matrix, i.e., a matrix such that the product of the original
2987 and the inverse (in that order) is a multiple of the identity matrix.
2988 The input matrix is assumed to be of full row-rank.
2990 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2992 The following function can be used to compute the (right) kernel
2993 (or null space) of a matrix, i.e., a matrix such that the product of
2994 the original and the kernel (in that order) is the zero matrix.
2996 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2998 =head2 Piecewise Quasi Affine Expressions
3000 The zero quasi affine expression on a given domain can be created using
3002 __isl_give isl_aff *isl_aff_zero_on_domain(
3003 __isl_take isl_local_space *ls);
3005 Note that the space in which the resulting object lives is a map space
3006 with the given space as domain and a one-dimensional range.
3008 An empty piecewise quasi affine expression (one with no cells)
3009 or a piecewise quasi affine expression with a single cell can
3010 be created using the following functions.
3012 #include <isl/aff.h>
3013 __isl_give isl_pw_aff *isl_pw_aff_empty(
3014 __isl_take isl_space *space);
3015 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3016 __isl_take isl_set *set, __isl_take isl_aff *aff);
3017 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3018 __isl_take isl_aff *aff);
3020 A piecewise quasi affine expression that is equal to 1 on a set
3021 and 0 outside the set can be created using the following function.
3023 #include <isl/aff.h>
3024 __isl_give isl_pw_aff *isl_set_indicator_function(
3025 __isl_take isl_set *set);
3027 Quasi affine expressions can be copied and freed using
3029 #include <isl/aff.h>
3030 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3031 void *isl_aff_free(__isl_take isl_aff *aff);
3033 __isl_give isl_pw_aff *isl_pw_aff_copy(
3034 __isl_keep isl_pw_aff *pwaff);
3035 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3037 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3038 using the following function. The constraint is required to have
3039 a non-zero coefficient for the specified dimension.
3041 #include <isl/constraint.h>
3042 __isl_give isl_aff *isl_constraint_get_bound(
3043 __isl_keep isl_constraint *constraint,
3044 enum isl_dim_type type, int pos);
3046 The entire affine expression of the constraint can also be extracted
3047 using the following function.
3049 #include <isl/constraint.h>
3050 __isl_give isl_aff *isl_constraint_get_aff(
3051 __isl_keep isl_constraint *constraint);
3053 Conversely, an equality constraint equating
3054 the affine expression to zero or an inequality constraint enforcing
3055 the affine expression to be non-negative, can be constructed using
3057 __isl_give isl_constraint *isl_equality_from_aff(
3058 __isl_take isl_aff *aff);
3059 __isl_give isl_constraint *isl_inequality_from_aff(
3060 __isl_take isl_aff *aff);
3062 The expression can be inspected using
3064 #include <isl/aff.h>
3065 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3066 int isl_aff_dim(__isl_keep isl_aff *aff,
3067 enum isl_dim_type type);
3068 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3069 __isl_keep isl_aff *aff);
3070 __isl_give isl_local_space *isl_aff_get_local_space(
3071 __isl_keep isl_aff *aff);
3072 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3073 enum isl_dim_type type, unsigned pos);
3074 const char *isl_pw_aff_get_dim_name(
3075 __isl_keep isl_pw_aff *pa,
3076 enum isl_dim_type type, unsigned pos);
3077 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3078 enum isl_dim_type type, unsigned pos);
3079 __isl_give isl_id *isl_pw_aff_get_dim_id(
3080 __isl_keep isl_pw_aff *pa,
3081 enum isl_dim_type type, unsigned pos);
3082 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3083 __isl_keep isl_pw_aff *pa,
3084 enum isl_dim_type type);
3085 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3087 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3088 enum isl_dim_type type, int pos, isl_int *v);
3089 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3091 __isl_give isl_aff *isl_aff_get_div(
3092 __isl_keep isl_aff *aff, int pos);
3094 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3095 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3096 int (*fn)(__isl_take isl_set *set,
3097 __isl_take isl_aff *aff,
3098 void *user), void *user);
3100 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3101 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3103 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3104 enum isl_dim_type type, unsigned first, unsigned n);
3105 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3106 enum isl_dim_type type, unsigned first, unsigned n);
3108 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3109 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3110 enum isl_dim_type type);
3111 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3113 It can be modified using
3115 #include <isl/aff.h>
3116 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3117 __isl_take isl_pw_aff *pwaff,
3118 enum isl_dim_type type, __isl_take isl_id *id);
3119 __isl_give isl_aff *isl_aff_set_dim_name(
3120 __isl_take isl_aff *aff, enum isl_dim_type type,
3121 unsigned pos, const char *s);
3122 __isl_give isl_aff *isl_aff_set_dim_id(
3123 __isl_take isl_aff *aff, enum isl_dim_type type,
3124 unsigned pos, __isl_take isl_id *id);
3125 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3126 __isl_take isl_pw_aff *pma,
3127 enum isl_dim_type type, unsigned pos,
3128 __isl_take isl_id *id);
3129 __isl_give isl_aff *isl_aff_set_constant(
3130 __isl_take isl_aff *aff, isl_int v);
3131 __isl_give isl_aff *isl_aff_set_constant_si(
3132 __isl_take isl_aff *aff, int v);
3133 __isl_give isl_aff *isl_aff_set_coefficient(
3134 __isl_take isl_aff *aff,
3135 enum isl_dim_type type, int pos, isl_int v);
3136 __isl_give isl_aff *isl_aff_set_coefficient_si(
3137 __isl_take isl_aff *aff,
3138 enum isl_dim_type type, int pos, int v);
3139 __isl_give isl_aff *isl_aff_set_denominator(
3140 __isl_take isl_aff *aff, isl_int v);
3142 __isl_give isl_aff *isl_aff_add_constant(
3143 __isl_take isl_aff *aff, isl_int v);
3144 __isl_give isl_aff *isl_aff_add_constant_si(
3145 __isl_take isl_aff *aff, int v);
3146 __isl_give isl_aff *isl_aff_add_constant_num(
3147 __isl_take isl_aff *aff, isl_int v);
3148 __isl_give isl_aff *isl_aff_add_constant_num_si(
3149 __isl_take isl_aff *aff, int v);
3150 __isl_give isl_aff *isl_aff_add_coefficient(
3151 __isl_take isl_aff *aff,
3152 enum isl_dim_type type, int pos, isl_int v);
3153 __isl_give isl_aff *isl_aff_add_coefficient_si(
3154 __isl_take isl_aff *aff,
3155 enum isl_dim_type type, int pos, int v);
3157 __isl_give isl_aff *isl_aff_insert_dims(
3158 __isl_take isl_aff *aff,
3159 enum isl_dim_type type, unsigned first, unsigned n);
3160 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3161 __isl_take isl_pw_aff *pwaff,
3162 enum isl_dim_type type, unsigned first, unsigned n);
3163 __isl_give isl_aff *isl_aff_add_dims(
3164 __isl_take isl_aff *aff,
3165 enum isl_dim_type type, unsigned n);
3166 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3167 __isl_take isl_pw_aff *pwaff,
3168 enum isl_dim_type type, unsigned n);
3169 __isl_give isl_aff *isl_aff_drop_dims(
3170 __isl_take isl_aff *aff,
3171 enum isl_dim_type type, unsigned first, unsigned n);
3172 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3173 __isl_take isl_pw_aff *pwaff,
3174 enum isl_dim_type type, unsigned first, unsigned n);
3176 Note that the C<set_constant> and C<set_coefficient> functions
3177 set the I<numerator> of the constant or coefficient, while
3178 C<add_constant> and C<add_coefficient> add an integer value to
3179 the possibly rational constant or coefficient.
3180 The C<add_constant_num> functions add an integer value to
3183 To check whether an affine expressions is obviously zero
3184 or obviously equal to some other affine expression, use
3186 #include <isl/aff.h>
3187 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3188 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3189 __isl_keep isl_aff *aff2);
3190 int isl_pw_aff_plain_is_equal(
3191 __isl_keep isl_pw_aff *pwaff1,
3192 __isl_keep isl_pw_aff *pwaff2);
3196 #include <isl/aff.h>
3197 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3198 __isl_take isl_aff *aff2);
3199 __isl_give isl_pw_aff *isl_pw_aff_add(
3200 __isl_take isl_pw_aff *pwaff1,
3201 __isl_take isl_pw_aff *pwaff2);
3202 __isl_give isl_pw_aff *isl_pw_aff_min(
3203 __isl_take isl_pw_aff *pwaff1,
3204 __isl_take isl_pw_aff *pwaff2);
3205 __isl_give isl_pw_aff *isl_pw_aff_max(
3206 __isl_take isl_pw_aff *pwaff1,
3207 __isl_take isl_pw_aff *pwaff2);
3208 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3209 __isl_take isl_aff *aff2);
3210 __isl_give isl_pw_aff *isl_pw_aff_sub(
3211 __isl_take isl_pw_aff *pwaff1,
3212 __isl_take isl_pw_aff *pwaff2);
3213 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3214 __isl_give isl_pw_aff *isl_pw_aff_neg(
3215 __isl_take isl_pw_aff *pwaff);
3216 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3217 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3218 __isl_take isl_pw_aff *pwaff);
3219 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3220 __isl_give isl_pw_aff *isl_pw_aff_floor(
3221 __isl_take isl_pw_aff *pwaff);
3222 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3224 __isl_give isl_pw_aff *isl_pw_aff_mod(
3225 __isl_take isl_pw_aff *pwaff, isl_int mod);
3226 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3228 __isl_give isl_pw_aff *isl_pw_aff_scale(
3229 __isl_take isl_pw_aff *pwaff, isl_int f);
3230 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3232 __isl_give isl_aff *isl_aff_scale_down_ui(
3233 __isl_take isl_aff *aff, unsigned f);
3234 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3235 __isl_take isl_pw_aff *pwaff, isl_int f);
3237 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3238 __isl_take isl_pw_aff_list *list);
3239 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3240 __isl_take isl_pw_aff_list *list);
3242 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3243 __isl_take isl_pw_aff *pwqp);
3245 __isl_give isl_aff *isl_aff_align_params(
3246 __isl_take isl_aff *aff,
3247 __isl_take isl_space *model);
3248 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3249 __isl_take isl_pw_aff *pwaff,
3250 __isl_take isl_space *model);
3252 __isl_give isl_aff *isl_aff_project_domain_on_params(
3253 __isl_take isl_aff *aff);
3255 __isl_give isl_aff *isl_aff_gist_params(
3256 __isl_take isl_aff *aff,
3257 __isl_take isl_set *context);
3258 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3259 __isl_take isl_set *context);
3260 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3261 __isl_take isl_pw_aff *pwaff,
3262 __isl_take isl_set *context);
3263 __isl_give isl_pw_aff *isl_pw_aff_gist(
3264 __isl_take isl_pw_aff *pwaff,
3265 __isl_take isl_set *context);
3267 __isl_give isl_set *isl_pw_aff_domain(
3268 __isl_take isl_pw_aff *pwaff);
3269 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3270 __isl_take isl_pw_aff *pa,
3271 __isl_take isl_set *set);
3272 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3273 __isl_take isl_pw_aff *pa,
3274 __isl_take isl_set *set);
3276 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3277 __isl_take isl_aff *aff2);
3278 __isl_give isl_pw_aff *isl_pw_aff_mul(
3279 __isl_take isl_pw_aff *pwaff1,
3280 __isl_take isl_pw_aff *pwaff2);
3282 When multiplying two affine expressions, at least one of the two needs
3285 #include <isl/aff.h>
3286 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3287 __isl_take isl_aff *aff);
3288 __isl_give isl_basic_set *isl_aff_le_basic_set(
3289 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3290 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3291 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3292 __isl_give isl_set *isl_pw_aff_eq_set(
3293 __isl_take isl_pw_aff *pwaff1,
3294 __isl_take isl_pw_aff *pwaff2);
3295 __isl_give isl_set *isl_pw_aff_ne_set(
3296 __isl_take isl_pw_aff *pwaff1,
3297 __isl_take isl_pw_aff *pwaff2);
3298 __isl_give isl_set *isl_pw_aff_le_set(
3299 __isl_take isl_pw_aff *pwaff1,
3300 __isl_take isl_pw_aff *pwaff2);
3301 __isl_give isl_set *isl_pw_aff_lt_set(
3302 __isl_take isl_pw_aff *pwaff1,
3303 __isl_take isl_pw_aff *pwaff2);
3304 __isl_give isl_set *isl_pw_aff_ge_set(
3305 __isl_take isl_pw_aff *pwaff1,
3306 __isl_take isl_pw_aff *pwaff2);
3307 __isl_give isl_set *isl_pw_aff_gt_set(
3308 __isl_take isl_pw_aff *pwaff1,
3309 __isl_take isl_pw_aff *pwaff2);
3311 __isl_give isl_set *isl_pw_aff_list_eq_set(
3312 __isl_take isl_pw_aff_list *list1,
3313 __isl_take isl_pw_aff_list *list2);
3314 __isl_give isl_set *isl_pw_aff_list_ne_set(
3315 __isl_take isl_pw_aff_list *list1,
3316 __isl_take isl_pw_aff_list *list2);
3317 __isl_give isl_set *isl_pw_aff_list_le_set(
3318 __isl_take isl_pw_aff_list *list1,
3319 __isl_take isl_pw_aff_list *list2);
3320 __isl_give isl_set *isl_pw_aff_list_lt_set(
3321 __isl_take isl_pw_aff_list *list1,
3322 __isl_take isl_pw_aff_list *list2);
3323 __isl_give isl_set *isl_pw_aff_list_ge_set(
3324 __isl_take isl_pw_aff_list *list1,
3325 __isl_take isl_pw_aff_list *list2);
3326 __isl_give isl_set *isl_pw_aff_list_gt_set(
3327 __isl_take isl_pw_aff_list *list1,
3328 __isl_take isl_pw_aff_list *list2);
3330 The function C<isl_aff_neg_basic_set> returns a basic set
3331 containing those elements in the domain space
3332 of C<aff> where C<aff> is negative.
3333 The function C<isl_aff_ge_basic_set> returns a basic set
3334 containing those elements in the shared space
3335 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3336 The function C<isl_pw_aff_ge_set> returns a set
3337 containing those elements in the shared domain
3338 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3339 The functions operating on C<isl_pw_aff_list> apply the corresponding
3340 C<isl_pw_aff> function to each pair of elements in the two lists.
3342 #include <isl/aff.h>
3343 __isl_give isl_set *isl_pw_aff_nonneg_set(
3344 __isl_take isl_pw_aff *pwaff);
3345 __isl_give isl_set *isl_pw_aff_zero_set(
3346 __isl_take isl_pw_aff *pwaff);
3347 __isl_give isl_set *isl_pw_aff_non_zero_set(
3348 __isl_take isl_pw_aff *pwaff);
3350 The function C<isl_pw_aff_nonneg_set> returns a set
3351 containing those elements in the domain
3352 of C<pwaff> where C<pwaff> is non-negative.
3354 #include <isl/aff.h>
3355 __isl_give isl_pw_aff *isl_pw_aff_cond(
3356 __isl_take isl_pw_aff *cond,
3357 __isl_take isl_pw_aff *pwaff_true,
3358 __isl_take isl_pw_aff *pwaff_false);
3360 The function C<isl_pw_aff_cond> performs a conditional operator
3361 and returns an expression that is equal to C<pwaff_true>
3362 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3363 where C<cond> is zero.
3365 #include <isl/aff.h>
3366 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3367 __isl_take isl_pw_aff *pwaff1,
3368 __isl_take isl_pw_aff *pwaff2);
3369 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3370 __isl_take isl_pw_aff *pwaff1,
3371 __isl_take isl_pw_aff *pwaff2);
3372 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3373 __isl_take isl_pw_aff *pwaff1,
3374 __isl_take isl_pw_aff *pwaff2);
3376 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3377 expression with a domain that is the union of those of C<pwaff1> and
3378 C<pwaff2> and such that on each cell, the quasi-affine expression is
3379 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3380 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3381 associated expression is the defined one.
3383 An expression can be read from input using
3385 #include <isl/aff.h>
3386 __isl_give isl_aff *isl_aff_read_from_str(
3387 isl_ctx *ctx, const char *str);
3388 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3389 isl_ctx *ctx, const char *str);
3391 An expression can be printed using
3393 #include <isl/aff.h>
3394 __isl_give isl_printer *isl_printer_print_aff(
3395 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3397 __isl_give isl_printer *isl_printer_print_pw_aff(
3398 __isl_take isl_printer *p,
3399 __isl_keep isl_pw_aff *pwaff);
3401 =head2 Piecewise Multiple Quasi Affine Expressions
3403 An C<isl_multi_aff> object represents a sequence of
3404 zero or more affine expressions, all defined on the same domain space.
3406 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3409 #include <isl/aff.h>
3410 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3411 __isl_take isl_space *space,
3412 __isl_take isl_aff_list *list);
3414 An empty piecewise multiple quasi affine expression (one with no cells),
3415 the zero piecewise multiple quasi affine expression (with value zero
3416 for each output dimension),
3417 a piecewise multiple quasi affine expression with a single cell (with
3418 either a universe or a specified domain) or
3419 a zero-dimensional piecewise multiple quasi affine expression
3421 can be created using the following functions.
3423 #include <isl/aff.h>
3424 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3425 __isl_take isl_space *space);
3426 __isl_give isl_multi_aff *isl_multi_aff_zero(
3427 __isl_take isl_space *space);
3428 __isl_give isl_multi_aff *isl_multi_aff_identity(
3429 __isl_take isl_space *space);
3430 __isl_give isl_pw_multi_aff *
3431 isl_pw_multi_aff_from_multi_aff(
3432 __isl_take isl_multi_aff *ma);
3433 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3434 __isl_take isl_set *set,
3435 __isl_take isl_multi_aff *maff);
3436 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3437 __isl_take isl_set *set);
3439 __isl_give isl_union_pw_multi_aff *
3440 isl_union_pw_multi_aff_empty(
3441 __isl_take isl_space *space);
3442 __isl_give isl_union_pw_multi_aff *
3443 isl_union_pw_multi_aff_add_pw_multi_aff(
3444 __isl_take isl_union_pw_multi_aff *upma,
3445 __isl_take isl_pw_multi_aff *pma);
3446 __isl_give isl_union_pw_multi_aff *
3447 isl_union_pw_multi_aff_from_domain(
3448 __isl_take isl_union_set *uset);
3450 A piecewise multiple quasi affine expression can also be initialized
3451 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3452 and the C<isl_map> is single-valued.
3454 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3455 __isl_take isl_set *set);
3456 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3457 __isl_take isl_map *map);
3459 Multiple quasi affine expressions can be copied and freed using
3461 #include <isl/aff.h>
3462 __isl_give isl_multi_aff *isl_multi_aff_copy(
3463 __isl_keep isl_multi_aff *maff);
3464 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3466 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3467 __isl_keep isl_pw_multi_aff *pma);
3468 void *isl_pw_multi_aff_free(
3469 __isl_take isl_pw_multi_aff *pma);
3471 __isl_give isl_union_pw_multi_aff *
3472 isl_union_pw_multi_aff_copy(
3473 __isl_keep isl_union_pw_multi_aff *upma);
3474 void *isl_union_pw_multi_aff_free(
3475 __isl_take isl_union_pw_multi_aff *upma);
3477 The expression can be inspected using
3479 #include <isl/aff.h>
3480 isl_ctx *isl_multi_aff_get_ctx(
3481 __isl_keep isl_multi_aff *maff);
3482 isl_ctx *isl_pw_multi_aff_get_ctx(
3483 __isl_keep isl_pw_multi_aff *pma);
3484 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3485 __isl_keep isl_union_pw_multi_aff *upma);
3486 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3487 enum isl_dim_type type);
3488 unsigned isl_pw_multi_aff_dim(
3489 __isl_keep isl_pw_multi_aff *pma,
3490 enum isl_dim_type type);
3491 __isl_give isl_aff *isl_multi_aff_get_aff(
3492 __isl_keep isl_multi_aff *multi, int pos);
3493 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3494 __isl_keep isl_pw_multi_aff *pma, int pos);
3495 const char *isl_pw_multi_aff_get_dim_name(
3496 __isl_keep isl_pw_multi_aff *pma,
3497 enum isl_dim_type type, unsigned pos);
3498 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3499 __isl_keep isl_pw_multi_aff *pma,
3500 enum isl_dim_type type, unsigned pos);
3501 const char *isl_multi_aff_get_tuple_name(
3502 __isl_keep isl_multi_aff *multi,
3503 enum isl_dim_type type);
3504 int isl_pw_multi_aff_has_tuple_name(
3505 __isl_keep isl_pw_multi_aff *pma,
3506 enum isl_dim_type type);
3507 const char *isl_pw_multi_aff_get_tuple_name(
3508 __isl_keep isl_pw_multi_aff *pma,
3509 enum isl_dim_type type);
3510 int isl_pw_multi_aff_has_tuple_id(
3511 __isl_keep isl_pw_multi_aff *pma,
3512 enum isl_dim_type type);
3513 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3514 __isl_keep isl_pw_multi_aff *pma,
3515 enum isl_dim_type type);
3517 int isl_pw_multi_aff_foreach_piece(
3518 __isl_keep isl_pw_multi_aff *pma,
3519 int (*fn)(__isl_take isl_set *set,
3520 __isl_take isl_multi_aff *maff,
3521 void *user), void *user);
3523 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3524 __isl_keep isl_union_pw_multi_aff *upma,
3525 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3526 void *user), void *user);
3528 It can be modified using
3530 #include <isl/aff.h>
3531 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3532 __isl_take isl_multi_aff *multi, int pos,
3533 __isl_take isl_aff *aff);
3534 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3535 __isl_take isl_multi_aff *maff,
3536 enum isl_dim_type type, unsigned pos, const char *s);
3537 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3538 __isl_take isl_multi_aff *maff,
3539 enum isl_dim_type type, __isl_take isl_id *id);
3540 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3541 __isl_take isl_pw_multi_aff *pma,
3542 enum isl_dim_type type, __isl_take isl_id *id);
3544 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3545 __isl_take isl_multi_aff *maff,
3546 enum isl_dim_type type, unsigned first, unsigned n);
3547 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
3548 __isl_take isl_pw_multi_aff *pma,
3549 enum isl_dim_type type, unsigned first, unsigned n);
3551 To check whether two multiple affine expressions are
3552 obviously equal to each other, use
3554 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3555 __isl_keep isl_multi_aff *maff2);
3556 int isl_pw_multi_aff_plain_is_equal(
3557 __isl_keep isl_pw_multi_aff *pma1,
3558 __isl_keep isl_pw_multi_aff *pma2);
3562 #include <isl/aff.h>
3563 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3564 __isl_take isl_pw_multi_aff *pma1,
3565 __isl_take isl_pw_multi_aff *pma2);
3566 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3567 __isl_take isl_pw_multi_aff *pma1,
3568 __isl_take isl_pw_multi_aff *pma2);
3569 __isl_give isl_multi_aff *isl_multi_aff_add(
3570 __isl_take isl_multi_aff *maff1,
3571 __isl_take isl_multi_aff *maff2);
3572 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3573 __isl_take isl_pw_multi_aff *pma1,
3574 __isl_take isl_pw_multi_aff *pma2);
3575 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3576 __isl_take isl_union_pw_multi_aff *upma1,
3577 __isl_take isl_union_pw_multi_aff *upma2);
3578 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3579 __isl_take isl_pw_multi_aff *pma1,
3580 __isl_take isl_pw_multi_aff *pma2);
3581 __isl_give isl_multi_aff *isl_multi_aff_scale(
3582 __isl_take isl_multi_aff *maff,
3584 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3585 __isl_take isl_pw_multi_aff *pma,
3586 __isl_take isl_set *set);
3587 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3588 __isl_take isl_pw_multi_aff *pma,
3589 __isl_take isl_set *set);
3590 __isl_give isl_multi_aff *isl_multi_aff_lift(
3591 __isl_take isl_multi_aff *maff,
3592 __isl_give isl_local_space **ls);
3593 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3594 __isl_take isl_pw_multi_aff *pma);
3595 __isl_give isl_multi_aff *isl_multi_aff_align_params(
3596 __isl_take isl_multi_aff *multi,
3597 __isl_take isl_space *model);
3598 __isl_give isl_pw_multi_aff *
3599 isl_pw_multi_aff_project_domain_on_params(
3600 __isl_take isl_pw_multi_aff *pma);
3601 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3602 __isl_take isl_multi_aff *maff,
3603 __isl_take isl_set *context);
3604 __isl_give isl_multi_aff *isl_multi_aff_gist(
3605 __isl_take isl_multi_aff *maff,
3606 __isl_take isl_set *context);
3607 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3608 __isl_take isl_pw_multi_aff *pma,
3609 __isl_take isl_set *set);
3610 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3611 __isl_take isl_pw_multi_aff *pma,
3612 __isl_take isl_set *set);
3613 __isl_give isl_set *isl_pw_multi_aff_domain(
3614 __isl_take isl_pw_multi_aff *pma);
3615 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3616 __isl_take isl_union_pw_multi_aff *upma);
3617 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3618 __isl_take isl_multi_aff *ma1,
3619 __isl_take isl_multi_aff *ma2);
3620 __isl_give isl_multi_aff *isl_multi_aff_product(
3621 __isl_take isl_multi_aff *ma1,
3622 __isl_take isl_multi_aff *ma2);
3623 __isl_give isl_pw_multi_aff *
3624 isl_pw_multi_aff_flat_range_product(
3625 __isl_take isl_pw_multi_aff *pma1,
3626 __isl_take isl_pw_multi_aff *pma2);
3627 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3628 __isl_take isl_pw_multi_aff *pma1,
3629 __isl_take isl_pw_multi_aff *pma2);
3630 __isl_give isl_union_pw_multi_aff *
3631 isl_union_pw_multi_aff_flat_range_product(
3632 __isl_take isl_union_pw_multi_aff *upma1,
3633 __isl_take isl_union_pw_multi_aff *upma2);
3635 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3636 then it is assigned the local space that lies at the basis of
3637 the lifting applied.
3639 __isl_give isl_set *isl_multi_aff_lex_le_set(
3640 __isl_take isl_multi_aff *ma1,
3641 __isl_take isl_multi_aff *ma2);
3642 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3643 __isl_take isl_multi_aff *ma1,
3644 __isl_take isl_multi_aff *ma2);
3646 The function C<isl_multi_aff_lex_le_set> returns a set
3647 containing those elements in the shared domain space
3648 where C<ma1> is lexicographically smaller than or
3651 An expression can be read from input using
3653 #include <isl/aff.h>
3654 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3655 isl_ctx *ctx, const char *str);
3656 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3657 isl_ctx *ctx, const char *str);
3659 An expression can be printed using
3661 #include <isl/aff.h>
3662 __isl_give isl_printer *isl_printer_print_multi_aff(
3663 __isl_take isl_printer *p,
3664 __isl_keep isl_multi_aff *maff);
3665 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3666 __isl_take isl_printer *p,
3667 __isl_keep isl_pw_multi_aff *pma);
3668 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3669 __isl_take isl_printer *p,
3670 __isl_keep isl_union_pw_multi_aff *upma);
3674 Points are elements of a set. They can be used to construct
3675 simple sets (boxes) or they can be used to represent the
3676 individual elements of a set.
3677 The zero point (the origin) can be created using
3679 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3681 The coordinates of a point can be inspected, set and changed
3684 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3685 enum isl_dim_type type, int pos, isl_int *v);
3686 __isl_give isl_point *isl_point_set_coordinate(
3687 __isl_take isl_point *pnt,
3688 enum isl_dim_type type, int pos, isl_int v);
3690 __isl_give isl_point *isl_point_add_ui(
3691 __isl_take isl_point *pnt,
3692 enum isl_dim_type type, int pos, unsigned val);
3693 __isl_give isl_point *isl_point_sub_ui(
3694 __isl_take isl_point *pnt,
3695 enum isl_dim_type type, int pos, unsigned val);
3697 Other properties can be obtained using
3699 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3701 Points can be copied or freed using
3703 __isl_give isl_point *isl_point_copy(
3704 __isl_keep isl_point *pnt);
3705 void isl_point_free(__isl_take isl_point *pnt);
3707 A singleton set can be created from a point using
3709 __isl_give isl_basic_set *isl_basic_set_from_point(
3710 __isl_take isl_point *pnt);
3711 __isl_give isl_set *isl_set_from_point(
3712 __isl_take isl_point *pnt);
3714 and a box can be created from two opposite extremal points using
3716 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3717 __isl_take isl_point *pnt1,
3718 __isl_take isl_point *pnt2);
3719 __isl_give isl_set *isl_set_box_from_points(
3720 __isl_take isl_point *pnt1,
3721 __isl_take isl_point *pnt2);
3723 All elements of a B<bounded> (union) set can be enumerated using
3724 the following functions.
3726 int isl_set_foreach_point(__isl_keep isl_set *set,
3727 int (*fn)(__isl_take isl_point *pnt, void *user),
3729 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3730 int (*fn)(__isl_take isl_point *pnt, void *user),
3733 The function C<fn> is called for each integer point in
3734 C<set> with as second argument the last argument of
3735 the C<isl_set_foreach_point> call. The function C<fn>
3736 should return C<0> on success and C<-1> on failure.
3737 In the latter case, C<isl_set_foreach_point> will stop
3738 enumerating and return C<-1> as well.
3739 If the enumeration is performed successfully and to completion,
3740 then C<isl_set_foreach_point> returns C<0>.
3742 To obtain a single point of a (basic) set, use
3744 __isl_give isl_point *isl_basic_set_sample_point(
3745 __isl_take isl_basic_set *bset);
3746 __isl_give isl_point *isl_set_sample_point(
3747 __isl_take isl_set *set);
3749 If C<set> does not contain any (integer) points, then the
3750 resulting point will be ``void'', a property that can be
3753 int isl_point_is_void(__isl_keep isl_point *pnt);
3755 =head2 Piecewise Quasipolynomials
3757 A piecewise quasipolynomial is a particular kind of function that maps
3758 a parametric point to a rational value.
3759 More specifically, a quasipolynomial is a polynomial expression in greatest
3760 integer parts of affine expressions of parameters and variables.
3761 A piecewise quasipolynomial is a subdivision of a given parametric
3762 domain into disjoint cells with a quasipolynomial associated to
3763 each cell. The value of the piecewise quasipolynomial at a given
3764 point is the value of the quasipolynomial associated to the cell
3765 that contains the point. Outside of the union of cells,
3766 the value is assumed to be zero.
3767 For example, the piecewise quasipolynomial
3769 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3771 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3772 A given piecewise quasipolynomial has a fixed domain dimension.
3773 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3774 defined over different domains.
3775 Piecewise quasipolynomials are mainly used by the C<barvinok>
3776 library for representing the number of elements in a parametric set or map.
3777 For example, the piecewise quasipolynomial above represents
3778 the number of points in the map
3780 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3782 =head3 Input and Output
3784 Piecewise quasipolynomials can be read from input using
3786 __isl_give isl_union_pw_qpolynomial *
3787 isl_union_pw_qpolynomial_read_from_str(
3788 isl_ctx *ctx, const char *str);
3790 Quasipolynomials and piecewise quasipolynomials can be printed
3791 using the following functions.
3793 __isl_give isl_printer *isl_printer_print_qpolynomial(
3794 __isl_take isl_printer *p,
3795 __isl_keep isl_qpolynomial *qp);
3797 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3798 __isl_take isl_printer *p,
3799 __isl_keep isl_pw_qpolynomial *pwqp);
3801 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3802 __isl_take isl_printer *p,
3803 __isl_keep isl_union_pw_qpolynomial *upwqp);
3805 The output format of the printer
3806 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3807 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3809 In case of printing in C<ISL_FORMAT_C>, the user may want
3810 to set the names of all dimensions
3812 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3813 __isl_take isl_qpolynomial *qp,
3814 enum isl_dim_type type, unsigned pos,
3816 __isl_give isl_pw_qpolynomial *
3817 isl_pw_qpolynomial_set_dim_name(
3818 __isl_take isl_pw_qpolynomial *pwqp,
3819 enum isl_dim_type type, unsigned pos,
3822 =head3 Creating New (Piecewise) Quasipolynomials
3824 Some simple quasipolynomials can be created using the following functions.
3825 More complicated quasipolynomials can be created by applying
3826 operations such as addition and multiplication
3827 on the resulting quasipolynomials
3829 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3830 __isl_take isl_space *domain);
3831 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3832 __isl_take isl_space *domain);
3833 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3834 __isl_take isl_space *domain);
3835 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3836 __isl_take isl_space *domain);
3837 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3838 __isl_take isl_space *domain);
3839 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3840 __isl_take isl_space *domain,
3841 const isl_int n, const isl_int d);
3842 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3843 __isl_take isl_space *domain,
3844 enum isl_dim_type type, unsigned pos);
3845 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3846 __isl_take isl_aff *aff);
3848 Note that the space in which a quasipolynomial lives is a map space
3849 with a one-dimensional range. The C<domain> argument in some of
3850 the functions above corresponds to the domain of this map space.
3852 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3853 with a single cell can be created using the following functions.
3854 Multiple of these single cell piecewise quasipolynomials can
3855 be combined to create more complicated piecewise quasipolynomials.
3857 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3858 __isl_take isl_space *space);
3859 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3860 __isl_take isl_set *set,
3861 __isl_take isl_qpolynomial *qp);
3862 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3863 __isl_take isl_qpolynomial *qp);
3864 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3865 __isl_take isl_pw_aff *pwaff);
3867 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3868 __isl_take isl_space *space);
3869 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3870 __isl_take isl_pw_qpolynomial *pwqp);
3871 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3872 __isl_take isl_union_pw_qpolynomial *upwqp,
3873 __isl_take isl_pw_qpolynomial *pwqp);
3875 Quasipolynomials can be copied and freed again using the following
3878 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3879 __isl_keep isl_qpolynomial *qp);
3880 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3882 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3883 __isl_keep isl_pw_qpolynomial *pwqp);
3884 void *isl_pw_qpolynomial_free(
3885 __isl_take isl_pw_qpolynomial *pwqp);
3887 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3888 __isl_keep isl_union_pw_qpolynomial *upwqp);
3889 void *isl_union_pw_qpolynomial_free(
3890 __isl_take isl_union_pw_qpolynomial *upwqp);
3892 =head3 Inspecting (Piecewise) Quasipolynomials
3894 To iterate over all piecewise quasipolynomials in a union
3895 piecewise quasipolynomial, use the following function
3897 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3898 __isl_keep isl_union_pw_qpolynomial *upwqp,
3899 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3902 To extract the piecewise quasipolynomial in a given space from a union, use
3904 __isl_give isl_pw_qpolynomial *
3905 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3906 __isl_keep isl_union_pw_qpolynomial *upwqp,
3907 __isl_take isl_space *space);
3909 To iterate over the cells in a piecewise quasipolynomial,
3910 use either of the following two functions
3912 int isl_pw_qpolynomial_foreach_piece(
3913 __isl_keep isl_pw_qpolynomial *pwqp,
3914 int (*fn)(__isl_take isl_set *set,
3915 __isl_take isl_qpolynomial *qp,
3916 void *user), void *user);
3917 int isl_pw_qpolynomial_foreach_lifted_piece(
3918 __isl_keep isl_pw_qpolynomial *pwqp,
3919 int (*fn)(__isl_take isl_set *set,
3920 __isl_take isl_qpolynomial *qp,
3921 void *user), void *user);
3923 As usual, the function C<fn> should return C<0> on success
3924 and C<-1> on failure. The difference between
3925 C<isl_pw_qpolynomial_foreach_piece> and
3926 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3927 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3928 compute unique representations for all existentially quantified
3929 variables and then turn these existentially quantified variables
3930 into extra set variables, adapting the associated quasipolynomial
3931 accordingly. This means that the C<set> passed to C<fn>
3932 will not have any existentially quantified variables, but that
3933 the dimensions of the sets may be different for different
3934 invocations of C<fn>.
3936 To iterate over all terms in a quasipolynomial,
3939 int isl_qpolynomial_foreach_term(
3940 __isl_keep isl_qpolynomial *qp,
3941 int (*fn)(__isl_take isl_term *term,
3942 void *user), void *user);
3944 The terms themselves can be inspected and freed using
3947 unsigned isl_term_dim(__isl_keep isl_term *term,
3948 enum isl_dim_type type);
3949 void isl_term_get_num(__isl_keep isl_term *term,
3951 void isl_term_get_den(__isl_keep isl_term *term,
3953 int isl_term_get_exp(__isl_keep isl_term *term,
3954 enum isl_dim_type type, unsigned pos);
3955 __isl_give isl_aff *isl_term_get_div(
3956 __isl_keep isl_term *term, unsigned pos);
3957 void isl_term_free(__isl_take isl_term *term);
3959 Each term is a product of parameters, set variables and
3960 integer divisions. The function C<isl_term_get_exp>
3961 returns the exponent of a given dimensions in the given term.
3962 The C<isl_int>s in the arguments of C<isl_term_get_num>
3963 and C<isl_term_get_den> need to have been initialized
3964 using C<isl_int_init> before calling these functions.
3966 =head3 Properties of (Piecewise) Quasipolynomials
3968 To check whether a quasipolynomial is actually a constant,
3969 use the following function.
3971 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3972 isl_int *n, isl_int *d);
3974 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3975 then the numerator and denominator of the constant
3976 are returned in C<*n> and C<*d>, respectively.
3978 To check whether two union piecewise quasipolynomials are
3979 obviously equal, use
3981 int isl_union_pw_qpolynomial_plain_is_equal(
3982 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3983 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3985 =head3 Operations on (Piecewise) Quasipolynomials
3987 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3988 __isl_take isl_qpolynomial *qp, isl_int v);
3989 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3990 __isl_take isl_qpolynomial *qp);
3991 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3992 __isl_take isl_qpolynomial *qp1,
3993 __isl_take isl_qpolynomial *qp2);
3994 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3995 __isl_take isl_qpolynomial *qp1,
3996 __isl_take isl_qpolynomial *qp2);
3997 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3998 __isl_take isl_qpolynomial *qp1,
3999 __isl_take isl_qpolynomial *qp2);
4000 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4001 __isl_take isl_qpolynomial *qp, unsigned exponent);
4003 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4004 __isl_take isl_pw_qpolynomial *pwqp1,
4005 __isl_take isl_pw_qpolynomial *pwqp2);
4006 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4007 __isl_take isl_pw_qpolynomial *pwqp1,
4008 __isl_take isl_pw_qpolynomial *pwqp2);
4009 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4010 __isl_take isl_pw_qpolynomial *pwqp1,
4011 __isl_take isl_pw_qpolynomial *pwqp2);
4012 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4013 __isl_take isl_pw_qpolynomial *pwqp);
4014 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4015 __isl_take isl_pw_qpolynomial *pwqp1,
4016 __isl_take isl_pw_qpolynomial *pwqp2);
4017 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4018 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4020 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4021 __isl_take isl_union_pw_qpolynomial *upwqp1,
4022 __isl_take isl_union_pw_qpolynomial *upwqp2);
4023 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4024 __isl_take isl_union_pw_qpolynomial *upwqp1,
4025 __isl_take isl_union_pw_qpolynomial *upwqp2);
4026 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4027 __isl_take isl_union_pw_qpolynomial *upwqp1,
4028 __isl_take isl_union_pw_qpolynomial *upwqp2);
4030 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4031 __isl_take isl_pw_qpolynomial *pwqp,
4032 __isl_take isl_point *pnt);
4034 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4035 __isl_take isl_union_pw_qpolynomial *upwqp,
4036 __isl_take isl_point *pnt);
4038 __isl_give isl_set *isl_pw_qpolynomial_domain(
4039 __isl_take isl_pw_qpolynomial *pwqp);
4040 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4041 __isl_take isl_pw_qpolynomial *pwpq,
4042 __isl_take isl_set *set);
4043 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4044 __isl_take isl_pw_qpolynomial *pwpq,
4045 __isl_take isl_set *set);
4047 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4048 __isl_take isl_union_pw_qpolynomial *upwqp);
4049 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4050 __isl_take isl_union_pw_qpolynomial *upwpq,
4051 __isl_take isl_union_set *uset);
4052 __isl_give isl_union_pw_qpolynomial *
4053 isl_union_pw_qpolynomial_intersect_params(
4054 __isl_take isl_union_pw_qpolynomial *upwpq,
4055 __isl_take isl_set *set);
4057 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4058 __isl_take isl_qpolynomial *qp,
4059 __isl_take isl_space *model);
4061 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4062 __isl_take isl_qpolynomial *qp);
4063 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4064 __isl_take isl_pw_qpolynomial *pwqp);
4066 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4067 __isl_take isl_union_pw_qpolynomial *upwqp);
4069 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4070 __isl_take isl_qpolynomial *qp,
4071 __isl_take isl_set *context);
4072 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4073 __isl_take isl_qpolynomial *qp,
4074 __isl_take isl_set *context);
4076 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4077 __isl_take isl_pw_qpolynomial *pwqp,
4078 __isl_take isl_set *context);
4079 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4080 __isl_take isl_pw_qpolynomial *pwqp,
4081 __isl_take isl_set *context);
4083 __isl_give isl_union_pw_qpolynomial *
4084 isl_union_pw_qpolynomial_gist_params(
4085 __isl_take isl_union_pw_qpolynomial *upwqp,
4086 __isl_take isl_set *context);
4087 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4088 __isl_take isl_union_pw_qpolynomial *upwqp,
4089 __isl_take isl_union_set *context);
4091 The gist operation applies the gist operation to each of
4092 the cells in the domain of the input piecewise quasipolynomial.
4093 The context is also exploited
4094 to simplify the quasipolynomials associated to each cell.
4096 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4097 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4098 __isl_give isl_union_pw_qpolynomial *
4099 isl_union_pw_qpolynomial_to_polynomial(
4100 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4102 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4103 the polynomial will be an overapproximation. If C<sign> is negative,
4104 it will be an underapproximation. If C<sign> is zero, the approximation
4105 will lie somewhere in between.
4107 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4109 A piecewise quasipolynomial reduction is a piecewise
4110 reduction (or fold) of quasipolynomials.
4111 In particular, the reduction can be maximum or a minimum.
4112 The objects are mainly used to represent the result of
4113 an upper or lower bound on a quasipolynomial over its domain,
4114 i.e., as the result of the following function.
4116 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4117 __isl_take isl_pw_qpolynomial *pwqp,
4118 enum isl_fold type, int *tight);
4120 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4121 __isl_take isl_union_pw_qpolynomial *upwqp,
4122 enum isl_fold type, int *tight);
4124 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4125 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4126 is the returned bound is known be tight, i.e., for each value
4127 of the parameters there is at least
4128 one element in the domain that reaches the bound.
4129 If the domain of C<pwqp> is not wrapping, then the bound is computed
4130 over all elements in that domain and the result has a purely parametric
4131 domain. If the domain of C<pwqp> is wrapping, then the bound is
4132 computed over the range of the wrapped relation. The domain of the
4133 wrapped relation becomes the domain of the result.
4135 A (piecewise) quasipolynomial reduction can be copied or freed using the
4136 following functions.
4138 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4139 __isl_keep isl_qpolynomial_fold *fold);
4140 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4141 __isl_keep isl_pw_qpolynomial_fold *pwf);
4142 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4143 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4144 void isl_qpolynomial_fold_free(
4145 __isl_take isl_qpolynomial_fold *fold);
4146 void *isl_pw_qpolynomial_fold_free(
4147 __isl_take isl_pw_qpolynomial_fold *pwf);
4148 void *isl_union_pw_qpolynomial_fold_free(
4149 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4151 =head3 Printing Piecewise Quasipolynomial Reductions
4153 Piecewise quasipolynomial reductions can be printed
4154 using the following function.
4156 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4157 __isl_take isl_printer *p,
4158 __isl_keep isl_pw_qpolynomial_fold *pwf);
4159 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4160 __isl_take isl_printer *p,
4161 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4163 For C<isl_printer_print_pw_qpolynomial_fold>,
4164 output format of the printer
4165 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4166 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4167 output format of the printer
4168 needs to be set to C<ISL_FORMAT_ISL>.
4169 In case of printing in C<ISL_FORMAT_C>, the user may want
4170 to set the names of all dimensions
4172 __isl_give isl_pw_qpolynomial_fold *
4173 isl_pw_qpolynomial_fold_set_dim_name(
4174 __isl_take isl_pw_qpolynomial_fold *pwf,
4175 enum isl_dim_type type, unsigned pos,
4178 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4180 To iterate over all piecewise quasipolynomial reductions in a union
4181 piecewise quasipolynomial reduction, use the following function
4183 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4184 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4185 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4186 void *user), void *user);
4188 To iterate over the cells in a piecewise quasipolynomial reduction,
4189 use either of the following two functions
4191 int isl_pw_qpolynomial_fold_foreach_piece(
4192 __isl_keep isl_pw_qpolynomial_fold *pwf,
4193 int (*fn)(__isl_take isl_set *set,
4194 __isl_take isl_qpolynomial_fold *fold,
4195 void *user), void *user);
4196 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4197 __isl_keep isl_pw_qpolynomial_fold *pwf,
4198 int (*fn)(__isl_take isl_set *set,
4199 __isl_take isl_qpolynomial_fold *fold,
4200 void *user), void *user);
4202 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4203 of the difference between these two functions.
4205 To iterate over all quasipolynomials in a reduction, use
4207 int isl_qpolynomial_fold_foreach_qpolynomial(
4208 __isl_keep isl_qpolynomial_fold *fold,
4209 int (*fn)(__isl_take isl_qpolynomial *qp,
4210 void *user), void *user);
4212 =head3 Properties of Piecewise Quasipolynomial Reductions
4214 To check whether two union piecewise quasipolynomial reductions are
4215 obviously equal, use
4217 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4218 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4219 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4221 =head3 Operations on Piecewise Quasipolynomial Reductions
4223 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4224 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4226 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4227 __isl_take isl_pw_qpolynomial_fold *pwf1,
4228 __isl_take isl_pw_qpolynomial_fold *pwf2);
4230 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4231 __isl_take isl_pw_qpolynomial_fold *pwf1,
4232 __isl_take isl_pw_qpolynomial_fold *pwf2);
4234 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4235 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4236 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4238 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4239 __isl_take isl_pw_qpolynomial_fold *pwf,
4240 __isl_take isl_point *pnt);
4242 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4243 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4244 __isl_take isl_point *pnt);
4246 __isl_give isl_pw_qpolynomial_fold *
4247 isl_pw_qpolynomial_fold_intersect_params(
4248 __isl_take isl_pw_qpolynomial_fold *pwf,
4249 __isl_take isl_set *set);
4251 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4252 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4253 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4254 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4255 __isl_take isl_union_set *uset);
4256 __isl_give isl_union_pw_qpolynomial_fold *
4257 isl_union_pw_qpolynomial_fold_intersect_params(
4258 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4259 __isl_take isl_set *set);
4261 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4262 __isl_take isl_pw_qpolynomial_fold *pwf);
4264 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4265 __isl_take isl_pw_qpolynomial_fold *pwf);
4267 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4268 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4270 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4271 __isl_take isl_qpolynomial_fold *fold,
4272 __isl_take isl_set *context);
4273 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4274 __isl_take isl_qpolynomial_fold *fold,
4275 __isl_take isl_set *context);
4277 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4278 __isl_take isl_pw_qpolynomial_fold *pwf,
4279 __isl_take isl_set *context);
4280 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4281 __isl_take isl_pw_qpolynomial_fold *pwf,
4282 __isl_take isl_set *context);
4284 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4285 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4286 __isl_take isl_union_set *context);
4287 __isl_give isl_union_pw_qpolynomial_fold *
4288 isl_union_pw_qpolynomial_fold_gist_params(
4289 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4290 __isl_take isl_set *context);
4292 The gist operation applies the gist operation to each of
4293 the cells in the domain of the input piecewise quasipolynomial reduction.
4294 In future, the operation will also exploit the context
4295 to simplify the quasipolynomial reductions associated to each cell.
4297 __isl_give isl_pw_qpolynomial_fold *
4298 isl_set_apply_pw_qpolynomial_fold(
4299 __isl_take isl_set *set,
4300 __isl_take isl_pw_qpolynomial_fold *pwf,
4302 __isl_give isl_pw_qpolynomial_fold *
4303 isl_map_apply_pw_qpolynomial_fold(
4304 __isl_take isl_map *map,
4305 __isl_take isl_pw_qpolynomial_fold *pwf,
4307 __isl_give isl_union_pw_qpolynomial_fold *
4308 isl_union_set_apply_union_pw_qpolynomial_fold(
4309 __isl_take isl_union_set *uset,
4310 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4312 __isl_give isl_union_pw_qpolynomial_fold *
4313 isl_union_map_apply_union_pw_qpolynomial_fold(
4314 __isl_take isl_union_map *umap,
4315 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4318 The functions taking a map
4319 compose the given map with the given piecewise quasipolynomial reduction.
4320 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4321 over all elements in the intersection of the range of the map
4322 and the domain of the piecewise quasipolynomial reduction
4323 as a function of an element in the domain of the map.
4324 The functions taking a set compute a bound over all elements in the
4325 intersection of the set and the domain of the
4326 piecewise quasipolynomial reduction.
4328 =head2 Dependence Analysis
4330 C<isl> contains specialized functionality for performing
4331 array dataflow analysis. That is, given a I<sink> access relation
4332 and a collection of possible I<source> access relations,
4333 C<isl> can compute relations that describe
4334 for each iteration of the sink access, which iteration
4335 of which of the source access relations was the last
4336 to access the same data element before the given iteration
4338 The resulting dependence relations map source iterations
4339 to the corresponding sink iterations.
4340 To compute standard flow dependences, the sink should be
4341 a read, while the sources should be writes.
4342 If any of the source accesses are marked as being I<may>
4343 accesses, then there will be a dependence from the last
4344 I<must> access B<and> from any I<may> access that follows
4345 this last I<must> access.
4346 In particular, if I<all> sources are I<may> accesses,
4347 then memory based dependence analysis is performed.
4348 If, on the other hand, all sources are I<must> accesses,
4349 then value based dependence analysis is performed.
4351 #include <isl/flow.h>
4353 typedef int (*isl_access_level_before)(void *first, void *second);
4355 __isl_give isl_access_info *isl_access_info_alloc(
4356 __isl_take isl_map *sink,
4357 void *sink_user, isl_access_level_before fn,
4359 __isl_give isl_access_info *isl_access_info_add_source(
4360 __isl_take isl_access_info *acc,
4361 __isl_take isl_map *source, int must,
4363 void *isl_access_info_free(__isl_take isl_access_info *acc);
4365 __isl_give isl_flow *isl_access_info_compute_flow(
4366 __isl_take isl_access_info *acc);
4368 int isl_flow_foreach(__isl_keep isl_flow *deps,
4369 int (*fn)(__isl_take isl_map *dep, int must,
4370 void *dep_user, void *user),
4372 __isl_give isl_map *isl_flow_get_no_source(
4373 __isl_keep isl_flow *deps, int must);
4374 void isl_flow_free(__isl_take isl_flow *deps);
4376 The function C<isl_access_info_compute_flow> performs the actual
4377 dependence analysis. The other functions are used to construct
4378 the input for this function or to read off the output.
4380 The input is collected in an C<isl_access_info>, which can
4381 be created through a call to C<isl_access_info_alloc>.
4382 The arguments to this functions are the sink access relation
4383 C<sink>, a token C<sink_user> used to identify the sink
4384 access to the user, a callback function for specifying the
4385 relative order of source and sink accesses, and the number
4386 of source access relations that will be added.
4387 The callback function has type C<int (*)(void *first, void *second)>.
4388 The function is called with two user supplied tokens identifying
4389 either a source or the sink and it should return the shared nesting
4390 level and the relative order of the two accesses.
4391 In particular, let I<n> be the number of loops shared by
4392 the two accesses. If C<first> precedes C<second> textually,
4393 then the function should return I<2 * n + 1>; otherwise,
4394 it should return I<2 * n>.
4395 The sources can be added to the C<isl_access_info> by performing
4396 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4397 C<must> indicates whether the source is a I<must> access
4398 or a I<may> access. Note that a multi-valued access relation
4399 should only be marked I<must> if every iteration in the domain
4400 of the relation accesses I<all> elements in its image.
4401 The C<source_user> token is again used to identify
4402 the source access. The range of the source access relation
4403 C<source> should have the same dimension as the range
4404 of the sink access relation.
4405 The C<isl_access_info_free> function should usually not be
4406 called explicitly, because it is called implicitly by
4407 C<isl_access_info_compute_flow>.
4409 The result of the dependence analysis is collected in an
4410 C<isl_flow>. There may be elements of
4411 the sink access for which no preceding source access could be
4412 found or for which all preceding sources are I<may> accesses.
4413 The relations containing these elements can be obtained through
4414 calls to C<isl_flow_get_no_source>, the first with C<must> set
4415 and the second with C<must> unset.
4416 In the case of standard flow dependence analysis,
4417 with the sink a read and the sources I<must> writes,
4418 the first relation corresponds to the reads from uninitialized
4419 array elements and the second relation is empty.
4420 The actual flow dependences can be extracted using
4421 C<isl_flow_foreach>. This function will call the user-specified
4422 callback function C<fn> for each B<non-empty> dependence between
4423 a source and the sink. The callback function is called
4424 with four arguments, the actual flow dependence relation
4425 mapping source iterations to sink iterations, a boolean that
4426 indicates whether it is a I<must> or I<may> dependence, a token
4427 identifying the source and an additional C<void *> with value
4428 equal to the third argument of the C<isl_flow_foreach> call.
4429 A dependence is marked I<must> if it originates from a I<must>
4430 source and if it is not followed by any I<may> sources.
4432 After finishing with an C<isl_flow>, the user should call
4433 C<isl_flow_free> to free all associated memory.
4435 A higher-level interface to dependence analysis is provided
4436 by the following function.
4438 #include <isl/flow.h>
4440 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4441 __isl_take isl_union_map *must_source,
4442 __isl_take isl_union_map *may_source,
4443 __isl_take isl_union_map *schedule,
4444 __isl_give isl_union_map **must_dep,
4445 __isl_give isl_union_map **may_dep,
4446 __isl_give isl_union_map **must_no_source,
4447 __isl_give isl_union_map **may_no_source);
4449 The arrays are identified by the tuple names of the ranges
4450 of the accesses. The iteration domains by the tuple names
4451 of the domains of the accesses and of the schedule.
4452 The relative order of the iteration domains is given by the
4453 schedule. The relations returned through C<must_no_source>
4454 and C<may_no_source> are subsets of C<sink>.
4455 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4456 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4457 any of the other arguments is treated as an error.
4459 =head3 Interaction with Dependence Analysis
4461 During the dependence analysis, we frequently need to perform
4462 the following operation. Given a relation between sink iterations
4463 and potential source iterations from a particular source domain,
4464 what is the last potential source iteration corresponding to each
4465 sink iteration. It can sometimes be convenient to adjust
4466 the set of potential source iterations before or after each such operation.
4467 The prototypical example is fuzzy array dataflow analysis,
4468 where we need to analyze if, based on data-dependent constraints,
4469 the sink iteration can ever be executed without one or more of
4470 the corresponding potential source iterations being executed.
4471 If so, we can introduce extra parameters and select an unknown
4472 but fixed source iteration from the potential source iterations.
4473 To be able to perform such manipulations, C<isl> provides the following
4476 #include <isl/flow.h>
4478 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4479 __isl_keep isl_map *source_map,
4480 __isl_keep isl_set *sink, void *source_user,
4482 __isl_give isl_access_info *isl_access_info_set_restrict(
4483 __isl_take isl_access_info *acc,
4484 isl_access_restrict fn, void *user);
4486 The function C<isl_access_info_set_restrict> should be called
4487 before calling C<isl_access_info_compute_flow> and registers a callback function
4488 that will be called any time C<isl> is about to compute the last
4489 potential source. The first argument is the (reverse) proto-dependence,
4490 mapping sink iterations to potential source iterations.
4491 The second argument represents the sink iterations for which
4492 we want to compute the last source iteration.
4493 The third argument is the token corresponding to the source
4494 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4495 The callback is expected to return a restriction on either the input or
4496 the output of the operation computing the last potential source.
4497 If the input needs to be restricted then restrictions are needed
4498 for both the source and the sink iterations. The sink iterations
4499 and the potential source iterations will be intersected with these sets.
4500 If the output needs to be restricted then only a restriction on the source
4501 iterations is required.
4502 If any error occurs, the callback should return C<NULL>.
4503 An C<isl_restriction> object can be created, freed and inspected
4504 using the following functions.
4506 #include <isl/flow.h>
4508 __isl_give isl_restriction *isl_restriction_input(
4509 __isl_take isl_set *source_restr,
4510 __isl_take isl_set *sink_restr);
4511 __isl_give isl_restriction *isl_restriction_output(
4512 __isl_take isl_set *source_restr);
4513 __isl_give isl_restriction *isl_restriction_none(
4514 __isl_take isl_map *source_map);
4515 __isl_give isl_restriction *isl_restriction_empty(
4516 __isl_take isl_map *source_map);
4517 void *isl_restriction_free(
4518 __isl_take isl_restriction *restr);
4519 isl_ctx *isl_restriction_get_ctx(
4520 __isl_keep isl_restriction *restr);
4522 C<isl_restriction_none> and C<isl_restriction_empty> are special
4523 cases of C<isl_restriction_input>. C<isl_restriction_none>
4524 is essentially equivalent to
4526 isl_restriction_input(isl_set_universe(
4527 isl_space_range(isl_map_get_space(source_map))),
4529 isl_space_domain(isl_map_get_space(source_map))));
4531 whereas C<isl_restriction_empty> is essentially equivalent to
4533 isl_restriction_input(isl_set_empty(
4534 isl_space_range(isl_map_get_space(source_map))),
4536 isl_space_domain(isl_map_get_space(source_map))));
4540 B<The functionality described in this section is fairly new
4541 and may be subject to change.>
4543 The following function can be used to compute a schedule
4544 for a union of domains.
4545 By default, the algorithm used to construct the schedule is similar
4546 to that of C<Pluto>.
4547 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4549 The generated schedule respects all C<validity> dependences.
4550 That is, all dependence distances over these dependences in the
4551 scheduled space are lexicographically positive.
4552 The default algorithm tries to minimize the dependence distances over
4553 C<proximity> dependences.
4554 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4555 for groups of domains where the dependence distances have only
4556 non-negative values.
4557 When using Feautrier's algorithm, the C<proximity> dependence
4558 distances are only minimized during the extension to a
4559 full-dimensional schedule.
4561 #include <isl/schedule.h>
4562 __isl_give isl_schedule *isl_union_set_compute_schedule(
4563 __isl_take isl_union_set *domain,
4564 __isl_take isl_union_map *validity,
4565 __isl_take isl_union_map *proximity);
4566 void *isl_schedule_free(__isl_take isl_schedule *sched);
4568 A mapping from the domains to the scheduled space can be obtained
4569 from an C<isl_schedule> using the following function.
4571 __isl_give isl_union_map *isl_schedule_get_map(
4572 __isl_keep isl_schedule *sched);
4574 A representation of the schedule can be printed using
4576 __isl_give isl_printer *isl_printer_print_schedule(
4577 __isl_take isl_printer *p,
4578 __isl_keep isl_schedule *schedule);
4580 A representation of the schedule as a forest of bands can be obtained
4581 using the following function.
4583 __isl_give isl_band_list *isl_schedule_get_band_forest(
4584 __isl_keep isl_schedule *schedule);
4586 The individual bands can be visited in depth-first post-order
4587 using the following function.
4589 #include <isl/schedule.h>
4590 int isl_schedule_foreach_band(
4591 __isl_keep isl_schedule *sched,
4592 int (*fn)(__isl_keep isl_band *band, void *user),
4595 The list can be manipulated as explained in L<"Lists">.
4596 The bands inside the list can be copied and freed using the following
4599 #include <isl/band.h>
4600 __isl_give isl_band *isl_band_copy(
4601 __isl_keep isl_band *band);
4602 void *isl_band_free(__isl_take isl_band *band);
4604 Each band contains zero or more scheduling dimensions.
4605 These are referred to as the members of the band.
4606 The section of the schedule that corresponds to the band is
4607 referred to as the partial schedule of the band.
4608 For those nodes that participate in a band, the outer scheduling
4609 dimensions form the prefix schedule, while the inner scheduling
4610 dimensions form the suffix schedule.
4611 That is, if we take a cut of the band forest, then the union of
4612 the concatenations of the prefix, partial and suffix schedules of
4613 each band in the cut is equal to the entire schedule (modulo
4614 some possible padding at the end with zero scheduling dimensions).
4615 The properties of a band can be inspected using the following functions.
4617 #include <isl/band.h>
4618 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4620 int isl_band_has_children(__isl_keep isl_band *band);
4621 __isl_give isl_band_list *isl_band_get_children(
4622 __isl_keep isl_band *band);
4624 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4625 __isl_keep isl_band *band);
4626 __isl_give isl_union_map *isl_band_get_partial_schedule(
4627 __isl_keep isl_band *band);
4628 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4629 __isl_keep isl_band *band);
4631 int isl_band_n_member(__isl_keep isl_band *band);
4632 int isl_band_member_is_zero_distance(
4633 __isl_keep isl_band *band, int pos);
4635 int isl_band_list_foreach_band(
4636 __isl_keep isl_band_list *list,
4637 int (*fn)(__isl_keep isl_band *band, void *user),
4640 Note that a scheduling dimension is considered to be ``zero
4641 distance'' if it does not carry any proximity dependences
4643 That is, if the dependence distances of the proximity
4644 dependences are all zero in that direction (for fixed
4645 iterations of outer bands).
4646 Like C<isl_schedule_foreach_band>,
4647 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4648 in depth-first post-order.
4650 A band can be tiled using the following function.
4652 #include <isl/band.h>
4653 int isl_band_tile(__isl_keep isl_band *band,
4654 __isl_take isl_vec *sizes);
4656 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4658 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4660 The C<isl_band_tile> function tiles the band using the given tile sizes
4661 inside its schedule.
4662 A new child band is created to represent the point loops and it is
4663 inserted between the modified band and its children.
4664 The C<tile_scale_tile_loops> option specifies whether the tile
4665 loops iterators should be scaled by the tile sizes.
4667 A representation of the band can be printed using
4669 #include <isl/band.h>
4670 __isl_give isl_printer *isl_printer_print_band(
4671 __isl_take isl_printer *p,
4672 __isl_keep isl_band *band);
4676 #include <isl/schedule.h>
4677 int isl_options_set_schedule_max_coefficient(
4678 isl_ctx *ctx, int val);
4679 int isl_options_get_schedule_max_coefficient(
4681 int isl_options_set_schedule_max_constant_term(
4682 isl_ctx *ctx, int val);
4683 int isl_options_get_schedule_max_constant_term(
4685 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4686 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4687 int isl_options_set_schedule_maximize_band_depth(
4688 isl_ctx *ctx, int val);
4689 int isl_options_get_schedule_maximize_band_depth(
4691 int isl_options_set_schedule_outer_zero_distance(
4692 isl_ctx *ctx, int val);
4693 int isl_options_get_schedule_outer_zero_distance(
4695 int isl_options_set_schedule_split_scaled(
4696 isl_ctx *ctx, int val);
4697 int isl_options_get_schedule_split_scaled(
4699 int isl_options_set_schedule_algorithm(
4700 isl_ctx *ctx, int val);
4701 int isl_options_get_schedule_algorithm(
4703 int isl_options_set_schedule_separate_components(
4704 isl_ctx *ctx, int val);
4705 int isl_options_get_schedule_separate_components(
4710 =item * schedule_max_coefficient
4712 This option enforces that the coefficients for variable and parameter
4713 dimensions in the calculated schedule are not larger than the specified value.
4714 This option can significantly increase the speed of the scheduling calculation
4715 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4716 this option does not introduce bounds on the variable or parameter
4719 =item * schedule_max_constant_term
4721 This option enforces that the constant coefficients in the calculated schedule
4722 are not larger than the maximal constant term. This option can significantly
4723 increase the speed of the scheduling calculation and may also prevent fusing of
4724 unrelated dimensions. A value of -1 means that this option does not introduce
4725 bounds on the constant coefficients.
4727 =item * schedule_fuse
4729 This option controls the level of fusion.
4730 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
4731 resulting schedule will be distributed as much as possible.
4732 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
4733 try to fuse loops in the resulting schedule.
4735 =item * schedule_maximize_band_depth
4737 If this option is set, we do not split bands at the point
4738 where we detect splitting is necessary. Instead, we
4739 backtrack and split bands as early as possible. This
4740 reduces the number of splits and maximizes the width of
4741 the bands. Wider bands give more possibilities for tiling.
4742 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
4743 then bands will be split as early as possible, even if there is no need.
4744 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
4746 =item * schedule_outer_zero_distance
4748 If this option is set, then we try to construct schedules
4749 where the outermost scheduling dimension in each band
4750 results in a zero dependence distance over the proximity
4753 =item * schedule_split_scaled
4755 If this option is set, then we try to construct schedules in which the
4756 constant term is split off from the linear part if the linear parts of
4757 the scheduling rows for all nodes in the graphs have a common non-trivial
4759 The constant term is then placed in a separate band and the linear
4762 =item * schedule_algorithm
4764 Selects the scheduling algorithm to be used.
4765 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4766 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4768 =item * schedule_separate_components
4770 If at any point the dependence graph contains any (weakly connected) components,
4771 then these components are scheduled separately.
4772 If this option is not set, then some iterations of the domains
4773 in these components may be scheduled together.
4774 If this option is set, then the components are given consecutive
4779 =head2 Parametric Vertex Enumeration
4781 The parametric vertex enumeration described in this section
4782 is mainly intended to be used internally and by the C<barvinok>
4785 #include <isl/vertices.h>
4786 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4787 __isl_keep isl_basic_set *bset);
4789 The function C<isl_basic_set_compute_vertices> performs the
4790 actual computation of the parametric vertices and the chamber
4791 decomposition and store the result in an C<isl_vertices> object.
4792 This information can be queried by either iterating over all
4793 the vertices or iterating over all the chambers or cells
4794 and then iterating over all vertices that are active on the chamber.
4796 int isl_vertices_foreach_vertex(
4797 __isl_keep isl_vertices *vertices,
4798 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4801 int isl_vertices_foreach_cell(
4802 __isl_keep isl_vertices *vertices,
4803 int (*fn)(__isl_take isl_cell *cell, void *user),
4805 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4806 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4809 Other operations that can be performed on an C<isl_vertices> object are
4812 isl_ctx *isl_vertices_get_ctx(
4813 __isl_keep isl_vertices *vertices);
4814 int isl_vertices_get_n_vertices(
4815 __isl_keep isl_vertices *vertices);
4816 void isl_vertices_free(__isl_take isl_vertices *vertices);
4818 Vertices can be inspected and destroyed using the following functions.
4820 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4821 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4822 __isl_give isl_basic_set *isl_vertex_get_domain(
4823 __isl_keep isl_vertex *vertex);
4824 __isl_give isl_basic_set *isl_vertex_get_expr(
4825 __isl_keep isl_vertex *vertex);
4826 void isl_vertex_free(__isl_take isl_vertex *vertex);
4828 C<isl_vertex_get_expr> returns a singleton parametric set describing
4829 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4831 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4832 B<rational> basic sets, so they should mainly be used for inspection
4833 and should not be mixed with integer sets.
4835 Chambers can be inspected and destroyed using the following functions.
4837 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4838 __isl_give isl_basic_set *isl_cell_get_domain(
4839 __isl_keep isl_cell *cell);
4840 void isl_cell_free(__isl_take isl_cell *cell);
4844 Although C<isl> is mainly meant to be used as a library,
4845 it also contains some basic applications that use some
4846 of the functionality of C<isl>.
4847 The input may be specified in either the L<isl format>
4848 or the L<PolyLib format>.
4850 =head2 C<isl_polyhedron_sample>
4852 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4853 an integer element of the polyhedron, if there is any.
4854 The first column in the output is the denominator and is always
4855 equal to 1. If the polyhedron contains no integer points,
4856 then a vector of length zero is printed.
4860 C<isl_pip> takes the same input as the C<example> program
4861 from the C<piplib> distribution, i.e., a set of constraints
4862 on the parameters, a line containing only -1 and finally a set
4863 of constraints on a parametric polyhedron.
4864 The coefficients of the parameters appear in the last columns
4865 (but before the final constant column).
4866 The output is the lexicographic minimum of the parametric polyhedron.
4867 As C<isl> currently does not have its own output format, the output
4868 is just a dump of the internal state.
4870 =head2 C<isl_polyhedron_minimize>
4872 C<isl_polyhedron_minimize> computes the minimum of some linear
4873 or affine objective function over the integer points in a polyhedron.
4874 If an affine objective function
4875 is given, then the constant should appear in the last column.
4877 =head2 C<isl_polytope_scan>
4879 Given a polytope, C<isl_polytope_scan> prints
4880 all integer points in the polytope.