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);
618 It is often useful to create objects that live in the
619 same space as some other object. This can be accomplished
620 by creating the new objects
621 (see L<Creating New Sets and Relations> or
622 L<Creating New (Piecewise) Quasipolynomials>) based on the space
623 of the original object.
626 __isl_give isl_space *isl_basic_set_get_space(
627 __isl_keep isl_basic_set *bset);
628 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
630 #include <isl/union_set.h>
631 __isl_give isl_space *isl_union_set_get_space(
632 __isl_keep isl_union_set *uset);
635 __isl_give isl_space *isl_basic_map_get_space(
636 __isl_keep isl_basic_map *bmap);
637 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
639 #include <isl/union_map.h>
640 __isl_give isl_space *isl_union_map_get_space(
641 __isl_keep isl_union_map *umap);
643 #include <isl/constraint.h>
644 __isl_give isl_space *isl_constraint_get_space(
645 __isl_keep isl_constraint *constraint);
647 #include <isl/polynomial.h>
648 __isl_give isl_space *isl_qpolynomial_get_domain_space(
649 __isl_keep isl_qpolynomial *qp);
650 __isl_give isl_space *isl_qpolynomial_get_space(
651 __isl_keep isl_qpolynomial *qp);
652 __isl_give isl_space *isl_qpolynomial_fold_get_space(
653 __isl_keep isl_qpolynomial_fold *fold);
654 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
655 __isl_keep isl_pw_qpolynomial *pwqp);
656 __isl_give isl_space *isl_pw_qpolynomial_get_space(
657 __isl_keep isl_pw_qpolynomial *pwqp);
658 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
659 __isl_keep isl_pw_qpolynomial_fold *pwf);
660 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
661 __isl_keep isl_pw_qpolynomial_fold *pwf);
662 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
663 __isl_keep isl_union_pw_qpolynomial *upwqp);
664 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
665 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
668 __isl_give isl_space *isl_aff_get_domain_space(
669 __isl_keep isl_aff *aff);
670 __isl_give isl_space *isl_aff_get_space(
671 __isl_keep isl_aff *aff);
672 __isl_give isl_space *isl_pw_aff_get_domain_space(
673 __isl_keep isl_pw_aff *pwaff);
674 __isl_give isl_space *isl_pw_aff_get_space(
675 __isl_keep isl_pw_aff *pwaff);
676 __isl_give isl_space *isl_multi_aff_get_domain_space(
677 __isl_keep isl_multi_aff *maff);
678 __isl_give isl_space *isl_multi_aff_get_space(
679 __isl_keep isl_multi_aff *maff);
680 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
681 __isl_keep isl_pw_multi_aff *pma);
682 __isl_give isl_space *isl_pw_multi_aff_get_space(
683 __isl_keep isl_pw_multi_aff *pma);
684 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
685 __isl_keep isl_union_pw_multi_aff *upma);
687 #include <isl/point.h>
688 __isl_give isl_space *isl_point_get_space(
689 __isl_keep isl_point *pnt);
691 The identifiers or names of the individual dimensions may be set or read off
692 using the following functions.
694 #include <isl/space.h>
695 __isl_give isl_space *isl_space_set_dim_id(
696 __isl_take isl_space *space,
697 enum isl_dim_type type, unsigned pos,
698 __isl_take isl_id *id);
699 int isl_space_has_dim_id(__isl_keep isl_space *space,
700 enum isl_dim_type type, unsigned pos);
701 __isl_give isl_id *isl_space_get_dim_id(
702 __isl_keep isl_space *space,
703 enum isl_dim_type type, unsigned pos);
704 __isl_give isl_space *isl_space_set_dim_name(
705 __isl_take isl_space *space,
706 enum isl_dim_type type, unsigned pos,
707 __isl_keep const char *name);
708 int isl_space_has_dim_name(__isl_keep isl_space *space,
709 enum isl_dim_type type, unsigned pos);
710 __isl_keep const char *isl_space_get_dim_name(
711 __isl_keep isl_space *space,
712 enum isl_dim_type type, unsigned pos);
714 Note that C<isl_space_get_name> returns a pointer to some internal
715 data structure, so the result can only be used while the
716 corresponding C<isl_space> is alive.
717 Also note that every function that operates on two sets or relations
718 requires that both arguments have the same parameters. This also
719 means that if one of the arguments has named parameters, then the
720 other needs to have named parameters too and the names need to match.
721 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
722 arguments may have different parameters (as long as they are named),
723 in which case the result will have as parameters the union of the parameters of
726 Given the identifier or name of a dimension (typically a parameter),
727 its position can be obtained from the following function.
729 #include <isl/space.h>
730 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
731 enum isl_dim_type type, __isl_keep isl_id *id);
732 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
733 enum isl_dim_type type, const char *name);
735 The identifiers or names of entire spaces may be set or read off
736 using the following functions.
738 #include <isl/space.h>
739 __isl_give isl_space *isl_space_set_tuple_id(
740 __isl_take isl_space *space,
741 enum isl_dim_type type, __isl_take isl_id *id);
742 __isl_give isl_space *isl_space_reset_tuple_id(
743 __isl_take isl_space *space, enum isl_dim_type type);
744 int isl_space_has_tuple_id(__isl_keep isl_space *space,
745 enum isl_dim_type type);
746 __isl_give isl_id *isl_space_get_tuple_id(
747 __isl_keep isl_space *space, enum isl_dim_type type);
748 __isl_give isl_space *isl_space_set_tuple_name(
749 __isl_take isl_space *space,
750 enum isl_dim_type type, const char *s);
751 int isl_space_has_tuple_name(__isl_keep isl_space *space,
752 enum isl_dim_type type);
753 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
754 enum isl_dim_type type);
756 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
757 or C<isl_dim_set>. As with C<isl_space_get_name>,
758 the C<isl_space_get_tuple_name> function returns a pointer to some internal
760 Binary operations require the corresponding spaces of their arguments
761 to have the same name.
763 Spaces can be nested. In particular, the domain of a set or
764 the domain or range of a relation can be a nested relation.
765 The following functions can be used to construct and deconstruct
768 #include <isl/space.h>
769 int isl_space_is_wrapping(__isl_keep isl_space *space);
770 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
771 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
773 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
774 be the space of a set, while that of
775 C<isl_space_wrap> should be the space of a relation.
776 Conversely, the output of C<isl_space_unwrap> is the space
777 of a relation, while that of C<isl_space_wrap> is the space of a set.
779 Spaces can be created from other spaces
780 using the following functions.
782 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
783 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
784 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
785 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
786 __isl_give isl_space *isl_space_params(
787 __isl_take isl_space *space);
788 __isl_give isl_space *isl_space_set_from_params(
789 __isl_take isl_space *space);
790 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
791 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
792 __isl_take isl_space *right);
793 __isl_give isl_space *isl_space_align_params(
794 __isl_take isl_space *space1, __isl_take isl_space *space2)
795 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
796 enum isl_dim_type type, unsigned pos, unsigned n);
797 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
798 enum isl_dim_type type, unsigned n);
799 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
800 enum isl_dim_type type, unsigned first, unsigned n);
801 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
802 enum isl_dim_type dst_type, unsigned dst_pos,
803 enum isl_dim_type src_type, unsigned src_pos,
805 __isl_give isl_space *isl_space_map_from_set(
806 __isl_take isl_space *space);
807 __isl_give isl_space *isl_space_map_from_domain_and_range(
808 __isl_take isl_space *domain,
809 __isl_take isl_space *range);
810 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
811 __isl_give isl_space *isl_space_curry(
812 __isl_take isl_space *space);
814 Note that if dimensions are added or removed from a space, then
815 the name and the internal structure are lost.
819 A local space is essentially a space with
820 zero or more existentially quantified variables.
821 The local space of a (constraint of a) basic set or relation can be obtained
822 using the following functions.
824 #include <isl/constraint.h>
825 __isl_give isl_local_space *isl_constraint_get_local_space(
826 __isl_keep isl_constraint *constraint);
829 __isl_give isl_local_space *isl_basic_set_get_local_space(
830 __isl_keep isl_basic_set *bset);
833 __isl_give isl_local_space *isl_basic_map_get_local_space(
834 __isl_keep isl_basic_map *bmap);
836 A new local space can be created from a space using
838 #include <isl/local_space.h>
839 __isl_give isl_local_space *isl_local_space_from_space(
840 __isl_take isl_space *space);
842 They can be inspected, modified, copied and freed using the following functions.
844 #include <isl/local_space.h>
845 isl_ctx *isl_local_space_get_ctx(
846 __isl_keep isl_local_space *ls);
847 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
848 int isl_local_space_dim(__isl_keep isl_local_space *ls,
849 enum isl_dim_type type);
850 int isl_local_space_has_dim_id(
851 __isl_keep isl_local_space *ls,
852 enum isl_dim_type type, unsigned pos);
853 __isl_give isl_id *isl_local_space_get_dim_id(
854 __isl_keep isl_local_space *ls,
855 enum isl_dim_type type, unsigned pos);
856 int isl_local_space_has_dim_name(
857 __isl_keep isl_local_space *ls,
858 enum isl_dim_type type, unsigned pos)
859 const char *isl_local_space_get_dim_name(
860 __isl_keep isl_local_space *ls,
861 enum isl_dim_type type, unsigned pos);
862 __isl_give isl_local_space *isl_local_space_set_dim_name(
863 __isl_take isl_local_space *ls,
864 enum isl_dim_type type, unsigned pos, const char *s);
865 __isl_give isl_local_space *isl_local_space_set_dim_id(
866 __isl_take isl_local_space *ls,
867 enum isl_dim_type type, unsigned pos,
868 __isl_take isl_id *id);
869 __isl_give isl_space *isl_local_space_get_space(
870 __isl_keep isl_local_space *ls);
871 __isl_give isl_aff *isl_local_space_get_div(
872 __isl_keep isl_local_space *ls, int pos);
873 __isl_give isl_local_space *isl_local_space_copy(
874 __isl_keep isl_local_space *ls);
875 void *isl_local_space_free(__isl_take isl_local_space *ls);
877 Two local spaces can be compared using
879 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
880 __isl_keep isl_local_space *ls2);
882 Local spaces can be created from other local spaces
883 using the following functions.
885 __isl_give isl_local_space *isl_local_space_domain(
886 __isl_take isl_local_space *ls);
887 __isl_give isl_local_space *isl_local_space_range(
888 __isl_take isl_local_space *ls);
889 __isl_give isl_local_space *isl_local_space_from_domain(
890 __isl_take isl_local_space *ls);
891 __isl_give isl_local_space *isl_local_space_intersect(
892 __isl_take isl_local_space *ls1,
893 __isl_take isl_local_space *ls2);
894 __isl_give isl_local_space *isl_local_space_add_dims(
895 __isl_take isl_local_space *ls,
896 enum isl_dim_type type, unsigned n);
897 __isl_give isl_local_space *isl_local_space_insert_dims(
898 __isl_take isl_local_space *ls,
899 enum isl_dim_type type, unsigned first, unsigned n);
900 __isl_give isl_local_space *isl_local_space_drop_dims(
901 __isl_take isl_local_space *ls,
902 enum isl_dim_type type, unsigned first, unsigned n);
904 =head2 Input and Output
906 C<isl> supports its own input/output format, which is similar
907 to the C<Omega> format, but also supports the C<PolyLib> format
912 The C<isl> format is similar to that of C<Omega>, but has a different
913 syntax for describing the parameters and allows for the definition
914 of an existentially quantified variable as the integer division
915 of an affine expression.
916 For example, the set of integers C<i> between C<0> and C<n>
917 such that C<i % 10 <= 6> can be described as
919 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
922 A set or relation can have several disjuncts, separated
923 by the keyword C<or>. Each disjunct is either a conjunction
924 of constraints or a projection (C<exists>) of a conjunction
925 of constraints. The constraints are separated by the keyword
928 =head3 C<PolyLib> format
930 If the represented set is a union, then the first line
931 contains a single number representing the number of disjuncts.
932 Otherwise, a line containing the number C<1> is optional.
934 Each disjunct is represented by a matrix of constraints.
935 The first line contains two numbers representing
936 the number of rows and columns,
937 where the number of rows is equal to the number of constraints
938 and the number of columns is equal to two plus the number of variables.
939 The following lines contain the actual rows of the constraint matrix.
940 In each row, the first column indicates whether the constraint
941 is an equality (C<0>) or inequality (C<1>). The final column
942 corresponds to the constant term.
944 If the set is parametric, then the coefficients of the parameters
945 appear in the last columns before the constant column.
946 The coefficients of any existentially quantified variables appear
947 between those of the set variables and those of the parameters.
949 =head3 Extended C<PolyLib> format
951 The extended C<PolyLib> format is nearly identical to the
952 C<PolyLib> format. The only difference is that the line
953 containing the number of rows and columns of a constraint matrix
954 also contains four additional numbers:
955 the number of output dimensions, the number of input dimensions,
956 the number of local dimensions (i.e., the number of existentially
957 quantified variables) and the number of parameters.
958 For sets, the number of ``output'' dimensions is equal
959 to the number of set dimensions, while the number of ``input''
965 __isl_give isl_basic_set *isl_basic_set_read_from_file(
966 isl_ctx *ctx, FILE *input);
967 __isl_give isl_basic_set *isl_basic_set_read_from_str(
968 isl_ctx *ctx, const char *str);
969 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
971 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
975 __isl_give isl_basic_map *isl_basic_map_read_from_file(
976 isl_ctx *ctx, FILE *input);
977 __isl_give isl_basic_map *isl_basic_map_read_from_str(
978 isl_ctx *ctx, const char *str);
979 __isl_give isl_map *isl_map_read_from_file(
980 isl_ctx *ctx, FILE *input);
981 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
984 #include <isl/union_set.h>
985 __isl_give isl_union_set *isl_union_set_read_from_file(
986 isl_ctx *ctx, FILE *input);
987 __isl_give isl_union_set *isl_union_set_read_from_str(
988 isl_ctx *ctx, const char *str);
990 #include <isl/union_map.h>
991 __isl_give isl_union_map *isl_union_map_read_from_file(
992 isl_ctx *ctx, FILE *input);
993 __isl_give isl_union_map *isl_union_map_read_from_str(
994 isl_ctx *ctx, const char *str);
996 The input format is autodetected and may be either the C<PolyLib> format
997 or the C<isl> format.
1001 Before anything can be printed, an C<isl_printer> needs to
1004 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1006 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1007 void isl_printer_free(__isl_take isl_printer *printer);
1008 __isl_give char *isl_printer_get_str(
1009 __isl_keep isl_printer *printer);
1011 The printer can be inspected using the following functions.
1013 FILE *isl_printer_get_file(
1014 __isl_keep isl_printer *printer);
1015 int isl_printer_get_output_format(
1016 __isl_keep isl_printer *p);
1018 The behavior of the printer can be modified in various ways
1020 __isl_give isl_printer *isl_printer_set_output_format(
1021 __isl_take isl_printer *p, int output_format);
1022 __isl_give isl_printer *isl_printer_set_indent(
1023 __isl_take isl_printer *p, int indent);
1024 __isl_give isl_printer *isl_printer_indent(
1025 __isl_take isl_printer *p, int indent);
1026 __isl_give isl_printer *isl_printer_set_prefix(
1027 __isl_take isl_printer *p, const char *prefix);
1028 __isl_give isl_printer *isl_printer_set_suffix(
1029 __isl_take isl_printer *p, const char *suffix);
1031 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1032 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1033 and defaults to C<ISL_FORMAT_ISL>.
1034 Each line in the output is indented by C<indent> (set by
1035 C<isl_printer_set_indent>) spaces
1036 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1037 In the C<PolyLib> format output,
1038 the coefficients of the existentially quantified variables
1039 appear between those of the set variables and those
1041 The function C<isl_printer_indent> increases the indentation
1042 by the specified amount (which may be negative).
1044 To actually print something, use
1046 #include <isl/printer.h>
1047 __isl_give isl_printer *isl_printer_print_double(
1048 __isl_take isl_printer *p, double d);
1050 #include <isl/set.h>
1051 __isl_give isl_printer *isl_printer_print_basic_set(
1052 __isl_take isl_printer *printer,
1053 __isl_keep isl_basic_set *bset);
1054 __isl_give isl_printer *isl_printer_print_set(
1055 __isl_take isl_printer *printer,
1056 __isl_keep isl_set *set);
1058 #include <isl/map.h>
1059 __isl_give isl_printer *isl_printer_print_basic_map(
1060 __isl_take isl_printer *printer,
1061 __isl_keep isl_basic_map *bmap);
1062 __isl_give isl_printer *isl_printer_print_map(
1063 __isl_take isl_printer *printer,
1064 __isl_keep isl_map *map);
1066 #include <isl/union_set.h>
1067 __isl_give isl_printer *isl_printer_print_union_set(
1068 __isl_take isl_printer *p,
1069 __isl_keep isl_union_set *uset);
1071 #include <isl/union_map.h>
1072 __isl_give isl_printer *isl_printer_print_union_map(
1073 __isl_take isl_printer *p,
1074 __isl_keep isl_union_map *umap);
1076 When called on a file printer, the following function flushes
1077 the file. When called on a string printer, the buffer is cleared.
1079 __isl_give isl_printer *isl_printer_flush(
1080 __isl_take isl_printer *p);
1082 =head2 Creating New Sets and Relations
1084 C<isl> has functions for creating some standard sets and relations.
1088 =item * Empty sets and relations
1090 __isl_give isl_basic_set *isl_basic_set_empty(
1091 __isl_take isl_space *space);
1092 __isl_give isl_basic_map *isl_basic_map_empty(
1093 __isl_take isl_space *space);
1094 __isl_give isl_set *isl_set_empty(
1095 __isl_take isl_space *space);
1096 __isl_give isl_map *isl_map_empty(
1097 __isl_take isl_space *space);
1098 __isl_give isl_union_set *isl_union_set_empty(
1099 __isl_take isl_space *space);
1100 __isl_give isl_union_map *isl_union_map_empty(
1101 __isl_take isl_space *space);
1103 For C<isl_union_set>s and C<isl_union_map>s, the space
1104 is only used to specify the parameters.
1106 =item * Universe sets and relations
1108 __isl_give isl_basic_set *isl_basic_set_universe(
1109 __isl_take isl_space *space);
1110 __isl_give isl_basic_map *isl_basic_map_universe(
1111 __isl_take isl_space *space);
1112 __isl_give isl_set *isl_set_universe(
1113 __isl_take isl_space *space);
1114 __isl_give isl_map *isl_map_universe(
1115 __isl_take isl_space *space);
1116 __isl_give isl_union_set *isl_union_set_universe(
1117 __isl_take isl_union_set *uset);
1118 __isl_give isl_union_map *isl_union_map_universe(
1119 __isl_take isl_union_map *umap);
1121 The sets and relations constructed by the functions above
1122 contain all integer values, while those constructed by the
1123 functions below only contain non-negative values.
1125 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1126 __isl_take isl_space *space);
1127 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1128 __isl_take isl_space *space);
1129 __isl_give isl_set *isl_set_nat_universe(
1130 __isl_take isl_space *space);
1131 __isl_give isl_map *isl_map_nat_universe(
1132 __isl_take isl_space *space);
1134 =item * Identity relations
1136 __isl_give isl_basic_map *isl_basic_map_identity(
1137 __isl_take isl_space *space);
1138 __isl_give isl_map *isl_map_identity(
1139 __isl_take isl_space *space);
1141 The number of input and output dimensions in C<space> needs
1144 =item * Lexicographic order
1146 __isl_give isl_map *isl_map_lex_lt(
1147 __isl_take isl_space *set_space);
1148 __isl_give isl_map *isl_map_lex_le(
1149 __isl_take isl_space *set_space);
1150 __isl_give isl_map *isl_map_lex_gt(
1151 __isl_take isl_space *set_space);
1152 __isl_give isl_map *isl_map_lex_ge(
1153 __isl_take isl_space *set_space);
1154 __isl_give isl_map *isl_map_lex_lt_first(
1155 __isl_take isl_space *space, unsigned n);
1156 __isl_give isl_map *isl_map_lex_le_first(
1157 __isl_take isl_space *space, unsigned n);
1158 __isl_give isl_map *isl_map_lex_gt_first(
1159 __isl_take isl_space *space, unsigned n);
1160 __isl_give isl_map *isl_map_lex_ge_first(
1161 __isl_take isl_space *space, unsigned n);
1163 The first four functions take a space for a B<set>
1164 and return relations that express that the elements in the domain
1165 are lexicographically less
1166 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1167 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1168 than the elements in the range.
1169 The last four functions take a space for a map
1170 and return relations that express that the first C<n> dimensions
1171 in the domain are lexicographically less
1172 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1173 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1174 than the first C<n> dimensions in the range.
1178 A basic set or relation can be converted to a set or relation
1179 using the following functions.
1181 __isl_give isl_set *isl_set_from_basic_set(
1182 __isl_take isl_basic_set *bset);
1183 __isl_give isl_map *isl_map_from_basic_map(
1184 __isl_take isl_basic_map *bmap);
1186 Sets and relations can be converted to union sets and relations
1187 using the following functions.
1189 __isl_give isl_union_set *isl_union_set_from_basic_set(
1190 __isl_take isl_basic_set *bset);
1191 __isl_give isl_union_map *isl_union_map_from_basic_map(
1192 __isl_take isl_basic_map *bmap);
1193 __isl_give isl_union_set *isl_union_set_from_set(
1194 __isl_take isl_set *set);
1195 __isl_give isl_union_map *isl_union_map_from_map(
1196 __isl_take isl_map *map);
1198 The inverse conversions below can only be used if the input
1199 union set or relation is known to contain elements in exactly one
1202 __isl_give isl_set *isl_set_from_union_set(
1203 __isl_take isl_union_set *uset);
1204 __isl_give isl_map *isl_map_from_union_map(
1205 __isl_take isl_union_map *umap);
1207 A zero-dimensional set can be constructed on a given parameter domain
1208 using the following function.
1210 __isl_give isl_set *isl_set_from_params(
1211 __isl_take isl_set *set);
1213 Sets and relations can be copied and freed again using the following
1216 __isl_give isl_basic_set *isl_basic_set_copy(
1217 __isl_keep isl_basic_set *bset);
1218 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1219 __isl_give isl_union_set *isl_union_set_copy(
1220 __isl_keep isl_union_set *uset);
1221 __isl_give isl_basic_map *isl_basic_map_copy(
1222 __isl_keep isl_basic_map *bmap);
1223 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1224 __isl_give isl_union_map *isl_union_map_copy(
1225 __isl_keep isl_union_map *umap);
1226 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1227 void *isl_set_free(__isl_take isl_set *set);
1228 void *isl_union_set_free(__isl_take isl_union_set *uset);
1229 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1230 void isl_map_free(__isl_take isl_map *map);
1231 void *isl_union_map_free(__isl_take isl_union_map *umap);
1233 Other sets and relations can be constructed by starting
1234 from a universe set or relation, adding equality and/or
1235 inequality constraints and then projecting out the
1236 existentially quantified variables, if any.
1237 Constraints can be constructed, manipulated and
1238 added to (or removed from) (basic) sets and relations
1239 using the following functions.
1241 #include <isl/constraint.h>
1242 __isl_give isl_constraint *isl_equality_alloc(
1243 __isl_take isl_local_space *ls);
1244 __isl_give isl_constraint *isl_inequality_alloc(
1245 __isl_take isl_local_space *ls);
1246 __isl_give isl_constraint *isl_constraint_set_constant(
1247 __isl_take isl_constraint *constraint, isl_int v);
1248 __isl_give isl_constraint *isl_constraint_set_constant_si(
1249 __isl_take isl_constraint *constraint, int v);
1250 __isl_give isl_constraint *isl_constraint_set_coefficient(
1251 __isl_take isl_constraint *constraint,
1252 enum isl_dim_type type, int pos, isl_int v);
1253 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1254 __isl_take isl_constraint *constraint,
1255 enum isl_dim_type type, int pos, int v);
1256 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1257 __isl_take isl_basic_map *bmap,
1258 __isl_take isl_constraint *constraint);
1259 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1260 __isl_take isl_basic_set *bset,
1261 __isl_take isl_constraint *constraint);
1262 __isl_give isl_map *isl_map_add_constraint(
1263 __isl_take isl_map *map,
1264 __isl_take isl_constraint *constraint);
1265 __isl_give isl_set *isl_set_add_constraint(
1266 __isl_take isl_set *set,
1267 __isl_take isl_constraint *constraint);
1268 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1269 __isl_take isl_basic_set *bset,
1270 __isl_take isl_constraint *constraint);
1272 For example, to create a set containing the even integers
1273 between 10 and 42, you would use the following code.
1276 isl_local_space *ls;
1278 isl_basic_set *bset;
1280 space = isl_space_set_alloc(ctx, 0, 2);
1281 bset = isl_basic_set_universe(isl_space_copy(space));
1282 ls = isl_local_space_from_space(space);
1284 c = isl_equality_alloc(isl_local_space_copy(ls));
1285 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1286 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1287 bset = isl_basic_set_add_constraint(bset, c);
1289 c = isl_inequality_alloc(isl_local_space_copy(ls));
1290 c = isl_constraint_set_constant_si(c, -10);
1291 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1292 bset = isl_basic_set_add_constraint(bset, c);
1294 c = isl_inequality_alloc(ls);
1295 c = isl_constraint_set_constant_si(c, 42);
1296 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1297 bset = isl_basic_set_add_constraint(bset, c);
1299 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1303 isl_basic_set *bset;
1304 bset = isl_basic_set_read_from_str(ctx,
1305 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1307 A basic set or relation can also be constructed from two matrices
1308 describing the equalities and the inequalities.
1310 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1311 __isl_take isl_space *space,
1312 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1313 enum isl_dim_type c1,
1314 enum isl_dim_type c2, enum isl_dim_type c3,
1315 enum isl_dim_type c4);
1316 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1317 __isl_take isl_space *space,
1318 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1319 enum isl_dim_type c1,
1320 enum isl_dim_type c2, enum isl_dim_type c3,
1321 enum isl_dim_type c4, enum isl_dim_type c5);
1323 The C<isl_dim_type> arguments indicate the order in which
1324 different kinds of variables appear in the input matrices
1325 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1326 C<isl_dim_set> and C<isl_dim_div> for sets and
1327 of C<isl_dim_cst>, C<isl_dim_param>,
1328 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1330 A (basic or union) set or relation can also be constructed from a
1331 (union) (piecewise) (multiple) affine expression
1332 or a list of affine expressions
1333 (See L<"Piecewise Quasi Affine Expressions"> and
1334 L<"Piecewise Multiple Quasi Affine Expressions">).
1336 __isl_give isl_basic_map *isl_basic_map_from_aff(
1337 __isl_take isl_aff *aff);
1338 __isl_give isl_map *isl_map_from_aff(
1339 __isl_take isl_aff *aff);
1340 __isl_give isl_set *isl_set_from_pw_aff(
1341 __isl_take isl_pw_aff *pwaff);
1342 __isl_give isl_map *isl_map_from_pw_aff(
1343 __isl_take isl_pw_aff *pwaff);
1344 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1345 __isl_take isl_space *domain_space,
1346 __isl_take isl_aff_list *list);
1347 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1348 __isl_take isl_multi_aff *maff)
1349 __isl_give isl_map *isl_map_from_multi_aff(
1350 __isl_take isl_multi_aff *maff)
1351 __isl_give isl_set *isl_set_from_pw_multi_aff(
1352 __isl_take isl_pw_multi_aff *pma);
1353 __isl_give isl_map *isl_map_from_pw_multi_aff(
1354 __isl_take isl_pw_multi_aff *pma);
1355 __isl_give isl_union_map *
1356 isl_union_map_from_union_pw_multi_aff(
1357 __isl_take isl_union_pw_multi_aff *upma);
1359 The C<domain_dim> argument describes the domain of the resulting
1360 basic relation. It is required because the C<list> may consist
1361 of zero affine expressions.
1363 =head2 Inspecting Sets and Relations
1365 Usually, the user should not have to care about the actual constraints
1366 of the sets and maps, but should instead apply the abstract operations
1367 explained in the following sections.
1368 Occasionally, however, it may be required to inspect the individual
1369 coefficients of the constraints. This section explains how to do so.
1370 In these cases, it may also be useful to have C<isl> compute
1371 an explicit representation of the existentially quantified variables.
1373 __isl_give isl_set *isl_set_compute_divs(
1374 __isl_take isl_set *set);
1375 __isl_give isl_map *isl_map_compute_divs(
1376 __isl_take isl_map *map);
1377 __isl_give isl_union_set *isl_union_set_compute_divs(
1378 __isl_take isl_union_set *uset);
1379 __isl_give isl_union_map *isl_union_map_compute_divs(
1380 __isl_take isl_union_map *umap);
1382 This explicit representation defines the existentially quantified
1383 variables as integer divisions of the other variables, possibly
1384 including earlier existentially quantified variables.
1385 An explicitly represented existentially quantified variable therefore
1386 has a unique value when the values of the other variables are known.
1387 If, furthermore, the same existentials, i.e., existentials
1388 with the same explicit representations, should appear in the
1389 same order in each of the disjuncts of a set or map, then the user should call
1390 either of the following functions.
1392 __isl_give isl_set *isl_set_align_divs(
1393 __isl_take isl_set *set);
1394 __isl_give isl_map *isl_map_align_divs(
1395 __isl_take isl_map *map);
1397 Alternatively, the existentially quantified variables can be removed
1398 using the following functions, which compute an overapproximation.
1400 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1401 __isl_take isl_basic_set *bset);
1402 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1403 __isl_take isl_basic_map *bmap);
1404 __isl_give isl_set *isl_set_remove_divs(
1405 __isl_take isl_set *set);
1406 __isl_give isl_map *isl_map_remove_divs(
1407 __isl_take isl_map *map);
1409 It is also possible to only remove those divs that are defined
1410 in terms of a given range of dimensions.
1412 __isl_give isl_basic_set *
1413 isl_basic_set_remove_divs_involving_dims(
1414 __isl_take isl_basic_set *bset,
1415 enum isl_dim_type type,
1416 unsigned first, unsigned n);
1417 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1418 __isl_take isl_set *set, enum isl_dim_type type,
1419 unsigned first, unsigned n);
1420 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1421 __isl_take isl_map *map, enum isl_dim_type type,
1422 unsigned first, unsigned n);
1424 To iterate over all the sets or maps in a union set or map, use
1426 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1427 int (*fn)(__isl_take isl_set *set, void *user),
1429 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1430 int (*fn)(__isl_take isl_map *map, void *user),
1433 The number of sets or maps in a union set or map can be obtained
1436 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1437 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1439 To extract the set or map in a given space from a union, use
1441 __isl_give isl_set *isl_union_set_extract_set(
1442 __isl_keep isl_union_set *uset,
1443 __isl_take isl_space *space);
1444 __isl_give isl_map *isl_union_map_extract_map(
1445 __isl_keep isl_union_map *umap,
1446 __isl_take isl_space *space);
1448 To iterate over all the basic sets or maps in a set or map, use
1450 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1451 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1453 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1454 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1457 The callback function C<fn> should return 0 if successful and
1458 -1 if an error occurs. In the latter case, or if any other error
1459 occurs, the above functions will return -1.
1461 It should be noted that C<isl> does not guarantee that
1462 the basic sets or maps passed to C<fn> are disjoint.
1463 If this is required, then the user should call one of
1464 the following functions first.
1466 __isl_give isl_set *isl_set_make_disjoint(
1467 __isl_take isl_set *set);
1468 __isl_give isl_map *isl_map_make_disjoint(
1469 __isl_take isl_map *map);
1471 The number of basic sets in a set can be obtained
1474 int isl_set_n_basic_set(__isl_keep isl_set *set);
1476 To iterate over the constraints of a basic set or map, use
1478 #include <isl/constraint.h>
1480 int isl_basic_set_n_constraint(
1481 __isl_keep isl_basic_set *bset);
1482 int isl_basic_set_foreach_constraint(
1483 __isl_keep isl_basic_set *bset,
1484 int (*fn)(__isl_take isl_constraint *c, void *user),
1486 int isl_basic_map_foreach_constraint(
1487 __isl_keep isl_basic_map *bmap,
1488 int (*fn)(__isl_take isl_constraint *c, void *user),
1490 void *isl_constraint_free(__isl_take isl_constraint *c);
1492 Again, the callback function C<fn> should return 0 if successful and
1493 -1 if an error occurs. In the latter case, or if any other error
1494 occurs, the above functions will return -1.
1495 The constraint C<c> represents either an equality or an inequality.
1496 Use the following function to find out whether a constraint
1497 represents an equality. If not, it represents an inequality.
1499 int isl_constraint_is_equality(
1500 __isl_keep isl_constraint *constraint);
1502 The coefficients of the constraints can be inspected using
1503 the following functions.
1505 int isl_constraint_is_lower_bound(
1506 __isl_keep isl_constraint *constraint,
1507 enum isl_dim_type type, unsigned pos);
1508 int isl_constraint_is_upper_bound(
1509 __isl_keep isl_constraint *constraint,
1510 enum isl_dim_type type, unsigned pos);
1511 void isl_constraint_get_constant(
1512 __isl_keep isl_constraint *constraint, isl_int *v);
1513 void isl_constraint_get_coefficient(
1514 __isl_keep isl_constraint *constraint,
1515 enum isl_dim_type type, int pos, isl_int *v);
1516 int isl_constraint_involves_dims(
1517 __isl_keep isl_constraint *constraint,
1518 enum isl_dim_type type, unsigned first, unsigned n);
1520 The explicit representations of the existentially quantified
1521 variables can be inspected using the following function.
1522 Note that the user is only allowed to use this function
1523 if the inspected set or map is the result of a call
1524 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1525 The existentially quantified variable is equal to the floor
1526 of the returned affine expression. The affine expression
1527 itself can be inspected using the functions in
1528 L<"Piecewise Quasi Affine Expressions">.
1530 __isl_give isl_aff *isl_constraint_get_div(
1531 __isl_keep isl_constraint *constraint, int pos);
1533 To obtain the constraints of a basic set or map in matrix
1534 form, use the following functions.
1536 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1537 __isl_keep isl_basic_set *bset,
1538 enum isl_dim_type c1, enum isl_dim_type c2,
1539 enum isl_dim_type c3, enum isl_dim_type c4);
1540 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1541 __isl_keep isl_basic_set *bset,
1542 enum isl_dim_type c1, enum isl_dim_type c2,
1543 enum isl_dim_type c3, enum isl_dim_type c4);
1544 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1545 __isl_keep isl_basic_map *bmap,
1546 enum isl_dim_type c1,
1547 enum isl_dim_type c2, enum isl_dim_type c3,
1548 enum isl_dim_type c4, enum isl_dim_type c5);
1549 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1550 __isl_keep isl_basic_map *bmap,
1551 enum isl_dim_type c1,
1552 enum isl_dim_type c2, enum isl_dim_type c3,
1553 enum isl_dim_type c4, enum isl_dim_type c5);
1555 The C<isl_dim_type> arguments dictate the order in which
1556 different kinds of variables appear in the resulting matrix
1557 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1558 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1560 The number of parameters, input, output or set dimensions can
1561 be obtained using the following functions.
1563 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1564 enum isl_dim_type type);
1565 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1566 enum isl_dim_type type);
1567 unsigned isl_set_dim(__isl_keep isl_set *set,
1568 enum isl_dim_type type);
1569 unsigned isl_map_dim(__isl_keep isl_map *map,
1570 enum isl_dim_type type);
1572 To check whether the description of a set or relation depends
1573 on one or more given dimensions, it is not necessary to iterate over all
1574 constraints. Instead the following functions can be used.
1576 int isl_basic_set_involves_dims(
1577 __isl_keep isl_basic_set *bset,
1578 enum isl_dim_type type, unsigned first, unsigned n);
1579 int isl_set_involves_dims(__isl_keep isl_set *set,
1580 enum isl_dim_type type, unsigned first, unsigned n);
1581 int isl_basic_map_involves_dims(
1582 __isl_keep isl_basic_map *bmap,
1583 enum isl_dim_type type, unsigned first, unsigned n);
1584 int isl_map_involves_dims(__isl_keep isl_map *map,
1585 enum isl_dim_type type, unsigned first, unsigned n);
1587 Similarly, the following functions can be used to check whether
1588 a given dimension is involved in any lower or upper bound.
1590 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1591 enum isl_dim_type type, unsigned pos);
1592 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1593 enum isl_dim_type type, unsigned pos);
1595 The identifiers or names of the domain and range spaces of a set
1596 or relation can be read off or set using the following functions.
1598 __isl_give isl_set *isl_set_set_tuple_id(
1599 __isl_take isl_set *set, __isl_take isl_id *id);
1600 __isl_give isl_set *isl_set_reset_tuple_id(
1601 __isl_take isl_set *set);
1602 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1603 __isl_give isl_id *isl_set_get_tuple_id(
1604 __isl_keep isl_set *set);
1605 __isl_give isl_map *isl_map_set_tuple_id(
1606 __isl_take isl_map *map, enum isl_dim_type type,
1607 __isl_take isl_id *id);
1608 __isl_give isl_map *isl_map_reset_tuple_id(
1609 __isl_take isl_map *map, enum isl_dim_type type);
1610 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1611 enum isl_dim_type type);
1612 __isl_give isl_id *isl_map_get_tuple_id(
1613 __isl_keep isl_map *map, enum isl_dim_type type);
1615 const char *isl_basic_set_get_tuple_name(
1616 __isl_keep isl_basic_set *bset);
1617 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1618 __isl_take isl_basic_set *set, const char *s);
1619 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1620 const char *isl_set_get_tuple_name(
1621 __isl_keep isl_set *set);
1622 const char *isl_basic_map_get_tuple_name(
1623 __isl_keep isl_basic_map *bmap,
1624 enum isl_dim_type type);
1625 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1626 __isl_take isl_basic_map *bmap,
1627 enum isl_dim_type type, const char *s);
1628 const char *isl_map_get_tuple_name(
1629 __isl_keep isl_map *map,
1630 enum isl_dim_type type);
1632 As with C<isl_space_get_tuple_name>, the value returned points to
1633 an internal data structure.
1634 The identifiers, positions or names of individual dimensions can be
1635 read off using the following functions.
1637 __isl_give isl_id *isl_basic_set_get_dim_id(
1638 __isl_keep isl_basic_set *bset,
1639 enum isl_dim_type type, unsigned pos);
1640 __isl_give isl_set *isl_set_set_dim_id(
1641 __isl_take isl_set *set, enum isl_dim_type type,
1642 unsigned pos, __isl_take isl_id *id);
1643 int isl_set_has_dim_id(__isl_keep isl_set *set,
1644 enum isl_dim_type type, unsigned pos);
1645 __isl_give isl_id *isl_set_get_dim_id(
1646 __isl_keep isl_set *set, enum isl_dim_type type,
1648 int isl_basic_map_has_dim_id(
1649 __isl_keep isl_basic_map *bmap,
1650 enum isl_dim_type type, unsigned pos);
1651 __isl_give isl_map *isl_map_set_dim_id(
1652 __isl_take isl_map *map, enum isl_dim_type type,
1653 unsigned pos, __isl_take isl_id *id);
1654 int isl_map_has_dim_id(__isl_keep isl_map *map,
1655 enum isl_dim_type type, unsigned pos);
1656 __isl_give isl_id *isl_map_get_dim_id(
1657 __isl_keep isl_map *map, enum isl_dim_type type,
1660 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1661 enum isl_dim_type type, __isl_keep isl_id *id);
1662 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1663 enum isl_dim_type type, __isl_keep isl_id *id);
1664 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1665 enum isl_dim_type type, const char *name);
1666 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1667 enum isl_dim_type type, const char *name);
1669 const char *isl_constraint_get_dim_name(
1670 __isl_keep isl_constraint *constraint,
1671 enum isl_dim_type type, unsigned pos);
1672 const char *isl_basic_set_get_dim_name(
1673 __isl_keep isl_basic_set *bset,
1674 enum isl_dim_type type, unsigned pos);
1675 int isl_set_has_dim_name(__isl_keep isl_set *set,
1676 enum isl_dim_type type, unsigned pos);
1677 const char *isl_set_get_dim_name(
1678 __isl_keep isl_set *set,
1679 enum isl_dim_type type, unsigned pos);
1680 const char *isl_basic_map_get_dim_name(
1681 __isl_keep isl_basic_map *bmap,
1682 enum isl_dim_type type, unsigned pos);
1683 int isl_map_has_dim_name(__isl_keep isl_map *map,
1684 enum isl_dim_type type, unsigned pos);
1685 const char *isl_map_get_dim_name(
1686 __isl_keep isl_map *map,
1687 enum isl_dim_type type, unsigned pos);
1689 These functions are mostly useful to obtain the identifiers, positions
1690 or names of the parameters. Identifiers of individual dimensions are
1691 essentially only useful for printing. They are ignored by all other
1692 operations and may not be preserved across those operations.
1696 =head3 Unary Properties
1702 The following functions test whether the given set or relation
1703 contains any integer points. The ``plain'' variants do not perform
1704 any computations, but simply check if the given set or relation
1705 is already known to be empty.
1707 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1708 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1709 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1710 int isl_set_is_empty(__isl_keep isl_set *set);
1711 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1712 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1713 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1714 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1715 int isl_map_is_empty(__isl_keep isl_map *map);
1716 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1718 =item * Universality
1720 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1721 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1722 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1724 =item * Single-valuedness
1726 int isl_basic_map_is_single_valued(
1727 __isl_keep isl_basic_map *bmap);
1728 int isl_map_plain_is_single_valued(
1729 __isl_keep isl_map *map);
1730 int isl_map_is_single_valued(__isl_keep isl_map *map);
1731 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1735 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1736 int isl_map_is_injective(__isl_keep isl_map *map);
1737 int isl_union_map_plain_is_injective(
1738 __isl_keep isl_union_map *umap);
1739 int isl_union_map_is_injective(
1740 __isl_keep isl_union_map *umap);
1744 int isl_map_is_bijective(__isl_keep isl_map *map);
1745 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1749 int isl_basic_map_plain_is_fixed(
1750 __isl_keep isl_basic_map *bmap,
1751 enum isl_dim_type type, unsigned pos,
1753 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1754 enum isl_dim_type type, unsigned pos,
1756 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1757 enum isl_dim_type type, unsigned pos,
1760 Check if the relation obviously lies on a hyperplane where the given dimension
1761 has a fixed value and if so, return that value in C<*val>.
1765 To check whether a set is a parameter domain, use this function:
1767 int isl_set_is_params(__isl_keep isl_set *set);
1768 int isl_union_set_is_params(
1769 __isl_keep isl_union_set *uset);
1773 The following functions check whether the domain of the given
1774 (basic) set is a wrapped relation.
1776 int isl_basic_set_is_wrapping(
1777 __isl_keep isl_basic_set *bset);
1778 int isl_set_is_wrapping(__isl_keep isl_set *set);
1780 =item * Internal Product
1782 int isl_basic_map_can_zip(
1783 __isl_keep isl_basic_map *bmap);
1784 int isl_map_can_zip(__isl_keep isl_map *map);
1786 Check whether the product of domain and range of the given relation
1788 i.e., whether both domain and range are nested relations.
1792 int isl_basic_map_can_curry(
1793 __isl_keep isl_basic_map *bmap);
1794 int isl_map_can_curry(__isl_keep isl_map *map);
1796 Check whether the domain of the (basic) relation is a wrapped relation.
1800 =head3 Binary Properties
1806 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1807 __isl_keep isl_set *set2);
1808 int isl_set_is_equal(__isl_keep isl_set *set1,
1809 __isl_keep isl_set *set2);
1810 int isl_union_set_is_equal(
1811 __isl_keep isl_union_set *uset1,
1812 __isl_keep isl_union_set *uset2);
1813 int isl_basic_map_is_equal(
1814 __isl_keep isl_basic_map *bmap1,
1815 __isl_keep isl_basic_map *bmap2);
1816 int isl_map_is_equal(__isl_keep isl_map *map1,
1817 __isl_keep isl_map *map2);
1818 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1819 __isl_keep isl_map *map2);
1820 int isl_union_map_is_equal(
1821 __isl_keep isl_union_map *umap1,
1822 __isl_keep isl_union_map *umap2);
1824 =item * Disjointness
1826 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1827 __isl_keep isl_set *set2);
1831 int isl_basic_set_is_subset(
1832 __isl_keep isl_basic_set *bset1,
1833 __isl_keep isl_basic_set *bset2);
1834 int isl_set_is_subset(__isl_keep isl_set *set1,
1835 __isl_keep isl_set *set2);
1836 int isl_set_is_strict_subset(
1837 __isl_keep isl_set *set1,
1838 __isl_keep isl_set *set2);
1839 int isl_union_set_is_subset(
1840 __isl_keep isl_union_set *uset1,
1841 __isl_keep isl_union_set *uset2);
1842 int isl_union_set_is_strict_subset(
1843 __isl_keep isl_union_set *uset1,
1844 __isl_keep isl_union_set *uset2);
1845 int isl_basic_map_is_subset(
1846 __isl_keep isl_basic_map *bmap1,
1847 __isl_keep isl_basic_map *bmap2);
1848 int isl_basic_map_is_strict_subset(
1849 __isl_keep isl_basic_map *bmap1,
1850 __isl_keep isl_basic_map *bmap2);
1851 int isl_map_is_subset(
1852 __isl_keep isl_map *map1,
1853 __isl_keep isl_map *map2);
1854 int isl_map_is_strict_subset(
1855 __isl_keep isl_map *map1,
1856 __isl_keep isl_map *map2);
1857 int isl_union_map_is_subset(
1858 __isl_keep isl_union_map *umap1,
1859 __isl_keep isl_union_map *umap2);
1860 int isl_union_map_is_strict_subset(
1861 __isl_keep isl_union_map *umap1,
1862 __isl_keep isl_union_map *umap2);
1864 Check whether the first argument is a (strict) subset of the
1869 =head2 Unary Operations
1875 __isl_give isl_set *isl_set_complement(
1876 __isl_take isl_set *set);
1877 __isl_give isl_map *isl_map_complement(
1878 __isl_take isl_map *map);
1882 __isl_give isl_basic_map *isl_basic_map_reverse(
1883 __isl_take isl_basic_map *bmap);
1884 __isl_give isl_map *isl_map_reverse(
1885 __isl_take isl_map *map);
1886 __isl_give isl_union_map *isl_union_map_reverse(
1887 __isl_take isl_union_map *umap);
1891 __isl_give isl_basic_set *isl_basic_set_project_out(
1892 __isl_take isl_basic_set *bset,
1893 enum isl_dim_type type, unsigned first, unsigned n);
1894 __isl_give isl_basic_map *isl_basic_map_project_out(
1895 __isl_take isl_basic_map *bmap,
1896 enum isl_dim_type type, unsigned first, unsigned n);
1897 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1898 enum isl_dim_type type, unsigned first, unsigned n);
1899 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1900 enum isl_dim_type type, unsigned first, unsigned n);
1901 __isl_give isl_basic_set *isl_basic_set_params(
1902 __isl_take isl_basic_set *bset);
1903 __isl_give isl_basic_set *isl_basic_map_domain(
1904 __isl_take isl_basic_map *bmap);
1905 __isl_give isl_basic_set *isl_basic_map_range(
1906 __isl_take isl_basic_map *bmap);
1907 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1908 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1909 __isl_give isl_set *isl_map_domain(
1910 __isl_take isl_map *bmap);
1911 __isl_give isl_set *isl_map_range(
1912 __isl_take isl_map *map);
1913 __isl_give isl_set *isl_union_set_params(
1914 __isl_take isl_union_set *uset);
1915 __isl_give isl_set *isl_union_map_params(
1916 __isl_take isl_union_map *umap);
1917 __isl_give isl_union_set *isl_union_map_domain(
1918 __isl_take isl_union_map *umap);
1919 __isl_give isl_union_set *isl_union_map_range(
1920 __isl_take isl_union_map *umap);
1922 __isl_give isl_basic_map *isl_basic_map_domain_map(
1923 __isl_take isl_basic_map *bmap);
1924 __isl_give isl_basic_map *isl_basic_map_range_map(
1925 __isl_take isl_basic_map *bmap);
1926 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1927 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1928 __isl_give isl_union_map *isl_union_map_domain_map(
1929 __isl_take isl_union_map *umap);
1930 __isl_give isl_union_map *isl_union_map_range_map(
1931 __isl_take isl_union_map *umap);
1933 The functions above construct a (basic, regular or union) relation
1934 that maps (a wrapped version of) the input relation to its domain or range.
1938 __isl_give isl_basic_set *isl_basic_set_eliminate(
1939 __isl_take isl_basic_set *bset,
1940 enum isl_dim_type type,
1941 unsigned first, unsigned n);
1942 __isl_give isl_set *isl_set_eliminate(
1943 __isl_take isl_set *set, enum isl_dim_type type,
1944 unsigned first, unsigned n);
1945 __isl_give isl_basic_map *isl_basic_map_eliminate(
1946 __isl_take isl_basic_map *bmap,
1947 enum isl_dim_type type,
1948 unsigned first, unsigned n);
1949 __isl_give isl_map *isl_map_eliminate(
1950 __isl_take isl_map *map, enum isl_dim_type type,
1951 unsigned first, unsigned n);
1953 Eliminate the coefficients for the given dimensions from the constraints,
1954 without removing the dimensions.
1958 __isl_give isl_basic_set *isl_basic_set_fix(
1959 __isl_take isl_basic_set *bset,
1960 enum isl_dim_type type, unsigned pos,
1962 __isl_give isl_basic_set *isl_basic_set_fix_si(
1963 __isl_take isl_basic_set *bset,
1964 enum isl_dim_type type, unsigned pos, int value);
1965 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1966 enum isl_dim_type type, unsigned pos,
1968 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1969 enum isl_dim_type type, unsigned pos, int value);
1970 __isl_give isl_basic_map *isl_basic_map_fix_si(
1971 __isl_take isl_basic_map *bmap,
1972 enum isl_dim_type type, unsigned pos, int value);
1973 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1974 enum isl_dim_type type, unsigned pos, int value);
1976 Intersect the set or relation with the hyperplane where the given
1977 dimension has the fixed given value.
1979 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1980 __isl_take isl_basic_map *bmap,
1981 enum isl_dim_type type, unsigned pos, int value);
1982 __isl_give isl_set *isl_set_lower_bound(
1983 __isl_take isl_set *set,
1984 enum isl_dim_type type, unsigned pos,
1986 __isl_give isl_set *isl_set_lower_bound_si(
1987 __isl_take isl_set *set,
1988 enum isl_dim_type type, unsigned pos, int value);
1989 __isl_give isl_map *isl_map_lower_bound_si(
1990 __isl_take isl_map *map,
1991 enum isl_dim_type type, unsigned pos, int value);
1992 __isl_give isl_set *isl_set_upper_bound(
1993 __isl_take isl_set *set,
1994 enum isl_dim_type type, unsigned pos,
1996 __isl_give isl_set *isl_set_upper_bound_si(
1997 __isl_take isl_set *set,
1998 enum isl_dim_type type, unsigned pos, int value);
1999 __isl_give isl_map *isl_map_upper_bound_si(
2000 __isl_take isl_map *map,
2001 enum isl_dim_type type, unsigned pos, int value);
2003 Intersect the set or relation with the half-space where the given
2004 dimension has a value bounded by the fixed given value.
2006 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2007 enum isl_dim_type type1, int pos1,
2008 enum isl_dim_type type2, int pos2);
2009 __isl_give isl_basic_map *isl_basic_map_equate(
2010 __isl_take isl_basic_map *bmap,
2011 enum isl_dim_type type1, int pos1,
2012 enum isl_dim_type type2, int pos2);
2013 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2014 enum isl_dim_type type1, int pos1,
2015 enum isl_dim_type type2, int pos2);
2017 Intersect the set or relation with the hyperplane where the given
2018 dimensions are equal to each other.
2020 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2021 enum isl_dim_type type1, int pos1,
2022 enum isl_dim_type type2, int pos2);
2024 Intersect the relation with the hyperplane where the given
2025 dimensions have opposite values.
2027 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2028 enum isl_dim_type type1, int pos1,
2029 enum isl_dim_type type2, int pos2);
2030 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2031 enum isl_dim_type type1, int pos1,
2032 enum isl_dim_type type2, int pos2);
2034 Intersect the relation with the half-space where the given
2035 dimensions satisfy the given ordering.
2039 __isl_give isl_map *isl_set_identity(
2040 __isl_take isl_set *set);
2041 __isl_give isl_union_map *isl_union_set_identity(
2042 __isl_take isl_union_set *uset);
2044 Construct an identity relation on the given (union) set.
2048 __isl_give isl_basic_set *isl_basic_map_deltas(
2049 __isl_take isl_basic_map *bmap);
2050 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2051 __isl_give isl_union_set *isl_union_map_deltas(
2052 __isl_take isl_union_map *umap);
2054 These functions return a (basic) set containing the differences
2055 between image elements and corresponding domain elements in the input.
2057 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2058 __isl_take isl_basic_map *bmap);
2059 __isl_give isl_map *isl_map_deltas_map(
2060 __isl_take isl_map *map);
2061 __isl_give isl_union_map *isl_union_map_deltas_map(
2062 __isl_take isl_union_map *umap);
2064 The functions above construct a (basic, regular or union) relation
2065 that maps (a wrapped version of) the input relation to its delta set.
2069 Simplify the representation of a set or relation by trying
2070 to combine pairs of basic sets or relations into a single
2071 basic set or relation.
2073 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2074 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2075 __isl_give isl_union_set *isl_union_set_coalesce(
2076 __isl_take isl_union_set *uset);
2077 __isl_give isl_union_map *isl_union_map_coalesce(
2078 __isl_take isl_union_map *umap);
2080 One of the methods for combining pairs of basic sets or relations
2081 can result in coefficients that are much larger than those that appear
2082 in the constraints of the input. By default, the coefficients are
2083 not allowed to grow larger, but this can be changed by unsetting
2084 the following option.
2086 int isl_options_set_coalesce_bounded_wrapping(
2087 isl_ctx *ctx, int val);
2088 int isl_options_get_coalesce_bounded_wrapping(
2091 =item * Detecting equalities
2093 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2094 __isl_take isl_basic_set *bset);
2095 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2096 __isl_take isl_basic_map *bmap);
2097 __isl_give isl_set *isl_set_detect_equalities(
2098 __isl_take isl_set *set);
2099 __isl_give isl_map *isl_map_detect_equalities(
2100 __isl_take isl_map *map);
2101 __isl_give isl_union_set *isl_union_set_detect_equalities(
2102 __isl_take isl_union_set *uset);
2103 __isl_give isl_union_map *isl_union_map_detect_equalities(
2104 __isl_take isl_union_map *umap);
2106 Simplify the representation of a set or relation by detecting implicit
2109 =item * Removing redundant constraints
2111 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2112 __isl_take isl_basic_set *bset);
2113 __isl_give isl_set *isl_set_remove_redundancies(
2114 __isl_take isl_set *set);
2115 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2116 __isl_take isl_basic_map *bmap);
2117 __isl_give isl_map *isl_map_remove_redundancies(
2118 __isl_take isl_map *map);
2122 __isl_give isl_basic_set *isl_set_convex_hull(
2123 __isl_take isl_set *set);
2124 __isl_give isl_basic_map *isl_map_convex_hull(
2125 __isl_take isl_map *map);
2127 If the input set or relation has any existentially quantified
2128 variables, then the result of these operations is currently undefined.
2132 __isl_give isl_basic_set *isl_set_simple_hull(
2133 __isl_take isl_set *set);
2134 __isl_give isl_basic_map *isl_map_simple_hull(
2135 __isl_take isl_map *map);
2136 __isl_give isl_union_map *isl_union_map_simple_hull(
2137 __isl_take isl_union_map *umap);
2139 These functions compute a single basic set or relation
2140 that contains the whole input set or relation.
2141 In particular, the output is described by translates
2142 of the constraints describing the basic sets or relations in the input.
2146 (See \autoref{s:simple hull}.)
2152 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2153 __isl_take isl_basic_set *bset);
2154 __isl_give isl_basic_set *isl_set_affine_hull(
2155 __isl_take isl_set *set);
2156 __isl_give isl_union_set *isl_union_set_affine_hull(
2157 __isl_take isl_union_set *uset);
2158 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2159 __isl_take isl_basic_map *bmap);
2160 __isl_give isl_basic_map *isl_map_affine_hull(
2161 __isl_take isl_map *map);
2162 __isl_give isl_union_map *isl_union_map_affine_hull(
2163 __isl_take isl_union_map *umap);
2165 In case of union sets and relations, the affine hull is computed
2168 =item * Polyhedral hull
2170 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2171 __isl_take isl_set *set);
2172 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2173 __isl_take isl_map *map);
2174 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2175 __isl_take isl_union_set *uset);
2176 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2177 __isl_take isl_union_map *umap);
2179 These functions compute a single basic set or relation
2180 not involving any existentially quantified variables
2181 that contains the whole input set or relation.
2182 In case of union sets and relations, the polyhedral hull is computed
2187 __isl_give isl_basic_set *isl_basic_set_sample(
2188 __isl_take isl_basic_set *bset);
2189 __isl_give isl_basic_set *isl_set_sample(
2190 __isl_take isl_set *set);
2191 __isl_give isl_basic_map *isl_basic_map_sample(
2192 __isl_take isl_basic_map *bmap);
2193 __isl_give isl_basic_map *isl_map_sample(
2194 __isl_take isl_map *map);
2196 If the input (basic) set or relation is non-empty, then return
2197 a singleton subset of the input. Otherwise, return an empty set.
2199 =item * Optimization
2201 #include <isl/ilp.h>
2202 enum isl_lp_result isl_basic_set_max(
2203 __isl_keep isl_basic_set *bset,
2204 __isl_keep isl_aff *obj, isl_int *opt)
2205 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2206 __isl_keep isl_aff *obj, isl_int *opt);
2207 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2208 __isl_keep isl_aff *obj, isl_int *opt);
2210 Compute the minimum or maximum of the integer affine expression C<obj>
2211 over the points in C<set>, returning the result in C<opt>.
2212 The return value may be one of C<isl_lp_error>,
2213 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2215 =item * Parametric optimization
2217 __isl_give isl_pw_aff *isl_set_dim_min(
2218 __isl_take isl_set *set, int pos);
2219 __isl_give isl_pw_aff *isl_set_dim_max(
2220 __isl_take isl_set *set, int pos);
2221 __isl_give isl_pw_aff *isl_map_dim_max(
2222 __isl_take isl_map *map, int pos);
2224 Compute the minimum or maximum of the given set or output dimension
2225 as a function of the parameters (and input dimensions), but independently
2226 of the other set or output dimensions.
2227 For lexicographic optimization, see L<"Lexicographic Optimization">.
2231 The following functions compute either the set of (rational) coefficient
2232 values of valid constraints for the given set or the set of (rational)
2233 values satisfying the constraints with coefficients from the given set.
2234 Internally, these two sets of functions perform essentially the
2235 same operations, except that the set of coefficients is assumed to
2236 be a cone, while the set of values may be any polyhedron.
2237 The current implementation is based on the Farkas lemma and
2238 Fourier-Motzkin elimination, but this may change or be made optional
2239 in future. In particular, future implementations may use different
2240 dualization algorithms or skip the elimination step.
2242 __isl_give isl_basic_set *isl_basic_set_coefficients(
2243 __isl_take isl_basic_set *bset);
2244 __isl_give isl_basic_set *isl_set_coefficients(
2245 __isl_take isl_set *set);
2246 __isl_give isl_union_set *isl_union_set_coefficients(
2247 __isl_take isl_union_set *bset);
2248 __isl_give isl_basic_set *isl_basic_set_solutions(
2249 __isl_take isl_basic_set *bset);
2250 __isl_give isl_basic_set *isl_set_solutions(
2251 __isl_take isl_set *set);
2252 __isl_give isl_union_set *isl_union_set_solutions(
2253 __isl_take isl_union_set *bset);
2257 __isl_give isl_map *isl_map_fixed_power(
2258 __isl_take isl_map *map, isl_int exp);
2259 __isl_give isl_union_map *isl_union_map_fixed_power(
2260 __isl_take isl_union_map *umap, isl_int exp);
2262 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2263 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2264 of C<map> is computed.
2266 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2268 __isl_give isl_union_map *isl_union_map_power(
2269 __isl_take isl_union_map *umap, int *exact);
2271 Compute a parametric representation for all positive powers I<k> of C<map>.
2272 The result maps I<k> to a nested relation corresponding to the
2273 I<k>th power of C<map>.
2274 The result may be an overapproximation. If the result is known to be exact,
2275 then C<*exact> is set to C<1>.
2277 =item * Transitive closure
2279 __isl_give isl_map *isl_map_transitive_closure(
2280 __isl_take isl_map *map, int *exact);
2281 __isl_give isl_union_map *isl_union_map_transitive_closure(
2282 __isl_take isl_union_map *umap, int *exact);
2284 Compute the transitive closure of C<map>.
2285 The result may be an overapproximation. If the result is known to be exact,
2286 then C<*exact> is set to C<1>.
2288 =item * Reaching path lengths
2290 __isl_give isl_map *isl_map_reaching_path_lengths(
2291 __isl_take isl_map *map, int *exact);
2293 Compute a relation that maps each element in the range of C<map>
2294 to the lengths of all paths composed of edges in C<map> that
2295 end up in the given element.
2296 The result may be an overapproximation. If the result is known to be exact,
2297 then C<*exact> is set to C<1>.
2298 To compute the I<maximal> path length, the resulting relation
2299 should be postprocessed by C<isl_map_lexmax>.
2300 In particular, if the input relation is a dependence relation
2301 (mapping sources to sinks), then the maximal path length corresponds
2302 to the free schedule.
2303 Note, however, that C<isl_map_lexmax> expects the maximum to be
2304 finite, so if the path lengths are unbounded (possibly due to
2305 the overapproximation), then you will get an error message.
2309 __isl_give isl_basic_set *isl_basic_map_wrap(
2310 __isl_take isl_basic_map *bmap);
2311 __isl_give isl_set *isl_map_wrap(
2312 __isl_take isl_map *map);
2313 __isl_give isl_union_set *isl_union_map_wrap(
2314 __isl_take isl_union_map *umap);
2315 __isl_give isl_basic_map *isl_basic_set_unwrap(
2316 __isl_take isl_basic_set *bset);
2317 __isl_give isl_map *isl_set_unwrap(
2318 __isl_take isl_set *set);
2319 __isl_give isl_union_map *isl_union_set_unwrap(
2320 __isl_take isl_union_set *uset);
2324 Remove any internal structure of domain (and range) of the given
2325 set or relation. If there is any such internal structure in the input,
2326 then the name of the space is also removed.
2328 __isl_give isl_basic_set *isl_basic_set_flatten(
2329 __isl_take isl_basic_set *bset);
2330 __isl_give isl_set *isl_set_flatten(
2331 __isl_take isl_set *set);
2332 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2333 __isl_take isl_basic_map *bmap);
2334 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2335 __isl_take isl_basic_map *bmap);
2336 __isl_give isl_map *isl_map_flatten_range(
2337 __isl_take isl_map *map);
2338 __isl_give isl_map *isl_map_flatten_domain(
2339 __isl_take isl_map *map);
2340 __isl_give isl_basic_map *isl_basic_map_flatten(
2341 __isl_take isl_basic_map *bmap);
2342 __isl_give isl_map *isl_map_flatten(
2343 __isl_take isl_map *map);
2345 __isl_give isl_map *isl_set_flatten_map(
2346 __isl_take isl_set *set);
2348 The function above constructs a relation
2349 that maps the input set to a flattened version of the set.
2353 Lift the input set to a space with extra dimensions corresponding
2354 to the existentially quantified variables in the input.
2355 In particular, the result lives in a wrapped map where the domain
2356 is the original space and the range corresponds to the original
2357 existentially quantified variables.
2359 __isl_give isl_basic_set *isl_basic_set_lift(
2360 __isl_take isl_basic_set *bset);
2361 __isl_give isl_set *isl_set_lift(
2362 __isl_take isl_set *set);
2363 __isl_give isl_union_set *isl_union_set_lift(
2364 __isl_take isl_union_set *uset);
2366 Given a local space that contains the existentially quantified
2367 variables of a set, a basic relation that, when applied to
2368 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2369 can be constructed using the following function.
2371 #include <isl/local_space.h>
2372 __isl_give isl_basic_map *isl_local_space_lifting(
2373 __isl_take isl_local_space *ls);
2375 =item * Internal Product
2377 __isl_give isl_basic_map *isl_basic_map_zip(
2378 __isl_take isl_basic_map *bmap);
2379 __isl_give isl_map *isl_map_zip(
2380 __isl_take isl_map *map);
2381 __isl_give isl_union_map *isl_union_map_zip(
2382 __isl_take isl_union_map *umap);
2384 Given a relation with nested relations for domain and range,
2385 interchange the range of the domain with the domain of the range.
2389 __isl_give isl_basic_map *isl_basic_map_curry(
2390 __isl_take isl_basic_map *bmap);
2391 __isl_give isl_map *isl_map_curry(
2392 __isl_take isl_map *map);
2393 __isl_give isl_union_map *isl_union_map_curry(
2394 __isl_take isl_union_map *umap);
2396 Given a relation with a nested relation for domain,
2397 move the range of the nested relation out of the domain
2398 and use it as the domain of a nested relation in the range,
2399 with the original range as range of this nested relation.
2401 =item * Aligning parameters
2403 __isl_give isl_basic_set *isl_basic_set_align_params(
2404 __isl_take isl_basic_set *bset,
2405 __isl_take isl_space *model);
2406 __isl_give isl_set *isl_set_align_params(
2407 __isl_take isl_set *set,
2408 __isl_take isl_space *model);
2409 __isl_give isl_basic_map *isl_basic_map_align_params(
2410 __isl_take isl_basic_map *bmap,
2411 __isl_take isl_space *model);
2412 __isl_give isl_map *isl_map_align_params(
2413 __isl_take isl_map *map,
2414 __isl_take isl_space *model);
2416 Change the order of the parameters of the given set or relation
2417 such that the first parameters match those of C<model>.
2418 This may involve the introduction of extra parameters.
2419 All parameters need to be named.
2421 =item * Dimension manipulation
2423 __isl_give isl_set *isl_set_add_dims(
2424 __isl_take isl_set *set,
2425 enum isl_dim_type type, unsigned n);
2426 __isl_give isl_map *isl_map_add_dims(
2427 __isl_take isl_map *map,
2428 enum isl_dim_type type, unsigned n);
2429 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2430 __isl_take isl_basic_set *bset,
2431 enum isl_dim_type type, unsigned pos,
2433 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2434 __isl_take isl_basic_map *bmap,
2435 enum isl_dim_type type, unsigned pos,
2437 __isl_give isl_set *isl_set_insert_dims(
2438 __isl_take isl_set *set,
2439 enum isl_dim_type type, unsigned pos, unsigned n);
2440 __isl_give isl_map *isl_map_insert_dims(
2441 __isl_take isl_map *map,
2442 enum isl_dim_type type, unsigned pos, unsigned n);
2443 __isl_give isl_basic_set *isl_basic_set_move_dims(
2444 __isl_take isl_basic_set *bset,
2445 enum isl_dim_type dst_type, unsigned dst_pos,
2446 enum isl_dim_type src_type, unsigned src_pos,
2448 __isl_give isl_basic_map *isl_basic_map_move_dims(
2449 __isl_take isl_basic_map *bmap,
2450 enum isl_dim_type dst_type, unsigned dst_pos,
2451 enum isl_dim_type src_type, unsigned src_pos,
2453 __isl_give isl_set *isl_set_move_dims(
2454 __isl_take isl_set *set,
2455 enum isl_dim_type dst_type, unsigned dst_pos,
2456 enum isl_dim_type src_type, unsigned src_pos,
2458 __isl_give isl_map *isl_map_move_dims(
2459 __isl_take isl_map *map,
2460 enum isl_dim_type dst_type, unsigned dst_pos,
2461 enum isl_dim_type src_type, unsigned src_pos,
2464 It is usually not advisable to directly change the (input or output)
2465 space of a set or a relation as this removes the name and the internal
2466 structure of the space. However, the above functions can be useful
2467 to add new parameters, assuming
2468 C<isl_set_align_params> and C<isl_map_align_params>
2473 =head2 Binary Operations
2475 The two arguments of a binary operation not only need to live
2476 in the same C<isl_ctx>, they currently also need to have
2477 the same (number of) parameters.
2479 =head3 Basic Operations
2483 =item * Intersection
2485 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2486 __isl_take isl_basic_set *bset1,
2487 __isl_take isl_basic_set *bset2);
2488 __isl_give isl_basic_set *isl_basic_set_intersect(
2489 __isl_take isl_basic_set *bset1,
2490 __isl_take isl_basic_set *bset2);
2491 __isl_give isl_set *isl_set_intersect_params(
2492 __isl_take isl_set *set,
2493 __isl_take isl_set *params);
2494 __isl_give isl_set *isl_set_intersect(
2495 __isl_take isl_set *set1,
2496 __isl_take isl_set *set2);
2497 __isl_give isl_union_set *isl_union_set_intersect_params(
2498 __isl_take isl_union_set *uset,
2499 __isl_take isl_set *set);
2500 __isl_give isl_union_map *isl_union_map_intersect_params(
2501 __isl_take isl_union_map *umap,
2502 __isl_take isl_set *set);
2503 __isl_give isl_union_set *isl_union_set_intersect(
2504 __isl_take isl_union_set *uset1,
2505 __isl_take isl_union_set *uset2);
2506 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2507 __isl_take isl_basic_map *bmap,
2508 __isl_take isl_basic_set *bset);
2509 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2510 __isl_take isl_basic_map *bmap,
2511 __isl_take isl_basic_set *bset);
2512 __isl_give isl_basic_map *isl_basic_map_intersect(
2513 __isl_take isl_basic_map *bmap1,
2514 __isl_take isl_basic_map *bmap2);
2515 __isl_give isl_map *isl_map_intersect_params(
2516 __isl_take isl_map *map,
2517 __isl_take isl_set *params);
2518 __isl_give isl_map *isl_map_intersect_domain(
2519 __isl_take isl_map *map,
2520 __isl_take isl_set *set);
2521 __isl_give isl_map *isl_map_intersect_range(
2522 __isl_take isl_map *map,
2523 __isl_take isl_set *set);
2524 __isl_give isl_map *isl_map_intersect(
2525 __isl_take isl_map *map1,
2526 __isl_take isl_map *map2);
2527 __isl_give isl_union_map *isl_union_map_intersect_domain(
2528 __isl_take isl_union_map *umap,
2529 __isl_take isl_union_set *uset);
2530 __isl_give isl_union_map *isl_union_map_intersect_range(
2531 __isl_take isl_union_map *umap,
2532 __isl_take isl_union_set *uset);
2533 __isl_give isl_union_map *isl_union_map_intersect(
2534 __isl_take isl_union_map *umap1,
2535 __isl_take isl_union_map *umap2);
2537 The second argument to the C<_params> functions needs to be
2538 a parametric (basic) set. For the other functions, a parametric set
2539 for either argument is only allowed if the other argument is
2540 a parametric set as well.
2544 __isl_give isl_set *isl_basic_set_union(
2545 __isl_take isl_basic_set *bset1,
2546 __isl_take isl_basic_set *bset2);
2547 __isl_give isl_map *isl_basic_map_union(
2548 __isl_take isl_basic_map *bmap1,
2549 __isl_take isl_basic_map *bmap2);
2550 __isl_give isl_set *isl_set_union(
2551 __isl_take isl_set *set1,
2552 __isl_take isl_set *set2);
2553 __isl_give isl_map *isl_map_union(
2554 __isl_take isl_map *map1,
2555 __isl_take isl_map *map2);
2556 __isl_give isl_union_set *isl_union_set_union(
2557 __isl_take isl_union_set *uset1,
2558 __isl_take isl_union_set *uset2);
2559 __isl_give isl_union_map *isl_union_map_union(
2560 __isl_take isl_union_map *umap1,
2561 __isl_take isl_union_map *umap2);
2563 =item * Set difference
2565 __isl_give isl_set *isl_set_subtract(
2566 __isl_take isl_set *set1,
2567 __isl_take isl_set *set2);
2568 __isl_give isl_map *isl_map_subtract(
2569 __isl_take isl_map *map1,
2570 __isl_take isl_map *map2);
2571 __isl_give isl_map *isl_map_subtract_domain(
2572 __isl_take isl_map *map,
2573 __isl_take isl_set *dom);
2574 __isl_give isl_map *isl_map_subtract_range(
2575 __isl_take isl_map *map,
2576 __isl_take isl_set *dom);
2577 __isl_give isl_union_set *isl_union_set_subtract(
2578 __isl_take isl_union_set *uset1,
2579 __isl_take isl_union_set *uset2);
2580 __isl_give isl_union_map *isl_union_map_subtract(
2581 __isl_take isl_union_map *umap1,
2582 __isl_take isl_union_map *umap2);
2586 __isl_give isl_basic_set *isl_basic_set_apply(
2587 __isl_take isl_basic_set *bset,
2588 __isl_take isl_basic_map *bmap);
2589 __isl_give isl_set *isl_set_apply(
2590 __isl_take isl_set *set,
2591 __isl_take isl_map *map);
2592 __isl_give isl_union_set *isl_union_set_apply(
2593 __isl_take isl_union_set *uset,
2594 __isl_take isl_union_map *umap);
2595 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2596 __isl_take isl_basic_map *bmap1,
2597 __isl_take isl_basic_map *bmap2);
2598 __isl_give isl_basic_map *isl_basic_map_apply_range(
2599 __isl_take isl_basic_map *bmap1,
2600 __isl_take isl_basic_map *bmap2);
2601 __isl_give isl_map *isl_map_apply_domain(
2602 __isl_take isl_map *map1,
2603 __isl_take isl_map *map2);
2604 __isl_give isl_union_map *isl_union_map_apply_domain(
2605 __isl_take isl_union_map *umap1,
2606 __isl_take isl_union_map *umap2);
2607 __isl_give isl_map *isl_map_apply_range(
2608 __isl_take isl_map *map1,
2609 __isl_take isl_map *map2);
2610 __isl_give isl_union_map *isl_union_map_apply_range(
2611 __isl_take isl_union_map *umap1,
2612 __isl_take isl_union_map *umap2);
2614 =item * Cartesian Product
2616 __isl_give isl_set *isl_set_product(
2617 __isl_take isl_set *set1,
2618 __isl_take isl_set *set2);
2619 __isl_give isl_union_set *isl_union_set_product(
2620 __isl_take isl_union_set *uset1,
2621 __isl_take isl_union_set *uset2);
2622 __isl_give isl_basic_map *isl_basic_map_domain_product(
2623 __isl_take isl_basic_map *bmap1,
2624 __isl_take isl_basic_map *bmap2);
2625 __isl_give isl_basic_map *isl_basic_map_range_product(
2626 __isl_take isl_basic_map *bmap1,
2627 __isl_take isl_basic_map *bmap2);
2628 __isl_give isl_basic_map *isl_basic_map_product(
2629 __isl_take isl_basic_map *bmap1,
2630 __isl_take isl_basic_map *bmap2);
2631 __isl_give isl_map *isl_map_domain_product(
2632 __isl_take isl_map *map1,
2633 __isl_take isl_map *map2);
2634 __isl_give isl_map *isl_map_range_product(
2635 __isl_take isl_map *map1,
2636 __isl_take isl_map *map2);
2637 __isl_give isl_union_map *isl_union_map_domain_product(
2638 __isl_take isl_union_map *umap1,
2639 __isl_take isl_union_map *umap2);
2640 __isl_give isl_union_map *isl_union_map_range_product(
2641 __isl_take isl_union_map *umap1,
2642 __isl_take isl_union_map *umap2);
2643 __isl_give isl_map *isl_map_product(
2644 __isl_take isl_map *map1,
2645 __isl_take isl_map *map2);
2646 __isl_give isl_union_map *isl_union_map_product(
2647 __isl_take isl_union_map *umap1,
2648 __isl_take isl_union_map *umap2);
2650 The above functions compute the cross product of the given
2651 sets or relations. The domains and ranges of the results
2652 are wrapped maps between domains and ranges of the inputs.
2653 To obtain a ``flat'' product, use the following functions
2656 __isl_give isl_basic_set *isl_basic_set_flat_product(
2657 __isl_take isl_basic_set *bset1,
2658 __isl_take isl_basic_set *bset2);
2659 __isl_give isl_set *isl_set_flat_product(
2660 __isl_take isl_set *set1,
2661 __isl_take isl_set *set2);
2662 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2663 __isl_take isl_basic_map *bmap1,
2664 __isl_take isl_basic_map *bmap2);
2665 __isl_give isl_map *isl_map_flat_domain_product(
2666 __isl_take isl_map *map1,
2667 __isl_take isl_map *map2);
2668 __isl_give isl_map *isl_map_flat_range_product(
2669 __isl_take isl_map *map1,
2670 __isl_take isl_map *map2);
2671 __isl_give isl_union_map *isl_union_map_flat_range_product(
2672 __isl_take isl_union_map *umap1,
2673 __isl_take isl_union_map *umap2);
2674 __isl_give isl_basic_map *isl_basic_map_flat_product(
2675 __isl_take isl_basic_map *bmap1,
2676 __isl_take isl_basic_map *bmap2);
2677 __isl_give isl_map *isl_map_flat_product(
2678 __isl_take isl_map *map1,
2679 __isl_take isl_map *map2);
2681 =item * Simplification
2683 __isl_give isl_basic_set *isl_basic_set_gist(
2684 __isl_take isl_basic_set *bset,
2685 __isl_take isl_basic_set *context);
2686 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2687 __isl_take isl_set *context);
2688 __isl_give isl_set *isl_set_gist_params(
2689 __isl_take isl_set *set,
2690 __isl_take isl_set *context);
2691 __isl_give isl_union_set *isl_union_set_gist(
2692 __isl_take isl_union_set *uset,
2693 __isl_take isl_union_set *context);
2694 __isl_give isl_union_set *isl_union_set_gist_params(
2695 __isl_take isl_union_set *uset,
2696 __isl_take isl_set *set);
2697 __isl_give isl_basic_map *isl_basic_map_gist(
2698 __isl_take isl_basic_map *bmap,
2699 __isl_take isl_basic_map *context);
2700 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2701 __isl_take isl_map *context);
2702 __isl_give isl_map *isl_map_gist_params(
2703 __isl_take isl_map *map,
2704 __isl_take isl_set *context);
2705 __isl_give isl_map *isl_map_gist_domain(
2706 __isl_take isl_map *map,
2707 __isl_take isl_set *context);
2708 __isl_give isl_map *isl_map_gist_range(
2709 __isl_take isl_map *map,
2710 __isl_take isl_set *context);
2711 __isl_give isl_union_map *isl_union_map_gist(
2712 __isl_take isl_union_map *umap,
2713 __isl_take isl_union_map *context);
2714 __isl_give isl_union_map *isl_union_map_gist_params(
2715 __isl_take isl_union_map *umap,
2716 __isl_take isl_set *set);
2717 __isl_give isl_union_map *isl_union_map_gist_domain(
2718 __isl_take isl_union_map *umap,
2719 __isl_take isl_union_set *uset);
2720 __isl_give isl_union_map *isl_union_map_gist_range(
2721 __isl_take isl_union_map *umap,
2722 __isl_take isl_union_set *uset);
2724 The gist operation returns a set or relation that has the
2725 same intersection with the context as the input set or relation.
2726 Any implicit equality in the intersection is made explicit in the result,
2727 while all inequalities that are redundant with respect to the intersection
2729 In case of union sets and relations, the gist operation is performed
2734 =head3 Lexicographic Optimization
2736 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2737 the following functions
2738 compute a set that contains the lexicographic minimum or maximum
2739 of the elements in C<set> (or C<bset>) for those values of the parameters
2740 that satisfy C<dom>.
2741 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2742 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2744 In other words, the union of the parameter values
2745 for which the result is non-empty and of C<*empty>
2748 __isl_give isl_set *isl_basic_set_partial_lexmin(
2749 __isl_take isl_basic_set *bset,
2750 __isl_take isl_basic_set *dom,
2751 __isl_give isl_set **empty);
2752 __isl_give isl_set *isl_basic_set_partial_lexmax(
2753 __isl_take isl_basic_set *bset,
2754 __isl_take isl_basic_set *dom,
2755 __isl_give isl_set **empty);
2756 __isl_give isl_set *isl_set_partial_lexmin(
2757 __isl_take isl_set *set, __isl_take isl_set *dom,
2758 __isl_give isl_set **empty);
2759 __isl_give isl_set *isl_set_partial_lexmax(
2760 __isl_take isl_set *set, __isl_take isl_set *dom,
2761 __isl_give isl_set **empty);
2763 Given a (basic) set C<set> (or C<bset>), the following functions simply
2764 return a set containing the lexicographic minimum or maximum
2765 of the elements in C<set> (or C<bset>).
2766 In case of union sets, the optimum is computed per space.
2768 __isl_give isl_set *isl_basic_set_lexmin(
2769 __isl_take isl_basic_set *bset);
2770 __isl_give isl_set *isl_basic_set_lexmax(
2771 __isl_take isl_basic_set *bset);
2772 __isl_give isl_set *isl_set_lexmin(
2773 __isl_take isl_set *set);
2774 __isl_give isl_set *isl_set_lexmax(
2775 __isl_take isl_set *set);
2776 __isl_give isl_union_set *isl_union_set_lexmin(
2777 __isl_take isl_union_set *uset);
2778 __isl_give isl_union_set *isl_union_set_lexmax(
2779 __isl_take isl_union_set *uset);
2781 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2782 the following functions
2783 compute a relation that maps each element of C<dom>
2784 to the single lexicographic minimum or maximum
2785 of the elements that are associated to that same
2786 element in C<map> (or C<bmap>).
2787 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2788 that contains the elements in C<dom> that do not map
2789 to any elements in C<map> (or C<bmap>).
2790 In other words, the union of the domain of the result and of C<*empty>
2793 __isl_give isl_map *isl_basic_map_partial_lexmax(
2794 __isl_take isl_basic_map *bmap,
2795 __isl_take isl_basic_set *dom,
2796 __isl_give isl_set **empty);
2797 __isl_give isl_map *isl_basic_map_partial_lexmin(
2798 __isl_take isl_basic_map *bmap,
2799 __isl_take isl_basic_set *dom,
2800 __isl_give isl_set **empty);
2801 __isl_give isl_map *isl_map_partial_lexmax(
2802 __isl_take isl_map *map, __isl_take isl_set *dom,
2803 __isl_give isl_set **empty);
2804 __isl_give isl_map *isl_map_partial_lexmin(
2805 __isl_take isl_map *map, __isl_take isl_set *dom,
2806 __isl_give isl_set **empty);
2808 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2809 return a map mapping each element in the domain of
2810 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2811 of all elements associated to that element.
2812 In case of union relations, the optimum is computed per space.
2814 __isl_give isl_map *isl_basic_map_lexmin(
2815 __isl_take isl_basic_map *bmap);
2816 __isl_give isl_map *isl_basic_map_lexmax(
2817 __isl_take isl_basic_map *bmap);
2818 __isl_give isl_map *isl_map_lexmin(
2819 __isl_take isl_map *map);
2820 __isl_give isl_map *isl_map_lexmax(
2821 __isl_take isl_map *map);
2822 __isl_give isl_union_map *isl_union_map_lexmin(
2823 __isl_take isl_union_map *umap);
2824 __isl_give isl_union_map *isl_union_map_lexmax(
2825 __isl_take isl_union_map *umap);
2827 The following functions return their result in the form of
2828 a piecewise multi-affine expression
2829 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2830 but are otherwise equivalent to the corresponding functions
2831 returning a basic set or relation.
2833 __isl_give isl_pw_multi_aff *
2834 isl_basic_map_lexmin_pw_multi_aff(
2835 __isl_take isl_basic_map *bmap);
2836 __isl_give isl_pw_multi_aff *
2837 isl_basic_set_partial_lexmin_pw_multi_aff(
2838 __isl_take isl_basic_set *bset,
2839 __isl_take isl_basic_set *dom,
2840 __isl_give isl_set **empty);
2841 __isl_give isl_pw_multi_aff *
2842 isl_basic_set_partial_lexmax_pw_multi_aff(
2843 __isl_take isl_basic_set *bset,
2844 __isl_take isl_basic_set *dom,
2845 __isl_give isl_set **empty);
2846 __isl_give isl_pw_multi_aff *
2847 isl_basic_map_partial_lexmin_pw_multi_aff(
2848 __isl_take isl_basic_map *bmap,
2849 __isl_take isl_basic_set *dom,
2850 __isl_give isl_set **empty);
2851 __isl_give isl_pw_multi_aff *
2852 isl_basic_map_partial_lexmax_pw_multi_aff(
2853 __isl_take isl_basic_map *bmap,
2854 __isl_take isl_basic_set *dom,
2855 __isl_give isl_set **empty);
2859 Lists are defined over several element types, including
2860 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2861 Here we take lists of C<isl_set>s as an example.
2862 Lists can be created, copied, modified and freed using the following functions.
2864 #include <isl/list.h>
2865 __isl_give isl_set_list *isl_set_list_from_set(
2866 __isl_take isl_set *el);
2867 __isl_give isl_set_list *isl_set_list_alloc(
2868 isl_ctx *ctx, int n);
2869 __isl_give isl_set_list *isl_set_list_copy(
2870 __isl_keep isl_set_list *list);
2871 __isl_give isl_set_list *isl_set_list_add(
2872 __isl_take isl_set_list *list,
2873 __isl_take isl_set *el);
2874 __isl_give isl_set_list *isl_set_list_set_set(
2875 __isl_take isl_set_list *list, int index,
2876 __isl_take isl_set *set);
2877 __isl_give isl_set_list *isl_set_list_concat(
2878 __isl_take isl_set_list *list1,
2879 __isl_take isl_set_list *list2);
2880 void *isl_set_list_free(__isl_take isl_set_list *list);
2882 C<isl_set_list_alloc> creates an empty list with a capacity for
2883 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2886 Lists can be inspected using the following functions.
2888 #include <isl/list.h>
2889 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2890 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2891 __isl_give isl_set *isl_set_list_get_set(
2892 __isl_keep isl_set_list *list, int index);
2893 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2894 int (*fn)(__isl_take isl_set *el, void *user),
2897 Lists can be printed using
2899 #include <isl/list.h>
2900 __isl_give isl_printer *isl_printer_print_set_list(
2901 __isl_take isl_printer *p,
2902 __isl_keep isl_set_list *list);
2906 Vectors can be created, copied and freed using the following functions.
2908 #include <isl/vec.h>
2909 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2911 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2912 void isl_vec_free(__isl_take isl_vec *vec);
2914 Note that the elements of a newly created vector may have arbitrary values.
2915 The elements can be changed and inspected using the following functions.
2917 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2918 int isl_vec_size(__isl_keep isl_vec *vec);
2919 int isl_vec_get_element(__isl_keep isl_vec *vec,
2920 int pos, isl_int *v);
2921 __isl_give isl_vec *isl_vec_set_element(
2922 __isl_take isl_vec *vec, int pos, isl_int v);
2923 __isl_give isl_vec *isl_vec_set_element_si(
2924 __isl_take isl_vec *vec, int pos, int v);
2925 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2927 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2930 C<isl_vec_get_element> will return a negative value if anything went wrong.
2931 In that case, the value of C<*v> is undefined.
2935 Matrices can be created, copied and freed using the following functions.
2937 #include <isl/mat.h>
2938 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2939 unsigned n_row, unsigned n_col);
2940 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2941 void isl_mat_free(__isl_take isl_mat *mat);
2943 Note that the elements of a newly created matrix may have arbitrary values.
2944 The elements can be changed and inspected using the following functions.
2946 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2947 int isl_mat_rows(__isl_keep isl_mat *mat);
2948 int isl_mat_cols(__isl_keep isl_mat *mat);
2949 int isl_mat_get_element(__isl_keep isl_mat *mat,
2950 int row, int col, isl_int *v);
2951 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2952 int row, int col, isl_int v);
2953 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2954 int row, int col, int v);
2956 C<isl_mat_get_element> will return a negative value if anything went wrong.
2957 In that case, the value of C<*v> is undefined.
2959 The following function can be used to compute the (right) inverse
2960 of a matrix, i.e., a matrix such that the product of the original
2961 and the inverse (in that order) is a multiple of the identity matrix.
2962 The input matrix is assumed to be of full row-rank.
2964 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2966 The following function can be used to compute the (right) kernel
2967 (or null space) of a matrix, i.e., a matrix such that the product of
2968 the original and the kernel (in that order) is the zero matrix.
2970 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2972 =head2 Piecewise Quasi Affine Expressions
2974 The zero quasi affine expression on a given domain can be created using
2976 __isl_give isl_aff *isl_aff_zero_on_domain(
2977 __isl_take isl_local_space *ls);
2979 Note that the space in which the resulting object lives is a map space
2980 with the given space as domain and a one-dimensional range.
2982 An empty piecewise quasi affine expression (one with no cells)
2983 or a piecewise quasi affine expression with a single cell can
2984 be created using the following functions.
2986 #include <isl/aff.h>
2987 __isl_give isl_pw_aff *isl_pw_aff_empty(
2988 __isl_take isl_space *space);
2989 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2990 __isl_take isl_set *set, __isl_take isl_aff *aff);
2991 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2992 __isl_take isl_aff *aff);
2994 A piecewise quasi affine expression that is equal to 1 on a set
2995 and 0 outside the set can be created using the following function.
2997 #include <isl/aff.h>
2998 __isl_give isl_pw_aff *isl_set_indicator_function(
2999 __isl_take isl_set *set);
3001 Quasi affine expressions can be copied and freed using
3003 #include <isl/aff.h>
3004 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3005 void *isl_aff_free(__isl_take isl_aff *aff);
3007 __isl_give isl_pw_aff *isl_pw_aff_copy(
3008 __isl_keep isl_pw_aff *pwaff);
3009 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3011 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3012 using the following function. The constraint is required to have
3013 a non-zero coefficient for the specified dimension.
3015 #include <isl/constraint.h>
3016 __isl_give isl_aff *isl_constraint_get_bound(
3017 __isl_keep isl_constraint *constraint,
3018 enum isl_dim_type type, int pos);
3020 The entire affine expression of the constraint can also be extracted
3021 using the following function.
3023 #include <isl/constraint.h>
3024 __isl_give isl_aff *isl_constraint_get_aff(
3025 __isl_keep isl_constraint *constraint);
3027 Conversely, an equality constraint equating
3028 the affine expression to zero or an inequality constraint enforcing
3029 the affine expression to be non-negative, can be constructed using
3031 __isl_give isl_constraint *isl_equality_from_aff(
3032 __isl_take isl_aff *aff);
3033 __isl_give isl_constraint *isl_inequality_from_aff(
3034 __isl_take isl_aff *aff);
3036 The expression can be inspected using
3038 #include <isl/aff.h>
3039 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3040 int isl_aff_dim(__isl_keep isl_aff *aff,
3041 enum isl_dim_type type);
3042 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3043 __isl_keep isl_aff *aff);
3044 __isl_give isl_local_space *isl_aff_get_local_space(
3045 __isl_keep isl_aff *aff);
3046 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3047 enum isl_dim_type type, unsigned pos);
3048 const char *isl_pw_aff_get_dim_name(
3049 __isl_keep isl_pw_aff *pa,
3050 enum isl_dim_type type, unsigned pos);
3051 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3052 enum isl_dim_type type, unsigned pos);
3053 __isl_give isl_id *isl_pw_aff_get_dim_id(
3054 __isl_keep isl_pw_aff *pa,
3055 enum isl_dim_type type, unsigned pos);
3056 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3057 __isl_keep isl_pw_aff *pa,
3058 enum isl_dim_type type);
3059 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3061 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3062 enum isl_dim_type type, int pos, isl_int *v);
3063 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3065 __isl_give isl_aff *isl_aff_get_div(
3066 __isl_keep isl_aff *aff, int pos);
3068 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3069 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3070 int (*fn)(__isl_take isl_set *set,
3071 __isl_take isl_aff *aff,
3072 void *user), void *user);
3074 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3075 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3077 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3078 enum isl_dim_type type, unsigned first, unsigned n);
3079 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3080 enum isl_dim_type type, unsigned first, unsigned n);
3082 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3083 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3084 enum isl_dim_type type);
3085 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3087 It can be modified using
3089 #include <isl/aff.h>
3090 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3091 __isl_take isl_pw_aff *pwaff,
3092 enum isl_dim_type type, __isl_take isl_id *id);
3093 __isl_give isl_aff *isl_aff_set_dim_name(
3094 __isl_take isl_aff *aff, enum isl_dim_type type,
3095 unsigned pos, const char *s);
3096 __isl_give isl_aff *isl_aff_set_dim_id(
3097 __isl_take isl_aff *aff, enum isl_dim_type type,
3098 unsigned pos, __isl_take isl_id *id);
3099 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3100 __isl_take isl_pw_aff *pma,
3101 enum isl_dim_type type, unsigned pos,
3102 __isl_take isl_id *id);
3103 __isl_give isl_aff *isl_aff_set_constant(
3104 __isl_take isl_aff *aff, isl_int v);
3105 __isl_give isl_aff *isl_aff_set_constant_si(
3106 __isl_take isl_aff *aff, int v);
3107 __isl_give isl_aff *isl_aff_set_coefficient(
3108 __isl_take isl_aff *aff,
3109 enum isl_dim_type type, int pos, isl_int v);
3110 __isl_give isl_aff *isl_aff_set_coefficient_si(
3111 __isl_take isl_aff *aff,
3112 enum isl_dim_type type, int pos, int v);
3113 __isl_give isl_aff *isl_aff_set_denominator(
3114 __isl_take isl_aff *aff, isl_int v);
3116 __isl_give isl_aff *isl_aff_add_constant(
3117 __isl_take isl_aff *aff, isl_int v);
3118 __isl_give isl_aff *isl_aff_add_constant_si(
3119 __isl_take isl_aff *aff, int v);
3120 __isl_give isl_aff *isl_aff_add_constant_num(
3121 __isl_take isl_aff *aff, isl_int v);
3122 __isl_give isl_aff *isl_aff_add_constant_num_si(
3123 __isl_take isl_aff *aff, int v);
3124 __isl_give isl_aff *isl_aff_add_coefficient(
3125 __isl_take isl_aff *aff,
3126 enum isl_dim_type type, int pos, isl_int v);
3127 __isl_give isl_aff *isl_aff_add_coefficient_si(
3128 __isl_take isl_aff *aff,
3129 enum isl_dim_type type, int pos, int v);
3131 __isl_give isl_aff *isl_aff_insert_dims(
3132 __isl_take isl_aff *aff,
3133 enum isl_dim_type type, unsigned first, unsigned n);
3134 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3135 __isl_take isl_pw_aff *pwaff,
3136 enum isl_dim_type type, unsigned first, unsigned n);
3137 __isl_give isl_aff *isl_aff_add_dims(
3138 __isl_take isl_aff *aff,
3139 enum isl_dim_type type, unsigned n);
3140 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3141 __isl_take isl_pw_aff *pwaff,
3142 enum isl_dim_type type, unsigned n);
3143 __isl_give isl_aff *isl_aff_drop_dims(
3144 __isl_take isl_aff *aff,
3145 enum isl_dim_type type, unsigned first, unsigned n);
3146 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3147 __isl_take isl_pw_aff *pwaff,
3148 enum isl_dim_type type, unsigned first, unsigned n);
3150 Note that the C<set_constant> and C<set_coefficient> functions
3151 set the I<numerator> of the constant or coefficient, while
3152 C<add_constant> and C<add_coefficient> add an integer value to
3153 the possibly rational constant or coefficient.
3154 The C<add_constant_num> functions add an integer value to
3157 To check whether an affine expressions is obviously zero
3158 or obviously equal to some other affine expression, use
3160 #include <isl/aff.h>
3161 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3162 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3163 __isl_keep isl_aff *aff2);
3164 int isl_pw_aff_plain_is_equal(
3165 __isl_keep isl_pw_aff *pwaff1,
3166 __isl_keep isl_pw_aff *pwaff2);
3170 #include <isl/aff.h>
3171 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3172 __isl_take isl_aff *aff2);
3173 __isl_give isl_pw_aff *isl_pw_aff_add(
3174 __isl_take isl_pw_aff *pwaff1,
3175 __isl_take isl_pw_aff *pwaff2);
3176 __isl_give isl_pw_aff *isl_pw_aff_min(
3177 __isl_take isl_pw_aff *pwaff1,
3178 __isl_take isl_pw_aff *pwaff2);
3179 __isl_give isl_pw_aff *isl_pw_aff_max(
3180 __isl_take isl_pw_aff *pwaff1,
3181 __isl_take isl_pw_aff *pwaff2);
3182 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3183 __isl_take isl_aff *aff2);
3184 __isl_give isl_pw_aff *isl_pw_aff_sub(
3185 __isl_take isl_pw_aff *pwaff1,
3186 __isl_take isl_pw_aff *pwaff2);
3187 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3188 __isl_give isl_pw_aff *isl_pw_aff_neg(
3189 __isl_take isl_pw_aff *pwaff);
3190 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3191 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3192 __isl_take isl_pw_aff *pwaff);
3193 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3194 __isl_give isl_pw_aff *isl_pw_aff_floor(
3195 __isl_take isl_pw_aff *pwaff);
3196 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3198 __isl_give isl_pw_aff *isl_pw_aff_mod(
3199 __isl_take isl_pw_aff *pwaff, isl_int mod);
3200 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3202 __isl_give isl_pw_aff *isl_pw_aff_scale(
3203 __isl_take isl_pw_aff *pwaff, isl_int f);
3204 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3206 __isl_give isl_aff *isl_aff_scale_down_ui(
3207 __isl_take isl_aff *aff, unsigned f);
3208 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3209 __isl_take isl_pw_aff *pwaff, isl_int f);
3211 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3212 __isl_take isl_pw_aff_list *list);
3213 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3214 __isl_take isl_pw_aff_list *list);
3216 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3217 __isl_take isl_pw_aff *pwqp);
3219 __isl_give isl_aff *isl_aff_align_params(
3220 __isl_take isl_aff *aff,
3221 __isl_take isl_space *model);
3222 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3223 __isl_take isl_pw_aff *pwaff,
3224 __isl_take isl_space *model);
3226 __isl_give isl_aff *isl_aff_project_domain_on_params(
3227 __isl_take isl_aff *aff);
3229 __isl_give isl_aff *isl_aff_gist_params(
3230 __isl_take isl_aff *aff,
3231 __isl_take isl_set *context);
3232 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3233 __isl_take isl_set *context);
3234 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3235 __isl_take isl_pw_aff *pwaff,
3236 __isl_take isl_set *context);
3237 __isl_give isl_pw_aff *isl_pw_aff_gist(
3238 __isl_take isl_pw_aff *pwaff,
3239 __isl_take isl_set *context);
3241 __isl_give isl_set *isl_pw_aff_domain(
3242 __isl_take isl_pw_aff *pwaff);
3243 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3244 __isl_take isl_pw_aff *pa,
3245 __isl_take isl_set *set);
3246 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3247 __isl_take isl_pw_aff *pa,
3248 __isl_take isl_set *set);
3250 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3251 __isl_take isl_aff *aff2);
3252 __isl_give isl_pw_aff *isl_pw_aff_mul(
3253 __isl_take isl_pw_aff *pwaff1,
3254 __isl_take isl_pw_aff *pwaff2);
3256 When multiplying two affine expressions, at least one of the two needs
3259 #include <isl/aff.h>
3260 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3261 __isl_take isl_aff *aff);
3262 __isl_give isl_basic_set *isl_aff_le_basic_set(
3263 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3264 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3265 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3266 __isl_give isl_set *isl_pw_aff_eq_set(
3267 __isl_take isl_pw_aff *pwaff1,
3268 __isl_take isl_pw_aff *pwaff2);
3269 __isl_give isl_set *isl_pw_aff_ne_set(
3270 __isl_take isl_pw_aff *pwaff1,
3271 __isl_take isl_pw_aff *pwaff2);
3272 __isl_give isl_set *isl_pw_aff_le_set(
3273 __isl_take isl_pw_aff *pwaff1,
3274 __isl_take isl_pw_aff *pwaff2);
3275 __isl_give isl_set *isl_pw_aff_lt_set(
3276 __isl_take isl_pw_aff *pwaff1,
3277 __isl_take isl_pw_aff *pwaff2);
3278 __isl_give isl_set *isl_pw_aff_ge_set(
3279 __isl_take isl_pw_aff *pwaff1,
3280 __isl_take isl_pw_aff *pwaff2);
3281 __isl_give isl_set *isl_pw_aff_gt_set(
3282 __isl_take isl_pw_aff *pwaff1,
3283 __isl_take isl_pw_aff *pwaff2);
3285 __isl_give isl_set *isl_pw_aff_list_eq_set(
3286 __isl_take isl_pw_aff_list *list1,
3287 __isl_take isl_pw_aff_list *list2);
3288 __isl_give isl_set *isl_pw_aff_list_ne_set(
3289 __isl_take isl_pw_aff_list *list1,
3290 __isl_take isl_pw_aff_list *list2);
3291 __isl_give isl_set *isl_pw_aff_list_le_set(
3292 __isl_take isl_pw_aff_list *list1,
3293 __isl_take isl_pw_aff_list *list2);
3294 __isl_give isl_set *isl_pw_aff_list_lt_set(
3295 __isl_take isl_pw_aff_list *list1,
3296 __isl_take isl_pw_aff_list *list2);
3297 __isl_give isl_set *isl_pw_aff_list_ge_set(
3298 __isl_take isl_pw_aff_list *list1,
3299 __isl_take isl_pw_aff_list *list2);
3300 __isl_give isl_set *isl_pw_aff_list_gt_set(
3301 __isl_take isl_pw_aff_list *list1,
3302 __isl_take isl_pw_aff_list *list2);
3304 The function C<isl_aff_neg_basic_set> returns a basic set
3305 containing those elements in the domain space
3306 of C<aff> where C<aff> is negative.
3307 The function C<isl_aff_ge_basic_set> returns a basic set
3308 containing those elements in the shared space
3309 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3310 The function C<isl_pw_aff_ge_set> returns a set
3311 containing those elements in the shared domain
3312 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3313 The functions operating on C<isl_pw_aff_list> apply the corresponding
3314 C<isl_pw_aff> function to each pair of elements in the two lists.
3316 #include <isl/aff.h>
3317 __isl_give isl_set *isl_pw_aff_nonneg_set(
3318 __isl_take isl_pw_aff *pwaff);
3319 __isl_give isl_set *isl_pw_aff_zero_set(
3320 __isl_take isl_pw_aff *pwaff);
3321 __isl_give isl_set *isl_pw_aff_non_zero_set(
3322 __isl_take isl_pw_aff *pwaff);
3324 The function C<isl_pw_aff_nonneg_set> returns a set
3325 containing those elements in the domain
3326 of C<pwaff> where C<pwaff> is non-negative.
3328 #include <isl/aff.h>
3329 __isl_give isl_pw_aff *isl_pw_aff_cond(
3330 __isl_take isl_pw_aff *cond,
3331 __isl_take isl_pw_aff *pwaff_true,
3332 __isl_take isl_pw_aff *pwaff_false);
3334 The function C<isl_pw_aff_cond> performs a conditional operator
3335 and returns an expression that is equal to C<pwaff_true>
3336 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3337 where C<cond> is zero.
3339 #include <isl/aff.h>
3340 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3341 __isl_take isl_pw_aff *pwaff1,
3342 __isl_take isl_pw_aff *pwaff2);
3343 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3344 __isl_take isl_pw_aff *pwaff1,
3345 __isl_take isl_pw_aff *pwaff2);
3346 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3347 __isl_take isl_pw_aff *pwaff1,
3348 __isl_take isl_pw_aff *pwaff2);
3350 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3351 expression with a domain that is the union of those of C<pwaff1> and
3352 C<pwaff2> and such that on each cell, the quasi-affine expression is
3353 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3354 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3355 associated expression is the defined one.
3357 An expression can be read from input using
3359 #include <isl/aff.h>
3360 __isl_give isl_aff *isl_aff_read_from_str(
3361 isl_ctx *ctx, const char *str);
3362 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3363 isl_ctx *ctx, const char *str);
3365 An expression can be printed using
3367 #include <isl/aff.h>
3368 __isl_give isl_printer *isl_printer_print_aff(
3369 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3371 __isl_give isl_printer *isl_printer_print_pw_aff(
3372 __isl_take isl_printer *p,
3373 __isl_keep isl_pw_aff *pwaff);
3375 =head2 Piecewise Multiple Quasi Affine Expressions
3377 An C<isl_multi_aff> object represents a sequence of
3378 zero or more affine expressions, all defined on the same domain space.
3380 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3383 #include <isl/aff.h>
3384 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3385 __isl_take isl_space *space,
3386 __isl_take isl_aff_list *list);
3388 An empty piecewise multiple quasi affine expression (one with no cells),
3389 the zero piecewise multiple quasi affine expression (with value zero
3390 for each output dimension),
3391 a piecewise multiple quasi affine expression with a single cell (with
3392 either a universe or a specified domain) or
3393 a zero-dimensional piecewise multiple quasi affine expression
3395 can be created using the following functions.
3397 #include <isl/aff.h>
3398 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3399 __isl_take isl_space *space);
3400 __isl_give isl_multi_aff *isl_multi_aff_zero(
3401 __isl_take isl_space *space);
3402 __isl_give isl_multi_aff *isl_multi_aff_identity(
3403 __isl_take isl_space *space);
3404 __isl_give isl_pw_multi_aff *
3405 isl_pw_multi_aff_from_multi_aff(
3406 __isl_take isl_multi_aff *ma);
3407 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3408 __isl_take isl_set *set,
3409 __isl_take isl_multi_aff *maff);
3410 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3411 __isl_take isl_set *set);
3413 __isl_give isl_union_pw_multi_aff *
3414 isl_union_pw_multi_aff_empty(
3415 __isl_take isl_space *space);
3416 __isl_give isl_union_pw_multi_aff *
3417 isl_union_pw_multi_aff_add_pw_multi_aff(
3418 __isl_take isl_union_pw_multi_aff *upma,
3419 __isl_take isl_pw_multi_aff *pma);
3420 __isl_give isl_union_pw_multi_aff *
3421 isl_union_pw_multi_aff_from_domain(
3422 __isl_take isl_union_set *uset);
3424 A piecewise multiple quasi affine expression can also be initialized
3425 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3426 and the C<isl_map> is single-valued.
3428 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3429 __isl_take isl_set *set);
3430 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3431 __isl_take isl_map *map);
3433 Multiple quasi affine expressions can be copied and freed using
3435 #include <isl/aff.h>
3436 __isl_give isl_multi_aff *isl_multi_aff_copy(
3437 __isl_keep isl_multi_aff *maff);
3438 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3440 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3441 __isl_keep isl_pw_multi_aff *pma);
3442 void *isl_pw_multi_aff_free(
3443 __isl_take isl_pw_multi_aff *pma);
3445 __isl_give isl_union_pw_multi_aff *
3446 isl_union_pw_multi_aff_copy(
3447 __isl_keep isl_union_pw_multi_aff *upma);
3448 void *isl_union_pw_multi_aff_free(
3449 __isl_take isl_union_pw_multi_aff *upma);
3451 The expression can be inspected using
3453 #include <isl/aff.h>
3454 isl_ctx *isl_multi_aff_get_ctx(
3455 __isl_keep isl_multi_aff *maff);
3456 isl_ctx *isl_pw_multi_aff_get_ctx(
3457 __isl_keep isl_pw_multi_aff *pma);
3458 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3459 __isl_keep isl_union_pw_multi_aff *upma);
3460 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3461 enum isl_dim_type type);
3462 unsigned isl_pw_multi_aff_dim(
3463 __isl_keep isl_pw_multi_aff *pma,
3464 enum isl_dim_type type);
3465 __isl_give isl_aff *isl_multi_aff_get_aff(
3466 __isl_keep isl_multi_aff *multi, int pos);
3467 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3468 __isl_keep isl_pw_multi_aff *pma, int pos);
3469 const char *isl_pw_multi_aff_get_dim_name(
3470 __isl_keep isl_pw_multi_aff *pma,
3471 enum isl_dim_type type, unsigned pos);
3472 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3473 __isl_keep isl_pw_multi_aff *pma,
3474 enum isl_dim_type type, unsigned pos);
3475 const char *isl_multi_aff_get_tuple_name(
3476 __isl_keep isl_multi_aff *multi,
3477 enum isl_dim_type type);
3478 int isl_pw_multi_aff_has_tuple_name(
3479 __isl_keep isl_pw_multi_aff *pma,
3480 enum isl_dim_type type);
3481 const char *isl_pw_multi_aff_get_tuple_name(
3482 __isl_keep isl_pw_multi_aff *pma,
3483 enum isl_dim_type type);
3484 int isl_pw_multi_aff_has_tuple_id(
3485 __isl_keep isl_pw_multi_aff *pma,
3486 enum isl_dim_type type);
3487 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3488 __isl_keep isl_pw_multi_aff *pma,
3489 enum isl_dim_type type);
3491 int isl_pw_multi_aff_foreach_piece(
3492 __isl_keep isl_pw_multi_aff *pma,
3493 int (*fn)(__isl_take isl_set *set,
3494 __isl_take isl_multi_aff *maff,
3495 void *user), void *user);
3497 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3498 __isl_keep isl_union_pw_multi_aff *upma,
3499 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3500 void *user), void *user);
3502 It can be modified using
3504 #include <isl/aff.h>
3505 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3506 __isl_take isl_multi_aff *multi, int pos,
3507 __isl_take isl_aff *aff);
3508 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3509 __isl_take isl_multi_aff *maff,
3510 enum isl_dim_type type, unsigned pos, const char *s);
3511 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3512 __isl_take isl_multi_aff *maff,
3513 enum isl_dim_type type, __isl_take isl_id *id);
3514 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3515 __isl_take isl_pw_multi_aff *pma,
3516 enum isl_dim_type type, __isl_take isl_id *id);
3518 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3519 __isl_take isl_multi_aff *maff,
3520 enum isl_dim_type type, unsigned first, unsigned n);
3522 To check whether two multiple affine expressions are
3523 obviously equal to each other, use
3525 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3526 __isl_keep isl_multi_aff *maff2);
3527 int isl_pw_multi_aff_plain_is_equal(
3528 __isl_keep isl_pw_multi_aff *pma1,
3529 __isl_keep isl_pw_multi_aff *pma2);
3533 #include <isl/aff.h>
3534 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3535 __isl_take isl_pw_multi_aff *pma1,
3536 __isl_take isl_pw_multi_aff *pma2);
3537 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3538 __isl_take isl_pw_multi_aff *pma1,
3539 __isl_take isl_pw_multi_aff *pma2);
3540 __isl_give isl_multi_aff *isl_multi_aff_add(
3541 __isl_take isl_multi_aff *maff1,
3542 __isl_take isl_multi_aff *maff2);
3543 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3544 __isl_take isl_pw_multi_aff *pma1,
3545 __isl_take isl_pw_multi_aff *pma2);
3546 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3547 __isl_take isl_union_pw_multi_aff *upma1,
3548 __isl_take isl_union_pw_multi_aff *upma2);
3549 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3550 __isl_take isl_pw_multi_aff *pma1,
3551 __isl_take isl_pw_multi_aff *pma2);
3552 __isl_give isl_multi_aff *isl_multi_aff_scale(
3553 __isl_take isl_multi_aff *maff,
3555 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3556 __isl_take isl_pw_multi_aff *pma,
3557 __isl_take isl_set *set);
3558 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3559 __isl_take isl_pw_multi_aff *pma,
3560 __isl_take isl_set *set);
3561 __isl_give isl_multi_aff *isl_multi_aff_lift(
3562 __isl_take isl_multi_aff *maff,
3563 __isl_give isl_local_space **ls);
3564 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3565 __isl_take isl_pw_multi_aff *pma);
3566 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3567 __isl_take isl_multi_aff *maff,
3568 __isl_take isl_set *context);
3569 __isl_give isl_multi_aff *isl_multi_aff_gist(
3570 __isl_take isl_multi_aff *maff,
3571 __isl_take isl_set *context);
3572 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3573 __isl_take isl_pw_multi_aff *pma,
3574 __isl_take isl_set *set);
3575 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3576 __isl_take isl_pw_multi_aff *pma,
3577 __isl_take isl_set *set);
3578 __isl_give isl_set *isl_pw_multi_aff_domain(
3579 __isl_take isl_pw_multi_aff *pma);
3580 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3581 __isl_take isl_union_pw_multi_aff *upma);
3582 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3583 __isl_take isl_multi_aff *ma1,
3584 __isl_take isl_multi_aff *ma2);
3585 __isl_give isl_multi_aff *isl_multi_aff_product(
3586 __isl_take isl_multi_aff *ma1,
3587 __isl_take isl_multi_aff *ma2);
3588 __isl_give isl_pw_multi_aff *
3589 isl_pw_multi_aff_flat_range_product(
3590 __isl_take isl_pw_multi_aff *pma1,
3591 __isl_take isl_pw_multi_aff *pma2);
3592 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3593 __isl_take isl_pw_multi_aff *pma1,
3594 __isl_take isl_pw_multi_aff *pma2);
3595 __isl_give isl_union_pw_multi_aff *
3596 isl_union_pw_multi_aff_flat_range_product(
3597 __isl_take isl_union_pw_multi_aff *upma1,
3598 __isl_take isl_union_pw_multi_aff *upma2);
3600 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3601 then it is assigned the local space that lies at the basis of
3602 the lifting applied.
3604 __isl_give isl_set *isl_multi_aff_lex_le_set(
3605 __isl_take isl_multi_aff *ma1,
3606 __isl_take isl_multi_aff *ma2);
3607 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3608 __isl_take isl_multi_aff *ma1,
3609 __isl_take isl_multi_aff *ma2);
3611 The function C<isl_multi_aff_lex_le_set> returns a set
3612 containing those elements in the shared domain space
3613 where C<ma1> is lexicographically smaller than or
3616 An expression can be read from input using
3618 #include <isl/aff.h>
3619 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3620 isl_ctx *ctx, const char *str);
3621 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3622 isl_ctx *ctx, const char *str);
3624 An expression can be printed using
3626 #include <isl/aff.h>
3627 __isl_give isl_printer *isl_printer_print_multi_aff(
3628 __isl_take isl_printer *p,
3629 __isl_keep isl_multi_aff *maff);
3630 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3631 __isl_take isl_printer *p,
3632 __isl_keep isl_pw_multi_aff *pma);
3633 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3634 __isl_take isl_printer *p,
3635 __isl_keep isl_union_pw_multi_aff *upma);
3639 Points are elements of a set. They can be used to construct
3640 simple sets (boxes) or they can be used to represent the
3641 individual elements of a set.
3642 The zero point (the origin) can be created using
3644 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3646 The coordinates of a point can be inspected, set and changed
3649 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3650 enum isl_dim_type type, int pos, isl_int *v);
3651 __isl_give isl_point *isl_point_set_coordinate(
3652 __isl_take isl_point *pnt,
3653 enum isl_dim_type type, int pos, isl_int v);
3655 __isl_give isl_point *isl_point_add_ui(
3656 __isl_take isl_point *pnt,
3657 enum isl_dim_type type, int pos, unsigned val);
3658 __isl_give isl_point *isl_point_sub_ui(
3659 __isl_take isl_point *pnt,
3660 enum isl_dim_type type, int pos, unsigned val);
3662 Other properties can be obtained using
3664 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3666 Points can be copied or freed using
3668 __isl_give isl_point *isl_point_copy(
3669 __isl_keep isl_point *pnt);
3670 void isl_point_free(__isl_take isl_point *pnt);
3672 A singleton set can be created from a point using
3674 __isl_give isl_basic_set *isl_basic_set_from_point(
3675 __isl_take isl_point *pnt);
3676 __isl_give isl_set *isl_set_from_point(
3677 __isl_take isl_point *pnt);
3679 and a box can be created from two opposite extremal points using
3681 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3682 __isl_take isl_point *pnt1,
3683 __isl_take isl_point *pnt2);
3684 __isl_give isl_set *isl_set_box_from_points(
3685 __isl_take isl_point *pnt1,
3686 __isl_take isl_point *pnt2);
3688 All elements of a B<bounded> (union) set can be enumerated using
3689 the following functions.
3691 int isl_set_foreach_point(__isl_keep isl_set *set,
3692 int (*fn)(__isl_take isl_point *pnt, void *user),
3694 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3695 int (*fn)(__isl_take isl_point *pnt, void *user),
3698 The function C<fn> is called for each integer point in
3699 C<set> with as second argument the last argument of
3700 the C<isl_set_foreach_point> call. The function C<fn>
3701 should return C<0> on success and C<-1> on failure.
3702 In the latter case, C<isl_set_foreach_point> will stop
3703 enumerating and return C<-1> as well.
3704 If the enumeration is performed successfully and to completion,
3705 then C<isl_set_foreach_point> returns C<0>.
3707 To obtain a single point of a (basic) set, use
3709 __isl_give isl_point *isl_basic_set_sample_point(
3710 __isl_take isl_basic_set *bset);
3711 __isl_give isl_point *isl_set_sample_point(
3712 __isl_take isl_set *set);
3714 If C<set> does not contain any (integer) points, then the
3715 resulting point will be ``void'', a property that can be
3718 int isl_point_is_void(__isl_keep isl_point *pnt);
3720 =head2 Piecewise Quasipolynomials
3722 A piecewise quasipolynomial is a particular kind of function that maps
3723 a parametric point to a rational value.
3724 More specifically, a quasipolynomial is a polynomial expression in greatest
3725 integer parts of affine expressions of parameters and variables.
3726 A piecewise quasipolynomial is a subdivision of a given parametric
3727 domain into disjoint cells with a quasipolynomial associated to
3728 each cell. The value of the piecewise quasipolynomial at a given
3729 point is the value of the quasipolynomial associated to the cell
3730 that contains the point. Outside of the union of cells,
3731 the value is assumed to be zero.
3732 For example, the piecewise quasipolynomial
3734 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3736 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3737 A given piecewise quasipolynomial has a fixed domain dimension.
3738 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3739 defined over different domains.
3740 Piecewise quasipolynomials are mainly used by the C<barvinok>
3741 library for representing the number of elements in a parametric set or map.
3742 For example, the piecewise quasipolynomial above represents
3743 the number of points in the map
3745 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3747 =head3 Input and Output
3749 Piecewise quasipolynomials can be read from input using
3751 __isl_give isl_union_pw_qpolynomial *
3752 isl_union_pw_qpolynomial_read_from_str(
3753 isl_ctx *ctx, const char *str);
3755 Quasipolynomials and piecewise quasipolynomials can be printed
3756 using the following functions.
3758 __isl_give isl_printer *isl_printer_print_qpolynomial(
3759 __isl_take isl_printer *p,
3760 __isl_keep isl_qpolynomial *qp);
3762 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3763 __isl_take isl_printer *p,
3764 __isl_keep isl_pw_qpolynomial *pwqp);
3766 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3767 __isl_take isl_printer *p,
3768 __isl_keep isl_union_pw_qpolynomial *upwqp);
3770 The output format of the printer
3771 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3772 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3774 In case of printing in C<ISL_FORMAT_C>, the user may want
3775 to set the names of all dimensions
3777 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3778 __isl_take isl_qpolynomial *qp,
3779 enum isl_dim_type type, unsigned pos,
3781 __isl_give isl_pw_qpolynomial *
3782 isl_pw_qpolynomial_set_dim_name(
3783 __isl_take isl_pw_qpolynomial *pwqp,
3784 enum isl_dim_type type, unsigned pos,
3787 =head3 Creating New (Piecewise) Quasipolynomials
3789 Some simple quasipolynomials can be created using the following functions.
3790 More complicated quasipolynomials can be created by applying
3791 operations such as addition and multiplication
3792 on the resulting quasipolynomials
3794 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3795 __isl_take isl_space *domain);
3796 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3797 __isl_take isl_space *domain);
3798 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3799 __isl_take isl_space *domain);
3800 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3801 __isl_take isl_space *domain);
3802 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3803 __isl_take isl_space *domain);
3804 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3805 __isl_take isl_space *domain,
3806 const isl_int n, const isl_int d);
3807 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3808 __isl_take isl_space *domain,
3809 enum isl_dim_type type, unsigned pos);
3810 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3811 __isl_take isl_aff *aff);
3813 Note that the space in which a quasipolynomial lives is a map space
3814 with a one-dimensional range. The C<domain> argument in some of
3815 the functions above corresponds to the domain of this map space.
3817 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3818 with a single cell can be created using the following functions.
3819 Multiple of these single cell piecewise quasipolynomials can
3820 be combined to create more complicated piecewise quasipolynomials.
3822 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3823 __isl_take isl_space *space);
3824 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3825 __isl_take isl_set *set,
3826 __isl_take isl_qpolynomial *qp);
3827 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3828 __isl_take isl_qpolynomial *qp);
3829 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3830 __isl_take isl_pw_aff *pwaff);
3832 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3833 __isl_take isl_space *space);
3834 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3835 __isl_take isl_pw_qpolynomial *pwqp);
3836 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3837 __isl_take isl_union_pw_qpolynomial *upwqp,
3838 __isl_take isl_pw_qpolynomial *pwqp);
3840 Quasipolynomials can be copied and freed again using the following
3843 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3844 __isl_keep isl_qpolynomial *qp);
3845 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3847 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3848 __isl_keep isl_pw_qpolynomial *pwqp);
3849 void *isl_pw_qpolynomial_free(
3850 __isl_take isl_pw_qpolynomial *pwqp);
3852 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3853 __isl_keep isl_union_pw_qpolynomial *upwqp);
3854 void *isl_union_pw_qpolynomial_free(
3855 __isl_take isl_union_pw_qpolynomial *upwqp);
3857 =head3 Inspecting (Piecewise) Quasipolynomials
3859 To iterate over all piecewise quasipolynomials in a union
3860 piecewise quasipolynomial, use the following function
3862 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3863 __isl_keep isl_union_pw_qpolynomial *upwqp,
3864 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3867 To extract the piecewise quasipolynomial in a given space from a union, use
3869 __isl_give isl_pw_qpolynomial *
3870 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3871 __isl_keep isl_union_pw_qpolynomial *upwqp,
3872 __isl_take isl_space *space);
3874 To iterate over the cells in a piecewise quasipolynomial,
3875 use either of the following two functions
3877 int isl_pw_qpolynomial_foreach_piece(
3878 __isl_keep isl_pw_qpolynomial *pwqp,
3879 int (*fn)(__isl_take isl_set *set,
3880 __isl_take isl_qpolynomial *qp,
3881 void *user), void *user);
3882 int isl_pw_qpolynomial_foreach_lifted_piece(
3883 __isl_keep isl_pw_qpolynomial *pwqp,
3884 int (*fn)(__isl_take isl_set *set,
3885 __isl_take isl_qpolynomial *qp,
3886 void *user), void *user);
3888 As usual, the function C<fn> should return C<0> on success
3889 and C<-1> on failure. The difference between
3890 C<isl_pw_qpolynomial_foreach_piece> and
3891 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3892 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3893 compute unique representations for all existentially quantified
3894 variables and then turn these existentially quantified variables
3895 into extra set variables, adapting the associated quasipolynomial
3896 accordingly. This means that the C<set> passed to C<fn>
3897 will not have any existentially quantified variables, but that
3898 the dimensions of the sets may be different for different
3899 invocations of C<fn>.
3901 To iterate over all terms in a quasipolynomial,
3904 int isl_qpolynomial_foreach_term(
3905 __isl_keep isl_qpolynomial *qp,
3906 int (*fn)(__isl_take isl_term *term,
3907 void *user), void *user);
3909 The terms themselves can be inspected and freed using
3912 unsigned isl_term_dim(__isl_keep isl_term *term,
3913 enum isl_dim_type type);
3914 void isl_term_get_num(__isl_keep isl_term *term,
3916 void isl_term_get_den(__isl_keep isl_term *term,
3918 int isl_term_get_exp(__isl_keep isl_term *term,
3919 enum isl_dim_type type, unsigned pos);
3920 __isl_give isl_aff *isl_term_get_div(
3921 __isl_keep isl_term *term, unsigned pos);
3922 void isl_term_free(__isl_take isl_term *term);
3924 Each term is a product of parameters, set variables and
3925 integer divisions. The function C<isl_term_get_exp>
3926 returns the exponent of a given dimensions in the given term.
3927 The C<isl_int>s in the arguments of C<isl_term_get_num>
3928 and C<isl_term_get_den> need to have been initialized
3929 using C<isl_int_init> before calling these functions.
3931 =head3 Properties of (Piecewise) Quasipolynomials
3933 To check whether a quasipolynomial is actually a constant,
3934 use the following function.
3936 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3937 isl_int *n, isl_int *d);
3939 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3940 then the numerator and denominator of the constant
3941 are returned in C<*n> and C<*d>, respectively.
3943 To check whether two union piecewise quasipolynomials are
3944 obviously equal, use
3946 int isl_union_pw_qpolynomial_plain_is_equal(
3947 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3948 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3950 =head3 Operations on (Piecewise) Quasipolynomials
3952 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3953 __isl_take isl_qpolynomial *qp, isl_int v);
3954 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3955 __isl_take isl_qpolynomial *qp);
3956 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3957 __isl_take isl_qpolynomial *qp1,
3958 __isl_take isl_qpolynomial *qp2);
3959 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3960 __isl_take isl_qpolynomial *qp1,
3961 __isl_take isl_qpolynomial *qp2);
3962 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3963 __isl_take isl_qpolynomial *qp1,
3964 __isl_take isl_qpolynomial *qp2);
3965 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3966 __isl_take isl_qpolynomial *qp, unsigned exponent);
3968 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3969 __isl_take isl_pw_qpolynomial *pwqp1,
3970 __isl_take isl_pw_qpolynomial *pwqp2);
3971 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3972 __isl_take isl_pw_qpolynomial *pwqp1,
3973 __isl_take isl_pw_qpolynomial *pwqp2);
3974 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3975 __isl_take isl_pw_qpolynomial *pwqp1,
3976 __isl_take isl_pw_qpolynomial *pwqp2);
3977 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3978 __isl_take isl_pw_qpolynomial *pwqp);
3979 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3980 __isl_take isl_pw_qpolynomial *pwqp1,
3981 __isl_take isl_pw_qpolynomial *pwqp2);
3982 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3983 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3985 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3986 __isl_take isl_union_pw_qpolynomial *upwqp1,
3987 __isl_take isl_union_pw_qpolynomial *upwqp2);
3988 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3989 __isl_take isl_union_pw_qpolynomial *upwqp1,
3990 __isl_take isl_union_pw_qpolynomial *upwqp2);
3991 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3992 __isl_take isl_union_pw_qpolynomial *upwqp1,
3993 __isl_take isl_union_pw_qpolynomial *upwqp2);
3995 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3996 __isl_take isl_pw_qpolynomial *pwqp,
3997 __isl_take isl_point *pnt);
3999 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4000 __isl_take isl_union_pw_qpolynomial *upwqp,
4001 __isl_take isl_point *pnt);
4003 __isl_give isl_set *isl_pw_qpolynomial_domain(
4004 __isl_take isl_pw_qpolynomial *pwqp);
4005 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4006 __isl_take isl_pw_qpolynomial *pwpq,
4007 __isl_take isl_set *set);
4008 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4009 __isl_take isl_pw_qpolynomial *pwpq,
4010 __isl_take isl_set *set);
4012 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4013 __isl_take isl_union_pw_qpolynomial *upwqp);
4014 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4015 __isl_take isl_union_pw_qpolynomial *upwpq,
4016 __isl_take isl_union_set *uset);
4017 __isl_give isl_union_pw_qpolynomial *
4018 isl_union_pw_qpolynomial_intersect_params(
4019 __isl_take isl_union_pw_qpolynomial *upwpq,
4020 __isl_take isl_set *set);
4022 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4023 __isl_take isl_qpolynomial *qp,
4024 __isl_take isl_space *model);
4026 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4027 __isl_take isl_qpolynomial *qp);
4028 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4029 __isl_take isl_pw_qpolynomial *pwqp);
4031 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4032 __isl_take isl_union_pw_qpolynomial *upwqp);
4034 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4035 __isl_take isl_qpolynomial *qp,
4036 __isl_take isl_set *context);
4037 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4038 __isl_take isl_qpolynomial *qp,
4039 __isl_take isl_set *context);
4041 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4042 __isl_take isl_pw_qpolynomial *pwqp,
4043 __isl_take isl_set *context);
4044 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4045 __isl_take isl_pw_qpolynomial *pwqp,
4046 __isl_take isl_set *context);
4048 __isl_give isl_union_pw_qpolynomial *
4049 isl_union_pw_qpolynomial_gist_params(
4050 __isl_take isl_union_pw_qpolynomial *upwqp,
4051 __isl_take isl_set *context);
4052 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4053 __isl_take isl_union_pw_qpolynomial *upwqp,
4054 __isl_take isl_union_set *context);
4056 The gist operation applies the gist operation to each of
4057 the cells in the domain of the input piecewise quasipolynomial.
4058 The context is also exploited
4059 to simplify the quasipolynomials associated to each cell.
4061 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4062 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4063 __isl_give isl_union_pw_qpolynomial *
4064 isl_union_pw_qpolynomial_to_polynomial(
4065 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4067 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4068 the polynomial will be an overapproximation. If C<sign> is negative,
4069 it will be an underapproximation. If C<sign> is zero, the approximation
4070 will lie somewhere in between.
4072 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4074 A piecewise quasipolynomial reduction is a piecewise
4075 reduction (or fold) of quasipolynomials.
4076 In particular, the reduction can be maximum or a minimum.
4077 The objects are mainly used to represent the result of
4078 an upper or lower bound on a quasipolynomial over its domain,
4079 i.e., as the result of the following function.
4081 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4082 __isl_take isl_pw_qpolynomial *pwqp,
4083 enum isl_fold type, int *tight);
4085 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4086 __isl_take isl_union_pw_qpolynomial *upwqp,
4087 enum isl_fold type, int *tight);
4089 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4090 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4091 is the returned bound is known be tight, i.e., for each value
4092 of the parameters there is at least
4093 one element in the domain that reaches the bound.
4094 If the domain of C<pwqp> is not wrapping, then the bound is computed
4095 over all elements in that domain and the result has a purely parametric
4096 domain. If the domain of C<pwqp> is wrapping, then the bound is
4097 computed over the range of the wrapped relation. The domain of the
4098 wrapped relation becomes the domain of the result.
4100 A (piecewise) quasipolynomial reduction can be copied or freed using the
4101 following functions.
4103 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4104 __isl_keep isl_qpolynomial_fold *fold);
4105 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4106 __isl_keep isl_pw_qpolynomial_fold *pwf);
4107 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4108 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4109 void isl_qpolynomial_fold_free(
4110 __isl_take isl_qpolynomial_fold *fold);
4111 void *isl_pw_qpolynomial_fold_free(
4112 __isl_take isl_pw_qpolynomial_fold *pwf);
4113 void *isl_union_pw_qpolynomial_fold_free(
4114 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4116 =head3 Printing Piecewise Quasipolynomial Reductions
4118 Piecewise quasipolynomial reductions can be printed
4119 using the following function.
4121 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4122 __isl_take isl_printer *p,
4123 __isl_keep isl_pw_qpolynomial_fold *pwf);
4124 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4125 __isl_take isl_printer *p,
4126 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4128 For C<isl_printer_print_pw_qpolynomial_fold>,
4129 output format of the printer
4130 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4131 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4132 output format of the printer
4133 needs to be set to C<ISL_FORMAT_ISL>.
4134 In case of printing in C<ISL_FORMAT_C>, the user may want
4135 to set the names of all dimensions
4137 __isl_give isl_pw_qpolynomial_fold *
4138 isl_pw_qpolynomial_fold_set_dim_name(
4139 __isl_take isl_pw_qpolynomial_fold *pwf,
4140 enum isl_dim_type type, unsigned pos,
4143 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4145 To iterate over all piecewise quasipolynomial reductions in a union
4146 piecewise quasipolynomial reduction, use the following function
4148 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4149 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4150 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4151 void *user), void *user);
4153 To iterate over the cells in a piecewise quasipolynomial reduction,
4154 use either of the following two functions
4156 int isl_pw_qpolynomial_fold_foreach_piece(
4157 __isl_keep isl_pw_qpolynomial_fold *pwf,
4158 int (*fn)(__isl_take isl_set *set,
4159 __isl_take isl_qpolynomial_fold *fold,
4160 void *user), void *user);
4161 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4162 __isl_keep isl_pw_qpolynomial_fold *pwf,
4163 int (*fn)(__isl_take isl_set *set,
4164 __isl_take isl_qpolynomial_fold *fold,
4165 void *user), void *user);
4167 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4168 of the difference between these two functions.
4170 To iterate over all quasipolynomials in a reduction, use
4172 int isl_qpolynomial_fold_foreach_qpolynomial(
4173 __isl_keep isl_qpolynomial_fold *fold,
4174 int (*fn)(__isl_take isl_qpolynomial *qp,
4175 void *user), void *user);
4177 =head3 Properties of Piecewise Quasipolynomial Reductions
4179 To check whether two union piecewise quasipolynomial reductions are
4180 obviously equal, use
4182 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4183 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4184 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4186 =head3 Operations on Piecewise Quasipolynomial Reductions
4188 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4189 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4191 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4192 __isl_take isl_pw_qpolynomial_fold *pwf1,
4193 __isl_take isl_pw_qpolynomial_fold *pwf2);
4195 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4196 __isl_take isl_pw_qpolynomial_fold *pwf1,
4197 __isl_take isl_pw_qpolynomial_fold *pwf2);
4199 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4200 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4201 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4203 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4204 __isl_take isl_pw_qpolynomial_fold *pwf,
4205 __isl_take isl_point *pnt);
4207 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4208 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4209 __isl_take isl_point *pnt);
4211 __isl_give isl_pw_qpolynomial_fold *
4212 isl_pw_qpolynomial_fold_intersect_params(
4213 __isl_take isl_pw_qpolynomial_fold *pwf,
4214 __isl_take isl_set *set);
4216 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4217 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4218 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4219 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4220 __isl_take isl_union_set *uset);
4221 __isl_give isl_union_pw_qpolynomial_fold *
4222 isl_union_pw_qpolynomial_fold_intersect_params(
4223 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4224 __isl_take isl_set *set);
4226 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4227 __isl_take isl_pw_qpolynomial_fold *pwf);
4229 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4230 __isl_take isl_pw_qpolynomial_fold *pwf);
4232 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4233 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4235 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4236 __isl_take isl_qpolynomial_fold *fold,
4237 __isl_take isl_set *context);
4238 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4239 __isl_take isl_qpolynomial_fold *fold,
4240 __isl_take isl_set *context);
4242 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4243 __isl_take isl_pw_qpolynomial_fold *pwf,
4244 __isl_take isl_set *context);
4245 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4246 __isl_take isl_pw_qpolynomial_fold *pwf,
4247 __isl_take isl_set *context);
4249 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4250 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4251 __isl_take isl_union_set *context);
4252 __isl_give isl_union_pw_qpolynomial_fold *
4253 isl_union_pw_qpolynomial_fold_gist_params(
4254 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4255 __isl_take isl_set *context);
4257 The gist operation applies the gist operation to each of
4258 the cells in the domain of the input piecewise quasipolynomial reduction.
4259 In future, the operation will also exploit the context
4260 to simplify the quasipolynomial reductions associated to each cell.
4262 __isl_give isl_pw_qpolynomial_fold *
4263 isl_set_apply_pw_qpolynomial_fold(
4264 __isl_take isl_set *set,
4265 __isl_take isl_pw_qpolynomial_fold *pwf,
4267 __isl_give isl_pw_qpolynomial_fold *
4268 isl_map_apply_pw_qpolynomial_fold(
4269 __isl_take isl_map *map,
4270 __isl_take isl_pw_qpolynomial_fold *pwf,
4272 __isl_give isl_union_pw_qpolynomial_fold *
4273 isl_union_set_apply_union_pw_qpolynomial_fold(
4274 __isl_take isl_union_set *uset,
4275 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4277 __isl_give isl_union_pw_qpolynomial_fold *
4278 isl_union_map_apply_union_pw_qpolynomial_fold(
4279 __isl_take isl_union_map *umap,
4280 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4283 The functions taking a map
4284 compose the given map with the given piecewise quasipolynomial reduction.
4285 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4286 over all elements in the intersection of the range of the map
4287 and the domain of the piecewise quasipolynomial reduction
4288 as a function of an element in the domain of the map.
4289 The functions taking a set compute a bound over all elements in the
4290 intersection of the set and the domain of the
4291 piecewise quasipolynomial reduction.
4293 =head2 Dependence Analysis
4295 C<isl> contains specialized functionality for performing
4296 array dataflow analysis. That is, given a I<sink> access relation
4297 and a collection of possible I<source> access relations,
4298 C<isl> can compute relations that describe
4299 for each iteration of the sink access, which iteration
4300 of which of the source access relations was the last
4301 to access the same data element before the given iteration
4303 The resulting dependence relations map source iterations
4304 to the corresponding sink iterations.
4305 To compute standard flow dependences, the sink should be
4306 a read, while the sources should be writes.
4307 If any of the source accesses are marked as being I<may>
4308 accesses, then there will be a dependence from the last
4309 I<must> access B<and> from any I<may> access that follows
4310 this last I<must> access.
4311 In particular, if I<all> sources are I<may> accesses,
4312 then memory based dependence analysis is performed.
4313 If, on the other hand, all sources are I<must> accesses,
4314 then value based dependence analysis is performed.
4316 #include <isl/flow.h>
4318 typedef int (*isl_access_level_before)(void *first, void *second);
4320 __isl_give isl_access_info *isl_access_info_alloc(
4321 __isl_take isl_map *sink,
4322 void *sink_user, isl_access_level_before fn,
4324 __isl_give isl_access_info *isl_access_info_add_source(
4325 __isl_take isl_access_info *acc,
4326 __isl_take isl_map *source, int must,
4328 void *isl_access_info_free(__isl_take isl_access_info *acc);
4330 __isl_give isl_flow *isl_access_info_compute_flow(
4331 __isl_take isl_access_info *acc);
4333 int isl_flow_foreach(__isl_keep isl_flow *deps,
4334 int (*fn)(__isl_take isl_map *dep, int must,
4335 void *dep_user, void *user),
4337 __isl_give isl_map *isl_flow_get_no_source(
4338 __isl_keep isl_flow *deps, int must);
4339 void isl_flow_free(__isl_take isl_flow *deps);
4341 The function C<isl_access_info_compute_flow> performs the actual
4342 dependence analysis. The other functions are used to construct
4343 the input for this function or to read off the output.
4345 The input is collected in an C<isl_access_info>, which can
4346 be created through a call to C<isl_access_info_alloc>.
4347 The arguments to this functions are the sink access relation
4348 C<sink>, a token C<sink_user> used to identify the sink
4349 access to the user, a callback function for specifying the
4350 relative order of source and sink accesses, and the number
4351 of source access relations that will be added.
4352 The callback function has type C<int (*)(void *first, void *second)>.
4353 The function is called with two user supplied tokens identifying
4354 either a source or the sink and it should return the shared nesting
4355 level and the relative order of the two accesses.
4356 In particular, let I<n> be the number of loops shared by
4357 the two accesses. If C<first> precedes C<second> textually,
4358 then the function should return I<2 * n + 1>; otherwise,
4359 it should return I<2 * n>.
4360 The sources can be added to the C<isl_access_info> by performing
4361 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4362 C<must> indicates whether the source is a I<must> access
4363 or a I<may> access. Note that a multi-valued access relation
4364 should only be marked I<must> if every iteration in the domain
4365 of the relation accesses I<all> elements in its image.
4366 The C<source_user> token is again used to identify
4367 the source access. The range of the source access relation
4368 C<source> should have the same dimension as the range
4369 of the sink access relation.
4370 The C<isl_access_info_free> function should usually not be
4371 called explicitly, because it is called implicitly by
4372 C<isl_access_info_compute_flow>.
4374 The result of the dependence analysis is collected in an
4375 C<isl_flow>. There may be elements of
4376 the sink access for which no preceding source access could be
4377 found or for which all preceding sources are I<may> accesses.
4378 The relations containing these elements can be obtained through
4379 calls to C<isl_flow_get_no_source>, the first with C<must> set
4380 and the second with C<must> unset.
4381 In the case of standard flow dependence analysis,
4382 with the sink a read and the sources I<must> writes,
4383 the first relation corresponds to the reads from uninitialized
4384 array elements and the second relation is empty.
4385 The actual flow dependences can be extracted using
4386 C<isl_flow_foreach>. This function will call the user-specified
4387 callback function C<fn> for each B<non-empty> dependence between
4388 a source and the sink. The callback function is called
4389 with four arguments, the actual flow dependence relation
4390 mapping source iterations to sink iterations, a boolean that
4391 indicates whether it is a I<must> or I<may> dependence, a token
4392 identifying the source and an additional C<void *> with value
4393 equal to the third argument of the C<isl_flow_foreach> call.
4394 A dependence is marked I<must> if it originates from a I<must>
4395 source and if it is not followed by any I<may> sources.
4397 After finishing with an C<isl_flow>, the user should call
4398 C<isl_flow_free> to free all associated memory.
4400 A higher-level interface to dependence analysis is provided
4401 by the following function.
4403 #include <isl/flow.h>
4405 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4406 __isl_take isl_union_map *must_source,
4407 __isl_take isl_union_map *may_source,
4408 __isl_take isl_union_map *schedule,
4409 __isl_give isl_union_map **must_dep,
4410 __isl_give isl_union_map **may_dep,
4411 __isl_give isl_union_map **must_no_source,
4412 __isl_give isl_union_map **may_no_source);
4414 The arrays are identified by the tuple names of the ranges
4415 of the accesses. The iteration domains by the tuple names
4416 of the domains of the accesses and of the schedule.
4417 The relative order of the iteration domains is given by the
4418 schedule. The relations returned through C<must_no_source>
4419 and C<may_no_source> are subsets of C<sink>.
4420 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4421 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4422 any of the other arguments is treated as an error.
4424 =head3 Interaction with Dependence Analysis
4426 During the dependence analysis, we frequently need to perform
4427 the following operation. Given a relation between sink iterations
4428 and potential source iterations from a particular source domain,
4429 what is the last potential source iteration corresponding to each
4430 sink iteration. It can sometimes be convenient to adjust
4431 the set of potential source iterations before or after each such operation.
4432 The prototypical example is fuzzy array dataflow analysis,
4433 where we need to analyze if, based on data-dependent constraints,
4434 the sink iteration can ever be executed without one or more of
4435 the corresponding potential source iterations being executed.
4436 If so, we can introduce extra parameters and select an unknown
4437 but fixed source iteration from the potential source iterations.
4438 To be able to perform such manipulations, C<isl> provides the following
4441 #include <isl/flow.h>
4443 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4444 __isl_keep isl_map *source_map,
4445 __isl_keep isl_set *sink, void *source_user,
4447 __isl_give isl_access_info *isl_access_info_set_restrict(
4448 __isl_take isl_access_info *acc,
4449 isl_access_restrict fn, void *user);
4451 The function C<isl_access_info_set_restrict> should be called
4452 before calling C<isl_access_info_compute_flow> and registers a callback function
4453 that will be called any time C<isl> is about to compute the last
4454 potential source. The first argument is the (reverse) proto-dependence,
4455 mapping sink iterations to potential source iterations.
4456 The second argument represents the sink iterations for which
4457 we want to compute the last source iteration.
4458 The third argument is the token corresponding to the source
4459 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4460 The callback is expected to return a restriction on either the input or
4461 the output of the operation computing the last potential source.
4462 If the input needs to be restricted then restrictions are needed
4463 for both the source and the sink iterations. The sink iterations
4464 and the potential source iterations will be intersected with these sets.
4465 If the output needs to be restricted then only a restriction on the source
4466 iterations is required.
4467 If any error occurs, the callback should return C<NULL>.
4468 An C<isl_restriction> object can be created, freed and inspected
4469 using the following functions.
4471 #include <isl/flow.h>
4473 __isl_give isl_restriction *isl_restriction_input(
4474 __isl_take isl_set *source_restr,
4475 __isl_take isl_set *sink_restr);
4476 __isl_give isl_restriction *isl_restriction_output(
4477 __isl_take isl_set *source_restr);
4478 __isl_give isl_restriction *isl_restriction_none(
4479 __isl_take isl_map *source_map);
4480 __isl_give isl_restriction *isl_restriction_empty(
4481 __isl_take isl_map *source_map);
4482 void *isl_restriction_free(
4483 __isl_take isl_restriction *restr);
4484 isl_ctx *isl_restriction_get_ctx(
4485 __isl_keep isl_restriction *restr);
4487 C<isl_restriction_none> and C<isl_restriction_empty> are special
4488 cases of C<isl_restriction_input>. C<isl_restriction_none>
4489 is essentially equivalent to
4491 isl_restriction_input(isl_set_universe(
4492 isl_space_range(isl_map_get_space(source_map))),
4494 isl_space_domain(isl_map_get_space(source_map))));
4496 whereas C<isl_restriction_empty> is essentially equivalent to
4498 isl_restriction_input(isl_set_empty(
4499 isl_space_range(isl_map_get_space(source_map))),
4501 isl_space_domain(isl_map_get_space(source_map))));
4505 B<The functionality described in this section is fairly new
4506 and may be subject to change.>
4508 The following function can be used to compute a schedule
4509 for a union of domains.
4510 By default, the algorithm used to construct the schedule is similar
4511 to that of C<Pluto>.
4512 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4514 The generated schedule respects all C<validity> dependences.
4515 That is, all dependence distances over these dependences in the
4516 scheduled space are lexicographically positive.
4517 The default algorithm tries to minimize the dependence distances over
4518 C<proximity> dependences.
4519 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4520 for groups of domains where the dependence distances have only
4521 non-negative values.
4522 When using Feautrier's algorithm, the C<proximity> dependence
4523 distances are only minimized during the extension to a
4524 full-dimensional schedule.
4526 #include <isl/schedule.h>
4527 __isl_give isl_schedule *isl_union_set_compute_schedule(
4528 __isl_take isl_union_set *domain,
4529 __isl_take isl_union_map *validity,
4530 __isl_take isl_union_map *proximity);
4531 void *isl_schedule_free(__isl_take isl_schedule *sched);
4533 A mapping from the domains to the scheduled space can be obtained
4534 from an C<isl_schedule> using the following function.
4536 __isl_give isl_union_map *isl_schedule_get_map(
4537 __isl_keep isl_schedule *sched);
4539 A representation of the schedule can be printed using
4541 __isl_give isl_printer *isl_printer_print_schedule(
4542 __isl_take isl_printer *p,
4543 __isl_keep isl_schedule *schedule);
4545 A representation of the schedule as a forest of bands can be obtained
4546 using the following function.
4548 __isl_give isl_band_list *isl_schedule_get_band_forest(
4549 __isl_keep isl_schedule *schedule);
4551 The individual bands can be visited in depth-first post-order
4552 using the following function.
4554 #include <isl/schedule.h>
4555 int isl_schedule_foreach_band(
4556 __isl_keep isl_schedule *sched,
4557 int (*fn)(__isl_keep isl_band *band, void *user),
4560 The list can be manipulated as explained in L<"Lists">.
4561 The bands inside the list can be copied and freed using the following
4564 #include <isl/band.h>
4565 __isl_give isl_band *isl_band_copy(
4566 __isl_keep isl_band *band);
4567 void *isl_band_free(__isl_take isl_band *band);
4569 Each band contains zero or more scheduling dimensions.
4570 These are referred to as the members of the band.
4571 The section of the schedule that corresponds to the band is
4572 referred to as the partial schedule of the band.
4573 For those nodes that participate in a band, the outer scheduling
4574 dimensions form the prefix schedule, while the inner scheduling
4575 dimensions form the suffix schedule.
4576 That is, if we take a cut of the band forest, then the union of
4577 the concatenations of the prefix, partial and suffix schedules of
4578 each band in the cut is equal to the entire schedule (modulo
4579 some possible padding at the end with zero scheduling dimensions).
4580 The properties of a band can be inspected using the following functions.
4582 #include <isl/band.h>
4583 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4585 int isl_band_has_children(__isl_keep isl_band *band);
4586 __isl_give isl_band_list *isl_band_get_children(
4587 __isl_keep isl_band *band);
4589 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4590 __isl_keep isl_band *band);
4591 __isl_give isl_union_map *isl_band_get_partial_schedule(
4592 __isl_keep isl_band *band);
4593 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4594 __isl_keep isl_band *band);
4596 int isl_band_n_member(__isl_keep isl_band *band);
4597 int isl_band_member_is_zero_distance(
4598 __isl_keep isl_band *band, int pos);
4600 int isl_band_list_foreach_band(
4601 __isl_keep isl_band_list *list,
4602 int (*fn)(__isl_keep isl_band *band, void *user),
4605 Note that a scheduling dimension is considered to be ``zero
4606 distance'' if it does not carry any proximity dependences
4608 That is, if the dependence distances of the proximity
4609 dependences are all zero in that direction (for fixed
4610 iterations of outer bands).
4611 Like C<isl_schedule_foreach_band>,
4612 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4613 in depth-first post-order.
4615 A band can be tiled using the following function.
4617 #include <isl/band.h>
4618 int isl_band_tile(__isl_keep isl_band *band,
4619 __isl_take isl_vec *sizes);
4621 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4623 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4625 The C<isl_band_tile> function tiles the band using the given tile sizes
4626 inside its schedule.
4627 A new child band is created to represent the point loops and it is
4628 inserted between the modified band and its children.
4629 The C<tile_scale_tile_loops> option specifies whether the tile
4630 loops iterators should be scaled by the tile sizes.
4632 A representation of the band can be printed using
4634 #include <isl/band.h>
4635 __isl_give isl_printer *isl_printer_print_band(
4636 __isl_take isl_printer *p,
4637 __isl_keep isl_band *band);
4641 #include <isl/schedule.h>
4642 int isl_options_set_schedule_max_coefficient(
4643 isl_ctx *ctx, int val);
4644 int isl_options_get_schedule_max_coefficient(
4646 int isl_options_set_schedule_max_constant_term(
4647 isl_ctx *ctx, int val);
4648 int isl_options_get_schedule_max_constant_term(
4650 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4651 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4652 int isl_options_set_schedule_maximize_band_depth(
4653 isl_ctx *ctx, int val);
4654 int isl_options_get_schedule_maximize_band_depth(
4656 int isl_options_set_schedule_outer_zero_distance(
4657 isl_ctx *ctx, int val);
4658 int isl_options_get_schedule_outer_zero_distance(
4660 int isl_options_set_schedule_split_scaled(
4661 isl_ctx *ctx, int val);
4662 int isl_options_get_schedule_split_scaled(
4664 int isl_options_set_schedule_algorithm(
4665 isl_ctx *ctx, int val);
4666 int isl_options_get_schedule_algorithm(
4668 int isl_options_set_schedule_separate_components(
4669 isl_ctx *ctx, int val);
4670 int isl_options_get_schedule_separate_components(
4675 =item * schedule_max_coefficient
4677 This option enforces that the coefficients for variable and parameter
4678 dimensions in the calculated schedule are not larger than the specified value.
4679 This option can significantly increase the speed of the scheduling calculation
4680 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4681 this option does not introduce bounds on the variable or parameter
4684 =item * schedule_max_constant_term
4686 This option enforces that the constant coefficients in the calculated schedule
4687 are not larger than the maximal constant term. This option can significantly
4688 increase the speed of the scheduling calculation and may also prevent fusing of
4689 unrelated dimensions. A value of -1 means that this option does not introduce
4690 bounds on the constant coefficients.
4692 =item * schedule_fuse
4694 This option controls the level of fusion.
4695 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
4696 resulting schedule will be distributed as much as possible.
4697 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
4698 try to fuse loops in the resulting schedule.
4700 =item * schedule_maximize_band_depth
4702 If this option is set, we do not split bands at the point
4703 where we detect splitting is necessary. Instead, we
4704 backtrack and split bands as early as possible. This
4705 reduces the number of splits and maximizes the width of
4706 the bands. Wider bands give more possibilities for tiling.
4707 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
4708 then bands will be split as early as possible, even if there is no need.
4709 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
4711 =item * schedule_outer_zero_distance
4713 If this option is set, then we try to construct schedules
4714 where the outermost scheduling dimension in each band
4715 results in a zero dependence distance over the proximity
4718 =item * schedule_split_scaled
4720 If this option is set, then we try to construct schedules in which the
4721 constant term is split off from the linear part if the linear parts of
4722 the scheduling rows for all nodes in the graphs have a common non-trivial
4724 The constant term is then placed in a separate band and the linear
4727 =item * schedule_algorithm
4729 Selects the scheduling algorithm to be used.
4730 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4731 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4733 =item * schedule_separate_components
4735 If at any point the dependence graph contains any (weakly connected) components,
4736 then these components are scheduled separately.
4737 If this option is not set, then some iterations of the domains
4738 in these components may be scheduled together.
4739 If this option is set, then the components are given consecutive
4744 =head2 Parametric Vertex Enumeration
4746 The parametric vertex enumeration described in this section
4747 is mainly intended to be used internally and by the C<barvinok>
4750 #include <isl/vertices.h>
4751 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4752 __isl_keep isl_basic_set *bset);
4754 The function C<isl_basic_set_compute_vertices> performs the
4755 actual computation of the parametric vertices and the chamber
4756 decomposition and store the result in an C<isl_vertices> object.
4757 This information can be queried by either iterating over all
4758 the vertices or iterating over all the chambers or cells
4759 and then iterating over all vertices that are active on the chamber.
4761 int isl_vertices_foreach_vertex(
4762 __isl_keep isl_vertices *vertices,
4763 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4766 int isl_vertices_foreach_cell(
4767 __isl_keep isl_vertices *vertices,
4768 int (*fn)(__isl_take isl_cell *cell, void *user),
4770 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4771 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4774 Other operations that can be performed on an C<isl_vertices> object are
4777 isl_ctx *isl_vertices_get_ctx(
4778 __isl_keep isl_vertices *vertices);
4779 int isl_vertices_get_n_vertices(
4780 __isl_keep isl_vertices *vertices);
4781 void isl_vertices_free(__isl_take isl_vertices *vertices);
4783 Vertices can be inspected and destroyed using the following functions.
4785 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4786 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4787 __isl_give isl_basic_set *isl_vertex_get_domain(
4788 __isl_keep isl_vertex *vertex);
4789 __isl_give isl_basic_set *isl_vertex_get_expr(
4790 __isl_keep isl_vertex *vertex);
4791 void isl_vertex_free(__isl_take isl_vertex *vertex);
4793 C<isl_vertex_get_expr> returns a singleton parametric set describing
4794 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4796 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4797 B<rational> basic sets, so they should mainly be used for inspection
4798 and should not be mixed with integer sets.
4800 Chambers can be inspected and destroyed using the following functions.
4802 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4803 __isl_give isl_basic_set *isl_cell_get_domain(
4804 __isl_keep isl_cell *cell);
4805 void isl_cell_free(__isl_take isl_cell *cell);
4809 Although C<isl> is mainly meant to be used as a library,
4810 it also contains some basic applications that use some
4811 of the functionality of C<isl>.
4812 The input may be specified in either the L<isl format>
4813 or the L<PolyLib format>.
4815 =head2 C<isl_polyhedron_sample>
4817 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4818 an integer element of the polyhedron, if there is any.
4819 The first column in the output is the denominator and is always
4820 equal to 1. If the polyhedron contains no integer points,
4821 then a vector of length zero is printed.
4825 C<isl_pip> takes the same input as the C<example> program
4826 from the C<piplib> distribution, i.e., a set of constraints
4827 on the parameters, a line containing only -1 and finally a set
4828 of constraints on a parametric polyhedron.
4829 The coefficients of the parameters appear in the last columns
4830 (but before the final constant column).
4831 The output is the lexicographic minimum of the parametric polyhedron.
4832 As C<isl> currently does not have its own output format, the output
4833 is just a dump of the internal state.
4835 =head2 C<isl_polyhedron_minimize>
4837 C<isl_polyhedron_minimize> computes the minimum of some linear
4838 or affine objective function over the integer points in a polyhedron.
4839 If an affine objective function
4840 is given, then the constant should appear in the last column.
4842 =head2 C<isl_polytope_scan>
4844 Given a polytope, C<isl_polytope_scan> prints
4845 all integer points in the polytope.