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_set_set(
2903 __isl_take isl_set_list *list, int index,
2904 __isl_take isl_set *set);
2905 __isl_give isl_set_list *isl_set_list_concat(
2906 __isl_take isl_set_list *list1,
2907 __isl_take isl_set_list *list2);
2908 void *isl_set_list_free(__isl_take isl_set_list *list);
2910 C<isl_set_list_alloc> creates an empty list with a capacity for
2911 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2914 Lists can be inspected using the following functions.
2916 #include <isl/list.h>
2917 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2918 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2919 __isl_give isl_set *isl_set_list_get_set(
2920 __isl_keep isl_set_list *list, int index);
2921 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2922 int (*fn)(__isl_take isl_set *el, void *user),
2925 Lists can be printed using
2927 #include <isl/list.h>
2928 __isl_give isl_printer *isl_printer_print_set_list(
2929 __isl_take isl_printer *p,
2930 __isl_keep isl_set_list *list);
2934 Vectors can be created, copied and freed using the following functions.
2936 #include <isl/vec.h>
2937 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2939 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2940 void isl_vec_free(__isl_take isl_vec *vec);
2942 Note that the elements of a newly created vector may have arbitrary values.
2943 The elements can be changed and inspected using the following functions.
2945 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2946 int isl_vec_size(__isl_keep isl_vec *vec);
2947 int isl_vec_get_element(__isl_keep isl_vec *vec,
2948 int pos, isl_int *v);
2949 __isl_give isl_vec *isl_vec_set_element(
2950 __isl_take isl_vec *vec, int pos, isl_int v);
2951 __isl_give isl_vec *isl_vec_set_element_si(
2952 __isl_take isl_vec *vec, int pos, int v);
2953 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2955 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2958 C<isl_vec_get_element> will return a negative value if anything went wrong.
2959 In that case, the value of C<*v> is undefined.
2963 Matrices can be created, copied and freed using the following functions.
2965 #include <isl/mat.h>
2966 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2967 unsigned n_row, unsigned n_col);
2968 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2969 void isl_mat_free(__isl_take isl_mat *mat);
2971 Note that the elements of a newly created matrix may have arbitrary values.
2972 The elements can be changed and inspected using the following functions.
2974 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2975 int isl_mat_rows(__isl_keep isl_mat *mat);
2976 int isl_mat_cols(__isl_keep isl_mat *mat);
2977 int isl_mat_get_element(__isl_keep isl_mat *mat,
2978 int row, int col, isl_int *v);
2979 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2980 int row, int col, isl_int v);
2981 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2982 int row, int col, int v);
2984 C<isl_mat_get_element> will return a negative value if anything went wrong.
2985 In that case, the value of C<*v> is undefined.
2987 The following function can be used to compute the (right) inverse
2988 of a matrix, i.e., a matrix such that the product of the original
2989 and the inverse (in that order) is a multiple of the identity matrix.
2990 The input matrix is assumed to be of full row-rank.
2992 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2994 The following function can be used to compute the (right) kernel
2995 (or null space) of a matrix, i.e., a matrix such that the product of
2996 the original and the kernel (in that order) is the zero matrix.
2998 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3000 =head2 Piecewise Quasi Affine Expressions
3002 The zero quasi affine expression on a given domain can be created using
3004 __isl_give isl_aff *isl_aff_zero_on_domain(
3005 __isl_take isl_local_space *ls);
3007 Note that the space in which the resulting object lives is a map space
3008 with the given space as domain and a one-dimensional range.
3010 An empty piecewise quasi affine expression (one with no cells)
3011 or a piecewise quasi affine expression with a single cell can
3012 be created using the following functions.
3014 #include <isl/aff.h>
3015 __isl_give isl_pw_aff *isl_pw_aff_empty(
3016 __isl_take isl_space *space);
3017 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3018 __isl_take isl_set *set, __isl_take isl_aff *aff);
3019 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3020 __isl_take isl_aff *aff);
3022 A piecewise quasi affine expression that is equal to 1 on a set
3023 and 0 outside the set can be created using the following function.
3025 #include <isl/aff.h>
3026 __isl_give isl_pw_aff *isl_set_indicator_function(
3027 __isl_take isl_set *set);
3029 Quasi affine expressions can be copied and freed using
3031 #include <isl/aff.h>
3032 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3033 void *isl_aff_free(__isl_take isl_aff *aff);
3035 __isl_give isl_pw_aff *isl_pw_aff_copy(
3036 __isl_keep isl_pw_aff *pwaff);
3037 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3039 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3040 using the following function. The constraint is required to have
3041 a non-zero coefficient for the specified dimension.
3043 #include <isl/constraint.h>
3044 __isl_give isl_aff *isl_constraint_get_bound(
3045 __isl_keep isl_constraint *constraint,
3046 enum isl_dim_type type, int pos);
3048 The entire affine expression of the constraint can also be extracted
3049 using the following function.
3051 #include <isl/constraint.h>
3052 __isl_give isl_aff *isl_constraint_get_aff(
3053 __isl_keep isl_constraint *constraint);
3055 Conversely, an equality constraint equating
3056 the affine expression to zero or an inequality constraint enforcing
3057 the affine expression to be non-negative, can be constructed using
3059 __isl_give isl_constraint *isl_equality_from_aff(
3060 __isl_take isl_aff *aff);
3061 __isl_give isl_constraint *isl_inequality_from_aff(
3062 __isl_take isl_aff *aff);
3064 The expression can be inspected using
3066 #include <isl/aff.h>
3067 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3068 int isl_aff_dim(__isl_keep isl_aff *aff,
3069 enum isl_dim_type type);
3070 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3071 __isl_keep isl_aff *aff);
3072 __isl_give isl_local_space *isl_aff_get_local_space(
3073 __isl_keep isl_aff *aff);
3074 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3075 enum isl_dim_type type, unsigned pos);
3076 const char *isl_pw_aff_get_dim_name(
3077 __isl_keep isl_pw_aff *pa,
3078 enum isl_dim_type type, unsigned pos);
3079 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3080 enum isl_dim_type type, unsigned pos);
3081 __isl_give isl_id *isl_pw_aff_get_dim_id(
3082 __isl_keep isl_pw_aff *pa,
3083 enum isl_dim_type type, unsigned pos);
3084 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3085 __isl_keep isl_pw_aff *pa,
3086 enum isl_dim_type type);
3087 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3089 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3090 enum isl_dim_type type, int pos, isl_int *v);
3091 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3093 __isl_give isl_aff *isl_aff_get_div(
3094 __isl_keep isl_aff *aff, int pos);
3096 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3097 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3098 int (*fn)(__isl_take isl_set *set,
3099 __isl_take isl_aff *aff,
3100 void *user), void *user);
3102 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3103 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3105 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3106 enum isl_dim_type type, unsigned first, unsigned n);
3107 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3108 enum isl_dim_type type, unsigned first, unsigned n);
3110 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3111 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3112 enum isl_dim_type type);
3113 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3115 It can be modified using
3117 #include <isl/aff.h>
3118 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3119 __isl_take isl_pw_aff *pwaff,
3120 enum isl_dim_type type, __isl_take isl_id *id);
3121 __isl_give isl_aff *isl_aff_set_dim_name(
3122 __isl_take isl_aff *aff, enum isl_dim_type type,
3123 unsigned pos, const char *s);
3124 __isl_give isl_aff *isl_aff_set_dim_id(
3125 __isl_take isl_aff *aff, enum isl_dim_type type,
3126 unsigned pos, __isl_take isl_id *id);
3127 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3128 __isl_take isl_pw_aff *pma,
3129 enum isl_dim_type type, unsigned pos,
3130 __isl_take isl_id *id);
3131 __isl_give isl_aff *isl_aff_set_constant(
3132 __isl_take isl_aff *aff, isl_int v);
3133 __isl_give isl_aff *isl_aff_set_constant_si(
3134 __isl_take isl_aff *aff, int v);
3135 __isl_give isl_aff *isl_aff_set_coefficient(
3136 __isl_take isl_aff *aff,
3137 enum isl_dim_type type, int pos, isl_int v);
3138 __isl_give isl_aff *isl_aff_set_coefficient_si(
3139 __isl_take isl_aff *aff,
3140 enum isl_dim_type type, int pos, int v);
3141 __isl_give isl_aff *isl_aff_set_denominator(
3142 __isl_take isl_aff *aff, isl_int v);
3144 __isl_give isl_aff *isl_aff_add_constant(
3145 __isl_take isl_aff *aff, isl_int v);
3146 __isl_give isl_aff *isl_aff_add_constant_si(
3147 __isl_take isl_aff *aff, int v);
3148 __isl_give isl_aff *isl_aff_add_constant_num(
3149 __isl_take isl_aff *aff, isl_int v);
3150 __isl_give isl_aff *isl_aff_add_constant_num_si(
3151 __isl_take isl_aff *aff, int v);
3152 __isl_give isl_aff *isl_aff_add_coefficient(
3153 __isl_take isl_aff *aff,
3154 enum isl_dim_type type, int pos, isl_int v);
3155 __isl_give isl_aff *isl_aff_add_coefficient_si(
3156 __isl_take isl_aff *aff,
3157 enum isl_dim_type type, int pos, int v);
3159 __isl_give isl_aff *isl_aff_insert_dims(
3160 __isl_take isl_aff *aff,
3161 enum isl_dim_type type, unsigned first, unsigned n);
3162 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3163 __isl_take isl_pw_aff *pwaff,
3164 enum isl_dim_type type, unsigned first, unsigned n);
3165 __isl_give isl_aff *isl_aff_add_dims(
3166 __isl_take isl_aff *aff,
3167 enum isl_dim_type type, unsigned n);
3168 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3169 __isl_take isl_pw_aff *pwaff,
3170 enum isl_dim_type type, unsigned n);
3171 __isl_give isl_aff *isl_aff_drop_dims(
3172 __isl_take isl_aff *aff,
3173 enum isl_dim_type type, unsigned first, unsigned n);
3174 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3175 __isl_take isl_pw_aff *pwaff,
3176 enum isl_dim_type type, unsigned first, unsigned n);
3178 Note that the C<set_constant> and C<set_coefficient> functions
3179 set the I<numerator> of the constant or coefficient, while
3180 C<add_constant> and C<add_coefficient> add an integer value to
3181 the possibly rational constant or coefficient.
3182 The C<add_constant_num> functions add an integer value to
3185 To check whether an affine expressions is obviously zero
3186 or obviously equal to some other affine expression, use
3188 #include <isl/aff.h>
3189 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3190 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3191 __isl_keep isl_aff *aff2);
3192 int isl_pw_aff_plain_is_equal(
3193 __isl_keep isl_pw_aff *pwaff1,
3194 __isl_keep isl_pw_aff *pwaff2);
3198 #include <isl/aff.h>
3199 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3200 __isl_take isl_aff *aff2);
3201 __isl_give isl_pw_aff *isl_pw_aff_add(
3202 __isl_take isl_pw_aff *pwaff1,
3203 __isl_take isl_pw_aff *pwaff2);
3204 __isl_give isl_pw_aff *isl_pw_aff_min(
3205 __isl_take isl_pw_aff *pwaff1,
3206 __isl_take isl_pw_aff *pwaff2);
3207 __isl_give isl_pw_aff *isl_pw_aff_max(
3208 __isl_take isl_pw_aff *pwaff1,
3209 __isl_take isl_pw_aff *pwaff2);
3210 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3211 __isl_take isl_aff *aff2);
3212 __isl_give isl_pw_aff *isl_pw_aff_sub(
3213 __isl_take isl_pw_aff *pwaff1,
3214 __isl_take isl_pw_aff *pwaff2);
3215 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3216 __isl_give isl_pw_aff *isl_pw_aff_neg(
3217 __isl_take isl_pw_aff *pwaff);
3218 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3219 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3220 __isl_take isl_pw_aff *pwaff);
3221 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3222 __isl_give isl_pw_aff *isl_pw_aff_floor(
3223 __isl_take isl_pw_aff *pwaff);
3224 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3226 __isl_give isl_pw_aff *isl_pw_aff_mod(
3227 __isl_take isl_pw_aff *pwaff, isl_int mod);
3228 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3230 __isl_give isl_pw_aff *isl_pw_aff_scale(
3231 __isl_take isl_pw_aff *pwaff, isl_int f);
3232 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3234 __isl_give isl_aff *isl_aff_scale_down_ui(
3235 __isl_take isl_aff *aff, unsigned f);
3236 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3237 __isl_take isl_pw_aff *pwaff, isl_int f);
3239 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3240 __isl_take isl_pw_aff_list *list);
3241 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3242 __isl_take isl_pw_aff_list *list);
3244 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3245 __isl_take isl_pw_aff *pwqp);
3247 __isl_give isl_aff *isl_aff_align_params(
3248 __isl_take isl_aff *aff,
3249 __isl_take isl_space *model);
3250 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3251 __isl_take isl_pw_aff *pwaff,
3252 __isl_take isl_space *model);
3254 __isl_give isl_aff *isl_aff_project_domain_on_params(
3255 __isl_take isl_aff *aff);
3257 __isl_give isl_aff *isl_aff_gist_params(
3258 __isl_take isl_aff *aff,
3259 __isl_take isl_set *context);
3260 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3261 __isl_take isl_set *context);
3262 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3263 __isl_take isl_pw_aff *pwaff,
3264 __isl_take isl_set *context);
3265 __isl_give isl_pw_aff *isl_pw_aff_gist(
3266 __isl_take isl_pw_aff *pwaff,
3267 __isl_take isl_set *context);
3269 __isl_give isl_set *isl_pw_aff_domain(
3270 __isl_take isl_pw_aff *pwaff);
3271 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3272 __isl_take isl_pw_aff *pa,
3273 __isl_take isl_set *set);
3274 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3275 __isl_take isl_pw_aff *pa,
3276 __isl_take isl_set *set);
3278 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3279 __isl_take isl_aff *aff2);
3280 __isl_give isl_pw_aff *isl_pw_aff_mul(
3281 __isl_take isl_pw_aff *pwaff1,
3282 __isl_take isl_pw_aff *pwaff2);
3284 When multiplying two affine expressions, at least one of the two needs
3287 #include <isl/aff.h>
3288 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3289 __isl_take isl_aff *aff);
3290 __isl_give isl_basic_set *isl_aff_le_basic_set(
3291 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3292 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3293 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3294 __isl_give isl_set *isl_pw_aff_eq_set(
3295 __isl_take isl_pw_aff *pwaff1,
3296 __isl_take isl_pw_aff *pwaff2);
3297 __isl_give isl_set *isl_pw_aff_ne_set(
3298 __isl_take isl_pw_aff *pwaff1,
3299 __isl_take isl_pw_aff *pwaff2);
3300 __isl_give isl_set *isl_pw_aff_le_set(
3301 __isl_take isl_pw_aff *pwaff1,
3302 __isl_take isl_pw_aff *pwaff2);
3303 __isl_give isl_set *isl_pw_aff_lt_set(
3304 __isl_take isl_pw_aff *pwaff1,
3305 __isl_take isl_pw_aff *pwaff2);
3306 __isl_give isl_set *isl_pw_aff_ge_set(
3307 __isl_take isl_pw_aff *pwaff1,
3308 __isl_take isl_pw_aff *pwaff2);
3309 __isl_give isl_set *isl_pw_aff_gt_set(
3310 __isl_take isl_pw_aff *pwaff1,
3311 __isl_take isl_pw_aff *pwaff2);
3313 __isl_give isl_set *isl_pw_aff_list_eq_set(
3314 __isl_take isl_pw_aff_list *list1,
3315 __isl_take isl_pw_aff_list *list2);
3316 __isl_give isl_set *isl_pw_aff_list_ne_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_le_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_lt_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_ge_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_gt_set(
3329 __isl_take isl_pw_aff_list *list1,
3330 __isl_take isl_pw_aff_list *list2);
3332 The function C<isl_aff_neg_basic_set> returns a basic set
3333 containing those elements in the domain space
3334 of C<aff> where C<aff> is negative.
3335 The function C<isl_aff_ge_basic_set> returns a basic set
3336 containing those elements in the shared space
3337 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3338 The function C<isl_pw_aff_ge_set> returns a set
3339 containing those elements in the shared domain
3340 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3341 The functions operating on C<isl_pw_aff_list> apply the corresponding
3342 C<isl_pw_aff> function to each pair of elements in the two lists.
3344 #include <isl/aff.h>
3345 __isl_give isl_set *isl_pw_aff_nonneg_set(
3346 __isl_take isl_pw_aff *pwaff);
3347 __isl_give isl_set *isl_pw_aff_zero_set(
3348 __isl_take isl_pw_aff *pwaff);
3349 __isl_give isl_set *isl_pw_aff_non_zero_set(
3350 __isl_take isl_pw_aff *pwaff);
3352 The function C<isl_pw_aff_nonneg_set> returns a set
3353 containing those elements in the domain
3354 of C<pwaff> where C<pwaff> is non-negative.
3356 #include <isl/aff.h>
3357 __isl_give isl_pw_aff *isl_pw_aff_cond(
3358 __isl_take isl_pw_aff *cond,
3359 __isl_take isl_pw_aff *pwaff_true,
3360 __isl_take isl_pw_aff *pwaff_false);
3362 The function C<isl_pw_aff_cond> performs a conditional operator
3363 and returns an expression that is equal to C<pwaff_true>
3364 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3365 where C<cond> is zero.
3367 #include <isl/aff.h>
3368 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3369 __isl_take isl_pw_aff *pwaff1,
3370 __isl_take isl_pw_aff *pwaff2);
3371 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3372 __isl_take isl_pw_aff *pwaff1,
3373 __isl_take isl_pw_aff *pwaff2);
3374 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3375 __isl_take isl_pw_aff *pwaff1,
3376 __isl_take isl_pw_aff *pwaff2);
3378 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3379 expression with a domain that is the union of those of C<pwaff1> and
3380 C<pwaff2> and such that on each cell, the quasi-affine expression is
3381 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3382 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3383 associated expression is the defined one.
3385 An expression can be read from input using
3387 #include <isl/aff.h>
3388 __isl_give isl_aff *isl_aff_read_from_str(
3389 isl_ctx *ctx, const char *str);
3390 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3391 isl_ctx *ctx, const char *str);
3393 An expression can be printed using
3395 #include <isl/aff.h>
3396 __isl_give isl_printer *isl_printer_print_aff(
3397 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3399 __isl_give isl_printer *isl_printer_print_pw_aff(
3400 __isl_take isl_printer *p,
3401 __isl_keep isl_pw_aff *pwaff);
3403 =head2 Piecewise Multiple Quasi Affine Expressions
3405 An C<isl_multi_aff> object represents a sequence of
3406 zero or more affine expressions, all defined on the same domain space.
3408 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3411 #include <isl/aff.h>
3412 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3413 __isl_take isl_space *space,
3414 __isl_take isl_aff_list *list);
3416 An empty piecewise multiple quasi affine expression (one with no cells),
3417 the zero piecewise multiple quasi affine expression (with value zero
3418 for each output dimension),
3419 a piecewise multiple quasi affine expression with a single cell (with
3420 either a universe or a specified domain) or
3421 a zero-dimensional piecewise multiple quasi affine expression
3423 can be created using the following functions.
3425 #include <isl/aff.h>
3426 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3427 __isl_take isl_space *space);
3428 __isl_give isl_multi_aff *isl_multi_aff_zero(
3429 __isl_take isl_space *space);
3430 __isl_give isl_multi_aff *isl_multi_aff_identity(
3431 __isl_take isl_space *space);
3432 __isl_give isl_pw_multi_aff *
3433 isl_pw_multi_aff_from_multi_aff(
3434 __isl_take isl_multi_aff *ma);
3435 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3436 __isl_take isl_set *set,
3437 __isl_take isl_multi_aff *maff);
3438 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3439 __isl_take isl_set *set);
3441 __isl_give isl_union_pw_multi_aff *
3442 isl_union_pw_multi_aff_empty(
3443 __isl_take isl_space *space);
3444 __isl_give isl_union_pw_multi_aff *
3445 isl_union_pw_multi_aff_add_pw_multi_aff(
3446 __isl_take isl_union_pw_multi_aff *upma,
3447 __isl_take isl_pw_multi_aff *pma);
3448 __isl_give isl_union_pw_multi_aff *
3449 isl_union_pw_multi_aff_from_domain(
3450 __isl_take isl_union_set *uset);
3452 A piecewise multiple quasi affine expression can also be initialized
3453 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3454 and the C<isl_map> is single-valued.
3456 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3457 __isl_take isl_set *set);
3458 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3459 __isl_take isl_map *map);
3461 Multiple quasi affine expressions can be copied and freed using
3463 #include <isl/aff.h>
3464 __isl_give isl_multi_aff *isl_multi_aff_copy(
3465 __isl_keep isl_multi_aff *maff);
3466 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3468 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3469 __isl_keep isl_pw_multi_aff *pma);
3470 void *isl_pw_multi_aff_free(
3471 __isl_take isl_pw_multi_aff *pma);
3473 __isl_give isl_union_pw_multi_aff *
3474 isl_union_pw_multi_aff_copy(
3475 __isl_keep isl_union_pw_multi_aff *upma);
3476 void *isl_union_pw_multi_aff_free(
3477 __isl_take isl_union_pw_multi_aff *upma);
3479 The expression can be inspected using
3481 #include <isl/aff.h>
3482 isl_ctx *isl_multi_aff_get_ctx(
3483 __isl_keep isl_multi_aff *maff);
3484 isl_ctx *isl_pw_multi_aff_get_ctx(
3485 __isl_keep isl_pw_multi_aff *pma);
3486 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3487 __isl_keep isl_union_pw_multi_aff *upma);
3488 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3489 enum isl_dim_type type);
3490 unsigned isl_pw_multi_aff_dim(
3491 __isl_keep isl_pw_multi_aff *pma,
3492 enum isl_dim_type type);
3493 __isl_give isl_aff *isl_multi_aff_get_aff(
3494 __isl_keep isl_multi_aff *multi, int pos);
3495 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3496 __isl_keep isl_pw_multi_aff *pma, int pos);
3497 const char *isl_pw_multi_aff_get_dim_name(
3498 __isl_keep isl_pw_multi_aff *pma,
3499 enum isl_dim_type type, unsigned pos);
3500 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3501 __isl_keep isl_pw_multi_aff *pma,
3502 enum isl_dim_type type, unsigned pos);
3503 const char *isl_multi_aff_get_tuple_name(
3504 __isl_keep isl_multi_aff *multi,
3505 enum isl_dim_type type);
3506 int isl_pw_multi_aff_has_tuple_name(
3507 __isl_keep isl_pw_multi_aff *pma,
3508 enum isl_dim_type type);
3509 const char *isl_pw_multi_aff_get_tuple_name(
3510 __isl_keep isl_pw_multi_aff *pma,
3511 enum isl_dim_type type);
3512 int isl_pw_multi_aff_has_tuple_id(
3513 __isl_keep isl_pw_multi_aff *pma,
3514 enum isl_dim_type type);
3515 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3516 __isl_keep isl_pw_multi_aff *pma,
3517 enum isl_dim_type type);
3519 int isl_pw_multi_aff_foreach_piece(
3520 __isl_keep isl_pw_multi_aff *pma,
3521 int (*fn)(__isl_take isl_set *set,
3522 __isl_take isl_multi_aff *maff,
3523 void *user), void *user);
3525 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3526 __isl_keep isl_union_pw_multi_aff *upma,
3527 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3528 void *user), void *user);
3530 It can be modified using
3532 #include <isl/aff.h>
3533 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3534 __isl_take isl_multi_aff *multi, int pos,
3535 __isl_take isl_aff *aff);
3536 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3537 __isl_take isl_multi_aff *maff,
3538 enum isl_dim_type type, unsigned pos, const char *s);
3539 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3540 __isl_take isl_multi_aff *maff,
3541 enum isl_dim_type type, __isl_take isl_id *id);
3542 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3543 __isl_take isl_pw_multi_aff *pma,
3544 enum isl_dim_type type, __isl_take isl_id *id);
3546 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3547 __isl_take isl_multi_aff *maff,
3548 enum isl_dim_type type, unsigned first, unsigned n);
3549 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
3550 __isl_take isl_pw_multi_aff *pma,
3551 enum isl_dim_type type, unsigned first, unsigned n);
3553 To check whether two multiple affine expressions are
3554 obviously equal to each other, use
3556 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3557 __isl_keep isl_multi_aff *maff2);
3558 int isl_pw_multi_aff_plain_is_equal(
3559 __isl_keep isl_pw_multi_aff *pma1,
3560 __isl_keep isl_pw_multi_aff *pma2);
3564 #include <isl/aff.h>
3565 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3566 __isl_take isl_pw_multi_aff *pma1,
3567 __isl_take isl_pw_multi_aff *pma2);
3568 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3569 __isl_take isl_pw_multi_aff *pma1,
3570 __isl_take isl_pw_multi_aff *pma2);
3571 __isl_give isl_multi_aff *isl_multi_aff_add(
3572 __isl_take isl_multi_aff *maff1,
3573 __isl_take isl_multi_aff *maff2);
3574 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3575 __isl_take isl_pw_multi_aff *pma1,
3576 __isl_take isl_pw_multi_aff *pma2);
3577 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3578 __isl_take isl_union_pw_multi_aff *upma1,
3579 __isl_take isl_union_pw_multi_aff *upma2);
3580 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3581 __isl_take isl_pw_multi_aff *pma1,
3582 __isl_take isl_pw_multi_aff *pma2);
3583 __isl_give isl_multi_aff *isl_multi_aff_scale(
3584 __isl_take isl_multi_aff *maff,
3586 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3587 __isl_take isl_pw_multi_aff *pma,
3588 __isl_take isl_set *set);
3589 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3590 __isl_take isl_pw_multi_aff *pma,
3591 __isl_take isl_set *set);
3592 __isl_give isl_multi_aff *isl_multi_aff_lift(
3593 __isl_take isl_multi_aff *maff,
3594 __isl_give isl_local_space **ls);
3595 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3596 __isl_take isl_pw_multi_aff *pma);
3597 __isl_give isl_multi_aff *isl_multi_aff_align_params(
3598 __isl_take isl_multi_aff *multi,
3599 __isl_take isl_space *model);
3600 __isl_give isl_pw_multi_aff *
3601 isl_pw_multi_aff_project_domain_on_params(
3602 __isl_take isl_pw_multi_aff *pma);
3603 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3604 __isl_take isl_multi_aff *maff,
3605 __isl_take isl_set *context);
3606 __isl_give isl_multi_aff *isl_multi_aff_gist(
3607 __isl_take isl_multi_aff *maff,
3608 __isl_take isl_set *context);
3609 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3610 __isl_take isl_pw_multi_aff *pma,
3611 __isl_take isl_set *set);
3612 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3613 __isl_take isl_pw_multi_aff *pma,
3614 __isl_take isl_set *set);
3615 __isl_give isl_set *isl_pw_multi_aff_domain(
3616 __isl_take isl_pw_multi_aff *pma);
3617 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3618 __isl_take isl_union_pw_multi_aff *upma);
3619 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3620 __isl_take isl_multi_aff *ma1,
3621 __isl_take isl_multi_aff *ma2);
3622 __isl_give isl_multi_aff *isl_multi_aff_product(
3623 __isl_take isl_multi_aff *ma1,
3624 __isl_take isl_multi_aff *ma2);
3625 __isl_give isl_pw_multi_aff *
3626 isl_pw_multi_aff_flat_range_product(
3627 __isl_take isl_pw_multi_aff *pma1,
3628 __isl_take isl_pw_multi_aff *pma2);
3629 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3630 __isl_take isl_pw_multi_aff *pma1,
3631 __isl_take isl_pw_multi_aff *pma2);
3632 __isl_give isl_union_pw_multi_aff *
3633 isl_union_pw_multi_aff_flat_range_product(
3634 __isl_take isl_union_pw_multi_aff *upma1,
3635 __isl_take isl_union_pw_multi_aff *upma2);
3637 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3638 then it is assigned the local space that lies at the basis of
3639 the lifting applied.
3641 __isl_give isl_set *isl_multi_aff_lex_le_set(
3642 __isl_take isl_multi_aff *ma1,
3643 __isl_take isl_multi_aff *ma2);
3644 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3645 __isl_take isl_multi_aff *ma1,
3646 __isl_take isl_multi_aff *ma2);
3648 The function C<isl_multi_aff_lex_le_set> returns a set
3649 containing those elements in the shared domain space
3650 where C<ma1> is lexicographically smaller than or
3653 An expression can be read from input using
3655 #include <isl/aff.h>
3656 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3657 isl_ctx *ctx, const char *str);
3658 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3659 isl_ctx *ctx, const char *str);
3661 An expression can be printed using
3663 #include <isl/aff.h>
3664 __isl_give isl_printer *isl_printer_print_multi_aff(
3665 __isl_take isl_printer *p,
3666 __isl_keep isl_multi_aff *maff);
3667 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3668 __isl_take isl_printer *p,
3669 __isl_keep isl_pw_multi_aff *pma);
3670 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3671 __isl_take isl_printer *p,
3672 __isl_keep isl_union_pw_multi_aff *upma);
3676 Points are elements of a set. They can be used to construct
3677 simple sets (boxes) or they can be used to represent the
3678 individual elements of a set.
3679 The zero point (the origin) can be created using
3681 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3683 The coordinates of a point can be inspected, set and changed
3686 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3687 enum isl_dim_type type, int pos, isl_int *v);
3688 __isl_give isl_point *isl_point_set_coordinate(
3689 __isl_take isl_point *pnt,
3690 enum isl_dim_type type, int pos, isl_int v);
3692 __isl_give isl_point *isl_point_add_ui(
3693 __isl_take isl_point *pnt,
3694 enum isl_dim_type type, int pos, unsigned val);
3695 __isl_give isl_point *isl_point_sub_ui(
3696 __isl_take isl_point *pnt,
3697 enum isl_dim_type type, int pos, unsigned val);
3699 Other properties can be obtained using
3701 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3703 Points can be copied or freed using
3705 __isl_give isl_point *isl_point_copy(
3706 __isl_keep isl_point *pnt);
3707 void isl_point_free(__isl_take isl_point *pnt);
3709 A singleton set can be created from a point using
3711 __isl_give isl_basic_set *isl_basic_set_from_point(
3712 __isl_take isl_point *pnt);
3713 __isl_give isl_set *isl_set_from_point(
3714 __isl_take isl_point *pnt);
3716 and a box can be created from two opposite extremal points using
3718 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3719 __isl_take isl_point *pnt1,
3720 __isl_take isl_point *pnt2);
3721 __isl_give isl_set *isl_set_box_from_points(
3722 __isl_take isl_point *pnt1,
3723 __isl_take isl_point *pnt2);
3725 All elements of a B<bounded> (union) set can be enumerated using
3726 the following functions.
3728 int isl_set_foreach_point(__isl_keep isl_set *set,
3729 int (*fn)(__isl_take isl_point *pnt, void *user),
3731 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3732 int (*fn)(__isl_take isl_point *pnt, void *user),
3735 The function C<fn> is called for each integer point in
3736 C<set> with as second argument the last argument of
3737 the C<isl_set_foreach_point> call. The function C<fn>
3738 should return C<0> on success and C<-1> on failure.
3739 In the latter case, C<isl_set_foreach_point> will stop
3740 enumerating and return C<-1> as well.
3741 If the enumeration is performed successfully and to completion,
3742 then C<isl_set_foreach_point> returns C<0>.
3744 To obtain a single point of a (basic) set, use
3746 __isl_give isl_point *isl_basic_set_sample_point(
3747 __isl_take isl_basic_set *bset);
3748 __isl_give isl_point *isl_set_sample_point(
3749 __isl_take isl_set *set);
3751 If C<set> does not contain any (integer) points, then the
3752 resulting point will be ``void'', a property that can be
3755 int isl_point_is_void(__isl_keep isl_point *pnt);
3757 =head2 Piecewise Quasipolynomials
3759 A piecewise quasipolynomial is a particular kind of function that maps
3760 a parametric point to a rational value.
3761 More specifically, a quasipolynomial is a polynomial expression in greatest
3762 integer parts of affine expressions of parameters and variables.
3763 A piecewise quasipolynomial is a subdivision of a given parametric
3764 domain into disjoint cells with a quasipolynomial associated to
3765 each cell. The value of the piecewise quasipolynomial at a given
3766 point is the value of the quasipolynomial associated to the cell
3767 that contains the point. Outside of the union of cells,
3768 the value is assumed to be zero.
3769 For example, the piecewise quasipolynomial
3771 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3773 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3774 A given piecewise quasipolynomial has a fixed domain dimension.
3775 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3776 defined over different domains.
3777 Piecewise quasipolynomials are mainly used by the C<barvinok>
3778 library for representing the number of elements in a parametric set or map.
3779 For example, the piecewise quasipolynomial above represents
3780 the number of points in the map
3782 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3784 =head3 Input and Output
3786 Piecewise quasipolynomials can be read from input using
3788 __isl_give isl_union_pw_qpolynomial *
3789 isl_union_pw_qpolynomial_read_from_str(
3790 isl_ctx *ctx, const char *str);
3792 Quasipolynomials and piecewise quasipolynomials can be printed
3793 using the following functions.
3795 __isl_give isl_printer *isl_printer_print_qpolynomial(
3796 __isl_take isl_printer *p,
3797 __isl_keep isl_qpolynomial *qp);
3799 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3800 __isl_take isl_printer *p,
3801 __isl_keep isl_pw_qpolynomial *pwqp);
3803 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3804 __isl_take isl_printer *p,
3805 __isl_keep isl_union_pw_qpolynomial *upwqp);
3807 The output format of the printer
3808 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3809 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3811 In case of printing in C<ISL_FORMAT_C>, the user may want
3812 to set the names of all dimensions
3814 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3815 __isl_take isl_qpolynomial *qp,
3816 enum isl_dim_type type, unsigned pos,
3818 __isl_give isl_pw_qpolynomial *
3819 isl_pw_qpolynomial_set_dim_name(
3820 __isl_take isl_pw_qpolynomial *pwqp,
3821 enum isl_dim_type type, unsigned pos,
3824 =head3 Creating New (Piecewise) Quasipolynomials
3826 Some simple quasipolynomials can be created using the following functions.
3827 More complicated quasipolynomials can be created by applying
3828 operations such as addition and multiplication
3829 on the resulting quasipolynomials
3831 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3832 __isl_take isl_space *domain);
3833 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3834 __isl_take isl_space *domain);
3835 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3836 __isl_take isl_space *domain);
3837 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3838 __isl_take isl_space *domain);
3839 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3840 __isl_take isl_space *domain);
3841 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3842 __isl_take isl_space *domain,
3843 const isl_int n, const isl_int d);
3844 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3845 __isl_take isl_space *domain,
3846 enum isl_dim_type type, unsigned pos);
3847 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3848 __isl_take isl_aff *aff);
3850 Note that the space in which a quasipolynomial lives is a map space
3851 with a one-dimensional range. The C<domain> argument in some of
3852 the functions above corresponds to the domain of this map space.
3854 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3855 with a single cell can be created using the following functions.
3856 Multiple of these single cell piecewise quasipolynomials can
3857 be combined to create more complicated piecewise quasipolynomials.
3859 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3860 __isl_take isl_space *space);
3861 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3862 __isl_take isl_set *set,
3863 __isl_take isl_qpolynomial *qp);
3864 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3865 __isl_take isl_qpolynomial *qp);
3866 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3867 __isl_take isl_pw_aff *pwaff);
3869 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3870 __isl_take isl_space *space);
3871 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3872 __isl_take isl_pw_qpolynomial *pwqp);
3873 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3874 __isl_take isl_union_pw_qpolynomial *upwqp,
3875 __isl_take isl_pw_qpolynomial *pwqp);
3877 Quasipolynomials can be copied and freed again using the following
3880 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3881 __isl_keep isl_qpolynomial *qp);
3882 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3884 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3885 __isl_keep isl_pw_qpolynomial *pwqp);
3886 void *isl_pw_qpolynomial_free(
3887 __isl_take isl_pw_qpolynomial *pwqp);
3889 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3890 __isl_keep isl_union_pw_qpolynomial *upwqp);
3891 void *isl_union_pw_qpolynomial_free(
3892 __isl_take isl_union_pw_qpolynomial *upwqp);
3894 =head3 Inspecting (Piecewise) Quasipolynomials
3896 To iterate over all piecewise quasipolynomials in a union
3897 piecewise quasipolynomial, use the following function
3899 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3900 __isl_keep isl_union_pw_qpolynomial *upwqp,
3901 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3904 To extract the piecewise quasipolynomial in a given space from a union, use
3906 __isl_give isl_pw_qpolynomial *
3907 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3908 __isl_keep isl_union_pw_qpolynomial *upwqp,
3909 __isl_take isl_space *space);
3911 To iterate over the cells in a piecewise quasipolynomial,
3912 use either of the following two functions
3914 int isl_pw_qpolynomial_foreach_piece(
3915 __isl_keep isl_pw_qpolynomial *pwqp,
3916 int (*fn)(__isl_take isl_set *set,
3917 __isl_take isl_qpolynomial *qp,
3918 void *user), void *user);
3919 int isl_pw_qpolynomial_foreach_lifted_piece(
3920 __isl_keep isl_pw_qpolynomial *pwqp,
3921 int (*fn)(__isl_take isl_set *set,
3922 __isl_take isl_qpolynomial *qp,
3923 void *user), void *user);
3925 As usual, the function C<fn> should return C<0> on success
3926 and C<-1> on failure. The difference between
3927 C<isl_pw_qpolynomial_foreach_piece> and
3928 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3929 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3930 compute unique representations for all existentially quantified
3931 variables and then turn these existentially quantified variables
3932 into extra set variables, adapting the associated quasipolynomial
3933 accordingly. This means that the C<set> passed to C<fn>
3934 will not have any existentially quantified variables, but that
3935 the dimensions of the sets may be different for different
3936 invocations of C<fn>.
3938 To iterate over all terms in a quasipolynomial,
3941 int isl_qpolynomial_foreach_term(
3942 __isl_keep isl_qpolynomial *qp,
3943 int (*fn)(__isl_take isl_term *term,
3944 void *user), void *user);
3946 The terms themselves can be inspected and freed using
3949 unsigned isl_term_dim(__isl_keep isl_term *term,
3950 enum isl_dim_type type);
3951 void isl_term_get_num(__isl_keep isl_term *term,
3953 void isl_term_get_den(__isl_keep isl_term *term,
3955 int isl_term_get_exp(__isl_keep isl_term *term,
3956 enum isl_dim_type type, unsigned pos);
3957 __isl_give isl_aff *isl_term_get_div(
3958 __isl_keep isl_term *term, unsigned pos);
3959 void isl_term_free(__isl_take isl_term *term);
3961 Each term is a product of parameters, set variables and
3962 integer divisions. The function C<isl_term_get_exp>
3963 returns the exponent of a given dimensions in the given term.
3964 The C<isl_int>s in the arguments of C<isl_term_get_num>
3965 and C<isl_term_get_den> need to have been initialized
3966 using C<isl_int_init> before calling these functions.
3968 =head3 Properties of (Piecewise) Quasipolynomials
3970 To check whether a quasipolynomial is actually a constant,
3971 use the following function.
3973 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3974 isl_int *n, isl_int *d);
3976 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3977 then the numerator and denominator of the constant
3978 are returned in C<*n> and C<*d>, respectively.
3980 To check whether two union piecewise quasipolynomials are
3981 obviously equal, use
3983 int isl_union_pw_qpolynomial_plain_is_equal(
3984 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3985 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3987 =head3 Operations on (Piecewise) Quasipolynomials
3989 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3990 __isl_take isl_qpolynomial *qp, isl_int v);
3991 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3992 __isl_take isl_qpolynomial *qp);
3993 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3994 __isl_take isl_qpolynomial *qp1,
3995 __isl_take isl_qpolynomial *qp2);
3996 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3997 __isl_take isl_qpolynomial *qp1,
3998 __isl_take isl_qpolynomial *qp2);
3999 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4000 __isl_take isl_qpolynomial *qp1,
4001 __isl_take isl_qpolynomial *qp2);
4002 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4003 __isl_take isl_qpolynomial *qp, unsigned exponent);
4005 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4006 __isl_take isl_pw_qpolynomial *pwqp1,
4007 __isl_take isl_pw_qpolynomial *pwqp2);
4008 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4009 __isl_take isl_pw_qpolynomial *pwqp1,
4010 __isl_take isl_pw_qpolynomial *pwqp2);
4011 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4012 __isl_take isl_pw_qpolynomial *pwqp1,
4013 __isl_take isl_pw_qpolynomial *pwqp2);
4014 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4015 __isl_take isl_pw_qpolynomial *pwqp);
4016 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4017 __isl_take isl_pw_qpolynomial *pwqp1,
4018 __isl_take isl_pw_qpolynomial *pwqp2);
4019 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4020 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4022 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4023 __isl_take isl_union_pw_qpolynomial *upwqp1,
4024 __isl_take isl_union_pw_qpolynomial *upwqp2);
4025 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
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_mul(
4029 __isl_take isl_union_pw_qpolynomial *upwqp1,
4030 __isl_take isl_union_pw_qpolynomial *upwqp2);
4032 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4033 __isl_take isl_pw_qpolynomial *pwqp,
4034 __isl_take isl_point *pnt);
4036 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4037 __isl_take isl_union_pw_qpolynomial *upwqp,
4038 __isl_take isl_point *pnt);
4040 __isl_give isl_set *isl_pw_qpolynomial_domain(
4041 __isl_take isl_pw_qpolynomial *pwqp);
4042 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4043 __isl_take isl_pw_qpolynomial *pwpq,
4044 __isl_take isl_set *set);
4045 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4046 __isl_take isl_pw_qpolynomial *pwpq,
4047 __isl_take isl_set *set);
4049 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4050 __isl_take isl_union_pw_qpolynomial *upwqp);
4051 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4052 __isl_take isl_union_pw_qpolynomial *upwpq,
4053 __isl_take isl_union_set *uset);
4054 __isl_give isl_union_pw_qpolynomial *
4055 isl_union_pw_qpolynomial_intersect_params(
4056 __isl_take isl_union_pw_qpolynomial *upwpq,
4057 __isl_take isl_set *set);
4059 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4060 __isl_take isl_qpolynomial *qp,
4061 __isl_take isl_space *model);
4063 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4064 __isl_take isl_qpolynomial *qp);
4065 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4066 __isl_take isl_pw_qpolynomial *pwqp);
4068 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4069 __isl_take isl_union_pw_qpolynomial *upwqp);
4071 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4072 __isl_take isl_qpolynomial *qp,
4073 __isl_take isl_set *context);
4074 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4075 __isl_take isl_qpolynomial *qp,
4076 __isl_take isl_set *context);
4078 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4079 __isl_take isl_pw_qpolynomial *pwqp,
4080 __isl_take isl_set *context);
4081 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4082 __isl_take isl_pw_qpolynomial *pwqp,
4083 __isl_take isl_set *context);
4085 __isl_give isl_union_pw_qpolynomial *
4086 isl_union_pw_qpolynomial_gist_params(
4087 __isl_take isl_union_pw_qpolynomial *upwqp,
4088 __isl_take isl_set *context);
4089 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4090 __isl_take isl_union_pw_qpolynomial *upwqp,
4091 __isl_take isl_union_set *context);
4093 The gist operation applies the gist operation to each of
4094 the cells in the domain of the input piecewise quasipolynomial.
4095 The context is also exploited
4096 to simplify the quasipolynomials associated to each cell.
4098 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4099 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4100 __isl_give isl_union_pw_qpolynomial *
4101 isl_union_pw_qpolynomial_to_polynomial(
4102 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4104 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4105 the polynomial will be an overapproximation. If C<sign> is negative,
4106 it will be an underapproximation. If C<sign> is zero, the approximation
4107 will lie somewhere in between.
4109 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4111 A piecewise quasipolynomial reduction is a piecewise
4112 reduction (or fold) of quasipolynomials.
4113 In particular, the reduction can be maximum or a minimum.
4114 The objects are mainly used to represent the result of
4115 an upper or lower bound on a quasipolynomial over its domain,
4116 i.e., as the result of the following function.
4118 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4119 __isl_take isl_pw_qpolynomial *pwqp,
4120 enum isl_fold type, int *tight);
4122 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4123 __isl_take isl_union_pw_qpolynomial *upwqp,
4124 enum isl_fold type, int *tight);
4126 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4127 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4128 is the returned bound is known be tight, i.e., for each value
4129 of the parameters there is at least
4130 one element in the domain that reaches the bound.
4131 If the domain of C<pwqp> is not wrapping, then the bound is computed
4132 over all elements in that domain and the result has a purely parametric
4133 domain. If the domain of C<pwqp> is wrapping, then the bound is
4134 computed over the range of the wrapped relation. The domain of the
4135 wrapped relation becomes the domain of the result.
4137 A (piecewise) quasipolynomial reduction can be copied or freed using the
4138 following functions.
4140 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4141 __isl_keep isl_qpolynomial_fold *fold);
4142 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4143 __isl_keep isl_pw_qpolynomial_fold *pwf);
4144 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4145 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4146 void isl_qpolynomial_fold_free(
4147 __isl_take isl_qpolynomial_fold *fold);
4148 void *isl_pw_qpolynomial_fold_free(
4149 __isl_take isl_pw_qpolynomial_fold *pwf);
4150 void *isl_union_pw_qpolynomial_fold_free(
4151 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4153 =head3 Printing Piecewise Quasipolynomial Reductions
4155 Piecewise quasipolynomial reductions can be printed
4156 using the following function.
4158 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4159 __isl_take isl_printer *p,
4160 __isl_keep isl_pw_qpolynomial_fold *pwf);
4161 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4162 __isl_take isl_printer *p,
4163 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4165 For C<isl_printer_print_pw_qpolynomial_fold>,
4166 output format of the printer
4167 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4168 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4169 output format of the printer
4170 needs to be set to C<ISL_FORMAT_ISL>.
4171 In case of printing in C<ISL_FORMAT_C>, the user may want
4172 to set the names of all dimensions
4174 __isl_give isl_pw_qpolynomial_fold *
4175 isl_pw_qpolynomial_fold_set_dim_name(
4176 __isl_take isl_pw_qpolynomial_fold *pwf,
4177 enum isl_dim_type type, unsigned pos,
4180 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4182 To iterate over all piecewise quasipolynomial reductions in a union
4183 piecewise quasipolynomial reduction, use the following function
4185 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4186 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4187 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4188 void *user), void *user);
4190 To iterate over the cells in a piecewise quasipolynomial reduction,
4191 use either of the following two functions
4193 int isl_pw_qpolynomial_fold_foreach_piece(
4194 __isl_keep isl_pw_qpolynomial_fold *pwf,
4195 int (*fn)(__isl_take isl_set *set,
4196 __isl_take isl_qpolynomial_fold *fold,
4197 void *user), void *user);
4198 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4199 __isl_keep isl_pw_qpolynomial_fold *pwf,
4200 int (*fn)(__isl_take isl_set *set,
4201 __isl_take isl_qpolynomial_fold *fold,
4202 void *user), void *user);
4204 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4205 of the difference between these two functions.
4207 To iterate over all quasipolynomials in a reduction, use
4209 int isl_qpolynomial_fold_foreach_qpolynomial(
4210 __isl_keep isl_qpolynomial_fold *fold,
4211 int (*fn)(__isl_take isl_qpolynomial *qp,
4212 void *user), void *user);
4214 =head3 Properties of Piecewise Quasipolynomial Reductions
4216 To check whether two union piecewise quasipolynomial reductions are
4217 obviously equal, use
4219 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4220 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4221 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4223 =head3 Operations on Piecewise Quasipolynomial Reductions
4225 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4226 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4228 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4229 __isl_take isl_pw_qpolynomial_fold *pwf1,
4230 __isl_take isl_pw_qpolynomial_fold *pwf2);
4232 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4233 __isl_take isl_pw_qpolynomial_fold *pwf1,
4234 __isl_take isl_pw_qpolynomial_fold *pwf2);
4236 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4237 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4238 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4240 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4241 __isl_take isl_pw_qpolynomial_fold *pwf,
4242 __isl_take isl_point *pnt);
4244 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4245 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4246 __isl_take isl_point *pnt);
4248 __isl_give isl_pw_qpolynomial_fold *
4249 isl_pw_qpolynomial_fold_intersect_params(
4250 __isl_take isl_pw_qpolynomial_fold *pwf,
4251 __isl_take isl_set *set);
4253 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4254 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4255 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4256 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4257 __isl_take isl_union_set *uset);
4258 __isl_give isl_union_pw_qpolynomial_fold *
4259 isl_union_pw_qpolynomial_fold_intersect_params(
4260 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4261 __isl_take isl_set *set);
4263 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4264 __isl_take isl_pw_qpolynomial_fold *pwf);
4266 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4267 __isl_take isl_pw_qpolynomial_fold *pwf);
4269 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4270 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4272 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4273 __isl_take isl_qpolynomial_fold *fold,
4274 __isl_take isl_set *context);
4275 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4276 __isl_take isl_qpolynomial_fold *fold,
4277 __isl_take isl_set *context);
4279 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4280 __isl_take isl_pw_qpolynomial_fold *pwf,
4281 __isl_take isl_set *context);
4282 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4283 __isl_take isl_pw_qpolynomial_fold *pwf,
4284 __isl_take isl_set *context);
4286 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4287 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4288 __isl_take isl_union_set *context);
4289 __isl_give isl_union_pw_qpolynomial_fold *
4290 isl_union_pw_qpolynomial_fold_gist_params(
4291 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4292 __isl_take isl_set *context);
4294 The gist operation applies the gist operation to each of
4295 the cells in the domain of the input piecewise quasipolynomial reduction.
4296 In future, the operation will also exploit the context
4297 to simplify the quasipolynomial reductions associated to each cell.
4299 __isl_give isl_pw_qpolynomial_fold *
4300 isl_set_apply_pw_qpolynomial_fold(
4301 __isl_take isl_set *set,
4302 __isl_take isl_pw_qpolynomial_fold *pwf,
4304 __isl_give isl_pw_qpolynomial_fold *
4305 isl_map_apply_pw_qpolynomial_fold(
4306 __isl_take isl_map *map,
4307 __isl_take isl_pw_qpolynomial_fold *pwf,
4309 __isl_give isl_union_pw_qpolynomial_fold *
4310 isl_union_set_apply_union_pw_qpolynomial_fold(
4311 __isl_take isl_union_set *uset,
4312 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4314 __isl_give isl_union_pw_qpolynomial_fold *
4315 isl_union_map_apply_union_pw_qpolynomial_fold(
4316 __isl_take isl_union_map *umap,
4317 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4320 The functions taking a map
4321 compose the given map with the given piecewise quasipolynomial reduction.
4322 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4323 over all elements in the intersection of the range of the map
4324 and the domain of the piecewise quasipolynomial reduction
4325 as a function of an element in the domain of the map.
4326 The functions taking a set compute a bound over all elements in the
4327 intersection of the set and the domain of the
4328 piecewise quasipolynomial reduction.
4330 =head2 Dependence Analysis
4332 C<isl> contains specialized functionality for performing
4333 array dataflow analysis. That is, given a I<sink> access relation
4334 and a collection of possible I<source> access relations,
4335 C<isl> can compute relations that describe
4336 for each iteration of the sink access, which iteration
4337 of which of the source access relations was the last
4338 to access the same data element before the given iteration
4340 The resulting dependence relations map source iterations
4341 to the corresponding sink iterations.
4342 To compute standard flow dependences, the sink should be
4343 a read, while the sources should be writes.
4344 If any of the source accesses are marked as being I<may>
4345 accesses, then there will be a dependence from the last
4346 I<must> access B<and> from any I<may> access that follows
4347 this last I<must> access.
4348 In particular, if I<all> sources are I<may> accesses,
4349 then memory based dependence analysis is performed.
4350 If, on the other hand, all sources are I<must> accesses,
4351 then value based dependence analysis is performed.
4353 #include <isl/flow.h>
4355 typedef int (*isl_access_level_before)(void *first, void *second);
4357 __isl_give isl_access_info *isl_access_info_alloc(
4358 __isl_take isl_map *sink,
4359 void *sink_user, isl_access_level_before fn,
4361 __isl_give isl_access_info *isl_access_info_add_source(
4362 __isl_take isl_access_info *acc,
4363 __isl_take isl_map *source, int must,
4365 void *isl_access_info_free(__isl_take isl_access_info *acc);
4367 __isl_give isl_flow *isl_access_info_compute_flow(
4368 __isl_take isl_access_info *acc);
4370 int isl_flow_foreach(__isl_keep isl_flow *deps,
4371 int (*fn)(__isl_take isl_map *dep, int must,
4372 void *dep_user, void *user),
4374 __isl_give isl_map *isl_flow_get_no_source(
4375 __isl_keep isl_flow *deps, int must);
4376 void isl_flow_free(__isl_take isl_flow *deps);
4378 The function C<isl_access_info_compute_flow> performs the actual
4379 dependence analysis. The other functions are used to construct
4380 the input for this function or to read off the output.
4382 The input is collected in an C<isl_access_info>, which can
4383 be created through a call to C<isl_access_info_alloc>.
4384 The arguments to this functions are the sink access relation
4385 C<sink>, a token C<sink_user> used to identify the sink
4386 access to the user, a callback function for specifying the
4387 relative order of source and sink accesses, and the number
4388 of source access relations that will be added.
4389 The callback function has type C<int (*)(void *first, void *second)>.
4390 The function is called with two user supplied tokens identifying
4391 either a source or the sink and it should return the shared nesting
4392 level and the relative order of the two accesses.
4393 In particular, let I<n> be the number of loops shared by
4394 the two accesses. If C<first> precedes C<second> textually,
4395 then the function should return I<2 * n + 1>; otherwise,
4396 it should return I<2 * n>.
4397 The sources can be added to the C<isl_access_info> by performing
4398 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4399 C<must> indicates whether the source is a I<must> access
4400 or a I<may> access. Note that a multi-valued access relation
4401 should only be marked I<must> if every iteration in the domain
4402 of the relation accesses I<all> elements in its image.
4403 The C<source_user> token is again used to identify
4404 the source access. The range of the source access relation
4405 C<source> should have the same dimension as the range
4406 of the sink access relation.
4407 The C<isl_access_info_free> function should usually not be
4408 called explicitly, because it is called implicitly by
4409 C<isl_access_info_compute_flow>.
4411 The result of the dependence analysis is collected in an
4412 C<isl_flow>. There may be elements of
4413 the sink access for which no preceding source access could be
4414 found or for which all preceding sources are I<may> accesses.
4415 The relations containing these elements can be obtained through
4416 calls to C<isl_flow_get_no_source>, the first with C<must> set
4417 and the second with C<must> unset.
4418 In the case of standard flow dependence analysis,
4419 with the sink a read and the sources I<must> writes,
4420 the first relation corresponds to the reads from uninitialized
4421 array elements and the second relation is empty.
4422 The actual flow dependences can be extracted using
4423 C<isl_flow_foreach>. This function will call the user-specified
4424 callback function C<fn> for each B<non-empty> dependence between
4425 a source and the sink. The callback function is called
4426 with four arguments, the actual flow dependence relation
4427 mapping source iterations to sink iterations, a boolean that
4428 indicates whether it is a I<must> or I<may> dependence, a token
4429 identifying the source and an additional C<void *> with value
4430 equal to the third argument of the C<isl_flow_foreach> call.
4431 A dependence is marked I<must> if it originates from a I<must>
4432 source and if it is not followed by any I<may> sources.
4434 After finishing with an C<isl_flow>, the user should call
4435 C<isl_flow_free> to free all associated memory.
4437 A higher-level interface to dependence analysis is provided
4438 by the following function.
4440 #include <isl/flow.h>
4442 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4443 __isl_take isl_union_map *must_source,
4444 __isl_take isl_union_map *may_source,
4445 __isl_take isl_union_map *schedule,
4446 __isl_give isl_union_map **must_dep,
4447 __isl_give isl_union_map **may_dep,
4448 __isl_give isl_union_map **must_no_source,
4449 __isl_give isl_union_map **may_no_source);
4451 The arrays are identified by the tuple names of the ranges
4452 of the accesses. The iteration domains by the tuple names
4453 of the domains of the accesses and of the schedule.
4454 The relative order of the iteration domains is given by the
4455 schedule. The relations returned through C<must_no_source>
4456 and C<may_no_source> are subsets of C<sink>.
4457 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4458 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4459 any of the other arguments is treated as an error.
4461 =head3 Interaction with Dependence Analysis
4463 During the dependence analysis, we frequently need to perform
4464 the following operation. Given a relation between sink iterations
4465 and potential source iterations from a particular source domain,
4466 what is the last potential source iteration corresponding to each
4467 sink iteration. It can sometimes be convenient to adjust
4468 the set of potential source iterations before or after each such operation.
4469 The prototypical example is fuzzy array dataflow analysis,
4470 where we need to analyze if, based on data-dependent constraints,
4471 the sink iteration can ever be executed without one or more of
4472 the corresponding potential source iterations being executed.
4473 If so, we can introduce extra parameters and select an unknown
4474 but fixed source iteration from the potential source iterations.
4475 To be able to perform such manipulations, C<isl> provides the following
4478 #include <isl/flow.h>
4480 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4481 __isl_keep isl_map *source_map,
4482 __isl_keep isl_set *sink, void *source_user,
4484 __isl_give isl_access_info *isl_access_info_set_restrict(
4485 __isl_take isl_access_info *acc,
4486 isl_access_restrict fn, void *user);
4488 The function C<isl_access_info_set_restrict> should be called
4489 before calling C<isl_access_info_compute_flow> and registers a callback function
4490 that will be called any time C<isl> is about to compute the last
4491 potential source. The first argument is the (reverse) proto-dependence,
4492 mapping sink iterations to potential source iterations.
4493 The second argument represents the sink iterations for which
4494 we want to compute the last source iteration.
4495 The third argument is the token corresponding to the source
4496 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4497 The callback is expected to return a restriction on either the input or
4498 the output of the operation computing the last potential source.
4499 If the input needs to be restricted then restrictions are needed
4500 for both the source and the sink iterations. The sink iterations
4501 and the potential source iterations will be intersected with these sets.
4502 If the output needs to be restricted then only a restriction on the source
4503 iterations is required.
4504 If any error occurs, the callback should return C<NULL>.
4505 An C<isl_restriction> object can be created, freed and inspected
4506 using the following functions.
4508 #include <isl/flow.h>
4510 __isl_give isl_restriction *isl_restriction_input(
4511 __isl_take isl_set *source_restr,
4512 __isl_take isl_set *sink_restr);
4513 __isl_give isl_restriction *isl_restriction_output(
4514 __isl_take isl_set *source_restr);
4515 __isl_give isl_restriction *isl_restriction_none(
4516 __isl_take isl_map *source_map);
4517 __isl_give isl_restriction *isl_restriction_empty(
4518 __isl_take isl_map *source_map);
4519 void *isl_restriction_free(
4520 __isl_take isl_restriction *restr);
4521 isl_ctx *isl_restriction_get_ctx(
4522 __isl_keep isl_restriction *restr);
4524 C<isl_restriction_none> and C<isl_restriction_empty> are special
4525 cases of C<isl_restriction_input>. C<isl_restriction_none>
4526 is essentially equivalent to
4528 isl_restriction_input(isl_set_universe(
4529 isl_space_range(isl_map_get_space(source_map))),
4531 isl_space_domain(isl_map_get_space(source_map))));
4533 whereas C<isl_restriction_empty> is essentially equivalent to
4535 isl_restriction_input(isl_set_empty(
4536 isl_space_range(isl_map_get_space(source_map))),
4538 isl_space_domain(isl_map_get_space(source_map))));
4542 B<The functionality described in this section is fairly new
4543 and may be subject to change.>
4545 The following function can be used to compute a schedule
4546 for a union of domains.
4547 By default, the algorithm used to construct the schedule is similar
4548 to that of C<Pluto>.
4549 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4551 The generated schedule respects all C<validity> dependences.
4552 That is, all dependence distances over these dependences in the
4553 scheduled space are lexicographically positive.
4554 The default algorithm tries to minimize the dependence distances over
4555 C<proximity> dependences.
4556 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4557 for groups of domains where the dependence distances have only
4558 non-negative values.
4559 When using Feautrier's algorithm, the C<proximity> dependence
4560 distances are only minimized during the extension to a
4561 full-dimensional schedule.
4563 #include <isl/schedule.h>
4564 __isl_give isl_schedule *isl_union_set_compute_schedule(
4565 __isl_take isl_union_set *domain,
4566 __isl_take isl_union_map *validity,
4567 __isl_take isl_union_map *proximity);
4568 void *isl_schedule_free(__isl_take isl_schedule *sched);
4570 A mapping from the domains to the scheduled space can be obtained
4571 from an C<isl_schedule> using the following function.
4573 __isl_give isl_union_map *isl_schedule_get_map(
4574 __isl_keep isl_schedule *sched);
4576 A representation of the schedule can be printed using
4578 __isl_give isl_printer *isl_printer_print_schedule(
4579 __isl_take isl_printer *p,
4580 __isl_keep isl_schedule *schedule);
4582 A representation of the schedule as a forest of bands can be obtained
4583 using the following function.
4585 __isl_give isl_band_list *isl_schedule_get_band_forest(
4586 __isl_keep isl_schedule *schedule);
4588 The individual bands can be visited in depth-first post-order
4589 using the following function.
4591 #include <isl/schedule.h>
4592 int isl_schedule_foreach_band(
4593 __isl_keep isl_schedule *sched,
4594 int (*fn)(__isl_keep isl_band *band, void *user),
4597 The list can be manipulated as explained in L<"Lists">.
4598 The bands inside the list can be copied and freed using the following
4601 #include <isl/band.h>
4602 __isl_give isl_band *isl_band_copy(
4603 __isl_keep isl_band *band);
4604 void *isl_band_free(__isl_take isl_band *band);
4606 Each band contains zero or more scheduling dimensions.
4607 These are referred to as the members of the band.
4608 The section of the schedule that corresponds to the band is
4609 referred to as the partial schedule of the band.
4610 For those nodes that participate in a band, the outer scheduling
4611 dimensions form the prefix schedule, while the inner scheduling
4612 dimensions form the suffix schedule.
4613 That is, if we take a cut of the band forest, then the union of
4614 the concatenations of the prefix, partial and suffix schedules of
4615 each band in the cut is equal to the entire schedule (modulo
4616 some possible padding at the end with zero scheduling dimensions).
4617 The properties of a band can be inspected using the following functions.
4619 #include <isl/band.h>
4620 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4622 int isl_band_has_children(__isl_keep isl_band *band);
4623 __isl_give isl_band_list *isl_band_get_children(
4624 __isl_keep isl_band *band);
4626 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4627 __isl_keep isl_band *band);
4628 __isl_give isl_union_map *isl_band_get_partial_schedule(
4629 __isl_keep isl_band *band);
4630 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4631 __isl_keep isl_band *band);
4633 int isl_band_n_member(__isl_keep isl_band *band);
4634 int isl_band_member_is_zero_distance(
4635 __isl_keep isl_band *band, int pos);
4637 int isl_band_list_foreach_band(
4638 __isl_keep isl_band_list *list,
4639 int (*fn)(__isl_keep isl_band *band, void *user),
4642 Note that a scheduling dimension is considered to be ``zero
4643 distance'' if it does not carry any proximity dependences
4645 That is, if the dependence distances of the proximity
4646 dependences are all zero in that direction (for fixed
4647 iterations of outer bands).
4648 Like C<isl_schedule_foreach_band>,
4649 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4650 in depth-first post-order.
4652 A band can be tiled using the following function.
4654 #include <isl/band.h>
4655 int isl_band_tile(__isl_keep isl_band *band,
4656 __isl_take isl_vec *sizes);
4658 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4660 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4662 The C<isl_band_tile> function tiles the band using the given tile sizes
4663 inside its schedule.
4664 A new child band is created to represent the point loops and it is
4665 inserted between the modified band and its children.
4666 The C<tile_scale_tile_loops> option specifies whether the tile
4667 loops iterators should be scaled by the tile sizes.
4669 A representation of the band can be printed using
4671 #include <isl/band.h>
4672 __isl_give isl_printer *isl_printer_print_band(
4673 __isl_take isl_printer *p,
4674 __isl_keep isl_band *band);
4678 #include <isl/schedule.h>
4679 int isl_options_set_schedule_max_coefficient(
4680 isl_ctx *ctx, int val);
4681 int isl_options_get_schedule_max_coefficient(
4683 int isl_options_set_schedule_max_constant_term(
4684 isl_ctx *ctx, int val);
4685 int isl_options_get_schedule_max_constant_term(
4687 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4688 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4689 int isl_options_set_schedule_maximize_band_depth(
4690 isl_ctx *ctx, int val);
4691 int isl_options_get_schedule_maximize_band_depth(
4693 int isl_options_set_schedule_outer_zero_distance(
4694 isl_ctx *ctx, int val);
4695 int isl_options_get_schedule_outer_zero_distance(
4697 int isl_options_set_schedule_split_scaled(
4698 isl_ctx *ctx, int val);
4699 int isl_options_get_schedule_split_scaled(
4701 int isl_options_set_schedule_algorithm(
4702 isl_ctx *ctx, int val);
4703 int isl_options_get_schedule_algorithm(
4705 int isl_options_set_schedule_separate_components(
4706 isl_ctx *ctx, int val);
4707 int isl_options_get_schedule_separate_components(
4712 =item * schedule_max_coefficient
4714 This option enforces that the coefficients for variable and parameter
4715 dimensions in the calculated schedule are not larger than the specified value.
4716 This option can significantly increase the speed of the scheduling calculation
4717 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4718 this option does not introduce bounds on the variable or parameter
4721 =item * schedule_max_constant_term
4723 This option enforces that the constant coefficients in the calculated schedule
4724 are not larger than the maximal constant term. This option can significantly
4725 increase the speed of the scheduling calculation and may also prevent fusing of
4726 unrelated dimensions. A value of -1 means that this option does not introduce
4727 bounds on the constant coefficients.
4729 =item * schedule_fuse
4731 This option controls the level of fusion.
4732 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
4733 resulting schedule will be distributed as much as possible.
4734 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
4735 try to fuse loops in the resulting schedule.
4737 =item * schedule_maximize_band_depth
4739 If this option is set, we do not split bands at the point
4740 where we detect splitting is necessary. Instead, we
4741 backtrack and split bands as early as possible. This
4742 reduces the number of splits and maximizes the width of
4743 the bands. Wider bands give more possibilities for tiling.
4744 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
4745 then bands will be split as early as possible, even if there is no need.
4746 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
4748 =item * schedule_outer_zero_distance
4750 If this option is set, then we try to construct schedules
4751 where the outermost scheduling dimension in each band
4752 results in a zero dependence distance over the proximity
4755 =item * schedule_split_scaled
4757 If this option is set, then we try to construct schedules in which the
4758 constant term is split off from the linear part if the linear parts of
4759 the scheduling rows for all nodes in the graphs have a common non-trivial
4761 The constant term is then placed in a separate band and the linear
4764 =item * schedule_algorithm
4766 Selects the scheduling algorithm to be used.
4767 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4768 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4770 =item * schedule_separate_components
4772 If at any point the dependence graph contains any (weakly connected) components,
4773 then these components are scheduled separately.
4774 If this option is not set, then some iterations of the domains
4775 in these components may be scheduled together.
4776 If this option is set, then the components are given consecutive
4781 =head2 Parametric Vertex Enumeration
4783 The parametric vertex enumeration described in this section
4784 is mainly intended to be used internally and by the C<barvinok>
4787 #include <isl/vertices.h>
4788 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4789 __isl_keep isl_basic_set *bset);
4791 The function C<isl_basic_set_compute_vertices> performs the
4792 actual computation of the parametric vertices and the chamber
4793 decomposition and store the result in an C<isl_vertices> object.
4794 This information can be queried by either iterating over all
4795 the vertices or iterating over all the chambers or cells
4796 and then iterating over all vertices that are active on the chamber.
4798 int isl_vertices_foreach_vertex(
4799 __isl_keep isl_vertices *vertices,
4800 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4803 int isl_vertices_foreach_cell(
4804 __isl_keep isl_vertices *vertices,
4805 int (*fn)(__isl_take isl_cell *cell, void *user),
4807 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4808 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4811 Other operations that can be performed on an C<isl_vertices> object are
4814 isl_ctx *isl_vertices_get_ctx(
4815 __isl_keep isl_vertices *vertices);
4816 int isl_vertices_get_n_vertices(
4817 __isl_keep isl_vertices *vertices);
4818 void isl_vertices_free(__isl_take isl_vertices *vertices);
4820 Vertices can be inspected and destroyed using the following functions.
4822 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4823 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4824 __isl_give isl_basic_set *isl_vertex_get_domain(
4825 __isl_keep isl_vertex *vertex);
4826 __isl_give isl_basic_set *isl_vertex_get_expr(
4827 __isl_keep isl_vertex *vertex);
4828 void isl_vertex_free(__isl_take isl_vertex *vertex);
4830 C<isl_vertex_get_expr> returns a singleton parametric set describing
4831 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4833 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4834 B<rational> basic sets, so they should mainly be used for inspection
4835 and should not be mixed with integer sets.
4837 Chambers can be inspected and destroyed using the following functions.
4839 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4840 __isl_give isl_basic_set *isl_cell_get_domain(
4841 __isl_keep isl_cell *cell);
4842 void isl_cell_free(__isl_take isl_cell *cell);
4846 Although C<isl> is mainly meant to be used as a library,
4847 it also contains some basic applications that use some
4848 of the functionality of C<isl>.
4849 The input may be specified in either the L<isl format>
4850 or the L<PolyLib format>.
4852 =head2 C<isl_polyhedron_sample>
4854 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4855 an integer element of the polyhedron, if there is any.
4856 The first column in the output is the denominator and is always
4857 equal to 1. If the polyhedron contains no integer points,
4858 then a vector of length zero is printed.
4862 C<isl_pip> takes the same input as the C<example> program
4863 from the C<piplib> distribution, i.e., a set of constraints
4864 on the parameters, a line containing only -1 and finally a set
4865 of constraints on a parametric polyhedron.
4866 The coefficients of the parameters appear in the last columns
4867 (but before the final constant column).
4868 The output is the lexicographic minimum of the parametric polyhedron.
4869 As C<isl> currently does not have its own output format, the output
4870 is just a dump of the internal state.
4872 =head2 C<isl_polyhedron_minimize>
4874 C<isl_polyhedron_minimize> computes the minimum of some linear
4875 or affine objective function over the integer points in a polyhedron.
4876 If an affine objective function
4877 is given, then the constant should appear in the last column.
4879 =head2 C<isl_polytope_scan>
4881 Given a polytope, C<isl_polytope_scan> prints
4882 all integer points in the polytope.