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_map *isl_union_map_from_map(
1190 __isl_take isl_map *map);
1191 __isl_give isl_union_set *isl_union_set_from_set(
1192 __isl_take isl_set *set);
1194 The inverse conversions below can only be used if the input
1195 union set or relation is known to contain elements in exactly one
1198 __isl_give isl_set *isl_set_from_union_set(
1199 __isl_take isl_union_set *uset);
1200 __isl_give isl_map *isl_map_from_union_map(
1201 __isl_take isl_union_map *umap);
1203 A zero-dimensional set can be constructed on a given parameter domain
1204 using the following function.
1206 __isl_give isl_set *isl_set_from_params(
1207 __isl_take isl_set *set);
1209 Sets and relations can be copied and freed again using the following
1212 __isl_give isl_basic_set *isl_basic_set_copy(
1213 __isl_keep isl_basic_set *bset);
1214 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1215 __isl_give isl_union_set *isl_union_set_copy(
1216 __isl_keep isl_union_set *uset);
1217 __isl_give isl_basic_map *isl_basic_map_copy(
1218 __isl_keep isl_basic_map *bmap);
1219 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1220 __isl_give isl_union_map *isl_union_map_copy(
1221 __isl_keep isl_union_map *umap);
1222 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1223 void *isl_set_free(__isl_take isl_set *set);
1224 void *isl_union_set_free(__isl_take isl_union_set *uset);
1225 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1226 void isl_map_free(__isl_take isl_map *map);
1227 void *isl_union_map_free(__isl_take isl_union_map *umap);
1229 Other sets and relations can be constructed by starting
1230 from a universe set or relation, adding equality and/or
1231 inequality constraints and then projecting out the
1232 existentially quantified variables, if any.
1233 Constraints can be constructed, manipulated and
1234 added to (or removed from) (basic) sets and relations
1235 using the following functions.
1237 #include <isl/constraint.h>
1238 __isl_give isl_constraint *isl_equality_alloc(
1239 __isl_take isl_local_space *ls);
1240 __isl_give isl_constraint *isl_inequality_alloc(
1241 __isl_take isl_local_space *ls);
1242 __isl_give isl_constraint *isl_constraint_set_constant(
1243 __isl_take isl_constraint *constraint, isl_int v);
1244 __isl_give isl_constraint *isl_constraint_set_constant_si(
1245 __isl_take isl_constraint *constraint, int v);
1246 __isl_give isl_constraint *isl_constraint_set_coefficient(
1247 __isl_take isl_constraint *constraint,
1248 enum isl_dim_type type, int pos, isl_int v);
1249 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1250 __isl_take isl_constraint *constraint,
1251 enum isl_dim_type type, int pos, int v);
1252 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1253 __isl_take isl_basic_map *bmap,
1254 __isl_take isl_constraint *constraint);
1255 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1256 __isl_take isl_basic_set *bset,
1257 __isl_take isl_constraint *constraint);
1258 __isl_give isl_map *isl_map_add_constraint(
1259 __isl_take isl_map *map,
1260 __isl_take isl_constraint *constraint);
1261 __isl_give isl_set *isl_set_add_constraint(
1262 __isl_take isl_set *set,
1263 __isl_take isl_constraint *constraint);
1264 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1265 __isl_take isl_basic_set *bset,
1266 __isl_take isl_constraint *constraint);
1268 For example, to create a set containing the even integers
1269 between 10 and 42, you would use the following code.
1272 isl_local_space *ls;
1274 isl_basic_set *bset;
1276 space = isl_space_set_alloc(ctx, 0, 2);
1277 bset = isl_basic_set_universe(isl_space_copy(space));
1278 ls = isl_local_space_from_space(space);
1280 c = isl_equality_alloc(isl_local_space_copy(ls));
1281 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1282 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1283 bset = isl_basic_set_add_constraint(bset, c);
1285 c = isl_inequality_alloc(isl_local_space_copy(ls));
1286 c = isl_constraint_set_constant_si(c, -10);
1287 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1288 bset = isl_basic_set_add_constraint(bset, c);
1290 c = isl_inequality_alloc(ls);
1291 c = isl_constraint_set_constant_si(c, 42);
1292 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1293 bset = isl_basic_set_add_constraint(bset, c);
1295 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1299 isl_basic_set *bset;
1300 bset = isl_basic_set_read_from_str(ctx,
1301 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1303 A basic set or relation can also be constructed from two matrices
1304 describing the equalities and the inequalities.
1306 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1307 __isl_take isl_space *space,
1308 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1309 enum isl_dim_type c1,
1310 enum isl_dim_type c2, enum isl_dim_type c3,
1311 enum isl_dim_type c4);
1312 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1313 __isl_take isl_space *space,
1314 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1315 enum isl_dim_type c1,
1316 enum isl_dim_type c2, enum isl_dim_type c3,
1317 enum isl_dim_type c4, enum isl_dim_type c5);
1319 The C<isl_dim_type> arguments indicate the order in which
1320 different kinds of variables appear in the input matrices
1321 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1322 C<isl_dim_set> and C<isl_dim_div> for sets and
1323 of C<isl_dim_cst>, C<isl_dim_param>,
1324 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1326 A (basic or union) set or relation can also be constructed from a
1327 (union) (piecewise) (multiple) affine expression
1328 or a list of affine expressions
1329 (See L<"Piecewise Quasi Affine Expressions"> and
1330 L<"Piecewise Multiple Quasi Affine Expressions">).
1332 __isl_give isl_basic_map *isl_basic_map_from_aff(
1333 __isl_take isl_aff *aff);
1334 __isl_give isl_map *isl_map_from_aff(
1335 __isl_take isl_aff *aff);
1336 __isl_give isl_set *isl_set_from_pw_aff(
1337 __isl_take isl_pw_aff *pwaff);
1338 __isl_give isl_map *isl_map_from_pw_aff(
1339 __isl_take isl_pw_aff *pwaff);
1340 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1341 __isl_take isl_space *domain_space,
1342 __isl_take isl_aff_list *list);
1343 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1344 __isl_take isl_multi_aff *maff)
1345 __isl_give isl_map *isl_map_from_multi_aff(
1346 __isl_take isl_multi_aff *maff)
1347 __isl_give isl_set *isl_set_from_pw_multi_aff(
1348 __isl_take isl_pw_multi_aff *pma);
1349 __isl_give isl_map *isl_map_from_pw_multi_aff(
1350 __isl_take isl_pw_multi_aff *pma);
1351 __isl_give isl_union_map *
1352 isl_union_map_from_union_pw_multi_aff(
1353 __isl_take isl_union_pw_multi_aff *upma);
1355 The C<domain_dim> argument describes the domain of the resulting
1356 basic relation. It is required because the C<list> may consist
1357 of zero affine expressions.
1359 =head2 Inspecting Sets and Relations
1361 Usually, the user should not have to care about the actual constraints
1362 of the sets and maps, but should instead apply the abstract operations
1363 explained in the following sections.
1364 Occasionally, however, it may be required to inspect the individual
1365 coefficients of the constraints. This section explains how to do so.
1366 In these cases, it may also be useful to have C<isl> compute
1367 an explicit representation of the existentially quantified variables.
1369 __isl_give isl_set *isl_set_compute_divs(
1370 __isl_take isl_set *set);
1371 __isl_give isl_map *isl_map_compute_divs(
1372 __isl_take isl_map *map);
1373 __isl_give isl_union_set *isl_union_set_compute_divs(
1374 __isl_take isl_union_set *uset);
1375 __isl_give isl_union_map *isl_union_map_compute_divs(
1376 __isl_take isl_union_map *umap);
1378 This explicit representation defines the existentially quantified
1379 variables as integer divisions of the other variables, possibly
1380 including earlier existentially quantified variables.
1381 An explicitly represented existentially quantified variable therefore
1382 has a unique value when the values of the other variables are known.
1383 If, furthermore, the same existentials, i.e., existentials
1384 with the same explicit representations, should appear in the
1385 same order in each of the disjuncts of a set or map, then the user should call
1386 either of the following functions.
1388 __isl_give isl_set *isl_set_align_divs(
1389 __isl_take isl_set *set);
1390 __isl_give isl_map *isl_map_align_divs(
1391 __isl_take isl_map *map);
1393 Alternatively, the existentially quantified variables can be removed
1394 using the following functions, which compute an overapproximation.
1396 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1397 __isl_take isl_basic_set *bset);
1398 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1399 __isl_take isl_basic_map *bmap);
1400 __isl_give isl_set *isl_set_remove_divs(
1401 __isl_take isl_set *set);
1402 __isl_give isl_map *isl_map_remove_divs(
1403 __isl_take isl_map *map);
1405 To iterate over all the sets or maps in a union set or map, use
1407 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1408 int (*fn)(__isl_take isl_set *set, void *user),
1410 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1411 int (*fn)(__isl_take isl_map *map, void *user),
1414 The number of sets or maps in a union set or map can be obtained
1417 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1418 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1420 To extract the set or map in a given space from a union, use
1422 __isl_give isl_set *isl_union_set_extract_set(
1423 __isl_keep isl_union_set *uset,
1424 __isl_take isl_space *space);
1425 __isl_give isl_map *isl_union_map_extract_map(
1426 __isl_keep isl_union_map *umap,
1427 __isl_take isl_space *space);
1429 To iterate over all the basic sets or maps in a set or map, use
1431 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1432 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1434 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1435 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1438 The callback function C<fn> should return 0 if successful and
1439 -1 if an error occurs. In the latter case, or if any other error
1440 occurs, the above functions will return -1.
1442 It should be noted that C<isl> does not guarantee that
1443 the basic sets or maps passed to C<fn> are disjoint.
1444 If this is required, then the user should call one of
1445 the following functions first.
1447 __isl_give isl_set *isl_set_make_disjoint(
1448 __isl_take isl_set *set);
1449 __isl_give isl_map *isl_map_make_disjoint(
1450 __isl_take isl_map *map);
1452 The number of basic sets in a set can be obtained
1455 int isl_set_n_basic_set(__isl_keep isl_set *set);
1457 To iterate over the constraints of a basic set or map, use
1459 #include <isl/constraint.h>
1461 int isl_basic_set_n_constraint(
1462 __isl_keep isl_basic_set *bset);
1463 int isl_basic_set_foreach_constraint(
1464 __isl_keep isl_basic_set *bset,
1465 int (*fn)(__isl_take isl_constraint *c, void *user),
1467 int isl_basic_map_foreach_constraint(
1468 __isl_keep isl_basic_map *bmap,
1469 int (*fn)(__isl_take isl_constraint *c, void *user),
1471 void *isl_constraint_free(__isl_take isl_constraint *c);
1473 Again, the callback function C<fn> should return 0 if successful and
1474 -1 if an error occurs. In the latter case, or if any other error
1475 occurs, the above functions will return -1.
1476 The constraint C<c> represents either an equality or an inequality.
1477 Use the following function to find out whether a constraint
1478 represents an equality. If not, it represents an inequality.
1480 int isl_constraint_is_equality(
1481 __isl_keep isl_constraint *constraint);
1483 The coefficients of the constraints can be inspected using
1484 the following functions.
1486 int isl_constraint_is_lower_bound(
1487 __isl_keep isl_constraint *constraint,
1488 enum isl_dim_type type, unsigned pos);
1489 int isl_constraint_is_upper_bound(
1490 __isl_keep isl_constraint *constraint,
1491 enum isl_dim_type type, unsigned pos);
1492 void isl_constraint_get_constant(
1493 __isl_keep isl_constraint *constraint, isl_int *v);
1494 void isl_constraint_get_coefficient(
1495 __isl_keep isl_constraint *constraint,
1496 enum isl_dim_type type, int pos, isl_int *v);
1497 int isl_constraint_involves_dims(
1498 __isl_keep isl_constraint *constraint,
1499 enum isl_dim_type type, unsigned first, unsigned n);
1501 The explicit representations of the existentially quantified
1502 variables can be inspected using the following function.
1503 Note that the user is only allowed to use this function
1504 if the inspected set or map is the result of a call
1505 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1506 The existentially quantified variable is equal to the floor
1507 of the returned affine expression. The affine expression
1508 itself can be inspected using the functions in
1509 L<"Piecewise Quasi Affine Expressions">.
1511 __isl_give isl_aff *isl_constraint_get_div(
1512 __isl_keep isl_constraint *constraint, int pos);
1514 To obtain the constraints of a basic set or map in matrix
1515 form, use the following functions.
1517 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1518 __isl_keep isl_basic_set *bset,
1519 enum isl_dim_type c1, enum isl_dim_type c2,
1520 enum isl_dim_type c3, enum isl_dim_type c4);
1521 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1522 __isl_keep isl_basic_set *bset,
1523 enum isl_dim_type c1, enum isl_dim_type c2,
1524 enum isl_dim_type c3, enum isl_dim_type c4);
1525 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1526 __isl_keep isl_basic_map *bmap,
1527 enum isl_dim_type c1,
1528 enum isl_dim_type c2, enum isl_dim_type c3,
1529 enum isl_dim_type c4, enum isl_dim_type c5);
1530 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1531 __isl_keep isl_basic_map *bmap,
1532 enum isl_dim_type c1,
1533 enum isl_dim_type c2, enum isl_dim_type c3,
1534 enum isl_dim_type c4, enum isl_dim_type c5);
1536 The C<isl_dim_type> arguments dictate the order in which
1537 different kinds of variables appear in the resulting matrix
1538 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1539 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1541 The number of parameters, input, output or set dimensions can
1542 be obtained using the following functions.
1544 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1545 enum isl_dim_type type);
1546 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1547 enum isl_dim_type type);
1548 unsigned isl_set_dim(__isl_keep isl_set *set,
1549 enum isl_dim_type type);
1550 unsigned isl_map_dim(__isl_keep isl_map *map,
1551 enum isl_dim_type type);
1553 To check whether the description of a set or relation depends
1554 on one or more given dimensions, it is not necessary to iterate over all
1555 constraints. Instead the following functions can be used.
1557 int isl_basic_set_involves_dims(
1558 __isl_keep isl_basic_set *bset,
1559 enum isl_dim_type type, unsigned first, unsigned n);
1560 int isl_set_involves_dims(__isl_keep isl_set *set,
1561 enum isl_dim_type type, unsigned first, unsigned n);
1562 int isl_basic_map_involves_dims(
1563 __isl_keep isl_basic_map *bmap,
1564 enum isl_dim_type type, unsigned first, unsigned n);
1565 int isl_map_involves_dims(__isl_keep isl_map *map,
1566 enum isl_dim_type type, unsigned first, unsigned n);
1568 Similarly, the following functions can be used to check whether
1569 a given dimension is involved in any lower or upper bound.
1571 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1572 enum isl_dim_type type, unsigned pos);
1573 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1574 enum isl_dim_type type, unsigned pos);
1576 The identifiers or names of the domain and range spaces of a set
1577 or relation can be read off or set using the following functions.
1579 __isl_give isl_set *isl_set_set_tuple_id(
1580 __isl_take isl_set *set, __isl_take isl_id *id);
1581 __isl_give isl_set *isl_set_reset_tuple_id(
1582 __isl_take isl_set *set);
1583 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1584 __isl_give isl_id *isl_set_get_tuple_id(
1585 __isl_keep isl_set *set);
1586 __isl_give isl_map *isl_map_set_tuple_id(
1587 __isl_take isl_map *map, enum isl_dim_type type,
1588 __isl_take isl_id *id);
1589 __isl_give isl_map *isl_map_reset_tuple_id(
1590 __isl_take isl_map *map, enum isl_dim_type type);
1591 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1592 enum isl_dim_type type);
1593 __isl_give isl_id *isl_map_get_tuple_id(
1594 __isl_keep isl_map *map, enum isl_dim_type type);
1596 const char *isl_basic_set_get_tuple_name(
1597 __isl_keep isl_basic_set *bset);
1598 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1599 __isl_take isl_basic_set *set, const char *s);
1600 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1601 const char *isl_set_get_tuple_name(
1602 __isl_keep isl_set *set);
1603 const char *isl_basic_map_get_tuple_name(
1604 __isl_keep isl_basic_map *bmap,
1605 enum isl_dim_type type);
1606 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1607 __isl_take isl_basic_map *bmap,
1608 enum isl_dim_type type, const char *s);
1609 const char *isl_map_get_tuple_name(
1610 __isl_keep isl_map *map,
1611 enum isl_dim_type type);
1613 As with C<isl_space_get_tuple_name>, the value returned points to
1614 an internal data structure.
1615 The identifiers, positions or names of individual dimensions can be
1616 read off using the following functions.
1618 __isl_give isl_id *isl_basic_set_get_dim_id(
1619 __isl_keep isl_basic_set *bset,
1620 enum isl_dim_type type, unsigned pos);
1621 __isl_give isl_set *isl_set_set_dim_id(
1622 __isl_take isl_set *set, enum isl_dim_type type,
1623 unsigned pos, __isl_take isl_id *id);
1624 int isl_set_has_dim_id(__isl_keep isl_set *set,
1625 enum isl_dim_type type, unsigned pos);
1626 __isl_give isl_id *isl_set_get_dim_id(
1627 __isl_keep isl_set *set, enum isl_dim_type type,
1629 int isl_basic_map_has_dim_id(
1630 __isl_keep isl_basic_map *bmap,
1631 enum isl_dim_type type, unsigned pos);
1632 __isl_give isl_map *isl_map_set_dim_id(
1633 __isl_take isl_map *map, enum isl_dim_type type,
1634 unsigned pos, __isl_take isl_id *id);
1635 int isl_map_has_dim_id(__isl_keep isl_map *map,
1636 enum isl_dim_type type, unsigned pos);
1637 __isl_give isl_id *isl_map_get_dim_id(
1638 __isl_keep isl_map *map, enum isl_dim_type type,
1641 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1642 enum isl_dim_type type, __isl_keep isl_id *id);
1643 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1644 enum isl_dim_type type, __isl_keep isl_id *id);
1645 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1646 enum isl_dim_type type, const char *name);
1647 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1648 enum isl_dim_type type, const char *name);
1650 const char *isl_constraint_get_dim_name(
1651 __isl_keep isl_constraint *constraint,
1652 enum isl_dim_type type, unsigned pos);
1653 const char *isl_basic_set_get_dim_name(
1654 __isl_keep isl_basic_set *bset,
1655 enum isl_dim_type type, unsigned pos);
1656 int isl_set_has_dim_name(__isl_keep isl_set *set,
1657 enum isl_dim_type type, unsigned pos);
1658 const char *isl_set_get_dim_name(
1659 __isl_keep isl_set *set,
1660 enum isl_dim_type type, unsigned pos);
1661 const char *isl_basic_map_get_dim_name(
1662 __isl_keep isl_basic_map *bmap,
1663 enum isl_dim_type type, unsigned pos);
1664 int isl_map_has_dim_name(__isl_keep isl_map *map,
1665 enum isl_dim_type type, unsigned pos);
1666 const char *isl_map_get_dim_name(
1667 __isl_keep isl_map *map,
1668 enum isl_dim_type type, unsigned pos);
1670 These functions are mostly useful to obtain the identifiers, positions
1671 or names of the parameters. Identifiers of individual dimensions are
1672 essentially only useful for printing. They are ignored by all other
1673 operations and may not be preserved across those operations.
1677 =head3 Unary Properties
1683 The following functions test whether the given set or relation
1684 contains any integer points. The ``plain'' variants do not perform
1685 any computations, but simply check if the given set or relation
1686 is already known to be empty.
1688 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1689 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1690 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1691 int isl_set_is_empty(__isl_keep isl_set *set);
1692 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1693 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1694 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1695 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1696 int isl_map_is_empty(__isl_keep isl_map *map);
1697 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1699 =item * Universality
1701 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1702 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1703 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1705 =item * Single-valuedness
1707 int isl_basic_map_is_single_valued(
1708 __isl_keep isl_basic_map *bmap);
1709 int isl_map_plain_is_single_valued(
1710 __isl_keep isl_map *map);
1711 int isl_map_is_single_valued(__isl_keep isl_map *map);
1712 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1716 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1717 int isl_map_is_injective(__isl_keep isl_map *map);
1718 int isl_union_map_plain_is_injective(
1719 __isl_keep isl_union_map *umap);
1720 int isl_union_map_is_injective(
1721 __isl_keep isl_union_map *umap);
1725 int isl_map_is_bijective(__isl_keep isl_map *map);
1726 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1730 int isl_basic_map_plain_is_fixed(
1731 __isl_keep isl_basic_map *bmap,
1732 enum isl_dim_type type, unsigned pos,
1734 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1735 enum isl_dim_type type, unsigned pos,
1737 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1738 enum isl_dim_type type, unsigned pos,
1741 Check if the relation obviously lies on a hyperplane where the given dimension
1742 has a fixed value and if so, return that value in C<*val>.
1746 To check whether a set is a parameter domain, use this function:
1748 int isl_set_is_params(__isl_keep isl_set *set);
1749 int isl_union_set_is_params(
1750 __isl_keep isl_union_set *uset);
1754 The following functions check whether the domain of the given
1755 (basic) set is a wrapped relation.
1757 int isl_basic_set_is_wrapping(
1758 __isl_keep isl_basic_set *bset);
1759 int isl_set_is_wrapping(__isl_keep isl_set *set);
1761 =item * Internal Product
1763 int isl_basic_map_can_zip(
1764 __isl_keep isl_basic_map *bmap);
1765 int isl_map_can_zip(__isl_keep isl_map *map);
1767 Check whether the product of domain and range of the given relation
1769 i.e., whether both domain and range are nested relations.
1773 int isl_basic_map_can_curry(
1774 __isl_keep isl_basic_map *bmap);
1775 int isl_map_can_curry(__isl_keep isl_map *map);
1777 Check whether the domain of the (basic) relation is a wrapped relation.
1781 =head3 Binary Properties
1787 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1788 __isl_keep isl_set *set2);
1789 int isl_set_is_equal(__isl_keep isl_set *set1,
1790 __isl_keep isl_set *set2);
1791 int isl_union_set_is_equal(
1792 __isl_keep isl_union_set *uset1,
1793 __isl_keep isl_union_set *uset2);
1794 int isl_basic_map_is_equal(
1795 __isl_keep isl_basic_map *bmap1,
1796 __isl_keep isl_basic_map *bmap2);
1797 int isl_map_is_equal(__isl_keep isl_map *map1,
1798 __isl_keep isl_map *map2);
1799 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1800 __isl_keep isl_map *map2);
1801 int isl_union_map_is_equal(
1802 __isl_keep isl_union_map *umap1,
1803 __isl_keep isl_union_map *umap2);
1805 =item * Disjointness
1807 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1808 __isl_keep isl_set *set2);
1812 int isl_basic_set_is_subset(
1813 __isl_keep isl_basic_set *bset1,
1814 __isl_keep isl_basic_set *bset2);
1815 int isl_set_is_subset(__isl_keep isl_set *set1,
1816 __isl_keep isl_set *set2);
1817 int isl_set_is_strict_subset(
1818 __isl_keep isl_set *set1,
1819 __isl_keep isl_set *set2);
1820 int isl_union_set_is_subset(
1821 __isl_keep isl_union_set *uset1,
1822 __isl_keep isl_union_set *uset2);
1823 int isl_union_set_is_strict_subset(
1824 __isl_keep isl_union_set *uset1,
1825 __isl_keep isl_union_set *uset2);
1826 int isl_basic_map_is_subset(
1827 __isl_keep isl_basic_map *bmap1,
1828 __isl_keep isl_basic_map *bmap2);
1829 int isl_basic_map_is_strict_subset(
1830 __isl_keep isl_basic_map *bmap1,
1831 __isl_keep isl_basic_map *bmap2);
1832 int isl_map_is_subset(
1833 __isl_keep isl_map *map1,
1834 __isl_keep isl_map *map2);
1835 int isl_map_is_strict_subset(
1836 __isl_keep isl_map *map1,
1837 __isl_keep isl_map *map2);
1838 int isl_union_map_is_subset(
1839 __isl_keep isl_union_map *umap1,
1840 __isl_keep isl_union_map *umap2);
1841 int isl_union_map_is_strict_subset(
1842 __isl_keep isl_union_map *umap1,
1843 __isl_keep isl_union_map *umap2);
1845 Check whether the first argument is a (strict) subset of the
1850 =head2 Unary Operations
1856 __isl_give isl_set *isl_set_complement(
1857 __isl_take isl_set *set);
1858 __isl_give isl_map *isl_map_complement(
1859 __isl_take isl_map *map);
1863 __isl_give isl_basic_map *isl_basic_map_reverse(
1864 __isl_take isl_basic_map *bmap);
1865 __isl_give isl_map *isl_map_reverse(
1866 __isl_take isl_map *map);
1867 __isl_give isl_union_map *isl_union_map_reverse(
1868 __isl_take isl_union_map *umap);
1872 __isl_give isl_basic_set *isl_basic_set_project_out(
1873 __isl_take isl_basic_set *bset,
1874 enum isl_dim_type type, unsigned first, unsigned n);
1875 __isl_give isl_basic_map *isl_basic_map_project_out(
1876 __isl_take isl_basic_map *bmap,
1877 enum isl_dim_type type, unsigned first, unsigned n);
1878 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1879 enum isl_dim_type type, unsigned first, unsigned n);
1880 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1881 enum isl_dim_type type, unsigned first, unsigned n);
1882 __isl_give isl_basic_set *isl_basic_set_params(
1883 __isl_take isl_basic_set *bset);
1884 __isl_give isl_basic_set *isl_basic_map_domain(
1885 __isl_take isl_basic_map *bmap);
1886 __isl_give isl_basic_set *isl_basic_map_range(
1887 __isl_take isl_basic_map *bmap);
1888 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1889 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1890 __isl_give isl_set *isl_map_domain(
1891 __isl_take isl_map *bmap);
1892 __isl_give isl_set *isl_map_range(
1893 __isl_take isl_map *map);
1894 __isl_give isl_set *isl_union_set_params(
1895 __isl_take isl_union_set *uset);
1896 __isl_give isl_set *isl_union_map_params(
1897 __isl_take isl_union_map *umap);
1898 __isl_give isl_union_set *isl_union_map_domain(
1899 __isl_take isl_union_map *umap);
1900 __isl_give isl_union_set *isl_union_map_range(
1901 __isl_take isl_union_map *umap);
1903 __isl_give isl_basic_map *isl_basic_map_domain_map(
1904 __isl_take isl_basic_map *bmap);
1905 __isl_give isl_basic_map *isl_basic_map_range_map(
1906 __isl_take isl_basic_map *bmap);
1907 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1908 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1909 __isl_give isl_union_map *isl_union_map_domain_map(
1910 __isl_take isl_union_map *umap);
1911 __isl_give isl_union_map *isl_union_map_range_map(
1912 __isl_take isl_union_map *umap);
1914 The functions above construct a (basic, regular or union) relation
1915 that maps (a wrapped version of) the input relation to its domain or range.
1919 __isl_give isl_set *isl_set_eliminate(
1920 __isl_take isl_set *set, enum isl_dim_type type,
1921 unsigned first, unsigned n);
1922 __isl_give isl_basic_map *isl_basic_map_eliminate(
1923 __isl_take isl_basic_map *bmap,
1924 enum isl_dim_type type,
1925 unsigned first, unsigned n);
1926 __isl_give isl_map *isl_map_eliminate(
1927 __isl_take isl_map *map, enum isl_dim_type type,
1928 unsigned first, unsigned n);
1930 Eliminate the coefficients for the given dimensions from the constraints,
1931 without removing the dimensions.
1935 __isl_give isl_basic_set *isl_basic_set_fix(
1936 __isl_take isl_basic_set *bset,
1937 enum isl_dim_type type, unsigned pos,
1939 __isl_give isl_basic_set *isl_basic_set_fix_si(
1940 __isl_take isl_basic_set *bset,
1941 enum isl_dim_type type, unsigned pos, int value);
1942 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1943 enum isl_dim_type type, unsigned pos,
1945 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1946 enum isl_dim_type type, unsigned pos, int value);
1947 __isl_give isl_basic_map *isl_basic_map_fix_si(
1948 __isl_take isl_basic_map *bmap,
1949 enum isl_dim_type type, unsigned pos, int value);
1950 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1951 enum isl_dim_type type, unsigned pos, int value);
1953 Intersect the set or relation with the hyperplane where the given
1954 dimension has the fixed given value.
1956 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1957 __isl_take isl_basic_map *bmap,
1958 enum isl_dim_type type, unsigned pos, int value);
1959 __isl_give isl_set *isl_set_lower_bound(
1960 __isl_take isl_set *set,
1961 enum isl_dim_type type, unsigned pos,
1963 __isl_give isl_set *isl_set_lower_bound_si(
1964 __isl_take isl_set *set,
1965 enum isl_dim_type type, unsigned pos, int value);
1966 __isl_give isl_map *isl_map_lower_bound_si(
1967 __isl_take isl_map *map,
1968 enum isl_dim_type type, unsigned pos, int value);
1969 __isl_give isl_set *isl_set_upper_bound(
1970 __isl_take isl_set *set,
1971 enum isl_dim_type type, unsigned pos,
1973 __isl_give isl_set *isl_set_upper_bound_si(
1974 __isl_take isl_set *set,
1975 enum isl_dim_type type, unsigned pos, int value);
1976 __isl_give isl_map *isl_map_upper_bound_si(
1977 __isl_take isl_map *map,
1978 enum isl_dim_type type, unsigned pos, int value);
1980 Intersect the set or relation with the half-space where the given
1981 dimension has a value bounded by the fixed given value.
1983 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1984 enum isl_dim_type type1, int pos1,
1985 enum isl_dim_type type2, int pos2);
1986 __isl_give isl_basic_map *isl_basic_map_equate(
1987 __isl_take isl_basic_map *bmap,
1988 enum isl_dim_type type1, int pos1,
1989 enum isl_dim_type type2, int pos2);
1990 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1991 enum isl_dim_type type1, int pos1,
1992 enum isl_dim_type type2, int pos2);
1994 Intersect the set or relation with the hyperplane where the given
1995 dimensions are equal to each other.
1997 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1998 enum isl_dim_type type1, int pos1,
1999 enum isl_dim_type type2, int pos2);
2001 Intersect the relation with the hyperplane where the given
2002 dimensions have opposite values.
2004 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2005 enum isl_dim_type type1, int pos1,
2006 enum isl_dim_type type2, int pos2);
2007 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2008 enum isl_dim_type type1, int pos1,
2009 enum isl_dim_type type2, int pos2);
2011 Intersect the relation with the half-space where the given
2012 dimensions satisfy the given ordering.
2016 __isl_give isl_map *isl_set_identity(
2017 __isl_take isl_set *set);
2018 __isl_give isl_union_map *isl_union_set_identity(
2019 __isl_take isl_union_set *uset);
2021 Construct an identity relation on the given (union) set.
2025 __isl_give isl_basic_set *isl_basic_map_deltas(
2026 __isl_take isl_basic_map *bmap);
2027 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2028 __isl_give isl_union_set *isl_union_map_deltas(
2029 __isl_take isl_union_map *umap);
2031 These functions return a (basic) set containing the differences
2032 between image elements and corresponding domain elements in the input.
2034 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2035 __isl_take isl_basic_map *bmap);
2036 __isl_give isl_map *isl_map_deltas_map(
2037 __isl_take isl_map *map);
2038 __isl_give isl_union_map *isl_union_map_deltas_map(
2039 __isl_take isl_union_map *umap);
2041 The functions above construct a (basic, regular or union) relation
2042 that maps (a wrapped version of) the input relation to its delta set.
2046 Simplify the representation of a set or relation by trying
2047 to combine pairs of basic sets or relations into a single
2048 basic set or relation.
2050 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2051 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2052 __isl_give isl_union_set *isl_union_set_coalesce(
2053 __isl_take isl_union_set *uset);
2054 __isl_give isl_union_map *isl_union_map_coalesce(
2055 __isl_take isl_union_map *umap);
2057 One of the methods for combining pairs of basic sets or relations
2058 can result in coefficients that are much larger than those that appear
2059 in the constraints of the input. By default, the coefficients are
2060 not allowed to grow larger, but this can be changed by unsetting
2061 the following option.
2063 int isl_options_set_coalesce_bounded_wrapping(
2064 isl_ctx *ctx, int val);
2065 int isl_options_get_coalesce_bounded_wrapping(
2068 =item * Detecting equalities
2070 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2071 __isl_take isl_basic_set *bset);
2072 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2073 __isl_take isl_basic_map *bmap);
2074 __isl_give isl_set *isl_set_detect_equalities(
2075 __isl_take isl_set *set);
2076 __isl_give isl_map *isl_map_detect_equalities(
2077 __isl_take isl_map *map);
2078 __isl_give isl_union_set *isl_union_set_detect_equalities(
2079 __isl_take isl_union_set *uset);
2080 __isl_give isl_union_map *isl_union_map_detect_equalities(
2081 __isl_take isl_union_map *umap);
2083 Simplify the representation of a set or relation by detecting implicit
2086 =item * Removing redundant constraints
2088 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2089 __isl_take isl_basic_set *bset);
2090 __isl_give isl_set *isl_set_remove_redundancies(
2091 __isl_take isl_set *set);
2092 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2093 __isl_take isl_basic_map *bmap);
2094 __isl_give isl_map *isl_map_remove_redundancies(
2095 __isl_take isl_map *map);
2099 __isl_give isl_basic_set *isl_set_convex_hull(
2100 __isl_take isl_set *set);
2101 __isl_give isl_basic_map *isl_map_convex_hull(
2102 __isl_take isl_map *map);
2104 If the input set or relation has any existentially quantified
2105 variables, then the result of these operations is currently undefined.
2109 __isl_give isl_basic_set *isl_set_simple_hull(
2110 __isl_take isl_set *set);
2111 __isl_give isl_basic_map *isl_map_simple_hull(
2112 __isl_take isl_map *map);
2113 __isl_give isl_union_map *isl_union_map_simple_hull(
2114 __isl_take isl_union_map *umap);
2116 These functions compute a single basic set or relation
2117 that contains the whole input set or relation.
2118 In particular, the output is described by translates
2119 of the constraints describing the basic sets or relations in the input.
2123 (See \autoref{s:simple hull}.)
2129 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2130 __isl_take isl_basic_set *bset);
2131 __isl_give isl_basic_set *isl_set_affine_hull(
2132 __isl_take isl_set *set);
2133 __isl_give isl_union_set *isl_union_set_affine_hull(
2134 __isl_take isl_union_set *uset);
2135 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2136 __isl_take isl_basic_map *bmap);
2137 __isl_give isl_basic_map *isl_map_affine_hull(
2138 __isl_take isl_map *map);
2139 __isl_give isl_union_map *isl_union_map_affine_hull(
2140 __isl_take isl_union_map *umap);
2142 In case of union sets and relations, the affine hull is computed
2145 =item * Polyhedral hull
2147 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2148 __isl_take isl_set *set);
2149 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2150 __isl_take isl_map *map);
2151 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2152 __isl_take isl_union_set *uset);
2153 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2154 __isl_take isl_union_map *umap);
2156 These functions compute a single basic set or relation
2157 not involving any existentially quantified variables
2158 that contains the whole input set or relation.
2159 In case of union sets and relations, the polyhedral hull is computed
2164 __isl_give isl_basic_set *isl_basic_set_sample(
2165 __isl_take isl_basic_set *bset);
2166 __isl_give isl_basic_set *isl_set_sample(
2167 __isl_take isl_set *set);
2168 __isl_give isl_basic_map *isl_basic_map_sample(
2169 __isl_take isl_basic_map *bmap);
2170 __isl_give isl_basic_map *isl_map_sample(
2171 __isl_take isl_map *map);
2173 If the input (basic) set or relation is non-empty, then return
2174 a singleton subset of the input. Otherwise, return an empty set.
2176 =item * Optimization
2178 #include <isl/ilp.h>
2179 enum isl_lp_result isl_basic_set_max(
2180 __isl_keep isl_basic_set *bset,
2181 __isl_keep isl_aff *obj, isl_int *opt)
2182 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2183 __isl_keep isl_aff *obj, isl_int *opt);
2184 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2185 __isl_keep isl_aff *obj, isl_int *opt);
2187 Compute the minimum or maximum of the integer affine expression C<obj>
2188 over the points in C<set>, returning the result in C<opt>.
2189 The return value may be one of C<isl_lp_error>,
2190 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2192 =item * Parametric optimization
2194 __isl_give isl_pw_aff *isl_set_dim_min(
2195 __isl_take isl_set *set, int pos);
2196 __isl_give isl_pw_aff *isl_set_dim_max(
2197 __isl_take isl_set *set, int pos);
2198 __isl_give isl_pw_aff *isl_map_dim_max(
2199 __isl_take isl_map *map, int pos);
2201 Compute the minimum or maximum of the given set or output dimension
2202 as a function of the parameters (and input dimensions), but independently
2203 of the other set or output dimensions.
2204 For lexicographic optimization, see L<"Lexicographic Optimization">.
2208 The following functions compute either the set of (rational) coefficient
2209 values of valid constraints for the given set or the set of (rational)
2210 values satisfying the constraints with coefficients from the given set.
2211 Internally, these two sets of functions perform essentially the
2212 same operations, except that the set of coefficients is assumed to
2213 be a cone, while the set of values may be any polyhedron.
2214 The current implementation is based on the Farkas lemma and
2215 Fourier-Motzkin elimination, but this may change or be made optional
2216 in future. In particular, future implementations may use different
2217 dualization algorithms or skip the elimination step.
2219 __isl_give isl_basic_set *isl_basic_set_coefficients(
2220 __isl_take isl_basic_set *bset);
2221 __isl_give isl_basic_set *isl_set_coefficients(
2222 __isl_take isl_set *set);
2223 __isl_give isl_union_set *isl_union_set_coefficients(
2224 __isl_take isl_union_set *bset);
2225 __isl_give isl_basic_set *isl_basic_set_solutions(
2226 __isl_take isl_basic_set *bset);
2227 __isl_give isl_basic_set *isl_set_solutions(
2228 __isl_take isl_set *set);
2229 __isl_give isl_union_set *isl_union_set_solutions(
2230 __isl_take isl_union_set *bset);
2234 __isl_give isl_map *isl_map_fixed_power(
2235 __isl_take isl_map *map, isl_int exp);
2236 __isl_give isl_union_map *isl_union_map_fixed_power(
2237 __isl_take isl_union_map *umap, isl_int exp);
2239 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2240 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2241 of C<map> is computed.
2243 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2245 __isl_give isl_union_map *isl_union_map_power(
2246 __isl_take isl_union_map *umap, int *exact);
2248 Compute a parametric representation for all positive powers I<k> of C<map>.
2249 The result maps I<k> to a nested relation corresponding to the
2250 I<k>th power of C<map>.
2251 The result may be an overapproximation. If the result is known to be exact,
2252 then C<*exact> is set to C<1>.
2254 =item * Transitive closure
2256 __isl_give isl_map *isl_map_transitive_closure(
2257 __isl_take isl_map *map, int *exact);
2258 __isl_give isl_union_map *isl_union_map_transitive_closure(
2259 __isl_take isl_union_map *umap, int *exact);
2261 Compute the transitive closure of C<map>.
2262 The result may be an overapproximation. If the result is known to be exact,
2263 then C<*exact> is set to C<1>.
2265 =item * Reaching path lengths
2267 __isl_give isl_map *isl_map_reaching_path_lengths(
2268 __isl_take isl_map *map, int *exact);
2270 Compute a relation that maps each element in the range of C<map>
2271 to the lengths of all paths composed of edges in C<map> that
2272 end up in the given element.
2273 The result may be an overapproximation. If the result is known to be exact,
2274 then C<*exact> is set to C<1>.
2275 To compute the I<maximal> path length, the resulting relation
2276 should be postprocessed by C<isl_map_lexmax>.
2277 In particular, if the input relation is a dependence relation
2278 (mapping sources to sinks), then the maximal path length corresponds
2279 to the free schedule.
2280 Note, however, that C<isl_map_lexmax> expects the maximum to be
2281 finite, so if the path lengths are unbounded (possibly due to
2282 the overapproximation), then you will get an error message.
2286 __isl_give isl_basic_set *isl_basic_map_wrap(
2287 __isl_take isl_basic_map *bmap);
2288 __isl_give isl_set *isl_map_wrap(
2289 __isl_take isl_map *map);
2290 __isl_give isl_union_set *isl_union_map_wrap(
2291 __isl_take isl_union_map *umap);
2292 __isl_give isl_basic_map *isl_basic_set_unwrap(
2293 __isl_take isl_basic_set *bset);
2294 __isl_give isl_map *isl_set_unwrap(
2295 __isl_take isl_set *set);
2296 __isl_give isl_union_map *isl_union_set_unwrap(
2297 __isl_take isl_union_set *uset);
2301 Remove any internal structure of domain (and range) of the given
2302 set or relation. If there is any such internal structure in the input,
2303 then the name of the space is also removed.
2305 __isl_give isl_basic_set *isl_basic_set_flatten(
2306 __isl_take isl_basic_set *bset);
2307 __isl_give isl_set *isl_set_flatten(
2308 __isl_take isl_set *set);
2309 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2310 __isl_take isl_basic_map *bmap);
2311 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2312 __isl_take isl_basic_map *bmap);
2313 __isl_give isl_map *isl_map_flatten_range(
2314 __isl_take isl_map *map);
2315 __isl_give isl_map *isl_map_flatten_domain(
2316 __isl_take isl_map *map);
2317 __isl_give isl_basic_map *isl_basic_map_flatten(
2318 __isl_take isl_basic_map *bmap);
2319 __isl_give isl_map *isl_map_flatten(
2320 __isl_take isl_map *map);
2322 __isl_give isl_map *isl_set_flatten_map(
2323 __isl_take isl_set *set);
2325 The function above constructs a relation
2326 that maps the input set to a flattened version of the set.
2330 Lift the input set to a space with extra dimensions corresponding
2331 to the existentially quantified variables in the input.
2332 In particular, the result lives in a wrapped map where the domain
2333 is the original space and the range corresponds to the original
2334 existentially quantified variables.
2336 __isl_give isl_basic_set *isl_basic_set_lift(
2337 __isl_take isl_basic_set *bset);
2338 __isl_give isl_set *isl_set_lift(
2339 __isl_take isl_set *set);
2340 __isl_give isl_union_set *isl_union_set_lift(
2341 __isl_take isl_union_set *uset);
2343 Given a local space that contains the existentially quantified
2344 variables of a set, a basic relation that, when applied to
2345 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2346 can be constructed using the following function.
2348 #include <isl/local_space.h>
2349 __isl_give isl_basic_map *isl_local_space_lifting(
2350 __isl_take isl_local_space *ls);
2352 =item * Internal Product
2354 __isl_give isl_basic_map *isl_basic_map_zip(
2355 __isl_take isl_basic_map *bmap);
2356 __isl_give isl_map *isl_map_zip(
2357 __isl_take isl_map *map);
2358 __isl_give isl_union_map *isl_union_map_zip(
2359 __isl_take isl_union_map *umap);
2361 Given a relation with nested relations for domain and range,
2362 interchange the range of the domain with the domain of the range.
2366 __isl_give isl_basic_map *isl_basic_map_curry(
2367 __isl_take isl_basic_map *bmap);
2368 __isl_give isl_map *isl_map_curry(
2369 __isl_take isl_map *map);
2370 __isl_give isl_union_map *isl_union_map_curry(
2371 __isl_take isl_union_map *umap);
2373 Given a relation with a nested relation for domain,
2374 move the range of the nested relation out of the domain
2375 and use it as the domain of a nested relation in the range,
2376 with the original range as range of this nested relation.
2378 =item * Aligning parameters
2380 __isl_give isl_basic_set *isl_basic_set_align_params(
2381 __isl_take isl_basic_set *bset,
2382 __isl_take isl_space *model);
2383 __isl_give isl_set *isl_set_align_params(
2384 __isl_take isl_set *set,
2385 __isl_take isl_space *model);
2386 __isl_give isl_basic_map *isl_basic_map_align_params(
2387 __isl_take isl_basic_map *bmap,
2388 __isl_take isl_space *model);
2389 __isl_give isl_map *isl_map_align_params(
2390 __isl_take isl_map *map,
2391 __isl_take isl_space *model);
2393 Change the order of the parameters of the given set or relation
2394 such that the first parameters match those of C<model>.
2395 This may involve the introduction of extra parameters.
2396 All parameters need to be named.
2398 =item * Dimension manipulation
2400 __isl_give isl_set *isl_set_add_dims(
2401 __isl_take isl_set *set,
2402 enum isl_dim_type type, unsigned n);
2403 __isl_give isl_map *isl_map_add_dims(
2404 __isl_take isl_map *map,
2405 enum isl_dim_type type, unsigned n);
2406 __isl_give isl_set *isl_set_insert_dims(
2407 __isl_take isl_set *set,
2408 enum isl_dim_type type, unsigned pos, unsigned n);
2409 __isl_give isl_map *isl_map_insert_dims(
2410 __isl_take isl_map *map,
2411 enum isl_dim_type type, unsigned pos, unsigned n);
2412 __isl_give isl_basic_set *isl_basic_set_move_dims(
2413 __isl_take isl_basic_set *bset,
2414 enum isl_dim_type dst_type, unsigned dst_pos,
2415 enum isl_dim_type src_type, unsigned src_pos,
2417 __isl_give isl_basic_map *isl_basic_map_move_dims(
2418 __isl_take isl_basic_map *bmap,
2419 enum isl_dim_type dst_type, unsigned dst_pos,
2420 enum isl_dim_type src_type, unsigned src_pos,
2422 __isl_give isl_set *isl_set_move_dims(
2423 __isl_take isl_set *set,
2424 enum isl_dim_type dst_type, unsigned dst_pos,
2425 enum isl_dim_type src_type, unsigned src_pos,
2427 __isl_give isl_map *isl_map_move_dims(
2428 __isl_take isl_map *map,
2429 enum isl_dim_type dst_type, unsigned dst_pos,
2430 enum isl_dim_type src_type, unsigned src_pos,
2433 It is usually not advisable to directly change the (input or output)
2434 space of a set or a relation as this removes the name and the internal
2435 structure of the space. However, the above functions can be useful
2436 to add new parameters, assuming
2437 C<isl_set_align_params> and C<isl_map_align_params>
2442 =head2 Binary Operations
2444 The two arguments of a binary operation not only need to live
2445 in the same C<isl_ctx>, they currently also need to have
2446 the same (number of) parameters.
2448 =head3 Basic Operations
2452 =item * Intersection
2454 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2455 __isl_take isl_basic_set *bset1,
2456 __isl_take isl_basic_set *bset2);
2457 __isl_give isl_basic_set *isl_basic_set_intersect(
2458 __isl_take isl_basic_set *bset1,
2459 __isl_take isl_basic_set *bset2);
2460 __isl_give isl_set *isl_set_intersect_params(
2461 __isl_take isl_set *set,
2462 __isl_take isl_set *params);
2463 __isl_give isl_set *isl_set_intersect(
2464 __isl_take isl_set *set1,
2465 __isl_take isl_set *set2);
2466 __isl_give isl_union_set *isl_union_set_intersect_params(
2467 __isl_take isl_union_set *uset,
2468 __isl_take isl_set *set);
2469 __isl_give isl_union_map *isl_union_map_intersect_params(
2470 __isl_take isl_union_map *umap,
2471 __isl_take isl_set *set);
2472 __isl_give isl_union_set *isl_union_set_intersect(
2473 __isl_take isl_union_set *uset1,
2474 __isl_take isl_union_set *uset2);
2475 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2476 __isl_take isl_basic_map *bmap,
2477 __isl_take isl_basic_set *bset);
2478 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2479 __isl_take isl_basic_map *bmap,
2480 __isl_take isl_basic_set *bset);
2481 __isl_give isl_basic_map *isl_basic_map_intersect(
2482 __isl_take isl_basic_map *bmap1,
2483 __isl_take isl_basic_map *bmap2);
2484 __isl_give isl_map *isl_map_intersect_params(
2485 __isl_take isl_map *map,
2486 __isl_take isl_set *params);
2487 __isl_give isl_map *isl_map_intersect_domain(
2488 __isl_take isl_map *map,
2489 __isl_take isl_set *set);
2490 __isl_give isl_map *isl_map_intersect_range(
2491 __isl_take isl_map *map,
2492 __isl_take isl_set *set);
2493 __isl_give isl_map *isl_map_intersect(
2494 __isl_take isl_map *map1,
2495 __isl_take isl_map *map2);
2496 __isl_give isl_union_map *isl_union_map_intersect_domain(
2497 __isl_take isl_union_map *umap,
2498 __isl_take isl_union_set *uset);
2499 __isl_give isl_union_map *isl_union_map_intersect_range(
2500 __isl_take isl_union_map *umap,
2501 __isl_take isl_union_set *uset);
2502 __isl_give isl_union_map *isl_union_map_intersect(
2503 __isl_take isl_union_map *umap1,
2504 __isl_take isl_union_map *umap2);
2506 The second argument to the C<_params> functions needs to be
2507 a parametric (basic) set. For the other functions, a parametric set
2508 for either argument is only allowed if the other argument is
2509 a parametric set as well.
2513 __isl_give isl_set *isl_basic_set_union(
2514 __isl_take isl_basic_set *bset1,
2515 __isl_take isl_basic_set *bset2);
2516 __isl_give isl_map *isl_basic_map_union(
2517 __isl_take isl_basic_map *bmap1,
2518 __isl_take isl_basic_map *bmap2);
2519 __isl_give isl_set *isl_set_union(
2520 __isl_take isl_set *set1,
2521 __isl_take isl_set *set2);
2522 __isl_give isl_map *isl_map_union(
2523 __isl_take isl_map *map1,
2524 __isl_take isl_map *map2);
2525 __isl_give isl_union_set *isl_union_set_union(
2526 __isl_take isl_union_set *uset1,
2527 __isl_take isl_union_set *uset2);
2528 __isl_give isl_union_map *isl_union_map_union(
2529 __isl_take isl_union_map *umap1,
2530 __isl_take isl_union_map *umap2);
2532 =item * Set difference
2534 __isl_give isl_set *isl_set_subtract(
2535 __isl_take isl_set *set1,
2536 __isl_take isl_set *set2);
2537 __isl_give isl_map *isl_map_subtract(
2538 __isl_take isl_map *map1,
2539 __isl_take isl_map *map2);
2540 __isl_give isl_map *isl_map_subtract_domain(
2541 __isl_take isl_map *map,
2542 __isl_take isl_set *dom);
2543 __isl_give isl_map *isl_map_subtract_range(
2544 __isl_take isl_map *map,
2545 __isl_take isl_set *dom);
2546 __isl_give isl_union_set *isl_union_set_subtract(
2547 __isl_take isl_union_set *uset1,
2548 __isl_take isl_union_set *uset2);
2549 __isl_give isl_union_map *isl_union_map_subtract(
2550 __isl_take isl_union_map *umap1,
2551 __isl_take isl_union_map *umap2);
2555 __isl_give isl_basic_set *isl_basic_set_apply(
2556 __isl_take isl_basic_set *bset,
2557 __isl_take isl_basic_map *bmap);
2558 __isl_give isl_set *isl_set_apply(
2559 __isl_take isl_set *set,
2560 __isl_take isl_map *map);
2561 __isl_give isl_union_set *isl_union_set_apply(
2562 __isl_take isl_union_set *uset,
2563 __isl_take isl_union_map *umap);
2564 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2565 __isl_take isl_basic_map *bmap1,
2566 __isl_take isl_basic_map *bmap2);
2567 __isl_give isl_basic_map *isl_basic_map_apply_range(
2568 __isl_take isl_basic_map *bmap1,
2569 __isl_take isl_basic_map *bmap2);
2570 __isl_give isl_map *isl_map_apply_domain(
2571 __isl_take isl_map *map1,
2572 __isl_take isl_map *map2);
2573 __isl_give isl_union_map *isl_union_map_apply_domain(
2574 __isl_take isl_union_map *umap1,
2575 __isl_take isl_union_map *umap2);
2576 __isl_give isl_map *isl_map_apply_range(
2577 __isl_take isl_map *map1,
2578 __isl_take isl_map *map2);
2579 __isl_give isl_union_map *isl_union_map_apply_range(
2580 __isl_take isl_union_map *umap1,
2581 __isl_take isl_union_map *umap2);
2583 =item * Cartesian Product
2585 __isl_give isl_set *isl_set_product(
2586 __isl_take isl_set *set1,
2587 __isl_take isl_set *set2);
2588 __isl_give isl_union_set *isl_union_set_product(
2589 __isl_take isl_union_set *uset1,
2590 __isl_take isl_union_set *uset2);
2591 __isl_give isl_basic_map *isl_basic_map_domain_product(
2592 __isl_take isl_basic_map *bmap1,
2593 __isl_take isl_basic_map *bmap2);
2594 __isl_give isl_basic_map *isl_basic_map_range_product(
2595 __isl_take isl_basic_map *bmap1,
2596 __isl_take isl_basic_map *bmap2);
2597 __isl_give isl_basic_map *isl_basic_map_product(
2598 __isl_take isl_basic_map *bmap1,
2599 __isl_take isl_basic_map *bmap2);
2600 __isl_give isl_map *isl_map_domain_product(
2601 __isl_take isl_map *map1,
2602 __isl_take isl_map *map2);
2603 __isl_give isl_map *isl_map_range_product(
2604 __isl_take isl_map *map1,
2605 __isl_take isl_map *map2);
2606 __isl_give isl_union_map *isl_union_map_domain_product(
2607 __isl_take isl_union_map *umap1,
2608 __isl_take isl_union_map *umap2);
2609 __isl_give isl_union_map *isl_union_map_range_product(
2610 __isl_take isl_union_map *umap1,
2611 __isl_take isl_union_map *umap2);
2612 __isl_give isl_map *isl_map_product(
2613 __isl_take isl_map *map1,
2614 __isl_take isl_map *map2);
2615 __isl_give isl_union_map *isl_union_map_product(
2616 __isl_take isl_union_map *umap1,
2617 __isl_take isl_union_map *umap2);
2619 The above functions compute the cross product of the given
2620 sets or relations. The domains and ranges of the results
2621 are wrapped maps between domains and ranges of the inputs.
2622 To obtain a ``flat'' product, use the following functions
2625 __isl_give isl_basic_set *isl_basic_set_flat_product(
2626 __isl_take isl_basic_set *bset1,
2627 __isl_take isl_basic_set *bset2);
2628 __isl_give isl_set *isl_set_flat_product(
2629 __isl_take isl_set *set1,
2630 __isl_take isl_set *set2);
2631 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2632 __isl_take isl_basic_map *bmap1,
2633 __isl_take isl_basic_map *bmap2);
2634 __isl_give isl_map *isl_map_flat_domain_product(
2635 __isl_take isl_map *map1,
2636 __isl_take isl_map *map2);
2637 __isl_give isl_map *isl_map_flat_range_product(
2638 __isl_take isl_map *map1,
2639 __isl_take isl_map *map2);
2640 __isl_give isl_union_map *isl_union_map_flat_range_product(
2641 __isl_take isl_union_map *umap1,
2642 __isl_take isl_union_map *umap2);
2643 __isl_give isl_basic_map *isl_basic_map_flat_product(
2644 __isl_take isl_basic_map *bmap1,
2645 __isl_take isl_basic_map *bmap2);
2646 __isl_give isl_map *isl_map_flat_product(
2647 __isl_take isl_map *map1,
2648 __isl_take isl_map *map2);
2650 =item * Simplification
2652 __isl_give isl_basic_set *isl_basic_set_gist(
2653 __isl_take isl_basic_set *bset,
2654 __isl_take isl_basic_set *context);
2655 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2656 __isl_take isl_set *context);
2657 __isl_give isl_set *isl_set_gist_params(
2658 __isl_take isl_set *set,
2659 __isl_take isl_set *context);
2660 __isl_give isl_union_set *isl_union_set_gist(
2661 __isl_take isl_union_set *uset,
2662 __isl_take isl_union_set *context);
2663 __isl_give isl_union_set *isl_union_set_gist_params(
2664 __isl_take isl_union_set *uset,
2665 __isl_take isl_set *set);
2666 __isl_give isl_basic_map *isl_basic_map_gist(
2667 __isl_take isl_basic_map *bmap,
2668 __isl_take isl_basic_map *context);
2669 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2670 __isl_take isl_map *context);
2671 __isl_give isl_map *isl_map_gist_params(
2672 __isl_take isl_map *map,
2673 __isl_take isl_set *context);
2674 __isl_give isl_map *isl_map_gist_domain(
2675 __isl_take isl_map *map,
2676 __isl_take isl_set *context);
2677 __isl_give isl_map *isl_map_gist_range(
2678 __isl_take isl_map *map,
2679 __isl_take isl_set *context);
2680 __isl_give isl_union_map *isl_union_map_gist(
2681 __isl_take isl_union_map *umap,
2682 __isl_take isl_union_map *context);
2683 __isl_give isl_union_map *isl_union_map_gist_params(
2684 __isl_take isl_union_map *umap,
2685 __isl_take isl_set *set);
2686 __isl_give isl_union_map *isl_union_map_gist_domain(
2687 __isl_take isl_union_map *umap,
2688 __isl_take isl_union_set *uset);
2689 __isl_give isl_union_map *isl_union_map_gist_range(
2690 __isl_take isl_union_map *umap,
2691 __isl_take isl_union_set *uset);
2693 The gist operation returns a set or relation that has the
2694 same intersection with the context as the input set or relation.
2695 Any implicit equality in the intersection is made explicit in the result,
2696 while all inequalities that are redundant with respect to the intersection
2698 In case of union sets and relations, the gist operation is performed
2703 =head3 Lexicographic Optimization
2705 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2706 the following functions
2707 compute a set that contains the lexicographic minimum or maximum
2708 of the elements in C<set> (or C<bset>) for those values of the parameters
2709 that satisfy C<dom>.
2710 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2711 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2713 In other words, the union of the parameter values
2714 for which the result is non-empty and of C<*empty>
2717 __isl_give isl_set *isl_basic_set_partial_lexmin(
2718 __isl_take isl_basic_set *bset,
2719 __isl_take isl_basic_set *dom,
2720 __isl_give isl_set **empty);
2721 __isl_give isl_set *isl_basic_set_partial_lexmax(
2722 __isl_take isl_basic_set *bset,
2723 __isl_take isl_basic_set *dom,
2724 __isl_give isl_set **empty);
2725 __isl_give isl_set *isl_set_partial_lexmin(
2726 __isl_take isl_set *set, __isl_take isl_set *dom,
2727 __isl_give isl_set **empty);
2728 __isl_give isl_set *isl_set_partial_lexmax(
2729 __isl_take isl_set *set, __isl_take isl_set *dom,
2730 __isl_give isl_set **empty);
2732 Given a (basic) set C<set> (or C<bset>), the following functions simply
2733 return a set containing the lexicographic minimum or maximum
2734 of the elements in C<set> (or C<bset>).
2735 In case of union sets, the optimum is computed per space.
2737 __isl_give isl_set *isl_basic_set_lexmin(
2738 __isl_take isl_basic_set *bset);
2739 __isl_give isl_set *isl_basic_set_lexmax(
2740 __isl_take isl_basic_set *bset);
2741 __isl_give isl_set *isl_set_lexmin(
2742 __isl_take isl_set *set);
2743 __isl_give isl_set *isl_set_lexmax(
2744 __isl_take isl_set *set);
2745 __isl_give isl_union_set *isl_union_set_lexmin(
2746 __isl_take isl_union_set *uset);
2747 __isl_give isl_union_set *isl_union_set_lexmax(
2748 __isl_take isl_union_set *uset);
2750 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2751 the following functions
2752 compute a relation that maps each element of C<dom>
2753 to the single lexicographic minimum or maximum
2754 of the elements that are associated to that same
2755 element in C<map> (or C<bmap>).
2756 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2757 that contains the elements in C<dom> that do not map
2758 to any elements in C<map> (or C<bmap>).
2759 In other words, the union of the domain of the result and of C<*empty>
2762 __isl_give isl_map *isl_basic_map_partial_lexmax(
2763 __isl_take isl_basic_map *bmap,
2764 __isl_take isl_basic_set *dom,
2765 __isl_give isl_set **empty);
2766 __isl_give isl_map *isl_basic_map_partial_lexmin(
2767 __isl_take isl_basic_map *bmap,
2768 __isl_take isl_basic_set *dom,
2769 __isl_give isl_set **empty);
2770 __isl_give isl_map *isl_map_partial_lexmax(
2771 __isl_take isl_map *map, __isl_take isl_set *dom,
2772 __isl_give isl_set **empty);
2773 __isl_give isl_map *isl_map_partial_lexmin(
2774 __isl_take isl_map *map, __isl_take isl_set *dom,
2775 __isl_give isl_set **empty);
2777 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2778 return a map mapping each element in the domain of
2779 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2780 of all elements associated to that element.
2781 In case of union relations, the optimum is computed per space.
2783 __isl_give isl_map *isl_basic_map_lexmin(
2784 __isl_take isl_basic_map *bmap);
2785 __isl_give isl_map *isl_basic_map_lexmax(
2786 __isl_take isl_basic_map *bmap);
2787 __isl_give isl_map *isl_map_lexmin(
2788 __isl_take isl_map *map);
2789 __isl_give isl_map *isl_map_lexmax(
2790 __isl_take isl_map *map);
2791 __isl_give isl_union_map *isl_union_map_lexmin(
2792 __isl_take isl_union_map *umap);
2793 __isl_give isl_union_map *isl_union_map_lexmax(
2794 __isl_take isl_union_map *umap);
2796 The following functions return their result in the form of
2797 a piecewise multi-affine expression
2798 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2799 but are otherwise equivalent to the corresponding functions
2800 returning a basic set or relation.
2802 __isl_give isl_pw_multi_aff *
2803 isl_basic_map_lexmin_pw_multi_aff(
2804 __isl_take isl_basic_map *bmap);
2805 __isl_give isl_pw_multi_aff *
2806 isl_basic_set_partial_lexmin_pw_multi_aff(
2807 __isl_take isl_basic_set *bset,
2808 __isl_take isl_basic_set *dom,
2809 __isl_give isl_set **empty);
2810 __isl_give isl_pw_multi_aff *
2811 isl_basic_set_partial_lexmax_pw_multi_aff(
2812 __isl_take isl_basic_set *bset,
2813 __isl_take isl_basic_set *dom,
2814 __isl_give isl_set **empty);
2815 __isl_give isl_pw_multi_aff *
2816 isl_basic_map_partial_lexmin_pw_multi_aff(
2817 __isl_take isl_basic_map *bmap,
2818 __isl_take isl_basic_set *dom,
2819 __isl_give isl_set **empty);
2820 __isl_give isl_pw_multi_aff *
2821 isl_basic_map_partial_lexmax_pw_multi_aff(
2822 __isl_take isl_basic_map *bmap,
2823 __isl_take isl_basic_set *dom,
2824 __isl_give isl_set **empty);
2828 Lists are defined over several element types, including
2829 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2830 Here we take lists of C<isl_set>s as an example.
2831 Lists can be created, copied, modified and freed using the following functions.
2833 #include <isl/list.h>
2834 __isl_give isl_set_list *isl_set_list_from_set(
2835 __isl_take isl_set *el);
2836 __isl_give isl_set_list *isl_set_list_alloc(
2837 isl_ctx *ctx, int n);
2838 __isl_give isl_set_list *isl_set_list_copy(
2839 __isl_keep isl_set_list *list);
2840 __isl_give isl_set_list *isl_set_list_add(
2841 __isl_take isl_set_list *list,
2842 __isl_take isl_set *el);
2843 __isl_give isl_set_list *isl_set_list_set_set(
2844 __isl_take isl_set_list *list, int index,
2845 __isl_take isl_set *set);
2846 __isl_give isl_set_list *isl_set_list_concat(
2847 __isl_take isl_set_list *list1,
2848 __isl_take isl_set_list *list2);
2849 void *isl_set_list_free(__isl_take isl_set_list *list);
2851 C<isl_set_list_alloc> creates an empty list with a capacity for
2852 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2855 Lists can be inspected using the following functions.
2857 #include <isl/list.h>
2858 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2859 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2860 __isl_give isl_set *isl_set_list_get_set(
2861 __isl_keep isl_set_list *list, int index);
2862 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2863 int (*fn)(__isl_take isl_set *el, void *user),
2866 Lists can be printed using
2868 #include <isl/list.h>
2869 __isl_give isl_printer *isl_printer_print_set_list(
2870 __isl_take isl_printer *p,
2871 __isl_keep isl_set_list *list);
2875 Vectors can be created, copied and freed using the following functions.
2877 #include <isl/vec.h>
2878 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2880 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2881 void isl_vec_free(__isl_take isl_vec *vec);
2883 Note that the elements of a newly created vector may have arbitrary values.
2884 The elements can be changed and inspected using the following functions.
2886 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2887 int isl_vec_size(__isl_keep isl_vec *vec);
2888 int isl_vec_get_element(__isl_keep isl_vec *vec,
2889 int pos, isl_int *v);
2890 __isl_give isl_vec *isl_vec_set_element(
2891 __isl_take isl_vec *vec, int pos, isl_int v);
2892 __isl_give isl_vec *isl_vec_set_element_si(
2893 __isl_take isl_vec *vec, int pos, int v);
2894 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2896 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2899 C<isl_vec_get_element> will return a negative value if anything went wrong.
2900 In that case, the value of C<*v> is undefined.
2904 Matrices can be created, copied and freed using the following functions.
2906 #include <isl/mat.h>
2907 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2908 unsigned n_row, unsigned n_col);
2909 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2910 void isl_mat_free(__isl_take isl_mat *mat);
2912 Note that the elements of a newly created matrix may have arbitrary values.
2913 The elements can be changed and inspected using the following functions.
2915 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2916 int isl_mat_rows(__isl_keep isl_mat *mat);
2917 int isl_mat_cols(__isl_keep isl_mat *mat);
2918 int isl_mat_get_element(__isl_keep isl_mat *mat,
2919 int row, int col, isl_int *v);
2920 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2921 int row, int col, isl_int v);
2922 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2923 int row, int col, int v);
2925 C<isl_mat_get_element> will return a negative value if anything went wrong.
2926 In that case, the value of C<*v> is undefined.
2928 The following function can be used to compute the (right) inverse
2929 of a matrix, i.e., a matrix such that the product of the original
2930 and the inverse (in that order) is a multiple of the identity matrix.
2931 The input matrix is assumed to be of full row-rank.
2933 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2935 The following function can be used to compute the (right) kernel
2936 (or null space) of a matrix, i.e., a matrix such that the product of
2937 the original and the kernel (in that order) is the zero matrix.
2939 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2941 =head2 Piecewise Quasi Affine Expressions
2943 The zero quasi affine expression on a given domain can be created using
2945 __isl_give isl_aff *isl_aff_zero_on_domain(
2946 __isl_take isl_local_space *ls);
2948 Note that the space in which the resulting object lives is a map space
2949 with the given space as domain and a one-dimensional range.
2951 An empty piecewise quasi affine expression (one with no cells)
2952 or a piecewise quasi affine expression with a single cell can
2953 be created using the following functions.
2955 #include <isl/aff.h>
2956 __isl_give isl_pw_aff *isl_pw_aff_empty(
2957 __isl_take isl_space *space);
2958 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2959 __isl_take isl_set *set, __isl_take isl_aff *aff);
2960 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2961 __isl_take isl_aff *aff);
2963 A piecewise quasi affine expression that is equal to 1 on a set
2964 and 0 outside the set can be created using the following function.
2966 #include <isl/aff.h>
2967 __isl_give isl_pw_aff *isl_set_indicator_function(
2968 __isl_take isl_set *set);
2970 Quasi affine expressions can be copied and freed using
2972 #include <isl/aff.h>
2973 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2974 void *isl_aff_free(__isl_take isl_aff *aff);
2976 __isl_give isl_pw_aff *isl_pw_aff_copy(
2977 __isl_keep isl_pw_aff *pwaff);
2978 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2980 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2981 using the following function. The constraint is required to have
2982 a non-zero coefficient for the specified dimension.
2984 #include <isl/constraint.h>
2985 __isl_give isl_aff *isl_constraint_get_bound(
2986 __isl_keep isl_constraint *constraint,
2987 enum isl_dim_type type, int pos);
2989 The entire affine expression of the constraint can also be extracted
2990 using the following function.
2992 #include <isl/constraint.h>
2993 __isl_give isl_aff *isl_constraint_get_aff(
2994 __isl_keep isl_constraint *constraint);
2996 Conversely, an equality constraint equating
2997 the affine expression to zero or an inequality constraint enforcing
2998 the affine expression to be non-negative, can be constructed using
3000 __isl_give isl_constraint *isl_equality_from_aff(
3001 __isl_take isl_aff *aff);
3002 __isl_give isl_constraint *isl_inequality_from_aff(
3003 __isl_take isl_aff *aff);
3005 The expression can be inspected using
3007 #include <isl/aff.h>
3008 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3009 int isl_aff_dim(__isl_keep isl_aff *aff,
3010 enum isl_dim_type type);
3011 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3012 __isl_keep isl_aff *aff);
3013 __isl_give isl_local_space *isl_aff_get_local_space(
3014 __isl_keep isl_aff *aff);
3015 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3016 enum isl_dim_type type, unsigned pos);
3017 const char *isl_pw_aff_get_dim_name(
3018 __isl_keep isl_pw_aff *pa,
3019 enum isl_dim_type type, unsigned pos);
3020 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3021 enum isl_dim_type type, unsigned pos);
3022 __isl_give isl_id *isl_pw_aff_get_dim_id(
3023 __isl_keep isl_pw_aff *pa,
3024 enum isl_dim_type type, unsigned pos);
3025 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3026 __isl_keep isl_pw_aff *pa,
3027 enum isl_dim_type type);
3028 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3030 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3031 enum isl_dim_type type, int pos, isl_int *v);
3032 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3034 __isl_give isl_aff *isl_aff_get_div(
3035 __isl_keep isl_aff *aff, int pos);
3037 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3038 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3039 int (*fn)(__isl_take isl_set *set,
3040 __isl_take isl_aff *aff,
3041 void *user), void *user);
3043 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3044 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3046 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3047 enum isl_dim_type type, unsigned first, unsigned n);
3048 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3049 enum isl_dim_type type, unsigned first, unsigned n);
3051 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3052 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3053 enum isl_dim_type type);
3054 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3056 It can be modified using
3058 #include <isl/aff.h>
3059 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3060 __isl_take isl_pw_aff *pwaff,
3061 enum isl_dim_type type, __isl_take isl_id *id);
3062 __isl_give isl_aff *isl_aff_set_dim_name(
3063 __isl_take isl_aff *aff, enum isl_dim_type type,
3064 unsigned pos, const char *s);
3065 __isl_give isl_aff *isl_aff_set_dim_id(
3066 __isl_take isl_aff *aff, enum isl_dim_type type,
3067 unsigned pos, __isl_take isl_id *id);
3068 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3069 __isl_take isl_pw_aff *pma,
3070 enum isl_dim_type type, unsigned pos,
3071 __isl_take isl_id *id);
3072 __isl_give isl_aff *isl_aff_set_constant(
3073 __isl_take isl_aff *aff, isl_int v);
3074 __isl_give isl_aff *isl_aff_set_constant_si(
3075 __isl_take isl_aff *aff, int v);
3076 __isl_give isl_aff *isl_aff_set_coefficient(
3077 __isl_take isl_aff *aff,
3078 enum isl_dim_type type, int pos, isl_int v);
3079 __isl_give isl_aff *isl_aff_set_coefficient_si(
3080 __isl_take isl_aff *aff,
3081 enum isl_dim_type type, int pos, int v);
3082 __isl_give isl_aff *isl_aff_set_denominator(
3083 __isl_take isl_aff *aff, isl_int v);
3085 __isl_give isl_aff *isl_aff_add_constant(
3086 __isl_take isl_aff *aff, isl_int v);
3087 __isl_give isl_aff *isl_aff_add_constant_si(
3088 __isl_take isl_aff *aff, int v);
3089 __isl_give isl_aff *isl_aff_add_constant_num(
3090 __isl_take isl_aff *aff, isl_int v);
3091 __isl_give isl_aff *isl_aff_add_constant_num_si(
3092 __isl_take isl_aff *aff, int v);
3093 __isl_give isl_aff *isl_aff_add_coefficient(
3094 __isl_take isl_aff *aff,
3095 enum isl_dim_type type, int pos, isl_int v);
3096 __isl_give isl_aff *isl_aff_add_coefficient_si(
3097 __isl_take isl_aff *aff,
3098 enum isl_dim_type type, int pos, int v);
3100 __isl_give isl_aff *isl_aff_insert_dims(
3101 __isl_take isl_aff *aff,
3102 enum isl_dim_type type, unsigned first, unsigned n);
3103 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3104 __isl_take isl_pw_aff *pwaff,
3105 enum isl_dim_type type, unsigned first, unsigned n);
3106 __isl_give isl_aff *isl_aff_add_dims(
3107 __isl_take isl_aff *aff,
3108 enum isl_dim_type type, unsigned n);
3109 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3110 __isl_take isl_pw_aff *pwaff,
3111 enum isl_dim_type type, unsigned n);
3112 __isl_give isl_aff *isl_aff_drop_dims(
3113 __isl_take isl_aff *aff,
3114 enum isl_dim_type type, unsigned first, unsigned n);
3115 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3116 __isl_take isl_pw_aff *pwaff,
3117 enum isl_dim_type type, unsigned first, unsigned n);
3119 Note that the C<set_constant> and C<set_coefficient> functions
3120 set the I<numerator> of the constant or coefficient, while
3121 C<add_constant> and C<add_coefficient> add an integer value to
3122 the possibly rational constant or coefficient.
3123 The C<add_constant_num> functions add an integer value to
3126 To check whether an affine expressions is obviously zero
3127 or obviously equal to some other affine expression, use
3129 #include <isl/aff.h>
3130 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3131 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3132 __isl_keep isl_aff *aff2);
3133 int isl_pw_aff_plain_is_equal(
3134 __isl_keep isl_pw_aff *pwaff1,
3135 __isl_keep isl_pw_aff *pwaff2);
3139 #include <isl/aff.h>
3140 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3141 __isl_take isl_aff *aff2);
3142 __isl_give isl_pw_aff *isl_pw_aff_add(
3143 __isl_take isl_pw_aff *pwaff1,
3144 __isl_take isl_pw_aff *pwaff2);
3145 __isl_give isl_pw_aff *isl_pw_aff_min(
3146 __isl_take isl_pw_aff *pwaff1,
3147 __isl_take isl_pw_aff *pwaff2);
3148 __isl_give isl_pw_aff *isl_pw_aff_max(
3149 __isl_take isl_pw_aff *pwaff1,
3150 __isl_take isl_pw_aff *pwaff2);
3151 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3152 __isl_take isl_aff *aff2);
3153 __isl_give isl_pw_aff *isl_pw_aff_sub(
3154 __isl_take isl_pw_aff *pwaff1,
3155 __isl_take isl_pw_aff *pwaff2);
3156 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3157 __isl_give isl_pw_aff *isl_pw_aff_neg(
3158 __isl_take isl_pw_aff *pwaff);
3159 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3160 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3161 __isl_take isl_pw_aff *pwaff);
3162 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3163 __isl_give isl_pw_aff *isl_pw_aff_floor(
3164 __isl_take isl_pw_aff *pwaff);
3165 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3167 __isl_give isl_pw_aff *isl_pw_aff_mod(
3168 __isl_take isl_pw_aff *pwaff, isl_int mod);
3169 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3171 __isl_give isl_pw_aff *isl_pw_aff_scale(
3172 __isl_take isl_pw_aff *pwaff, isl_int f);
3173 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3175 __isl_give isl_aff *isl_aff_scale_down_ui(
3176 __isl_take isl_aff *aff, unsigned f);
3177 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3178 __isl_take isl_pw_aff *pwaff, isl_int f);
3180 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3181 __isl_take isl_pw_aff_list *list);
3182 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3183 __isl_take isl_pw_aff_list *list);
3185 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3186 __isl_take isl_pw_aff *pwqp);
3188 __isl_give isl_aff *isl_aff_align_params(
3189 __isl_take isl_aff *aff,
3190 __isl_take isl_space *model);
3191 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3192 __isl_take isl_pw_aff *pwaff,
3193 __isl_take isl_space *model);
3195 __isl_give isl_aff *isl_aff_project_domain_on_params(
3196 __isl_take isl_aff *aff);
3198 __isl_give isl_aff *isl_aff_gist_params(
3199 __isl_take isl_aff *aff,
3200 __isl_take isl_set *context);
3201 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3202 __isl_take isl_set *context);
3203 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3204 __isl_take isl_pw_aff *pwaff,
3205 __isl_take isl_set *context);
3206 __isl_give isl_pw_aff *isl_pw_aff_gist(
3207 __isl_take isl_pw_aff *pwaff,
3208 __isl_take isl_set *context);
3210 __isl_give isl_set *isl_pw_aff_domain(
3211 __isl_take isl_pw_aff *pwaff);
3212 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3213 __isl_take isl_pw_aff *pa,
3214 __isl_take isl_set *set);
3215 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3216 __isl_take isl_pw_aff *pa,
3217 __isl_take isl_set *set);
3219 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3220 __isl_take isl_aff *aff2);
3221 __isl_give isl_pw_aff *isl_pw_aff_mul(
3222 __isl_take isl_pw_aff *pwaff1,
3223 __isl_take isl_pw_aff *pwaff2);
3225 When multiplying two affine expressions, at least one of the two needs
3228 #include <isl/aff.h>
3229 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3230 __isl_take isl_aff *aff);
3231 __isl_give isl_basic_set *isl_aff_le_basic_set(
3232 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3233 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3234 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3235 __isl_give isl_set *isl_pw_aff_eq_set(
3236 __isl_take isl_pw_aff *pwaff1,
3237 __isl_take isl_pw_aff *pwaff2);
3238 __isl_give isl_set *isl_pw_aff_ne_set(
3239 __isl_take isl_pw_aff *pwaff1,
3240 __isl_take isl_pw_aff *pwaff2);
3241 __isl_give isl_set *isl_pw_aff_le_set(
3242 __isl_take isl_pw_aff *pwaff1,
3243 __isl_take isl_pw_aff *pwaff2);
3244 __isl_give isl_set *isl_pw_aff_lt_set(
3245 __isl_take isl_pw_aff *pwaff1,
3246 __isl_take isl_pw_aff *pwaff2);
3247 __isl_give isl_set *isl_pw_aff_ge_set(
3248 __isl_take isl_pw_aff *pwaff1,
3249 __isl_take isl_pw_aff *pwaff2);
3250 __isl_give isl_set *isl_pw_aff_gt_set(
3251 __isl_take isl_pw_aff *pwaff1,
3252 __isl_take isl_pw_aff *pwaff2);
3254 __isl_give isl_set *isl_pw_aff_list_eq_set(
3255 __isl_take isl_pw_aff_list *list1,
3256 __isl_take isl_pw_aff_list *list2);
3257 __isl_give isl_set *isl_pw_aff_list_ne_set(
3258 __isl_take isl_pw_aff_list *list1,
3259 __isl_take isl_pw_aff_list *list2);
3260 __isl_give isl_set *isl_pw_aff_list_le_set(
3261 __isl_take isl_pw_aff_list *list1,
3262 __isl_take isl_pw_aff_list *list2);
3263 __isl_give isl_set *isl_pw_aff_list_lt_set(
3264 __isl_take isl_pw_aff_list *list1,
3265 __isl_take isl_pw_aff_list *list2);
3266 __isl_give isl_set *isl_pw_aff_list_ge_set(
3267 __isl_take isl_pw_aff_list *list1,
3268 __isl_take isl_pw_aff_list *list2);
3269 __isl_give isl_set *isl_pw_aff_list_gt_set(
3270 __isl_take isl_pw_aff_list *list1,
3271 __isl_take isl_pw_aff_list *list2);
3273 The function C<isl_aff_neg_basic_set> returns a basic set
3274 containing those elements in the domain space
3275 of C<aff> where C<aff> is negative.
3276 The function C<isl_aff_ge_basic_set> returns a basic set
3277 containing those elements in the shared space
3278 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3279 The function C<isl_pw_aff_ge_set> returns a set
3280 containing those elements in the shared domain
3281 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3282 The functions operating on C<isl_pw_aff_list> apply the corresponding
3283 C<isl_pw_aff> function to each pair of elements in the two lists.
3285 #include <isl/aff.h>
3286 __isl_give isl_set *isl_pw_aff_nonneg_set(
3287 __isl_take isl_pw_aff *pwaff);
3288 __isl_give isl_set *isl_pw_aff_zero_set(
3289 __isl_take isl_pw_aff *pwaff);
3290 __isl_give isl_set *isl_pw_aff_non_zero_set(
3291 __isl_take isl_pw_aff *pwaff);
3293 The function C<isl_pw_aff_nonneg_set> returns a set
3294 containing those elements in the domain
3295 of C<pwaff> where C<pwaff> is non-negative.
3297 #include <isl/aff.h>
3298 __isl_give isl_pw_aff *isl_pw_aff_cond(
3299 __isl_take isl_pw_aff *cond,
3300 __isl_take isl_pw_aff *pwaff_true,
3301 __isl_take isl_pw_aff *pwaff_false);
3303 The function C<isl_pw_aff_cond> performs a conditional operator
3304 and returns an expression that is equal to C<pwaff_true>
3305 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3306 where C<cond> is zero.
3308 #include <isl/aff.h>
3309 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3310 __isl_take isl_pw_aff *pwaff1,
3311 __isl_take isl_pw_aff *pwaff2);
3312 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3313 __isl_take isl_pw_aff *pwaff1,
3314 __isl_take isl_pw_aff *pwaff2);
3315 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3316 __isl_take isl_pw_aff *pwaff1,
3317 __isl_take isl_pw_aff *pwaff2);
3319 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3320 expression with a domain that is the union of those of C<pwaff1> and
3321 C<pwaff2> and such that on each cell, the quasi-affine expression is
3322 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3323 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3324 associated expression is the defined one.
3326 An expression can be read from input using
3328 #include <isl/aff.h>
3329 __isl_give isl_aff *isl_aff_read_from_str(
3330 isl_ctx *ctx, const char *str);
3331 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3332 isl_ctx *ctx, const char *str);
3334 An expression can be printed using
3336 #include <isl/aff.h>
3337 __isl_give isl_printer *isl_printer_print_aff(
3338 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3340 __isl_give isl_printer *isl_printer_print_pw_aff(
3341 __isl_take isl_printer *p,
3342 __isl_keep isl_pw_aff *pwaff);
3344 =head2 Piecewise Multiple Quasi Affine Expressions
3346 An C<isl_multi_aff> object represents a sequence of
3347 zero or more affine expressions, all defined on the same domain space.
3349 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3352 #include <isl/aff.h>
3353 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3354 __isl_take isl_space *space,
3355 __isl_take isl_aff_list *list);
3357 An empty piecewise multiple quasi affine expression (one with no cells),
3358 the zero piecewise multiple quasi affine expression (with value zero
3359 for each output dimension),
3360 a piecewise multiple quasi affine expression with a single cell (with
3361 either a universe or a specified domain) or
3362 a zero-dimensional piecewise multiple quasi affine expression
3364 can be created using the following functions.
3366 #include <isl/aff.h>
3367 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3368 __isl_take isl_space *space);
3369 __isl_give isl_multi_aff *isl_multi_aff_zero(
3370 __isl_take isl_space *space);
3371 __isl_give isl_multi_aff *isl_multi_aff_identity(
3372 __isl_take isl_space *space);
3373 __isl_give isl_pw_multi_aff *
3374 isl_pw_multi_aff_from_multi_aff(
3375 __isl_take isl_multi_aff *ma);
3376 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3377 __isl_take isl_set *set,
3378 __isl_take isl_multi_aff *maff);
3379 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3380 __isl_take isl_set *set);
3382 __isl_give isl_union_pw_multi_aff *
3383 isl_union_pw_multi_aff_empty(
3384 __isl_take isl_space *space);
3385 __isl_give isl_union_pw_multi_aff *
3386 isl_union_pw_multi_aff_add_pw_multi_aff(
3387 __isl_take isl_union_pw_multi_aff *upma,
3388 __isl_take isl_pw_multi_aff *pma);
3389 __isl_give isl_union_pw_multi_aff *
3390 isl_union_pw_multi_aff_from_domain(
3391 __isl_take isl_union_set *uset);
3393 A piecewise multiple quasi affine expression can also be initialized
3394 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3395 and the C<isl_map> is single-valued.
3397 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3398 __isl_take isl_set *set);
3399 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3400 __isl_take isl_map *map);
3402 Multiple quasi affine expressions can be copied and freed using
3404 #include <isl/aff.h>
3405 __isl_give isl_multi_aff *isl_multi_aff_copy(
3406 __isl_keep isl_multi_aff *maff);
3407 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3409 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3410 __isl_keep isl_pw_multi_aff *pma);
3411 void *isl_pw_multi_aff_free(
3412 __isl_take isl_pw_multi_aff *pma);
3414 __isl_give isl_union_pw_multi_aff *
3415 isl_union_pw_multi_aff_copy(
3416 __isl_keep isl_union_pw_multi_aff *upma);
3417 void *isl_union_pw_multi_aff_free(
3418 __isl_take isl_union_pw_multi_aff *upma);
3420 The expression can be inspected using
3422 #include <isl/aff.h>
3423 isl_ctx *isl_multi_aff_get_ctx(
3424 __isl_keep isl_multi_aff *maff);
3425 isl_ctx *isl_pw_multi_aff_get_ctx(
3426 __isl_keep isl_pw_multi_aff *pma);
3427 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3428 __isl_keep isl_union_pw_multi_aff *upma);
3429 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3430 enum isl_dim_type type);
3431 unsigned isl_pw_multi_aff_dim(
3432 __isl_keep isl_pw_multi_aff *pma,
3433 enum isl_dim_type type);
3434 __isl_give isl_aff *isl_multi_aff_get_aff(
3435 __isl_keep isl_multi_aff *multi, int pos);
3436 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3437 __isl_keep isl_pw_multi_aff *pma, int pos);
3438 const char *isl_pw_multi_aff_get_dim_name(
3439 __isl_keep isl_pw_multi_aff *pma,
3440 enum isl_dim_type type, unsigned pos);
3441 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3442 __isl_keep isl_pw_multi_aff *pma,
3443 enum isl_dim_type type, unsigned pos);
3444 const char *isl_multi_aff_get_tuple_name(
3445 __isl_keep isl_multi_aff *multi,
3446 enum isl_dim_type type);
3447 int isl_pw_multi_aff_has_tuple_name(
3448 __isl_keep isl_pw_multi_aff *pma,
3449 enum isl_dim_type type);
3450 const char *isl_pw_multi_aff_get_tuple_name(
3451 __isl_keep isl_pw_multi_aff *pma,
3452 enum isl_dim_type type);
3453 int isl_pw_multi_aff_has_tuple_id(
3454 __isl_keep isl_pw_multi_aff *pma,
3455 enum isl_dim_type type);
3456 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3457 __isl_keep isl_pw_multi_aff *pma,
3458 enum isl_dim_type type);
3460 int isl_pw_multi_aff_foreach_piece(
3461 __isl_keep isl_pw_multi_aff *pma,
3462 int (*fn)(__isl_take isl_set *set,
3463 __isl_take isl_multi_aff *maff,
3464 void *user), void *user);
3466 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3467 __isl_keep isl_union_pw_multi_aff *upma,
3468 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3469 void *user), void *user);
3471 It can be modified using
3473 #include <isl/aff.h>
3474 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3475 __isl_take isl_multi_aff *multi, int pos,
3476 __isl_take isl_aff *aff);
3477 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3478 __isl_take isl_multi_aff *maff,
3479 enum isl_dim_type type, unsigned pos, const char *s);
3480 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3481 __isl_take isl_multi_aff *maff,
3482 enum isl_dim_type type, __isl_take isl_id *id);
3483 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3484 __isl_take isl_pw_multi_aff *pma,
3485 enum isl_dim_type type, __isl_take isl_id *id);
3487 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3488 __isl_take isl_multi_aff *maff,
3489 enum isl_dim_type type, unsigned first, unsigned n);
3491 To check whether two multiple affine expressions are
3492 obviously equal to each other, use
3494 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3495 __isl_keep isl_multi_aff *maff2);
3496 int isl_pw_multi_aff_plain_is_equal(
3497 __isl_keep isl_pw_multi_aff *pma1,
3498 __isl_keep isl_pw_multi_aff *pma2);
3502 #include <isl/aff.h>
3503 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3504 __isl_take isl_pw_multi_aff *pma1,
3505 __isl_take isl_pw_multi_aff *pma2);
3506 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3507 __isl_take isl_pw_multi_aff *pma1,
3508 __isl_take isl_pw_multi_aff *pma2);
3509 __isl_give isl_multi_aff *isl_multi_aff_add(
3510 __isl_take isl_multi_aff *maff1,
3511 __isl_take isl_multi_aff *maff2);
3512 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3513 __isl_take isl_pw_multi_aff *pma1,
3514 __isl_take isl_pw_multi_aff *pma2);
3515 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3516 __isl_take isl_union_pw_multi_aff *upma1,
3517 __isl_take isl_union_pw_multi_aff *upma2);
3518 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3519 __isl_take isl_pw_multi_aff *pma1,
3520 __isl_take isl_pw_multi_aff *pma2);
3521 __isl_give isl_multi_aff *isl_multi_aff_scale(
3522 __isl_take isl_multi_aff *maff,
3524 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3525 __isl_take isl_pw_multi_aff *pma,
3526 __isl_take isl_set *set);
3527 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3528 __isl_take isl_pw_multi_aff *pma,
3529 __isl_take isl_set *set);
3530 __isl_give isl_multi_aff *isl_multi_aff_lift(
3531 __isl_take isl_multi_aff *maff,
3532 __isl_give isl_local_space **ls);
3533 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3534 __isl_take isl_pw_multi_aff *pma);
3535 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3536 __isl_take isl_multi_aff *maff,
3537 __isl_take isl_set *context);
3538 __isl_give isl_multi_aff *isl_multi_aff_gist(
3539 __isl_take isl_multi_aff *maff,
3540 __isl_take isl_set *context);
3541 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3542 __isl_take isl_pw_multi_aff *pma,
3543 __isl_take isl_set *set);
3544 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3545 __isl_take isl_pw_multi_aff *pma,
3546 __isl_take isl_set *set);
3547 __isl_give isl_set *isl_pw_multi_aff_domain(
3548 __isl_take isl_pw_multi_aff *pma);
3549 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3550 __isl_take isl_union_pw_multi_aff *upma);
3551 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3552 __isl_take isl_multi_aff *ma1,
3553 __isl_take isl_multi_aff *ma2);
3554 __isl_give isl_multi_aff *isl_multi_aff_product(
3555 __isl_take isl_multi_aff *ma1,
3556 __isl_take isl_multi_aff *ma2);
3557 __isl_give isl_pw_multi_aff *
3558 isl_pw_multi_aff_flat_range_product(
3559 __isl_take isl_pw_multi_aff *pma1,
3560 __isl_take isl_pw_multi_aff *pma2);
3561 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3562 __isl_take isl_pw_multi_aff *pma1,
3563 __isl_take isl_pw_multi_aff *pma2);
3564 __isl_give isl_union_pw_multi_aff *
3565 isl_union_pw_multi_aff_flat_range_product(
3566 __isl_take isl_union_pw_multi_aff *upma1,
3567 __isl_take isl_union_pw_multi_aff *upma2);
3569 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3570 then it is assigned the local space that lies at the basis of
3571 the lifting applied.
3573 __isl_give isl_set *isl_multi_aff_lex_le_set(
3574 __isl_take isl_multi_aff *ma1,
3575 __isl_take isl_multi_aff *ma2);
3576 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3577 __isl_take isl_multi_aff *ma1,
3578 __isl_take isl_multi_aff *ma2);
3580 The function C<isl_multi_aff_lex_le_set> returns a set
3581 containing those elements in the shared domain space
3582 where C<ma1> is lexicographically smaller than or
3585 An expression can be read from input using
3587 #include <isl/aff.h>
3588 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3589 isl_ctx *ctx, const char *str);
3590 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3591 isl_ctx *ctx, const char *str);
3593 An expression can be printed using
3595 #include <isl/aff.h>
3596 __isl_give isl_printer *isl_printer_print_multi_aff(
3597 __isl_take isl_printer *p,
3598 __isl_keep isl_multi_aff *maff);
3599 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3600 __isl_take isl_printer *p,
3601 __isl_keep isl_pw_multi_aff *pma);
3602 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3603 __isl_take isl_printer *p,
3604 __isl_keep isl_union_pw_multi_aff *upma);
3608 Points are elements of a set. They can be used to construct
3609 simple sets (boxes) or they can be used to represent the
3610 individual elements of a set.
3611 The zero point (the origin) can be created using
3613 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3615 The coordinates of a point can be inspected, set and changed
3618 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3619 enum isl_dim_type type, int pos, isl_int *v);
3620 __isl_give isl_point *isl_point_set_coordinate(
3621 __isl_take isl_point *pnt,
3622 enum isl_dim_type type, int pos, isl_int v);
3624 __isl_give isl_point *isl_point_add_ui(
3625 __isl_take isl_point *pnt,
3626 enum isl_dim_type type, int pos, unsigned val);
3627 __isl_give isl_point *isl_point_sub_ui(
3628 __isl_take isl_point *pnt,
3629 enum isl_dim_type type, int pos, unsigned val);
3631 Other properties can be obtained using
3633 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3635 Points can be copied or freed using
3637 __isl_give isl_point *isl_point_copy(
3638 __isl_keep isl_point *pnt);
3639 void isl_point_free(__isl_take isl_point *pnt);
3641 A singleton set can be created from a point using
3643 __isl_give isl_basic_set *isl_basic_set_from_point(
3644 __isl_take isl_point *pnt);
3645 __isl_give isl_set *isl_set_from_point(
3646 __isl_take isl_point *pnt);
3648 and a box can be created from two opposite extremal points using
3650 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3651 __isl_take isl_point *pnt1,
3652 __isl_take isl_point *pnt2);
3653 __isl_give isl_set *isl_set_box_from_points(
3654 __isl_take isl_point *pnt1,
3655 __isl_take isl_point *pnt2);
3657 All elements of a B<bounded> (union) set can be enumerated using
3658 the following functions.
3660 int isl_set_foreach_point(__isl_keep isl_set *set,
3661 int (*fn)(__isl_take isl_point *pnt, void *user),
3663 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3664 int (*fn)(__isl_take isl_point *pnt, void *user),
3667 The function C<fn> is called for each integer point in
3668 C<set> with as second argument the last argument of
3669 the C<isl_set_foreach_point> call. The function C<fn>
3670 should return C<0> on success and C<-1> on failure.
3671 In the latter case, C<isl_set_foreach_point> will stop
3672 enumerating and return C<-1> as well.
3673 If the enumeration is performed successfully and to completion,
3674 then C<isl_set_foreach_point> returns C<0>.
3676 To obtain a single point of a (basic) set, use
3678 __isl_give isl_point *isl_basic_set_sample_point(
3679 __isl_take isl_basic_set *bset);
3680 __isl_give isl_point *isl_set_sample_point(
3681 __isl_take isl_set *set);
3683 If C<set> does not contain any (integer) points, then the
3684 resulting point will be ``void'', a property that can be
3687 int isl_point_is_void(__isl_keep isl_point *pnt);
3689 =head2 Piecewise Quasipolynomials
3691 A piecewise quasipolynomial is a particular kind of function that maps
3692 a parametric point to a rational value.
3693 More specifically, a quasipolynomial is a polynomial expression in greatest
3694 integer parts of affine expressions of parameters and variables.
3695 A piecewise quasipolynomial is a subdivision of a given parametric
3696 domain into disjoint cells with a quasipolynomial associated to
3697 each cell. The value of the piecewise quasipolynomial at a given
3698 point is the value of the quasipolynomial associated to the cell
3699 that contains the point. Outside of the union of cells,
3700 the value is assumed to be zero.
3701 For example, the piecewise quasipolynomial
3703 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3705 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3706 A given piecewise quasipolynomial has a fixed domain dimension.
3707 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3708 defined over different domains.
3709 Piecewise quasipolynomials are mainly used by the C<barvinok>
3710 library for representing the number of elements in a parametric set or map.
3711 For example, the piecewise quasipolynomial above represents
3712 the number of points in the map
3714 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3716 =head3 Input and Output
3718 Piecewise quasipolynomials can be read from input using
3720 __isl_give isl_union_pw_qpolynomial *
3721 isl_union_pw_qpolynomial_read_from_str(
3722 isl_ctx *ctx, const char *str);
3724 Quasipolynomials and piecewise quasipolynomials can be printed
3725 using the following functions.
3727 __isl_give isl_printer *isl_printer_print_qpolynomial(
3728 __isl_take isl_printer *p,
3729 __isl_keep isl_qpolynomial *qp);
3731 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3732 __isl_take isl_printer *p,
3733 __isl_keep isl_pw_qpolynomial *pwqp);
3735 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3736 __isl_take isl_printer *p,
3737 __isl_keep isl_union_pw_qpolynomial *upwqp);
3739 The output format of the printer
3740 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3741 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3743 In case of printing in C<ISL_FORMAT_C>, the user may want
3744 to set the names of all dimensions
3746 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3747 __isl_take isl_qpolynomial *qp,
3748 enum isl_dim_type type, unsigned pos,
3750 __isl_give isl_pw_qpolynomial *
3751 isl_pw_qpolynomial_set_dim_name(
3752 __isl_take isl_pw_qpolynomial *pwqp,
3753 enum isl_dim_type type, unsigned pos,
3756 =head3 Creating New (Piecewise) Quasipolynomials
3758 Some simple quasipolynomials can be created using the following functions.
3759 More complicated quasipolynomials can be created by applying
3760 operations such as addition and multiplication
3761 on the resulting quasipolynomials
3763 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3764 __isl_take isl_space *domain);
3765 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3766 __isl_take isl_space *domain);
3767 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3768 __isl_take isl_space *domain);
3769 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3770 __isl_take isl_space *domain);
3771 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3772 __isl_take isl_space *domain);
3773 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3774 __isl_take isl_space *domain,
3775 const isl_int n, const isl_int d);
3776 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3777 __isl_take isl_space *domain,
3778 enum isl_dim_type type, unsigned pos);
3779 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3780 __isl_take isl_aff *aff);
3782 Note that the space in which a quasipolynomial lives is a map space
3783 with a one-dimensional range. The C<domain> argument in some of
3784 the functions above corresponds to the domain of this map space.
3786 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3787 with a single cell can be created using the following functions.
3788 Multiple of these single cell piecewise quasipolynomials can
3789 be combined to create more complicated piecewise quasipolynomials.
3791 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3792 __isl_take isl_space *space);
3793 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3794 __isl_take isl_set *set,
3795 __isl_take isl_qpolynomial *qp);
3796 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3797 __isl_take isl_qpolynomial *qp);
3798 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3799 __isl_take isl_pw_aff *pwaff);
3801 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3802 __isl_take isl_space *space);
3803 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3804 __isl_take isl_pw_qpolynomial *pwqp);
3805 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3806 __isl_take isl_union_pw_qpolynomial *upwqp,
3807 __isl_take isl_pw_qpolynomial *pwqp);
3809 Quasipolynomials can be copied and freed again using the following
3812 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3813 __isl_keep isl_qpolynomial *qp);
3814 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3816 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3817 __isl_keep isl_pw_qpolynomial *pwqp);
3818 void *isl_pw_qpolynomial_free(
3819 __isl_take isl_pw_qpolynomial *pwqp);
3821 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3822 __isl_keep isl_union_pw_qpolynomial *upwqp);
3823 void *isl_union_pw_qpolynomial_free(
3824 __isl_take isl_union_pw_qpolynomial *upwqp);
3826 =head3 Inspecting (Piecewise) Quasipolynomials
3828 To iterate over all piecewise quasipolynomials in a union
3829 piecewise quasipolynomial, use the following function
3831 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3832 __isl_keep isl_union_pw_qpolynomial *upwqp,
3833 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3836 To extract the piecewise quasipolynomial in a given space from a union, use
3838 __isl_give isl_pw_qpolynomial *
3839 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3840 __isl_keep isl_union_pw_qpolynomial *upwqp,
3841 __isl_take isl_space *space);
3843 To iterate over the cells in a piecewise quasipolynomial,
3844 use either of the following two functions
3846 int isl_pw_qpolynomial_foreach_piece(
3847 __isl_keep isl_pw_qpolynomial *pwqp,
3848 int (*fn)(__isl_take isl_set *set,
3849 __isl_take isl_qpolynomial *qp,
3850 void *user), void *user);
3851 int isl_pw_qpolynomial_foreach_lifted_piece(
3852 __isl_keep isl_pw_qpolynomial *pwqp,
3853 int (*fn)(__isl_take isl_set *set,
3854 __isl_take isl_qpolynomial *qp,
3855 void *user), void *user);
3857 As usual, the function C<fn> should return C<0> on success
3858 and C<-1> on failure. The difference between
3859 C<isl_pw_qpolynomial_foreach_piece> and
3860 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3861 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3862 compute unique representations for all existentially quantified
3863 variables and then turn these existentially quantified variables
3864 into extra set variables, adapting the associated quasipolynomial
3865 accordingly. This means that the C<set> passed to C<fn>
3866 will not have any existentially quantified variables, but that
3867 the dimensions of the sets may be different for different
3868 invocations of C<fn>.
3870 To iterate over all terms in a quasipolynomial,
3873 int isl_qpolynomial_foreach_term(
3874 __isl_keep isl_qpolynomial *qp,
3875 int (*fn)(__isl_take isl_term *term,
3876 void *user), void *user);
3878 The terms themselves can be inspected and freed using
3881 unsigned isl_term_dim(__isl_keep isl_term *term,
3882 enum isl_dim_type type);
3883 void isl_term_get_num(__isl_keep isl_term *term,
3885 void isl_term_get_den(__isl_keep isl_term *term,
3887 int isl_term_get_exp(__isl_keep isl_term *term,
3888 enum isl_dim_type type, unsigned pos);
3889 __isl_give isl_aff *isl_term_get_div(
3890 __isl_keep isl_term *term, unsigned pos);
3891 void isl_term_free(__isl_take isl_term *term);
3893 Each term is a product of parameters, set variables and
3894 integer divisions. The function C<isl_term_get_exp>
3895 returns the exponent of a given dimensions in the given term.
3896 The C<isl_int>s in the arguments of C<isl_term_get_num>
3897 and C<isl_term_get_den> need to have been initialized
3898 using C<isl_int_init> before calling these functions.
3900 =head3 Properties of (Piecewise) Quasipolynomials
3902 To check whether a quasipolynomial is actually a constant,
3903 use the following function.
3905 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3906 isl_int *n, isl_int *d);
3908 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3909 then the numerator and denominator of the constant
3910 are returned in C<*n> and C<*d>, respectively.
3912 To check whether two union piecewise quasipolynomials are
3913 obviously equal, use
3915 int isl_union_pw_qpolynomial_plain_is_equal(
3916 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3917 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3919 =head3 Operations on (Piecewise) Quasipolynomials
3921 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3922 __isl_take isl_qpolynomial *qp, isl_int v);
3923 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3924 __isl_take isl_qpolynomial *qp);
3925 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3926 __isl_take isl_qpolynomial *qp1,
3927 __isl_take isl_qpolynomial *qp2);
3928 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3929 __isl_take isl_qpolynomial *qp1,
3930 __isl_take isl_qpolynomial *qp2);
3931 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3932 __isl_take isl_qpolynomial *qp1,
3933 __isl_take isl_qpolynomial *qp2);
3934 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3935 __isl_take isl_qpolynomial *qp, unsigned exponent);
3937 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3938 __isl_take isl_pw_qpolynomial *pwqp1,
3939 __isl_take isl_pw_qpolynomial *pwqp2);
3940 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3941 __isl_take isl_pw_qpolynomial *pwqp1,
3942 __isl_take isl_pw_qpolynomial *pwqp2);
3943 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3944 __isl_take isl_pw_qpolynomial *pwqp1,
3945 __isl_take isl_pw_qpolynomial *pwqp2);
3946 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3947 __isl_take isl_pw_qpolynomial *pwqp);
3948 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3949 __isl_take isl_pw_qpolynomial *pwqp1,
3950 __isl_take isl_pw_qpolynomial *pwqp2);
3951 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3952 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3954 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3955 __isl_take isl_union_pw_qpolynomial *upwqp1,
3956 __isl_take isl_union_pw_qpolynomial *upwqp2);
3957 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3958 __isl_take isl_union_pw_qpolynomial *upwqp1,
3959 __isl_take isl_union_pw_qpolynomial *upwqp2);
3960 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3961 __isl_take isl_union_pw_qpolynomial *upwqp1,
3962 __isl_take isl_union_pw_qpolynomial *upwqp2);
3964 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3965 __isl_take isl_pw_qpolynomial *pwqp,
3966 __isl_take isl_point *pnt);
3968 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3969 __isl_take isl_union_pw_qpolynomial *upwqp,
3970 __isl_take isl_point *pnt);
3972 __isl_give isl_set *isl_pw_qpolynomial_domain(
3973 __isl_take isl_pw_qpolynomial *pwqp);
3974 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3975 __isl_take isl_pw_qpolynomial *pwpq,
3976 __isl_take isl_set *set);
3977 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3978 __isl_take isl_pw_qpolynomial *pwpq,
3979 __isl_take isl_set *set);
3981 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3982 __isl_take isl_union_pw_qpolynomial *upwqp);
3983 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3984 __isl_take isl_union_pw_qpolynomial *upwpq,
3985 __isl_take isl_union_set *uset);
3986 __isl_give isl_union_pw_qpolynomial *
3987 isl_union_pw_qpolynomial_intersect_params(
3988 __isl_take isl_union_pw_qpolynomial *upwpq,
3989 __isl_take isl_set *set);
3991 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3992 __isl_take isl_qpolynomial *qp,
3993 __isl_take isl_space *model);
3995 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3996 __isl_take isl_qpolynomial *qp);
3997 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3998 __isl_take isl_pw_qpolynomial *pwqp);
4000 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4001 __isl_take isl_union_pw_qpolynomial *upwqp);
4003 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4004 __isl_take isl_qpolynomial *qp,
4005 __isl_take isl_set *context);
4006 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4007 __isl_take isl_qpolynomial *qp,
4008 __isl_take isl_set *context);
4010 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4011 __isl_take isl_pw_qpolynomial *pwqp,
4012 __isl_take isl_set *context);
4013 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4014 __isl_take isl_pw_qpolynomial *pwqp,
4015 __isl_take isl_set *context);
4017 __isl_give isl_union_pw_qpolynomial *
4018 isl_union_pw_qpolynomial_gist_params(
4019 __isl_take isl_union_pw_qpolynomial *upwqp,
4020 __isl_take isl_set *context);
4021 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4022 __isl_take isl_union_pw_qpolynomial *upwqp,
4023 __isl_take isl_union_set *context);
4025 The gist operation applies the gist operation to each of
4026 the cells in the domain of the input piecewise quasipolynomial.
4027 The context is also exploited
4028 to simplify the quasipolynomials associated to each cell.
4030 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4031 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4032 __isl_give isl_union_pw_qpolynomial *
4033 isl_union_pw_qpolynomial_to_polynomial(
4034 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4036 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4037 the polynomial will be an overapproximation. If C<sign> is negative,
4038 it will be an underapproximation. If C<sign> is zero, the approximation
4039 will lie somewhere in between.
4041 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4043 A piecewise quasipolynomial reduction is a piecewise
4044 reduction (or fold) of quasipolynomials.
4045 In particular, the reduction can be maximum or a minimum.
4046 The objects are mainly used to represent the result of
4047 an upper or lower bound on a quasipolynomial over its domain,
4048 i.e., as the result of the following function.
4050 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4051 __isl_take isl_pw_qpolynomial *pwqp,
4052 enum isl_fold type, int *tight);
4054 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4055 __isl_take isl_union_pw_qpolynomial *upwqp,
4056 enum isl_fold type, int *tight);
4058 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4059 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4060 is the returned bound is known be tight, i.e., for each value
4061 of the parameters there is at least
4062 one element in the domain that reaches the bound.
4063 If the domain of C<pwqp> is not wrapping, then the bound is computed
4064 over all elements in that domain and the result has a purely parametric
4065 domain. If the domain of C<pwqp> is wrapping, then the bound is
4066 computed over the range of the wrapped relation. The domain of the
4067 wrapped relation becomes the domain of the result.
4069 A (piecewise) quasipolynomial reduction can be copied or freed using the
4070 following functions.
4072 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4073 __isl_keep isl_qpolynomial_fold *fold);
4074 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4075 __isl_keep isl_pw_qpolynomial_fold *pwf);
4076 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4077 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4078 void isl_qpolynomial_fold_free(
4079 __isl_take isl_qpolynomial_fold *fold);
4080 void *isl_pw_qpolynomial_fold_free(
4081 __isl_take isl_pw_qpolynomial_fold *pwf);
4082 void *isl_union_pw_qpolynomial_fold_free(
4083 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4085 =head3 Printing Piecewise Quasipolynomial Reductions
4087 Piecewise quasipolynomial reductions can be printed
4088 using the following function.
4090 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4091 __isl_take isl_printer *p,
4092 __isl_keep isl_pw_qpolynomial_fold *pwf);
4093 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4094 __isl_take isl_printer *p,
4095 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4097 For C<isl_printer_print_pw_qpolynomial_fold>,
4098 output format of the printer
4099 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4100 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4101 output format of the printer
4102 needs to be set to C<ISL_FORMAT_ISL>.
4103 In case of printing in C<ISL_FORMAT_C>, the user may want
4104 to set the names of all dimensions
4106 __isl_give isl_pw_qpolynomial_fold *
4107 isl_pw_qpolynomial_fold_set_dim_name(
4108 __isl_take isl_pw_qpolynomial_fold *pwf,
4109 enum isl_dim_type type, unsigned pos,
4112 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4114 To iterate over all piecewise quasipolynomial reductions in a union
4115 piecewise quasipolynomial reduction, use the following function
4117 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4118 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4119 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4120 void *user), void *user);
4122 To iterate over the cells in a piecewise quasipolynomial reduction,
4123 use either of the following two functions
4125 int isl_pw_qpolynomial_fold_foreach_piece(
4126 __isl_keep isl_pw_qpolynomial_fold *pwf,
4127 int (*fn)(__isl_take isl_set *set,
4128 __isl_take isl_qpolynomial_fold *fold,
4129 void *user), void *user);
4130 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4131 __isl_keep isl_pw_qpolynomial_fold *pwf,
4132 int (*fn)(__isl_take isl_set *set,
4133 __isl_take isl_qpolynomial_fold *fold,
4134 void *user), void *user);
4136 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4137 of the difference between these two functions.
4139 To iterate over all quasipolynomials in a reduction, use
4141 int isl_qpolynomial_fold_foreach_qpolynomial(
4142 __isl_keep isl_qpolynomial_fold *fold,
4143 int (*fn)(__isl_take isl_qpolynomial *qp,
4144 void *user), void *user);
4146 =head3 Properties of Piecewise Quasipolynomial Reductions
4148 To check whether two union piecewise quasipolynomial reductions are
4149 obviously equal, use
4151 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4152 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4153 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4155 =head3 Operations on Piecewise Quasipolynomial Reductions
4157 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4158 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4160 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4161 __isl_take isl_pw_qpolynomial_fold *pwf1,
4162 __isl_take isl_pw_qpolynomial_fold *pwf2);
4164 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4165 __isl_take isl_pw_qpolynomial_fold *pwf1,
4166 __isl_take isl_pw_qpolynomial_fold *pwf2);
4168 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4169 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4170 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4172 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4173 __isl_take isl_pw_qpolynomial_fold *pwf,
4174 __isl_take isl_point *pnt);
4176 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4177 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4178 __isl_take isl_point *pnt);
4180 __isl_give isl_pw_qpolynomial_fold *
4181 isl_pw_qpolynomial_fold_intersect_params(
4182 __isl_take isl_pw_qpolynomial_fold *pwf,
4183 __isl_take isl_set *set);
4185 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4186 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4187 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4188 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4189 __isl_take isl_union_set *uset);
4190 __isl_give isl_union_pw_qpolynomial_fold *
4191 isl_union_pw_qpolynomial_fold_intersect_params(
4192 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4193 __isl_take isl_set *set);
4195 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4196 __isl_take isl_pw_qpolynomial_fold *pwf);
4198 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4199 __isl_take isl_pw_qpolynomial_fold *pwf);
4201 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4202 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4204 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4205 __isl_take isl_qpolynomial_fold *fold,
4206 __isl_take isl_set *context);
4207 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4208 __isl_take isl_qpolynomial_fold *fold,
4209 __isl_take isl_set *context);
4211 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4212 __isl_take isl_pw_qpolynomial_fold *pwf,
4213 __isl_take isl_set *context);
4214 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4215 __isl_take isl_pw_qpolynomial_fold *pwf,
4216 __isl_take isl_set *context);
4218 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4219 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4220 __isl_take isl_union_set *context);
4221 __isl_give isl_union_pw_qpolynomial_fold *
4222 isl_union_pw_qpolynomial_fold_gist_params(
4223 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4224 __isl_take isl_set *context);
4226 The gist operation applies the gist operation to each of
4227 the cells in the domain of the input piecewise quasipolynomial reduction.
4228 In future, the operation will also exploit the context
4229 to simplify the quasipolynomial reductions associated to each cell.
4231 __isl_give isl_pw_qpolynomial_fold *
4232 isl_set_apply_pw_qpolynomial_fold(
4233 __isl_take isl_set *set,
4234 __isl_take isl_pw_qpolynomial_fold *pwf,
4236 __isl_give isl_pw_qpolynomial_fold *
4237 isl_map_apply_pw_qpolynomial_fold(
4238 __isl_take isl_map *map,
4239 __isl_take isl_pw_qpolynomial_fold *pwf,
4241 __isl_give isl_union_pw_qpolynomial_fold *
4242 isl_union_set_apply_union_pw_qpolynomial_fold(
4243 __isl_take isl_union_set *uset,
4244 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4246 __isl_give isl_union_pw_qpolynomial_fold *
4247 isl_union_map_apply_union_pw_qpolynomial_fold(
4248 __isl_take isl_union_map *umap,
4249 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4252 The functions taking a map
4253 compose the given map with the given piecewise quasipolynomial reduction.
4254 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4255 over all elements in the intersection of the range of the map
4256 and the domain of the piecewise quasipolynomial reduction
4257 as a function of an element in the domain of the map.
4258 The functions taking a set compute a bound over all elements in the
4259 intersection of the set and the domain of the
4260 piecewise quasipolynomial reduction.
4262 =head2 Dependence Analysis
4264 C<isl> contains specialized functionality for performing
4265 array dataflow analysis. That is, given a I<sink> access relation
4266 and a collection of possible I<source> access relations,
4267 C<isl> can compute relations that describe
4268 for each iteration of the sink access, which iteration
4269 of which of the source access relations was the last
4270 to access the same data element before the given iteration
4272 The resulting dependence relations map source iterations
4273 to the corresponding sink iterations.
4274 To compute standard flow dependences, the sink should be
4275 a read, while the sources should be writes.
4276 If any of the source accesses are marked as being I<may>
4277 accesses, then there will be a dependence from the last
4278 I<must> access B<and> from any I<may> access that follows
4279 this last I<must> access.
4280 In particular, if I<all> sources are I<may> accesses,
4281 then memory based dependence analysis is performed.
4282 If, on the other hand, all sources are I<must> accesses,
4283 then value based dependence analysis is performed.
4285 #include <isl/flow.h>
4287 typedef int (*isl_access_level_before)(void *first, void *second);
4289 __isl_give isl_access_info *isl_access_info_alloc(
4290 __isl_take isl_map *sink,
4291 void *sink_user, isl_access_level_before fn,
4293 __isl_give isl_access_info *isl_access_info_add_source(
4294 __isl_take isl_access_info *acc,
4295 __isl_take isl_map *source, int must,
4297 void *isl_access_info_free(__isl_take isl_access_info *acc);
4299 __isl_give isl_flow *isl_access_info_compute_flow(
4300 __isl_take isl_access_info *acc);
4302 int isl_flow_foreach(__isl_keep isl_flow *deps,
4303 int (*fn)(__isl_take isl_map *dep, int must,
4304 void *dep_user, void *user),
4306 __isl_give isl_map *isl_flow_get_no_source(
4307 __isl_keep isl_flow *deps, int must);
4308 void isl_flow_free(__isl_take isl_flow *deps);
4310 The function C<isl_access_info_compute_flow> performs the actual
4311 dependence analysis. The other functions are used to construct
4312 the input for this function or to read off the output.
4314 The input is collected in an C<isl_access_info>, which can
4315 be created through a call to C<isl_access_info_alloc>.
4316 The arguments to this functions are the sink access relation
4317 C<sink>, a token C<sink_user> used to identify the sink
4318 access to the user, a callback function for specifying the
4319 relative order of source and sink accesses, and the number
4320 of source access relations that will be added.
4321 The callback function has type C<int (*)(void *first, void *second)>.
4322 The function is called with two user supplied tokens identifying
4323 either a source or the sink and it should return the shared nesting
4324 level and the relative order of the two accesses.
4325 In particular, let I<n> be the number of loops shared by
4326 the two accesses. If C<first> precedes C<second> textually,
4327 then the function should return I<2 * n + 1>; otherwise,
4328 it should return I<2 * n>.
4329 The sources can be added to the C<isl_access_info> by performing
4330 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4331 C<must> indicates whether the source is a I<must> access
4332 or a I<may> access. Note that a multi-valued access relation
4333 should only be marked I<must> if every iteration in the domain
4334 of the relation accesses I<all> elements in its image.
4335 The C<source_user> token is again used to identify
4336 the source access. The range of the source access relation
4337 C<source> should have the same dimension as the range
4338 of the sink access relation.
4339 The C<isl_access_info_free> function should usually not be
4340 called explicitly, because it is called implicitly by
4341 C<isl_access_info_compute_flow>.
4343 The result of the dependence analysis is collected in an
4344 C<isl_flow>. There may be elements of
4345 the sink access for which no preceding source access could be
4346 found or for which all preceding sources are I<may> accesses.
4347 The relations containing these elements can be obtained through
4348 calls to C<isl_flow_get_no_source>, the first with C<must> set
4349 and the second with C<must> unset.
4350 In the case of standard flow dependence analysis,
4351 with the sink a read and the sources I<must> writes,
4352 the first relation corresponds to the reads from uninitialized
4353 array elements and the second relation is empty.
4354 The actual flow dependences can be extracted using
4355 C<isl_flow_foreach>. This function will call the user-specified
4356 callback function C<fn> for each B<non-empty> dependence between
4357 a source and the sink. The callback function is called
4358 with four arguments, the actual flow dependence relation
4359 mapping source iterations to sink iterations, a boolean that
4360 indicates whether it is a I<must> or I<may> dependence, a token
4361 identifying the source and an additional C<void *> with value
4362 equal to the third argument of the C<isl_flow_foreach> call.
4363 A dependence is marked I<must> if it originates from a I<must>
4364 source and if it is not followed by any I<may> sources.
4366 After finishing with an C<isl_flow>, the user should call
4367 C<isl_flow_free> to free all associated memory.
4369 A higher-level interface to dependence analysis is provided
4370 by the following function.
4372 #include <isl/flow.h>
4374 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4375 __isl_take isl_union_map *must_source,
4376 __isl_take isl_union_map *may_source,
4377 __isl_take isl_union_map *schedule,
4378 __isl_give isl_union_map **must_dep,
4379 __isl_give isl_union_map **may_dep,
4380 __isl_give isl_union_map **must_no_source,
4381 __isl_give isl_union_map **may_no_source);
4383 The arrays are identified by the tuple names of the ranges
4384 of the accesses. The iteration domains by the tuple names
4385 of the domains of the accesses and of the schedule.
4386 The relative order of the iteration domains is given by the
4387 schedule. The relations returned through C<must_no_source>
4388 and C<may_no_source> are subsets of C<sink>.
4389 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4390 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4391 any of the other arguments is treated as an error.
4393 =head3 Interaction with Dependence Analysis
4395 During the dependence analysis, we frequently need to perform
4396 the following operation. Given a relation between sink iterations
4397 and potential source iterations from a particular source domain,
4398 what is the last potential source iteration corresponding to each
4399 sink iteration. It can sometimes be convenient to adjust
4400 the set of potential source iterations before or after each such operation.
4401 The prototypical example is fuzzy array dataflow analysis,
4402 where we need to analyze if, based on data-dependent constraints,
4403 the sink iteration can ever be executed without one or more of
4404 the corresponding potential source iterations being executed.
4405 If so, we can introduce extra parameters and select an unknown
4406 but fixed source iteration from the potential source iterations.
4407 To be able to perform such manipulations, C<isl> provides the following
4410 #include <isl/flow.h>
4412 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4413 __isl_keep isl_map *source_map,
4414 __isl_keep isl_set *sink, void *source_user,
4416 __isl_give isl_access_info *isl_access_info_set_restrict(
4417 __isl_take isl_access_info *acc,
4418 isl_access_restrict fn, void *user);
4420 The function C<isl_access_info_set_restrict> should be called
4421 before calling C<isl_access_info_compute_flow> and registers a callback function
4422 that will be called any time C<isl> is about to compute the last
4423 potential source. The first argument is the (reverse) proto-dependence,
4424 mapping sink iterations to potential source iterations.
4425 The second argument represents the sink iterations for which
4426 we want to compute the last source iteration.
4427 The third argument is the token corresponding to the source
4428 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4429 The callback is expected to return a restriction on either the input or
4430 the output of the operation computing the last potential source.
4431 If the input needs to be restricted then restrictions are needed
4432 for both the source and the sink iterations. The sink iterations
4433 and the potential source iterations will be intersected with these sets.
4434 If the output needs to be restricted then only a restriction on the source
4435 iterations is required.
4436 If any error occurs, the callback should return C<NULL>.
4437 An C<isl_restriction> object can be created, freed and inspected
4438 using the following functions.
4440 #include <isl/flow.h>
4442 __isl_give isl_restriction *isl_restriction_input(
4443 __isl_take isl_set *source_restr,
4444 __isl_take isl_set *sink_restr);
4445 __isl_give isl_restriction *isl_restriction_output(
4446 __isl_take isl_set *source_restr);
4447 __isl_give isl_restriction *isl_restriction_none(
4448 __isl_take isl_map *source_map);
4449 __isl_give isl_restriction *isl_restriction_empty(
4450 __isl_take isl_map *source_map);
4451 void *isl_restriction_free(
4452 __isl_take isl_restriction *restr);
4453 isl_ctx *isl_restriction_get_ctx(
4454 __isl_keep isl_restriction *restr);
4456 C<isl_restriction_none> and C<isl_restriction_empty> are special
4457 cases of C<isl_restriction_input>. C<isl_restriction_none>
4458 is essentially equivalent to
4460 isl_restriction_input(isl_set_universe(
4461 isl_space_range(isl_map_get_space(source_map))),
4463 isl_space_domain(isl_map_get_space(source_map))));
4465 whereas C<isl_restriction_empty> is essentially equivalent to
4467 isl_restriction_input(isl_set_empty(
4468 isl_space_range(isl_map_get_space(source_map))),
4470 isl_space_domain(isl_map_get_space(source_map))));
4474 B<The functionality described in this section is fairly new
4475 and may be subject to change.>
4477 The following function can be used to compute a schedule
4478 for a union of domains.
4479 By default, the algorithm used to construct the schedule is similar
4480 to that of C<Pluto>.
4481 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4483 The generated schedule respects all C<validity> dependences.
4484 That is, all dependence distances over these dependences in the
4485 scheduled space are lexicographically positive.
4486 The default algorithm tries to minimize the dependence distances over
4487 C<proximity> dependences.
4488 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4489 for groups of domains where the dependence distances have only
4490 non-negative values.
4491 When using Feautrier's algorithm, the C<proximity> dependence
4492 distances are only minimized during the extension to a
4493 full-dimensional schedule.
4495 #include <isl/schedule.h>
4496 __isl_give isl_schedule *isl_union_set_compute_schedule(
4497 __isl_take isl_union_set *domain,
4498 __isl_take isl_union_map *validity,
4499 __isl_take isl_union_map *proximity);
4500 void *isl_schedule_free(__isl_take isl_schedule *sched);
4502 A mapping from the domains to the scheduled space can be obtained
4503 from an C<isl_schedule> using the following function.
4505 __isl_give isl_union_map *isl_schedule_get_map(
4506 __isl_keep isl_schedule *sched);
4508 A representation of the schedule can be printed using
4510 __isl_give isl_printer *isl_printer_print_schedule(
4511 __isl_take isl_printer *p,
4512 __isl_keep isl_schedule *schedule);
4514 A representation of the schedule as a forest of bands can be obtained
4515 using the following function.
4517 __isl_give isl_band_list *isl_schedule_get_band_forest(
4518 __isl_keep isl_schedule *schedule);
4520 The individual bands can be visited in depth-first post-order
4521 using the following function.
4523 #include <isl/schedule.h>
4524 int isl_schedule_foreach_band(
4525 __isl_keep isl_schedule *sched,
4526 int (*fn)(__isl_keep isl_band *band, void *user),
4529 The list can be manipulated as explained in L<"Lists">.
4530 The bands inside the list can be copied and freed using the following
4533 #include <isl/band.h>
4534 __isl_give isl_band *isl_band_copy(
4535 __isl_keep isl_band *band);
4536 void *isl_band_free(__isl_take isl_band *band);
4538 Each band contains zero or more scheduling dimensions.
4539 These are referred to as the members of the band.
4540 The section of the schedule that corresponds to the band is
4541 referred to as the partial schedule of the band.
4542 For those nodes that participate in a band, the outer scheduling
4543 dimensions form the prefix schedule, while the inner scheduling
4544 dimensions form the suffix schedule.
4545 That is, if we take a cut of the band forest, then the union of
4546 the concatenations of the prefix, partial and suffix schedules of
4547 each band in the cut is equal to the entire schedule (modulo
4548 some possible padding at the end with zero scheduling dimensions).
4549 The properties of a band can be inspected using the following functions.
4551 #include <isl/band.h>
4552 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4554 int isl_band_has_children(__isl_keep isl_band *band);
4555 __isl_give isl_band_list *isl_band_get_children(
4556 __isl_keep isl_band *band);
4558 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4559 __isl_keep isl_band *band);
4560 __isl_give isl_union_map *isl_band_get_partial_schedule(
4561 __isl_keep isl_band *band);
4562 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4563 __isl_keep isl_band *band);
4565 int isl_band_n_member(__isl_keep isl_band *band);
4566 int isl_band_member_is_zero_distance(
4567 __isl_keep isl_band *band, int pos);
4569 int isl_band_list_foreach_band(
4570 __isl_keep isl_band_list *list,
4571 int (*fn)(__isl_keep isl_band *band, void *user),
4574 Note that a scheduling dimension is considered to be ``zero
4575 distance'' if it does not carry any proximity dependences
4577 That is, if the dependence distances of the proximity
4578 dependences are all zero in that direction (for fixed
4579 iterations of outer bands).
4580 Like C<isl_schedule_foreach_band>,
4581 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4582 in depth-first post-order.
4584 A band can be tiled using the following function.
4586 #include <isl/band.h>
4587 int isl_band_tile(__isl_keep isl_band *band,
4588 __isl_take isl_vec *sizes);
4590 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4592 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4594 The C<isl_band_tile> function tiles the band using the given tile sizes
4595 inside its schedule.
4596 A new child band is created to represent the point loops and it is
4597 inserted between the modified band and its children.
4598 The C<tile_scale_tile_loops> option specifies whether the tile
4599 loops iterators should be scaled by the tile sizes.
4601 A representation of the band can be printed using
4603 #include <isl/band.h>
4604 __isl_give isl_printer *isl_printer_print_band(
4605 __isl_take isl_printer *p,
4606 __isl_keep isl_band *band);
4610 #include <isl/schedule.h>
4611 int isl_options_set_schedule_max_coefficient(
4612 isl_ctx *ctx, int val);
4613 int isl_options_get_schedule_max_coefficient(
4615 int isl_options_set_schedule_max_constant_term(
4616 isl_ctx *ctx, int val);
4617 int isl_options_get_schedule_max_constant_term(
4619 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4620 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4621 int isl_options_set_schedule_maximize_band_depth(
4622 isl_ctx *ctx, int val);
4623 int isl_options_get_schedule_maximize_band_depth(
4625 int isl_options_set_schedule_outer_zero_distance(
4626 isl_ctx *ctx, int val);
4627 int isl_options_get_schedule_outer_zero_distance(
4629 int isl_options_set_schedule_split_scaled(
4630 isl_ctx *ctx, int val);
4631 int isl_options_get_schedule_split_scaled(
4633 int isl_options_set_schedule_algorithm(
4634 isl_ctx *ctx, int val);
4635 int isl_options_get_schedule_algorithm(
4637 int isl_options_set_schedule_separate_components(
4638 isl_ctx *ctx, int val);
4639 int isl_options_get_schedule_separate_components(
4644 =item * schedule_max_coefficient
4646 This option enforces that the coefficients for variable and parameter
4647 dimensions in the calculated schedule are not larger than the specified value.
4648 This option can significantly increase the speed of the scheduling calculation
4649 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4650 this option does not introduce bounds on the variable or parameter
4653 =item * schedule_max_constant_term
4655 This option enforces that the constant coefficients in the calculated schedule
4656 are not larger than the maximal constant term. This option can significantly
4657 increase the speed of the scheduling calculation and may also prevent fusing of
4658 unrelated dimensions. A value of -1 means that this option does not introduce
4659 bounds on the constant coefficients.
4661 =item * schedule_fuse
4663 This option controls the level of fusion.
4664 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
4665 resulting schedule will be distributed as much as possible.
4666 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
4667 try to fuse loops in the resulting schedule.
4669 =item * schedule_maximize_band_depth
4671 If this option is set, we do not split bands at the point
4672 where we detect splitting is necessary. Instead, we
4673 backtrack and split bands as early as possible. This
4674 reduces the number of splits and maximizes the width of
4675 the bands. Wider bands give more possibilities for tiling.
4676 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
4677 then bands will be split as early as possible, even if there is no need.
4678 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
4680 =item * schedule_outer_zero_distance
4682 If this option is set, then we try to construct schedules
4683 where the outermost scheduling dimension in each band
4684 results in a zero dependence distance over the proximity
4687 =item * schedule_split_scaled
4689 If this option is set, then we try to construct schedules in which the
4690 constant term is split off from the linear part if the linear parts of
4691 the scheduling rows for all nodes in the graphs have a common non-trivial
4693 The constant term is then placed in a separate band and the linear
4696 =item * schedule_algorithm
4698 Selects the scheduling algorithm to be used.
4699 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4700 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4702 =item * schedule_separate_components
4704 If at any point the dependence graph contains any (weakly connected) components,
4705 then these components are scheduled separately.
4706 If this option is not set, then some iterations of the domains
4707 in these components may be scheduled together.
4708 If this option is set, then the components are given consecutive
4713 =head2 Parametric Vertex Enumeration
4715 The parametric vertex enumeration described in this section
4716 is mainly intended to be used internally and by the C<barvinok>
4719 #include <isl/vertices.h>
4720 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4721 __isl_keep isl_basic_set *bset);
4723 The function C<isl_basic_set_compute_vertices> performs the
4724 actual computation of the parametric vertices and the chamber
4725 decomposition and store the result in an C<isl_vertices> object.
4726 This information can be queried by either iterating over all
4727 the vertices or iterating over all the chambers or cells
4728 and then iterating over all vertices that are active on the chamber.
4730 int isl_vertices_foreach_vertex(
4731 __isl_keep isl_vertices *vertices,
4732 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4735 int isl_vertices_foreach_cell(
4736 __isl_keep isl_vertices *vertices,
4737 int (*fn)(__isl_take isl_cell *cell, void *user),
4739 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4740 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4743 Other operations that can be performed on an C<isl_vertices> object are
4746 isl_ctx *isl_vertices_get_ctx(
4747 __isl_keep isl_vertices *vertices);
4748 int isl_vertices_get_n_vertices(
4749 __isl_keep isl_vertices *vertices);
4750 void isl_vertices_free(__isl_take isl_vertices *vertices);
4752 Vertices can be inspected and destroyed using the following functions.
4754 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4755 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4756 __isl_give isl_basic_set *isl_vertex_get_domain(
4757 __isl_keep isl_vertex *vertex);
4758 __isl_give isl_basic_set *isl_vertex_get_expr(
4759 __isl_keep isl_vertex *vertex);
4760 void isl_vertex_free(__isl_take isl_vertex *vertex);
4762 C<isl_vertex_get_expr> returns a singleton parametric set describing
4763 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4765 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4766 B<rational> basic sets, so they should mainly be used for inspection
4767 and should not be mixed with integer sets.
4769 Chambers can be inspected and destroyed using the following functions.
4771 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4772 __isl_give isl_basic_set *isl_cell_get_domain(
4773 __isl_keep isl_cell *cell);
4774 void isl_cell_free(__isl_take isl_cell *cell);
4778 Although C<isl> is mainly meant to be used as a library,
4779 it also contains some basic applications that use some
4780 of the functionality of C<isl>.
4781 The input may be specified in either the L<isl format>
4782 or the L<PolyLib format>.
4784 =head2 C<isl_polyhedron_sample>
4786 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4787 an integer element of the polyhedron, if there is any.
4788 The first column in the output is the denominator and is always
4789 equal to 1. If the polyhedron contains no integer points,
4790 then a vector of length zero is printed.
4794 C<isl_pip> takes the same input as the C<example> program
4795 from the C<piplib> distribution, i.e., a set of constraints
4796 on the parameters, a line containing only -1 and finally a set
4797 of constraints on a parametric polyhedron.
4798 The coefficients of the parameters appear in the last columns
4799 (but before the final constant column).
4800 The output is the lexicographic minimum of the parametric polyhedron.
4801 As C<isl> currently does not have its own output format, the output
4802 is just a dump of the internal state.
4804 =head2 C<isl_polyhedron_minimize>
4806 C<isl_polyhedron_minimize> computes the minimum of some linear
4807 or affine objective function over the integer points in a polyhedron.
4808 If an affine objective function
4809 is given, then the constant should appear in the last column.
4811 =head2 C<isl_polytope_scan>
4813 Given a polytope, C<isl_polytope_scan> prints
4814 all integer points in the polytope.