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);
626 int isl_space_is_range(__isl_keep isl_space *space1,
627 __isl_keep isl_space *space2);
629 C<isl_space_is_domain> checks whether the first argument is equal
630 to the domain of the second argument. This requires in particular that
631 the first argument is a set space and that the second argument
634 It is often useful to create objects that live in the
635 same space as some other object. This can be accomplished
636 by creating the new objects
637 (see L<Creating New Sets and Relations> or
638 L<Creating New (Piecewise) Quasipolynomials>) based on the space
639 of the original object.
642 __isl_give isl_space *isl_basic_set_get_space(
643 __isl_keep isl_basic_set *bset);
644 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
646 #include <isl/union_set.h>
647 __isl_give isl_space *isl_union_set_get_space(
648 __isl_keep isl_union_set *uset);
651 __isl_give isl_space *isl_basic_map_get_space(
652 __isl_keep isl_basic_map *bmap);
653 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
655 #include <isl/union_map.h>
656 __isl_give isl_space *isl_union_map_get_space(
657 __isl_keep isl_union_map *umap);
659 #include <isl/constraint.h>
660 __isl_give isl_space *isl_constraint_get_space(
661 __isl_keep isl_constraint *constraint);
663 #include <isl/polynomial.h>
664 __isl_give isl_space *isl_qpolynomial_get_domain_space(
665 __isl_keep isl_qpolynomial *qp);
666 __isl_give isl_space *isl_qpolynomial_get_space(
667 __isl_keep isl_qpolynomial *qp);
668 __isl_give isl_space *isl_qpolynomial_fold_get_space(
669 __isl_keep isl_qpolynomial_fold *fold);
670 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
671 __isl_keep isl_pw_qpolynomial *pwqp);
672 __isl_give isl_space *isl_pw_qpolynomial_get_space(
673 __isl_keep isl_pw_qpolynomial *pwqp);
674 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
675 __isl_keep isl_pw_qpolynomial_fold *pwf);
676 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
677 __isl_keep isl_pw_qpolynomial_fold *pwf);
678 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
679 __isl_keep isl_union_pw_qpolynomial *upwqp);
680 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
681 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
684 __isl_give isl_space *isl_aff_get_domain_space(
685 __isl_keep isl_aff *aff);
686 __isl_give isl_space *isl_aff_get_space(
687 __isl_keep isl_aff *aff);
688 __isl_give isl_space *isl_pw_aff_get_domain_space(
689 __isl_keep isl_pw_aff *pwaff);
690 __isl_give isl_space *isl_pw_aff_get_space(
691 __isl_keep isl_pw_aff *pwaff);
692 __isl_give isl_space *isl_multi_aff_get_domain_space(
693 __isl_keep isl_multi_aff *maff);
694 __isl_give isl_space *isl_multi_aff_get_space(
695 __isl_keep isl_multi_aff *maff);
696 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
697 __isl_keep isl_pw_multi_aff *pma);
698 __isl_give isl_space *isl_pw_multi_aff_get_space(
699 __isl_keep isl_pw_multi_aff *pma);
700 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
701 __isl_keep isl_union_pw_multi_aff *upma);
703 #include <isl/point.h>
704 __isl_give isl_space *isl_point_get_space(
705 __isl_keep isl_point *pnt);
707 The identifiers or names of the individual dimensions may be set or read off
708 using the following functions.
710 #include <isl/space.h>
711 __isl_give isl_space *isl_space_set_dim_id(
712 __isl_take isl_space *space,
713 enum isl_dim_type type, unsigned pos,
714 __isl_take isl_id *id);
715 int isl_space_has_dim_id(__isl_keep isl_space *space,
716 enum isl_dim_type type, unsigned pos);
717 __isl_give isl_id *isl_space_get_dim_id(
718 __isl_keep isl_space *space,
719 enum isl_dim_type type, unsigned pos);
720 __isl_give isl_space *isl_space_set_dim_name(
721 __isl_take isl_space *space,
722 enum isl_dim_type type, unsigned pos,
723 __isl_keep const char *name);
724 int isl_space_has_dim_name(__isl_keep isl_space *space,
725 enum isl_dim_type type, unsigned pos);
726 __isl_keep const char *isl_space_get_dim_name(
727 __isl_keep isl_space *space,
728 enum isl_dim_type type, unsigned pos);
730 Note that C<isl_space_get_name> returns a pointer to some internal
731 data structure, so the result can only be used while the
732 corresponding C<isl_space> is alive.
733 Also note that every function that operates on two sets or relations
734 requires that both arguments have the same parameters. This also
735 means that if one of the arguments has named parameters, then the
736 other needs to have named parameters too and the names need to match.
737 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
738 arguments may have different parameters (as long as they are named),
739 in which case the result will have as parameters the union of the parameters of
742 Given the identifier or name of a dimension (typically a parameter),
743 its position can be obtained from the following function.
745 #include <isl/space.h>
746 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
747 enum isl_dim_type type, __isl_keep isl_id *id);
748 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
749 enum isl_dim_type type, const char *name);
751 The identifiers or names of entire spaces may be set or read off
752 using the following functions.
754 #include <isl/space.h>
755 __isl_give isl_space *isl_space_set_tuple_id(
756 __isl_take isl_space *space,
757 enum isl_dim_type type, __isl_take isl_id *id);
758 __isl_give isl_space *isl_space_reset_tuple_id(
759 __isl_take isl_space *space, enum isl_dim_type type);
760 int isl_space_has_tuple_id(__isl_keep isl_space *space,
761 enum isl_dim_type type);
762 __isl_give isl_id *isl_space_get_tuple_id(
763 __isl_keep isl_space *space, enum isl_dim_type type);
764 __isl_give isl_space *isl_space_set_tuple_name(
765 __isl_take isl_space *space,
766 enum isl_dim_type type, const char *s);
767 int isl_space_has_tuple_name(__isl_keep isl_space *space,
768 enum isl_dim_type type);
769 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
770 enum isl_dim_type type);
772 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
773 or C<isl_dim_set>. As with C<isl_space_get_name>,
774 the C<isl_space_get_tuple_name> function returns a pointer to some internal
776 Binary operations require the corresponding spaces of their arguments
777 to have the same name.
779 Spaces can be nested. In particular, the domain of a set or
780 the domain or range of a relation can be a nested relation.
781 The following functions can be used to construct and deconstruct
784 #include <isl/space.h>
785 int isl_space_is_wrapping(__isl_keep isl_space *space);
786 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
787 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
789 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
790 be the space of a set, while that of
791 C<isl_space_wrap> should be the space of a relation.
792 Conversely, the output of C<isl_space_unwrap> is the space
793 of a relation, while that of C<isl_space_wrap> is the space of a set.
795 Spaces can be created from other spaces
796 using the following functions.
798 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
799 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
800 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
801 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
802 __isl_give isl_space *isl_space_params(
803 __isl_take isl_space *space);
804 __isl_give isl_space *isl_space_set_from_params(
805 __isl_take isl_space *space);
806 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
807 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
808 __isl_take isl_space *right);
809 __isl_give isl_space *isl_space_align_params(
810 __isl_take isl_space *space1, __isl_take isl_space *space2)
811 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
812 enum isl_dim_type type, unsigned pos, unsigned n);
813 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
814 enum isl_dim_type type, unsigned n);
815 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
816 enum isl_dim_type type, unsigned first, unsigned n);
817 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
818 enum isl_dim_type dst_type, unsigned dst_pos,
819 enum isl_dim_type src_type, unsigned src_pos,
821 __isl_give isl_space *isl_space_map_from_set(
822 __isl_take isl_space *space);
823 __isl_give isl_space *isl_space_map_from_domain_and_range(
824 __isl_take isl_space *domain,
825 __isl_take isl_space *range);
826 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
827 __isl_give isl_space *isl_space_curry(
828 __isl_take isl_space *space);
830 Note that if dimensions are added or removed from a space, then
831 the name and the internal structure are lost.
835 A local space is essentially a space with
836 zero or more existentially quantified variables.
837 The local space of a (constraint of a) basic set or relation can be obtained
838 using the following functions.
840 #include <isl/constraint.h>
841 __isl_give isl_local_space *isl_constraint_get_local_space(
842 __isl_keep isl_constraint *constraint);
845 __isl_give isl_local_space *isl_basic_set_get_local_space(
846 __isl_keep isl_basic_set *bset);
849 __isl_give isl_local_space *isl_basic_map_get_local_space(
850 __isl_keep isl_basic_map *bmap);
852 A new local space can be created from a space using
854 #include <isl/local_space.h>
855 __isl_give isl_local_space *isl_local_space_from_space(
856 __isl_take isl_space *space);
858 They can be inspected, modified, copied and freed using the following functions.
860 #include <isl/local_space.h>
861 isl_ctx *isl_local_space_get_ctx(
862 __isl_keep isl_local_space *ls);
863 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
864 int isl_local_space_dim(__isl_keep isl_local_space *ls,
865 enum isl_dim_type type);
866 int isl_local_space_has_dim_id(
867 __isl_keep isl_local_space *ls,
868 enum isl_dim_type type, unsigned pos);
869 __isl_give isl_id *isl_local_space_get_dim_id(
870 __isl_keep isl_local_space *ls,
871 enum isl_dim_type type, unsigned pos);
872 int isl_local_space_has_dim_name(
873 __isl_keep isl_local_space *ls,
874 enum isl_dim_type type, unsigned pos)
875 const char *isl_local_space_get_dim_name(
876 __isl_keep isl_local_space *ls,
877 enum isl_dim_type type, unsigned pos);
878 __isl_give isl_local_space *isl_local_space_set_dim_name(
879 __isl_take isl_local_space *ls,
880 enum isl_dim_type type, unsigned pos, const char *s);
881 __isl_give isl_local_space *isl_local_space_set_dim_id(
882 __isl_take isl_local_space *ls,
883 enum isl_dim_type type, unsigned pos,
884 __isl_take isl_id *id);
885 __isl_give isl_space *isl_local_space_get_space(
886 __isl_keep isl_local_space *ls);
887 __isl_give isl_aff *isl_local_space_get_div(
888 __isl_keep isl_local_space *ls, int pos);
889 __isl_give isl_local_space *isl_local_space_copy(
890 __isl_keep isl_local_space *ls);
891 void *isl_local_space_free(__isl_take isl_local_space *ls);
893 Two local spaces can be compared using
895 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
896 __isl_keep isl_local_space *ls2);
898 Local spaces can be created from other local spaces
899 using the following functions.
901 __isl_give isl_local_space *isl_local_space_domain(
902 __isl_take isl_local_space *ls);
903 __isl_give isl_local_space *isl_local_space_range(
904 __isl_take isl_local_space *ls);
905 __isl_give isl_local_space *isl_local_space_from_domain(
906 __isl_take isl_local_space *ls);
907 __isl_give isl_local_space *isl_local_space_intersect(
908 __isl_take isl_local_space *ls1,
909 __isl_take isl_local_space *ls2);
910 __isl_give isl_local_space *isl_local_space_add_dims(
911 __isl_take isl_local_space *ls,
912 enum isl_dim_type type, unsigned n);
913 __isl_give isl_local_space *isl_local_space_insert_dims(
914 __isl_take isl_local_space *ls,
915 enum isl_dim_type type, unsigned first, unsigned n);
916 __isl_give isl_local_space *isl_local_space_drop_dims(
917 __isl_take isl_local_space *ls,
918 enum isl_dim_type type, unsigned first, unsigned n);
920 =head2 Input and Output
922 C<isl> supports its own input/output format, which is similar
923 to the C<Omega> format, but also supports the C<PolyLib> format
928 The C<isl> format is similar to that of C<Omega>, but has a different
929 syntax for describing the parameters and allows for the definition
930 of an existentially quantified variable as the integer division
931 of an affine expression.
932 For example, the set of integers C<i> between C<0> and C<n>
933 such that C<i % 10 <= 6> can be described as
935 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
938 A set or relation can have several disjuncts, separated
939 by the keyword C<or>. Each disjunct is either a conjunction
940 of constraints or a projection (C<exists>) of a conjunction
941 of constraints. The constraints are separated by the keyword
944 =head3 C<PolyLib> format
946 If the represented set is a union, then the first line
947 contains a single number representing the number of disjuncts.
948 Otherwise, a line containing the number C<1> is optional.
950 Each disjunct is represented by a matrix of constraints.
951 The first line contains two numbers representing
952 the number of rows and columns,
953 where the number of rows is equal to the number of constraints
954 and the number of columns is equal to two plus the number of variables.
955 The following lines contain the actual rows of the constraint matrix.
956 In each row, the first column indicates whether the constraint
957 is an equality (C<0>) or inequality (C<1>). The final column
958 corresponds to the constant term.
960 If the set is parametric, then the coefficients of the parameters
961 appear in the last columns before the constant column.
962 The coefficients of any existentially quantified variables appear
963 between those of the set variables and those of the parameters.
965 =head3 Extended C<PolyLib> format
967 The extended C<PolyLib> format is nearly identical to the
968 C<PolyLib> format. The only difference is that the line
969 containing the number of rows and columns of a constraint matrix
970 also contains four additional numbers:
971 the number of output dimensions, the number of input dimensions,
972 the number of local dimensions (i.e., the number of existentially
973 quantified variables) and the number of parameters.
974 For sets, the number of ``output'' dimensions is equal
975 to the number of set dimensions, while the number of ``input''
981 __isl_give isl_basic_set *isl_basic_set_read_from_file(
982 isl_ctx *ctx, FILE *input);
983 __isl_give isl_basic_set *isl_basic_set_read_from_str(
984 isl_ctx *ctx, const char *str);
985 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
987 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
991 __isl_give isl_basic_map *isl_basic_map_read_from_file(
992 isl_ctx *ctx, FILE *input);
993 __isl_give isl_basic_map *isl_basic_map_read_from_str(
994 isl_ctx *ctx, const char *str);
995 __isl_give isl_map *isl_map_read_from_file(
996 isl_ctx *ctx, FILE *input);
997 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1000 #include <isl/union_set.h>
1001 __isl_give isl_union_set *isl_union_set_read_from_file(
1002 isl_ctx *ctx, FILE *input);
1003 __isl_give isl_union_set *isl_union_set_read_from_str(
1004 isl_ctx *ctx, const char *str);
1006 #include <isl/union_map.h>
1007 __isl_give isl_union_map *isl_union_map_read_from_file(
1008 isl_ctx *ctx, FILE *input);
1009 __isl_give isl_union_map *isl_union_map_read_from_str(
1010 isl_ctx *ctx, const char *str);
1012 The input format is autodetected and may be either the C<PolyLib> format
1013 or the C<isl> format.
1017 Before anything can be printed, an C<isl_printer> needs to
1020 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1022 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1023 void *isl_printer_free(__isl_take isl_printer *printer);
1024 __isl_give char *isl_printer_get_str(
1025 __isl_keep isl_printer *printer);
1027 The printer can be inspected using the following functions.
1029 FILE *isl_printer_get_file(
1030 __isl_keep isl_printer *printer);
1031 int isl_printer_get_output_format(
1032 __isl_keep isl_printer *p);
1034 The behavior of the printer can be modified in various ways
1036 __isl_give isl_printer *isl_printer_set_output_format(
1037 __isl_take isl_printer *p, int output_format);
1038 __isl_give isl_printer *isl_printer_set_indent(
1039 __isl_take isl_printer *p, int indent);
1040 __isl_give isl_printer *isl_printer_indent(
1041 __isl_take isl_printer *p, int indent);
1042 __isl_give isl_printer *isl_printer_set_prefix(
1043 __isl_take isl_printer *p, const char *prefix);
1044 __isl_give isl_printer *isl_printer_set_suffix(
1045 __isl_take isl_printer *p, const char *suffix);
1047 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1048 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1049 and defaults to C<ISL_FORMAT_ISL>.
1050 Each line in the output is indented by C<indent> (set by
1051 C<isl_printer_set_indent>) spaces
1052 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1053 In the C<PolyLib> format output,
1054 the coefficients of the existentially quantified variables
1055 appear between those of the set variables and those
1057 The function C<isl_printer_indent> increases the indentation
1058 by the specified amount (which may be negative).
1060 To actually print something, use
1062 #include <isl/printer.h>
1063 __isl_give isl_printer *isl_printer_print_double(
1064 __isl_take isl_printer *p, double d);
1066 #include <isl/set.h>
1067 __isl_give isl_printer *isl_printer_print_basic_set(
1068 __isl_take isl_printer *printer,
1069 __isl_keep isl_basic_set *bset);
1070 __isl_give isl_printer *isl_printer_print_set(
1071 __isl_take isl_printer *printer,
1072 __isl_keep isl_set *set);
1074 #include <isl/map.h>
1075 __isl_give isl_printer *isl_printer_print_basic_map(
1076 __isl_take isl_printer *printer,
1077 __isl_keep isl_basic_map *bmap);
1078 __isl_give isl_printer *isl_printer_print_map(
1079 __isl_take isl_printer *printer,
1080 __isl_keep isl_map *map);
1082 #include <isl/union_set.h>
1083 __isl_give isl_printer *isl_printer_print_union_set(
1084 __isl_take isl_printer *p,
1085 __isl_keep isl_union_set *uset);
1087 #include <isl/union_map.h>
1088 __isl_give isl_printer *isl_printer_print_union_map(
1089 __isl_take isl_printer *p,
1090 __isl_keep isl_union_map *umap);
1092 When called on a file printer, the following function flushes
1093 the file. When called on a string printer, the buffer is cleared.
1095 __isl_give isl_printer *isl_printer_flush(
1096 __isl_take isl_printer *p);
1098 =head2 Creating New Sets and Relations
1100 C<isl> has functions for creating some standard sets and relations.
1104 =item * Empty sets and relations
1106 __isl_give isl_basic_set *isl_basic_set_empty(
1107 __isl_take isl_space *space);
1108 __isl_give isl_basic_map *isl_basic_map_empty(
1109 __isl_take isl_space *space);
1110 __isl_give isl_set *isl_set_empty(
1111 __isl_take isl_space *space);
1112 __isl_give isl_map *isl_map_empty(
1113 __isl_take isl_space *space);
1114 __isl_give isl_union_set *isl_union_set_empty(
1115 __isl_take isl_space *space);
1116 __isl_give isl_union_map *isl_union_map_empty(
1117 __isl_take isl_space *space);
1119 For C<isl_union_set>s and C<isl_union_map>s, the space
1120 is only used to specify the parameters.
1122 =item * Universe sets and relations
1124 __isl_give isl_basic_set *isl_basic_set_universe(
1125 __isl_take isl_space *space);
1126 __isl_give isl_basic_map *isl_basic_map_universe(
1127 __isl_take isl_space *space);
1128 __isl_give isl_set *isl_set_universe(
1129 __isl_take isl_space *space);
1130 __isl_give isl_map *isl_map_universe(
1131 __isl_take isl_space *space);
1132 __isl_give isl_union_set *isl_union_set_universe(
1133 __isl_take isl_union_set *uset);
1134 __isl_give isl_union_map *isl_union_map_universe(
1135 __isl_take isl_union_map *umap);
1137 The sets and relations constructed by the functions above
1138 contain all integer values, while those constructed by the
1139 functions below only contain non-negative values.
1141 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1142 __isl_take isl_space *space);
1143 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1144 __isl_take isl_space *space);
1145 __isl_give isl_set *isl_set_nat_universe(
1146 __isl_take isl_space *space);
1147 __isl_give isl_map *isl_map_nat_universe(
1148 __isl_take isl_space *space);
1150 =item * Identity relations
1152 __isl_give isl_basic_map *isl_basic_map_identity(
1153 __isl_take isl_space *space);
1154 __isl_give isl_map *isl_map_identity(
1155 __isl_take isl_space *space);
1157 The number of input and output dimensions in C<space> needs
1160 =item * Lexicographic order
1162 __isl_give isl_map *isl_map_lex_lt(
1163 __isl_take isl_space *set_space);
1164 __isl_give isl_map *isl_map_lex_le(
1165 __isl_take isl_space *set_space);
1166 __isl_give isl_map *isl_map_lex_gt(
1167 __isl_take isl_space *set_space);
1168 __isl_give isl_map *isl_map_lex_ge(
1169 __isl_take isl_space *set_space);
1170 __isl_give isl_map *isl_map_lex_lt_first(
1171 __isl_take isl_space *space, unsigned n);
1172 __isl_give isl_map *isl_map_lex_le_first(
1173 __isl_take isl_space *space, unsigned n);
1174 __isl_give isl_map *isl_map_lex_gt_first(
1175 __isl_take isl_space *space, unsigned n);
1176 __isl_give isl_map *isl_map_lex_ge_first(
1177 __isl_take isl_space *space, unsigned n);
1179 The first four functions take a space for a B<set>
1180 and return relations that express that the elements in the domain
1181 are lexicographically less
1182 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1183 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1184 than the elements in the range.
1185 The last four functions take a space for a map
1186 and return relations that express that the first C<n> dimensions
1187 in the domain are lexicographically less
1188 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1189 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1190 than the first C<n> dimensions in the range.
1194 A basic set or relation can be converted to a set or relation
1195 using the following functions.
1197 __isl_give isl_set *isl_set_from_basic_set(
1198 __isl_take isl_basic_set *bset);
1199 __isl_give isl_map *isl_map_from_basic_map(
1200 __isl_take isl_basic_map *bmap);
1202 Sets and relations can be converted to union sets and relations
1203 using the following functions.
1205 __isl_give isl_union_set *isl_union_set_from_basic_set(
1206 __isl_take isl_basic_set *bset);
1207 __isl_give isl_union_map *isl_union_map_from_basic_map(
1208 __isl_take isl_basic_map *bmap);
1209 __isl_give isl_union_set *isl_union_set_from_set(
1210 __isl_take isl_set *set);
1211 __isl_give isl_union_map *isl_union_map_from_map(
1212 __isl_take isl_map *map);
1214 The inverse conversions below can only be used if the input
1215 union set or relation is known to contain elements in exactly one
1218 __isl_give isl_set *isl_set_from_union_set(
1219 __isl_take isl_union_set *uset);
1220 __isl_give isl_map *isl_map_from_union_map(
1221 __isl_take isl_union_map *umap);
1223 A zero-dimensional set can be constructed on a given parameter domain
1224 using the following function.
1226 __isl_give isl_set *isl_set_from_params(
1227 __isl_take isl_set *set);
1229 Sets and relations can be copied and freed again using the following
1232 __isl_give isl_basic_set *isl_basic_set_copy(
1233 __isl_keep isl_basic_set *bset);
1234 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1235 __isl_give isl_union_set *isl_union_set_copy(
1236 __isl_keep isl_union_set *uset);
1237 __isl_give isl_basic_map *isl_basic_map_copy(
1238 __isl_keep isl_basic_map *bmap);
1239 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1240 __isl_give isl_union_map *isl_union_map_copy(
1241 __isl_keep isl_union_map *umap);
1242 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1243 void *isl_set_free(__isl_take isl_set *set);
1244 void *isl_union_set_free(__isl_take isl_union_set *uset);
1245 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1246 void isl_map_free(__isl_take isl_map *map);
1247 void *isl_union_map_free(__isl_take isl_union_map *umap);
1249 Other sets and relations can be constructed by starting
1250 from a universe set or relation, adding equality and/or
1251 inequality constraints and then projecting out the
1252 existentially quantified variables, if any.
1253 Constraints can be constructed, manipulated and
1254 added to (or removed from) (basic) sets and relations
1255 using the following functions.
1257 #include <isl/constraint.h>
1258 __isl_give isl_constraint *isl_equality_alloc(
1259 __isl_take isl_local_space *ls);
1260 __isl_give isl_constraint *isl_inequality_alloc(
1261 __isl_take isl_local_space *ls);
1262 __isl_give isl_constraint *isl_constraint_set_constant(
1263 __isl_take isl_constraint *constraint, isl_int v);
1264 __isl_give isl_constraint *isl_constraint_set_constant_si(
1265 __isl_take isl_constraint *constraint, int v);
1266 __isl_give isl_constraint *isl_constraint_set_coefficient(
1267 __isl_take isl_constraint *constraint,
1268 enum isl_dim_type type, int pos, isl_int v);
1269 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1270 __isl_take isl_constraint *constraint,
1271 enum isl_dim_type type, int pos, int v);
1272 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1273 __isl_take isl_basic_map *bmap,
1274 __isl_take isl_constraint *constraint);
1275 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1276 __isl_take isl_basic_set *bset,
1277 __isl_take isl_constraint *constraint);
1278 __isl_give isl_map *isl_map_add_constraint(
1279 __isl_take isl_map *map,
1280 __isl_take isl_constraint *constraint);
1281 __isl_give isl_set *isl_set_add_constraint(
1282 __isl_take isl_set *set,
1283 __isl_take isl_constraint *constraint);
1284 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1285 __isl_take isl_basic_set *bset,
1286 __isl_take isl_constraint *constraint);
1288 For example, to create a set containing the even integers
1289 between 10 and 42, you would use the following code.
1292 isl_local_space *ls;
1294 isl_basic_set *bset;
1296 space = isl_space_set_alloc(ctx, 0, 2);
1297 bset = isl_basic_set_universe(isl_space_copy(space));
1298 ls = isl_local_space_from_space(space);
1300 c = isl_equality_alloc(isl_local_space_copy(ls));
1301 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1302 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1303 bset = isl_basic_set_add_constraint(bset, c);
1305 c = isl_inequality_alloc(isl_local_space_copy(ls));
1306 c = isl_constraint_set_constant_si(c, -10);
1307 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1308 bset = isl_basic_set_add_constraint(bset, c);
1310 c = isl_inequality_alloc(ls);
1311 c = isl_constraint_set_constant_si(c, 42);
1312 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1313 bset = isl_basic_set_add_constraint(bset, c);
1315 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1319 isl_basic_set *bset;
1320 bset = isl_basic_set_read_from_str(ctx,
1321 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1323 A basic set or relation can also be constructed from two matrices
1324 describing the equalities and the inequalities.
1326 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1327 __isl_take isl_space *space,
1328 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1329 enum isl_dim_type c1,
1330 enum isl_dim_type c2, enum isl_dim_type c3,
1331 enum isl_dim_type c4);
1332 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1333 __isl_take isl_space *space,
1334 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1335 enum isl_dim_type c1,
1336 enum isl_dim_type c2, enum isl_dim_type c3,
1337 enum isl_dim_type c4, enum isl_dim_type c5);
1339 The C<isl_dim_type> arguments indicate the order in which
1340 different kinds of variables appear in the input matrices
1341 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1342 C<isl_dim_set> and C<isl_dim_div> for sets and
1343 of C<isl_dim_cst>, C<isl_dim_param>,
1344 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1346 A (basic or union) set or relation can also be constructed from a
1347 (union) (piecewise) (multiple) affine expression
1348 or a list of affine expressions
1349 (See L<"Piecewise Quasi Affine Expressions"> and
1350 L<"Piecewise Multiple Quasi Affine Expressions">).
1352 __isl_give isl_basic_map *isl_basic_map_from_aff(
1353 __isl_take isl_aff *aff);
1354 __isl_give isl_map *isl_map_from_aff(
1355 __isl_take isl_aff *aff);
1356 __isl_give isl_set *isl_set_from_pw_aff(
1357 __isl_take isl_pw_aff *pwaff);
1358 __isl_give isl_map *isl_map_from_pw_aff(
1359 __isl_take isl_pw_aff *pwaff);
1360 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1361 __isl_take isl_space *domain_space,
1362 __isl_take isl_aff_list *list);
1363 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1364 __isl_take isl_multi_aff *maff)
1365 __isl_give isl_map *isl_map_from_multi_aff(
1366 __isl_take isl_multi_aff *maff)
1367 __isl_give isl_set *isl_set_from_pw_multi_aff(
1368 __isl_take isl_pw_multi_aff *pma);
1369 __isl_give isl_map *isl_map_from_pw_multi_aff(
1370 __isl_take isl_pw_multi_aff *pma);
1371 __isl_give isl_union_map *
1372 isl_union_map_from_union_pw_multi_aff(
1373 __isl_take isl_union_pw_multi_aff *upma);
1375 The C<domain_dim> argument describes the domain of the resulting
1376 basic relation. It is required because the C<list> may consist
1377 of zero affine expressions.
1379 =head2 Inspecting Sets and Relations
1381 Usually, the user should not have to care about the actual constraints
1382 of the sets and maps, but should instead apply the abstract operations
1383 explained in the following sections.
1384 Occasionally, however, it may be required to inspect the individual
1385 coefficients of the constraints. This section explains how to do so.
1386 In these cases, it may also be useful to have C<isl> compute
1387 an explicit representation of the existentially quantified variables.
1389 __isl_give isl_set *isl_set_compute_divs(
1390 __isl_take isl_set *set);
1391 __isl_give isl_map *isl_map_compute_divs(
1392 __isl_take isl_map *map);
1393 __isl_give isl_union_set *isl_union_set_compute_divs(
1394 __isl_take isl_union_set *uset);
1395 __isl_give isl_union_map *isl_union_map_compute_divs(
1396 __isl_take isl_union_map *umap);
1398 This explicit representation defines the existentially quantified
1399 variables as integer divisions of the other variables, possibly
1400 including earlier existentially quantified variables.
1401 An explicitly represented existentially quantified variable therefore
1402 has a unique value when the values of the other variables are known.
1403 If, furthermore, the same existentials, i.e., existentials
1404 with the same explicit representations, should appear in the
1405 same order in each of the disjuncts of a set or map, then the user should call
1406 either of the following functions.
1408 __isl_give isl_set *isl_set_align_divs(
1409 __isl_take isl_set *set);
1410 __isl_give isl_map *isl_map_align_divs(
1411 __isl_take isl_map *map);
1413 Alternatively, the existentially quantified variables can be removed
1414 using the following functions, which compute an overapproximation.
1416 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1417 __isl_take isl_basic_set *bset);
1418 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1419 __isl_take isl_basic_map *bmap);
1420 __isl_give isl_set *isl_set_remove_divs(
1421 __isl_take isl_set *set);
1422 __isl_give isl_map *isl_map_remove_divs(
1423 __isl_take isl_map *map);
1425 It is also possible to only remove those divs that are defined
1426 in terms of a given range of dimensions or only those for which
1427 no explicit representation is known.
1429 __isl_give isl_basic_set *
1430 isl_basic_set_remove_divs_involving_dims(
1431 __isl_take isl_basic_set *bset,
1432 enum isl_dim_type type,
1433 unsigned first, unsigned n);
1434 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1435 __isl_take isl_set *set, enum isl_dim_type type,
1436 unsigned first, unsigned n);
1437 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1438 __isl_take isl_map *map, enum isl_dim_type type,
1439 unsigned first, unsigned n);
1441 __isl_give isl_set *isl_set_remove_unknown_divs(
1442 __isl_take isl_set *set);
1443 __isl_give isl_map *isl_map_remove_unknown_divs(
1444 __isl_take isl_map *map);
1446 To iterate over all the sets or maps in a union set or map, use
1448 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1449 int (*fn)(__isl_take isl_set *set, void *user),
1451 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1452 int (*fn)(__isl_take isl_map *map, void *user),
1455 The number of sets or maps in a union set or map can be obtained
1458 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1459 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1461 To extract the set or map in a given space from a union, use
1463 __isl_give isl_set *isl_union_set_extract_set(
1464 __isl_keep isl_union_set *uset,
1465 __isl_take isl_space *space);
1466 __isl_give isl_map *isl_union_map_extract_map(
1467 __isl_keep isl_union_map *umap,
1468 __isl_take isl_space *space);
1470 To iterate over all the basic sets or maps in a set or map, use
1472 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1473 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1475 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1476 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1479 The callback function C<fn> should return 0 if successful and
1480 -1 if an error occurs. In the latter case, or if any other error
1481 occurs, the above functions will return -1.
1483 It should be noted that C<isl> does not guarantee that
1484 the basic sets or maps passed to C<fn> are disjoint.
1485 If this is required, then the user should call one of
1486 the following functions first.
1488 __isl_give isl_set *isl_set_make_disjoint(
1489 __isl_take isl_set *set);
1490 __isl_give isl_map *isl_map_make_disjoint(
1491 __isl_take isl_map *map);
1493 The number of basic sets in a set can be obtained
1496 int isl_set_n_basic_set(__isl_keep isl_set *set);
1498 To iterate over the constraints of a basic set or map, use
1500 #include <isl/constraint.h>
1502 int isl_basic_set_n_constraint(
1503 __isl_keep isl_basic_set *bset);
1504 int isl_basic_set_foreach_constraint(
1505 __isl_keep isl_basic_set *bset,
1506 int (*fn)(__isl_take isl_constraint *c, void *user),
1508 int isl_basic_map_foreach_constraint(
1509 __isl_keep isl_basic_map *bmap,
1510 int (*fn)(__isl_take isl_constraint *c, void *user),
1512 void *isl_constraint_free(__isl_take isl_constraint *c);
1514 Again, the callback function C<fn> should return 0 if successful and
1515 -1 if an error occurs. In the latter case, or if any other error
1516 occurs, the above functions will return -1.
1517 The constraint C<c> represents either an equality or an inequality.
1518 Use the following function to find out whether a constraint
1519 represents an equality. If not, it represents an inequality.
1521 int isl_constraint_is_equality(
1522 __isl_keep isl_constraint *constraint);
1524 The coefficients of the constraints can be inspected using
1525 the following functions.
1527 int isl_constraint_is_lower_bound(
1528 __isl_keep isl_constraint *constraint,
1529 enum isl_dim_type type, unsigned pos);
1530 int isl_constraint_is_upper_bound(
1531 __isl_keep isl_constraint *constraint,
1532 enum isl_dim_type type, unsigned pos);
1533 void isl_constraint_get_constant(
1534 __isl_keep isl_constraint *constraint, isl_int *v);
1535 void isl_constraint_get_coefficient(
1536 __isl_keep isl_constraint *constraint,
1537 enum isl_dim_type type, int pos, isl_int *v);
1538 int isl_constraint_involves_dims(
1539 __isl_keep isl_constraint *constraint,
1540 enum isl_dim_type type, unsigned first, unsigned n);
1542 The explicit representations of the existentially quantified
1543 variables can be inspected using the following function.
1544 Note that the user is only allowed to use this function
1545 if the inspected set or map is the result of a call
1546 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1547 The existentially quantified variable is equal to the floor
1548 of the returned affine expression. The affine expression
1549 itself can be inspected using the functions in
1550 L<"Piecewise Quasi Affine Expressions">.
1552 __isl_give isl_aff *isl_constraint_get_div(
1553 __isl_keep isl_constraint *constraint, int pos);
1555 To obtain the constraints of a basic set or map in matrix
1556 form, use the following functions.
1558 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1559 __isl_keep isl_basic_set *bset,
1560 enum isl_dim_type c1, enum isl_dim_type c2,
1561 enum isl_dim_type c3, enum isl_dim_type c4);
1562 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1563 __isl_keep isl_basic_set *bset,
1564 enum isl_dim_type c1, enum isl_dim_type c2,
1565 enum isl_dim_type c3, enum isl_dim_type c4);
1566 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1567 __isl_keep isl_basic_map *bmap,
1568 enum isl_dim_type c1,
1569 enum isl_dim_type c2, enum isl_dim_type c3,
1570 enum isl_dim_type c4, enum isl_dim_type c5);
1571 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1572 __isl_keep isl_basic_map *bmap,
1573 enum isl_dim_type c1,
1574 enum isl_dim_type c2, enum isl_dim_type c3,
1575 enum isl_dim_type c4, enum isl_dim_type c5);
1577 The C<isl_dim_type> arguments dictate the order in which
1578 different kinds of variables appear in the resulting matrix
1579 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1580 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1582 The number of parameters, input, output or set dimensions can
1583 be obtained using the following functions.
1585 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1586 enum isl_dim_type type);
1587 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1588 enum isl_dim_type type);
1589 unsigned isl_set_dim(__isl_keep isl_set *set,
1590 enum isl_dim_type type);
1591 unsigned isl_map_dim(__isl_keep isl_map *map,
1592 enum isl_dim_type type);
1594 To check whether the description of a set or relation depends
1595 on one or more given dimensions, it is not necessary to iterate over all
1596 constraints. Instead the following functions can be used.
1598 int isl_basic_set_involves_dims(
1599 __isl_keep isl_basic_set *bset,
1600 enum isl_dim_type type, unsigned first, unsigned n);
1601 int isl_set_involves_dims(__isl_keep isl_set *set,
1602 enum isl_dim_type type, unsigned first, unsigned n);
1603 int isl_basic_map_involves_dims(
1604 __isl_keep isl_basic_map *bmap,
1605 enum isl_dim_type type, unsigned first, unsigned n);
1606 int isl_map_involves_dims(__isl_keep isl_map *map,
1607 enum isl_dim_type type, unsigned first, unsigned n);
1609 Similarly, the following functions can be used to check whether
1610 a given dimension is involved in any lower or upper bound.
1612 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1613 enum isl_dim_type type, unsigned pos);
1614 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1615 enum isl_dim_type type, unsigned pos);
1617 The identifiers or names of the domain and range spaces of a set
1618 or relation can be read off or set using the following functions.
1620 __isl_give isl_set *isl_set_set_tuple_id(
1621 __isl_take isl_set *set, __isl_take isl_id *id);
1622 __isl_give isl_set *isl_set_reset_tuple_id(
1623 __isl_take isl_set *set);
1624 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1625 __isl_give isl_id *isl_set_get_tuple_id(
1626 __isl_keep isl_set *set);
1627 __isl_give isl_map *isl_map_set_tuple_id(
1628 __isl_take isl_map *map, enum isl_dim_type type,
1629 __isl_take isl_id *id);
1630 __isl_give isl_map *isl_map_reset_tuple_id(
1631 __isl_take isl_map *map, enum isl_dim_type type);
1632 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1633 enum isl_dim_type type);
1634 __isl_give isl_id *isl_map_get_tuple_id(
1635 __isl_keep isl_map *map, enum isl_dim_type type);
1637 const char *isl_basic_set_get_tuple_name(
1638 __isl_keep isl_basic_set *bset);
1639 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1640 __isl_take isl_basic_set *set, const char *s);
1641 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1642 const char *isl_set_get_tuple_name(
1643 __isl_keep isl_set *set);
1644 const char *isl_basic_map_get_tuple_name(
1645 __isl_keep isl_basic_map *bmap,
1646 enum isl_dim_type type);
1647 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1648 __isl_take isl_basic_map *bmap,
1649 enum isl_dim_type type, const char *s);
1650 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1651 enum isl_dim_type type);
1652 const char *isl_map_get_tuple_name(
1653 __isl_keep isl_map *map,
1654 enum isl_dim_type type);
1656 As with C<isl_space_get_tuple_name>, the value returned points to
1657 an internal data structure.
1658 The identifiers, positions or names of individual dimensions can be
1659 read off using the following functions.
1661 __isl_give isl_id *isl_basic_set_get_dim_id(
1662 __isl_keep isl_basic_set *bset,
1663 enum isl_dim_type type, unsigned pos);
1664 __isl_give isl_set *isl_set_set_dim_id(
1665 __isl_take isl_set *set, enum isl_dim_type type,
1666 unsigned pos, __isl_take isl_id *id);
1667 int isl_set_has_dim_id(__isl_keep isl_set *set,
1668 enum isl_dim_type type, unsigned pos);
1669 __isl_give isl_id *isl_set_get_dim_id(
1670 __isl_keep isl_set *set, enum isl_dim_type type,
1672 int isl_basic_map_has_dim_id(
1673 __isl_keep isl_basic_map *bmap,
1674 enum isl_dim_type type, unsigned pos);
1675 __isl_give isl_map *isl_map_set_dim_id(
1676 __isl_take isl_map *map, enum isl_dim_type type,
1677 unsigned pos, __isl_take isl_id *id);
1678 int isl_map_has_dim_id(__isl_keep isl_map *map,
1679 enum isl_dim_type type, unsigned pos);
1680 __isl_give isl_id *isl_map_get_dim_id(
1681 __isl_keep isl_map *map, enum isl_dim_type type,
1684 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1685 enum isl_dim_type type, __isl_keep isl_id *id);
1686 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1687 enum isl_dim_type type, __isl_keep isl_id *id);
1688 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1689 enum isl_dim_type type, const char *name);
1690 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1691 enum isl_dim_type type, const char *name);
1693 const char *isl_constraint_get_dim_name(
1694 __isl_keep isl_constraint *constraint,
1695 enum isl_dim_type type, unsigned pos);
1696 const char *isl_basic_set_get_dim_name(
1697 __isl_keep isl_basic_set *bset,
1698 enum isl_dim_type type, unsigned pos);
1699 int isl_set_has_dim_name(__isl_keep isl_set *set,
1700 enum isl_dim_type type, unsigned pos);
1701 const char *isl_set_get_dim_name(
1702 __isl_keep isl_set *set,
1703 enum isl_dim_type type, unsigned pos);
1704 const char *isl_basic_map_get_dim_name(
1705 __isl_keep isl_basic_map *bmap,
1706 enum isl_dim_type type, unsigned pos);
1707 int isl_map_has_dim_name(__isl_keep isl_map *map,
1708 enum isl_dim_type type, unsigned pos);
1709 const char *isl_map_get_dim_name(
1710 __isl_keep isl_map *map,
1711 enum isl_dim_type type, unsigned pos);
1713 These functions are mostly useful to obtain the identifiers, positions
1714 or names of the parameters. Identifiers of individual dimensions are
1715 essentially only useful for printing. They are ignored by all other
1716 operations and may not be preserved across those operations.
1720 =head3 Unary Properties
1726 The following functions test whether the given set or relation
1727 contains any integer points. The ``plain'' variants do not perform
1728 any computations, but simply check if the given set or relation
1729 is already known to be empty.
1731 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1732 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1733 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1734 int isl_set_is_empty(__isl_keep isl_set *set);
1735 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1736 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1737 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1738 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1739 int isl_map_is_empty(__isl_keep isl_map *map);
1740 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1742 =item * Universality
1744 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1745 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1746 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1748 =item * Single-valuedness
1750 int isl_basic_map_is_single_valued(
1751 __isl_keep isl_basic_map *bmap);
1752 int isl_map_plain_is_single_valued(
1753 __isl_keep isl_map *map);
1754 int isl_map_is_single_valued(__isl_keep isl_map *map);
1755 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1759 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1760 int isl_map_is_injective(__isl_keep isl_map *map);
1761 int isl_union_map_plain_is_injective(
1762 __isl_keep isl_union_map *umap);
1763 int isl_union_map_is_injective(
1764 __isl_keep isl_union_map *umap);
1768 int isl_map_is_bijective(__isl_keep isl_map *map);
1769 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1773 int isl_basic_map_plain_is_fixed(
1774 __isl_keep isl_basic_map *bmap,
1775 enum isl_dim_type type, unsigned pos,
1777 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1778 enum isl_dim_type type, unsigned pos,
1780 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1781 enum isl_dim_type type, unsigned pos,
1784 Check if the relation obviously lies on a hyperplane where the given dimension
1785 has a fixed value and if so, return that value in C<*val>.
1789 To check whether a set is a parameter domain, use this function:
1791 int isl_set_is_params(__isl_keep isl_set *set);
1792 int isl_union_set_is_params(
1793 __isl_keep isl_union_set *uset);
1797 The following functions check whether the domain of the given
1798 (basic) set is a wrapped relation.
1800 int isl_basic_set_is_wrapping(
1801 __isl_keep isl_basic_set *bset);
1802 int isl_set_is_wrapping(__isl_keep isl_set *set);
1804 =item * Internal Product
1806 int isl_basic_map_can_zip(
1807 __isl_keep isl_basic_map *bmap);
1808 int isl_map_can_zip(__isl_keep isl_map *map);
1810 Check whether the product of domain and range of the given relation
1812 i.e., whether both domain and range are nested relations.
1816 int isl_basic_map_can_curry(
1817 __isl_keep isl_basic_map *bmap);
1818 int isl_map_can_curry(__isl_keep isl_map *map);
1820 Check whether the domain of the (basic) relation is a wrapped relation.
1824 =head3 Binary Properties
1830 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1831 __isl_keep isl_set *set2);
1832 int isl_set_is_equal(__isl_keep isl_set *set1,
1833 __isl_keep isl_set *set2);
1834 int isl_union_set_is_equal(
1835 __isl_keep isl_union_set *uset1,
1836 __isl_keep isl_union_set *uset2);
1837 int isl_basic_map_is_equal(
1838 __isl_keep isl_basic_map *bmap1,
1839 __isl_keep isl_basic_map *bmap2);
1840 int isl_map_is_equal(__isl_keep isl_map *map1,
1841 __isl_keep isl_map *map2);
1842 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1843 __isl_keep isl_map *map2);
1844 int isl_union_map_is_equal(
1845 __isl_keep isl_union_map *umap1,
1846 __isl_keep isl_union_map *umap2);
1848 =item * Disjointness
1850 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1851 __isl_keep isl_set *set2);
1855 int isl_basic_set_is_subset(
1856 __isl_keep isl_basic_set *bset1,
1857 __isl_keep isl_basic_set *bset2);
1858 int isl_set_is_subset(__isl_keep isl_set *set1,
1859 __isl_keep isl_set *set2);
1860 int isl_set_is_strict_subset(
1861 __isl_keep isl_set *set1,
1862 __isl_keep isl_set *set2);
1863 int isl_union_set_is_subset(
1864 __isl_keep isl_union_set *uset1,
1865 __isl_keep isl_union_set *uset2);
1866 int isl_union_set_is_strict_subset(
1867 __isl_keep isl_union_set *uset1,
1868 __isl_keep isl_union_set *uset2);
1869 int isl_basic_map_is_subset(
1870 __isl_keep isl_basic_map *bmap1,
1871 __isl_keep isl_basic_map *bmap2);
1872 int isl_basic_map_is_strict_subset(
1873 __isl_keep isl_basic_map *bmap1,
1874 __isl_keep isl_basic_map *bmap2);
1875 int isl_map_is_subset(
1876 __isl_keep isl_map *map1,
1877 __isl_keep isl_map *map2);
1878 int isl_map_is_strict_subset(
1879 __isl_keep isl_map *map1,
1880 __isl_keep isl_map *map2);
1881 int isl_union_map_is_subset(
1882 __isl_keep isl_union_map *umap1,
1883 __isl_keep isl_union_map *umap2);
1884 int isl_union_map_is_strict_subset(
1885 __isl_keep isl_union_map *umap1,
1886 __isl_keep isl_union_map *umap2);
1888 Check whether the first argument is a (strict) subset of the
1893 =head2 Unary Operations
1899 __isl_give isl_set *isl_set_complement(
1900 __isl_take isl_set *set);
1901 __isl_give isl_map *isl_map_complement(
1902 __isl_take isl_map *map);
1906 __isl_give isl_basic_map *isl_basic_map_reverse(
1907 __isl_take isl_basic_map *bmap);
1908 __isl_give isl_map *isl_map_reverse(
1909 __isl_take isl_map *map);
1910 __isl_give isl_union_map *isl_union_map_reverse(
1911 __isl_take isl_union_map *umap);
1915 __isl_give isl_basic_set *isl_basic_set_project_out(
1916 __isl_take isl_basic_set *bset,
1917 enum isl_dim_type type, unsigned first, unsigned n);
1918 __isl_give isl_basic_map *isl_basic_map_project_out(
1919 __isl_take isl_basic_map *bmap,
1920 enum isl_dim_type type, unsigned first, unsigned n);
1921 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1922 enum isl_dim_type type, unsigned first, unsigned n);
1923 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1924 enum isl_dim_type type, unsigned first, unsigned n);
1925 __isl_give isl_basic_set *isl_basic_set_params(
1926 __isl_take isl_basic_set *bset);
1927 __isl_give isl_basic_set *isl_basic_map_domain(
1928 __isl_take isl_basic_map *bmap);
1929 __isl_give isl_basic_set *isl_basic_map_range(
1930 __isl_take isl_basic_map *bmap);
1931 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1932 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1933 __isl_give isl_set *isl_map_domain(
1934 __isl_take isl_map *bmap);
1935 __isl_give isl_set *isl_map_range(
1936 __isl_take isl_map *map);
1937 __isl_give isl_set *isl_union_set_params(
1938 __isl_take isl_union_set *uset);
1939 __isl_give isl_set *isl_union_map_params(
1940 __isl_take isl_union_map *umap);
1941 __isl_give isl_union_set *isl_union_map_domain(
1942 __isl_take isl_union_map *umap);
1943 __isl_give isl_union_set *isl_union_map_range(
1944 __isl_take isl_union_map *umap);
1946 __isl_give isl_basic_map *isl_basic_map_domain_map(
1947 __isl_take isl_basic_map *bmap);
1948 __isl_give isl_basic_map *isl_basic_map_range_map(
1949 __isl_take isl_basic_map *bmap);
1950 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1951 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1952 __isl_give isl_union_map *isl_union_map_domain_map(
1953 __isl_take isl_union_map *umap);
1954 __isl_give isl_union_map *isl_union_map_range_map(
1955 __isl_take isl_union_map *umap);
1957 The functions above construct a (basic, regular or union) relation
1958 that maps (a wrapped version of) the input relation to its domain or range.
1962 __isl_give isl_basic_set *isl_basic_set_eliminate(
1963 __isl_take isl_basic_set *bset,
1964 enum isl_dim_type type,
1965 unsigned first, unsigned n);
1966 __isl_give isl_set *isl_set_eliminate(
1967 __isl_take isl_set *set, enum isl_dim_type type,
1968 unsigned first, unsigned n);
1969 __isl_give isl_basic_map *isl_basic_map_eliminate(
1970 __isl_take isl_basic_map *bmap,
1971 enum isl_dim_type type,
1972 unsigned first, unsigned n);
1973 __isl_give isl_map *isl_map_eliminate(
1974 __isl_take isl_map *map, enum isl_dim_type type,
1975 unsigned first, unsigned n);
1977 Eliminate the coefficients for the given dimensions from the constraints,
1978 without removing the dimensions.
1982 __isl_give isl_basic_set *isl_basic_set_fix(
1983 __isl_take isl_basic_set *bset,
1984 enum isl_dim_type type, unsigned pos,
1986 __isl_give isl_basic_set *isl_basic_set_fix_si(
1987 __isl_take isl_basic_set *bset,
1988 enum isl_dim_type type, unsigned pos, int value);
1989 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1990 enum isl_dim_type type, unsigned pos,
1992 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1993 enum isl_dim_type type, unsigned pos, int value);
1994 __isl_give isl_basic_map *isl_basic_map_fix_si(
1995 __isl_take isl_basic_map *bmap,
1996 enum isl_dim_type type, unsigned pos, int value);
1997 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1998 enum isl_dim_type type, unsigned pos, int value);
2000 Intersect the set or relation with the hyperplane where the given
2001 dimension has the fixed given value.
2003 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2004 __isl_take isl_basic_map *bmap,
2005 enum isl_dim_type type, unsigned pos, int value);
2006 __isl_give isl_set *isl_set_lower_bound(
2007 __isl_take isl_set *set,
2008 enum isl_dim_type type, unsigned pos,
2010 __isl_give isl_set *isl_set_lower_bound_si(
2011 __isl_take isl_set *set,
2012 enum isl_dim_type type, unsigned pos, int value);
2013 __isl_give isl_map *isl_map_lower_bound_si(
2014 __isl_take isl_map *map,
2015 enum isl_dim_type type, unsigned pos, int value);
2016 __isl_give isl_set *isl_set_upper_bound(
2017 __isl_take isl_set *set,
2018 enum isl_dim_type type, unsigned pos,
2020 __isl_give isl_set *isl_set_upper_bound_si(
2021 __isl_take isl_set *set,
2022 enum isl_dim_type type, unsigned pos, int value);
2023 __isl_give isl_map *isl_map_upper_bound_si(
2024 __isl_take isl_map *map,
2025 enum isl_dim_type type, unsigned pos, int value);
2027 Intersect the set or relation with the half-space where the given
2028 dimension has a value bounded by the fixed given value.
2030 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2031 enum isl_dim_type type1, int pos1,
2032 enum isl_dim_type type2, int pos2);
2033 __isl_give isl_basic_map *isl_basic_map_equate(
2034 __isl_take isl_basic_map *bmap,
2035 enum isl_dim_type type1, int pos1,
2036 enum isl_dim_type type2, int pos2);
2037 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2038 enum isl_dim_type type1, int pos1,
2039 enum isl_dim_type type2, int pos2);
2041 Intersect the set or relation with the hyperplane where the given
2042 dimensions are equal to each other.
2044 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2045 enum isl_dim_type type1, int pos1,
2046 enum isl_dim_type type2, int pos2);
2048 Intersect the relation with the hyperplane where the given
2049 dimensions have opposite values.
2051 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2052 enum isl_dim_type type1, int pos1,
2053 enum isl_dim_type type2, int pos2);
2054 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2055 enum isl_dim_type type1, int pos1,
2056 enum isl_dim_type type2, int pos2);
2058 Intersect the relation with the half-space where the given
2059 dimensions satisfy the given ordering.
2063 __isl_give isl_map *isl_set_identity(
2064 __isl_take isl_set *set);
2065 __isl_give isl_union_map *isl_union_set_identity(
2066 __isl_take isl_union_set *uset);
2068 Construct an identity relation on the given (union) set.
2072 __isl_give isl_basic_set *isl_basic_map_deltas(
2073 __isl_take isl_basic_map *bmap);
2074 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2075 __isl_give isl_union_set *isl_union_map_deltas(
2076 __isl_take isl_union_map *umap);
2078 These functions return a (basic) set containing the differences
2079 between image elements and corresponding domain elements in the input.
2081 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2082 __isl_take isl_basic_map *bmap);
2083 __isl_give isl_map *isl_map_deltas_map(
2084 __isl_take isl_map *map);
2085 __isl_give isl_union_map *isl_union_map_deltas_map(
2086 __isl_take isl_union_map *umap);
2088 The functions above construct a (basic, regular or union) relation
2089 that maps (a wrapped version of) the input relation to its delta set.
2093 Simplify the representation of a set or relation by trying
2094 to combine pairs of basic sets or relations into a single
2095 basic set or relation.
2097 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2098 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2099 __isl_give isl_union_set *isl_union_set_coalesce(
2100 __isl_take isl_union_set *uset);
2101 __isl_give isl_union_map *isl_union_map_coalesce(
2102 __isl_take isl_union_map *umap);
2104 One of the methods for combining pairs of basic sets or relations
2105 can result in coefficients that are much larger than those that appear
2106 in the constraints of the input. By default, the coefficients are
2107 not allowed to grow larger, but this can be changed by unsetting
2108 the following option.
2110 int isl_options_set_coalesce_bounded_wrapping(
2111 isl_ctx *ctx, int val);
2112 int isl_options_get_coalesce_bounded_wrapping(
2115 =item * Detecting equalities
2117 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2118 __isl_take isl_basic_set *bset);
2119 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2120 __isl_take isl_basic_map *bmap);
2121 __isl_give isl_set *isl_set_detect_equalities(
2122 __isl_take isl_set *set);
2123 __isl_give isl_map *isl_map_detect_equalities(
2124 __isl_take isl_map *map);
2125 __isl_give isl_union_set *isl_union_set_detect_equalities(
2126 __isl_take isl_union_set *uset);
2127 __isl_give isl_union_map *isl_union_map_detect_equalities(
2128 __isl_take isl_union_map *umap);
2130 Simplify the representation of a set or relation by detecting implicit
2133 =item * Removing redundant constraints
2135 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2136 __isl_take isl_basic_set *bset);
2137 __isl_give isl_set *isl_set_remove_redundancies(
2138 __isl_take isl_set *set);
2139 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2140 __isl_take isl_basic_map *bmap);
2141 __isl_give isl_map *isl_map_remove_redundancies(
2142 __isl_take isl_map *map);
2146 __isl_give isl_basic_set *isl_set_convex_hull(
2147 __isl_take isl_set *set);
2148 __isl_give isl_basic_map *isl_map_convex_hull(
2149 __isl_take isl_map *map);
2151 If the input set or relation has any existentially quantified
2152 variables, then the result of these operations is currently undefined.
2156 __isl_give isl_basic_set *isl_set_simple_hull(
2157 __isl_take isl_set *set);
2158 __isl_give isl_basic_map *isl_map_simple_hull(
2159 __isl_take isl_map *map);
2160 __isl_give isl_union_map *isl_union_map_simple_hull(
2161 __isl_take isl_union_map *umap);
2163 These functions compute a single basic set or relation
2164 that contains the whole input set or relation.
2165 In particular, the output is described by translates
2166 of the constraints describing the basic sets or relations in the input.
2170 (See \autoref{s:simple hull}.)
2176 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2177 __isl_take isl_basic_set *bset);
2178 __isl_give isl_basic_set *isl_set_affine_hull(
2179 __isl_take isl_set *set);
2180 __isl_give isl_union_set *isl_union_set_affine_hull(
2181 __isl_take isl_union_set *uset);
2182 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2183 __isl_take isl_basic_map *bmap);
2184 __isl_give isl_basic_map *isl_map_affine_hull(
2185 __isl_take isl_map *map);
2186 __isl_give isl_union_map *isl_union_map_affine_hull(
2187 __isl_take isl_union_map *umap);
2189 In case of union sets and relations, the affine hull is computed
2192 =item * Polyhedral hull
2194 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2195 __isl_take isl_set *set);
2196 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2197 __isl_take isl_map *map);
2198 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2199 __isl_take isl_union_set *uset);
2200 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2201 __isl_take isl_union_map *umap);
2203 These functions compute a single basic set or relation
2204 not involving any existentially quantified variables
2205 that contains the whole input set or relation.
2206 In case of union sets and relations, the polyhedral hull is computed
2211 __isl_give isl_basic_set *isl_basic_set_sample(
2212 __isl_take isl_basic_set *bset);
2213 __isl_give isl_basic_set *isl_set_sample(
2214 __isl_take isl_set *set);
2215 __isl_give isl_basic_map *isl_basic_map_sample(
2216 __isl_take isl_basic_map *bmap);
2217 __isl_give isl_basic_map *isl_map_sample(
2218 __isl_take isl_map *map);
2220 If the input (basic) set or relation is non-empty, then return
2221 a singleton subset of the input. Otherwise, return an empty set.
2223 =item * Optimization
2225 #include <isl/ilp.h>
2226 enum isl_lp_result isl_basic_set_max(
2227 __isl_keep isl_basic_set *bset,
2228 __isl_keep isl_aff *obj, isl_int *opt)
2229 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2230 __isl_keep isl_aff *obj, isl_int *opt);
2231 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2232 __isl_keep isl_aff *obj, isl_int *opt);
2234 Compute the minimum or maximum of the integer affine expression C<obj>
2235 over the points in C<set>, returning the result in C<opt>.
2236 The return value may be one of C<isl_lp_error>,
2237 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2239 =item * Parametric optimization
2241 __isl_give isl_pw_aff *isl_set_dim_min(
2242 __isl_take isl_set *set, int pos);
2243 __isl_give isl_pw_aff *isl_set_dim_max(
2244 __isl_take isl_set *set, int pos);
2245 __isl_give isl_pw_aff *isl_map_dim_max(
2246 __isl_take isl_map *map, int pos);
2248 Compute the minimum or maximum of the given set or output dimension
2249 as a function of the parameters (and input dimensions), but independently
2250 of the other set or output dimensions.
2251 For lexicographic optimization, see L<"Lexicographic Optimization">.
2255 The following functions compute either the set of (rational) coefficient
2256 values of valid constraints for the given set or the set of (rational)
2257 values satisfying the constraints with coefficients from the given set.
2258 Internally, these two sets of functions perform essentially the
2259 same operations, except that the set of coefficients is assumed to
2260 be a cone, while the set of values may be any polyhedron.
2261 The current implementation is based on the Farkas lemma and
2262 Fourier-Motzkin elimination, but this may change or be made optional
2263 in future. In particular, future implementations may use different
2264 dualization algorithms or skip the elimination step.
2266 __isl_give isl_basic_set *isl_basic_set_coefficients(
2267 __isl_take isl_basic_set *bset);
2268 __isl_give isl_basic_set *isl_set_coefficients(
2269 __isl_take isl_set *set);
2270 __isl_give isl_union_set *isl_union_set_coefficients(
2271 __isl_take isl_union_set *bset);
2272 __isl_give isl_basic_set *isl_basic_set_solutions(
2273 __isl_take isl_basic_set *bset);
2274 __isl_give isl_basic_set *isl_set_solutions(
2275 __isl_take isl_set *set);
2276 __isl_give isl_union_set *isl_union_set_solutions(
2277 __isl_take isl_union_set *bset);
2281 __isl_give isl_map *isl_map_fixed_power(
2282 __isl_take isl_map *map, isl_int exp);
2283 __isl_give isl_union_map *isl_union_map_fixed_power(
2284 __isl_take isl_union_map *umap, isl_int exp);
2286 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2287 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2288 of C<map> is computed.
2290 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2292 __isl_give isl_union_map *isl_union_map_power(
2293 __isl_take isl_union_map *umap, int *exact);
2295 Compute a parametric representation for all positive powers I<k> of C<map>.
2296 The result maps I<k> to a nested relation corresponding to the
2297 I<k>th power of C<map>.
2298 The result may be an overapproximation. If the result is known to be exact,
2299 then C<*exact> is set to C<1>.
2301 =item * Transitive closure
2303 __isl_give isl_map *isl_map_transitive_closure(
2304 __isl_take isl_map *map, int *exact);
2305 __isl_give isl_union_map *isl_union_map_transitive_closure(
2306 __isl_take isl_union_map *umap, int *exact);
2308 Compute the transitive closure of C<map>.
2309 The result may be an overapproximation. If the result is known to be exact,
2310 then C<*exact> is set to C<1>.
2312 =item * Reaching path lengths
2314 __isl_give isl_map *isl_map_reaching_path_lengths(
2315 __isl_take isl_map *map, int *exact);
2317 Compute a relation that maps each element in the range of C<map>
2318 to the lengths of all paths composed of edges in C<map> that
2319 end up in the given element.
2320 The result may be an overapproximation. If the result is known to be exact,
2321 then C<*exact> is set to C<1>.
2322 To compute the I<maximal> path length, the resulting relation
2323 should be postprocessed by C<isl_map_lexmax>.
2324 In particular, if the input relation is a dependence relation
2325 (mapping sources to sinks), then the maximal path length corresponds
2326 to the free schedule.
2327 Note, however, that C<isl_map_lexmax> expects the maximum to be
2328 finite, so if the path lengths are unbounded (possibly due to
2329 the overapproximation), then you will get an error message.
2333 __isl_give isl_basic_set *isl_basic_map_wrap(
2334 __isl_take isl_basic_map *bmap);
2335 __isl_give isl_set *isl_map_wrap(
2336 __isl_take isl_map *map);
2337 __isl_give isl_union_set *isl_union_map_wrap(
2338 __isl_take isl_union_map *umap);
2339 __isl_give isl_basic_map *isl_basic_set_unwrap(
2340 __isl_take isl_basic_set *bset);
2341 __isl_give isl_map *isl_set_unwrap(
2342 __isl_take isl_set *set);
2343 __isl_give isl_union_map *isl_union_set_unwrap(
2344 __isl_take isl_union_set *uset);
2348 Remove any internal structure of domain (and range) of the given
2349 set or relation. If there is any such internal structure in the input,
2350 then the name of the space is also removed.
2352 __isl_give isl_basic_set *isl_basic_set_flatten(
2353 __isl_take isl_basic_set *bset);
2354 __isl_give isl_set *isl_set_flatten(
2355 __isl_take isl_set *set);
2356 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2357 __isl_take isl_basic_map *bmap);
2358 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2359 __isl_take isl_basic_map *bmap);
2360 __isl_give isl_map *isl_map_flatten_range(
2361 __isl_take isl_map *map);
2362 __isl_give isl_map *isl_map_flatten_domain(
2363 __isl_take isl_map *map);
2364 __isl_give isl_basic_map *isl_basic_map_flatten(
2365 __isl_take isl_basic_map *bmap);
2366 __isl_give isl_map *isl_map_flatten(
2367 __isl_take isl_map *map);
2369 __isl_give isl_map *isl_set_flatten_map(
2370 __isl_take isl_set *set);
2372 The function above constructs a relation
2373 that maps the input set to a flattened version of the set.
2377 Lift the input set to a space with extra dimensions corresponding
2378 to the existentially quantified variables in the input.
2379 In particular, the result lives in a wrapped map where the domain
2380 is the original space and the range corresponds to the original
2381 existentially quantified variables.
2383 __isl_give isl_basic_set *isl_basic_set_lift(
2384 __isl_take isl_basic_set *bset);
2385 __isl_give isl_set *isl_set_lift(
2386 __isl_take isl_set *set);
2387 __isl_give isl_union_set *isl_union_set_lift(
2388 __isl_take isl_union_set *uset);
2390 Given a local space that contains the existentially quantified
2391 variables of a set, a basic relation that, when applied to
2392 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2393 can be constructed using the following function.
2395 #include <isl/local_space.h>
2396 __isl_give isl_basic_map *isl_local_space_lifting(
2397 __isl_take isl_local_space *ls);
2399 =item * Internal Product
2401 __isl_give isl_basic_map *isl_basic_map_zip(
2402 __isl_take isl_basic_map *bmap);
2403 __isl_give isl_map *isl_map_zip(
2404 __isl_take isl_map *map);
2405 __isl_give isl_union_map *isl_union_map_zip(
2406 __isl_take isl_union_map *umap);
2408 Given a relation with nested relations for domain and range,
2409 interchange the range of the domain with the domain of the range.
2413 __isl_give isl_basic_map *isl_basic_map_curry(
2414 __isl_take isl_basic_map *bmap);
2415 __isl_give isl_map *isl_map_curry(
2416 __isl_take isl_map *map);
2417 __isl_give isl_union_map *isl_union_map_curry(
2418 __isl_take isl_union_map *umap);
2420 Given a relation with a nested relation for domain,
2421 move the range of the nested relation out of the domain
2422 and use it as the domain of a nested relation in the range,
2423 with the original range as range of this nested relation.
2425 =item * Aligning parameters
2427 __isl_give isl_basic_set *isl_basic_set_align_params(
2428 __isl_take isl_basic_set *bset,
2429 __isl_take isl_space *model);
2430 __isl_give isl_set *isl_set_align_params(
2431 __isl_take isl_set *set,
2432 __isl_take isl_space *model);
2433 __isl_give isl_basic_map *isl_basic_map_align_params(
2434 __isl_take isl_basic_map *bmap,
2435 __isl_take isl_space *model);
2436 __isl_give isl_map *isl_map_align_params(
2437 __isl_take isl_map *map,
2438 __isl_take isl_space *model);
2440 Change the order of the parameters of the given set or relation
2441 such that the first parameters match those of C<model>.
2442 This may involve the introduction of extra parameters.
2443 All parameters need to be named.
2445 =item * Dimension manipulation
2447 __isl_give isl_set *isl_set_add_dims(
2448 __isl_take isl_set *set,
2449 enum isl_dim_type type, unsigned n);
2450 __isl_give isl_map *isl_map_add_dims(
2451 __isl_take isl_map *map,
2452 enum isl_dim_type type, unsigned n);
2453 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2454 __isl_take isl_basic_set *bset,
2455 enum isl_dim_type type, unsigned pos,
2457 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2458 __isl_take isl_basic_map *bmap,
2459 enum isl_dim_type type, unsigned pos,
2461 __isl_give isl_set *isl_set_insert_dims(
2462 __isl_take isl_set *set,
2463 enum isl_dim_type type, unsigned pos, unsigned n);
2464 __isl_give isl_map *isl_map_insert_dims(
2465 __isl_take isl_map *map,
2466 enum isl_dim_type type, unsigned pos, unsigned n);
2467 __isl_give isl_basic_set *isl_basic_set_move_dims(
2468 __isl_take isl_basic_set *bset,
2469 enum isl_dim_type dst_type, unsigned dst_pos,
2470 enum isl_dim_type src_type, unsigned src_pos,
2472 __isl_give isl_basic_map *isl_basic_map_move_dims(
2473 __isl_take isl_basic_map *bmap,
2474 enum isl_dim_type dst_type, unsigned dst_pos,
2475 enum isl_dim_type src_type, unsigned src_pos,
2477 __isl_give isl_set *isl_set_move_dims(
2478 __isl_take isl_set *set,
2479 enum isl_dim_type dst_type, unsigned dst_pos,
2480 enum isl_dim_type src_type, unsigned src_pos,
2482 __isl_give isl_map *isl_map_move_dims(
2483 __isl_take isl_map *map,
2484 enum isl_dim_type dst_type, unsigned dst_pos,
2485 enum isl_dim_type src_type, unsigned src_pos,
2488 It is usually not advisable to directly change the (input or output)
2489 space of a set or a relation as this removes the name and the internal
2490 structure of the space. However, the above functions can be useful
2491 to add new parameters, assuming
2492 C<isl_set_align_params> and C<isl_map_align_params>
2497 =head2 Binary Operations
2499 The two arguments of a binary operation not only need to live
2500 in the same C<isl_ctx>, they currently also need to have
2501 the same (number of) parameters.
2503 =head3 Basic Operations
2507 =item * Intersection
2509 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2510 __isl_take isl_basic_set *bset1,
2511 __isl_take isl_basic_set *bset2);
2512 __isl_give isl_basic_set *isl_basic_set_intersect(
2513 __isl_take isl_basic_set *bset1,
2514 __isl_take isl_basic_set *bset2);
2515 __isl_give isl_set *isl_set_intersect_params(
2516 __isl_take isl_set *set,
2517 __isl_take isl_set *params);
2518 __isl_give isl_set *isl_set_intersect(
2519 __isl_take isl_set *set1,
2520 __isl_take isl_set *set2);
2521 __isl_give isl_union_set *isl_union_set_intersect_params(
2522 __isl_take isl_union_set *uset,
2523 __isl_take isl_set *set);
2524 __isl_give isl_union_map *isl_union_map_intersect_params(
2525 __isl_take isl_union_map *umap,
2526 __isl_take isl_set *set);
2527 __isl_give isl_union_set *isl_union_set_intersect(
2528 __isl_take isl_union_set *uset1,
2529 __isl_take isl_union_set *uset2);
2530 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2531 __isl_take isl_basic_map *bmap,
2532 __isl_take isl_basic_set *bset);
2533 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2534 __isl_take isl_basic_map *bmap,
2535 __isl_take isl_basic_set *bset);
2536 __isl_give isl_basic_map *isl_basic_map_intersect(
2537 __isl_take isl_basic_map *bmap1,
2538 __isl_take isl_basic_map *bmap2);
2539 __isl_give isl_map *isl_map_intersect_params(
2540 __isl_take isl_map *map,
2541 __isl_take isl_set *params);
2542 __isl_give isl_map *isl_map_intersect_domain(
2543 __isl_take isl_map *map,
2544 __isl_take isl_set *set);
2545 __isl_give isl_map *isl_map_intersect_range(
2546 __isl_take isl_map *map,
2547 __isl_take isl_set *set);
2548 __isl_give isl_map *isl_map_intersect(
2549 __isl_take isl_map *map1,
2550 __isl_take isl_map *map2);
2551 __isl_give isl_union_map *isl_union_map_intersect_domain(
2552 __isl_take isl_union_map *umap,
2553 __isl_take isl_union_set *uset);
2554 __isl_give isl_union_map *isl_union_map_intersect_range(
2555 __isl_take isl_union_map *umap,
2556 __isl_take isl_union_set *uset);
2557 __isl_give isl_union_map *isl_union_map_intersect(
2558 __isl_take isl_union_map *umap1,
2559 __isl_take isl_union_map *umap2);
2561 The second argument to the C<_params> functions needs to be
2562 a parametric (basic) set. For the other functions, a parametric set
2563 for either argument is only allowed if the other argument is
2564 a parametric set as well.
2568 __isl_give isl_set *isl_basic_set_union(
2569 __isl_take isl_basic_set *bset1,
2570 __isl_take isl_basic_set *bset2);
2571 __isl_give isl_map *isl_basic_map_union(
2572 __isl_take isl_basic_map *bmap1,
2573 __isl_take isl_basic_map *bmap2);
2574 __isl_give isl_set *isl_set_union(
2575 __isl_take isl_set *set1,
2576 __isl_take isl_set *set2);
2577 __isl_give isl_map *isl_map_union(
2578 __isl_take isl_map *map1,
2579 __isl_take isl_map *map2);
2580 __isl_give isl_union_set *isl_union_set_union(
2581 __isl_take isl_union_set *uset1,
2582 __isl_take isl_union_set *uset2);
2583 __isl_give isl_union_map *isl_union_map_union(
2584 __isl_take isl_union_map *umap1,
2585 __isl_take isl_union_map *umap2);
2587 =item * Set difference
2589 __isl_give isl_set *isl_set_subtract(
2590 __isl_take isl_set *set1,
2591 __isl_take isl_set *set2);
2592 __isl_give isl_map *isl_map_subtract(
2593 __isl_take isl_map *map1,
2594 __isl_take isl_map *map2);
2595 __isl_give isl_map *isl_map_subtract_domain(
2596 __isl_take isl_map *map,
2597 __isl_take isl_set *dom);
2598 __isl_give isl_map *isl_map_subtract_range(
2599 __isl_take isl_map *map,
2600 __isl_take isl_set *dom);
2601 __isl_give isl_union_set *isl_union_set_subtract(
2602 __isl_take isl_union_set *uset1,
2603 __isl_take isl_union_set *uset2);
2604 __isl_give isl_union_map *isl_union_map_subtract(
2605 __isl_take isl_union_map *umap1,
2606 __isl_take isl_union_map *umap2);
2610 __isl_give isl_basic_set *isl_basic_set_apply(
2611 __isl_take isl_basic_set *bset,
2612 __isl_take isl_basic_map *bmap);
2613 __isl_give isl_set *isl_set_apply(
2614 __isl_take isl_set *set,
2615 __isl_take isl_map *map);
2616 __isl_give isl_union_set *isl_union_set_apply(
2617 __isl_take isl_union_set *uset,
2618 __isl_take isl_union_map *umap);
2619 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2620 __isl_take isl_basic_map *bmap1,
2621 __isl_take isl_basic_map *bmap2);
2622 __isl_give isl_basic_map *isl_basic_map_apply_range(
2623 __isl_take isl_basic_map *bmap1,
2624 __isl_take isl_basic_map *bmap2);
2625 __isl_give isl_map *isl_map_apply_domain(
2626 __isl_take isl_map *map1,
2627 __isl_take isl_map *map2);
2628 __isl_give isl_union_map *isl_union_map_apply_domain(
2629 __isl_take isl_union_map *umap1,
2630 __isl_take isl_union_map *umap2);
2631 __isl_give isl_map *isl_map_apply_range(
2632 __isl_take isl_map *map1,
2633 __isl_take isl_map *map2);
2634 __isl_give isl_union_map *isl_union_map_apply_range(
2635 __isl_take isl_union_map *umap1,
2636 __isl_take isl_union_map *umap2);
2638 =item * Cartesian Product
2640 __isl_give isl_set *isl_set_product(
2641 __isl_take isl_set *set1,
2642 __isl_take isl_set *set2);
2643 __isl_give isl_union_set *isl_union_set_product(
2644 __isl_take isl_union_set *uset1,
2645 __isl_take isl_union_set *uset2);
2646 __isl_give isl_basic_map *isl_basic_map_domain_product(
2647 __isl_take isl_basic_map *bmap1,
2648 __isl_take isl_basic_map *bmap2);
2649 __isl_give isl_basic_map *isl_basic_map_range_product(
2650 __isl_take isl_basic_map *bmap1,
2651 __isl_take isl_basic_map *bmap2);
2652 __isl_give isl_basic_map *isl_basic_map_product(
2653 __isl_take isl_basic_map *bmap1,
2654 __isl_take isl_basic_map *bmap2);
2655 __isl_give isl_map *isl_map_domain_product(
2656 __isl_take isl_map *map1,
2657 __isl_take isl_map *map2);
2658 __isl_give isl_map *isl_map_range_product(
2659 __isl_take isl_map *map1,
2660 __isl_take isl_map *map2);
2661 __isl_give isl_union_map *isl_union_map_domain_product(
2662 __isl_take isl_union_map *umap1,
2663 __isl_take isl_union_map *umap2);
2664 __isl_give isl_union_map *isl_union_map_range_product(
2665 __isl_take isl_union_map *umap1,
2666 __isl_take isl_union_map *umap2);
2667 __isl_give isl_map *isl_map_product(
2668 __isl_take isl_map *map1,
2669 __isl_take isl_map *map2);
2670 __isl_give isl_union_map *isl_union_map_product(
2671 __isl_take isl_union_map *umap1,
2672 __isl_take isl_union_map *umap2);
2674 The above functions compute the cross product of the given
2675 sets or relations. The domains and ranges of the results
2676 are wrapped maps between domains and ranges of the inputs.
2677 To obtain a ``flat'' product, use the following functions
2680 __isl_give isl_basic_set *isl_basic_set_flat_product(
2681 __isl_take isl_basic_set *bset1,
2682 __isl_take isl_basic_set *bset2);
2683 __isl_give isl_set *isl_set_flat_product(
2684 __isl_take isl_set *set1,
2685 __isl_take isl_set *set2);
2686 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2687 __isl_take isl_basic_map *bmap1,
2688 __isl_take isl_basic_map *bmap2);
2689 __isl_give isl_map *isl_map_flat_domain_product(
2690 __isl_take isl_map *map1,
2691 __isl_take isl_map *map2);
2692 __isl_give isl_map *isl_map_flat_range_product(
2693 __isl_take isl_map *map1,
2694 __isl_take isl_map *map2);
2695 __isl_give isl_union_map *isl_union_map_flat_range_product(
2696 __isl_take isl_union_map *umap1,
2697 __isl_take isl_union_map *umap2);
2698 __isl_give isl_basic_map *isl_basic_map_flat_product(
2699 __isl_take isl_basic_map *bmap1,
2700 __isl_take isl_basic_map *bmap2);
2701 __isl_give isl_map *isl_map_flat_product(
2702 __isl_take isl_map *map1,
2703 __isl_take isl_map *map2);
2705 =item * Simplification
2707 __isl_give isl_basic_set *isl_basic_set_gist(
2708 __isl_take isl_basic_set *bset,
2709 __isl_take isl_basic_set *context);
2710 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2711 __isl_take isl_set *context);
2712 __isl_give isl_set *isl_set_gist_params(
2713 __isl_take isl_set *set,
2714 __isl_take isl_set *context);
2715 __isl_give isl_union_set *isl_union_set_gist(
2716 __isl_take isl_union_set *uset,
2717 __isl_take isl_union_set *context);
2718 __isl_give isl_union_set *isl_union_set_gist_params(
2719 __isl_take isl_union_set *uset,
2720 __isl_take isl_set *set);
2721 __isl_give isl_basic_map *isl_basic_map_gist(
2722 __isl_take isl_basic_map *bmap,
2723 __isl_take isl_basic_map *context);
2724 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2725 __isl_take isl_map *context);
2726 __isl_give isl_map *isl_map_gist_params(
2727 __isl_take isl_map *map,
2728 __isl_take isl_set *context);
2729 __isl_give isl_map *isl_map_gist_domain(
2730 __isl_take isl_map *map,
2731 __isl_take isl_set *context);
2732 __isl_give isl_map *isl_map_gist_range(
2733 __isl_take isl_map *map,
2734 __isl_take isl_set *context);
2735 __isl_give isl_union_map *isl_union_map_gist(
2736 __isl_take isl_union_map *umap,
2737 __isl_take isl_union_map *context);
2738 __isl_give isl_union_map *isl_union_map_gist_params(
2739 __isl_take isl_union_map *umap,
2740 __isl_take isl_set *set);
2741 __isl_give isl_union_map *isl_union_map_gist_domain(
2742 __isl_take isl_union_map *umap,
2743 __isl_take isl_union_set *uset);
2744 __isl_give isl_union_map *isl_union_map_gist_range(
2745 __isl_take isl_union_map *umap,
2746 __isl_take isl_union_set *uset);
2748 The gist operation returns a set or relation that has the
2749 same intersection with the context as the input set or relation.
2750 Any implicit equality in the intersection is made explicit in the result,
2751 while all inequalities that are redundant with respect to the intersection
2753 In case of union sets and relations, the gist operation is performed
2758 =head3 Lexicographic Optimization
2760 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2761 the following functions
2762 compute a set that contains the lexicographic minimum or maximum
2763 of the elements in C<set> (or C<bset>) for those values of the parameters
2764 that satisfy C<dom>.
2765 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2766 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2768 In other words, the union of the parameter values
2769 for which the result is non-empty and of C<*empty>
2772 __isl_give isl_set *isl_basic_set_partial_lexmin(
2773 __isl_take isl_basic_set *bset,
2774 __isl_take isl_basic_set *dom,
2775 __isl_give isl_set **empty);
2776 __isl_give isl_set *isl_basic_set_partial_lexmax(
2777 __isl_take isl_basic_set *bset,
2778 __isl_take isl_basic_set *dom,
2779 __isl_give isl_set **empty);
2780 __isl_give isl_set *isl_set_partial_lexmin(
2781 __isl_take isl_set *set, __isl_take isl_set *dom,
2782 __isl_give isl_set **empty);
2783 __isl_give isl_set *isl_set_partial_lexmax(
2784 __isl_take isl_set *set, __isl_take isl_set *dom,
2785 __isl_give isl_set **empty);
2787 Given a (basic) set C<set> (or C<bset>), the following functions simply
2788 return a set containing the lexicographic minimum or maximum
2789 of the elements in C<set> (or C<bset>).
2790 In case of union sets, the optimum is computed per space.
2792 __isl_give isl_set *isl_basic_set_lexmin(
2793 __isl_take isl_basic_set *bset);
2794 __isl_give isl_set *isl_basic_set_lexmax(
2795 __isl_take isl_basic_set *bset);
2796 __isl_give isl_set *isl_set_lexmin(
2797 __isl_take isl_set *set);
2798 __isl_give isl_set *isl_set_lexmax(
2799 __isl_take isl_set *set);
2800 __isl_give isl_union_set *isl_union_set_lexmin(
2801 __isl_take isl_union_set *uset);
2802 __isl_give isl_union_set *isl_union_set_lexmax(
2803 __isl_take isl_union_set *uset);
2805 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2806 the following functions
2807 compute a relation that maps each element of C<dom>
2808 to the single lexicographic minimum or maximum
2809 of the elements that are associated to that same
2810 element in C<map> (or C<bmap>).
2811 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2812 that contains the elements in C<dom> that do not map
2813 to any elements in C<map> (or C<bmap>).
2814 In other words, the union of the domain of the result and of C<*empty>
2817 __isl_give isl_map *isl_basic_map_partial_lexmax(
2818 __isl_take isl_basic_map *bmap,
2819 __isl_take isl_basic_set *dom,
2820 __isl_give isl_set **empty);
2821 __isl_give isl_map *isl_basic_map_partial_lexmin(
2822 __isl_take isl_basic_map *bmap,
2823 __isl_take isl_basic_set *dom,
2824 __isl_give isl_set **empty);
2825 __isl_give isl_map *isl_map_partial_lexmax(
2826 __isl_take isl_map *map, __isl_take isl_set *dom,
2827 __isl_give isl_set **empty);
2828 __isl_give isl_map *isl_map_partial_lexmin(
2829 __isl_take isl_map *map, __isl_take isl_set *dom,
2830 __isl_give isl_set **empty);
2832 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2833 return a map mapping each element in the domain of
2834 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2835 of all elements associated to that element.
2836 In case of union relations, the optimum is computed per space.
2838 __isl_give isl_map *isl_basic_map_lexmin(
2839 __isl_take isl_basic_map *bmap);
2840 __isl_give isl_map *isl_basic_map_lexmax(
2841 __isl_take isl_basic_map *bmap);
2842 __isl_give isl_map *isl_map_lexmin(
2843 __isl_take isl_map *map);
2844 __isl_give isl_map *isl_map_lexmax(
2845 __isl_take isl_map *map);
2846 __isl_give isl_union_map *isl_union_map_lexmin(
2847 __isl_take isl_union_map *umap);
2848 __isl_give isl_union_map *isl_union_map_lexmax(
2849 __isl_take isl_union_map *umap);
2851 The following functions return their result in the form of
2852 a piecewise multi-affine expression
2853 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2854 but are otherwise equivalent to the corresponding functions
2855 returning a basic set or relation.
2857 __isl_give isl_pw_multi_aff *
2858 isl_basic_map_lexmin_pw_multi_aff(
2859 __isl_take isl_basic_map *bmap);
2860 __isl_give isl_pw_multi_aff *
2861 isl_basic_set_partial_lexmin_pw_multi_aff(
2862 __isl_take isl_basic_set *bset,
2863 __isl_take isl_basic_set *dom,
2864 __isl_give isl_set **empty);
2865 __isl_give isl_pw_multi_aff *
2866 isl_basic_set_partial_lexmax_pw_multi_aff(
2867 __isl_take isl_basic_set *bset,
2868 __isl_take isl_basic_set *dom,
2869 __isl_give isl_set **empty);
2870 __isl_give isl_pw_multi_aff *
2871 isl_basic_map_partial_lexmin_pw_multi_aff(
2872 __isl_take isl_basic_map *bmap,
2873 __isl_take isl_basic_set *dom,
2874 __isl_give isl_set **empty);
2875 __isl_give isl_pw_multi_aff *
2876 isl_basic_map_partial_lexmax_pw_multi_aff(
2877 __isl_take isl_basic_map *bmap,
2878 __isl_take isl_basic_set *dom,
2879 __isl_give isl_set **empty);
2880 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
2881 __isl_take isl_map *map);
2882 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
2883 __isl_take isl_map *map);
2887 Lists are defined over several element types, including
2888 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2889 Here we take lists of C<isl_set>s as an example.
2890 Lists can be created, copied, modified and freed using the following functions.
2892 #include <isl/list.h>
2893 __isl_give isl_set_list *isl_set_list_from_set(
2894 __isl_take isl_set *el);
2895 __isl_give isl_set_list *isl_set_list_alloc(
2896 isl_ctx *ctx, int n);
2897 __isl_give isl_set_list *isl_set_list_copy(
2898 __isl_keep isl_set_list *list);
2899 __isl_give isl_set_list *isl_set_list_add(
2900 __isl_take isl_set_list *list,
2901 __isl_take isl_set *el);
2902 __isl_give isl_set_list *isl_set_list_drop(
2903 __isl_take isl_set_list *list,
2904 unsigned first, unsigned n);
2905 __isl_give isl_set_list *isl_set_list_set_set(
2906 __isl_take isl_set_list *list, int index,
2907 __isl_take isl_set *set);
2908 __isl_give isl_set_list *isl_set_list_concat(
2909 __isl_take isl_set_list *list1,
2910 __isl_take isl_set_list *list2);
2911 void *isl_set_list_free(__isl_take isl_set_list *list);
2913 C<isl_set_list_alloc> creates an empty list with a capacity for
2914 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2917 Lists can be inspected using the following functions.
2919 #include <isl/list.h>
2920 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2921 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2922 __isl_give isl_set *isl_set_list_get_set(
2923 __isl_keep isl_set_list *list, int index);
2924 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2925 int (*fn)(__isl_take isl_set *el, void *user),
2928 Lists can be printed using
2930 #include <isl/list.h>
2931 __isl_give isl_printer *isl_printer_print_set_list(
2932 __isl_take isl_printer *p,
2933 __isl_keep isl_set_list *list);
2937 Vectors can be created, copied and freed using the following functions.
2939 #include <isl/vec.h>
2940 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2942 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2943 void isl_vec_free(__isl_take isl_vec *vec);
2945 Note that the elements of a newly created vector may have arbitrary values.
2946 The elements can be changed and inspected using the following functions.
2948 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2949 int isl_vec_size(__isl_keep isl_vec *vec);
2950 int isl_vec_get_element(__isl_keep isl_vec *vec,
2951 int pos, isl_int *v);
2952 __isl_give isl_vec *isl_vec_set_element(
2953 __isl_take isl_vec *vec, int pos, isl_int v);
2954 __isl_give isl_vec *isl_vec_set_element_si(
2955 __isl_take isl_vec *vec, int pos, int v);
2956 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2958 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2961 C<isl_vec_get_element> will return a negative value if anything went wrong.
2962 In that case, the value of C<*v> is undefined.
2966 Matrices can be created, copied and freed using the following functions.
2968 #include <isl/mat.h>
2969 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2970 unsigned n_row, unsigned n_col);
2971 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2972 void isl_mat_free(__isl_take isl_mat *mat);
2974 Note that the elements of a newly created matrix may have arbitrary values.
2975 The elements can be changed and inspected using the following functions.
2977 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2978 int isl_mat_rows(__isl_keep isl_mat *mat);
2979 int isl_mat_cols(__isl_keep isl_mat *mat);
2980 int isl_mat_get_element(__isl_keep isl_mat *mat,
2981 int row, int col, isl_int *v);
2982 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2983 int row, int col, isl_int v);
2984 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2985 int row, int col, int v);
2987 C<isl_mat_get_element> will return a negative value if anything went wrong.
2988 In that case, the value of C<*v> is undefined.
2990 The following function can be used to compute the (right) inverse
2991 of a matrix, i.e., a matrix such that the product of the original
2992 and the inverse (in that order) is a multiple of the identity matrix.
2993 The input matrix is assumed to be of full row-rank.
2995 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2997 The following function can be used to compute the (right) kernel
2998 (or null space) of a matrix, i.e., a matrix such that the product of
2999 the original and the kernel (in that order) is the zero matrix.
3001 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3003 =head2 Piecewise Quasi Affine Expressions
3005 The zero quasi affine expression on a given domain can be created using
3007 __isl_give isl_aff *isl_aff_zero_on_domain(
3008 __isl_take isl_local_space *ls);
3010 Note that the space in which the resulting object lives is a map space
3011 with the given space as domain and a one-dimensional range.
3013 An empty piecewise quasi affine expression (one with no cells)
3014 or a piecewise quasi affine expression with a single cell can
3015 be created using the following functions.
3017 #include <isl/aff.h>
3018 __isl_give isl_pw_aff *isl_pw_aff_empty(
3019 __isl_take isl_space *space);
3020 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3021 __isl_take isl_set *set, __isl_take isl_aff *aff);
3022 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3023 __isl_take isl_aff *aff);
3025 A piecewise quasi affine expression that is equal to 1 on a set
3026 and 0 outside the set can be created using the following function.
3028 #include <isl/aff.h>
3029 __isl_give isl_pw_aff *isl_set_indicator_function(
3030 __isl_take isl_set *set);
3032 Quasi affine expressions can be copied and freed using
3034 #include <isl/aff.h>
3035 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3036 void *isl_aff_free(__isl_take isl_aff *aff);
3038 __isl_give isl_pw_aff *isl_pw_aff_copy(
3039 __isl_keep isl_pw_aff *pwaff);
3040 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3042 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3043 using the following function. The constraint is required to have
3044 a non-zero coefficient for the specified dimension.
3046 #include <isl/constraint.h>
3047 __isl_give isl_aff *isl_constraint_get_bound(
3048 __isl_keep isl_constraint *constraint,
3049 enum isl_dim_type type, int pos);
3051 The entire affine expression of the constraint can also be extracted
3052 using the following function.
3054 #include <isl/constraint.h>
3055 __isl_give isl_aff *isl_constraint_get_aff(
3056 __isl_keep isl_constraint *constraint);
3058 Conversely, an equality constraint equating
3059 the affine expression to zero or an inequality constraint enforcing
3060 the affine expression to be non-negative, can be constructed using
3062 __isl_give isl_constraint *isl_equality_from_aff(
3063 __isl_take isl_aff *aff);
3064 __isl_give isl_constraint *isl_inequality_from_aff(
3065 __isl_take isl_aff *aff);
3067 The expression can be inspected using
3069 #include <isl/aff.h>
3070 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3071 int isl_aff_dim(__isl_keep isl_aff *aff,
3072 enum isl_dim_type type);
3073 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3074 __isl_keep isl_aff *aff);
3075 __isl_give isl_local_space *isl_aff_get_local_space(
3076 __isl_keep isl_aff *aff);
3077 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3078 enum isl_dim_type type, unsigned pos);
3079 const char *isl_pw_aff_get_dim_name(
3080 __isl_keep isl_pw_aff *pa,
3081 enum isl_dim_type type, unsigned pos);
3082 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3083 enum isl_dim_type type, unsigned pos);
3084 __isl_give isl_id *isl_pw_aff_get_dim_id(
3085 __isl_keep isl_pw_aff *pa,
3086 enum isl_dim_type type, unsigned pos);
3087 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3088 __isl_keep isl_pw_aff *pa,
3089 enum isl_dim_type type);
3090 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3092 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3093 enum isl_dim_type type, int pos, isl_int *v);
3094 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3096 __isl_give isl_aff *isl_aff_get_div(
3097 __isl_keep isl_aff *aff, int pos);
3099 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3100 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3101 int (*fn)(__isl_take isl_set *set,
3102 __isl_take isl_aff *aff,
3103 void *user), void *user);
3105 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3106 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3108 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3109 enum isl_dim_type type, unsigned first, unsigned n);
3110 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3111 enum isl_dim_type type, unsigned first, unsigned n);
3113 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3114 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3115 enum isl_dim_type type);
3116 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3118 It can be modified using
3120 #include <isl/aff.h>
3121 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3122 __isl_take isl_pw_aff *pwaff,
3123 enum isl_dim_type type, __isl_take isl_id *id);
3124 __isl_give isl_aff *isl_aff_set_dim_name(
3125 __isl_take isl_aff *aff, enum isl_dim_type type,
3126 unsigned pos, const char *s);
3127 __isl_give isl_aff *isl_aff_set_dim_id(
3128 __isl_take isl_aff *aff, enum isl_dim_type type,
3129 unsigned pos, __isl_take isl_id *id);
3130 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3131 __isl_take isl_pw_aff *pma,
3132 enum isl_dim_type type, unsigned pos,
3133 __isl_take isl_id *id);
3134 __isl_give isl_aff *isl_aff_set_constant(
3135 __isl_take isl_aff *aff, isl_int v);
3136 __isl_give isl_aff *isl_aff_set_constant_si(
3137 __isl_take isl_aff *aff, int v);
3138 __isl_give isl_aff *isl_aff_set_coefficient(
3139 __isl_take isl_aff *aff,
3140 enum isl_dim_type type, int pos, isl_int v);
3141 __isl_give isl_aff *isl_aff_set_coefficient_si(
3142 __isl_take isl_aff *aff,
3143 enum isl_dim_type type, int pos, int v);
3144 __isl_give isl_aff *isl_aff_set_denominator(
3145 __isl_take isl_aff *aff, isl_int v);
3147 __isl_give isl_aff *isl_aff_add_constant(
3148 __isl_take isl_aff *aff, isl_int v);
3149 __isl_give isl_aff *isl_aff_add_constant_si(
3150 __isl_take isl_aff *aff, int v);
3151 __isl_give isl_aff *isl_aff_add_constant_num(
3152 __isl_take isl_aff *aff, isl_int v);
3153 __isl_give isl_aff *isl_aff_add_constant_num_si(
3154 __isl_take isl_aff *aff, int v);
3155 __isl_give isl_aff *isl_aff_add_coefficient(
3156 __isl_take isl_aff *aff,
3157 enum isl_dim_type type, int pos, isl_int v);
3158 __isl_give isl_aff *isl_aff_add_coefficient_si(
3159 __isl_take isl_aff *aff,
3160 enum isl_dim_type type, int pos, int v);
3162 __isl_give isl_aff *isl_aff_insert_dims(
3163 __isl_take isl_aff *aff,
3164 enum isl_dim_type type, unsigned first, unsigned n);
3165 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3166 __isl_take isl_pw_aff *pwaff,
3167 enum isl_dim_type type, unsigned first, unsigned n);
3168 __isl_give isl_aff *isl_aff_add_dims(
3169 __isl_take isl_aff *aff,
3170 enum isl_dim_type type, unsigned n);
3171 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3172 __isl_take isl_pw_aff *pwaff,
3173 enum isl_dim_type type, unsigned n);
3174 __isl_give isl_aff *isl_aff_drop_dims(
3175 __isl_take isl_aff *aff,
3176 enum isl_dim_type type, unsigned first, unsigned n);
3177 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3178 __isl_take isl_pw_aff *pwaff,
3179 enum isl_dim_type type, unsigned first, unsigned n);
3181 Note that the C<set_constant> and C<set_coefficient> functions
3182 set the I<numerator> of the constant or coefficient, while
3183 C<add_constant> and C<add_coefficient> add an integer value to
3184 the possibly rational constant or coefficient.
3185 The C<add_constant_num> functions add an integer value to
3188 To check whether an affine expressions is obviously zero
3189 or obviously equal to some other affine expression, use
3191 #include <isl/aff.h>
3192 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3193 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3194 __isl_keep isl_aff *aff2);
3195 int isl_pw_aff_plain_is_equal(
3196 __isl_keep isl_pw_aff *pwaff1,
3197 __isl_keep isl_pw_aff *pwaff2);
3201 #include <isl/aff.h>
3202 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3203 __isl_take isl_aff *aff2);
3204 __isl_give isl_pw_aff *isl_pw_aff_add(
3205 __isl_take isl_pw_aff *pwaff1,
3206 __isl_take isl_pw_aff *pwaff2);
3207 __isl_give isl_pw_aff *isl_pw_aff_min(
3208 __isl_take isl_pw_aff *pwaff1,
3209 __isl_take isl_pw_aff *pwaff2);
3210 __isl_give isl_pw_aff *isl_pw_aff_max(
3211 __isl_take isl_pw_aff *pwaff1,
3212 __isl_take isl_pw_aff *pwaff2);
3213 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3214 __isl_take isl_aff *aff2);
3215 __isl_give isl_pw_aff *isl_pw_aff_sub(
3216 __isl_take isl_pw_aff *pwaff1,
3217 __isl_take isl_pw_aff *pwaff2);
3218 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3219 __isl_give isl_pw_aff *isl_pw_aff_neg(
3220 __isl_take isl_pw_aff *pwaff);
3221 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3222 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3223 __isl_take isl_pw_aff *pwaff);
3224 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3225 __isl_give isl_pw_aff *isl_pw_aff_floor(
3226 __isl_take isl_pw_aff *pwaff);
3227 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3229 __isl_give isl_pw_aff *isl_pw_aff_mod(
3230 __isl_take isl_pw_aff *pwaff, isl_int mod);
3231 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3233 __isl_give isl_pw_aff *isl_pw_aff_scale(
3234 __isl_take isl_pw_aff *pwaff, isl_int f);
3235 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3237 __isl_give isl_aff *isl_aff_scale_down_ui(
3238 __isl_take isl_aff *aff, unsigned f);
3239 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3240 __isl_take isl_pw_aff *pwaff, isl_int f);
3242 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3243 __isl_take isl_pw_aff_list *list);
3244 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3245 __isl_take isl_pw_aff_list *list);
3247 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3248 __isl_take isl_pw_aff *pwqp);
3250 __isl_give isl_aff *isl_aff_align_params(
3251 __isl_take isl_aff *aff,
3252 __isl_take isl_space *model);
3253 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3254 __isl_take isl_pw_aff *pwaff,
3255 __isl_take isl_space *model);
3257 __isl_give isl_aff *isl_aff_project_domain_on_params(
3258 __isl_take isl_aff *aff);
3260 __isl_give isl_aff *isl_aff_gist_params(
3261 __isl_take isl_aff *aff,
3262 __isl_take isl_set *context);
3263 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3264 __isl_take isl_set *context);
3265 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3266 __isl_take isl_pw_aff *pwaff,
3267 __isl_take isl_set *context);
3268 __isl_give isl_pw_aff *isl_pw_aff_gist(
3269 __isl_take isl_pw_aff *pwaff,
3270 __isl_take isl_set *context);
3272 __isl_give isl_set *isl_pw_aff_domain(
3273 __isl_take isl_pw_aff *pwaff);
3274 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3275 __isl_take isl_pw_aff *pa,
3276 __isl_take isl_set *set);
3277 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3278 __isl_take isl_pw_aff *pa,
3279 __isl_take isl_set *set);
3281 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3282 __isl_take isl_aff *aff2);
3283 __isl_give isl_pw_aff *isl_pw_aff_mul(
3284 __isl_take isl_pw_aff *pwaff1,
3285 __isl_take isl_pw_aff *pwaff2);
3287 When multiplying two affine expressions, at least one of the two needs
3290 #include <isl/aff.h>
3291 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3292 __isl_take isl_aff *aff);
3293 __isl_give isl_basic_set *isl_aff_le_basic_set(
3294 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3295 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3296 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3297 __isl_give isl_set *isl_pw_aff_eq_set(
3298 __isl_take isl_pw_aff *pwaff1,
3299 __isl_take isl_pw_aff *pwaff2);
3300 __isl_give isl_set *isl_pw_aff_ne_set(
3301 __isl_take isl_pw_aff *pwaff1,
3302 __isl_take isl_pw_aff *pwaff2);
3303 __isl_give isl_set *isl_pw_aff_le_set(
3304 __isl_take isl_pw_aff *pwaff1,
3305 __isl_take isl_pw_aff *pwaff2);
3306 __isl_give isl_set *isl_pw_aff_lt_set(
3307 __isl_take isl_pw_aff *pwaff1,
3308 __isl_take isl_pw_aff *pwaff2);
3309 __isl_give isl_set *isl_pw_aff_ge_set(
3310 __isl_take isl_pw_aff *pwaff1,
3311 __isl_take isl_pw_aff *pwaff2);
3312 __isl_give isl_set *isl_pw_aff_gt_set(
3313 __isl_take isl_pw_aff *pwaff1,
3314 __isl_take isl_pw_aff *pwaff2);
3316 __isl_give isl_set *isl_pw_aff_list_eq_set(
3317 __isl_take isl_pw_aff_list *list1,
3318 __isl_take isl_pw_aff_list *list2);
3319 __isl_give isl_set *isl_pw_aff_list_ne_set(
3320 __isl_take isl_pw_aff_list *list1,
3321 __isl_take isl_pw_aff_list *list2);
3322 __isl_give isl_set *isl_pw_aff_list_le_set(
3323 __isl_take isl_pw_aff_list *list1,
3324 __isl_take isl_pw_aff_list *list2);
3325 __isl_give isl_set *isl_pw_aff_list_lt_set(
3326 __isl_take isl_pw_aff_list *list1,
3327 __isl_take isl_pw_aff_list *list2);
3328 __isl_give isl_set *isl_pw_aff_list_ge_set(
3329 __isl_take isl_pw_aff_list *list1,
3330 __isl_take isl_pw_aff_list *list2);
3331 __isl_give isl_set *isl_pw_aff_list_gt_set(
3332 __isl_take isl_pw_aff_list *list1,
3333 __isl_take isl_pw_aff_list *list2);
3335 The function C<isl_aff_neg_basic_set> returns a basic set
3336 containing those elements in the domain space
3337 of C<aff> where C<aff> is negative.
3338 The function C<isl_aff_ge_basic_set> returns a basic set
3339 containing those elements in the shared space
3340 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3341 The function C<isl_pw_aff_ge_set> returns a set
3342 containing those elements in the shared domain
3343 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3344 The functions operating on C<isl_pw_aff_list> apply the corresponding
3345 C<isl_pw_aff> function to each pair of elements in the two lists.
3347 #include <isl/aff.h>
3348 __isl_give isl_set *isl_pw_aff_nonneg_set(
3349 __isl_take isl_pw_aff *pwaff);
3350 __isl_give isl_set *isl_pw_aff_zero_set(
3351 __isl_take isl_pw_aff *pwaff);
3352 __isl_give isl_set *isl_pw_aff_non_zero_set(
3353 __isl_take isl_pw_aff *pwaff);
3355 The function C<isl_pw_aff_nonneg_set> returns a set
3356 containing those elements in the domain
3357 of C<pwaff> where C<pwaff> is non-negative.
3359 #include <isl/aff.h>
3360 __isl_give isl_pw_aff *isl_pw_aff_cond(
3361 __isl_take isl_pw_aff *cond,
3362 __isl_take isl_pw_aff *pwaff_true,
3363 __isl_take isl_pw_aff *pwaff_false);
3365 The function C<isl_pw_aff_cond> performs a conditional operator
3366 and returns an expression that is equal to C<pwaff_true>
3367 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3368 where C<cond> is zero.
3370 #include <isl/aff.h>
3371 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3372 __isl_take isl_pw_aff *pwaff1,
3373 __isl_take isl_pw_aff *pwaff2);
3374 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3375 __isl_take isl_pw_aff *pwaff1,
3376 __isl_take isl_pw_aff *pwaff2);
3377 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3378 __isl_take isl_pw_aff *pwaff1,
3379 __isl_take isl_pw_aff *pwaff2);
3381 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3382 expression with a domain that is the union of those of C<pwaff1> and
3383 C<pwaff2> and such that on each cell, the quasi-affine expression is
3384 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3385 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3386 associated expression is the defined one.
3388 An expression can be read from input using
3390 #include <isl/aff.h>
3391 __isl_give isl_aff *isl_aff_read_from_str(
3392 isl_ctx *ctx, const char *str);
3393 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3394 isl_ctx *ctx, const char *str);
3396 An expression can be printed using
3398 #include <isl/aff.h>
3399 __isl_give isl_printer *isl_printer_print_aff(
3400 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3402 __isl_give isl_printer *isl_printer_print_pw_aff(
3403 __isl_take isl_printer *p,
3404 __isl_keep isl_pw_aff *pwaff);
3406 =head2 Piecewise Multiple Quasi Affine Expressions
3408 An C<isl_multi_aff> object represents a sequence of
3409 zero or more affine expressions, all defined on the same domain space.
3411 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3414 #include <isl/aff.h>
3415 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3416 __isl_take isl_space *space,
3417 __isl_take isl_aff_list *list);
3419 An empty piecewise multiple quasi affine expression (one with no cells),
3420 the zero piecewise multiple quasi affine expression (with value zero
3421 for each output dimension),
3422 a piecewise multiple quasi affine expression with a single cell (with
3423 either a universe or a specified domain) or
3424 a zero-dimensional piecewise multiple quasi affine expression
3426 can be created using the following functions.
3428 #include <isl/aff.h>
3429 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3430 __isl_take isl_space *space);
3431 __isl_give isl_multi_aff *isl_multi_aff_zero(
3432 __isl_take isl_space *space);
3433 __isl_give isl_multi_aff *isl_multi_aff_identity(
3434 __isl_take isl_space *space);
3435 __isl_give isl_pw_multi_aff *
3436 isl_pw_multi_aff_from_multi_aff(
3437 __isl_take isl_multi_aff *ma);
3438 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3439 __isl_take isl_set *set,
3440 __isl_take isl_multi_aff *maff);
3441 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3442 __isl_take isl_set *set);
3444 __isl_give isl_union_pw_multi_aff *
3445 isl_union_pw_multi_aff_empty(
3446 __isl_take isl_space *space);
3447 __isl_give isl_union_pw_multi_aff *
3448 isl_union_pw_multi_aff_add_pw_multi_aff(
3449 __isl_take isl_union_pw_multi_aff *upma,
3450 __isl_take isl_pw_multi_aff *pma);
3451 __isl_give isl_union_pw_multi_aff *
3452 isl_union_pw_multi_aff_from_domain(
3453 __isl_take isl_union_set *uset);
3455 A piecewise multiple quasi affine expression can also be initialized
3456 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3457 and the C<isl_map> is single-valued.
3459 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3460 __isl_take isl_set *set);
3461 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3462 __isl_take isl_map *map);
3464 Multiple quasi affine expressions can be copied and freed using
3466 #include <isl/aff.h>
3467 __isl_give isl_multi_aff *isl_multi_aff_copy(
3468 __isl_keep isl_multi_aff *maff);
3469 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3471 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3472 __isl_keep isl_pw_multi_aff *pma);
3473 void *isl_pw_multi_aff_free(
3474 __isl_take isl_pw_multi_aff *pma);
3476 __isl_give isl_union_pw_multi_aff *
3477 isl_union_pw_multi_aff_copy(
3478 __isl_keep isl_union_pw_multi_aff *upma);
3479 void *isl_union_pw_multi_aff_free(
3480 __isl_take isl_union_pw_multi_aff *upma);
3482 The expression can be inspected using
3484 #include <isl/aff.h>
3485 isl_ctx *isl_multi_aff_get_ctx(
3486 __isl_keep isl_multi_aff *maff);
3487 isl_ctx *isl_pw_multi_aff_get_ctx(
3488 __isl_keep isl_pw_multi_aff *pma);
3489 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3490 __isl_keep isl_union_pw_multi_aff *upma);
3491 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3492 enum isl_dim_type type);
3493 unsigned isl_pw_multi_aff_dim(
3494 __isl_keep isl_pw_multi_aff *pma,
3495 enum isl_dim_type type);
3496 __isl_give isl_aff *isl_multi_aff_get_aff(
3497 __isl_keep isl_multi_aff *multi, int pos);
3498 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3499 __isl_keep isl_pw_multi_aff *pma, int pos);
3500 const char *isl_pw_multi_aff_get_dim_name(
3501 __isl_keep isl_pw_multi_aff *pma,
3502 enum isl_dim_type type, unsigned pos);
3503 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3504 __isl_keep isl_pw_multi_aff *pma,
3505 enum isl_dim_type type, unsigned pos);
3506 const char *isl_multi_aff_get_tuple_name(
3507 __isl_keep isl_multi_aff *multi,
3508 enum isl_dim_type type);
3509 int isl_pw_multi_aff_has_tuple_name(
3510 __isl_keep isl_pw_multi_aff *pma,
3511 enum isl_dim_type type);
3512 const char *isl_pw_multi_aff_get_tuple_name(
3513 __isl_keep isl_pw_multi_aff *pma,
3514 enum isl_dim_type type);
3515 int isl_pw_multi_aff_has_tuple_id(
3516 __isl_keep isl_pw_multi_aff *pma,
3517 enum isl_dim_type type);
3518 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3519 __isl_keep isl_pw_multi_aff *pma,
3520 enum isl_dim_type type);
3522 int isl_pw_multi_aff_foreach_piece(
3523 __isl_keep isl_pw_multi_aff *pma,
3524 int (*fn)(__isl_take isl_set *set,
3525 __isl_take isl_multi_aff *maff,
3526 void *user), void *user);
3528 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3529 __isl_keep isl_union_pw_multi_aff *upma,
3530 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3531 void *user), void *user);
3533 It can be modified using
3535 #include <isl/aff.h>
3536 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3537 __isl_take isl_multi_aff *multi, int pos,
3538 __isl_take isl_aff *aff);
3539 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3540 __isl_take isl_multi_aff *maff,
3541 enum isl_dim_type type, unsigned pos, const char *s);
3542 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3543 __isl_take isl_multi_aff *maff,
3544 enum isl_dim_type type, __isl_take isl_id *id);
3545 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3546 __isl_take isl_pw_multi_aff *pma,
3547 enum isl_dim_type type, __isl_take isl_id *id);
3549 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3550 __isl_take isl_multi_aff *maff,
3551 enum isl_dim_type type, unsigned first, unsigned n);
3552 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
3553 __isl_take isl_pw_multi_aff *pma,
3554 enum isl_dim_type type, unsigned first, unsigned n);
3556 To check whether two multiple affine expressions are
3557 obviously equal to each other, use
3559 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3560 __isl_keep isl_multi_aff *maff2);
3561 int isl_pw_multi_aff_plain_is_equal(
3562 __isl_keep isl_pw_multi_aff *pma1,
3563 __isl_keep isl_pw_multi_aff *pma2);
3567 #include <isl/aff.h>
3568 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3569 __isl_take isl_pw_multi_aff *pma1,
3570 __isl_take isl_pw_multi_aff *pma2);
3571 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3572 __isl_take isl_pw_multi_aff *pma1,
3573 __isl_take isl_pw_multi_aff *pma2);
3574 __isl_give isl_multi_aff *isl_multi_aff_add(
3575 __isl_take isl_multi_aff *maff1,
3576 __isl_take isl_multi_aff *maff2);
3577 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3578 __isl_take isl_pw_multi_aff *pma1,
3579 __isl_take isl_pw_multi_aff *pma2);
3580 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3581 __isl_take isl_union_pw_multi_aff *upma1,
3582 __isl_take isl_union_pw_multi_aff *upma2);
3583 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3584 __isl_take isl_pw_multi_aff *pma1,
3585 __isl_take isl_pw_multi_aff *pma2);
3586 __isl_give isl_multi_aff *isl_multi_aff_scale(
3587 __isl_take isl_multi_aff *maff,
3589 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3590 __isl_take isl_pw_multi_aff *pma,
3591 __isl_take isl_set *set);
3592 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3593 __isl_take isl_pw_multi_aff *pma,
3594 __isl_take isl_set *set);
3595 __isl_give isl_multi_aff *isl_multi_aff_lift(
3596 __isl_take isl_multi_aff *maff,
3597 __isl_give isl_local_space **ls);
3598 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3599 __isl_take isl_pw_multi_aff *pma);
3600 __isl_give isl_multi_aff *isl_multi_aff_align_params(
3601 __isl_take isl_multi_aff *multi,
3602 __isl_take isl_space *model);
3603 __isl_give isl_pw_multi_aff *
3604 isl_pw_multi_aff_project_domain_on_params(
3605 __isl_take isl_pw_multi_aff *pma);
3606 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3607 __isl_take isl_multi_aff *maff,
3608 __isl_take isl_set *context);
3609 __isl_give isl_multi_aff *isl_multi_aff_gist(
3610 __isl_take isl_multi_aff *maff,
3611 __isl_take isl_set *context);
3612 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3613 __isl_take isl_pw_multi_aff *pma,
3614 __isl_take isl_set *set);
3615 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3616 __isl_take isl_pw_multi_aff *pma,
3617 __isl_take isl_set *set);
3618 __isl_give isl_set *isl_pw_multi_aff_domain(
3619 __isl_take isl_pw_multi_aff *pma);
3620 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3621 __isl_take isl_union_pw_multi_aff *upma);
3622 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3623 __isl_take isl_multi_aff *ma1,
3624 __isl_take isl_multi_aff *ma2);
3625 __isl_give isl_multi_aff *isl_multi_aff_product(
3626 __isl_take isl_multi_aff *ma1,
3627 __isl_take isl_multi_aff *ma2);
3628 __isl_give isl_pw_multi_aff *
3629 isl_pw_multi_aff_flat_range_product(
3630 __isl_take isl_pw_multi_aff *pma1,
3631 __isl_take isl_pw_multi_aff *pma2);
3632 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3633 __isl_take isl_pw_multi_aff *pma1,
3634 __isl_take isl_pw_multi_aff *pma2);
3635 __isl_give isl_union_pw_multi_aff *
3636 isl_union_pw_multi_aff_flat_range_product(
3637 __isl_take isl_union_pw_multi_aff *upma1,
3638 __isl_take isl_union_pw_multi_aff *upma2);
3640 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3641 then it is assigned the local space that lies at the basis of
3642 the lifting applied.
3644 __isl_give isl_set *isl_multi_aff_lex_le_set(
3645 __isl_take isl_multi_aff *ma1,
3646 __isl_take isl_multi_aff *ma2);
3647 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3648 __isl_take isl_multi_aff *ma1,
3649 __isl_take isl_multi_aff *ma2);
3651 The function C<isl_multi_aff_lex_le_set> returns a set
3652 containing those elements in the shared domain space
3653 where C<ma1> is lexicographically smaller than or
3656 An expression can be read from input using
3658 #include <isl/aff.h>
3659 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3660 isl_ctx *ctx, const char *str);
3661 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3662 isl_ctx *ctx, const char *str);
3664 An expression can be printed using
3666 #include <isl/aff.h>
3667 __isl_give isl_printer *isl_printer_print_multi_aff(
3668 __isl_take isl_printer *p,
3669 __isl_keep isl_multi_aff *maff);
3670 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3671 __isl_take isl_printer *p,
3672 __isl_keep isl_pw_multi_aff *pma);
3673 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3674 __isl_take isl_printer *p,
3675 __isl_keep isl_union_pw_multi_aff *upma);
3679 Points are elements of a set. They can be used to construct
3680 simple sets (boxes) or they can be used to represent the
3681 individual elements of a set.
3682 The zero point (the origin) can be created using
3684 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3686 The coordinates of a point can be inspected, set and changed
3689 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3690 enum isl_dim_type type, int pos, isl_int *v);
3691 __isl_give isl_point *isl_point_set_coordinate(
3692 __isl_take isl_point *pnt,
3693 enum isl_dim_type type, int pos, isl_int v);
3695 __isl_give isl_point *isl_point_add_ui(
3696 __isl_take isl_point *pnt,
3697 enum isl_dim_type type, int pos, unsigned val);
3698 __isl_give isl_point *isl_point_sub_ui(
3699 __isl_take isl_point *pnt,
3700 enum isl_dim_type type, int pos, unsigned val);
3702 Other properties can be obtained using
3704 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3706 Points can be copied or freed using
3708 __isl_give isl_point *isl_point_copy(
3709 __isl_keep isl_point *pnt);
3710 void isl_point_free(__isl_take isl_point *pnt);
3712 A singleton set can be created from a point using
3714 __isl_give isl_basic_set *isl_basic_set_from_point(
3715 __isl_take isl_point *pnt);
3716 __isl_give isl_set *isl_set_from_point(
3717 __isl_take isl_point *pnt);
3719 and a box can be created from two opposite extremal points using
3721 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3722 __isl_take isl_point *pnt1,
3723 __isl_take isl_point *pnt2);
3724 __isl_give isl_set *isl_set_box_from_points(
3725 __isl_take isl_point *pnt1,
3726 __isl_take isl_point *pnt2);
3728 All elements of a B<bounded> (union) set can be enumerated using
3729 the following functions.
3731 int isl_set_foreach_point(__isl_keep isl_set *set,
3732 int (*fn)(__isl_take isl_point *pnt, void *user),
3734 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3735 int (*fn)(__isl_take isl_point *pnt, void *user),
3738 The function C<fn> is called for each integer point in
3739 C<set> with as second argument the last argument of
3740 the C<isl_set_foreach_point> call. The function C<fn>
3741 should return C<0> on success and C<-1> on failure.
3742 In the latter case, C<isl_set_foreach_point> will stop
3743 enumerating and return C<-1> as well.
3744 If the enumeration is performed successfully and to completion,
3745 then C<isl_set_foreach_point> returns C<0>.
3747 To obtain a single point of a (basic) set, use
3749 __isl_give isl_point *isl_basic_set_sample_point(
3750 __isl_take isl_basic_set *bset);
3751 __isl_give isl_point *isl_set_sample_point(
3752 __isl_take isl_set *set);
3754 If C<set> does not contain any (integer) points, then the
3755 resulting point will be ``void'', a property that can be
3758 int isl_point_is_void(__isl_keep isl_point *pnt);
3760 =head2 Piecewise Quasipolynomials
3762 A piecewise quasipolynomial is a particular kind of function that maps
3763 a parametric point to a rational value.
3764 More specifically, a quasipolynomial is a polynomial expression in greatest
3765 integer parts of affine expressions of parameters and variables.
3766 A piecewise quasipolynomial is a subdivision of a given parametric
3767 domain into disjoint cells with a quasipolynomial associated to
3768 each cell. The value of the piecewise quasipolynomial at a given
3769 point is the value of the quasipolynomial associated to the cell
3770 that contains the point. Outside of the union of cells,
3771 the value is assumed to be zero.
3772 For example, the piecewise quasipolynomial
3774 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3776 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3777 A given piecewise quasipolynomial has a fixed domain dimension.
3778 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3779 defined over different domains.
3780 Piecewise quasipolynomials are mainly used by the C<barvinok>
3781 library for representing the number of elements in a parametric set or map.
3782 For example, the piecewise quasipolynomial above represents
3783 the number of points in the map
3785 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3787 =head3 Input and Output
3789 Piecewise quasipolynomials can be read from input using
3791 __isl_give isl_union_pw_qpolynomial *
3792 isl_union_pw_qpolynomial_read_from_str(
3793 isl_ctx *ctx, const char *str);
3795 Quasipolynomials and piecewise quasipolynomials can be printed
3796 using the following functions.
3798 __isl_give isl_printer *isl_printer_print_qpolynomial(
3799 __isl_take isl_printer *p,
3800 __isl_keep isl_qpolynomial *qp);
3802 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3803 __isl_take isl_printer *p,
3804 __isl_keep isl_pw_qpolynomial *pwqp);
3806 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3807 __isl_take isl_printer *p,
3808 __isl_keep isl_union_pw_qpolynomial *upwqp);
3810 The output format of the printer
3811 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3812 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3814 In case of printing in C<ISL_FORMAT_C>, the user may want
3815 to set the names of all dimensions
3817 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3818 __isl_take isl_qpolynomial *qp,
3819 enum isl_dim_type type, unsigned pos,
3821 __isl_give isl_pw_qpolynomial *
3822 isl_pw_qpolynomial_set_dim_name(
3823 __isl_take isl_pw_qpolynomial *pwqp,
3824 enum isl_dim_type type, unsigned pos,
3827 =head3 Creating New (Piecewise) Quasipolynomials
3829 Some simple quasipolynomials can be created using the following functions.
3830 More complicated quasipolynomials can be created by applying
3831 operations such as addition and multiplication
3832 on the resulting quasipolynomials
3834 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3835 __isl_take isl_space *domain);
3836 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3837 __isl_take isl_space *domain);
3838 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3839 __isl_take isl_space *domain);
3840 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3841 __isl_take isl_space *domain);
3842 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3843 __isl_take isl_space *domain);
3844 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3845 __isl_take isl_space *domain,
3846 const isl_int n, const isl_int d);
3847 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3848 __isl_take isl_space *domain,
3849 enum isl_dim_type type, unsigned pos);
3850 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3851 __isl_take isl_aff *aff);
3853 Note that the space in which a quasipolynomial lives is a map space
3854 with a one-dimensional range. The C<domain> argument in some of
3855 the functions above corresponds to the domain of this map space.
3857 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3858 with a single cell can be created using the following functions.
3859 Multiple of these single cell piecewise quasipolynomials can
3860 be combined to create more complicated piecewise quasipolynomials.
3862 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3863 __isl_take isl_space *space);
3864 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3865 __isl_take isl_set *set,
3866 __isl_take isl_qpolynomial *qp);
3867 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3868 __isl_take isl_qpolynomial *qp);
3869 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3870 __isl_take isl_pw_aff *pwaff);
3872 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3873 __isl_take isl_space *space);
3874 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3875 __isl_take isl_pw_qpolynomial *pwqp);
3876 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3877 __isl_take isl_union_pw_qpolynomial *upwqp,
3878 __isl_take isl_pw_qpolynomial *pwqp);
3880 Quasipolynomials can be copied and freed again using the following
3883 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3884 __isl_keep isl_qpolynomial *qp);
3885 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3887 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3888 __isl_keep isl_pw_qpolynomial *pwqp);
3889 void *isl_pw_qpolynomial_free(
3890 __isl_take isl_pw_qpolynomial *pwqp);
3892 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3893 __isl_keep isl_union_pw_qpolynomial *upwqp);
3894 void *isl_union_pw_qpolynomial_free(
3895 __isl_take isl_union_pw_qpolynomial *upwqp);
3897 =head3 Inspecting (Piecewise) Quasipolynomials
3899 To iterate over all piecewise quasipolynomials in a union
3900 piecewise quasipolynomial, use the following function
3902 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3903 __isl_keep isl_union_pw_qpolynomial *upwqp,
3904 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3907 To extract the piecewise quasipolynomial in a given space from a union, use
3909 __isl_give isl_pw_qpolynomial *
3910 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3911 __isl_keep isl_union_pw_qpolynomial *upwqp,
3912 __isl_take isl_space *space);
3914 To iterate over the cells in a piecewise quasipolynomial,
3915 use either of the following two functions
3917 int isl_pw_qpolynomial_foreach_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);
3922 int isl_pw_qpolynomial_foreach_lifted_piece(
3923 __isl_keep isl_pw_qpolynomial *pwqp,
3924 int (*fn)(__isl_take isl_set *set,
3925 __isl_take isl_qpolynomial *qp,
3926 void *user), void *user);
3928 As usual, the function C<fn> should return C<0> on success
3929 and C<-1> on failure. The difference between
3930 C<isl_pw_qpolynomial_foreach_piece> and
3931 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3932 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3933 compute unique representations for all existentially quantified
3934 variables and then turn these existentially quantified variables
3935 into extra set variables, adapting the associated quasipolynomial
3936 accordingly. This means that the C<set> passed to C<fn>
3937 will not have any existentially quantified variables, but that
3938 the dimensions of the sets may be different for different
3939 invocations of C<fn>.
3941 To iterate over all terms in a quasipolynomial,
3944 int isl_qpolynomial_foreach_term(
3945 __isl_keep isl_qpolynomial *qp,
3946 int (*fn)(__isl_take isl_term *term,
3947 void *user), void *user);
3949 The terms themselves can be inspected and freed using
3952 unsigned isl_term_dim(__isl_keep isl_term *term,
3953 enum isl_dim_type type);
3954 void isl_term_get_num(__isl_keep isl_term *term,
3956 void isl_term_get_den(__isl_keep isl_term *term,
3958 int isl_term_get_exp(__isl_keep isl_term *term,
3959 enum isl_dim_type type, unsigned pos);
3960 __isl_give isl_aff *isl_term_get_div(
3961 __isl_keep isl_term *term, unsigned pos);
3962 void isl_term_free(__isl_take isl_term *term);
3964 Each term is a product of parameters, set variables and
3965 integer divisions. The function C<isl_term_get_exp>
3966 returns the exponent of a given dimensions in the given term.
3967 The C<isl_int>s in the arguments of C<isl_term_get_num>
3968 and C<isl_term_get_den> need to have been initialized
3969 using C<isl_int_init> before calling these functions.
3971 =head3 Properties of (Piecewise) Quasipolynomials
3973 To check whether a quasipolynomial is actually a constant,
3974 use the following function.
3976 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3977 isl_int *n, isl_int *d);
3979 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3980 then the numerator and denominator of the constant
3981 are returned in C<*n> and C<*d>, respectively.
3983 To check whether two union piecewise quasipolynomials are
3984 obviously equal, use
3986 int isl_union_pw_qpolynomial_plain_is_equal(
3987 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3988 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3990 =head3 Operations on (Piecewise) Quasipolynomials
3992 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3993 __isl_take isl_qpolynomial *qp, isl_int v);
3994 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3995 __isl_take isl_qpolynomial *qp);
3996 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3997 __isl_take isl_qpolynomial *qp1,
3998 __isl_take isl_qpolynomial *qp2);
3999 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4000 __isl_take isl_qpolynomial *qp1,
4001 __isl_take isl_qpolynomial *qp2);
4002 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4003 __isl_take isl_qpolynomial *qp1,
4004 __isl_take isl_qpolynomial *qp2);
4005 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4006 __isl_take isl_qpolynomial *qp, unsigned exponent);
4008 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4009 __isl_take isl_pw_qpolynomial *pwqp1,
4010 __isl_take isl_pw_qpolynomial *pwqp2);
4011 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4012 __isl_take isl_pw_qpolynomial *pwqp1,
4013 __isl_take isl_pw_qpolynomial *pwqp2);
4014 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4015 __isl_take isl_pw_qpolynomial *pwqp1,
4016 __isl_take isl_pw_qpolynomial *pwqp2);
4017 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4018 __isl_take isl_pw_qpolynomial *pwqp);
4019 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4020 __isl_take isl_pw_qpolynomial *pwqp1,
4021 __isl_take isl_pw_qpolynomial *pwqp2);
4022 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4023 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4025 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4026 __isl_take isl_union_pw_qpolynomial *upwqp1,
4027 __isl_take isl_union_pw_qpolynomial *upwqp2);
4028 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4029 __isl_take isl_union_pw_qpolynomial *upwqp1,
4030 __isl_take isl_union_pw_qpolynomial *upwqp2);
4031 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4032 __isl_take isl_union_pw_qpolynomial *upwqp1,
4033 __isl_take isl_union_pw_qpolynomial *upwqp2);
4035 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4036 __isl_take isl_pw_qpolynomial *pwqp,
4037 __isl_take isl_point *pnt);
4039 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4040 __isl_take isl_union_pw_qpolynomial *upwqp,
4041 __isl_take isl_point *pnt);
4043 __isl_give isl_set *isl_pw_qpolynomial_domain(
4044 __isl_take isl_pw_qpolynomial *pwqp);
4045 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4046 __isl_take isl_pw_qpolynomial *pwpq,
4047 __isl_take isl_set *set);
4048 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4049 __isl_take isl_pw_qpolynomial *pwpq,
4050 __isl_take isl_set *set);
4052 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4053 __isl_take isl_union_pw_qpolynomial *upwqp);
4054 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4055 __isl_take isl_union_pw_qpolynomial *upwpq,
4056 __isl_take isl_union_set *uset);
4057 __isl_give isl_union_pw_qpolynomial *
4058 isl_union_pw_qpolynomial_intersect_params(
4059 __isl_take isl_union_pw_qpolynomial *upwpq,
4060 __isl_take isl_set *set);
4062 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4063 __isl_take isl_qpolynomial *qp,
4064 __isl_take isl_space *model);
4066 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4067 __isl_take isl_qpolynomial *qp);
4068 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4069 __isl_take isl_pw_qpolynomial *pwqp);
4071 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4072 __isl_take isl_union_pw_qpolynomial *upwqp);
4074 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4075 __isl_take isl_qpolynomial *qp,
4076 __isl_take isl_set *context);
4077 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4078 __isl_take isl_qpolynomial *qp,
4079 __isl_take isl_set *context);
4081 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4082 __isl_take isl_pw_qpolynomial *pwqp,
4083 __isl_take isl_set *context);
4084 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4085 __isl_take isl_pw_qpolynomial *pwqp,
4086 __isl_take isl_set *context);
4088 __isl_give isl_union_pw_qpolynomial *
4089 isl_union_pw_qpolynomial_gist_params(
4090 __isl_take isl_union_pw_qpolynomial *upwqp,
4091 __isl_take isl_set *context);
4092 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4093 __isl_take isl_union_pw_qpolynomial *upwqp,
4094 __isl_take isl_union_set *context);
4096 The gist operation applies the gist operation to each of
4097 the cells in the domain of the input piecewise quasipolynomial.
4098 The context is also exploited
4099 to simplify the quasipolynomials associated to each cell.
4101 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4102 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4103 __isl_give isl_union_pw_qpolynomial *
4104 isl_union_pw_qpolynomial_to_polynomial(
4105 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4107 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4108 the polynomial will be an overapproximation. If C<sign> is negative,
4109 it will be an underapproximation. If C<sign> is zero, the approximation
4110 will lie somewhere in between.
4112 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4114 A piecewise quasipolynomial reduction is a piecewise
4115 reduction (or fold) of quasipolynomials.
4116 In particular, the reduction can be maximum or a minimum.
4117 The objects are mainly used to represent the result of
4118 an upper or lower bound on a quasipolynomial over its domain,
4119 i.e., as the result of the following function.
4121 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4122 __isl_take isl_pw_qpolynomial *pwqp,
4123 enum isl_fold type, int *tight);
4125 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4126 __isl_take isl_union_pw_qpolynomial *upwqp,
4127 enum isl_fold type, int *tight);
4129 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4130 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4131 is the returned bound is known be tight, i.e., for each value
4132 of the parameters there is at least
4133 one element in the domain that reaches the bound.
4134 If the domain of C<pwqp> is not wrapping, then the bound is computed
4135 over all elements in that domain and the result has a purely parametric
4136 domain. If the domain of C<pwqp> is wrapping, then the bound is
4137 computed over the range of the wrapped relation. The domain of the
4138 wrapped relation becomes the domain of the result.
4140 A (piecewise) quasipolynomial reduction can be copied or freed using the
4141 following functions.
4143 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4144 __isl_keep isl_qpolynomial_fold *fold);
4145 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4146 __isl_keep isl_pw_qpolynomial_fold *pwf);
4147 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4148 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4149 void isl_qpolynomial_fold_free(
4150 __isl_take isl_qpolynomial_fold *fold);
4151 void *isl_pw_qpolynomial_fold_free(
4152 __isl_take isl_pw_qpolynomial_fold *pwf);
4153 void *isl_union_pw_qpolynomial_fold_free(
4154 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4156 =head3 Printing Piecewise Quasipolynomial Reductions
4158 Piecewise quasipolynomial reductions can be printed
4159 using the following function.
4161 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4162 __isl_take isl_printer *p,
4163 __isl_keep isl_pw_qpolynomial_fold *pwf);
4164 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4165 __isl_take isl_printer *p,
4166 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4168 For C<isl_printer_print_pw_qpolynomial_fold>,
4169 output format of the printer
4170 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4171 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4172 output format of the printer
4173 needs to be set to C<ISL_FORMAT_ISL>.
4174 In case of printing in C<ISL_FORMAT_C>, the user may want
4175 to set the names of all dimensions
4177 __isl_give isl_pw_qpolynomial_fold *
4178 isl_pw_qpolynomial_fold_set_dim_name(
4179 __isl_take isl_pw_qpolynomial_fold *pwf,
4180 enum isl_dim_type type, unsigned pos,
4183 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4185 To iterate over all piecewise quasipolynomial reductions in a union
4186 piecewise quasipolynomial reduction, use the following function
4188 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4189 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4190 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4191 void *user), void *user);
4193 To iterate over the cells in a piecewise quasipolynomial reduction,
4194 use either of the following two functions
4196 int isl_pw_qpolynomial_fold_foreach_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);
4201 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4202 __isl_keep isl_pw_qpolynomial_fold *pwf,
4203 int (*fn)(__isl_take isl_set *set,
4204 __isl_take isl_qpolynomial_fold *fold,
4205 void *user), void *user);
4207 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4208 of the difference between these two functions.
4210 To iterate over all quasipolynomials in a reduction, use
4212 int isl_qpolynomial_fold_foreach_qpolynomial(
4213 __isl_keep isl_qpolynomial_fold *fold,
4214 int (*fn)(__isl_take isl_qpolynomial *qp,
4215 void *user), void *user);
4217 =head3 Properties of Piecewise Quasipolynomial Reductions
4219 To check whether two union piecewise quasipolynomial reductions are
4220 obviously equal, use
4222 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4223 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4224 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4226 =head3 Operations on Piecewise Quasipolynomial Reductions
4228 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4229 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4231 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4232 __isl_take isl_pw_qpolynomial_fold *pwf1,
4233 __isl_take isl_pw_qpolynomial_fold *pwf2);
4235 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4236 __isl_take isl_pw_qpolynomial_fold *pwf1,
4237 __isl_take isl_pw_qpolynomial_fold *pwf2);
4239 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4240 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4241 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4243 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4244 __isl_take isl_pw_qpolynomial_fold *pwf,
4245 __isl_take isl_point *pnt);
4247 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4248 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4249 __isl_take isl_point *pnt);
4251 __isl_give isl_pw_qpolynomial_fold *
4252 isl_pw_qpolynomial_fold_intersect_params(
4253 __isl_take isl_pw_qpolynomial_fold *pwf,
4254 __isl_take isl_set *set);
4256 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4257 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4258 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4259 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4260 __isl_take isl_union_set *uset);
4261 __isl_give isl_union_pw_qpolynomial_fold *
4262 isl_union_pw_qpolynomial_fold_intersect_params(
4263 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4264 __isl_take isl_set *set);
4266 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4267 __isl_take isl_pw_qpolynomial_fold *pwf);
4269 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4270 __isl_take isl_pw_qpolynomial_fold *pwf);
4272 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4273 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4275 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4276 __isl_take isl_qpolynomial_fold *fold,
4277 __isl_take isl_set *context);
4278 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4279 __isl_take isl_qpolynomial_fold *fold,
4280 __isl_take isl_set *context);
4282 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4283 __isl_take isl_pw_qpolynomial_fold *pwf,
4284 __isl_take isl_set *context);
4285 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4286 __isl_take isl_pw_qpolynomial_fold *pwf,
4287 __isl_take isl_set *context);
4289 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4290 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4291 __isl_take isl_union_set *context);
4292 __isl_give isl_union_pw_qpolynomial_fold *
4293 isl_union_pw_qpolynomial_fold_gist_params(
4294 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4295 __isl_take isl_set *context);
4297 The gist operation applies the gist operation to each of
4298 the cells in the domain of the input piecewise quasipolynomial reduction.
4299 In future, the operation will also exploit the context
4300 to simplify the quasipolynomial reductions associated to each cell.
4302 __isl_give isl_pw_qpolynomial_fold *
4303 isl_set_apply_pw_qpolynomial_fold(
4304 __isl_take isl_set *set,
4305 __isl_take isl_pw_qpolynomial_fold *pwf,
4307 __isl_give isl_pw_qpolynomial_fold *
4308 isl_map_apply_pw_qpolynomial_fold(
4309 __isl_take isl_map *map,
4310 __isl_take isl_pw_qpolynomial_fold *pwf,
4312 __isl_give isl_union_pw_qpolynomial_fold *
4313 isl_union_set_apply_union_pw_qpolynomial_fold(
4314 __isl_take isl_union_set *uset,
4315 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4317 __isl_give isl_union_pw_qpolynomial_fold *
4318 isl_union_map_apply_union_pw_qpolynomial_fold(
4319 __isl_take isl_union_map *umap,
4320 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4323 The functions taking a map
4324 compose the given map with the given piecewise quasipolynomial reduction.
4325 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4326 over all elements in the intersection of the range of the map
4327 and the domain of the piecewise quasipolynomial reduction
4328 as a function of an element in the domain of the map.
4329 The functions taking a set compute a bound over all elements in the
4330 intersection of the set and the domain of the
4331 piecewise quasipolynomial reduction.
4333 =head2 Dependence Analysis
4335 C<isl> contains specialized functionality for performing
4336 array dataflow analysis. That is, given a I<sink> access relation
4337 and a collection of possible I<source> access relations,
4338 C<isl> can compute relations that describe
4339 for each iteration of the sink access, which iteration
4340 of which of the source access relations was the last
4341 to access the same data element before the given iteration
4343 The resulting dependence relations map source iterations
4344 to the corresponding sink iterations.
4345 To compute standard flow dependences, the sink should be
4346 a read, while the sources should be writes.
4347 If any of the source accesses are marked as being I<may>
4348 accesses, then there will be a dependence from the last
4349 I<must> access B<and> from any I<may> access that follows
4350 this last I<must> access.
4351 In particular, if I<all> sources are I<may> accesses,
4352 then memory based dependence analysis is performed.
4353 If, on the other hand, all sources are I<must> accesses,
4354 then value based dependence analysis is performed.
4356 #include <isl/flow.h>
4358 typedef int (*isl_access_level_before)(void *first, void *second);
4360 __isl_give isl_access_info *isl_access_info_alloc(
4361 __isl_take isl_map *sink,
4362 void *sink_user, isl_access_level_before fn,
4364 __isl_give isl_access_info *isl_access_info_add_source(
4365 __isl_take isl_access_info *acc,
4366 __isl_take isl_map *source, int must,
4368 void *isl_access_info_free(__isl_take isl_access_info *acc);
4370 __isl_give isl_flow *isl_access_info_compute_flow(
4371 __isl_take isl_access_info *acc);
4373 int isl_flow_foreach(__isl_keep isl_flow *deps,
4374 int (*fn)(__isl_take isl_map *dep, int must,
4375 void *dep_user, void *user),
4377 __isl_give isl_map *isl_flow_get_no_source(
4378 __isl_keep isl_flow *deps, int must);
4379 void isl_flow_free(__isl_take isl_flow *deps);
4381 The function C<isl_access_info_compute_flow> performs the actual
4382 dependence analysis. The other functions are used to construct
4383 the input for this function or to read off the output.
4385 The input is collected in an C<isl_access_info>, which can
4386 be created through a call to C<isl_access_info_alloc>.
4387 The arguments to this functions are the sink access relation
4388 C<sink>, a token C<sink_user> used to identify the sink
4389 access to the user, a callback function for specifying the
4390 relative order of source and sink accesses, and the number
4391 of source access relations that will be added.
4392 The callback function has type C<int (*)(void *first, void *second)>.
4393 The function is called with two user supplied tokens identifying
4394 either a source or the sink and it should return the shared nesting
4395 level and the relative order of the two accesses.
4396 In particular, let I<n> be the number of loops shared by
4397 the two accesses. If C<first> precedes C<second> textually,
4398 then the function should return I<2 * n + 1>; otherwise,
4399 it should return I<2 * n>.
4400 The sources can be added to the C<isl_access_info> by performing
4401 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4402 C<must> indicates whether the source is a I<must> access
4403 or a I<may> access. Note that a multi-valued access relation
4404 should only be marked I<must> if every iteration in the domain
4405 of the relation accesses I<all> elements in its image.
4406 The C<source_user> token is again used to identify
4407 the source access. The range of the source access relation
4408 C<source> should have the same dimension as the range
4409 of the sink access relation.
4410 The C<isl_access_info_free> function should usually not be
4411 called explicitly, because it is called implicitly by
4412 C<isl_access_info_compute_flow>.
4414 The result of the dependence analysis is collected in an
4415 C<isl_flow>. There may be elements of
4416 the sink access for which no preceding source access could be
4417 found or for which all preceding sources are I<may> accesses.
4418 The relations containing these elements can be obtained through
4419 calls to C<isl_flow_get_no_source>, the first with C<must> set
4420 and the second with C<must> unset.
4421 In the case of standard flow dependence analysis,
4422 with the sink a read and the sources I<must> writes,
4423 the first relation corresponds to the reads from uninitialized
4424 array elements and the second relation is empty.
4425 The actual flow dependences can be extracted using
4426 C<isl_flow_foreach>. This function will call the user-specified
4427 callback function C<fn> for each B<non-empty> dependence between
4428 a source and the sink. The callback function is called
4429 with four arguments, the actual flow dependence relation
4430 mapping source iterations to sink iterations, a boolean that
4431 indicates whether it is a I<must> or I<may> dependence, a token
4432 identifying the source and an additional C<void *> with value
4433 equal to the third argument of the C<isl_flow_foreach> call.
4434 A dependence is marked I<must> if it originates from a I<must>
4435 source and if it is not followed by any I<may> sources.
4437 After finishing with an C<isl_flow>, the user should call
4438 C<isl_flow_free> to free all associated memory.
4440 A higher-level interface to dependence analysis is provided
4441 by the following function.
4443 #include <isl/flow.h>
4445 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4446 __isl_take isl_union_map *must_source,
4447 __isl_take isl_union_map *may_source,
4448 __isl_take isl_union_map *schedule,
4449 __isl_give isl_union_map **must_dep,
4450 __isl_give isl_union_map **may_dep,
4451 __isl_give isl_union_map **must_no_source,
4452 __isl_give isl_union_map **may_no_source);
4454 The arrays are identified by the tuple names of the ranges
4455 of the accesses. The iteration domains by the tuple names
4456 of the domains of the accesses and of the schedule.
4457 The relative order of the iteration domains is given by the
4458 schedule. The relations returned through C<must_no_source>
4459 and C<may_no_source> are subsets of C<sink>.
4460 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4461 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4462 any of the other arguments is treated as an error.
4464 =head3 Interaction with Dependence Analysis
4466 During the dependence analysis, we frequently need to perform
4467 the following operation. Given a relation between sink iterations
4468 and potential source iterations from a particular source domain,
4469 what is the last potential source iteration corresponding to each
4470 sink iteration. It can sometimes be convenient to adjust
4471 the set of potential source iterations before or after each such operation.
4472 The prototypical example is fuzzy array dataflow analysis,
4473 where we need to analyze if, based on data-dependent constraints,
4474 the sink iteration can ever be executed without one or more of
4475 the corresponding potential source iterations being executed.
4476 If so, we can introduce extra parameters and select an unknown
4477 but fixed source iteration from the potential source iterations.
4478 To be able to perform such manipulations, C<isl> provides the following
4481 #include <isl/flow.h>
4483 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4484 __isl_keep isl_map *source_map,
4485 __isl_keep isl_set *sink, void *source_user,
4487 __isl_give isl_access_info *isl_access_info_set_restrict(
4488 __isl_take isl_access_info *acc,
4489 isl_access_restrict fn, void *user);
4491 The function C<isl_access_info_set_restrict> should be called
4492 before calling C<isl_access_info_compute_flow> and registers a callback function
4493 that will be called any time C<isl> is about to compute the last
4494 potential source. The first argument is the (reverse) proto-dependence,
4495 mapping sink iterations to potential source iterations.
4496 The second argument represents the sink iterations for which
4497 we want to compute the last source iteration.
4498 The third argument is the token corresponding to the source
4499 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4500 The callback is expected to return a restriction on either the input or
4501 the output of the operation computing the last potential source.
4502 If the input needs to be restricted then restrictions are needed
4503 for both the source and the sink iterations. The sink iterations
4504 and the potential source iterations will be intersected with these sets.
4505 If the output needs to be restricted then only a restriction on the source
4506 iterations is required.
4507 If any error occurs, the callback should return C<NULL>.
4508 An C<isl_restriction> object can be created, freed and inspected
4509 using the following functions.
4511 #include <isl/flow.h>
4513 __isl_give isl_restriction *isl_restriction_input(
4514 __isl_take isl_set *source_restr,
4515 __isl_take isl_set *sink_restr);
4516 __isl_give isl_restriction *isl_restriction_output(
4517 __isl_take isl_set *source_restr);
4518 __isl_give isl_restriction *isl_restriction_none(
4519 __isl_take isl_map *source_map);
4520 __isl_give isl_restriction *isl_restriction_empty(
4521 __isl_take isl_map *source_map);
4522 void *isl_restriction_free(
4523 __isl_take isl_restriction *restr);
4524 isl_ctx *isl_restriction_get_ctx(
4525 __isl_keep isl_restriction *restr);
4527 C<isl_restriction_none> and C<isl_restriction_empty> are special
4528 cases of C<isl_restriction_input>. C<isl_restriction_none>
4529 is essentially equivalent to
4531 isl_restriction_input(isl_set_universe(
4532 isl_space_range(isl_map_get_space(source_map))),
4534 isl_space_domain(isl_map_get_space(source_map))));
4536 whereas C<isl_restriction_empty> is essentially equivalent to
4538 isl_restriction_input(isl_set_empty(
4539 isl_space_range(isl_map_get_space(source_map))),
4541 isl_space_domain(isl_map_get_space(source_map))));
4545 B<The functionality described in this section is fairly new
4546 and may be subject to change.>
4548 The following function can be used to compute a schedule
4549 for a union of domains.
4550 By default, the algorithm used to construct the schedule is similar
4551 to that of C<Pluto>.
4552 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4554 The generated schedule respects all C<validity> dependences.
4555 That is, all dependence distances over these dependences in the
4556 scheduled space are lexicographically positive.
4557 The default algorithm tries to minimize the dependence distances over
4558 C<proximity> dependences.
4559 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4560 for groups of domains where the dependence distances have only
4561 non-negative values.
4562 When using Feautrier's algorithm, the C<proximity> dependence
4563 distances are only minimized during the extension to a
4564 full-dimensional schedule.
4566 #include <isl/schedule.h>
4567 __isl_give isl_schedule *isl_union_set_compute_schedule(
4568 __isl_take isl_union_set *domain,
4569 __isl_take isl_union_map *validity,
4570 __isl_take isl_union_map *proximity);
4571 void *isl_schedule_free(__isl_take isl_schedule *sched);
4573 A mapping from the domains to the scheduled space can be obtained
4574 from an C<isl_schedule> using the following function.
4576 __isl_give isl_union_map *isl_schedule_get_map(
4577 __isl_keep isl_schedule *sched);
4579 A representation of the schedule can be printed using
4581 __isl_give isl_printer *isl_printer_print_schedule(
4582 __isl_take isl_printer *p,
4583 __isl_keep isl_schedule *schedule);
4585 A representation of the schedule as a forest of bands can be obtained
4586 using the following function.
4588 __isl_give isl_band_list *isl_schedule_get_band_forest(
4589 __isl_keep isl_schedule *schedule);
4591 The individual bands can be visited in depth-first post-order
4592 using the following function.
4594 #include <isl/schedule.h>
4595 int isl_schedule_foreach_band(
4596 __isl_keep isl_schedule *sched,
4597 int (*fn)(__isl_keep isl_band *band, void *user),
4600 The list can be manipulated as explained in L<"Lists">.
4601 The bands inside the list can be copied and freed using the following
4604 #include <isl/band.h>
4605 __isl_give isl_band *isl_band_copy(
4606 __isl_keep isl_band *band);
4607 void *isl_band_free(__isl_take isl_band *band);
4609 Each band contains zero or more scheduling dimensions.
4610 These are referred to as the members of the band.
4611 The section of the schedule that corresponds to the band is
4612 referred to as the partial schedule of the band.
4613 For those nodes that participate in a band, the outer scheduling
4614 dimensions form the prefix schedule, while the inner scheduling
4615 dimensions form the suffix schedule.
4616 That is, if we take a cut of the band forest, then the union of
4617 the concatenations of the prefix, partial and suffix schedules of
4618 each band in the cut is equal to the entire schedule (modulo
4619 some possible padding at the end with zero scheduling dimensions).
4620 The properties of a band can be inspected using the following functions.
4622 #include <isl/band.h>
4623 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4625 int isl_band_has_children(__isl_keep isl_band *band);
4626 __isl_give isl_band_list *isl_band_get_children(
4627 __isl_keep isl_band *band);
4629 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4630 __isl_keep isl_band *band);
4631 __isl_give isl_union_map *isl_band_get_partial_schedule(
4632 __isl_keep isl_band *band);
4633 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4634 __isl_keep isl_band *band);
4636 int isl_band_n_member(__isl_keep isl_band *band);
4637 int isl_band_member_is_zero_distance(
4638 __isl_keep isl_band *band, int pos);
4640 int isl_band_list_foreach_band(
4641 __isl_keep isl_band_list *list,
4642 int (*fn)(__isl_keep isl_band *band, void *user),
4645 Note that a scheduling dimension is considered to be ``zero
4646 distance'' if it does not carry any proximity dependences
4648 That is, if the dependence distances of the proximity
4649 dependences are all zero in that direction (for fixed
4650 iterations of outer bands).
4651 Like C<isl_schedule_foreach_band>,
4652 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4653 in depth-first post-order.
4655 A band can be tiled using the following function.
4657 #include <isl/band.h>
4658 int isl_band_tile(__isl_keep isl_band *band,
4659 __isl_take isl_vec *sizes);
4661 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4663 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4665 The C<isl_band_tile> function tiles the band using the given tile sizes
4666 inside its schedule.
4667 A new child band is created to represent the point loops and it is
4668 inserted between the modified band and its children.
4669 The C<tile_scale_tile_loops> option specifies whether the tile
4670 loops iterators should be scaled by the tile sizes.
4672 A representation of the band can be printed using
4674 #include <isl/band.h>
4675 __isl_give isl_printer *isl_printer_print_band(
4676 __isl_take isl_printer *p,
4677 __isl_keep isl_band *band);
4681 #include <isl/schedule.h>
4682 int isl_options_set_schedule_max_coefficient(
4683 isl_ctx *ctx, int val);
4684 int isl_options_get_schedule_max_coefficient(
4686 int isl_options_set_schedule_max_constant_term(
4687 isl_ctx *ctx, int val);
4688 int isl_options_get_schedule_max_constant_term(
4690 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4691 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4692 int isl_options_set_schedule_maximize_band_depth(
4693 isl_ctx *ctx, int val);
4694 int isl_options_get_schedule_maximize_band_depth(
4696 int isl_options_set_schedule_outer_zero_distance(
4697 isl_ctx *ctx, int val);
4698 int isl_options_get_schedule_outer_zero_distance(
4700 int isl_options_set_schedule_split_scaled(
4701 isl_ctx *ctx, int val);
4702 int isl_options_get_schedule_split_scaled(
4704 int isl_options_set_schedule_algorithm(
4705 isl_ctx *ctx, int val);
4706 int isl_options_get_schedule_algorithm(
4708 int isl_options_set_schedule_separate_components(
4709 isl_ctx *ctx, int val);
4710 int isl_options_get_schedule_separate_components(
4715 =item * schedule_max_coefficient
4717 This option enforces that the coefficients for variable and parameter
4718 dimensions in the calculated schedule are not larger than the specified value.
4719 This option can significantly increase the speed of the scheduling calculation
4720 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4721 this option does not introduce bounds on the variable or parameter
4724 =item * schedule_max_constant_term
4726 This option enforces that the constant coefficients in the calculated schedule
4727 are not larger than the maximal constant term. This option can significantly
4728 increase the speed of the scheduling calculation and may also prevent fusing of
4729 unrelated dimensions. A value of -1 means that this option does not introduce
4730 bounds on the constant coefficients.
4732 =item * schedule_fuse
4734 This option controls the level of fusion.
4735 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
4736 resulting schedule will be distributed as much as possible.
4737 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
4738 try to fuse loops in the resulting schedule.
4740 =item * schedule_maximize_band_depth
4742 If this option is set, we do not split bands at the point
4743 where we detect splitting is necessary. Instead, we
4744 backtrack and split bands as early as possible. This
4745 reduces the number of splits and maximizes the width of
4746 the bands. Wider bands give more possibilities for tiling.
4747 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
4748 then bands will be split as early as possible, even if there is no need.
4749 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
4751 =item * schedule_outer_zero_distance
4753 If this option is set, then we try to construct schedules
4754 where the outermost scheduling dimension in each band
4755 results in a zero dependence distance over the proximity
4758 =item * schedule_split_scaled
4760 If this option is set, then we try to construct schedules in which the
4761 constant term is split off from the linear part if the linear parts of
4762 the scheduling rows for all nodes in the graphs have a common non-trivial
4764 The constant term is then placed in a separate band and the linear
4767 =item * schedule_algorithm
4769 Selects the scheduling algorithm to be used.
4770 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4771 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4773 =item * schedule_separate_components
4775 If at any point the dependence graph contains any (weakly connected) components,
4776 then these components are scheduled separately.
4777 If this option is not set, then some iterations of the domains
4778 in these components may be scheduled together.
4779 If this option is set, then the components are given consecutive
4784 =head2 Parametric Vertex Enumeration
4786 The parametric vertex enumeration described in this section
4787 is mainly intended to be used internally and by the C<barvinok>
4790 #include <isl/vertices.h>
4791 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4792 __isl_keep isl_basic_set *bset);
4794 The function C<isl_basic_set_compute_vertices> performs the
4795 actual computation of the parametric vertices and the chamber
4796 decomposition and store the result in an C<isl_vertices> object.
4797 This information can be queried by either iterating over all
4798 the vertices or iterating over all the chambers or cells
4799 and then iterating over all vertices that are active on the chamber.
4801 int isl_vertices_foreach_vertex(
4802 __isl_keep isl_vertices *vertices,
4803 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4806 int isl_vertices_foreach_cell(
4807 __isl_keep isl_vertices *vertices,
4808 int (*fn)(__isl_take isl_cell *cell, void *user),
4810 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4811 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4814 Other operations that can be performed on an C<isl_vertices> object are
4817 isl_ctx *isl_vertices_get_ctx(
4818 __isl_keep isl_vertices *vertices);
4819 int isl_vertices_get_n_vertices(
4820 __isl_keep isl_vertices *vertices);
4821 void isl_vertices_free(__isl_take isl_vertices *vertices);
4823 Vertices can be inspected and destroyed using the following functions.
4825 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4826 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4827 __isl_give isl_basic_set *isl_vertex_get_domain(
4828 __isl_keep isl_vertex *vertex);
4829 __isl_give isl_basic_set *isl_vertex_get_expr(
4830 __isl_keep isl_vertex *vertex);
4831 void isl_vertex_free(__isl_take isl_vertex *vertex);
4833 C<isl_vertex_get_expr> returns a singleton parametric set describing
4834 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4836 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4837 B<rational> basic sets, so they should mainly be used for inspection
4838 and should not be mixed with integer sets.
4840 Chambers can be inspected and destroyed using the following functions.
4842 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4843 __isl_give isl_basic_set *isl_cell_get_domain(
4844 __isl_keep isl_cell *cell);
4845 void isl_cell_free(__isl_take isl_cell *cell);
4849 Although C<isl> is mainly meant to be used as a library,
4850 it also contains some basic applications that use some
4851 of the functionality of C<isl>.
4852 The input may be specified in either the L<isl format>
4853 or the L<PolyLib format>.
4855 =head2 C<isl_polyhedron_sample>
4857 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4858 an integer element of the polyhedron, if there is any.
4859 The first column in the output is the denominator and is always
4860 equal to 1. If the polyhedron contains no integer points,
4861 then a vector of length zero is printed.
4865 C<isl_pip> takes the same input as the C<example> program
4866 from the C<piplib> distribution, i.e., a set of constraints
4867 on the parameters, a line containing only -1 and finally a set
4868 of constraints on a parametric polyhedron.
4869 The coefficients of the parameters appear in the last columns
4870 (but before the final constant column).
4871 The output is the lexicographic minimum of the parametric polyhedron.
4872 As C<isl> currently does not have its own output format, the output
4873 is just a dump of the internal state.
4875 =head2 C<isl_polyhedron_minimize>
4877 C<isl_polyhedron_minimize> computes the minimum of some linear
4878 or affine objective function over the integer points in a polyhedron.
4879 If an affine objective function
4880 is given, then the constant should appear in the last column.
4882 =head2 C<isl_polytope_scan>
4884 Given a polytope, C<isl_polytope_scan> prints
4885 all integer points in the polytope.