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);
1421 To iterate over all the sets or maps in a union set or map, use
1423 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1424 int (*fn)(__isl_take isl_set *set, void *user),
1426 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1427 int (*fn)(__isl_take isl_map *map, void *user),
1430 The number of sets or maps in a union set or map can be obtained
1433 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1434 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1436 To extract the set or map in a given space from a union, use
1438 __isl_give isl_set *isl_union_set_extract_set(
1439 __isl_keep isl_union_set *uset,
1440 __isl_take isl_space *space);
1441 __isl_give isl_map *isl_union_map_extract_map(
1442 __isl_keep isl_union_map *umap,
1443 __isl_take isl_space *space);
1445 To iterate over all the basic sets or maps in a set or map, use
1447 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1448 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1450 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1451 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1454 The callback function C<fn> should return 0 if successful and
1455 -1 if an error occurs. In the latter case, or if any other error
1456 occurs, the above functions will return -1.
1458 It should be noted that C<isl> does not guarantee that
1459 the basic sets or maps passed to C<fn> are disjoint.
1460 If this is required, then the user should call one of
1461 the following functions first.
1463 __isl_give isl_set *isl_set_make_disjoint(
1464 __isl_take isl_set *set);
1465 __isl_give isl_map *isl_map_make_disjoint(
1466 __isl_take isl_map *map);
1468 The number of basic sets in a set can be obtained
1471 int isl_set_n_basic_set(__isl_keep isl_set *set);
1473 To iterate over the constraints of a basic set or map, use
1475 #include <isl/constraint.h>
1477 int isl_basic_set_n_constraint(
1478 __isl_keep isl_basic_set *bset);
1479 int isl_basic_set_foreach_constraint(
1480 __isl_keep isl_basic_set *bset,
1481 int (*fn)(__isl_take isl_constraint *c, void *user),
1483 int isl_basic_map_foreach_constraint(
1484 __isl_keep isl_basic_map *bmap,
1485 int (*fn)(__isl_take isl_constraint *c, void *user),
1487 void *isl_constraint_free(__isl_take isl_constraint *c);
1489 Again, the callback function C<fn> should return 0 if successful and
1490 -1 if an error occurs. In the latter case, or if any other error
1491 occurs, the above functions will return -1.
1492 The constraint C<c> represents either an equality or an inequality.
1493 Use the following function to find out whether a constraint
1494 represents an equality. If not, it represents an inequality.
1496 int isl_constraint_is_equality(
1497 __isl_keep isl_constraint *constraint);
1499 The coefficients of the constraints can be inspected using
1500 the following functions.
1502 int isl_constraint_is_lower_bound(
1503 __isl_keep isl_constraint *constraint,
1504 enum isl_dim_type type, unsigned pos);
1505 int isl_constraint_is_upper_bound(
1506 __isl_keep isl_constraint *constraint,
1507 enum isl_dim_type type, unsigned pos);
1508 void isl_constraint_get_constant(
1509 __isl_keep isl_constraint *constraint, isl_int *v);
1510 void isl_constraint_get_coefficient(
1511 __isl_keep isl_constraint *constraint,
1512 enum isl_dim_type type, int pos, isl_int *v);
1513 int isl_constraint_involves_dims(
1514 __isl_keep isl_constraint *constraint,
1515 enum isl_dim_type type, unsigned first, unsigned n);
1517 The explicit representations of the existentially quantified
1518 variables can be inspected using the following function.
1519 Note that the user is only allowed to use this function
1520 if the inspected set or map is the result of a call
1521 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1522 The existentially quantified variable is equal to the floor
1523 of the returned affine expression. The affine expression
1524 itself can be inspected using the functions in
1525 L<"Piecewise Quasi Affine Expressions">.
1527 __isl_give isl_aff *isl_constraint_get_div(
1528 __isl_keep isl_constraint *constraint, int pos);
1530 To obtain the constraints of a basic set or map in matrix
1531 form, use the following functions.
1533 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1534 __isl_keep isl_basic_set *bset,
1535 enum isl_dim_type c1, enum isl_dim_type c2,
1536 enum isl_dim_type c3, enum isl_dim_type c4);
1537 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1538 __isl_keep isl_basic_set *bset,
1539 enum isl_dim_type c1, enum isl_dim_type c2,
1540 enum isl_dim_type c3, enum isl_dim_type c4);
1541 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1542 __isl_keep isl_basic_map *bmap,
1543 enum isl_dim_type c1,
1544 enum isl_dim_type c2, enum isl_dim_type c3,
1545 enum isl_dim_type c4, enum isl_dim_type c5);
1546 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1547 __isl_keep isl_basic_map *bmap,
1548 enum isl_dim_type c1,
1549 enum isl_dim_type c2, enum isl_dim_type c3,
1550 enum isl_dim_type c4, enum isl_dim_type c5);
1552 The C<isl_dim_type> arguments dictate the order in which
1553 different kinds of variables appear in the resulting matrix
1554 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1555 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1557 The number of parameters, input, output or set dimensions can
1558 be obtained using the following functions.
1560 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1561 enum isl_dim_type type);
1562 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1563 enum isl_dim_type type);
1564 unsigned isl_set_dim(__isl_keep isl_set *set,
1565 enum isl_dim_type type);
1566 unsigned isl_map_dim(__isl_keep isl_map *map,
1567 enum isl_dim_type type);
1569 To check whether the description of a set or relation depends
1570 on one or more given dimensions, it is not necessary to iterate over all
1571 constraints. Instead the following functions can be used.
1573 int isl_basic_set_involves_dims(
1574 __isl_keep isl_basic_set *bset,
1575 enum isl_dim_type type, unsigned first, unsigned n);
1576 int isl_set_involves_dims(__isl_keep isl_set *set,
1577 enum isl_dim_type type, unsigned first, unsigned n);
1578 int isl_basic_map_involves_dims(
1579 __isl_keep isl_basic_map *bmap,
1580 enum isl_dim_type type, unsigned first, unsigned n);
1581 int isl_map_involves_dims(__isl_keep isl_map *map,
1582 enum isl_dim_type type, unsigned first, unsigned n);
1584 Similarly, the following functions can be used to check whether
1585 a given dimension is involved in any lower or upper bound.
1587 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1588 enum isl_dim_type type, unsigned pos);
1589 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1590 enum isl_dim_type type, unsigned pos);
1592 The identifiers or names of the domain and range spaces of a set
1593 or relation can be read off or set using the following functions.
1595 __isl_give isl_set *isl_set_set_tuple_id(
1596 __isl_take isl_set *set, __isl_take isl_id *id);
1597 __isl_give isl_set *isl_set_reset_tuple_id(
1598 __isl_take isl_set *set);
1599 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1600 __isl_give isl_id *isl_set_get_tuple_id(
1601 __isl_keep isl_set *set);
1602 __isl_give isl_map *isl_map_set_tuple_id(
1603 __isl_take isl_map *map, enum isl_dim_type type,
1604 __isl_take isl_id *id);
1605 __isl_give isl_map *isl_map_reset_tuple_id(
1606 __isl_take isl_map *map, enum isl_dim_type type);
1607 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1608 enum isl_dim_type type);
1609 __isl_give isl_id *isl_map_get_tuple_id(
1610 __isl_keep isl_map *map, enum isl_dim_type type);
1612 const char *isl_basic_set_get_tuple_name(
1613 __isl_keep isl_basic_set *bset);
1614 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1615 __isl_take isl_basic_set *set, const char *s);
1616 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1617 const char *isl_set_get_tuple_name(
1618 __isl_keep isl_set *set);
1619 const char *isl_basic_map_get_tuple_name(
1620 __isl_keep isl_basic_map *bmap,
1621 enum isl_dim_type type);
1622 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1623 __isl_take isl_basic_map *bmap,
1624 enum isl_dim_type type, const char *s);
1625 const char *isl_map_get_tuple_name(
1626 __isl_keep isl_map *map,
1627 enum isl_dim_type type);
1629 As with C<isl_space_get_tuple_name>, the value returned points to
1630 an internal data structure.
1631 The identifiers, positions or names of individual dimensions can be
1632 read off using the following functions.
1634 __isl_give isl_id *isl_basic_set_get_dim_id(
1635 __isl_keep isl_basic_set *bset,
1636 enum isl_dim_type type, unsigned pos);
1637 __isl_give isl_set *isl_set_set_dim_id(
1638 __isl_take isl_set *set, enum isl_dim_type type,
1639 unsigned pos, __isl_take isl_id *id);
1640 int isl_set_has_dim_id(__isl_keep isl_set *set,
1641 enum isl_dim_type type, unsigned pos);
1642 __isl_give isl_id *isl_set_get_dim_id(
1643 __isl_keep isl_set *set, enum isl_dim_type type,
1645 int isl_basic_map_has_dim_id(
1646 __isl_keep isl_basic_map *bmap,
1647 enum isl_dim_type type, unsigned pos);
1648 __isl_give isl_map *isl_map_set_dim_id(
1649 __isl_take isl_map *map, enum isl_dim_type type,
1650 unsigned pos, __isl_take isl_id *id);
1651 int isl_map_has_dim_id(__isl_keep isl_map *map,
1652 enum isl_dim_type type, unsigned pos);
1653 __isl_give isl_id *isl_map_get_dim_id(
1654 __isl_keep isl_map *map, enum isl_dim_type type,
1657 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1658 enum isl_dim_type type, __isl_keep isl_id *id);
1659 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1660 enum isl_dim_type type, __isl_keep isl_id *id);
1661 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1662 enum isl_dim_type type, const char *name);
1663 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1664 enum isl_dim_type type, const char *name);
1666 const char *isl_constraint_get_dim_name(
1667 __isl_keep isl_constraint *constraint,
1668 enum isl_dim_type type, unsigned pos);
1669 const char *isl_basic_set_get_dim_name(
1670 __isl_keep isl_basic_set *bset,
1671 enum isl_dim_type type, unsigned pos);
1672 int isl_set_has_dim_name(__isl_keep isl_set *set,
1673 enum isl_dim_type type, unsigned pos);
1674 const char *isl_set_get_dim_name(
1675 __isl_keep isl_set *set,
1676 enum isl_dim_type type, unsigned pos);
1677 const char *isl_basic_map_get_dim_name(
1678 __isl_keep isl_basic_map *bmap,
1679 enum isl_dim_type type, unsigned pos);
1680 int isl_map_has_dim_name(__isl_keep isl_map *map,
1681 enum isl_dim_type type, unsigned pos);
1682 const char *isl_map_get_dim_name(
1683 __isl_keep isl_map *map,
1684 enum isl_dim_type type, unsigned pos);
1686 These functions are mostly useful to obtain the identifiers, positions
1687 or names of the parameters. Identifiers of individual dimensions are
1688 essentially only useful for printing. They are ignored by all other
1689 operations and may not be preserved across those operations.
1693 =head3 Unary Properties
1699 The following functions test whether the given set or relation
1700 contains any integer points. The ``plain'' variants do not perform
1701 any computations, but simply check if the given set or relation
1702 is already known to be empty.
1704 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1705 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1706 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1707 int isl_set_is_empty(__isl_keep isl_set *set);
1708 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1709 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1710 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1711 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1712 int isl_map_is_empty(__isl_keep isl_map *map);
1713 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1715 =item * Universality
1717 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1718 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1719 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1721 =item * Single-valuedness
1723 int isl_basic_map_is_single_valued(
1724 __isl_keep isl_basic_map *bmap);
1725 int isl_map_plain_is_single_valued(
1726 __isl_keep isl_map *map);
1727 int isl_map_is_single_valued(__isl_keep isl_map *map);
1728 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1732 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1733 int isl_map_is_injective(__isl_keep isl_map *map);
1734 int isl_union_map_plain_is_injective(
1735 __isl_keep isl_union_map *umap);
1736 int isl_union_map_is_injective(
1737 __isl_keep isl_union_map *umap);
1741 int isl_map_is_bijective(__isl_keep isl_map *map);
1742 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1746 int isl_basic_map_plain_is_fixed(
1747 __isl_keep isl_basic_map *bmap,
1748 enum isl_dim_type type, unsigned pos,
1750 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1751 enum isl_dim_type type, unsigned pos,
1753 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1754 enum isl_dim_type type, unsigned pos,
1757 Check if the relation obviously lies on a hyperplane where the given dimension
1758 has a fixed value and if so, return that value in C<*val>.
1762 To check whether a set is a parameter domain, use this function:
1764 int isl_set_is_params(__isl_keep isl_set *set);
1765 int isl_union_set_is_params(
1766 __isl_keep isl_union_set *uset);
1770 The following functions check whether the domain of the given
1771 (basic) set is a wrapped relation.
1773 int isl_basic_set_is_wrapping(
1774 __isl_keep isl_basic_set *bset);
1775 int isl_set_is_wrapping(__isl_keep isl_set *set);
1777 =item * Internal Product
1779 int isl_basic_map_can_zip(
1780 __isl_keep isl_basic_map *bmap);
1781 int isl_map_can_zip(__isl_keep isl_map *map);
1783 Check whether the product of domain and range of the given relation
1785 i.e., whether both domain and range are nested relations.
1789 int isl_basic_map_can_curry(
1790 __isl_keep isl_basic_map *bmap);
1791 int isl_map_can_curry(__isl_keep isl_map *map);
1793 Check whether the domain of the (basic) relation is a wrapped relation.
1797 =head3 Binary Properties
1803 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1804 __isl_keep isl_set *set2);
1805 int isl_set_is_equal(__isl_keep isl_set *set1,
1806 __isl_keep isl_set *set2);
1807 int isl_union_set_is_equal(
1808 __isl_keep isl_union_set *uset1,
1809 __isl_keep isl_union_set *uset2);
1810 int isl_basic_map_is_equal(
1811 __isl_keep isl_basic_map *bmap1,
1812 __isl_keep isl_basic_map *bmap2);
1813 int isl_map_is_equal(__isl_keep isl_map *map1,
1814 __isl_keep isl_map *map2);
1815 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1816 __isl_keep isl_map *map2);
1817 int isl_union_map_is_equal(
1818 __isl_keep isl_union_map *umap1,
1819 __isl_keep isl_union_map *umap2);
1821 =item * Disjointness
1823 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1824 __isl_keep isl_set *set2);
1828 int isl_basic_set_is_subset(
1829 __isl_keep isl_basic_set *bset1,
1830 __isl_keep isl_basic_set *bset2);
1831 int isl_set_is_subset(__isl_keep isl_set *set1,
1832 __isl_keep isl_set *set2);
1833 int isl_set_is_strict_subset(
1834 __isl_keep isl_set *set1,
1835 __isl_keep isl_set *set2);
1836 int isl_union_set_is_subset(
1837 __isl_keep isl_union_set *uset1,
1838 __isl_keep isl_union_set *uset2);
1839 int isl_union_set_is_strict_subset(
1840 __isl_keep isl_union_set *uset1,
1841 __isl_keep isl_union_set *uset2);
1842 int isl_basic_map_is_subset(
1843 __isl_keep isl_basic_map *bmap1,
1844 __isl_keep isl_basic_map *bmap2);
1845 int isl_basic_map_is_strict_subset(
1846 __isl_keep isl_basic_map *bmap1,
1847 __isl_keep isl_basic_map *bmap2);
1848 int isl_map_is_subset(
1849 __isl_keep isl_map *map1,
1850 __isl_keep isl_map *map2);
1851 int isl_map_is_strict_subset(
1852 __isl_keep isl_map *map1,
1853 __isl_keep isl_map *map2);
1854 int isl_union_map_is_subset(
1855 __isl_keep isl_union_map *umap1,
1856 __isl_keep isl_union_map *umap2);
1857 int isl_union_map_is_strict_subset(
1858 __isl_keep isl_union_map *umap1,
1859 __isl_keep isl_union_map *umap2);
1861 Check whether the first argument is a (strict) subset of the
1866 =head2 Unary Operations
1872 __isl_give isl_set *isl_set_complement(
1873 __isl_take isl_set *set);
1874 __isl_give isl_map *isl_map_complement(
1875 __isl_take isl_map *map);
1879 __isl_give isl_basic_map *isl_basic_map_reverse(
1880 __isl_take isl_basic_map *bmap);
1881 __isl_give isl_map *isl_map_reverse(
1882 __isl_take isl_map *map);
1883 __isl_give isl_union_map *isl_union_map_reverse(
1884 __isl_take isl_union_map *umap);
1888 __isl_give isl_basic_set *isl_basic_set_project_out(
1889 __isl_take isl_basic_set *bset,
1890 enum isl_dim_type type, unsigned first, unsigned n);
1891 __isl_give isl_basic_map *isl_basic_map_project_out(
1892 __isl_take isl_basic_map *bmap,
1893 enum isl_dim_type type, unsigned first, unsigned n);
1894 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1895 enum isl_dim_type type, unsigned first, unsigned n);
1896 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1897 enum isl_dim_type type, unsigned first, unsigned n);
1898 __isl_give isl_basic_set *isl_basic_set_params(
1899 __isl_take isl_basic_set *bset);
1900 __isl_give isl_basic_set *isl_basic_map_domain(
1901 __isl_take isl_basic_map *bmap);
1902 __isl_give isl_basic_set *isl_basic_map_range(
1903 __isl_take isl_basic_map *bmap);
1904 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1905 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1906 __isl_give isl_set *isl_map_domain(
1907 __isl_take isl_map *bmap);
1908 __isl_give isl_set *isl_map_range(
1909 __isl_take isl_map *map);
1910 __isl_give isl_set *isl_union_set_params(
1911 __isl_take isl_union_set *uset);
1912 __isl_give isl_set *isl_union_map_params(
1913 __isl_take isl_union_map *umap);
1914 __isl_give isl_union_set *isl_union_map_domain(
1915 __isl_take isl_union_map *umap);
1916 __isl_give isl_union_set *isl_union_map_range(
1917 __isl_take isl_union_map *umap);
1919 __isl_give isl_basic_map *isl_basic_map_domain_map(
1920 __isl_take isl_basic_map *bmap);
1921 __isl_give isl_basic_map *isl_basic_map_range_map(
1922 __isl_take isl_basic_map *bmap);
1923 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1924 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1925 __isl_give isl_union_map *isl_union_map_domain_map(
1926 __isl_take isl_union_map *umap);
1927 __isl_give isl_union_map *isl_union_map_range_map(
1928 __isl_take isl_union_map *umap);
1930 The functions above construct a (basic, regular or union) relation
1931 that maps (a wrapped version of) the input relation to its domain or range.
1935 __isl_give isl_basic_set *isl_basic_set_eliminate(
1936 __isl_take isl_basic_set *bset,
1937 enum isl_dim_type type,
1938 unsigned first, unsigned n);
1939 __isl_give isl_set *isl_set_eliminate(
1940 __isl_take isl_set *set, enum isl_dim_type type,
1941 unsigned first, unsigned n);
1942 __isl_give isl_basic_map *isl_basic_map_eliminate(
1943 __isl_take isl_basic_map *bmap,
1944 enum isl_dim_type type,
1945 unsigned first, unsigned n);
1946 __isl_give isl_map *isl_map_eliminate(
1947 __isl_take isl_map *map, enum isl_dim_type type,
1948 unsigned first, unsigned n);
1950 Eliminate the coefficients for the given dimensions from the constraints,
1951 without removing the dimensions.
1955 __isl_give isl_basic_set *isl_basic_set_fix(
1956 __isl_take isl_basic_set *bset,
1957 enum isl_dim_type type, unsigned pos,
1959 __isl_give isl_basic_set *isl_basic_set_fix_si(
1960 __isl_take isl_basic_set *bset,
1961 enum isl_dim_type type, unsigned pos, int value);
1962 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1963 enum isl_dim_type type, unsigned pos,
1965 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1966 enum isl_dim_type type, unsigned pos, int value);
1967 __isl_give isl_basic_map *isl_basic_map_fix_si(
1968 __isl_take isl_basic_map *bmap,
1969 enum isl_dim_type type, unsigned pos, int value);
1970 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1971 enum isl_dim_type type, unsigned pos, int value);
1973 Intersect the set or relation with the hyperplane where the given
1974 dimension has the fixed given value.
1976 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1977 __isl_take isl_basic_map *bmap,
1978 enum isl_dim_type type, unsigned pos, int value);
1979 __isl_give isl_set *isl_set_lower_bound(
1980 __isl_take isl_set *set,
1981 enum isl_dim_type type, unsigned pos,
1983 __isl_give isl_set *isl_set_lower_bound_si(
1984 __isl_take isl_set *set,
1985 enum isl_dim_type type, unsigned pos, int value);
1986 __isl_give isl_map *isl_map_lower_bound_si(
1987 __isl_take isl_map *map,
1988 enum isl_dim_type type, unsigned pos, int value);
1989 __isl_give isl_set *isl_set_upper_bound(
1990 __isl_take isl_set *set,
1991 enum isl_dim_type type, unsigned pos,
1993 __isl_give isl_set *isl_set_upper_bound_si(
1994 __isl_take isl_set *set,
1995 enum isl_dim_type type, unsigned pos, int value);
1996 __isl_give isl_map *isl_map_upper_bound_si(
1997 __isl_take isl_map *map,
1998 enum isl_dim_type type, unsigned pos, int value);
2000 Intersect the set or relation with the half-space where the given
2001 dimension has a value bounded by the fixed given value.
2003 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2004 enum isl_dim_type type1, int pos1,
2005 enum isl_dim_type type2, int pos2);
2006 __isl_give isl_basic_map *isl_basic_map_equate(
2007 __isl_take isl_basic_map *bmap,
2008 enum isl_dim_type type1, int pos1,
2009 enum isl_dim_type type2, int pos2);
2010 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2011 enum isl_dim_type type1, int pos1,
2012 enum isl_dim_type type2, int pos2);
2014 Intersect the set or relation with the hyperplane where the given
2015 dimensions are equal to each other.
2017 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2018 enum isl_dim_type type1, int pos1,
2019 enum isl_dim_type type2, int pos2);
2021 Intersect the relation with the hyperplane where the given
2022 dimensions have opposite values.
2024 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2025 enum isl_dim_type type1, int pos1,
2026 enum isl_dim_type type2, int pos2);
2027 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2028 enum isl_dim_type type1, int pos1,
2029 enum isl_dim_type type2, int pos2);
2031 Intersect the relation with the half-space where the given
2032 dimensions satisfy the given ordering.
2036 __isl_give isl_map *isl_set_identity(
2037 __isl_take isl_set *set);
2038 __isl_give isl_union_map *isl_union_set_identity(
2039 __isl_take isl_union_set *uset);
2041 Construct an identity relation on the given (union) set.
2045 __isl_give isl_basic_set *isl_basic_map_deltas(
2046 __isl_take isl_basic_map *bmap);
2047 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2048 __isl_give isl_union_set *isl_union_map_deltas(
2049 __isl_take isl_union_map *umap);
2051 These functions return a (basic) set containing the differences
2052 between image elements and corresponding domain elements in the input.
2054 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2055 __isl_take isl_basic_map *bmap);
2056 __isl_give isl_map *isl_map_deltas_map(
2057 __isl_take isl_map *map);
2058 __isl_give isl_union_map *isl_union_map_deltas_map(
2059 __isl_take isl_union_map *umap);
2061 The functions above construct a (basic, regular or union) relation
2062 that maps (a wrapped version of) the input relation to its delta set.
2066 Simplify the representation of a set or relation by trying
2067 to combine pairs of basic sets or relations into a single
2068 basic set or relation.
2070 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2071 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2072 __isl_give isl_union_set *isl_union_set_coalesce(
2073 __isl_take isl_union_set *uset);
2074 __isl_give isl_union_map *isl_union_map_coalesce(
2075 __isl_take isl_union_map *umap);
2077 One of the methods for combining pairs of basic sets or relations
2078 can result in coefficients that are much larger than those that appear
2079 in the constraints of the input. By default, the coefficients are
2080 not allowed to grow larger, but this can be changed by unsetting
2081 the following option.
2083 int isl_options_set_coalesce_bounded_wrapping(
2084 isl_ctx *ctx, int val);
2085 int isl_options_get_coalesce_bounded_wrapping(
2088 =item * Detecting equalities
2090 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2091 __isl_take isl_basic_set *bset);
2092 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2093 __isl_take isl_basic_map *bmap);
2094 __isl_give isl_set *isl_set_detect_equalities(
2095 __isl_take isl_set *set);
2096 __isl_give isl_map *isl_map_detect_equalities(
2097 __isl_take isl_map *map);
2098 __isl_give isl_union_set *isl_union_set_detect_equalities(
2099 __isl_take isl_union_set *uset);
2100 __isl_give isl_union_map *isl_union_map_detect_equalities(
2101 __isl_take isl_union_map *umap);
2103 Simplify the representation of a set or relation by detecting implicit
2106 =item * Removing redundant constraints
2108 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2109 __isl_take isl_basic_set *bset);
2110 __isl_give isl_set *isl_set_remove_redundancies(
2111 __isl_take isl_set *set);
2112 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2113 __isl_take isl_basic_map *bmap);
2114 __isl_give isl_map *isl_map_remove_redundancies(
2115 __isl_take isl_map *map);
2119 __isl_give isl_basic_set *isl_set_convex_hull(
2120 __isl_take isl_set *set);
2121 __isl_give isl_basic_map *isl_map_convex_hull(
2122 __isl_take isl_map *map);
2124 If the input set or relation has any existentially quantified
2125 variables, then the result of these operations is currently undefined.
2129 __isl_give isl_basic_set *isl_set_simple_hull(
2130 __isl_take isl_set *set);
2131 __isl_give isl_basic_map *isl_map_simple_hull(
2132 __isl_take isl_map *map);
2133 __isl_give isl_union_map *isl_union_map_simple_hull(
2134 __isl_take isl_union_map *umap);
2136 These functions compute a single basic set or relation
2137 that contains the whole input set or relation.
2138 In particular, the output is described by translates
2139 of the constraints describing the basic sets or relations in the input.
2143 (See \autoref{s:simple hull}.)
2149 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2150 __isl_take isl_basic_set *bset);
2151 __isl_give isl_basic_set *isl_set_affine_hull(
2152 __isl_take isl_set *set);
2153 __isl_give isl_union_set *isl_union_set_affine_hull(
2154 __isl_take isl_union_set *uset);
2155 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2156 __isl_take isl_basic_map *bmap);
2157 __isl_give isl_basic_map *isl_map_affine_hull(
2158 __isl_take isl_map *map);
2159 __isl_give isl_union_map *isl_union_map_affine_hull(
2160 __isl_take isl_union_map *umap);
2162 In case of union sets and relations, the affine hull is computed
2165 =item * Polyhedral hull
2167 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2168 __isl_take isl_set *set);
2169 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2170 __isl_take isl_map *map);
2171 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2172 __isl_take isl_union_set *uset);
2173 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2174 __isl_take isl_union_map *umap);
2176 These functions compute a single basic set or relation
2177 not involving any existentially quantified variables
2178 that contains the whole input set or relation.
2179 In case of union sets and relations, the polyhedral hull is computed
2184 __isl_give isl_basic_set *isl_basic_set_sample(
2185 __isl_take isl_basic_set *bset);
2186 __isl_give isl_basic_set *isl_set_sample(
2187 __isl_take isl_set *set);
2188 __isl_give isl_basic_map *isl_basic_map_sample(
2189 __isl_take isl_basic_map *bmap);
2190 __isl_give isl_basic_map *isl_map_sample(
2191 __isl_take isl_map *map);
2193 If the input (basic) set or relation is non-empty, then return
2194 a singleton subset of the input. Otherwise, return an empty set.
2196 =item * Optimization
2198 #include <isl/ilp.h>
2199 enum isl_lp_result isl_basic_set_max(
2200 __isl_keep isl_basic_set *bset,
2201 __isl_keep isl_aff *obj, isl_int *opt)
2202 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2203 __isl_keep isl_aff *obj, isl_int *opt);
2204 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2205 __isl_keep isl_aff *obj, isl_int *opt);
2207 Compute the minimum or maximum of the integer affine expression C<obj>
2208 over the points in C<set>, returning the result in C<opt>.
2209 The return value may be one of C<isl_lp_error>,
2210 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2212 =item * Parametric optimization
2214 __isl_give isl_pw_aff *isl_set_dim_min(
2215 __isl_take isl_set *set, int pos);
2216 __isl_give isl_pw_aff *isl_set_dim_max(
2217 __isl_take isl_set *set, int pos);
2218 __isl_give isl_pw_aff *isl_map_dim_max(
2219 __isl_take isl_map *map, int pos);
2221 Compute the minimum or maximum of the given set or output dimension
2222 as a function of the parameters (and input dimensions), but independently
2223 of the other set or output dimensions.
2224 For lexicographic optimization, see L<"Lexicographic Optimization">.
2228 The following functions compute either the set of (rational) coefficient
2229 values of valid constraints for the given set or the set of (rational)
2230 values satisfying the constraints with coefficients from the given set.
2231 Internally, these two sets of functions perform essentially the
2232 same operations, except that the set of coefficients is assumed to
2233 be a cone, while the set of values may be any polyhedron.
2234 The current implementation is based on the Farkas lemma and
2235 Fourier-Motzkin elimination, but this may change or be made optional
2236 in future. In particular, future implementations may use different
2237 dualization algorithms or skip the elimination step.
2239 __isl_give isl_basic_set *isl_basic_set_coefficients(
2240 __isl_take isl_basic_set *bset);
2241 __isl_give isl_basic_set *isl_set_coefficients(
2242 __isl_take isl_set *set);
2243 __isl_give isl_union_set *isl_union_set_coefficients(
2244 __isl_take isl_union_set *bset);
2245 __isl_give isl_basic_set *isl_basic_set_solutions(
2246 __isl_take isl_basic_set *bset);
2247 __isl_give isl_basic_set *isl_set_solutions(
2248 __isl_take isl_set *set);
2249 __isl_give isl_union_set *isl_union_set_solutions(
2250 __isl_take isl_union_set *bset);
2254 __isl_give isl_map *isl_map_fixed_power(
2255 __isl_take isl_map *map, isl_int exp);
2256 __isl_give isl_union_map *isl_union_map_fixed_power(
2257 __isl_take isl_union_map *umap, isl_int exp);
2259 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2260 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2261 of C<map> is computed.
2263 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2265 __isl_give isl_union_map *isl_union_map_power(
2266 __isl_take isl_union_map *umap, int *exact);
2268 Compute a parametric representation for all positive powers I<k> of C<map>.
2269 The result maps I<k> to a nested relation corresponding to the
2270 I<k>th power of C<map>.
2271 The result may be an overapproximation. If the result is known to be exact,
2272 then C<*exact> is set to C<1>.
2274 =item * Transitive closure
2276 __isl_give isl_map *isl_map_transitive_closure(
2277 __isl_take isl_map *map, int *exact);
2278 __isl_give isl_union_map *isl_union_map_transitive_closure(
2279 __isl_take isl_union_map *umap, int *exact);
2281 Compute the transitive closure of C<map>.
2282 The result may be an overapproximation. If the result is known to be exact,
2283 then C<*exact> is set to C<1>.
2285 =item * Reaching path lengths
2287 __isl_give isl_map *isl_map_reaching_path_lengths(
2288 __isl_take isl_map *map, int *exact);
2290 Compute a relation that maps each element in the range of C<map>
2291 to the lengths of all paths composed of edges in C<map> that
2292 end up in the given element.
2293 The result may be an overapproximation. If the result is known to be exact,
2294 then C<*exact> is set to C<1>.
2295 To compute the I<maximal> path length, the resulting relation
2296 should be postprocessed by C<isl_map_lexmax>.
2297 In particular, if the input relation is a dependence relation
2298 (mapping sources to sinks), then the maximal path length corresponds
2299 to the free schedule.
2300 Note, however, that C<isl_map_lexmax> expects the maximum to be
2301 finite, so if the path lengths are unbounded (possibly due to
2302 the overapproximation), then you will get an error message.
2306 __isl_give isl_basic_set *isl_basic_map_wrap(
2307 __isl_take isl_basic_map *bmap);
2308 __isl_give isl_set *isl_map_wrap(
2309 __isl_take isl_map *map);
2310 __isl_give isl_union_set *isl_union_map_wrap(
2311 __isl_take isl_union_map *umap);
2312 __isl_give isl_basic_map *isl_basic_set_unwrap(
2313 __isl_take isl_basic_set *bset);
2314 __isl_give isl_map *isl_set_unwrap(
2315 __isl_take isl_set *set);
2316 __isl_give isl_union_map *isl_union_set_unwrap(
2317 __isl_take isl_union_set *uset);
2321 Remove any internal structure of domain (and range) of the given
2322 set or relation. If there is any such internal structure in the input,
2323 then the name of the space is also removed.
2325 __isl_give isl_basic_set *isl_basic_set_flatten(
2326 __isl_take isl_basic_set *bset);
2327 __isl_give isl_set *isl_set_flatten(
2328 __isl_take isl_set *set);
2329 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2330 __isl_take isl_basic_map *bmap);
2331 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2332 __isl_take isl_basic_map *bmap);
2333 __isl_give isl_map *isl_map_flatten_range(
2334 __isl_take isl_map *map);
2335 __isl_give isl_map *isl_map_flatten_domain(
2336 __isl_take isl_map *map);
2337 __isl_give isl_basic_map *isl_basic_map_flatten(
2338 __isl_take isl_basic_map *bmap);
2339 __isl_give isl_map *isl_map_flatten(
2340 __isl_take isl_map *map);
2342 __isl_give isl_map *isl_set_flatten_map(
2343 __isl_take isl_set *set);
2345 The function above constructs a relation
2346 that maps the input set to a flattened version of the set.
2350 Lift the input set to a space with extra dimensions corresponding
2351 to the existentially quantified variables in the input.
2352 In particular, the result lives in a wrapped map where the domain
2353 is the original space and the range corresponds to the original
2354 existentially quantified variables.
2356 __isl_give isl_basic_set *isl_basic_set_lift(
2357 __isl_take isl_basic_set *bset);
2358 __isl_give isl_set *isl_set_lift(
2359 __isl_take isl_set *set);
2360 __isl_give isl_union_set *isl_union_set_lift(
2361 __isl_take isl_union_set *uset);
2363 Given a local space that contains the existentially quantified
2364 variables of a set, a basic relation that, when applied to
2365 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2366 can be constructed using the following function.
2368 #include <isl/local_space.h>
2369 __isl_give isl_basic_map *isl_local_space_lifting(
2370 __isl_take isl_local_space *ls);
2372 =item * Internal Product
2374 __isl_give isl_basic_map *isl_basic_map_zip(
2375 __isl_take isl_basic_map *bmap);
2376 __isl_give isl_map *isl_map_zip(
2377 __isl_take isl_map *map);
2378 __isl_give isl_union_map *isl_union_map_zip(
2379 __isl_take isl_union_map *umap);
2381 Given a relation with nested relations for domain and range,
2382 interchange the range of the domain with the domain of the range.
2386 __isl_give isl_basic_map *isl_basic_map_curry(
2387 __isl_take isl_basic_map *bmap);
2388 __isl_give isl_map *isl_map_curry(
2389 __isl_take isl_map *map);
2390 __isl_give isl_union_map *isl_union_map_curry(
2391 __isl_take isl_union_map *umap);
2393 Given a relation with a nested relation for domain,
2394 move the range of the nested relation out of the domain
2395 and use it as the domain of a nested relation in the range,
2396 with the original range as range of this nested relation.
2398 =item * Aligning parameters
2400 __isl_give isl_basic_set *isl_basic_set_align_params(
2401 __isl_take isl_basic_set *bset,
2402 __isl_take isl_space *model);
2403 __isl_give isl_set *isl_set_align_params(
2404 __isl_take isl_set *set,
2405 __isl_take isl_space *model);
2406 __isl_give isl_basic_map *isl_basic_map_align_params(
2407 __isl_take isl_basic_map *bmap,
2408 __isl_take isl_space *model);
2409 __isl_give isl_map *isl_map_align_params(
2410 __isl_take isl_map *map,
2411 __isl_take isl_space *model);
2413 Change the order of the parameters of the given set or relation
2414 such that the first parameters match those of C<model>.
2415 This may involve the introduction of extra parameters.
2416 All parameters need to be named.
2418 =item * Dimension manipulation
2420 __isl_give isl_set *isl_set_add_dims(
2421 __isl_take isl_set *set,
2422 enum isl_dim_type type, unsigned n);
2423 __isl_give isl_map *isl_map_add_dims(
2424 __isl_take isl_map *map,
2425 enum isl_dim_type type, unsigned n);
2426 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2427 __isl_take isl_basic_set *bset,
2428 enum isl_dim_type type, unsigned pos,
2430 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2431 __isl_take isl_basic_map *bmap,
2432 enum isl_dim_type type, unsigned pos,
2434 __isl_give isl_set *isl_set_insert_dims(
2435 __isl_take isl_set *set,
2436 enum isl_dim_type type, unsigned pos, unsigned n);
2437 __isl_give isl_map *isl_map_insert_dims(
2438 __isl_take isl_map *map,
2439 enum isl_dim_type type, unsigned pos, unsigned n);
2440 __isl_give isl_basic_set *isl_basic_set_move_dims(
2441 __isl_take isl_basic_set *bset,
2442 enum isl_dim_type dst_type, unsigned dst_pos,
2443 enum isl_dim_type src_type, unsigned src_pos,
2445 __isl_give isl_basic_map *isl_basic_map_move_dims(
2446 __isl_take isl_basic_map *bmap,
2447 enum isl_dim_type dst_type, unsigned dst_pos,
2448 enum isl_dim_type src_type, unsigned src_pos,
2450 __isl_give isl_set *isl_set_move_dims(
2451 __isl_take isl_set *set,
2452 enum isl_dim_type dst_type, unsigned dst_pos,
2453 enum isl_dim_type src_type, unsigned src_pos,
2455 __isl_give isl_map *isl_map_move_dims(
2456 __isl_take isl_map *map,
2457 enum isl_dim_type dst_type, unsigned dst_pos,
2458 enum isl_dim_type src_type, unsigned src_pos,
2461 It is usually not advisable to directly change the (input or output)
2462 space of a set or a relation as this removes the name and the internal
2463 structure of the space. However, the above functions can be useful
2464 to add new parameters, assuming
2465 C<isl_set_align_params> and C<isl_map_align_params>
2470 =head2 Binary Operations
2472 The two arguments of a binary operation not only need to live
2473 in the same C<isl_ctx>, they currently also need to have
2474 the same (number of) parameters.
2476 =head3 Basic Operations
2480 =item * Intersection
2482 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2483 __isl_take isl_basic_set *bset1,
2484 __isl_take isl_basic_set *bset2);
2485 __isl_give isl_basic_set *isl_basic_set_intersect(
2486 __isl_take isl_basic_set *bset1,
2487 __isl_take isl_basic_set *bset2);
2488 __isl_give isl_set *isl_set_intersect_params(
2489 __isl_take isl_set *set,
2490 __isl_take isl_set *params);
2491 __isl_give isl_set *isl_set_intersect(
2492 __isl_take isl_set *set1,
2493 __isl_take isl_set *set2);
2494 __isl_give isl_union_set *isl_union_set_intersect_params(
2495 __isl_take isl_union_set *uset,
2496 __isl_take isl_set *set);
2497 __isl_give isl_union_map *isl_union_map_intersect_params(
2498 __isl_take isl_union_map *umap,
2499 __isl_take isl_set *set);
2500 __isl_give isl_union_set *isl_union_set_intersect(
2501 __isl_take isl_union_set *uset1,
2502 __isl_take isl_union_set *uset2);
2503 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2504 __isl_take isl_basic_map *bmap,
2505 __isl_take isl_basic_set *bset);
2506 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2507 __isl_take isl_basic_map *bmap,
2508 __isl_take isl_basic_set *bset);
2509 __isl_give isl_basic_map *isl_basic_map_intersect(
2510 __isl_take isl_basic_map *bmap1,
2511 __isl_take isl_basic_map *bmap2);
2512 __isl_give isl_map *isl_map_intersect_params(
2513 __isl_take isl_map *map,
2514 __isl_take isl_set *params);
2515 __isl_give isl_map *isl_map_intersect_domain(
2516 __isl_take isl_map *map,
2517 __isl_take isl_set *set);
2518 __isl_give isl_map *isl_map_intersect_range(
2519 __isl_take isl_map *map,
2520 __isl_take isl_set *set);
2521 __isl_give isl_map *isl_map_intersect(
2522 __isl_take isl_map *map1,
2523 __isl_take isl_map *map2);
2524 __isl_give isl_union_map *isl_union_map_intersect_domain(
2525 __isl_take isl_union_map *umap,
2526 __isl_take isl_union_set *uset);
2527 __isl_give isl_union_map *isl_union_map_intersect_range(
2528 __isl_take isl_union_map *umap,
2529 __isl_take isl_union_set *uset);
2530 __isl_give isl_union_map *isl_union_map_intersect(
2531 __isl_take isl_union_map *umap1,
2532 __isl_take isl_union_map *umap2);
2534 The second argument to the C<_params> functions needs to be
2535 a parametric (basic) set. For the other functions, a parametric set
2536 for either argument is only allowed if the other argument is
2537 a parametric set as well.
2541 __isl_give isl_set *isl_basic_set_union(
2542 __isl_take isl_basic_set *bset1,
2543 __isl_take isl_basic_set *bset2);
2544 __isl_give isl_map *isl_basic_map_union(
2545 __isl_take isl_basic_map *bmap1,
2546 __isl_take isl_basic_map *bmap2);
2547 __isl_give isl_set *isl_set_union(
2548 __isl_take isl_set *set1,
2549 __isl_take isl_set *set2);
2550 __isl_give isl_map *isl_map_union(
2551 __isl_take isl_map *map1,
2552 __isl_take isl_map *map2);
2553 __isl_give isl_union_set *isl_union_set_union(
2554 __isl_take isl_union_set *uset1,
2555 __isl_take isl_union_set *uset2);
2556 __isl_give isl_union_map *isl_union_map_union(
2557 __isl_take isl_union_map *umap1,
2558 __isl_take isl_union_map *umap2);
2560 =item * Set difference
2562 __isl_give isl_set *isl_set_subtract(
2563 __isl_take isl_set *set1,
2564 __isl_take isl_set *set2);
2565 __isl_give isl_map *isl_map_subtract(
2566 __isl_take isl_map *map1,
2567 __isl_take isl_map *map2);
2568 __isl_give isl_map *isl_map_subtract_domain(
2569 __isl_take isl_map *map,
2570 __isl_take isl_set *dom);
2571 __isl_give isl_map *isl_map_subtract_range(
2572 __isl_take isl_map *map,
2573 __isl_take isl_set *dom);
2574 __isl_give isl_union_set *isl_union_set_subtract(
2575 __isl_take isl_union_set *uset1,
2576 __isl_take isl_union_set *uset2);
2577 __isl_give isl_union_map *isl_union_map_subtract(
2578 __isl_take isl_union_map *umap1,
2579 __isl_take isl_union_map *umap2);
2583 __isl_give isl_basic_set *isl_basic_set_apply(
2584 __isl_take isl_basic_set *bset,
2585 __isl_take isl_basic_map *bmap);
2586 __isl_give isl_set *isl_set_apply(
2587 __isl_take isl_set *set,
2588 __isl_take isl_map *map);
2589 __isl_give isl_union_set *isl_union_set_apply(
2590 __isl_take isl_union_set *uset,
2591 __isl_take isl_union_map *umap);
2592 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2593 __isl_take isl_basic_map *bmap1,
2594 __isl_take isl_basic_map *bmap2);
2595 __isl_give isl_basic_map *isl_basic_map_apply_range(
2596 __isl_take isl_basic_map *bmap1,
2597 __isl_take isl_basic_map *bmap2);
2598 __isl_give isl_map *isl_map_apply_domain(
2599 __isl_take isl_map *map1,
2600 __isl_take isl_map *map2);
2601 __isl_give isl_union_map *isl_union_map_apply_domain(
2602 __isl_take isl_union_map *umap1,
2603 __isl_take isl_union_map *umap2);
2604 __isl_give isl_map *isl_map_apply_range(
2605 __isl_take isl_map *map1,
2606 __isl_take isl_map *map2);
2607 __isl_give isl_union_map *isl_union_map_apply_range(
2608 __isl_take isl_union_map *umap1,
2609 __isl_take isl_union_map *umap2);
2611 =item * Cartesian Product
2613 __isl_give isl_set *isl_set_product(
2614 __isl_take isl_set *set1,
2615 __isl_take isl_set *set2);
2616 __isl_give isl_union_set *isl_union_set_product(
2617 __isl_take isl_union_set *uset1,
2618 __isl_take isl_union_set *uset2);
2619 __isl_give isl_basic_map *isl_basic_map_domain_product(
2620 __isl_take isl_basic_map *bmap1,
2621 __isl_take isl_basic_map *bmap2);
2622 __isl_give isl_basic_map *isl_basic_map_range_product(
2623 __isl_take isl_basic_map *bmap1,
2624 __isl_take isl_basic_map *bmap2);
2625 __isl_give isl_basic_map *isl_basic_map_product(
2626 __isl_take isl_basic_map *bmap1,
2627 __isl_take isl_basic_map *bmap2);
2628 __isl_give isl_map *isl_map_domain_product(
2629 __isl_take isl_map *map1,
2630 __isl_take isl_map *map2);
2631 __isl_give isl_map *isl_map_range_product(
2632 __isl_take isl_map *map1,
2633 __isl_take isl_map *map2);
2634 __isl_give isl_union_map *isl_union_map_domain_product(
2635 __isl_take isl_union_map *umap1,
2636 __isl_take isl_union_map *umap2);
2637 __isl_give isl_union_map *isl_union_map_range_product(
2638 __isl_take isl_union_map *umap1,
2639 __isl_take isl_union_map *umap2);
2640 __isl_give isl_map *isl_map_product(
2641 __isl_take isl_map *map1,
2642 __isl_take isl_map *map2);
2643 __isl_give isl_union_map *isl_union_map_product(
2644 __isl_take isl_union_map *umap1,
2645 __isl_take isl_union_map *umap2);
2647 The above functions compute the cross product of the given
2648 sets or relations. The domains and ranges of the results
2649 are wrapped maps between domains and ranges of the inputs.
2650 To obtain a ``flat'' product, use the following functions
2653 __isl_give isl_basic_set *isl_basic_set_flat_product(
2654 __isl_take isl_basic_set *bset1,
2655 __isl_take isl_basic_set *bset2);
2656 __isl_give isl_set *isl_set_flat_product(
2657 __isl_take isl_set *set1,
2658 __isl_take isl_set *set2);
2659 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2660 __isl_take isl_basic_map *bmap1,
2661 __isl_take isl_basic_map *bmap2);
2662 __isl_give isl_map *isl_map_flat_domain_product(
2663 __isl_take isl_map *map1,
2664 __isl_take isl_map *map2);
2665 __isl_give isl_map *isl_map_flat_range_product(
2666 __isl_take isl_map *map1,
2667 __isl_take isl_map *map2);
2668 __isl_give isl_union_map *isl_union_map_flat_range_product(
2669 __isl_take isl_union_map *umap1,
2670 __isl_take isl_union_map *umap2);
2671 __isl_give isl_basic_map *isl_basic_map_flat_product(
2672 __isl_take isl_basic_map *bmap1,
2673 __isl_take isl_basic_map *bmap2);
2674 __isl_give isl_map *isl_map_flat_product(
2675 __isl_take isl_map *map1,
2676 __isl_take isl_map *map2);
2678 =item * Simplification
2680 __isl_give isl_basic_set *isl_basic_set_gist(
2681 __isl_take isl_basic_set *bset,
2682 __isl_take isl_basic_set *context);
2683 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2684 __isl_take isl_set *context);
2685 __isl_give isl_set *isl_set_gist_params(
2686 __isl_take isl_set *set,
2687 __isl_take isl_set *context);
2688 __isl_give isl_union_set *isl_union_set_gist(
2689 __isl_take isl_union_set *uset,
2690 __isl_take isl_union_set *context);
2691 __isl_give isl_union_set *isl_union_set_gist_params(
2692 __isl_take isl_union_set *uset,
2693 __isl_take isl_set *set);
2694 __isl_give isl_basic_map *isl_basic_map_gist(
2695 __isl_take isl_basic_map *bmap,
2696 __isl_take isl_basic_map *context);
2697 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2698 __isl_take isl_map *context);
2699 __isl_give isl_map *isl_map_gist_params(
2700 __isl_take isl_map *map,
2701 __isl_take isl_set *context);
2702 __isl_give isl_map *isl_map_gist_domain(
2703 __isl_take isl_map *map,
2704 __isl_take isl_set *context);
2705 __isl_give isl_map *isl_map_gist_range(
2706 __isl_take isl_map *map,
2707 __isl_take isl_set *context);
2708 __isl_give isl_union_map *isl_union_map_gist(
2709 __isl_take isl_union_map *umap,
2710 __isl_take isl_union_map *context);
2711 __isl_give isl_union_map *isl_union_map_gist_params(
2712 __isl_take isl_union_map *umap,
2713 __isl_take isl_set *set);
2714 __isl_give isl_union_map *isl_union_map_gist_domain(
2715 __isl_take isl_union_map *umap,
2716 __isl_take isl_union_set *uset);
2717 __isl_give isl_union_map *isl_union_map_gist_range(
2718 __isl_take isl_union_map *umap,
2719 __isl_take isl_union_set *uset);
2721 The gist operation returns a set or relation that has the
2722 same intersection with the context as the input set or relation.
2723 Any implicit equality in the intersection is made explicit in the result,
2724 while all inequalities that are redundant with respect to the intersection
2726 In case of union sets and relations, the gist operation is performed
2731 =head3 Lexicographic Optimization
2733 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2734 the following functions
2735 compute a set that contains the lexicographic minimum or maximum
2736 of the elements in C<set> (or C<bset>) for those values of the parameters
2737 that satisfy C<dom>.
2738 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2739 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2741 In other words, the union of the parameter values
2742 for which the result is non-empty and of C<*empty>
2745 __isl_give isl_set *isl_basic_set_partial_lexmin(
2746 __isl_take isl_basic_set *bset,
2747 __isl_take isl_basic_set *dom,
2748 __isl_give isl_set **empty);
2749 __isl_give isl_set *isl_basic_set_partial_lexmax(
2750 __isl_take isl_basic_set *bset,
2751 __isl_take isl_basic_set *dom,
2752 __isl_give isl_set **empty);
2753 __isl_give isl_set *isl_set_partial_lexmin(
2754 __isl_take isl_set *set, __isl_take isl_set *dom,
2755 __isl_give isl_set **empty);
2756 __isl_give isl_set *isl_set_partial_lexmax(
2757 __isl_take isl_set *set, __isl_take isl_set *dom,
2758 __isl_give isl_set **empty);
2760 Given a (basic) set C<set> (or C<bset>), the following functions simply
2761 return a set containing the lexicographic minimum or maximum
2762 of the elements in C<set> (or C<bset>).
2763 In case of union sets, the optimum is computed per space.
2765 __isl_give isl_set *isl_basic_set_lexmin(
2766 __isl_take isl_basic_set *bset);
2767 __isl_give isl_set *isl_basic_set_lexmax(
2768 __isl_take isl_basic_set *bset);
2769 __isl_give isl_set *isl_set_lexmin(
2770 __isl_take isl_set *set);
2771 __isl_give isl_set *isl_set_lexmax(
2772 __isl_take isl_set *set);
2773 __isl_give isl_union_set *isl_union_set_lexmin(
2774 __isl_take isl_union_set *uset);
2775 __isl_give isl_union_set *isl_union_set_lexmax(
2776 __isl_take isl_union_set *uset);
2778 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2779 the following functions
2780 compute a relation that maps each element of C<dom>
2781 to the single lexicographic minimum or maximum
2782 of the elements that are associated to that same
2783 element in C<map> (or C<bmap>).
2784 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2785 that contains the elements in C<dom> that do not map
2786 to any elements in C<map> (or C<bmap>).
2787 In other words, the union of the domain of the result and of C<*empty>
2790 __isl_give isl_map *isl_basic_map_partial_lexmax(
2791 __isl_take isl_basic_map *bmap,
2792 __isl_take isl_basic_set *dom,
2793 __isl_give isl_set **empty);
2794 __isl_give isl_map *isl_basic_map_partial_lexmin(
2795 __isl_take isl_basic_map *bmap,
2796 __isl_take isl_basic_set *dom,
2797 __isl_give isl_set **empty);
2798 __isl_give isl_map *isl_map_partial_lexmax(
2799 __isl_take isl_map *map, __isl_take isl_set *dom,
2800 __isl_give isl_set **empty);
2801 __isl_give isl_map *isl_map_partial_lexmin(
2802 __isl_take isl_map *map, __isl_take isl_set *dom,
2803 __isl_give isl_set **empty);
2805 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2806 return a map mapping each element in the domain of
2807 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2808 of all elements associated to that element.
2809 In case of union relations, the optimum is computed per space.
2811 __isl_give isl_map *isl_basic_map_lexmin(
2812 __isl_take isl_basic_map *bmap);
2813 __isl_give isl_map *isl_basic_map_lexmax(
2814 __isl_take isl_basic_map *bmap);
2815 __isl_give isl_map *isl_map_lexmin(
2816 __isl_take isl_map *map);
2817 __isl_give isl_map *isl_map_lexmax(
2818 __isl_take isl_map *map);
2819 __isl_give isl_union_map *isl_union_map_lexmin(
2820 __isl_take isl_union_map *umap);
2821 __isl_give isl_union_map *isl_union_map_lexmax(
2822 __isl_take isl_union_map *umap);
2824 The following functions return their result in the form of
2825 a piecewise multi-affine expression
2826 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2827 but are otherwise equivalent to the corresponding functions
2828 returning a basic set or relation.
2830 __isl_give isl_pw_multi_aff *
2831 isl_basic_map_lexmin_pw_multi_aff(
2832 __isl_take isl_basic_map *bmap);
2833 __isl_give isl_pw_multi_aff *
2834 isl_basic_set_partial_lexmin_pw_multi_aff(
2835 __isl_take isl_basic_set *bset,
2836 __isl_take isl_basic_set *dom,
2837 __isl_give isl_set **empty);
2838 __isl_give isl_pw_multi_aff *
2839 isl_basic_set_partial_lexmax_pw_multi_aff(
2840 __isl_take isl_basic_set *bset,
2841 __isl_take isl_basic_set *dom,
2842 __isl_give isl_set **empty);
2843 __isl_give isl_pw_multi_aff *
2844 isl_basic_map_partial_lexmin_pw_multi_aff(
2845 __isl_take isl_basic_map *bmap,
2846 __isl_take isl_basic_set *dom,
2847 __isl_give isl_set **empty);
2848 __isl_give isl_pw_multi_aff *
2849 isl_basic_map_partial_lexmax_pw_multi_aff(
2850 __isl_take isl_basic_map *bmap,
2851 __isl_take isl_basic_set *dom,
2852 __isl_give isl_set **empty);
2856 Lists are defined over several element types, including
2857 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2858 Here we take lists of C<isl_set>s as an example.
2859 Lists can be created, copied, modified and freed using the following functions.
2861 #include <isl/list.h>
2862 __isl_give isl_set_list *isl_set_list_from_set(
2863 __isl_take isl_set *el);
2864 __isl_give isl_set_list *isl_set_list_alloc(
2865 isl_ctx *ctx, int n);
2866 __isl_give isl_set_list *isl_set_list_copy(
2867 __isl_keep isl_set_list *list);
2868 __isl_give isl_set_list *isl_set_list_add(
2869 __isl_take isl_set_list *list,
2870 __isl_take isl_set *el);
2871 __isl_give isl_set_list *isl_set_list_set_set(
2872 __isl_take isl_set_list *list, int index,
2873 __isl_take isl_set *set);
2874 __isl_give isl_set_list *isl_set_list_concat(
2875 __isl_take isl_set_list *list1,
2876 __isl_take isl_set_list *list2);
2877 void *isl_set_list_free(__isl_take isl_set_list *list);
2879 C<isl_set_list_alloc> creates an empty list with a capacity for
2880 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2883 Lists can be inspected using the following functions.
2885 #include <isl/list.h>
2886 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2887 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2888 __isl_give isl_set *isl_set_list_get_set(
2889 __isl_keep isl_set_list *list, int index);
2890 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2891 int (*fn)(__isl_take isl_set *el, void *user),
2894 Lists can be printed using
2896 #include <isl/list.h>
2897 __isl_give isl_printer *isl_printer_print_set_list(
2898 __isl_take isl_printer *p,
2899 __isl_keep isl_set_list *list);
2903 Vectors can be created, copied and freed using the following functions.
2905 #include <isl/vec.h>
2906 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2908 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2909 void isl_vec_free(__isl_take isl_vec *vec);
2911 Note that the elements of a newly created vector may have arbitrary values.
2912 The elements can be changed and inspected using the following functions.
2914 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2915 int isl_vec_size(__isl_keep isl_vec *vec);
2916 int isl_vec_get_element(__isl_keep isl_vec *vec,
2917 int pos, isl_int *v);
2918 __isl_give isl_vec *isl_vec_set_element(
2919 __isl_take isl_vec *vec, int pos, isl_int v);
2920 __isl_give isl_vec *isl_vec_set_element_si(
2921 __isl_take isl_vec *vec, int pos, int v);
2922 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2924 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2927 C<isl_vec_get_element> will return a negative value if anything went wrong.
2928 In that case, the value of C<*v> is undefined.
2932 Matrices can be created, copied and freed using the following functions.
2934 #include <isl/mat.h>
2935 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2936 unsigned n_row, unsigned n_col);
2937 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2938 void isl_mat_free(__isl_take isl_mat *mat);
2940 Note that the elements of a newly created matrix may have arbitrary values.
2941 The elements can be changed and inspected using the following functions.
2943 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2944 int isl_mat_rows(__isl_keep isl_mat *mat);
2945 int isl_mat_cols(__isl_keep isl_mat *mat);
2946 int isl_mat_get_element(__isl_keep isl_mat *mat,
2947 int row, int col, isl_int *v);
2948 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2949 int row, int col, isl_int v);
2950 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2951 int row, int col, int v);
2953 C<isl_mat_get_element> will return a negative value if anything went wrong.
2954 In that case, the value of C<*v> is undefined.
2956 The following function can be used to compute the (right) inverse
2957 of a matrix, i.e., a matrix such that the product of the original
2958 and the inverse (in that order) is a multiple of the identity matrix.
2959 The input matrix is assumed to be of full row-rank.
2961 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2963 The following function can be used to compute the (right) kernel
2964 (or null space) of a matrix, i.e., a matrix such that the product of
2965 the original and the kernel (in that order) is the zero matrix.
2967 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2969 =head2 Piecewise Quasi Affine Expressions
2971 The zero quasi affine expression on a given domain can be created using
2973 __isl_give isl_aff *isl_aff_zero_on_domain(
2974 __isl_take isl_local_space *ls);
2976 Note that the space in which the resulting object lives is a map space
2977 with the given space as domain and a one-dimensional range.
2979 An empty piecewise quasi affine expression (one with no cells)
2980 or a piecewise quasi affine expression with a single cell can
2981 be created using the following functions.
2983 #include <isl/aff.h>
2984 __isl_give isl_pw_aff *isl_pw_aff_empty(
2985 __isl_take isl_space *space);
2986 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2987 __isl_take isl_set *set, __isl_take isl_aff *aff);
2988 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2989 __isl_take isl_aff *aff);
2991 A piecewise quasi affine expression that is equal to 1 on a set
2992 and 0 outside the set can be created using the following function.
2994 #include <isl/aff.h>
2995 __isl_give isl_pw_aff *isl_set_indicator_function(
2996 __isl_take isl_set *set);
2998 Quasi affine expressions can be copied and freed using
3000 #include <isl/aff.h>
3001 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3002 void *isl_aff_free(__isl_take isl_aff *aff);
3004 __isl_give isl_pw_aff *isl_pw_aff_copy(
3005 __isl_keep isl_pw_aff *pwaff);
3006 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3008 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3009 using the following function. The constraint is required to have
3010 a non-zero coefficient for the specified dimension.
3012 #include <isl/constraint.h>
3013 __isl_give isl_aff *isl_constraint_get_bound(
3014 __isl_keep isl_constraint *constraint,
3015 enum isl_dim_type type, int pos);
3017 The entire affine expression of the constraint can also be extracted
3018 using the following function.
3020 #include <isl/constraint.h>
3021 __isl_give isl_aff *isl_constraint_get_aff(
3022 __isl_keep isl_constraint *constraint);
3024 Conversely, an equality constraint equating
3025 the affine expression to zero or an inequality constraint enforcing
3026 the affine expression to be non-negative, can be constructed using
3028 __isl_give isl_constraint *isl_equality_from_aff(
3029 __isl_take isl_aff *aff);
3030 __isl_give isl_constraint *isl_inequality_from_aff(
3031 __isl_take isl_aff *aff);
3033 The expression can be inspected using
3035 #include <isl/aff.h>
3036 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3037 int isl_aff_dim(__isl_keep isl_aff *aff,
3038 enum isl_dim_type type);
3039 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3040 __isl_keep isl_aff *aff);
3041 __isl_give isl_local_space *isl_aff_get_local_space(
3042 __isl_keep isl_aff *aff);
3043 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3044 enum isl_dim_type type, unsigned pos);
3045 const char *isl_pw_aff_get_dim_name(
3046 __isl_keep isl_pw_aff *pa,
3047 enum isl_dim_type type, unsigned pos);
3048 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3049 enum isl_dim_type type, unsigned pos);
3050 __isl_give isl_id *isl_pw_aff_get_dim_id(
3051 __isl_keep isl_pw_aff *pa,
3052 enum isl_dim_type type, unsigned pos);
3053 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3054 __isl_keep isl_pw_aff *pa,
3055 enum isl_dim_type type);
3056 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3058 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3059 enum isl_dim_type type, int pos, isl_int *v);
3060 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3062 __isl_give isl_aff *isl_aff_get_div(
3063 __isl_keep isl_aff *aff, int pos);
3065 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3066 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3067 int (*fn)(__isl_take isl_set *set,
3068 __isl_take isl_aff *aff,
3069 void *user), void *user);
3071 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3072 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3074 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3075 enum isl_dim_type type, unsigned first, unsigned n);
3076 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3077 enum isl_dim_type type, unsigned first, unsigned n);
3079 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3080 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3081 enum isl_dim_type type);
3082 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3084 It can be modified using
3086 #include <isl/aff.h>
3087 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3088 __isl_take isl_pw_aff *pwaff,
3089 enum isl_dim_type type, __isl_take isl_id *id);
3090 __isl_give isl_aff *isl_aff_set_dim_name(
3091 __isl_take isl_aff *aff, enum isl_dim_type type,
3092 unsigned pos, const char *s);
3093 __isl_give isl_aff *isl_aff_set_dim_id(
3094 __isl_take isl_aff *aff, enum isl_dim_type type,
3095 unsigned pos, __isl_take isl_id *id);
3096 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3097 __isl_take isl_pw_aff *pma,
3098 enum isl_dim_type type, unsigned pos,
3099 __isl_take isl_id *id);
3100 __isl_give isl_aff *isl_aff_set_constant(
3101 __isl_take isl_aff *aff, isl_int v);
3102 __isl_give isl_aff *isl_aff_set_constant_si(
3103 __isl_take isl_aff *aff, int v);
3104 __isl_give isl_aff *isl_aff_set_coefficient(
3105 __isl_take isl_aff *aff,
3106 enum isl_dim_type type, int pos, isl_int v);
3107 __isl_give isl_aff *isl_aff_set_coefficient_si(
3108 __isl_take isl_aff *aff,
3109 enum isl_dim_type type, int pos, int v);
3110 __isl_give isl_aff *isl_aff_set_denominator(
3111 __isl_take isl_aff *aff, isl_int v);
3113 __isl_give isl_aff *isl_aff_add_constant(
3114 __isl_take isl_aff *aff, isl_int v);
3115 __isl_give isl_aff *isl_aff_add_constant_si(
3116 __isl_take isl_aff *aff, int v);
3117 __isl_give isl_aff *isl_aff_add_constant_num(
3118 __isl_take isl_aff *aff, isl_int v);
3119 __isl_give isl_aff *isl_aff_add_constant_num_si(
3120 __isl_take isl_aff *aff, int v);
3121 __isl_give isl_aff *isl_aff_add_coefficient(
3122 __isl_take isl_aff *aff,
3123 enum isl_dim_type type, int pos, isl_int v);
3124 __isl_give isl_aff *isl_aff_add_coefficient_si(
3125 __isl_take isl_aff *aff,
3126 enum isl_dim_type type, int pos, int v);
3128 __isl_give isl_aff *isl_aff_insert_dims(
3129 __isl_take isl_aff *aff,
3130 enum isl_dim_type type, unsigned first, unsigned n);
3131 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3132 __isl_take isl_pw_aff *pwaff,
3133 enum isl_dim_type type, unsigned first, unsigned n);
3134 __isl_give isl_aff *isl_aff_add_dims(
3135 __isl_take isl_aff *aff,
3136 enum isl_dim_type type, unsigned n);
3137 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3138 __isl_take isl_pw_aff *pwaff,
3139 enum isl_dim_type type, unsigned n);
3140 __isl_give isl_aff *isl_aff_drop_dims(
3141 __isl_take isl_aff *aff,
3142 enum isl_dim_type type, unsigned first, unsigned n);
3143 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3144 __isl_take isl_pw_aff *pwaff,
3145 enum isl_dim_type type, unsigned first, unsigned n);
3147 Note that the C<set_constant> and C<set_coefficient> functions
3148 set the I<numerator> of the constant or coefficient, while
3149 C<add_constant> and C<add_coefficient> add an integer value to
3150 the possibly rational constant or coefficient.
3151 The C<add_constant_num> functions add an integer value to
3154 To check whether an affine expressions is obviously zero
3155 or obviously equal to some other affine expression, use
3157 #include <isl/aff.h>
3158 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3159 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3160 __isl_keep isl_aff *aff2);
3161 int isl_pw_aff_plain_is_equal(
3162 __isl_keep isl_pw_aff *pwaff1,
3163 __isl_keep isl_pw_aff *pwaff2);
3167 #include <isl/aff.h>
3168 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3169 __isl_take isl_aff *aff2);
3170 __isl_give isl_pw_aff *isl_pw_aff_add(
3171 __isl_take isl_pw_aff *pwaff1,
3172 __isl_take isl_pw_aff *pwaff2);
3173 __isl_give isl_pw_aff *isl_pw_aff_min(
3174 __isl_take isl_pw_aff *pwaff1,
3175 __isl_take isl_pw_aff *pwaff2);
3176 __isl_give isl_pw_aff *isl_pw_aff_max(
3177 __isl_take isl_pw_aff *pwaff1,
3178 __isl_take isl_pw_aff *pwaff2);
3179 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3180 __isl_take isl_aff *aff2);
3181 __isl_give isl_pw_aff *isl_pw_aff_sub(
3182 __isl_take isl_pw_aff *pwaff1,
3183 __isl_take isl_pw_aff *pwaff2);
3184 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3185 __isl_give isl_pw_aff *isl_pw_aff_neg(
3186 __isl_take isl_pw_aff *pwaff);
3187 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3188 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3189 __isl_take isl_pw_aff *pwaff);
3190 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3191 __isl_give isl_pw_aff *isl_pw_aff_floor(
3192 __isl_take isl_pw_aff *pwaff);
3193 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3195 __isl_give isl_pw_aff *isl_pw_aff_mod(
3196 __isl_take isl_pw_aff *pwaff, isl_int mod);
3197 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3199 __isl_give isl_pw_aff *isl_pw_aff_scale(
3200 __isl_take isl_pw_aff *pwaff, isl_int f);
3201 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3203 __isl_give isl_aff *isl_aff_scale_down_ui(
3204 __isl_take isl_aff *aff, unsigned f);
3205 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3206 __isl_take isl_pw_aff *pwaff, isl_int f);
3208 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3209 __isl_take isl_pw_aff_list *list);
3210 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3211 __isl_take isl_pw_aff_list *list);
3213 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3214 __isl_take isl_pw_aff *pwqp);
3216 __isl_give isl_aff *isl_aff_align_params(
3217 __isl_take isl_aff *aff,
3218 __isl_take isl_space *model);
3219 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3220 __isl_take isl_pw_aff *pwaff,
3221 __isl_take isl_space *model);
3223 __isl_give isl_aff *isl_aff_project_domain_on_params(
3224 __isl_take isl_aff *aff);
3226 __isl_give isl_aff *isl_aff_gist_params(
3227 __isl_take isl_aff *aff,
3228 __isl_take isl_set *context);
3229 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3230 __isl_take isl_set *context);
3231 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3232 __isl_take isl_pw_aff *pwaff,
3233 __isl_take isl_set *context);
3234 __isl_give isl_pw_aff *isl_pw_aff_gist(
3235 __isl_take isl_pw_aff *pwaff,
3236 __isl_take isl_set *context);
3238 __isl_give isl_set *isl_pw_aff_domain(
3239 __isl_take isl_pw_aff *pwaff);
3240 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3241 __isl_take isl_pw_aff *pa,
3242 __isl_take isl_set *set);
3243 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3244 __isl_take isl_pw_aff *pa,
3245 __isl_take isl_set *set);
3247 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3248 __isl_take isl_aff *aff2);
3249 __isl_give isl_pw_aff *isl_pw_aff_mul(
3250 __isl_take isl_pw_aff *pwaff1,
3251 __isl_take isl_pw_aff *pwaff2);
3253 When multiplying two affine expressions, at least one of the two needs
3256 #include <isl/aff.h>
3257 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3258 __isl_take isl_aff *aff);
3259 __isl_give isl_basic_set *isl_aff_le_basic_set(
3260 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3261 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3262 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3263 __isl_give isl_set *isl_pw_aff_eq_set(
3264 __isl_take isl_pw_aff *pwaff1,
3265 __isl_take isl_pw_aff *pwaff2);
3266 __isl_give isl_set *isl_pw_aff_ne_set(
3267 __isl_take isl_pw_aff *pwaff1,
3268 __isl_take isl_pw_aff *pwaff2);
3269 __isl_give isl_set *isl_pw_aff_le_set(
3270 __isl_take isl_pw_aff *pwaff1,
3271 __isl_take isl_pw_aff *pwaff2);
3272 __isl_give isl_set *isl_pw_aff_lt_set(
3273 __isl_take isl_pw_aff *pwaff1,
3274 __isl_take isl_pw_aff *pwaff2);
3275 __isl_give isl_set *isl_pw_aff_ge_set(
3276 __isl_take isl_pw_aff *pwaff1,
3277 __isl_take isl_pw_aff *pwaff2);
3278 __isl_give isl_set *isl_pw_aff_gt_set(
3279 __isl_take isl_pw_aff *pwaff1,
3280 __isl_take isl_pw_aff *pwaff2);
3282 __isl_give isl_set *isl_pw_aff_list_eq_set(
3283 __isl_take isl_pw_aff_list *list1,
3284 __isl_take isl_pw_aff_list *list2);
3285 __isl_give isl_set *isl_pw_aff_list_ne_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_le_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_lt_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_ge_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_gt_set(
3298 __isl_take isl_pw_aff_list *list1,
3299 __isl_take isl_pw_aff_list *list2);
3301 The function C<isl_aff_neg_basic_set> returns a basic set
3302 containing those elements in the domain space
3303 of C<aff> where C<aff> is negative.
3304 The function C<isl_aff_ge_basic_set> returns a basic set
3305 containing those elements in the shared space
3306 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3307 The function C<isl_pw_aff_ge_set> returns a set
3308 containing those elements in the shared domain
3309 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3310 The functions operating on C<isl_pw_aff_list> apply the corresponding
3311 C<isl_pw_aff> function to each pair of elements in the two lists.
3313 #include <isl/aff.h>
3314 __isl_give isl_set *isl_pw_aff_nonneg_set(
3315 __isl_take isl_pw_aff *pwaff);
3316 __isl_give isl_set *isl_pw_aff_zero_set(
3317 __isl_take isl_pw_aff *pwaff);
3318 __isl_give isl_set *isl_pw_aff_non_zero_set(
3319 __isl_take isl_pw_aff *pwaff);
3321 The function C<isl_pw_aff_nonneg_set> returns a set
3322 containing those elements in the domain
3323 of C<pwaff> where C<pwaff> is non-negative.
3325 #include <isl/aff.h>
3326 __isl_give isl_pw_aff *isl_pw_aff_cond(
3327 __isl_take isl_pw_aff *cond,
3328 __isl_take isl_pw_aff *pwaff_true,
3329 __isl_take isl_pw_aff *pwaff_false);
3331 The function C<isl_pw_aff_cond> performs a conditional operator
3332 and returns an expression that is equal to C<pwaff_true>
3333 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3334 where C<cond> is zero.
3336 #include <isl/aff.h>
3337 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3338 __isl_take isl_pw_aff *pwaff1,
3339 __isl_take isl_pw_aff *pwaff2);
3340 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3341 __isl_take isl_pw_aff *pwaff1,
3342 __isl_take isl_pw_aff *pwaff2);
3343 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3344 __isl_take isl_pw_aff *pwaff1,
3345 __isl_take isl_pw_aff *pwaff2);
3347 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3348 expression with a domain that is the union of those of C<pwaff1> and
3349 C<pwaff2> and such that on each cell, the quasi-affine expression is
3350 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3351 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3352 associated expression is the defined one.
3354 An expression can be read from input using
3356 #include <isl/aff.h>
3357 __isl_give isl_aff *isl_aff_read_from_str(
3358 isl_ctx *ctx, const char *str);
3359 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3360 isl_ctx *ctx, const char *str);
3362 An expression can be printed using
3364 #include <isl/aff.h>
3365 __isl_give isl_printer *isl_printer_print_aff(
3366 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3368 __isl_give isl_printer *isl_printer_print_pw_aff(
3369 __isl_take isl_printer *p,
3370 __isl_keep isl_pw_aff *pwaff);
3372 =head2 Piecewise Multiple Quasi Affine Expressions
3374 An C<isl_multi_aff> object represents a sequence of
3375 zero or more affine expressions, all defined on the same domain space.
3377 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3380 #include <isl/aff.h>
3381 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3382 __isl_take isl_space *space,
3383 __isl_take isl_aff_list *list);
3385 An empty piecewise multiple quasi affine expression (one with no cells),
3386 the zero piecewise multiple quasi affine expression (with value zero
3387 for each output dimension),
3388 a piecewise multiple quasi affine expression with a single cell (with
3389 either a universe or a specified domain) or
3390 a zero-dimensional piecewise multiple quasi affine expression
3392 can be created using the following functions.
3394 #include <isl/aff.h>
3395 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3396 __isl_take isl_space *space);
3397 __isl_give isl_multi_aff *isl_multi_aff_zero(
3398 __isl_take isl_space *space);
3399 __isl_give isl_multi_aff *isl_multi_aff_identity(
3400 __isl_take isl_space *space);
3401 __isl_give isl_pw_multi_aff *
3402 isl_pw_multi_aff_from_multi_aff(
3403 __isl_take isl_multi_aff *ma);
3404 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3405 __isl_take isl_set *set,
3406 __isl_take isl_multi_aff *maff);
3407 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3408 __isl_take isl_set *set);
3410 __isl_give isl_union_pw_multi_aff *
3411 isl_union_pw_multi_aff_empty(
3412 __isl_take isl_space *space);
3413 __isl_give isl_union_pw_multi_aff *
3414 isl_union_pw_multi_aff_add_pw_multi_aff(
3415 __isl_take isl_union_pw_multi_aff *upma,
3416 __isl_take isl_pw_multi_aff *pma);
3417 __isl_give isl_union_pw_multi_aff *
3418 isl_union_pw_multi_aff_from_domain(
3419 __isl_take isl_union_set *uset);
3421 A piecewise multiple quasi affine expression can also be initialized
3422 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3423 and the C<isl_map> is single-valued.
3425 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3426 __isl_take isl_set *set);
3427 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3428 __isl_take isl_map *map);
3430 Multiple quasi affine expressions can be copied and freed using
3432 #include <isl/aff.h>
3433 __isl_give isl_multi_aff *isl_multi_aff_copy(
3434 __isl_keep isl_multi_aff *maff);
3435 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3437 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3438 __isl_keep isl_pw_multi_aff *pma);
3439 void *isl_pw_multi_aff_free(
3440 __isl_take isl_pw_multi_aff *pma);
3442 __isl_give isl_union_pw_multi_aff *
3443 isl_union_pw_multi_aff_copy(
3444 __isl_keep isl_union_pw_multi_aff *upma);
3445 void *isl_union_pw_multi_aff_free(
3446 __isl_take isl_union_pw_multi_aff *upma);
3448 The expression can be inspected using
3450 #include <isl/aff.h>
3451 isl_ctx *isl_multi_aff_get_ctx(
3452 __isl_keep isl_multi_aff *maff);
3453 isl_ctx *isl_pw_multi_aff_get_ctx(
3454 __isl_keep isl_pw_multi_aff *pma);
3455 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3456 __isl_keep isl_union_pw_multi_aff *upma);
3457 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3458 enum isl_dim_type type);
3459 unsigned isl_pw_multi_aff_dim(
3460 __isl_keep isl_pw_multi_aff *pma,
3461 enum isl_dim_type type);
3462 __isl_give isl_aff *isl_multi_aff_get_aff(
3463 __isl_keep isl_multi_aff *multi, int pos);
3464 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3465 __isl_keep isl_pw_multi_aff *pma, int pos);
3466 const char *isl_pw_multi_aff_get_dim_name(
3467 __isl_keep isl_pw_multi_aff *pma,
3468 enum isl_dim_type type, unsigned pos);
3469 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3470 __isl_keep isl_pw_multi_aff *pma,
3471 enum isl_dim_type type, unsigned pos);
3472 const char *isl_multi_aff_get_tuple_name(
3473 __isl_keep isl_multi_aff *multi,
3474 enum isl_dim_type type);
3475 int isl_pw_multi_aff_has_tuple_name(
3476 __isl_keep isl_pw_multi_aff *pma,
3477 enum isl_dim_type type);
3478 const char *isl_pw_multi_aff_get_tuple_name(
3479 __isl_keep isl_pw_multi_aff *pma,
3480 enum isl_dim_type type);
3481 int isl_pw_multi_aff_has_tuple_id(
3482 __isl_keep isl_pw_multi_aff *pma,
3483 enum isl_dim_type type);
3484 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3485 __isl_keep isl_pw_multi_aff *pma,
3486 enum isl_dim_type type);
3488 int isl_pw_multi_aff_foreach_piece(
3489 __isl_keep isl_pw_multi_aff *pma,
3490 int (*fn)(__isl_take isl_set *set,
3491 __isl_take isl_multi_aff *maff,
3492 void *user), void *user);
3494 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3495 __isl_keep isl_union_pw_multi_aff *upma,
3496 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3497 void *user), void *user);
3499 It can be modified using
3501 #include <isl/aff.h>
3502 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3503 __isl_take isl_multi_aff *multi, int pos,
3504 __isl_take isl_aff *aff);
3505 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3506 __isl_take isl_multi_aff *maff,
3507 enum isl_dim_type type, unsigned pos, const char *s);
3508 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3509 __isl_take isl_multi_aff *maff,
3510 enum isl_dim_type type, __isl_take isl_id *id);
3511 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3512 __isl_take isl_pw_multi_aff *pma,
3513 enum isl_dim_type type, __isl_take isl_id *id);
3515 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3516 __isl_take isl_multi_aff *maff,
3517 enum isl_dim_type type, unsigned first, unsigned n);
3519 To check whether two multiple affine expressions are
3520 obviously equal to each other, use
3522 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3523 __isl_keep isl_multi_aff *maff2);
3524 int isl_pw_multi_aff_plain_is_equal(
3525 __isl_keep isl_pw_multi_aff *pma1,
3526 __isl_keep isl_pw_multi_aff *pma2);
3530 #include <isl/aff.h>
3531 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3532 __isl_take isl_pw_multi_aff *pma1,
3533 __isl_take isl_pw_multi_aff *pma2);
3534 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3535 __isl_take isl_pw_multi_aff *pma1,
3536 __isl_take isl_pw_multi_aff *pma2);
3537 __isl_give isl_multi_aff *isl_multi_aff_add(
3538 __isl_take isl_multi_aff *maff1,
3539 __isl_take isl_multi_aff *maff2);
3540 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3541 __isl_take isl_pw_multi_aff *pma1,
3542 __isl_take isl_pw_multi_aff *pma2);
3543 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3544 __isl_take isl_union_pw_multi_aff *upma1,
3545 __isl_take isl_union_pw_multi_aff *upma2);
3546 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3547 __isl_take isl_pw_multi_aff *pma1,
3548 __isl_take isl_pw_multi_aff *pma2);
3549 __isl_give isl_multi_aff *isl_multi_aff_scale(
3550 __isl_take isl_multi_aff *maff,
3552 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3553 __isl_take isl_pw_multi_aff *pma,
3554 __isl_take isl_set *set);
3555 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3556 __isl_take isl_pw_multi_aff *pma,
3557 __isl_take isl_set *set);
3558 __isl_give isl_multi_aff *isl_multi_aff_lift(
3559 __isl_take isl_multi_aff *maff,
3560 __isl_give isl_local_space **ls);
3561 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3562 __isl_take isl_pw_multi_aff *pma);
3563 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3564 __isl_take isl_multi_aff *maff,
3565 __isl_take isl_set *context);
3566 __isl_give isl_multi_aff *isl_multi_aff_gist(
3567 __isl_take isl_multi_aff *maff,
3568 __isl_take isl_set *context);
3569 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3570 __isl_take isl_pw_multi_aff *pma,
3571 __isl_take isl_set *set);
3572 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3573 __isl_take isl_pw_multi_aff *pma,
3574 __isl_take isl_set *set);
3575 __isl_give isl_set *isl_pw_multi_aff_domain(
3576 __isl_take isl_pw_multi_aff *pma);
3577 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3578 __isl_take isl_union_pw_multi_aff *upma);
3579 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3580 __isl_take isl_multi_aff *ma1,
3581 __isl_take isl_multi_aff *ma2);
3582 __isl_give isl_multi_aff *isl_multi_aff_product(
3583 __isl_take isl_multi_aff *ma1,
3584 __isl_take isl_multi_aff *ma2);
3585 __isl_give isl_pw_multi_aff *
3586 isl_pw_multi_aff_flat_range_product(
3587 __isl_take isl_pw_multi_aff *pma1,
3588 __isl_take isl_pw_multi_aff *pma2);
3589 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3590 __isl_take isl_pw_multi_aff *pma1,
3591 __isl_take isl_pw_multi_aff *pma2);
3592 __isl_give isl_union_pw_multi_aff *
3593 isl_union_pw_multi_aff_flat_range_product(
3594 __isl_take isl_union_pw_multi_aff *upma1,
3595 __isl_take isl_union_pw_multi_aff *upma2);
3597 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3598 then it is assigned the local space that lies at the basis of
3599 the lifting applied.
3601 __isl_give isl_set *isl_multi_aff_lex_le_set(
3602 __isl_take isl_multi_aff *ma1,
3603 __isl_take isl_multi_aff *ma2);
3604 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3605 __isl_take isl_multi_aff *ma1,
3606 __isl_take isl_multi_aff *ma2);
3608 The function C<isl_multi_aff_lex_le_set> returns a set
3609 containing those elements in the shared domain space
3610 where C<ma1> is lexicographically smaller than or
3613 An expression can be read from input using
3615 #include <isl/aff.h>
3616 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3617 isl_ctx *ctx, const char *str);
3618 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3619 isl_ctx *ctx, const char *str);
3621 An expression can be printed using
3623 #include <isl/aff.h>
3624 __isl_give isl_printer *isl_printer_print_multi_aff(
3625 __isl_take isl_printer *p,
3626 __isl_keep isl_multi_aff *maff);
3627 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3628 __isl_take isl_printer *p,
3629 __isl_keep isl_pw_multi_aff *pma);
3630 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3631 __isl_take isl_printer *p,
3632 __isl_keep isl_union_pw_multi_aff *upma);
3636 Points are elements of a set. They can be used to construct
3637 simple sets (boxes) or they can be used to represent the
3638 individual elements of a set.
3639 The zero point (the origin) can be created using
3641 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3643 The coordinates of a point can be inspected, set and changed
3646 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3647 enum isl_dim_type type, int pos, isl_int *v);
3648 __isl_give isl_point *isl_point_set_coordinate(
3649 __isl_take isl_point *pnt,
3650 enum isl_dim_type type, int pos, isl_int v);
3652 __isl_give isl_point *isl_point_add_ui(
3653 __isl_take isl_point *pnt,
3654 enum isl_dim_type type, int pos, unsigned val);
3655 __isl_give isl_point *isl_point_sub_ui(
3656 __isl_take isl_point *pnt,
3657 enum isl_dim_type type, int pos, unsigned val);
3659 Other properties can be obtained using
3661 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3663 Points can be copied or freed using
3665 __isl_give isl_point *isl_point_copy(
3666 __isl_keep isl_point *pnt);
3667 void isl_point_free(__isl_take isl_point *pnt);
3669 A singleton set can be created from a point using
3671 __isl_give isl_basic_set *isl_basic_set_from_point(
3672 __isl_take isl_point *pnt);
3673 __isl_give isl_set *isl_set_from_point(
3674 __isl_take isl_point *pnt);
3676 and a box can be created from two opposite extremal points using
3678 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3679 __isl_take isl_point *pnt1,
3680 __isl_take isl_point *pnt2);
3681 __isl_give isl_set *isl_set_box_from_points(
3682 __isl_take isl_point *pnt1,
3683 __isl_take isl_point *pnt2);
3685 All elements of a B<bounded> (union) set can be enumerated using
3686 the following functions.
3688 int isl_set_foreach_point(__isl_keep isl_set *set,
3689 int (*fn)(__isl_take isl_point *pnt, void *user),
3691 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3692 int (*fn)(__isl_take isl_point *pnt, void *user),
3695 The function C<fn> is called for each integer point in
3696 C<set> with as second argument the last argument of
3697 the C<isl_set_foreach_point> call. The function C<fn>
3698 should return C<0> on success and C<-1> on failure.
3699 In the latter case, C<isl_set_foreach_point> will stop
3700 enumerating and return C<-1> as well.
3701 If the enumeration is performed successfully and to completion,
3702 then C<isl_set_foreach_point> returns C<0>.
3704 To obtain a single point of a (basic) set, use
3706 __isl_give isl_point *isl_basic_set_sample_point(
3707 __isl_take isl_basic_set *bset);
3708 __isl_give isl_point *isl_set_sample_point(
3709 __isl_take isl_set *set);
3711 If C<set> does not contain any (integer) points, then the
3712 resulting point will be ``void'', a property that can be
3715 int isl_point_is_void(__isl_keep isl_point *pnt);
3717 =head2 Piecewise Quasipolynomials
3719 A piecewise quasipolynomial is a particular kind of function that maps
3720 a parametric point to a rational value.
3721 More specifically, a quasipolynomial is a polynomial expression in greatest
3722 integer parts of affine expressions of parameters and variables.
3723 A piecewise quasipolynomial is a subdivision of a given parametric
3724 domain into disjoint cells with a quasipolynomial associated to
3725 each cell. The value of the piecewise quasipolynomial at a given
3726 point is the value of the quasipolynomial associated to the cell
3727 that contains the point. Outside of the union of cells,
3728 the value is assumed to be zero.
3729 For example, the piecewise quasipolynomial
3731 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3733 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3734 A given piecewise quasipolynomial has a fixed domain dimension.
3735 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3736 defined over different domains.
3737 Piecewise quasipolynomials are mainly used by the C<barvinok>
3738 library for representing the number of elements in a parametric set or map.
3739 For example, the piecewise quasipolynomial above represents
3740 the number of points in the map
3742 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3744 =head3 Input and Output
3746 Piecewise quasipolynomials can be read from input using
3748 __isl_give isl_union_pw_qpolynomial *
3749 isl_union_pw_qpolynomial_read_from_str(
3750 isl_ctx *ctx, const char *str);
3752 Quasipolynomials and piecewise quasipolynomials can be printed
3753 using the following functions.
3755 __isl_give isl_printer *isl_printer_print_qpolynomial(
3756 __isl_take isl_printer *p,
3757 __isl_keep isl_qpolynomial *qp);
3759 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3760 __isl_take isl_printer *p,
3761 __isl_keep isl_pw_qpolynomial *pwqp);
3763 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3764 __isl_take isl_printer *p,
3765 __isl_keep isl_union_pw_qpolynomial *upwqp);
3767 The output format of the printer
3768 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3769 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3771 In case of printing in C<ISL_FORMAT_C>, the user may want
3772 to set the names of all dimensions
3774 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3775 __isl_take isl_qpolynomial *qp,
3776 enum isl_dim_type type, unsigned pos,
3778 __isl_give isl_pw_qpolynomial *
3779 isl_pw_qpolynomial_set_dim_name(
3780 __isl_take isl_pw_qpolynomial *pwqp,
3781 enum isl_dim_type type, unsigned pos,
3784 =head3 Creating New (Piecewise) Quasipolynomials
3786 Some simple quasipolynomials can be created using the following functions.
3787 More complicated quasipolynomials can be created by applying
3788 operations such as addition and multiplication
3789 on the resulting quasipolynomials
3791 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3792 __isl_take isl_space *domain);
3793 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3794 __isl_take isl_space *domain);
3795 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3796 __isl_take isl_space *domain);
3797 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3798 __isl_take isl_space *domain);
3799 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3800 __isl_take isl_space *domain);
3801 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3802 __isl_take isl_space *domain,
3803 const isl_int n, const isl_int d);
3804 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3805 __isl_take isl_space *domain,
3806 enum isl_dim_type type, unsigned pos);
3807 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3808 __isl_take isl_aff *aff);
3810 Note that the space in which a quasipolynomial lives is a map space
3811 with a one-dimensional range. The C<domain> argument in some of
3812 the functions above corresponds to the domain of this map space.
3814 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3815 with a single cell can be created using the following functions.
3816 Multiple of these single cell piecewise quasipolynomials can
3817 be combined to create more complicated piecewise quasipolynomials.
3819 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3820 __isl_take isl_space *space);
3821 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3822 __isl_take isl_set *set,
3823 __isl_take isl_qpolynomial *qp);
3824 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3825 __isl_take isl_qpolynomial *qp);
3826 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3827 __isl_take isl_pw_aff *pwaff);
3829 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3830 __isl_take isl_space *space);
3831 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3832 __isl_take isl_pw_qpolynomial *pwqp);
3833 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3834 __isl_take isl_union_pw_qpolynomial *upwqp,
3835 __isl_take isl_pw_qpolynomial *pwqp);
3837 Quasipolynomials can be copied and freed again using the following
3840 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3841 __isl_keep isl_qpolynomial *qp);
3842 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3844 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3845 __isl_keep isl_pw_qpolynomial *pwqp);
3846 void *isl_pw_qpolynomial_free(
3847 __isl_take isl_pw_qpolynomial *pwqp);
3849 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3850 __isl_keep isl_union_pw_qpolynomial *upwqp);
3851 void *isl_union_pw_qpolynomial_free(
3852 __isl_take isl_union_pw_qpolynomial *upwqp);
3854 =head3 Inspecting (Piecewise) Quasipolynomials
3856 To iterate over all piecewise quasipolynomials in a union
3857 piecewise quasipolynomial, use the following function
3859 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3860 __isl_keep isl_union_pw_qpolynomial *upwqp,
3861 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3864 To extract the piecewise quasipolynomial in a given space from a union, use
3866 __isl_give isl_pw_qpolynomial *
3867 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3868 __isl_keep isl_union_pw_qpolynomial *upwqp,
3869 __isl_take isl_space *space);
3871 To iterate over the cells in a piecewise quasipolynomial,
3872 use either of the following two functions
3874 int isl_pw_qpolynomial_foreach_piece(
3875 __isl_keep isl_pw_qpolynomial *pwqp,
3876 int (*fn)(__isl_take isl_set *set,
3877 __isl_take isl_qpolynomial *qp,
3878 void *user), void *user);
3879 int isl_pw_qpolynomial_foreach_lifted_piece(
3880 __isl_keep isl_pw_qpolynomial *pwqp,
3881 int (*fn)(__isl_take isl_set *set,
3882 __isl_take isl_qpolynomial *qp,
3883 void *user), void *user);
3885 As usual, the function C<fn> should return C<0> on success
3886 and C<-1> on failure. The difference between
3887 C<isl_pw_qpolynomial_foreach_piece> and
3888 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3889 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3890 compute unique representations for all existentially quantified
3891 variables and then turn these existentially quantified variables
3892 into extra set variables, adapting the associated quasipolynomial
3893 accordingly. This means that the C<set> passed to C<fn>
3894 will not have any existentially quantified variables, but that
3895 the dimensions of the sets may be different for different
3896 invocations of C<fn>.
3898 To iterate over all terms in a quasipolynomial,
3901 int isl_qpolynomial_foreach_term(
3902 __isl_keep isl_qpolynomial *qp,
3903 int (*fn)(__isl_take isl_term *term,
3904 void *user), void *user);
3906 The terms themselves can be inspected and freed using
3909 unsigned isl_term_dim(__isl_keep isl_term *term,
3910 enum isl_dim_type type);
3911 void isl_term_get_num(__isl_keep isl_term *term,
3913 void isl_term_get_den(__isl_keep isl_term *term,
3915 int isl_term_get_exp(__isl_keep isl_term *term,
3916 enum isl_dim_type type, unsigned pos);
3917 __isl_give isl_aff *isl_term_get_div(
3918 __isl_keep isl_term *term, unsigned pos);
3919 void isl_term_free(__isl_take isl_term *term);
3921 Each term is a product of parameters, set variables and
3922 integer divisions. The function C<isl_term_get_exp>
3923 returns the exponent of a given dimensions in the given term.
3924 The C<isl_int>s in the arguments of C<isl_term_get_num>
3925 and C<isl_term_get_den> need to have been initialized
3926 using C<isl_int_init> before calling these functions.
3928 =head3 Properties of (Piecewise) Quasipolynomials
3930 To check whether a quasipolynomial is actually a constant,
3931 use the following function.
3933 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3934 isl_int *n, isl_int *d);
3936 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3937 then the numerator and denominator of the constant
3938 are returned in C<*n> and C<*d>, respectively.
3940 To check whether two union piecewise quasipolynomials are
3941 obviously equal, use
3943 int isl_union_pw_qpolynomial_plain_is_equal(
3944 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3945 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3947 =head3 Operations on (Piecewise) Quasipolynomials
3949 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3950 __isl_take isl_qpolynomial *qp, isl_int v);
3951 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3952 __isl_take isl_qpolynomial *qp);
3953 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3954 __isl_take isl_qpolynomial *qp1,
3955 __isl_take isl_qpolynomial *qp2);
3956 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3957 __isl_take isl_qpolynomial *qp1,
3958 __isl_take isl_qpolynomial *qp2);
3959 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3960 __isl_take isl_qpolynomial *qp1,
3961 __isl_take isl_qpolynomial *qp2);
3962 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3963 __isl_take isl_qpolynomial *qp, unsigned exponent);
3965 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3966 __isl_take isl_pw_qpolynomial *pwqp1,
3967 __isl_take isl_pw_qpolynomial *pwqp2);
3968 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3969 __isl_take isl_pw_qpolynomial *pwqp1,
3970 __isl_take isl_pw_qpolynomial *pwqp2);
3971 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3972 __isl_take isl_pw_qpolynomial *pwqp1,
3973 __isl_take isl_pw_qpolynomial *pwqp2);
3974 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3975 __isl_take isl_pw_qpolynomial *pwqp);
3976 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3977 __isl_take isl_pw_qpolynomial *pwqp1,
3978 __isl_take isl_pw_qpolynomial *pwqp2);
3979 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3980 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3982 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3983 __isl_take isl_union_pw_qpolynomial *upwqp1,
3984 __isl_take isl_union_pw_qpolynomial *upwqp2);
3985 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
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_mul(
3989 __isl_take isl_union_pw_qpolynomial *upwqp1,
3990 __isl_take isl_union_pw_qpolynomial *upwqp2);
3992 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3993 __isl_take isl_pw_qpolynomial *pwqp,
3994 __isl_take isl_point *pnt);
3996 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3997 __isl_take isl_union_pw_qpolynomial *upwqp,
3998 __isl_take isl_point *pnt);
4000 __isl_give isl_set *isl_pw_qpolynomial_domain(
4001 __isl_take isl_pw_qpolynomial *pwqp);
4002 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4003 __isl_take isl_pw_qpolynomial *pwpq,
4004 __isl_take isl_set *set);
4005 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4006 __isl_take isl_pw_qpolynomial *pwpq,
4007 __isl_take isl_set *set);
4009 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4010 __isl_take isl_union_pw_qpolynomial *upwqp);
4011 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4012 __isl_take isl_union_pw_qpolynomial *upwpq,
4013 __isl_take isl_union_set *uset);
4014 __isl_give isl_union_pw_qpolynomial *
4015 isl_union_pw_qpolynomial_intersect_params(
4016 __isl_take isl_union_pw_qpolynomial *upwpq,
4017 __isl_take isl_set *set);
4019 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4020 __isl_take isl_qpolynomial *qp,
4021 __isl_take isl_space *model);
4023 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4024 __isl_take isl_qpolynomial *qp);
4025 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4026 __isl_take isl_pw_qpolynomial *pwqp);
4028 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4029 __isl_take isl_union_pw_qpolynomial *upwqp);
4031 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4032 __isl_take isl_qpolynomial *qp,
4033 __isl_take isl_set *context);
4034 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4035 __isl_take isl_qpolynomial *qp,
4036 __isl_take isl_set *context);
4038 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4039 __isl_take isl_pw_qpolynomial *pwqp,
4040 __isl_take isl_set *context);
4041 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4042 __isl_take isl_pw_qpolynomial *pwqp,
4043 __isl_take isl_set *context);
4045 __isl_give isl_union_pw_qpolynomial *
4046 isl_union_pw_qpolynomial_gist_params(
4047 __isl_take isl_union_pw_qpolynomial *upwqp,
4048 __isl_take isl_set *context);
4049 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4050 __isl_take isl_union_pw_qpolynomial *upwqp,
4051 __isl_take isl_union_set *context);
4053 The gist operation applies the gist operation to each of
4054 the cells in the domain of the input piecewise quasipolynomial.
4055 The context is also exploited
4056 to simplify the quasipolynomials associated to each cell.
4058 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4059 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4060 __isl_give isl_union_pw_qpolynomial *
4061 isl_union_pw_qpolynomial_to_polynomial(
4062 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4064 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4065 the polynomial will be an overapproximation. If C<sign> is negative,
4066 it will be an underapproximation. If C<sign> is zero, the approximation
4067 will lie somewhere in between.
4069 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4071 A piecewise quasipolynomial reduction is a piecewise
4072 reduction (or fold) of quasipolynomials.
4073 In particular, the reduction can be maximum or a minimum.
4074 The objects are mainly used to represent the result of
4075 an upper or lower bound on a quasipolynomial over its domain,
4076 i.e., as the result of the following function.
4078 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4079 __isl_take isl_pw_qpolynomial *pwqp,
4080 enum isl_fold type, int *tight);
4082 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4083 __isl_take isl_union_pw_qpolynomial *upwqp,
4084 enum isl_fold type, int *tight);
4086 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4087 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4088 is the returned bound is known be tight, i.e., for each value
4089 of the parameters there is at least
4090 one element in the domain that reaches the bound.
4091 If the domain of C<pwqp> is not wrapping, then the bound is computed
4092 over all elements in that domain and the result has a purely parametric
4093 domain. If the domain of C<pwqp> is wrapping, then the bound is
4094 computed over the range of the wrapped relation. The domain of the
4095 wrapped relation becomes the domain of the result.
4097 A (piecewise) quasipolynomial reduction can be copied or freed using the
4098 following functions.
4100 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4101 __isl_keep isl_qpolynomial_fold *fold);
4102 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4103 __isl_keep isl_pw_qpolynomial_fold *pwf);
4104 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4105 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4106 void isl_qpolynomial_fold_free(
4107 __isl_take isl_qpolynomial_fold *fold);
4108 void *isl_pw_qpolynomial_fold_free(
4109 __isl_take isl_pw_qpolynomial_fold *pwf);
4110 void *isl_union_pw_qpolynomial_fold_free(
4111 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4113 =head3 Printing Piecewise Quasipolynomial Reductions
4115 Piecewise quasipolynomial reductions can be printed
4116 using the following function.
4118 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4119 __isl_take isl_printer *p,
4120 __isl_keep isl_pw_qpolynomial_fold *pwf);
4121 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4122 __isl_take isl_printer *p,
4123 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4125 For C<isl_printer_print_pw_qpolynomial_fold>,
4126 output format of the printer
4127 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4128 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4129 output format of the printer
4130 needs to be set to C<ISL_FORMAT_ISL>.
4131 In case of printing in C<ISL_FORMAT_C>, the user may want
4132 to set the names of all dimensions
4134 __isl_give isl_pw_qpolynomial_fold *
4135 isl_pw_qpolynomial_fold_set_dim_name(
4136 __isl_take isl_pw_qpolynomial_fold *pwf,
4137 enum isl_dim_type type, unsigned pos,
4140 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4142 To iterate over all piecewise quasipolynomial reductions in a union
4143 piecewise quasipolynomial reduction, use the following function
4145 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4146 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4147 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4148 void *user), void *user);
4150 To iterate over the cells in a piecewise quasipolynomial reduction,
4151 use either of the following two functions
4153 int isl_pw_qpolynomial_fold_foreach_piece(
4154 __isl_keep isl_pw_qpolynomial_fold *pwf,
4155 int (*fn)(__isl_take isl_set *set,
4156 __isl_take isl_qpolynomial_fold *fold,
4157 void *user), void *user);
4158 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4159 __isl_keep isl_pw_qpolynomial_fold *pwf,
4160 int (*fn)(__isl_take isl_set *set,
4161 __isl_take isl_qpolynomial_fold *fold,
4162 void *user), void *user);
4164 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4165 of the difference between these two functions.
4167 To iterate over all quasipolynomials in a reduction, use
4169 int isl_qpolynomial_fold_foreach_qpolynomial(
4170 __isl_keep isl_qpolynomial_fold *fold,
4171 int (*fn)(__isl_take isl_qpolynomial *qp,
4172 void *user), void *user);
4174 =head3 Properties of Piecewise Quasipolynomial Reductions
4176 To check whether two union piecewise quasipolynomial reductions are
4177 obviously equal, use
4179 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4180 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4181 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4183 =head3 Operations on Piecewise Quasipolynomial Reductions
4185 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4186 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4188 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4189 __isl_take isl_pw_qpolynomial_fold *pwf1,
4190 __isl_take isl_pw_qpolynomial_fold *pwf2);
4192 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4193 __isl_take isl_pw_qpolynomial_fold *pwf1,
4194 __isl_take isl_pw_qpolynomial_fold *pwf2);
4196 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4197 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4198 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4200 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4201 __isl_take isl_pw_qpolynomial_fold *pwf,
4202 __isl_take isl_point *pnt);
4204 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4205 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4206 __isl_take isl_point *pnt);
4208 __isl_give isl_pw_qpolynomial_fold *
4209 isl_pw_qpolynomial_fold_intersect_params(
4210 __isl_take isl_pw_qpolynomial_fold *pwf,
4211 __isl_take isl_set *set);
4213 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4214 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4215 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4216 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4217 __isl_take isl_union_set *uset);
4218 __isl_give isl_union_pw_qpolynomial_fold *
4219 isl_union_pw_qpolynomial_fold_intersect_params(
4220 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4221 __isl_take isl_set *set);
4223 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4224 __isl_take isl_pw_qpolynomial_fold *pwf);
4226 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4227 __isl_take isl_pw_qpolynomial_fold *pwf);
4229 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4230 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4232 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4233 __isl_take isl_qpolynomial_fold *fold,
4234 __isl_take isl_set *context);
4235 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4236 __isl_take isl_qpolynomial_fold *fold,
4237 __isl_take isl_set *context);
4239 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4240 __isl_take isl_pw_qpolynomial_fold *pwf,
4241 __isl_take isl_set *context);
4242 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4243 __isl_take isl_pw_qpolynomial_fold *pwf,
4244 __isl_take isl_set *context);
4246 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4247 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4248 __isl_take isl_union_set *context);
4249 __isl_give isl_union_pw_qpolynomial_fold *
4250 isl_union_pw_qpolynomial_fold_gist_params(
4251 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4252 __isl_take isl_set *context);
4254 The gist operation applies the gist operation to each of
4255 the cells in the domain of the input piecewise quasipolynomial reduction.
4256 In future, the operation will also exploit the context
4257 to simplify the quasipolynomial reductions associated to each cell.
4259 __isl_give isl_pw_qpolynomial_fold *
4260 isl_set_apply_pw_qpolynomial_fold(
4261 __isl_take isl_set *set,
4262 __isl_take isl_pw_qpolynomial_fold *pwf,
4264 __isl_give isl_pw_qpolynomial_fold *
4265 isl_map_apply_pw_qpolynomial_fold(
4266 __isl_take isl_map *map,
4267 __isl_take isl_pw_qpolynomial_fold *pwf,
4269 __isl_give isl_union_pw_qpolynomial_fold *
4270 isl_union_set_apply_union_pw_qpolynomial_fold(
4271 __isl_take isl_union_set *uset,
4272 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4274 __isl_give isl_union_pw_qpolynomial_fold *
4275 isl_union_map_apply_union_pw_qpolynomial_fold(
4276 __isl_take isl_union_map *umap,
4277 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4280 The functions taking a map
4281 compose the given map with the given piecewise quasipolynomial reduction.
4282 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4283 over all elements in the intersection of the range of the map
4284 and the domain of the piecewise quasipolynomial reduction
4285 as a function of an element in the domain of the map.
4286 The functions taking a set compute a bound over all elements in the
4287 intersection of the set and the domain of the
4288 piecewise quasipolynomial reduction.
4290 =head2 Dependence Analysis
4292 C<isl> contains specialized functionality for performing
4293 array dataflow analysis. That is, given a I<sink> access relation
4294 and a collection of possible I<source> access relations,
4295 C<isl> can compute relations that describe
4296 for each iteration of the sink access, which iteration
4297 of which of the source access relations was the last
4298 to access the same data element before the given iteration
4300 The resulting dependence relations map source iterations
4301 to the corresponding sink iterations.
4302 To compute standard flow dependences, the sink should be
4303 a read, while the sources should be writes.
4304 If any of the source accesses are marked as being I<may>
4305 accesses, then there will be a dependence from the last
4306 I<must> access B<and> from any I<may> access that follows
4307 this last I<must> access.
4308 In particular, if I<all> sources are I<may> accesses,
4309 then memory based dependence analysis is performed.
4310 If, on the other hand, all sources are I<must> accesses,
4311 then value based dependence analysis is performed.
4313 #include <isl/flow.h>
4315 typedef int (*isl_access_level_before)(void *first, void *second);
4317 __isl_give isl_access_info *isl_access_info_alloc(
4318 __isl_take isl_map *sink,
4319 void *sink_user, isl_access_level_before fn,
4321 __isl_give isl_access_info *isl_access_info_add_source(
4322 __isl_take isl_access_info *acc,
4323 __isl_take isl_map *source, int must,
4325 void *isl_access_info_free(__isl_take isl_access_info *acc);
4327 __isl_give isl_flow *isl_access_info_compute_flow(
4328 __isl_take isl_access_info *acc);
4330 int isl_flow_foreach(__isl_keep isl_flow *deps,
4331 int (*fn)(__isl_take isl_map *dep, int must,
4332 void *dep_user, void *user),
4334 __isl_give isl_map *isl_flow_get_no_source(
4335 __isl_keep isl_flow *deps, int must);
4336 void isl_flow_free(__isl_take isl_flow *deps);
4338 The function C<isl_access_info_compute_flow> performs the actual
4339 dependence analysis. The other functions are used to construct
4340 the input for this function or to read off the output.
4342 The input is collected in an C<isl_access_info>, which can
4343 be created through a call to C<isl_access_info_alloc>.
4344 The arguments to this functions are the sink access relation
4345 C<sink>, a token C<sink_user> used to identify the sink
4346 access to the user, a callback function for specifying the
4347 relative order of source and sink accesses, and the number
4348 of source access relations that will be added.
4349 The callback function has type C<int (*)(void *first, void *second)>.
4350 The function is called with two user supplied tokens identifying
4351 either a source or the sink and it should return the shared nesting
4352 level and the relative order of the two accesses.
4353 In particular, let I<n> be the number of loops shared by
4354 the two accesses. If C<first> precedes C<second> textually,
4355 then the function should return I<2 * n + 1>; otherwise,
4356 it should return I<2 * n>.
4357 The sources can be added to the C<isl_access_info> by performing
4358 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4359 C<must> indicates whether the source is a I<must> access
4360 or a I<may> access. Note that a multi-valued access relation
4361 should only be marked I<must> if every iteration in the domain
4362 of the relation accesses I<all> elements in its image.
4363 The C<source_user> token is again used to identify
4364 the source access. The range of the source access relation
4365 C<source> should have the same dimension as the range
4366 of the sink access relation.
4367 The C<isl_access_info_free> function should usually not be
4368 called explicitly, because it is called implicitly by
4369 C<isl_access_info_compute_flow>.
4371 The result of the dependence analysis is collected in an
4372 C<isl_flow>. There may be elements of
4373 the sink access for which no preceding source access could be
4374 found or for which all preceding sources are I<may> accesses.
4375 The relations containing these elements can be obtained through
4376 calls to C<isl_flow_get_no_source>, the first with C<must> set
4377 and the second with C<must> unset.
4378 In the case of standard flow dependence analysis,
4379 with the sink a read and the sources I<must> writes,
4380 the first relation corresponds to the reads from uninitialized
4381 array elements and the second relation is empty.
4382 The actual flow dependences can be extracted using
4383 C<isl_flow_foreach>. This function will call the user-specified
4384 callback function C<fn> for each B<non-empty> dependence between
4385 a source and the sink. The callback function is called
4386 with four arguments, the actual flow dependence relation
4387 mapping source iterations to sink iterations, a boolean that
4388 indicates whether it is a I<must> or I<may> dependence, a token
4389 identifying the source and an additional C<void *> with value
4390 equal to the third argument of the C<isl_flow_foreach> call.
4391 A dependence is marked I<must> if it originates from a I<must>
4392 source and if it is not followed by any I<may> sources.
4394 After finishing with an C<isl_flow>, the user should call
4395 C<isl_flow_free> to free all associated memory.
4397 A higher-level interface to dependence analysis is provided
4398 by the following function.
4400 #include <isl/flow.h>
4402 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4403 __isl_take isl_union_map *must_source,
4404 __isl_take isl_union_map *may_source,
4405 __isl_take isl_union_map *schedule,
4406 __isl_give isl_union_map **must_dep,
4407 __isl_give isl_union_map **may_dep,
4408 __isl_give isl_union_map **must_no_source,
4409 __isl_give isl_union_map **may_no_source);
4411 The arrays are identified by the tuple names of the ranges
4412 of the accesses. The iteration domains by the tuple names
4413 of the domains of the accesses and of the schedule.
4414 The relative order of the iteration domains is given by the
4415 schedule. The relations returned through C<must_no_source>
4416 and C<may_no_source> are subsets of C<sink>.
4417 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4418 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4419 any of the other arguments is treated as an error.
4421 =head3 Interaction with Dependence Analysis
4423 During the dependence analysis, we frequently need to perform
4424 the following operation. Given a relation between sink iterations
4425 and potential source iterations from a particular source domain,
4426 what is the last potential source iteration corresponding to each
4427 sink iteration. It can sometimes be convenient to adjust
4428 the set of potential source iterations before or after each such operation.
4429 The prototypical example is fuzzy array dataflow analysis,
4430 where we need to analyze if, based on data-dependent constraints,
4431 the sink iteration can ever be executed without one or more of
4432 the corresponding potential source iterations being executed.
4433 If so, we can introduce extra parameters and select an unknown
4434 but fixed source iteration from the potential source iterations.
4435 To be able to perform such manipulations, C<isl> provides the following
4438 #include <isl/flow.h>
4440 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4441 __isl_keep isl_map *source_map,
4442 __isl_keep isl_set *sink, void *source_user,
4444 __isl_give isl_access_info *isl_access_info_set_restrict(
4445 __isl_take isl_access_info *acc,
4446 isl_access_restrict fn, void *user);
4448 The function C<isl_access_info_set_restrict> should be called
4449 before calling C<isl_access_info_compute_flow> and registers a callback function
4450 that will be called any time C<isl> is about to compute the last
4451 potential source. The first argument is the (reverse) proto-dependence,
4452 mapping sink iterations to potential source iterations.
4453 The second argument represents the sink iterations for which
4454 we want to compute the last source iteration.
4455 The third argument is the token corresponding to the source
4456 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4457 The callback is expected to return a restriction on either the input or
4458 the output of the operation computing the last potential source.
4459 If the input needs to be restricted then restrictions are needed
4460 for both the source and the sink iterations. The sink iterations
4461 and the potential source iterations will be intersected with these sets.
4462 If the output needs to be restricted then only a restriction on the source
4463 iterations is required.
4464 If any error occurs, the callback should return C<NULL>.
4465 An C<isl_restriction> object can be created, freed and inspected
4466 using the following functions.
4468 #include <isl/flow.h>
4470 __isl_give isl_restriction *isl_restriction_input(
4471 __isl_take isl_set *source_restr,
4472 __isl_take isl_set *sink_restr);
4473 __isl_give isl_restriction *isl_restriction_output(
4474 __isl_take isl_set *source_restr);
4475 __isl_give isl_restriction *isl_restriction_none(
4476 __isl_take isl_map *source_map);
4477 __isl_give isl_restriction *isl_restriction_empty(
4478 __isl_take isl_map *source_map);
4479 void *isl_restriction_free(
4480 __isl_take isl_restriction *restr);
4481 isl_ctx *isl_restriction_get_ctx(
4482 __isl_keep isl_restriction *restr);
4484 C<isl_restriction_none> and C<isl_restriction_empty> are special
4485 cases of C<isl_restriction_input>. C<isl_restriction_none>
4486 is essentially equivalent to
4488 isl_restriction_input(isl_set_universe(
4489 isl_space_range(isl_map_get_space(source_map))),
4491 isl_space_domain(isl_map_get_space(source_map))));
4493 whereas C<isl_restriction_empty> is essentially equivalent to
4495 isl_restriction_input(isl_set_empty(
4496 isl_space_range(isl_map_get_space(source_map))),
4498 isl_space_domain(isl_map_get_space(source_map))));
4502 B<The functionality described in this section is fairly new
4503 and may be subject to change.>
4505 The following function can be used to compute a schedule
4506 for a union of domains.
4507 By default, the algorithm used to construct the schedule is similar
4508 to that of C<Pluto>.
4509 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4511 The generated schedule respects all C<validity> dependences.
4512 That is, all dependence distances over these dependences in the
4513 scheduled space are lexicographically positive.
4514 The default algorithm tries to minimize the dependence distances over
4515 C<proximity> dependences.
4516 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4517 for groups of domains where the dependence distances have only
4518 non-negative values.
4519 When using Feautrier's algorithm, the C<proximity> dependence
4520 distances are only minimized during the extension to a
4521 full-dimensional schedule.
4523 #include <isl/schedule.h>
4524 __isl_give isl_schedule *isl_union_set_compute_schedule(
4525 __isl_take isl_union_set *domain,
4526 __isl_take isl_union_map *validity,
4527 __isl_take isl_union_map *proximity);
4528 void *isl_schedule_free(__isl_take isl_schedule *sched);
4530 A mapping from the domains to the scheduled space can be obtained
4531 from an C<isl_schedule> using the following function.
4533 __isl_give isl_union_map *isl_schedule_get_map(
4534 __isl_keep isl_schedule *sched);
4536 A representation of the schedule can be printed using
4538 __isl_give isl_printer *isl_printer_print_schedule(
4539 __isl_take isl_printer *p,
4540 __isl_keep isl_schedule *schedule);
4542 A representation of the schedule as a forest of bands can be obtained
4543 using the following function.
4545 __isl_give isl_band_list *isl_schedule_get_band_forest(
4546 __isl_keep isl_schedule *schedule);
4548 The individual bands can be visited in depth-first post-order
4549 using the following function.
4551 #include <isl/schedule.h>
4552 int isl_schedule_foreach_band(
4553 __isl_keep isl_schedule *sched,
4554 int (*fn)(__isl_keep isl_band *band, void *user),
4557 The list can be manipulated as explained in L<"Lists">.
4558 The bands inside the list can be copied and freed using the following
4561 #include <isl/band.h>
4562 __isl_give isl_band *isl_band_copy(
4563 __isl_keep isl_band *band);
4564 void *isl_band_free(__isl_take isl_band *band);
4566 Each band contains zero or more scheduling dimensions.
4567 These are referred to as the members of the band.
4568 The section of the schedule that corresponds to the band is
4569 referred to as the partial schedule of the band.
4570 For those nodes that participate in a band, the outer scheduling
4571 dimensions form the prefix schedule, while the inner scheduling
4572 dimensions form the suffix schedule.
4573 That is, if we take a cut of the band forest, then the union of
4574 the concatenations of the prefix, partial and suffix schedules of
4575 each band in the cut is equal to the entire schedule (modulo
4576 some possible padding at the end with zero scheduling dimensions).
4577 The properties of a band can be inspected using the following functions.
4579 #include <isl/band.h>
4580 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4582 int isl_band_has_children(__isl_keep isl_band *band);
4583 __isl_give isl_band_list *isl_band_get_children(
4584 __isl_keep isl_band *band);
4586 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4587 __isl_keep isl_band *band);
4588 __isl_give isl_union_map *isl_band_get_partial_schedule(
4589 __isl_keep isl_band *band);
4590 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4591 __isl_keep isl_band *band);
4593 int isl_band_n_member(__isl_keep isl_band *band);
4594 int isl_band_member_is_zero_distance(
4595 __isl_keep isl_band *band, int pos);
4597 int isl_band_list_foreach_band(
4598 __isl_keep isl_band_list *list,
4599 int (*fn)(__isl_keep isl_band *band, void *user),
4602 Note that a scheduling dimension is considered to be ``zero
4603 distance'' if it does not carry any proximity dependences
4605 That is, if the dependence distances of the proximity
4606 dependences are all zero in that direction (for fixed
4607 iterations of outer bands).
4608 Like C<isl_schedule_foreach_band>,
4609 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4610 in depth-first post-order.
4612 A band can be tiled using the following function.
4614 #include <isl/band.h>
4615 int isl_band_tile(__isl_keep isl_band *band,
4616 __isl_take isl_vec *sizes);
4618 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4620 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4622 The C<isl_band_tile> function tiles the band using the given tile sizes
4623 inside its schedule.
4624 A new child band is created to represent the point loops and it is
4625 inserted between the modified band and its children.
4626 The C<tile_scale_tile_loops> option specifies whether the tile
4627 loops iterators should be scaled by the tile sizes.
4629 A representation of the band can be printed using
4631 #include <isl/band.h>
4632 __isl_give isl_printer *isl_printer_print_band(
4633 __isl_take isl_printer *p,
4634 __isl_keep isl_band *band);
4638 #include <isl/schedule.h>
4639 int isl_options_set_schedule_max_coefficient(
4640 isl_ctx *ctx, int val);
4641 int isl_options_get_schedule_max_coefficient(
4643 int isl_options_set_schedule_max_constant_term(
4644 isl_ctx *ctx, int val);
4645 int isl_options_get_schedule_max_constant_term(
4647 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4648 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4649 int isl_options_set_schedule_maximize_band_depth(
4650 isl_ctx *ctx, int val);
4651 int isl_options_get_schedule_maximize_band_depth(
4653 int isl_options_set_schedule_outer_zero_distance(
4654 isl_ctx *ctx, int val);
4655 int isl_options_get_schedule_outer_zero_distance(
4657 int isl_options_set_schedule_split_scaled(
4658 isl_ctx *ctx, int val);
4659 int isl_options_get_schedule_split_scaled(
4661 int isl_options_set_schedule_algorithm(
4662 isl_ctx *ctx, int val);
4663 int isl_options_get_schedule_algorithm(
4665 int isl_options_set_schedule_separate_components(
4666 isl_ctx *ctx, int val);
4667 int isl_options_get_schedule_separate_components(
4672 =item * schedule_max_coefficient
4674 This option enforces that the coefficients for variable and parameter
4675 dimensions in the calculated schedule are not larger than the specified value.
4676 This option can significantly increase the speed of the scheduling calculation
4677 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4678 this option does not introduce bounds on the variable or parameter
4681 =item * schedule_max_constant_term
4683 This option enforces that the constant coefficients in the calculated schedule
4684 are not larger than the maximal constant term. This option can significantly
4685 increase the speed of the scheduling calculation and may also prevent fusing of
4686 unrelated dimensions. A value of -1 means that this option does not introduce
4687 bounds on the constant coefficients.
4689 =item * schedule_fuse
4691 This option controls the level of fusion.
4692 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
4693 resulting schedule will be distributed as much as possible.
4694 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
4695 try to fuse loops in the resulting schedule.
4697 =item * schedule_maximize_band_depth
4699 If this option is set, we do not split bands at the point
4700 where we detect splitting is necessary. Instead, we
4701 backtrack and split bands as early as possible. This
4702 reduces the number of splits and maximizes the width of
4703 the bands. Wider bands give more possibilities for tiling.
4704 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
4705 then bands will be split as early as possible, even if there is no need.
4706 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
4708 =item * schedule_outer_zero_distance
4710 If this option is set, then we try to construct schedules
4711 where the outermost scheduling dimension in each band
4712 results in a zero dependence distance over the proximity
4715 =item * schedule_split_scaled
4717 If this option is set, then we try to construct schedules in which the
4718 constant term is split off from the linear part if the linear parts of
4719 the scheduling rows for all nodes in the graphs have a common non-trivial
4721 The constant term is then placed in a separate band and the linear
4724 =item * schedule_algorithm
4726 Selects the scheduling algorithm to be used.
4727 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4728 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4730 =item * schedule_separate_components
4732 If at any point the dependence graph contains any (weakly connected) components,
4733 then these components are scheduled separately.
4734 If this option is not set, then some iterations of the domains
4735 in these components may be scheduled together.
4736 If this option is set, then the components are given consecutive
4741 =head2 Parametric Vertex Enumeration
4743 The parametric vertex enumeration described in this section
4744 is mainly intended to be used internally and by the C<barvinok>
4747 #include <isl/vertices.h>
4748 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4749 __isl_keep isl_basic_set *bset);
4751 The function C<isl_basic_set_compute_vertices> performs the
4752 actual computation of the parametric vertices and the chamber
4753 decomposition and store the result in an C<isl_vertices> object.
4754 This information can be queried by either iterating over all
4755 the vertices or iterating over all the chambers or cells
4756 and then iterating over all vertices that are active on the chamber.
4758 int isl_vertices_foreach_vertex(
4759 __isl_keep isl_vertices *vertices,
4760 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4763 int isl_vertices_foreach_cell(
4764 __isl_keep isl_vertices *vertices,
4765 int (*fn)(__isl_take isl_cell *cell, void *user),
4767 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4768 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4771 Other operations that can be performed on an C<isl_vertices> object are
4774 isl_ctx *isl_vertices_get_ctx(
4775 __isl_keep isl_vertices *vertices);
4776 int isl_vertices_get_n_vertices(
4777 __isl_keep isl_vertices *vertices);
4778 void isl_vertices_free(__isl_take isl_vertices *vertices);
4780 Vertices can be inspected and destroyed using the following functions.
4782 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4783 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4784 __isl_give isl_basic_set *isl_vertex_get_domain(
4785 __isl_keep isl_vertex *vertex);
4786 __isl_give isl_basic_set *isl_vertex_get_expr(
4787 __isl_keep isl_vertex *vertex);
4788 void isl_vertex_free(__isl_take isl_vertex *vertex);
4790 C<isl_vertex_get_expr> returns a singleton parametric set describing
4791 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4793 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4794 B<rational> basic sets, so they should mainly be used for inspection
4795 and should not be mixed with integer sets.
4797 Chambers can be inspected and destroyed using the following functions.
4799 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4800 __isl_give isl_basic_set *isl_cell_get_domain(
4801 __isl_keep isl_cell *cell);
4802 void isl_cell_free(__isl_take isl_cell *cell);
4806 Although C<isl> is mainly meant to be used as a library,
4807 it also contains some basic applications that use some
4808 of the functionality of C<isl>.
4809 The input may be specified in either the L<isl format>
4810 or the L<PolyLib format>.
4812 =head2 C<isl_polyhedron_sample>
4814 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4815 an integer element of the polyhedron, if there is any.
4816 The first column in the output is the denominator and is always
4817 equal to 1. If the polyhedron contains no integer points,
4818 then a vector of length zero is printed.
4822 C<isl_pip> takes the same input as the C<example> program
4823 from the C<piplib> distribution, i.e., a set of constraints
4824 on the parameters, a line containing only -1 and finally a set
4825 of constraints on a parametric polyhedron.
4826 The coefficients of the parameters appear in the last columns
4827 (but before the final constant column).
4828 The output is the lexicographic minimum of the parametric polyhedron.
4829 As C<isl> currently does not have its own output format, the output
4830 is just a dump of the internal state.
4832 =head2 C<isl_polyhedron_minimize>
4834 C<isl_polyhedron_minimize> computes the minimum of some linear
4835 or affine objective function over the integer points in a polyhedron.
4836 If an affine objective function
4837 is given, then the constant should appear in the last column.
4839 =head2 C<isl_polytope_scan>
4841 Given a polytope, C<isl_polytope_scan> prints
4842 all integer points in the polytope.