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_space(
677 __isl_keep isl_multi_aff *maff);
678 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
679 __isl_keep isl_pw_multi_aff *pma);
680 __isl_give isl_space *isl_pw_multi_aff_get_space(
681 __isl_keep isl_pw_multi_aff *pma);
682 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
683 __isl_keep isl_union_pw_multi_aff *upma);
685 #include <isl/point.h>
686 __isl_give isl_space *isl_point_get_space(
687 __isl_keep isl_point *pnt);
689 The identifiers or names of the individual dimensions may be set or read off
690 using the following functions.
692 #include <isl/space.h>
693 __isl_give isl_space *isl_space_set_dim_id(
694 __isl_take isl_space *space,
695 enum isl_dim_type type, unsigned pos,
696 __isl_take isl_id *id);
697 int isl_space_has_dim_id(__isl_keep isl_space *space,
698 enum isl_dim_type type, unsigned pos);
699 __isl_give isl_id *isl_space_get_dim_id(
700 __isl_keep isl_space *space,
701 enum isl_dim_type type, unsigned pos);
702 __isl_give isl_space *isl_space_set_dim_name(
703 __isl_take isl_space *space,
704 enum isl_dim_type type, unsigned pos,
705 __isl_keep const char *name);
706 int isl_space_has_dim_name(__isl_keep isl_space *space,
707 enum isl_dim_type type, unsigned pos);
708 __isl_keep const char *isl_space_get_dim_name(
709 __isl_keep isl_space *space,
710 enum isl_dim_type type, unsigned pos);
712 Note that C<isl_space_get_name> returns a pointer to some internal
713 data structure, so the result can only be used while the
714 corresponding C<isl_space> is alive.
715 Also note that every function that operates on two sets or relations
716 requires that both arguments have the same parameters. This also
717 means that if one of the arguments has named parameters, then the
718 other needs to have named parameters too and the names need to match.
719 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
720 arguments may have different parameters (as long as they are named),
721 in which case the result will have as parameters the union of the parameters of
724 Given the identifier or name of a dimension (typically a parameter),
725 its position can be obtained from the following function.
727 #include <isl/space.h>
728 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
729 enum isl_dim_type type, __isl_keep isl_id *id);
730 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
731 enum isl_dim_type type, const char *name);
733 The identifiers or names of entire spaces may be set or read off
734 using the following functions.
736 #include <isl/space.h>
737 __isl_give isl_space *isl_space_set_tuple_id(
738 __isl_take isl_space *space,
739 enum isl_dim_type type, __isl_take isl_id *id);
740 __isl_give isl_space *isl_space_reset_tuple_id(
741 __isl_take isl_space *space, enum isl_dim_type type);
742 int isl_space_has_tuple_id(__isl_keep isl_space *space,
743 enum isl_dim_type type);
744 __isl_give isl_id *isl_space_get_tuple_id(
745 __isl_keep isl_space *space, enum isl_dim_type type);
746 __isl_give isl_space *isl_space_set_tuple_name(
747 __isl_take isl_space *space,
748 enum isl_dim_type type, const char *s);
749 int isl_space_has_tuple_name(__isl_keep isl_space *space,
750 enum isl_dim_type type);
751 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
752 enum isl_dim_type type);
754 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
755 or C<isl_dim_set>. As with C<isl_space_get_name>,
756 the C<isl_space_get_tuple_name> function returns a pointer to some internal
758 Binary operations require the corresponding spaces of their arguments
759 to have the same name.
761 Spaces can be nested. In particular, the domain of a set or
762 the domain or range of a relation can be a nested relation.
763 The following functions can be used to construct and deconstruct
766 #include <isl/space.h>
767 int isl_space_is_wrapping(__isl_keep isl_space *space);
768 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
769 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
771 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
772 be the space of a set, while that of
773 C<isl_space_wrap> should be the space of a relation.
774 Conversely, the output of C<isl_space_unwrap> is the space
775 of a relation, while that of C<isl_space_wrap> is the space of a set.
777 Spaces can be created from other spaces
778 using the following functions.
780 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
781 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
782 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
783 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
784 __isl_give isl_space *isl_space_params(
785 __isl_take isl_space *space);
786 __isl_give isl_space *isl_space_set_from_params(
787 __isl_take isl_space *space);
788 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
789 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
790 __isl_take isl_space *right);
791 __isl_give isl_space *isl_space_align_params(
792 __isl_take isl_space *space1, __isl_take isl_space *space2)
793 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
794 enum isl_dim_type type, unsigned pos, unsigned n);
795 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
796 enum isl_dim_type type, unsigned n);
797 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
798 enum isl_dim_type type, unsigned first, unsigned n);
799 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
800 enum isl_dim_type dst_type, unsigned dst_pos,
801 enum isl_dim_type src_type, unsigned src_pos,
803 __isl_give isl_space *isl_space_map_from_set(
804 __isl_take isl_space *space);
805 __isl_give isl_space *isl_space_map_from_domain_and_range(
806 __isl_take isl_space *domain,
807 __isl_take isl_space *range);
808 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
809 __isl_give isl_space *isl_space_curry(
810 __isl_take isl_space *space);
812 Note that if dimensions are added or removed from a space, then
813 the name and the internal structure are lost.
817 A local space is essentially a space with
818 zero or more existentially quantified variables.
819 The local space of a (constraint of a) basic set or relation can be obtained
820 using the following functions.
822 #include <isl/constraint.h>
823 __isl_give isl_local_space *isl_constraint_get_local_space(
824 __isl_keep isl_constraint *constraint);
827 __isl_give isl_local_space *isl_basic_set_get_local_space(
828 __isl_keep isl_basic_set *bset);
831 __isl_give isl_local_space *isl_basic_map_get_local_space(
832 __isl_keep isl_basic_map *bmap);
834 A new local space can be created from a space using
836 #include <isl/local_space.h>
837 __isl_give isl_local_space *isl_local_space_from_space(
838 __isl_take isl_space *space);
840 They can be inspected, modified, copied and freed using the following functions.
842 #include <isl/local_space.h>
843 isl_ctx *isl_local_space_get_ctx(
844 __isl_keep isl_local_space *ls);
845 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
846 int isl_local_space_dim(__isl_keep isl_local_space *ls,
847 enum isl_dim_type type);
848 int isl_local_space_has_dim_id(
849 __isl_keep isl_local_space *ls,
850 enum isl_dim_type type, unsigned pos);
851 __isl_give isl_id *isl_local_space_get_dim_id(
852 __isl_keep isl_local_space *ls,
853 enum isl_dim_type type, unsigned pos);
854 int isl_local_space_has_dim_name(
855 __isl_keep isl_local_space *ls,
856 enum isl_dim_type type, unsigned pos)
857 const char *isl_local_space_get_dim_name(
858 __isl_keep isl_local_space *ls,
859 enum isl_dim_type type, unsigned pos);
860 __isl_give isl_local_space *isl_local_space_set_dim_name(
861 __isl_take isl_local_space *ls,
862 enum isl_dim_type type, unsigned pos, const char *s);
863 __isl_give isl_local_space *isl_local_space_set_dim_id(
864 __isl_take isl_local_space *ls,
865 enum isl_dim_type type, unsigned pos,
866 __isl_take isl_id *id);
867 __isl_give isl_space *isl_local_space_get_space(
868 __isl_keep isl_local_space *ls);
869 __isl_give isl_aff *isl_local_space_get_div(
870 __isl_keep isl_local_space *ls, int pos);
871 __isl_give isl_local_space *isl_local_space_copy(
872 __isl_keep isl_local_space *ls);
873 void *isl_local_space_free(__isl_take isl_local_space *ls);
875 Two local spaces can be compared using
877 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
878 __isl_keep isl_local_space *ls2);
880 Local spaces can be created from other local spaces
881 using the following functions.
883 __isl_give isl_local_space *isl_local_space_domain(
884 __isl_take isl_local_space *ls);
885 __isl_give isl_local_space *isl_local_space_range(
886 __isl_take isl_local_space *ls);
887 __isl_give isl_local_space *isl_local_space_from_domain(
888 __isl_take isl_local_space *ls);
889 __isl_give isl_local_space *isl_local_space_intersect(
890 __isl_take isl_local_space *ls1,
891 __isl_take isl_local_space *ls2);
892 __isl_give isl_local_space *isl_local_space_add_dims(
893 __isl_take isl_local_space *ls,
894 enum isl_dim_type type, unsigned n);
895 __isl_give isl_local_space *isl_local_space_insert_dims(
896 __isl_take isl_local_space *ls,
897 enum isl_dim_type type, unsigned first, unsigned n);
898 __isl_give isl_local_space *isl_local_space_drop_dims(
899 __isl_take isl_local_space *ls,
900 enum isl_dim_type type, unsigned first, unsigned n);
902 =head2 Input and Output
904 C<isl> supports its own input/output format, which is similar
905 to the C<Omega> format, but also supports the C<PolyLib> format
910 The C<isl> format is similar to that of C<Omega>, but has a different
911 syntax for describing the parameters and allows for the definition
912 of an existentially quantified variable as the integer division
913 of an affine expression.
914 For example, the set of integers C<i> between C<0> and C<n>
915 such that C<i % 10 <= 6> can be described as
917 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
920 A set or relation can have several disjuncts, separated
921 by the keyword C<or>. Each disjunct is either a conjunction
922 of constraints or a projection (C<exists>) of a conjunction
923 of constraints. The constraints are separated by the keyword
926 =head3 C<PolyLib> format
928 If the represented set is a union, then the first line
929 contains a single number representing the number of disjuncts.
930 Otherwise, a line containing the number C<1> is optional.
932 Each disjunct is represented by a matrix of constraints.
933 The first line contains two numbers representing
934 the number of rows and columns,
935 where the number of rows is equal to the number of constraints
936 and the number of columns is equal to two plus the number of variables.
937 The following lines contain the actual rows of the constraint matrix.
938 In each row, the first column indicates whether the constraint
939 is an equality (C<0>) or inequality (C<1>). The final column
940 corresponds to the constant term.
942 If the set is parametric, then the coefficients of the parameters
943 appear in the last columns before the constant column.
944 The coefficients of any existentially quantified variables appear
945 between those of the set variables and those of the parameters.
947 =head3 Extended C<PolyLib> format
949 The extended C<PolyLib> format is nearly identical to the
950 C<PolyLib> format. The only difference is that the line
951 containing the number of rows and columns of a constraint matrix
952 also contains four additional numbers:
953 the number of output dimensions, the number of input dimensions,
954 the number of local dimensions (i.e., the number of existentially
955 quantified variables) and the number of parameters.
956 For sets, the number of ``output'' dimensions is equal
957 to the number of set dimensions, while the number of ``input''
963 __isl_give isl_basic_set *isl_basic_set_read_from_file(
964 isl_ctx *ctx, FILE *input);
965 __isl_give isl_basic_set *isl_basic_set_read_from_str(
966 isl_ctx *ctx, const char *str);
967 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
969 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
973 __isl_give isl_basic_map *isl_basic_map_read_from_file(
974 isl_ctx *ctx, FILE *input);
975 __isl_give isl_basic_map *isl_basic_map_read_from_str(
976 isl_ctx *ctx, const char *str);
977 __isl_give isl_map *isl_map_read_from_file(
978 isl_ctx *ctx, FILE *input);
979 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
982 #include <isl/union_set.h>
983 __isl_give isl_union_set *isl_union_set_read_from_file(
984 isl_ctx *ctx, FILE *input);
985 __isl_give isl_union_set *isl_union_set_read_from_str(
986 isl_ctx *ctx, const char *str);
988 #include <isl/union_map.h>
989 __isl_give isl_union_map *isl_union_map_read_from_file(
990 isl_ctx *ctx, FILE *input);
991 __isl_give isl_union_map *isl_union_map_read_from_str(
992 isl_ctx *ctx, const char *str);
994 The input format is autodetected and may be either the C<PolyLib> format
995 or the C<isl> format.
999 Before anything can be printed, an C<isl_printer> needs to
1002 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1004 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1005 void isl_printer_free(__isl_take isl_printer *printer);
1006 __isl_give char *isl_printer_get_str(
1007 __isl_keep isl_printer *printer);
1009 The printer can be inspected using the following functions.
1011 FILE *isl_printer_get_file(
1012 __isl_keep isl_printer *printer);
1013 int isl_printer_get_output_format(
1014 __isl_keep isl_printer *p);
1016 The behavior of the printer can be modified in various ways
1018 __isl_give isl_printer *isl_printer_set_output_format(
1019 __isl_take isl_printer *p, int output_format);
1020 __isl_give isl_printer *isl_printer_set_indent(
1021 __isl_take isl_printer *p, int indent);
1022 __isl_give isl_printer *isl_printer_indent(
1023 __isl_take isl_printer *p, int indent);
1024 __isl_give isl_printer *isl_printer_set_prefix(
1025 __isl_take isl_printer *p, const char *prefix);
1026 __isl_give isl_printer *isl_printer_set_suffix(
1027 __isl_take isl_printer *p, const char *suffix);
1029 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1030 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1031 and defaults to C<ISL_FORMAT_ISL>.
1032 Each line in the output is indented by C<indent> (set by
1033 C<isl_printer_set_indent>) spaces
1034 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1035 In the C<PolyLib> format output,
1036 the coefficients of the existentially quantified variables
1037 appear between those of the set variables and those
1039 The function C<isl_printer_indent> increases the indentation
1040 by the specified amount (which may be negative).
1042 To actually print something, use
1044 #include <isl/printer.h>
1045 __isl_give isl_printer *isl_printer_print_double(
1046 __isl_take isl_printer *p, double d);
1048 #include <isl/set.h>
1049 __isl_give isl_printer *isl_printer_print_basic_set(
1050 __isl_take isl_printer *printer,
1051 __isl_keep isl_basic_set *bset);
1052 __isl_give isl_printer *isl_printer_print_set(
1053 __isl_take isl_printer *printer,
1054 __isl_keep isl_set *set);
1056 #include <isl/map.h>
1057 __isl_give isl_printer *isl_printer_print_basic_map(
1058 __isl_take isl_printer *printer,
1059 __isl_keep isl_basic_map *bmap);
1060 __isl_give isl_printer *isl_printer_print_map(
1061 __isl_take isl_printer *printer,
1062 __isl_keep isl_map *map);
1064 #include <isl/union_set.h>
1065 __isl_give isl_printer *isl_printer_print_union_set(
1066 __isl_take isl_printer *p,
1067 __isl_keep isl_union_set *uset);
1069 #include <isl/union_map.h>
1070 __isl_give isl_printer *isl_printer_print_union_map(
1071 __isl_take isl_printer *p,
1072 __isl_keep isl_union_map *umap);
1074 When called on a file printer, the following function flushes
1075 the file. When called on a string printer, the buffer is cleared.
1077 __isl_give isl_printer *isl_printer_flush(
1078 __isl_take isl_printer *p);
1080 =head2 Creating New Sets and Relations
1082 C<isl> has functions for creating some standard sets and relations.
1086 =item * Empty sets and relations
1088 __isl_give isl_basic_set *isl_basic_set_empty(
1089 __isl_take isl_space *space);
1090 __isl_give isl_basic_map *isl_basic_map_empty(
1091 __isl_take isl_space *space);
1092 __isl_give isl_set *isl_set_empty(
1093 __isl_take isl_space *space);
1094 __isl_give isl_map *isl_map_empty(
1095 __isl_take isl_space *space);
1096 __isl_give isl_union_set *isl_union_set_empty(
1097 __isl_take isl_space *space);
1098 __isl_give isl_union_map *isl_union_map_empty(
1099 __isl_take isl_space *space);
1101 For C<isl_union_set>s and C<isl_union_map>s, the space
1102 is only used to specify the parameters.
1104 =item * Universe sets and relations
1106 __isl_give isl_basic_set *isl_basic_set_universe(
1107 __isl_take isl_space *space);
1108 __isl_give isl_basic_map *isl_basic_map_universe(
1109 __isl_take isl_space *space);
1110 __isl_give isl_set *isl_set_universe(
1111 __isl_take isl_space *space);
1112 __isl_give isl_map *isl_map_universe(
1113 __isl_take isl_space *space);
1114 __isl_give isl_union_set *isl_union_set_universe(
1115 __isl_take isl_union_set *uset);
1116 __isl_give isl_union_map *isl_union_map_universe(
1117 __isl_take isl_union_map *umap);
1119 The sets and relations constructed by the functions above
1120 contain all integer values, while those constructed by the
1121 functions below only contain non-negative values.
1123 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1124 __isl_take isl_space *space);
1125 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1126 __isl_take isl_space *space);
1127 __isl_give isl_set *isl_set_nat_universe(
1128 __isl_take isl_space *space);
1129 __isl_give isl_map *isl_map_nat_universe(
1130 __isl_take isl_space *space);
1132 =item * Identity relations
1134 __isl_give isl_basic_map *isl_basic_map_identity(
1135 __isl_take isl_space *space);
1136 __isl_give isl_map *isl_map_identity(
1137 __isl_take isl_space *space);
1139 The number of input and output dimensions in C<space> needs
1142 =item * Lexicographic order
1144 __isl_give isl_map *isl_map_lex_lt(
1145 __isl_take isl_space *set_space);
1146 __isl_give isl_map *isl_map_lex_le(
1147 __isl_take isl_space *set_space);
1148 __isl_give isl_map *isl_map_lex_gt(
1149 __isl_take isl_space *set_space);
1150 __isl_give isl_map *isl_map_lex_ge(
1151 __isl_take isl_space *set_space);
1152 __isl_give isl_map *isl_map_lex_lt_first(
1153 __isl_take isl_space *space, unsigned n);
1154 __isl_give isl_map *isl_map_lex_le_first(
1155 __isl_take isl_space *space, unsigned n);
1156 __isl_give isl_map *isl_map_lex_gt_first(
1157 __isl_take isl_space *space, unsigned n);
1158 __isl_give isl_map *isl_map_lex_ge_first(
1159 __isl_take isl_space *space, unsigned n);
1161 The first four functions take a space for a B<set>
1162 and return relations that express that the elements in the domain
1163 are lexicographically less
1164 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1165 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1166 than the elements in the range.
1167 The last four functions take a space for a map
1168 and return relations that express that the first C<n> dimensions
1169 in the domain are lexicographically less
1170 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1171 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1172 than the first C<n> dimensions in the range.
1176 A basic set or relation can be converted to a set or relation
1177 using the following functions.
1179 __isl_give isl_set *isl_set_from_basic_set(
1180 __isl_take isl_basic_set *bset);
1181 __isl_give isl_map *isl_map_from_basic_map(
1182 __isl_take isl_basic_map *bmap);
1184 Sets and relations can be converted to union sets and relations
1185 using the following functions.
1187 __isl_give isl_union_map *isl_union_map_from_map(
1188 __isl_take isl_map *map);
1189 __isl_give isl_union_set *isl_union_set_from_set(
1190 __isl_take isl_set *set);
1192 The inverse conversions below can only be used if the input
1193 union set or relation is known to contain elements in exactly one
1196 __isl_give isl_set *isl_set_from_union_set(
1197 __isl_take isl_union_set *uset);
1198 __isl_give isl_map *isl_map_from_union_map(
1199 __isl_take isl_union_map *umap);
1201 A zero-dimensional set can be constructed on a given parameter domain
1202 using the following function.
1204 __isl_give isl_set *isl_set_from_params(
1205 __isl_take isl_set *set);
1207 Sets and relations can be copied and freed again using the following
1210 __isl_give isl_basic_set *isl_basic_set_copy(
1211 __isl_keep isl_basic_set *bset);
1212 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1213 __isl_give isl_union_set *isl_union_set_copy(
1214 __isl_keep isl_union_set *uset);
1215 __isl_give isl_basic_map *isl_basic_map_copy(
1216 __isl_keep isl_basic_map *bmap);
1217 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1218 __isl_give isl_union_map *isl_union_map_copy(
1219 __isl_keep isl_union_map *umap);
1220 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1221 void isl_set_free(__isl_take isl_set *set);
1222 void *isl_union_set_free(__isl_take isl_union_set *uset);
1223 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1224 void isl_map_free(__isl_take isl_map *map);
1225 void *isl_union_map_free(__isl_take isl_union_map *umap);
1227 Other sets and relations can be constructed by starting
1228 from a universe set or relation, adding equality and/or
1229 inequality constraints and then projecting out the
1230 existentially quantified variables, if any.
1231 Constraints can be constructed, manipulated and
1232 added to (or removed from) (basic) sets and relations
1233 using the following functions.
1235 #include <isl/constraint.h>
1236 __isl_give isl_constraint *isl_equality_alloc(
1237 __isl_take isl_local_space *ls);
1238 __isl_give isl_constraint *isl_inequality_alloc(
1239 __isl_take isl_local_space *ls);
1240 __isl_give isl_constraint *isl_constraint_set_constant(
1241 __isl_take isl_constraint *constraint, isl_int v);
1242 __isl_give isl_constraint *isl_constraint_set_constant_si(
1243 __isl_take isl_constraint *constraint, int v);
1244 __isl_give isl_constraint *isl_constraint_set_coefficient(
1245 __isl_take isl_constraint *constraint,
1246 enum isl_dim_type type, int pos, isl_int v);
1247 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1248 __isl_take isl_constraint *constraint,
1249 enum isl_dim_type type, int pos, int v);
1250 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1251 __isl_take isl_basic_map *bmap,
1252 __isl_take isl_constraint *constraint);
1253 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1254 __isl_take isl_basic_set *bset,
1255 __isl_take isl_constraint *constraint);
1256 __isl_give isl_map *isl_map_add_constraint(
1257 __isl_take isl_map *map,
1258 __isl_take isl_constraint *constraint);
1259 __isl_give isl_set *isl_set_add_constraint(
1260 __isl_take isl_set *set,
1261 __isl_take isl_constraint *constraint);
1262 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1263 __isl_take isl_basic_set *bset,
1264 __isl_take isl_constraint *constraint);
1266 For example, to create a set containing the even integers
1267 between 10 and 42, you would use the following code.
1270 isl_local_space *ls;
1272 isl_basic_set *bset;
1274 space = isl_space_set_alloc(ctx, 0, 2);
1275 bset = isl_basic_set_universe(isl_space_copy(space));
1276 ls = isl_local_space_from_space(space);
1278 c = isl_equality_alloc(isl_local_space_copy(ls));
1279 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1280 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1281 bset = isl_basic_set_add_constraint(bset, c);
1283 c = isl_inequality_alloc(isl_local_space_copy(ls));
1284 c = isl_constraint_set_constant_si(c, -10);
1285 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1286 bset = isl_basic_set_add_constraint(bset, c);
1288 c = isl_inequality_alloc(ls);
1289 c = isl_constraint_set_constant_si(c, 42);
1290 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1291 bset = isl_basic_set_add_constraint(bset, c);
1293 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1297 isl_basic_set *bset;
1298 bset = isl_basic_set_read_from_str(ctx,
1299 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1301 A basic set or relation can also be constructed from two matrices
1302 describing the equalities and the inequalities.
1304 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1305 __isl_take isl_space *space,
1306 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1307 enum isl_dim_type c1,
1308 enum isl_dim_type c2, enum isl_dim_type c3,
1309 enum isl_dim_type c4);
1310 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1311 __isl_take isl_space *space,
1312 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1313 enum isl_dim_type c1,
1314 enum isl_dim_type c2, enum isl_dim_type c3,
1315 enum isl_dim_type c4, enum isl_dim_type c5);
1317 The C<isl_dim_type> arguments indicate the order in which
1318 different kinds of variables appear in the input matrices
1319 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1320 C<isl_dim_set> and C<isl_dim_div> for sets and
1321 of C<isl_dim_cst>, C<isl_dim_param>,
1322 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1324 A (basic or union) set or relation can also be constructed from a
1325 (union) (piecewise) (multiple) affine expression
1326 or a list of affine expressions
1327 (See L<"Piecewise Quasi Affine Expressions"> and
1328 L<"Piecewise Multiple Quasi Affine Expressions">).
1330 __isl_give isl_basic_map *isl_basic_map_from_aff(
1331 __isl_take isl_aff *aff);
1332 __isl_give isl_map *isl_map_from_aff(
1333 __isl_take isl_aff *aff);
1334 __isl_give isl_set *isl_set_from_pw_aff(
1335 __isl_take isl_pw_aff *pwaff);
1336 __isl_give isl_map *isl_map_from_pw_aff(
1337 __isl_take isl_pw_aff *pwaff);
1338 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1339 __isl_take isl_space *domain_space,
1340 __isl_take isl_aff_list *list);
1341 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1342 __isl_take isl_multi_aff *maff)
1343 __isl_give isl_map *isl_map_from_multi_aff(
1344 __isl_take isl_multi_aff *maff)
1345 __isl_give isl_set *isl_set_from_pw_multi_aff(
1346 __isl_take isl_pw_multi_aff *pma);
1347 __isl_give isl_map *isl_map_from_pw_multi_aff(
1348 __isl_take isl_pw_multi_aff *pma);
1349 __isl_give isl_union_map *
1350 isl_union_map_from_union_pw_multi_aff(
1351 __isl_take isl_union_pw_multi_aff *upma);
1353 The C<domain_dim> argument describes the domain of the resulting
1354 basic relation. It is required because the C<list> may consist
1355 of zero affine expressions.
1357 =head2 Inspecting Sets and Relations
1359 Usually, the user should not have to care about the actual constraints
1360 of the sets and maps, but should instead apply the abstract operations
1361 explained in the following sections.
1362 Occasionally, however, it may be required to inspect the individual
1363 coefficients of the constraints. This section explains how to do so.
1364 In these cases, it may also be useful to have C<isl> compute
1365 an explicit representation of the existentially quantified variables.
1367 __isl_give isl_set *isl_set_compute_divs(
1368 __isl_take isl_set *set);
1369 __isl_give isl_map *isl_map_compute_divs(
1370 __isl_take isl_map *map);
1371 __isl_give isl_union_set *isl_union_set_compute_divs(
1372 __isl_take isl_union_set *uset);
1373 __isl_give isl_union_map *isl_union_map_compute_divs(
1374 __isl_take isl_union_map *umap);
1376 This explicit representation defines the existentially quantified
1377 variables as integer divisions of the other variables, possibly
1378 including earlier existentially quantified variables.
1379 An explicitly represented existentially quantified variable therefore
1380 has a unique value when the values of the other variables are known.
1381 If, furthermore, the same existentials, i.e., existentials
1382 with the same explicit representations, should appear in the
1383 same order in each of the disjuncts of a set or map, then the user should call
1384 either of the following functions.
1386 __isl_give isl_set *isl_set_align_divs(
1387 __isl_take isl_set *set);
1388 __isl_give isl_map *isl_map_align_divs(
1389 __isl_take isl_map *map);
1391 Alternatively, the existentially quantified variables can be removed
1392 using the following functions, which compute an overapproximation.
1394 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1395 __isl_take isl_basic_set *bset);
1396 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1397 __isl_take isl_basic_map *bmap);
1398 __isl_give isl_set *isl_set_remove_divs(
1399 __isl_take isl_set *set);
1400 __isl_give isl_map *isl_map_remove_divs(
1401 __isl_take isl_map *map);
1403 To iterate over all the sets or maps in a union set or map, use
1405 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1406 int (*fn)(__isl_take isl_set *set, void *user),
1408 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1409 int (*fn)(__isl_take isl_map *map, void *user),
1412 The number of sets or maps in a union set or map can be obtained
1415 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1416 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1418 To extract the set or map in a given space from a union, use
1420 __isl_give isl_set *isl_union_set_extract_set(
1421 __isl_keep isl_union_set *uset,
1422 __isl_take isl_space *space);
1423 __isl_give isl_map *isl_union_map_extract_map(
1424 __isl_keep isl_union_map *umap,
1425 __isl_take isl_space *space);
1427 To iterate over all the basic sets or maps in a set or map, use
1429 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1430 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1432 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1433 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1436 The callback function C<fn> should return 0 if successful and
1437 -1 if an error occurs. In the latter case, or if any other error
1438 occurs, the above functions will return -1.
1440 It should be noted that C<isl> does not guarantee that
1441 the basic sets or maps passed to C<fn> are disjoint.
1442 If this is required, then the user should call one of
1443 the following functions first.
1445 __isl_give isl_set *isl_set_make_disjoint(
1446 __isl_take isl_set *set);
1447 __isl_give isl_map *isl_map_make_disjoint(
1448 __isl_take isl_map *map);
1450 The number of basic sets in a set can be obtained
1453 int isl_set_n_basic_set(__isl_keep isl_set *set);
1455 To iterate over the constraints of a basic set or map, use
1457 #include <isl/constraint.h>
1459 int isl_basic_set_n_constraint(
1460 __isl_keep isl_basic_set *bset);
1461 int isl_basic_set_foreach_constraint(
1462 __isl_keep isl_basic_set *bset,
1463 int (*fn)(__isl_take isl_constraint *c, void *user),
1465 int isl_basic_map_foreach_constraint(
1466 __isl_keep isl_basic_map *bmap,
1467 int (*fn)(__isl_take isl_constraint *c, void *user),
1469 void *isl_constraint_free(__isl_take isl_constraint *c);
1471 Again, the callback function C<fn> should return 0 if successful and
1472 -1 if an error occurs. In the latter case, or if any other error
1473 occurs, the above functions will return -1.
1474 The constraint C<c> represents either an equality or an inequality.
1475 Use the following function to find out whether a constraint
1476 represents an equality. If not, it represents an inequality.
1478 int isl_constraint_is_equality(
1479 __isl_keep isl_constraint *constraint);
1481 The coefficients of the constraints can be inspected using
1482 the following functions.
1484 int isl_constraint_is_lower_bound(
1485 __isl_keep isl_constraint *constraint,
1486 enum isl_dim_type type, unsigned pos);
1487 int isl_constraint_is_upper_bound(
1488 __isl_keep isl_constraint *constraint,
1489 enum isl_dim_type type, unsigned pos);
1490 void isl_constraint_get_constant(
1491 __isl_keep isl_constraint *constraint, isl_int *v);
1492 void isl_constraint_get_coefficient(
1493 __isl_keep isl_constraint *constraint,
1494 enum isl_dim_type type, int pos, isl_int *v);
1495 int isl_constraint_involves_dims(
1496 __isl_keep isl_constraint *constraint,
1497 enum isl_dim_type type, unsigned first, unsigned n);
1499 The explicit representations of the existentially quantified
1500 variables can be inspected using the following function.
1501 Note that the user is only allowed to use this function
1502 if the inspected set or map is the result of a call
1503 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1504 The existentially quantified variable is equal to the floor
1505 of the returned affine expression. The affine expression
1506 itself can be inspected using the functions in
1507 L<"Piecewise Quasi Affine Expressions">.
1509 __isl_give isl_aff *isl_constraint_get_div(
1510 __isl_keep isl_constraint *constraint, int pos);
1512 To obtain the constraints of a basic set or map in matrix
1513 form, use the following functions.
1515 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1516 __isl_keep isl_basic_set *bset,
1517 enum isl_dim_type c1, enum isl_dim_type c2,
1518 enum isl_dim_type c3, enum isl_dim_type c4);
1519 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1520 __isl_keep isl_basic_set *bset,
1521 enum isl_dim_type c1, enum isl_dim_type c2,
1522 enum isl_dim_type c3, enum isl_dim_type c4);
1523 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1524 __isl_keep isl_basic_map *bmap,
1525 enum isl_dim_type c1,
1526 enum isl_dim_type c2, enum isl_dim_type c3,
1527 enum isl_dim_type c4, enum isl_dim_type c5);
1528 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1529 __isl_keep isl_basic_map *bmap,
1530 enum isl_dim_type c1,
1531 enum isl_dim_type c2, enum isl_dim_type c3,
1532 enum isl_dim_type c4, enum isl_dim_type c5);
1534 The C<isl_dim_type> arguments dictate the order in which
1535 different kinds of variables appear in the resulting matrix
1536 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1537 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1539 The number of parameters, input, output or set dimensions can
1540 be obtained using the following functions.
1542 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1543 enum isl_dim_type type);
1544 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1545 enum isl_dim_type type);
1546 unsigned isl_set_dim(__isl_keep isl_set *set,
1547 enum isl_dim_type type);
1548 unsigned isl_map_dim(__isl_keep isl_map *map,
1549 enum isl_dim_type type);
1551 To check whether the description of a set or relation depends
1552 on one or more given dimensions, it is not necessary to iterate over all
1553 constraints. Instead the following functions can be used.
1555 int isl_basic_set_involves_dims(
1556 __isl_keep isl_basic_set *bset,
1557 enum isl_dim_type type, unsigned first, unsigned n);
1558 int isl_set_involves_dims(__isl_keep isl_set *set,
1559 enum isl_dim_type type, unsigned first, unsigned n);
1560 int isl_basic_map_involves_dims(
1561 __isl_keep isl_basic_map *bmap,
1562 enum isl_dim_type type, unsigned first, unsigned n);
1563 int isl_map_involves_dims(__isl_keep isl_map *map,
1564 enum isl_dim_type type, unsigned first, unsigned n);
1566 Similarly, the following functions can be used to check whether
1567 a given dimension is involved in any lower or upper bound.
1569 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1570 enum isl_dim_type type, unsigned pos);
1571 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1572 enum isl_dim_type type, unsigned pos);
1574 The identifiers or names of the domain and range spaces of a set
1575 or relation can be read off or set using the following functions.
1577 __isl_give isl_set *isl_set_set_tuple_id(
1578 __isl_take isl_set *set, __isl_take isl_id *id);
1579 __isl_give isl_set *isl_set_reset_tuple_id(
1580 __isl_take isl_set *set);
1581 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1582 __isl_give isl_id *isl_set_get_tuple_id(
1583 __isl_keep isl_set *set);
1584 __isl_give isl_map *isl_map_set_tuple_id(
1585 __isl_take isl_map *map, enum isl_dim_type type,
1586 __isl_take isl_id *id);
1587 __isl_give isl_map *isl_map_reset_tuple_id(
1588 __isl_take isl_map *map, enum isl_dim_type type);
1589 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1590 enum isl_dim_type type);
1591 __isl_give isl_id *isl_map_get_tuple_id(
1592 __isl_keep isl_map *map, enum isl_dim_type type);
1594 const char *isl_basic_set_get_tuple_name(
1595 __isl_keep isl_basic_set *bset);
1596 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1597 __isl_take isl_basic_set *set, const char *s);
1598 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1599 const char *isl_set_get_tuple_name(
1600 __isl_keep isl_set *set);
1601 const char *isl_basic_map_get_tuple_name(
1602 __isl_keep isl_basic_map *bmap,
1603 enum isl_dim_type type);
1604 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1605 __isl_take isl_basic_map *bmap,
1606 enum isl_dim_type type, const char *s);
1607 const char *isl_map_get_tuple_name(
1608 __isl_keep isl_map *map,
1609 enum isl_dim_type type);
1611 As with C<isl_space_get_tuple_name>, the value returned points to
1612 an internal data structure.
1613 The identifiers, positions or names of individual dimensions can be
1614 read off using the following functions.
1616 __isl_give isl_id *isl_basic_set_get_dim_id(
1617 __isl_keep isl_basic_set *bset,
1618 enum isl_dim_type type, unsigned pos);
1619 __isl_give isl_set *isl_set_set_dim_id(
1620 __isl_take isl_set *set, enum isl_dim_type type,
1621 unsigned pos, __isl_take isl_id *id);
1622 int isl_set_has_dim_id(__isl_keep isl_set *set,
1623 enum isl_dim_type type, unsigned pos);
1624 __isl_give isl_id *isl_set_get_dim_id(
1625 __isl_keep isl_set *set, enum isl_dim_type type,
1627 int isl_basic_map_has_dim_id(
1628 __isl_keep isl_basic_map *bmap,
1629 enum isl_dim_type type, unsigned pos);
1630 __isl_give isl_map *isl_map_set_dim_id(
1631 __isl_take isl_map *map, enum isl_dim_type type,
1632 unsigned pos, __isl_take isl_id *id);
1633 int isl_map_has_dim_id(__isl_keep isl_map *map,
1634 enum isl_dim_type type, unsigned pos);
1635 __isl_give isl_id *isl_map_get_dim_id(
1636 __isl_keep isl_map *map, enum isl_dim_type type,
1639 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1640 enum isl_dim_type type, __isl_keep isl_id *id);
1641 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1642 enum isl_dim_type type, __isl_keep isl_id *id);
1643 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1644 enum isl_dim_type type, const char *name);
1645 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1646 enum isl_dim_type type, const char *name);
1648 const char *isl_constraint_get_dim_name(
1649 __isl_keep isl_constraint *constraint,
1650 enum isl_dim_type type, unsigned pos);
1651 const char *isl_basic_set_get_dim_name(
1652 __isl_keep isl_basic_set *bset,
1653 enum isl_dim_type type, unsigned pos);
1654 int isl_set_has_dim_name(__isl_keep isl_set *set,
1655 enum isl_dim_type type, unsigned pos);
1656 const char *isl_set_get_dim_name(
1657 __isl_keep isl_set *set,
1658 enum isl_dim_type type, unsigned pos);
1659 const char *isl_basic_map_get_dim_name(
1660 __isl_keep isl_basic_map *bmap,
1661 enum isl_dim_type type, unsigned pos);
1662 const char *isl_map_get_dim_name(
1663 __isl_keep isl_map *map,
1664 enum isl_dim_type type, unsigned pos);
1666 These functions are mostly useful to obtain the identifiers, positions
1667 or names of the parameters. Identifiers of individual dimensions are
1668 essentially only useful for printing. They are ignored by all other
1669 operations and may not be preserved across those operations.
1673 =head3 Unary Properties
1679 The following functions test whether the given set or relation
1680 contains any integer points. The ``plain'' variants do not perform
1681 any computations, but simply check if the given set or relation
1682 is already known to be empty.
1684 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1685 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1686 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1687 int isl_set_is_empty(__isl_keep isl_set *set);
1688 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1689 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1690 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1691 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1692 int isl_map_is_empty(__isl_keep isl_map *map);
1693 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1695 =item * Universality
1697 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1698 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1699 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1701 =item * Single-valuedness
1703 int isl_basic_map_is_single_valued(
1704 __isl_keep isl_basic_map *bmap);
1705 int isl_map_plain_is_single_valued(
1706 __isl_keep isl_map *map);
1707 int isl_map_is_single_valued(__isl_keep isl_map *map);
1708 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1712 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1713 int isl_map_is_injective(__isl_keep isl_map *map);
1714 int isl_union_map_plain_is_injective(
1715 __isl_keep isl_union_map *umap);
1716 int isl_union_map_is_injective(
1717 __isl_keep isl_union_map *umap);
1721 int isl_map_is_bijective(__isl_keep isl_map *map);
1722 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1726 int isl_basic_map_plain_is_fixed(
1727 __isl_keep isl_basic_map *bmap,
1728 enum isl_dim_type type, unsigned pos,
1730 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1731 enum isl_dim_type type, unsigned pos,
1733 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1734 enum isl_dim_type type, unsigned pos,
1737 Check if the relation obviously lies on a hyperplane where the given dimension
1738 has a fixed value and if so, return that value in C<*val>.
1742 To check whether a set is a parameter domain, use this function:
1744 int isl_set_is_params(__isl_keep isl_set *set);
1745 int isl_union_set_is_params(
1746 __isl_keep isl_union_set *uset);
1750 The following functions check whether the domain of the given
1751 (basic) set is a wrapped relation.
1753 int isl_basic_set_is_wrapping(
1754 __isl_keep isl_basic_set *bset);
1755 int isl_set_is_wrapping(__isl_keep isl_set *set);
1757 =item * Internal Product
1759 int isl_basic_map_can_zip(
1760 __isl_keep isl_basic_map *bmap);
1761 int isl_map_can_zip(__isl_keep isl_map *map);
1763 Check whether the product of domain and range of the given relation
1765 i.e., whether both domain and range are nested relations.
1769 int isl_basic_map_can_curry(
1770 __isl_keep isl_basic_map *bmap);
1771 int isl_map_can_curry(__isl_keep isl_map *map);
1773 Check whether the domain of the (basic) relation is a wrapped relation.
1777 =head3 Binary Properties
1783 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1784 __isl_keep isl_set *set2);
1785 int isl_set_is_equal(__isl_keep isl_set *set1,
1786 __isl_keep isl_set *set2);
1787 int isl_union_set_is_equal(
1788 __isl_keep isl_union_set *uset1,
1789 __isl_keep isl_union_set *uset2);
1790 int isl_basic_map_is_equal(
1791 __isl_keep isl_basic_map *bmap1,
1792 __isl_keep isl_basic_map *bmap2);
1793 int isl_map_is_equal(__isl_keep isl_map *map1,
1794 __isl_keep isl_map *map2);
1795 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1796 __isl_keep isl_map *map2);
1797 int isl_union_map_is_equal(
1798 __isl_keep isl_union_map *umap1,
1799 __isl_keep isl_union_map *umap2);
1801 =item * Disjointness
1803 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1804 __isl_keep isl_set *set2);
1808 int isl_basic_set_is_subset(
1809 __isl_keep isl_basic_set *bset1,
1810 __isl_keep isl_basic_set *bset2);
1811 int isl_set_is_subset(__isl_keep isl_set *set1,
1812 __isl_keep isl_set *set2);
1813 int isl_set_is_strict_subset(
1814 __isl_keep isl_set *set1,
1815 __isl_keep isl_set *set2);
1816 int isl_union_set_is_subset(
1817 __isl_keep isl_union_set *uset1,
1818 __isl_keep isl_union_set *uset2);
1819 int isl_union_set_is_strict_subset(
1820 __isl_keep isl_union_set *uset1,
1821 __isl_keep isl_union_set *uset2);
1822 int isl_basic_map_is_subset(
1823 __isl_keep isl_basic_map *bmap1,
1824 __isl_keep isl_basic_map *bmap2);
1825 int isl_basic_map_is_strict_subset(
1826 __isl_keep isl_basic_map *bmap1,
1827 __isl_keep isl_basic_map *bmap2);
1828 int isl_map_is_subset(
1829 __isl_keep isl_map *map1,
1830 __isl_keep isl_map *map2);
1831 int isl_map_is_strict_subset(
1832 __isl_keep isl_map *map1,
1833 __isl_keep isl_map *map2);
1834 int isl_union_map_is_subset(
1835 __isl_keep isl_union_map *umap1,
1836 __isl_keep isl_union_map *umap2);
1837 int isl_union_map_is_strict_subset(
1838 __isl_keep isl_union_map *umap1,
1839 __isl_keep isl_union_map *umap2);
1841 Check whether the first argument is a (strict) subset of the
1846 =head2 Unary Operations
1852 __isl_give isl_set *isl_set_complement(
1853 __isl_take isl_set *set);
1854 __isl_give isl_map *isl_map_complement(
1855 __isl_take isl_map *map);
1859 __isl_give isl_basic_map *isl_basic_map_reverse(
1860 __isl_take isl_basic_map *bmap);
1861 __isl_give isl_map *isl_map_reverse(
1862 __isl_take isl_map *map);
1863 __isl_give isl_union_map *isl_union_map_reverse(
1864 __isl_take isl_union_map *umap);
1868 __isl_give isl_basic_set *isl_basic_set_project_out(
1869 __isl_take isl_basic_set *bset,
1870 enum isl_dim_type type, unsigned first, unsigned n);
1871 __isl_give isl_basic_map *isl_basic_map_project_out(
1872 __isl_take isl_basic_map *bmap,
1873 enum isl_dim_type type, unsigned first, unsigned n);
1874 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1875 enum isl_dim_type type, unsigned first, unsigned n);
1876 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1877 enum isl_dim_type type, unsigned first, unsigned n);
1878 __isl_give isl_basic_set *isl_basic_set_params(
1879 __isl_take isl_basic_set *bset);
1880 __isl_give isl_basic_set *isl_basic_map_domain(
1881 __isl_take isl_basic_map *bmap);
1882 __isl_give isl_basic_set *isl_basic_map_range(
1883 __isl_take isl_basic_map *bmap);
1884 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1885 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1886 __isl_give isl_set *isl_map_domain(
1887 __isl_take isl_map *bmap);
1888 __isl_give isl_set *isl_map_range(
1889 __isl_take isl_map *map);
1890 __isl_give isl_set *isl_union_set_params(
1891 __isl_take isl_union_set *uset);
1892 __isl_give isl_set *isl_union_map_params(
1893 __isl_take isl_union_map *umap);
1894 __isl_give isl_union_set *isl_union_map_domain(
1895 __isl_take isl_union_map *umap);
1896 __isl_give isl_union_set *isl_union_map_range(
1897 __isl_take isl_union_map *umap);
1899 __isl_give isl_basic_map *isl_basic_map_domain_map(
1900 __isl_take isl_basic_map *bmap);
1901 __isl_give isl_basic_map *isl_basic_map_range_map(
1902 __isl_take isl_basic_map *bmap);
1903 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1904 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1905 __isl_give isl_union_map *isl_union_map_domain_map(
1906 __isl_take isl_union_map *umap);
1907 __isl_give isl_union_map *isl_union_map_range_map(
1908 __isl_take isl_union_map *umap);
1910 The functions above construct a (basic, regular or union) relation
1911 that maps (a wrapped version of) the input relation to its domain or range.
1915 __isl_give isl_set *isl_set_eliminate(
1916 __isl_take isl_set *set, enum isl_dim_type type,
1917 unsigned first, unsigned n);
1918 __isl_give isl_basic_map *isl_basic_map_eliminate(
1919 __isl_take isl_basic_map *bmap,
1920 enum isl_dim_type type,
1921 unsigned first, unsigned n);
1922 __isl_give isl_map *isl_map_eliminate(
1923 __isl_take isl_map *map, enum isl_dim_type type,
1924 unsigned first, unsigned n);
1926 Eliminate the coefficients for the given dimensions from the constraints,
1927 without removing the dimensions.
1931 __isl_give isl_basic_set *isl_basic_set_fix(
1932 __isl_take isl_basic_set *bset,
1933 enum isl_dim_type type, unsigned pos,
1935 __isl_give isl_basic_set *isl_basic_set_fix_si(
1936 __isl_take isl_basic_set *bset,
1937 enum isl_dim_type type, unsigned pos, int value);
1938 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1939 enum isl_dim_type type, unsigned pos,
1941 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1942 enum isl_dim_type type, unsigned pos, int value);
1943 __isl_give isl_basic_map *isl_basic_map_fix_si(
1944 __isl_take isl_basic_map *bmap,
1945 enum isl_dim_type type, unsigned pos, int value);
1946 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1947 enum isl_dim_type type, unsigned pos, int value);
1949 Intersect the set or relation with the hyperplane where the given
1950 dimension has the fixed given value.
1952 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1953 __isl_take isl_basic_map *bmap,
1954 enum isl_dim_type type, unsigned pos, int value);
1955 __isl_give isl_set *isl_set_lower_bound(
1956 __isl_take isl_set *set,
1957 enum isl_dim_type type, unsigned pos,
1959 __isl_give isl_set *isl_set_lower_bound_si(
1960 __isl_take isl_set *set,
1961 enum isl_dim_type type, unsigned pos, int value);
1962 __isl_give isl_map *isl_map_lower_bound_si(
1963 __isl_take isl_map *map,
1964 enum isl_dim_type type, unsigned pos, int value);
1965 __isl_give isl_set *isl_set_upper_bound(
1966 __isl_take isl_set *set,
1967 enum isl_dim_type type, unsigned pos,
1969 __isl_give isl_set *isl_set_upper_bound_si(
1970 __isl_take isl_set *set,
1971 enum isl_dim_type type, unsigned pos, int value);
1972 __isl_give isl_map *isl_map_upper_bound_si(
1973 __isl_take isl_map *map,
1974 enum isl_dim_type type, unsigned pos, int value);
1976 Intersect the set or relation with the half-space where the given
1977 dimension has a value bounded by the fixed given value.
1979 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1980 enum isl_dim_type type1, int pos1,
1981 enum isl_dim_type type2, int pos2);
1982 __isl_give isl_basic_map *isl_basic_map_equate(
1983 __isl_take isl_basic_map *bmap,
1984 enum isl_dim_type type1, int pos1,
1985 enum isl_dim_type type2, int pos2);
1986 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1987 enum isl_dim_type type1, int pos1,
1988 enum isl_dim_type type2, int pos2);
1990 Intersect the set or relation with the hyperplane where the given
1991 dimensions are equal to each other.
1993 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1994 enum isl_dim_type type1, int pos1,
1995 enum isl_dim_type type2, int pos2);
1997 Intersect the relation with the hyperplane where the given
1998 dimensions have opposite values.
2000 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2001 enum isl_dim_type type1, int pos1,
2002 enum isl_dim_type type2, int pos2);
2003 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2004 enum isl_dim_type type1, int pos1,
2005 enum isl_dim_type type2, int pos2);
2007 Intersect the relation with the half-space where the given
2008 dimensions satisfy the given ordering.
2012 __isl_give isl_map *isl_set_identity(
2013 __isl_take isl_set *set);
2014 __isl_give isl_union_map *isl_union_set_identity(
2015 __isl_take isl_union_set *uset);
2017 Construct an identity relation on the given (union) set.
2021 __isl_give isl_basic_set *isl_basic_map_deltas(
2022 __isl_take isl_basic_map *bmap);
2023 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2024 __isl_give isl_union_set *isl_union_map_deltas(
2025 __isl_take isl_union_map *umap);
2027 These functions return a (basic) set containing the differences
2028 between image elements and corresponding domain elements in the input.
2030 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2031 __isl_take isl_basic_map *bmap);
2032 __isl_give isl_map *isl_map_deltas_map(
2033 __isl_take isl_map *map);
2034 __isl_give isl_union_map *isl_union_map_deltas_map(
2035 __isl_take isl_union_map *umap);
2037 The functions above construct a (basic, regular or union) relation
2038 that maps (a wrapped version of) the input relation to its delta set.
2042 Simplify the representation of a set or relation by trying
2043 to combine pairs of basic sets or relations into a single
2044 basic set or relation.
2046 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2047 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2048 __isl_give isl_union_set *isl_union_set_coalesce(
2049 __isl_take isl_union_set *uset);
2050 __isl_give isl_union_map *isl_union_map_coalesce(
2051 __isl_take isl_union_map *umap);
2053 One of the methods for combining pairs of basic sets or relations
2054 can result in coefficients that are much larger than those that appear
2055 in the constraints of the input. By default, the coefficients are
2056 not allowed to grow larger, but this can be changed by unsetting
2057 the following option.
2059 int isl_options_set_coalesce_bounded_wrapping(
2060 isl_ctx *ctx, int val);
2061 int isl_options_get_coalesce_bounded_wrapping(
2064 =item * Detecting equalities
2066 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2067 __isl_take isl_basic_set *bset);
2068 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2069 __isl_take isl_basic_map *bmap);
2070 __isl_give isl_set *isl_set_detect_equalities(
2071 __isl_take isl_set *set);
2072 __isl_give isl_map *isl_map_detect_equalities(
2073 __isl_take isl_map *map);
2074 __isl_give isl_union_set *isl_union_set_detect_equalities(
2075 __isl_take isl_union_set *uset);
2076 __isl_give isl_union_map *isl_union_map_detect_equalities(
2077 __isl_take isl_union_map *umap);
2079 Simplify the representation of a set or relation by detecting implicit
2082 =item * Removing redundant constraints
2084 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2085 __isl_take isl_basic_set *bset);
2086 __isl_give isl_set *isl_set_remove_redundancies(
2087 __isl_take isl_set *set);
2088 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2089 __isl_take isl_basic_map *bmap);
2090 __isl_give isl_map *isl_map_remove_redundancies(
2091 __isl_take isl_map *map);
2095 __isl_give isl_basic_set *isl_set_convex_hull(
2096 __isl_take isl_set *set);
2097 __isl_give isl_basic_map *isl_map_convex_hull(
2098 __isl_take isl_map *map);
2100 If the input set or relation has any existentially quantified
2101 variables, then the result of these operations is currently undefined.
2105 __isl_give isl_basic_set *isl_set_simple_hull(
2106 __isl_take isl_set *set);
2107 __isl_give isl_basic_map *isl_map_simple_hull(
2108 __isl_take isl_map *map);
2109 __isl_give isl_union_map *isl_union_map_simple_hull(
2110 __isl_take isl_union_map *umap);
2112 These functions compute a single basic set or relation
2113 that contains the whole input set or relation.
2114 In particular, the output is described by translates
2115 of the constraints describing the basic sets or relations in the input.
2119 (See \autoref{s:simple hull}.)
2125 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2126 __isl_take isl_basic_set *bset);
2127 __isl_give isl_basic_set *isl_set_affine_hull(
2128 __isl_take isl_set *set);
2129 __isl_give isl_union_set *isl_union_set_affine_hull(
2130 __isl_take isl_union_set *uset);
2131 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2132 __isl_take isl_basic_map *bmap);
2133 __isl_give isl_basic_map *isl_map_affine_hull(
2134 __isl_take isl_map *map);
2135 __isl_give isl_union_map *isl_union_map_affine_hull(
2136 __isl_take isl_union_map *umap);
2138 In case of union sets and relations, the affine hull is computed
2141 =item * Polyhedral hull
2143 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2144 __isl_take isl_set *set);
2145 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2146 __isl_take isl_map *map);
2147 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2148 __isl_take isl_union_set *uset);
2149 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2150 __isl_take isl_union_map *umap);
2152 These functions compute a single basic set or relation
2153 not involving any existentially quantified variables
2154 that contains the whole input set or relation.
2155 In case of union sets and relations, the polyhedral hull is computed
2160 __isl_give isl_basic_set *isl_basic_set_sample(
2161 __isl_take isl_basic_set *bset);
2162 __isl_give isl_basic_set *isl_set_sample(
2163 __isl_take isl_set *set);
2164 __isl_give isl_basic_map *isl_basic_map_sample(
2165 __isl_take isl_basic_map *bmap);
2166 __isl_give isl_basic_map *isl_map_sample(
2167 __isl_take isl_map *map);
2169 If the input (basic) set or relation is non-empty, then return
2170 a singleton subset of the input. Otherwise, return an empty set.
2172 =item * Optimization
2174 #include <isl/ilp.h>
2175 enum isl_lp_result isl_basic_set_max(
2176 __isl_keep isl_basic_set *bset,
2177 __isl_keep isl_aff *obj, isl_int *opt)
2178 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2179 __isl_keep isl_aff *obj, isl_int *opt);
2180 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2181 __isl_keep isl_aff *obj, isl_int *opt);
2183 Compute the minimum or maximum of the integer affine expression C<obj>
2184 over the points in C<set>, returning the result in C<opt>.
2185 The return value may be one of C<isl_lp_error>,
2186 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2188 =item * Parametric optimization
2190 __isl_give isl_pw_aff *isl_set_dim_min(
2191 __isl_take isl_set *set, int pos);
2192 __isl_give isl_pw_aff *isl_set_dim_max(
2193 __isl_take isl_set *set, int pos);
2194 __isl_give isl_pw_aff *isl_map_dim_max(
2195 __isl_take isl_map *map, int pos);
2197 Compute the minimum or maximum of the given set or output dimension
2198 as a function of the parameters (and input dimensions), but independently
2199 of the other set or output dimensions.
2200 For lexicographic optimization, see L<"Lexicographic Optimization">.
2204 The following functions compute either the set of (rational) coefficient
2205 values of valid constraints for the given set or the set of (rational)
2206 values satisfying the constraints with coefficients from the given set.
2207 Internally, these two sets of functions perform essentially the
2208 same operations, except that the set of coefficients is assumed to
2209 be a cone, while the set of values may be any polyhedron.
2210 The current implementation is based on the Farkas lemma and
2211 Fourier-Motzkin elimination, but this may change or be made optional
2212 in future. In particular, future implementations may use different
2213 dualization algorithms or skip the elimination step.
2215 __isl_give isl_basic_set *isl_basic_set_coefficients(
2216 __isl_take isl_basic_set *bset);
2217 __isl_give isl_basic_set *isl_set_coefficients(
2218 __isl_take isl_set *set);
2219 __isl_give isl_union_set *isl_union_set_coefficients(
2220 __isl_take isl_union_set *bset);
2221 __isl_give isl_basic_set *isl_basic_set_solutions(
2222 __isl_take isl_basic_set *bset);
2223 __isl_give isl_basic_set *isl_set_solutions(
2224 __isl_take isl_set *set);
2225 __isl_give isl_union_set *isl_union_set_solutions(
2226 __isl_take isl_union_set *bset);
2230 __isl_give isl_map *isl_map_fixed_power(
2231 __isl_take isl_map *map, isl_int exp);
2232 __isl_give isl_union_map *isl_union_map_fixed_power(
2233 __isl_take isl_union_map *umap, isl_int exp);
2235 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2236 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2237 of C<map> is computed.
2239 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2241 __isl_give isl_union_map *isl_union_map_power(
2242 __isl_take isl_union_map *umap, int *exact);
2244 Compute a parametric representation for all positive powers I<k> of C<map>.
2245 The result maps I<k> to a nested relation corresponding to the
2246 I<k>th power of C<map>.
2247 The result may be an overapproximation. If the result is known to be exact,
2248 then C<*exact> is set to C<1>.
2250 =item * Transitive closure
2252 __isl_give isl_map *isl_map_transitive_closure(
2253 __isl_take isl_map *map, int *exact);
2254 __isl_give isl_union_map *isl_union_map_transitive_closure(
2255 __isl_take isl_union_map *umap, int *exact);
2257 Compute the transitive closure of C<map>.
2258 The result may be an overapproximation. If the result is known to be exact,
2259 then C<*exact> is set to C<1>.
2261 =item * Reaching path lengths
2263 __isl_give isl_map *isl_map_reaching_path_lengths(
2264 __isl_take isl_map *map, int *exact);
2266 Compute a relation that maps each element in the range of C<map>
2267 to the lengths of all paths composed of edges in C<map> that
2268 end up in the given element.
2269 The result may be an overapproximation. If the result is known to be exact,
2270 then C<*exact> is set to C<1>.
2271 To compute the I<maximal> path length, the resulting relation
2272 should be postprocessed by C<isl_map_lexmax>.
2273 In particular, if the input relation is a dependence relation
2274 (mapping sources to sinks), then the maximal path length corresponds
2275 to the free schedule.
2276 Note, however, that C<isl_map_lexmax> expects the maximum to be
2277 finite, so if the path lengths are unbounded (possibly due to
2278 the overapproximation), then you will get an error message.
2282 __isl_give isl_basic_set *isl_basic_map_wrap(
2283 __isl_take isl_basic_map *bmap);
2284 __isl_give isl_set *isl_map_wrap(
2285 __isl_take isl_map *map);
2286 __isl_give isl_union_set *isl_union_map_wrap(
2287 __isl_take isl_union_map *umap);
2288 __isl_give isl_basic_map *isl_basic_set_unwrap(
2289 __isl_take isl_basic_set *bset);
2290 __isl_give isl_map *isl_set_unwrap(
2291 __isl_take isl_set *set);
2292 __isl_give isl_union_map *isl_union_set_unwrap(
2293 __isl_take isl_union_set *uset);
2297 Remove any internal structure of domain (and range) of the given
2298 set or relation. If there is any such internal structure in the input,
2299 then the name of the space is also removed.
2301 __isl_give isl_basic_set *isl_basic_set_flatten(
2302 __isl_take isl_basic_set *bset);
2303 __isl_give isl_set *isl_set_flatten(
2304 __isl_take isl_set *set);
2305 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2306 __isl_take isl_basic_map *bmap);
2307 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2308 __isl_take isl_basic_map *bmap);
2309 __isl_give isl_map *isl_map_flatten_range(
2310 __isl_take isl_map *map);
2311 __isl_give isl_map *isl_map_flatten_domain(
2312 __isl_take isl_map *map);
2313 __isl_give isl_basic_map *isl_basic_map_flatten(
2314 __isl_take isl_basic_map *bmap);
2315 __isl_give isl_map *isl_map_flatten(
2316 __isl_take isl_map *map);
2318 __isl_give isl_map *isl_set_flatten_map(
2319 __isl_take isl_set *set);
2321 The function above constructs a relation
2322 that maps the input set to a flattened version of the set.
2326 Lift the input set to a space with extra dimensions corresponding
2327 to the existentially quantified variables in the input.
2328 In particular, the result lives in a wrapped map where the domain
2329 is the original space and the range corresponds to the original
2330 existentially quantified variables.
2332 __isl_give isl_basic_set *isl_basic_set_lift(
2333 __isl_take isl_basic_set *bset);
2334 __isl_give isl_set *isl_set_lift(
2335 __isl_take isl_set *set);
2336 __isl_give isl_union_set *isl_union_set_lift(
2337 __isl_take isl_union_set *uset);
2339 Given a local space that contains the existentially quantified
2340 variables of a set, a basic relation that, when applied to
2341 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2342 can be constructed using the following function.
2344 #include <isl/local_space.h>
2345 __isl_give isl_basic_map *isl_local_space_lifting(
2346 __isl_take isl_local_space *ls);
2348 =item * Internal Product
2350 __isl_give isl_basic_map *isl_basic_map_zip(
2351 __isl_take isl_basic_map *bmap);
2352 __isl_give isl_map *isl_map_zip(
2353 __isl_take isl_map *map);
2354 __isl_give isl_union_map *isl_union_map_zip(
2355 __isl_take isl_union_map *umap);
2357 Given a relation with nested relations for domain and range,
2358 interchange the range of the domain with the domain of the range.
2362 __isl_give isl_basic_map *isl_basic_map_curry(
2363 __isl_take isl_basic_map *bmap);
2364 __isl_give isl_map *isl_map_curry(
2365 __isl_take isl_map *map);
2366 __isl_give isl_union_map *isl_union_map_curry(
2367 __isl_take isl_union_map *umap);
2369 Given a relation with a nested relation for domain,
2370 move the range of the nested relation out of the domain
2371 and use it as the domain of a nested relation in the range,
2372 with the original range as range of this nested relation.
2374 =item * Aligning parameters
2376 __isl_give isl_set *isl_set_align_params(
2377 __isl_take isl_set *set,
2378 __isl_take isl_space *model);
2379 __isl_give isl_map *isl_map_align_params(
2380 __isl_take isl_map *map,
2381 __isl_take isl_space *model);
2383 Change the order of the parameters of the given set or relation
2384 such that the first parameters match those of C<model>.
2385 This may involve the introduction of extra parameters.
2386 All parameters need to be named.
2388 =item * Dimension manipulation
2390 __isl_give isl_set *isl_set_add_dims(
2391 __isl_take isl_set *set,
2392 enum isl_dim_type type, unsigned n);
2393 __isl_give isl_map *isl_map_add_dims(
2394 __isl_take isl_map *map,
2395 enum isl_dim_type type, unsigned n);
2396 __isl_give isl_set *isl_set_insert_dims(
2397 __isl_take isl_set *set,
2398 enum isl_dim_type type, unsigned pos, unsigned n);
2399 __isl_give isl_map *isl_map_insert_dims(
2400 __isl_take isl_map *map,
2401 enum isl_dim_type type, unsigned pos, unsigned n);
2402 __isl_give isl_basic_set *isl_basic_set_move_dims(
2403 __isl_take isl_basic_set *bset,
2404 enum isl_dim_type dst_type, unsigned dst_pos,
2405 enum isl_dim_type src_type, unsigned src_pos,
2407 __isl_give isl_basic_map *isl_basic_map_move_dims(
2408 __isl_take isl_basic_map *bmap,
2409 enum isl_dim_type dst_type, unsigned dst_pos,
2410 enum isl_dim_type src_type, unsigned src_pos,
2412 __isl_give isl_set *isl_set_move_dims(
2413 __isl_take isl_set *set,
2414 enum isl_dim_type dst_type, unsigned dst_pos,
2415 enum isl_dim_type src_type, unsigned src_pos,
2417 __isl_give isl_map *isl_map_move_dims(
2418 __isl_take isl_map *map,
2419 enum isl_dim_type dst_type, unsigned dst_pos,
2420 enum isl_dim_type src_type, unsigned src_pos,
2423 It is usually not advisable to directly change the (input or output)
2424 space of a set or a relation as this removes the name and the internal
2425 structure of the space. However, the above functions can be useful
2426 to add new parameters, assuming
2427 C<isl_set_align_params> and C<isl_map_align_params>
2432 =head2 Binary Operations
2434 The two arguments of a binary operation not only need to live
2435 in the same C<isl_ctx>, they currently also need to have
2436 the same (number of) parameters.
2438 =head3 Basic Operations
2442 =item * Intersection
2444 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2445 __isl_take isl_basic_set *bset1,
2446 __isl_take isl_basic_set *bset2);
2447 __isl_give isl_basic_set *isl_basic_set_intersect(
2448 __isl_take isl_basic_set *bset1,
2449 __isl_take isl_basic_set *bset2);
2450 __isl_give isl_set *isl_set_intersect_params(
2451 __isl_take isl_set *set,
2452 __isl_take isl_set *params);
2453 __isl_give isl_set *isl_set_intersect(
2454 __isl_take isl_set *set1,
2455 __isl_take isl_set *set2);
2456 __isl_give isl_union_set *isl_union_set_intersect_params(
2457 __isl_take isl_union_set *uset,
2458 __isl_take isl_set *set);
2459 __isl_give isl_union_map *isl_union_map_intersect_params(
2460 __isl_take isl_union_map *umap,
2461 __isl_take isl_set *set);
2462 __isl_give isl_union_set *isl_union_set_intersect(
2463 __isl_take isl_union_set *uset1,
2464 __isl_take isl_union_set *uset2);
2465 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2466 __isl_take isl_basic_map *bmap,
2467 __isl_take isl_basic_set *bset);
2468 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2469 __isl_take isl_basic_map *bmap,
2470 __isl_take isl_basic_set *bset);
2471 __isl_give isl_basic_map *isl_basic_map_intersect(
2472 __isl_take isl_basic_map *bmap1,
2473 __isl_take isl_basic_map *bmap2);
2474 __isl_give isl_map *isl_map_intersect_params(
2475 __isl_take isl_map *map,
2476 __isl_take isl_set *params);
2477 __isl_give isl_map *isl_map_intersect_domain(
2478 __isl_take isl_map *map,
2479 __isl_take isl_set *set);
2480 __isl_give isl_map *isl_map_intersect_range(
2481 __isl_take isl_map *map,
2482 __isl_take isl_set *set);
2483 __isl_give isl_map *isl_map_intersect(
2484 __isl_take isl_map *map1,
2485 __isl_take isl_map *map2);
2486 __isl_give isl_union_map *isl_union_map_intersect_domain(
2487 __isl_take isl_union_map *umap,
2488 __isl_take isl_union_set *uset);
2489 __isl_give isl_union_map *isl_union_map_intersect_range(
2490 __isl_take isl_union_map *umap,
2491 __isl_take isl_union_set *uset);
2492 __isl_give isl_union_map *isl_union_map_intersect(
2493 __isl_take isl_union_map *umap1,
2494 __isl_take isl_union_map *umap2);
2496 The second argument to the C<_params> functions needs to be
2497 a parametric (basic) set. For the other functions, a parametric set
2498 for either argument is only allowed if the other argument is
2499 a parametric set as well.
2503 __isl_give isl_set *isl_basic_set_union(
2504 __isl_take isl_basic_set *bset1,
2505 __isl_take isl_basic_set *bset2);
2506 __isl_give isl_map *isl_basic_map_union(
2507 __isl_take isl_basic_map *bmap1,
2508 __isl_take isl_basic_map *bmap2);
2509 __isl_give isl_set *isl_set_union(
2510 __isl_take isl_set *set1,
2511 __isl_take isl_set *set2);
2512 __isl_give isl_map *isl_map_union(
2513 __isl_take isl_map *map1,
2514 __isl_take isl_map *map2);
2515 __isl_give isl_union_set *isl_union_set_union(
2516 __isl_take isl_union_set *uset1,
2517 __isl_take isl_union_set *uset2);
2518 __isl_give isl_union_map *isl_union_map_union(
2519 __isl_take isl_union_map *umap1,
2520 __isl_take isl_union_map *umap2);
2522 =item * Set difference
2524 __isl_give isl_set *isl_set_subtract(
2525 __isl_take isl_set *set1,
2526 __isl_take isl_set *set2);
2527 __isl_give isl_map *isl_map_subtract(
2528 __isl_take isl_map *map1,
2529 __isl_take isl_map *map2);
2530 __isl_give isl_map *isl_map_subtract_domain(
2531 __isl_take isl_map *map,
2532 __isl_take isl_set *dom);
2533 __isl_give isl_map *isl_map_subtract_range(
2534 __isl_take isl_map *map,
2535 __isl_take isl_set *dom);
2536 __isl_give isl_union_set *isl_union_set_subtract(
2537 __isl_take isl_union_set *uset1,
2538 __isl_take isl_union_set *uset2);
2539 __isl_give isl_union_map *isl_union_map_subtract(
2540 __isl_take isl_union_map *umap1,
2541 __isl_take isl_union_map *umap2);
2545 __isl_give isl_basic_set *isl_basic_set_apply(
2546 __isl_take isl_basic_set *bset,
2547 __isl_take isl_basic_map *bmap);
2548 __isl_give isl_set *isl_set_apply(
2549 __isl_take isl_set *set,
2550 __isl_take isl_map *map);
2551 __isl_give isl_union_set *isl_union_set_apply(
2552 __isl_take isl_union_set *uset,
2553 __isl_take isl_union_map *umap);
2554 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2555 __isl_take isl_basic_map *bmap1,
2556 __isl_take isl_basic_map *bmap2);
2557 __isl_give isl_basic_map *isl_basic_map_apply_range(
2558 __isl_take isl_basic_map *bmap1,
2559 __isl_take isl_basic_map *bmap2);
2560 __isl_give isl_map *isl_map_apply_domain(
2561 __isl_take isl_map *map1,
2562 __isl_take isl_map *map2);
2563 __isl_give isl_union_map *isl_union_map_apply_domain(
2564 __isl_take isl_union_map *umap1,
2565 __isl_take isl_union_map *umap2);
2566 __isl_give isl_map *isl_map_apply_range(
2567 __isl_take isl_map *map1,
2568 __isl_take isl_map *map2);
2569 __isl_give isl_union_map *isl_union_map_apply_range(
2570 __isl_take isl_union_map *umap1,
2571 __isl_take isl_union_map *umap2);
2573 =item * Cartesian Product
2575 __isl_give isl_set *isl_set_product(
2576 __isl_take isl_set *set1,
2577 __isl_take isl_set *set2);
2578 __isl_give isl_union_set *isl_union_set_product(
2579 __isl_take isl_union_set *uset1,
2580 __isl_take isl_union_set *uset2);
2581 __isl_give isl_basic_map *isl_basic_map_domain_product(
2582 __isl_take isl_basic_map *bmap1,
2583 __isl_take isl_basic_map *bmap2);
2584 __isl_give isl_basic_map *isl_basic_map_range_product(
2585 __isl_take isl_basic_map *bmap1,
2586 __isl_take isl_basic_map *bmap2);
2587 __isl_give isl_map *isl_map_domain_product(
2588 __isl_take isl_map *map1,
2589 __isl_take isl_map *map2);
2590 __isl_give isl_map *isl_map_range_product(
2591 __isl_take isl_map *map1,
2592 __isl_take isl_map *map2);
2593 __isl_give isl_union_map *isl_union_map_range_product(
2594 __isl_take isl_union_map *umap1,
2595 __isl_take isl_union_map *umap2);
2596 __isl_give isl_map *isl_map_product(
2597 __isl_take isl_map *map1,
2598 __isl_take isl_map *map2);
2599 __isl_give isl_union_map *isl_union_map_product(
2600 __isl_take isl_union_map *umap1,
2601 __isl_take isl_union_map *umap2);
2603 The above functions compute the cross product of the given
2604 sets or relations. The domains and ranges of the results
2605 are wrapped maps between domains and ranges of the inputs.
2606 To obtain a ``flat'' product, use the following functions
2609 __isl_give isl_basic_set *isl_basic_set_flat_product(
2610 __isl_take isl_basic_set *bset1,
2611 __isl_take isl_basic_set *bset2);
2612 __isl_give isl_set *isl_set_flat_product(
2613 __isl_take isl_set *set1,
2614 __isl_take isl_set *set2);
2615 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2616 __isl_take isl_basic_map *bmap1,
2617 __isl_take isl_basic_map *bmap2);
2618 __isl_give isl_map *isl_map_flat_domain_product(
2619 __isl_take isl_map *map1,
2620 __isl_take isl_map *map2);
2621 __isl_give isl_map *isl_map_flat_range_product(
2622 __isl_take isl_map *map1,
2623 __isl_take isl_map *map2);
2624 __isl_give isl_union_map *isl_union_map_flat_range_product(
2625 __isl_take isl_union_map *umap1,
2626 __isl_take isl_union_map *umap2);
2627 __isl_give isl_basic_map *isl_basic_map_flat_product(
2628 __isl_take isl_basic_map *bmap1,
2629 __isl_take isl_basic_map *bmap2);
2630 __isl_give isl_map *isl_map_flat_product(
2631 __isl_take isl_map *map1,
2632 __isl_take isl_map *map2);
2634 =item * Simplification
2636 __isl_give isl_basic_set *isl_basic_set_gist(
2637 __isl_take isl_basic_set *bset,
2638 __isl_take isl_basic_set *context);
2639 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2640 __isl_take isl_set *context);
2641 __isl_give isl_set *isl_set_gist_params(
2642 __isl_take isl_set *set,
2643 __isl_take isl_set *context);
2644 __isl_give isl_union_set *isl_union_set_gist(
2645 __isl_take isl_union_set *uset,
2646 __isl_take isl_union_set *context);
2647 __isl_give isl_union_set *isl_union_set_gist_params(
2648 __isl_take isl_union_set *uset,
2649 __isl_take isl_set *set);
2650 __isl_give isl_basic_map *isl_basic_map_gist(
2651 __isl_take isl_basic_map *bmap,
2652 __isl_take isl_basic_map *context);
2653 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2654 __isl_take isl_map *context);
2655 __isl_give isl_map *isl_map_gist_params(
2656 __isl_take isl_map *map,
2657 __isl_take isl_set *context);
2658 __isl_give isl_map *isl_map_gist_domain(
2659 __isl_take isl_map *map,
2660 __isl_take isl_set *context);
2661 __isl_give isl_map *isl_map_gist_range(
2662 __isl_take isl_map *map,
2663 __isl_take isl_set *context);
2664 __isl_give isl_union_map *isl_union_map_gist(
2665 __isl_take isl_union_map *umap,
2666 __isl_take isl_union_map *context);
2667 __isl_give isl_union_map *isl_union_map_gist_params(
2668 __isl_take isl_union_map *umap,
2669 __isl_take isl_set *set);
2670 __isl_give isl_union_map *isl_union_map_gist_domain(
2671 __isl_take isl_union_map *umap,
2672 __isl_take isl_union_set *uset);
2673 __isl_give isl_union_map *isl_union_map_gist_range(
2674 __isl_take isl_union_map *umap,
2675 __isl_take isl_union_set *uset);
2677 The gist operation returns a set or relation that has the
2678 same intersection with the context as the input set or relation.
2679 Any implicit equality in the intersection is made explicit in the result,
2680 while all inequalities that are redundant with respect to the intersection
2682 In case of union sets and relations, the gist operation is performed
2687 =head3 Lexicographic Optimization
2689 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2690 the following functions
2691 compute a set that contains the lexicographic minimum or maximum
2692 of the elements in C<set> (or C<bset>) for those values of the parameters
2693 that satisfy C<dom>.
2694 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2695 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2697 In other words, the union of the parameter values
2698 for which the result is non-empty and of C<*empty>
2701 __isl_give isl_set *isl_basic_set_partial_lexmin(
2702 __isl_take isl_basic_set *bset,
2703 __isl_take isl_basic_set *dom,
2704 __isl_give isl_set **empty);
2705 __isl_give isl_set *isl_basic_set_partial_lexmax(
2706 __isl_take isl_basic_set *bset,
2707 __isl_take isl_basic_set *dom,
2708 __isl_give isl_set **empty);
2709 __isl_give isl_set *isl_set_partial_lexmin(
2710 __isl_take isl_set *set, __isl_take isl_set *dom,
2711 __isl_give isl_set **empty);
2712 __isl_give isl_set *isl_set_partial_lexmax(
2713 __isl_take isl_set *set, __isl_take isl_set *dom,
2714 __isl_give isl_set **empty);
2716 Given a (basic) set C<set> (or C<bset>), the following functions simply
2717 return a set containing the lexicographic minimum or maximum
2718 of the elements in C<set> (or C<bset>).
2719 In case of union sets, the optimum is computed per space.
2721 __isl_give isl_set *isl_basic_set_lexmin(
2722 __isl_take isl_basic_set *bset);
2723 __isl_give isl_set *isl_basic_set_lexmax(
2724 __isl_take isl_basic_set *bset);
2725 __isl_give isl_set *isl_set_lexmin(
2726 __isl_take isl_set *set);
2727 __isl_give isl_set *isl_set_lexmax(
2728 __isl_take isl_set *set);
2729 __isl_give isl_union_set *isl_union_set_lexmin(
2730 __isl_take isl_union_set *uset);
2731 __isl_give isl_union_set *isl_union_set_lexmax(
2732 __isl_take isl_union_set *uset);
2734 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2735 the following functions
2736 compute a relation that maps each element of C<dom>
2737 to the single lexicographic minimum or maximum
2738 of the elements that are associated to that same
2739 element in C<map> (or C<bmap>).
2740 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2741 that contains the elements in C<dom> that do not map
2742 to any elements in C<map> (or C<bmap>).
2743 In other words, the union of the domain of the result and of C<*empty>
2746 __isl_give isl_map *isl_basic_map_partial_lexmax(
2747 __isl_take isl_basic_map *bmap,
2748 __isl_take isl_basic_set *dom,
2749 __isl_give isl_set **empty);
2750 __isl_give isl_map *isl_basic_map_partial_lexmin(
2751 __isl_take isl_basic_map *bmap,
2752 __isl_take isl_basic_set *dom,
2753 __isl_give isl_set **empty);
2754 __isl_give isl_map *isl_map_partial_lexmax(
2755 __isl_take isl_map *map, __isl_take isl_set *dom,
2756 __isl_give isl_set **empty);
2757 __isl_give isl_map *isl_map_partial_lexmin(
2758 __isl_take isl_map *map, __isl_take isl_set *dom,
2759 __isl_give isl_set **empty);
2761 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2762 return a map mapping each element in the domain of
2763 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2764 of all elements associated to that element.
2765 In case of union relations, the optimum is computed per space.
2767 __isl_give isl_map *isl_basic_map_lexmin(
2768 __isl_take isl_basic_map *bmap);
2769 __isl_give isl_map *isl_basic_map_lexmax(
2770 __isl_take isl_basic_map *bmap);
2771 __isl_give isl_map *isl_map_lexmin(
2772 __isl_take isl_map *map);
2773 __isl_give isl_map *isl_map_lexmax(
2774 __isl_take isl_map *map);
2775 __isl_give isl_union_map *isl_union_map_lexmin(
2776 __isl_take isl_union_map *umap);
2777 __isl_give isl_union_map *isl_union_map_lexmax(
2778 __isl_take isl_union_map *umap);
2780 The following functions return their result in the form of
2781 a piecewise multi-affine expression
2782 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2783 but are otherwise equivalent to the corresponding functions
2784 returning a basic set or relation.
2786 __isl_give isl_pw_multi_aff *
2787 isl_basic_map_lexmin_pw_multi_aff(
2788 __isl_take isl_basic_map *bmap);
2789 __isl_give isl_pw_multi_aff *
2790 isl_basic_set_partial_lexmin_pw_multi_aff(
2791 __isl_take isl_basic_set *bset,
2792 __isl_take isl_basic_set *dom,
2793 __isl_give isl_set **empty);
2794 __isl_give isl_pw_multi_aff *
2795 isl_basic_set_partial_lexmax_pw_multi_aff(
2796 __isl_take isl_basic_set *bset,
2797 __isl_take isl_basic_set *dom,
2798 __isl_give isl_set **empty);
2799 __isl_give isl_pw_multi_aff *
2800 isl_basic_map_partial_lexmin_pw_multi_aff(
2801 __isl_take isl_basic_map *bmap,
2802 __isl_take isl_basic_set *dom,
2803 __isl_give isl_set **empty);
2804 __isl_give isl_pw_multi_aff *
2805 isl_basic_map_partial_lexmax_pw_multi_aff(
2806 __isl_take isl_basic_map *bmap,
2807 __isl_take isl_basic_set *dom,
2808 __isl_give isl_set **empty);
2812 Lists are defined over several element types, including
2813 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2814 Here we take lists of C<isl_set>s as an example.
2815 Lists can be created, copied and freed using the following functions.
2817 #include <isl/list.h>
2818 __isl_give isl_set_list *isl_set_list_from_set(
2819 __isl_take isl_set *el);
2820 __isl_give isl_set_list *isl_set_list_alloc(
2821 isl_ctx *ctx, int n);
2822 __isl_give isl_set_list *isl_set_list_copy(
2823 __isl_keep isl_set_list *list);
2824 __isl_give isl_set_list *isl_set_list_add(
2825 __isl_take isl_set_list *list,
2826 __isl_take isl_set *el);
2827 __isl_give isl_set_list *isl_set_list_concat(
2828 __isl_take isl_set_list *list1,
2829 __isl_take isl_set_list *list2);
2830 void *isl_set_list_free(__isl_take isl_set_list *list);
2832 C<isl_set_list_alloc> creates an empty list with a capacity for
2833 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2836 Lists can be inspected using the following functions.
2838 #include <isl/list.h>
2839 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2840 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2841 __isl_give isl_set *isl_set_list_get_set(
2842 __isl_keep isl_set_list *list, int index);
2843 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2844 int (*fn)(__isl_take isl_set *el, void *user),
2847 Lists can be printed using
2849 #include <isl/list.h>
2850 __isl_give isl_printer *isl_printer_print_set_list(
2851 __isl_take isl_printer *p,
2852 __isl_keep isl_set_list *list);
2856 Vectors can be created, copied and freed using the following functions.
2858 #include <isl/vec.h>
2859 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2861 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2862 void isl_vec_free(__isl_take isl_vec *vec);
2864 Note that the elements of a newly created vector may have arbitrary values.
2865 The elements can be changed and inspected using the following functions.
2867 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2868 int isl_vec_size(__isl_keep isl_vec *vec);
2869 int isl_vec_get_element(__isl_keep isl_vec *vec,
2870 int pos, isl_int *v);
2871 __isl_give isl_vec *isl_vec_set_element(
2872 __isl_take isl_vec *vec, int pos, isl_int v);
2873 __isl_give isl_vec *isl_vec_set_element_si(
2874 __isl_take isl_vec *vec, int pos, int v);
2875 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2877 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2880 C<isl_vec_get_element> will return a negative value if anything went wrong.
2881 In that case, the value of C<*v> is undefined.
2885 Matrices can be created, copied and freed using the following functions.
2887 #include <isl/mat.h>
2888 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2889 unsigned n_row, unsigned n_col);
2890 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2891 void isl_mat_free(__isl_take isl_mat *mat);
2893 Note that the elements of a newly created matrix may have arbitrary values.
2894 The elements can be changed and inspected using the following functions.
2896 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2897 int isl_mat_rows(__isl_keep isl_mat *mat);
2898 int isl_mat_cols(__isl_keep isl_mat *mat);
2899 int isl_mat_get_element(__isl_keep isl_mat *mat,
2900 int row, int col, isl_int *v);
2901 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2902 int row, int col, isl_int v);
2903 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2904 int row, int col, int v);
2906 C<isl_mat_get_element> will return a negative value if anything went wrong.
2907 In that case, the value of C<*v> is undefined.
2909 The following function can be used to compute the (right) inverse
2910 of a matrix, i.e., a matrix such that the product of the original
2911 and the inverse (in that order) is a multiple of the identity matrix.
2912 The input matrix is assumed to be of full row-rank.
2914 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2916 The following function can be used to compute the (right) kernel
2917 (or null space) of a matrix, i.e., a matrix such that the product of
2918 the original and the kernel (in that order) is the zero matrix.
2920 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2922 =head2 Piecewise Quasi Affine Expressions
2924 The zero quasi affine expression on a given domain can be created using
2926 __isl_give isl_aff *isl_aff_zero_on_domain(
2927 __isl_take isl_local_space *ls);
2929 Note that the space in which the resulting object lives is a map space
2930 with the given space as domain and a one-dimensional range.
2932 An empty piecewise quasi affine expression (one with no cells)
2933 or a piecewise quasi affine expression with a single cell can
2934 be created using the following functions.
2936 #include <isl/aff.h>
2937 __isl_give isl_pw_aff *isl_pw_aff_empty(
2938 __isl_take isl_space *space);
2939 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2940 __isl_take isl_set *set, __isl_take isl_aff *aff);
2941 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2942 __isl_take isl_aff *aff);
2944 A piecewise quasi affine expression that is equal to 1 on a set
2945 and 0 outside the set can be created using the following function.
2947 #include <isl/aff.h>
2948 __isl_give isl_pw_aff *isl_set_indicator_function(
2949 __isl_take isl_set *set);
2951 Quasi affine expressions can be copied and freed using
2953 #include <isl/aff.h>
2954 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2955 void *isl_aff_free(__isl_take isl_aff *aff);
2957 __isl_give isl_pw_aff *isl_pw_aff_copy(
2958 __isl_keep isl_pw_aff *pwaff);
2959 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2961 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2962 using the following function. The constraint is required to have
2963 a non-zero coefficient for the specified dimension.
2965 #include <isl/constraint.h>
2966 __isl_give isl_aff *isl_constraint_get_bound(
2967 __isl_keep isl_constraint *constraint,
2968 enum isl_dim_type type, int pos);
2970 The entire affine expression of the constraint can also be extracted
2971 using the following function.
2973 #include <isl/constraint.h>
2974 __isl_give isl_aff *isl_constraint_get_aff(
2975 __isl_keep isl_constraint *constraint);
2977 Conversely, an equality constraint equating
2978 the affine expression to zero or an inequality constraint enforcing
2979 the affine expression to be non-negative, can be constructed using
2981 __isl_give isl_constraint *isl_equality_from_aff(
2982 __isl_take isl_aff *aff);
2983 __isl_give isl_constraint *isl_inequality_from_aff(
2984 __isl_take isl_aff *aff);
2986 The expression can be inspected using
2988 #include <isl/aff.h>
2989 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2990 int isl_aff_dim(__isl_keep isl_aff *aff,
2991 enum isl_dim_type type);
2992 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2993 __isl_keep isl_aff *aff);
2994 __isl_give isl_local_space *isl_aff_get_local_space(
2995 __isl_keep isl_aff *aff);
2996 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2997 enum isl_dim_type type, unsigned pos);
2998 const char *isl_pw_aff_get_dim_name(
2999 __isl_keep isl_pw_aff *pa,
3000 enum isl_dim_type type, unsigned pos);
3001 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3002 enum isl_dim_type type, unsigned pos);
3003 __isl_give isl_id *isl_pw_aff_get_dim_id(
3004 __isl_keep isl_pw_aff *pa,
3005 enum isl_dim_type type, unsigned pos);
3006 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3008 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3009 enum isl_dim_type type, int pos, isl_int *v);
3010 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3012 __isl_give isl_aff *isl_aff_get_div(
3013 __isl_keep isl_aff *aff, int pos);
3015 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3016 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3017 int (*fn)(__isl_take isl_set *set,
3018 __isl_take isl_aff *aff,
3019 void *user), void *user);
3021 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3022 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3024 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3025 enum isl_dim_type type, unsigned first, unsigned n);
3026 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3027 enum isl_dim_type type, unsigned first, unsigned n);
3029 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3030 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3031 enum isl_dim_type type);
3032 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3034 It can be modified using
3036 #include <isl/aff.h>
3037 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3038 __isl_take isl_pw_aff *pwaff,
3039 enum isl_dim_type type, __isl_take isl_id *id);
3040 __isl_give isl_aff *isl_aff_set_dim_name(
3041 __isl_take isl_aff *aff, enum isl_dim_type type,
3042 unsigned pos, const char *s);
3043 __isl_give isl_aff *isl_aff_set_dim_id(
3044 __isl_take isl_aff *aff, enum isl_dim_type type,
3045 unsigned pos, __isl_take isl_id *id);
3046 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3047 __isl_take isl_pw_aff *pma,
3048 enum isl_dim_type type, unsigned pos,
3049 __isl_take isl_id *id);
3050 __isl_give isl_aff *isl_aff_set_constant(
3051 __isl_take isl_aff *aff, isl_int v);
3052 __isl_give isl_aff *isl_aff_set_constant_si(
3053 __isl_take isl_aff *aff, int v);
3054 __isl_give isl_aff *isl_aff_set_coefficient(
3055 __isl_take isl_aff *aff,
3056 enum isl_dim_type type, int pos, isl_int v);
3057 __isl_give isl_aff *isl_aff_set_coefficient_si(
3058 __isl_take isl_aff *aff,
3059 enum isl_dim_type type, int pos, int v);
3060 __isl_give isl_aff *isl_aff_set_denominator(
3061 __isl_take isl_aff *aff, isl_int v);
3063 __isl_give isl_aff *isl_aff_add_constant(
3064 __isl_take isl_aff *aff, isl_int v);
3065 __isl_give isl_aff *isl_aff_add_constant_si(
3066 __isl_take isl_aff *aff, int v);
3067 __isl_give isl_aff *isl_aff_add_coefficient(
3068 __isl_take isl_aff *aff,
3069 enum isl_dim_type type, int pos, isl_int v);
3070 __isl_give isl_aff *isl_aff_add_coefficient_si(
3071 __isl_take isl_aff *aff,
3072 enum isl_dim_type type, int pos, int v);
3074 __isl_give isl_aff *isl_aff_insert_dims(
3075 __isl_take isl_aff *aff,
3076 enum isl_dim_type type, unsigned first, unsigned n);
3077 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3078 __isl_take isl_pw_aff *pwaff,
3079 enum isl_dim_type type, unsigned first, unsigned n);
3080 __isl_give isl_aff *isl_aff_add_dims(
3081 __isl_take isl_aff *aff,
3082 enum isl_dim_type type, unsigned n);
3083 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3084 __isl_take isl_pw_aff *pwaff,
3085 enum isl_dim_type type, unsigned n);
3086 __isl_give isl_aff *isl_aff_drop_dims(
3087 __isl_take isl_aff *aff,
3088 enum isl_dim_type type, unsigned first, unsigned n);
3089 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3090 __isl_take isl_pw_aff *pwaff,
3091 enum isl_dim_type type, unsigned first, unsigned n);
3093 Note that the C<set_constant> and C<set_coefficient> functions
3094 set the I<numerator> of the constant or coefficient, while
3095 C<add_constant> and C<add_coefficient> add an integer value to
3096 the possibly rational constant or coefficient.
3098 To check whether an affine expressions is obviously zero
3099 or obviously equal to some other affine expression, use
3101 #include <isl/aff.h>
3102 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3103 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3104 __isl_keep isl_aff *aff2);
3105 int isl_pw_aff_plain_is_equal(
3106 __isl_keep isl_pw_aff *pwaff1,
3107 __isl_keep isl_pw_aff *pwaff2);
3111 #include <isl/aff.h>
3112 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3113 __isl_take isl_aff *aff2);
3114 __isl_give isl_pw_aff *isl_pw_aff_add(
3115 __isl_take isl_pw_aff *pwaff1,
3116 __isl_take isl_pw_aff *pwaff2);
3117 __isl_give isl_pw_aff *isl_pw_aff_min(
3118 __isl_take isl_pw_aff *pwaff1,
3119 __isl_take isl_pw_aff *pwaff2);
3120 __isl_give isl_pw_aff *isl_pw_aff_max(
3121 __isl_take isl_pw_aff *pwaff1,
3122 __isl_take isl_pw_aff *pwaff2);
3123 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3124 __isl_take isl_aff *aff2);
3125 __isl_give isl_pw_aff *isl_pw_aff_sub(
3126 __isl_take isl_pw_aff *pwaff1,
3127 __isl_take isl_pw_aff *pwaff2);
3128 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3129 __isl_give isl_pw_aff *isl_pw_aff_neg(
3130 __isl_take isl_pw_aff *pwaff);
3131 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3132 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3133 __isl_take isl_pw_aff *pwaff);
3134 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3135 __isl_give isl_pw_aff *isl_pw_aff_floor(
3136 __isl_take isl_pw_aff *pwaff);
3137 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3139 __isl_give isl_pw_aff *isl_pw_aff_mod(
3140 __isl_take isl_pw_aff *pwaff, isl_int mod);
3141 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3143 __isl_give isl_pw_aff *isl_pw_aff_scale(
3144 __isl_take isl_pw_aff *pwaff, isl_int f);
3145 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3147 __isl_give isl_aff *isl_aff_scale_down_ui(
3148 __isl_take isl_aff *aff, unsigned f);
3149 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3150 __isl_take isl_pw_aff *pwaff, isl_int f);
3152 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3153 __isl_take isl_pw_aff_list *list);
3154 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3155 __isl_take isl_pw_aff_list *list);
3157 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3158 __isl_take isl_pw_aff *pwqp);
3160 __isl_give isl_aff *isl_aff_align_params(
3161 __isl_take isl_aff *aff,
3162 __isl_take isl_space *model);
3163 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3164 __isl_take isl_pw_aff *pwaff,
3165 __isl_take isl_space *model);
3167 __isl_give isl_aff *isl_aff_project_domain_on_params(
3168 __isl_take isl_aff *aff);
3170 __isl_give isl_aff *isl_aff_gist_params(
3171 __isl_take isl_aff *aff,
3172 __isl_take isl_set *context);
3173 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3174 __isl_take isl_set *context);
3175 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3176 __isl_take isl_pw_aff *pwaff,
3177 __isl_take isl_set *context);
3178 __isl_give isl_pw_aff *isl_pw_aff_gist(
3179 __isl_take isl_pw_aff *pwaff,
3180 __isl_take isl_set *context);
3182 __isl_give isl_set *isl_pw_aff_domain(
3183 __isl_take isl_pw_aff *pwaff);
3184 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3185 __isl_take isl_pw_aff *pa,
3186 __isl_take isl_set *set);
3187 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3188 __isl_take isl_pw_aff *pa,
3189 __isl_take isl_set *set);
3191 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3192 __isl_take isl_aff *aff2);
3193 __isl_give isl_pw_aff *isl_pw_aff_mul(
3194 __isl_take isl_pw_aff *pwaff1,
3195 __isl_take isl_pw_aff *pwaff2);
3197 When multiplying two affine expressions, at least one of the two needs
3200 #include <isl/aff.h>
3201 __isl_give isl_basic_set *isl_aff_le_basic_set(
3202 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3203 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3204 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3205 __isl_give isl_set *isl_pw_aff_eq_set(
3206 __isl_take isl_pw_aff *pwaff1,
3207 __isl_take isl_pw_aff *pwaff2);
3208 __isl_give isl_set *isl_pw_aff_ne_set(
3209 __isl_take isl_pw_aff *pwaff1,
3210 __isl_take isl_pw_aff *pwaff2);
3211 __isl_give isl_set *isl_pw_aff_le_set(
3212 __isl_take isl_pw_aff *pwaff1,
3213 __isl_take isl_pw_aff *pwaff2);
3214 __isl_give isl_set *isl_pw_aff_lt_set(
3215 __isl_take isl_pw_aff *pwaff1,
3216 __isl_take isl_pw_aff *pwaff2);
3217 __isl_give isl_set *isl_pw_aff_ge_set(
3218 __isl_take isl_pw_aff *pwaff1,
3219 __isl_take isl_pw_aff *pwaff2);
3220 __isl_give isl_set *isl_pw_aff_gt_set(
3221 __isl_take isl_pw_aff *pwaff1,
3222 __isl_take isl_pw_aff *pwaff2);
3224 __isl_give isl_set *isl_pw_aff_list_eq_set(
3225 __isl_take isl_pw_aff_list *list1,
3226 __isl_take isl_pw_aff_list *list2);
3227 __isl_give isl_set *isl_pw_aff_list_ne_set(
3228 __isl_take isl_pw_aff_list *list1,
3229 __isl_take isl_pw_aff_list *list2);
3230 __isl_give isl_set *isl_pw_aff_list_le_set(
3231 __isl_take isl_pw_aff_list *list1,
3232 __isl_take isl_pw_aff_list *list2);
3233 __isl_give isl_set *isl_pw_aff_list_lt_set(
3234 __isl_take isl_pw_aff_list *list1,
3235 __isl_take isl_pw_aff_list *list2);
3236 __isl_give isl_set *isl_pw_aff_list_ge_set(
3237 __isl_take isl_pw_aff_list *list1,
3238 __isl_take isl_pw_aff_list *list2);
3239 __isl_give isl_set *isl_pw_aff_list_gt_set(
3240 __isl_take isl_pw_aff_list *list1,
3241 __isl_take isl_pw_aff_list *list2);
3243 The function C<isl_aff_ge_basic_set> returns a basic set
3244 containing those elements in the shared space
3245 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3246 The function C<isl_pw_aff_ge_set> returns a set
3247 containing those elements in the shared domain
3248 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3249 The functions operating on C<isl_pw_aff_list> apply the corresponding
3250 C<isl_pw_aff> function to each pair of elements in the two lists.
3252 #include <isl/aff.h>
3253 __isl_give isl_set *isl_pw_aff_nonneg_set(
3254 __isl_take isl_pw_aff *pwaff);
3255 __isl_give isl_set *isl_pw_aff_zero_set(
3256 __isl_take isl_pw_aff *pwaff);
3257 __isl_give isl_set *isl_pw_aff_non_zero_set(
3258 __isl_take isl_pw_aff *pwaff);
3260 The function C<isl_pw_aff_nonneg_set> returns a set
3261 containing those elements in the domain
3262 of C<pwaff> where C<pwaff> is non-negative.
3264 #include <isl/aff.h>
3265 __isl_give isl_pw_aff *isl_pw_aff_cond(
3266 __isl_take isl_pw_aff *cond,
3267 __isl_take isl_pw_aff *pwaff_true,
3268 __isl_take isl_pw_aff *pwaff_false);
3270 The function C<isl_pw_aff_cond> performs a conditional operator
3271 and returns an expression that is equal to C<pwaff_true>
3272 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3273 where C<cond> is zero.
3275 #include <isl/aff.h>
3276 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3277 __isl_take isl_pw_aff *pwaff1,
3278 __isl_take isl_pw_aff *pwaff2);
3279 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3280 __isl_take isl_pw_aff *pwaff1,
3281 __isl_take isl_pw_aff *pwaff2);
3282 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3283 __isl_take isl_pw_aff *pwaff1,
3284 __isl_take isl_pw_aff *pwaff2);
3286 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3287 expression with a domain that is the union of those of C<pwaff1> and
3288 C<pwaff2> and such that on each cell, the quasi-affine expression is
3289 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3290 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3291 associated expression is the defined one.
3293 An expression can be read from input using
3295 #include <isl/aff.h>
3296 __isl_give isl_aff *isl_aff_read_from_str(
3297 isl_ctx *ctx, const char *str);
3298 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3299 isl_ctx *ctx, const char *str);
3301 An expression can be printed using
3303 #include <isl/aff.h>
3304 __isl_give isl_printer *isl_printer_print_aff(
3305 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3307 __isl_give isl_printer *isl_printer_print_pw_aff(
3308 __isl_take isl_printer *p,
3309 __isl_keep isl_pw_aff *pwaff);
3311 =head2 Piecewise Multiple Quasi Affine Expressions
3313 An C<isl_multi_aff> object represents a sequence of
3314 zero or more affine expressions, all defined on the same domain space.
3316 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3319 #include <isl/aff.h>
3320 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3321 __isl_take isl_space *space,
3322 __isl_take isl_aff_list *list);
3324 An empty piecewise multiple quasi affine expression (one with no cells),
3325 the zero piecewise multiple quasi affine expression (with value zero
3326 for each output dimension),
3327 a piecewise multiple quasi affine expression with a single cell (with
3328 either a universe or a specified domain) or
3329 a zero-dimensional piecewise multiple quasi affine expression
3331 can be created using the following functions.
3333 #include <isl/aff.h>
3334 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3335 __isl_take isl_space *space);
3336 __isl_give isl_multi_aff *isl_multi_aff_zero(
3337 __isl_take isl_space *space);
3338 __isl_give isl_pw_multi_aff *
3339 isl_pw_multi_aff_from_multi_aff(
3340 __isl_take isl_multi_aff *ma);
3341 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3342 __isl_take isl_set *set,
3343 __isl_take isl_multi_aff *maff);
3344 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3345 __isl_take isl_set *set);
3347 __isl_give isl_union_pw_multi_aff *
3348 isl_union_pw_multi_aff_empty(
3349 __isl_take isl_space *space);
3350 __isl_give isl_union_pw_multi_aff *
3351 isl_union_pw_multi_aff_add_pw_multi_aff(
3352 __isl_take isl_union_pw_multi_aff *upma,
3353 __isl_take isl_pw_multi_aff *pma);
3354 __isl_give isl_union_pw_multi_aff *
3355 isl_union_pw_multi_aff_from_domain(
3356 __isl_take isl_union_set *uset);
3358 A piecewise multiple quasi affine expression can also be initialized
3359 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3360 and the C<isl_map> is single-valued.
3362 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3363 __isl_take isl_set *set);
3364 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3365 __isl_take isl_map *map);
3367 Multiple quasi affine expressions can be copied and freed using
3369 #include <isl/aff.h>
3370 __isl_give isl_multi_aff *isl_multi_aff_copy(
3371 __isl_keep isl_multi_aff *maff);
3372 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3374 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3375 __isl_keep isl_pw_multi_aff *pma);
3376 void *isl_pw_multi_aff_free(
3377 __isl_take isl_pw_multi_aff *pma);
3379 __isl_give isl_union_pw_multi_aff *
3380 isl_union_pw_multi_aff_copy(
3381 __isl_keep isl_union_pw_multi_aff *upma);
3382 void *isl_union_pw_multi_aff_free(
3383 __isl_take isl_union_pw_multi_aff *upma);
3385 The expression can be inspected using
3387 #include <isl/aff.h>
3388 isl_ctx *isl_multi_aff_get_ctx(
3389 __isl_keep isl_multi_aff *maff);
3390 isl_ctx *isl_pw_multi_aff_get_ctx(
3391 __isl_keep isl_pw_multi_aff *pma);
3392 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3393 __isl_keep isl_union_pw_multi_aff *upma);
3394 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3395 enum isl_dim_type type);
3396 unsigned isl_pw_multi_aff_dim(
3397 __isl_keep isl_pw_multi_aff *pma,
3398 enum isl_dim_type type);
3399 __isl_give isl_aff *isl_multi_aff_get_aff(
3400 __isl_keep isl_multi_aff *multi, int pos);
3401 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3402 __isl_keep isl_pw_multi_aff *pma, int pos);
3403 const char *isl_pw_multi_aff_get_dim_name(
3404 __isl_keep isl_pw_multi_aff *pma,
3405 enum isl_dim_type type, unsigned pos);
3406 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3407 __isl_keep isl_pw_multi_aff *pma,
3408 enum isl_dim_type type, unsigned pos);
3409 const char *isl_multi_aff_get_tuple_name(
3410 __isl_keep isl_multi_aff *multi,
3411 enum isl_dim_type type);
3412 const char *isl_pw_multi_aff_get_tuple_name(
3413 __isl_keep isl_pw_multi_aff *pma,
3414 enum isl_dim_type type);
3415 int isl_pw_multi_aff_has_tuple_id(
3416 __isl_keep isl_pw_multi_aff *pma,
3417 enum isl_dim_type type);
3418 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3419 __isl_keep isl_pw_multi_aff *pma,
3420 enum isl_dim_type type);
3422 int isl_pw_multi_aff_foreach_piece(
3423 __isl_keep isl_pw_multi_aff *pma,
3424 int (*fn)(__isl_take isl_set *set,
3425 __isl_take isl_multi_aff *maff,
3426 void *user), void *user);
3428 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3429 __isl_keep isl_union_pw_multi_aff *upma,
3430 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3431 void *user), void *user);
3433 It can be modified using
3435 #include <isl/aff.h>
3436 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3437 __isl_take isl_multi_aff *multi, int pos,
3438 __isl_take isl_aff *aff);
3439 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3440 __isl_take isl_multi_aff *maff,
3441 enum isl_dim_type type, unsigned pos, const char *s);
3442 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3443 __isl_take isl_multi_aff *maff,
3444 enum isl_dim_type type, __isl_take isl_id *id);
3445 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3446 __isl_take isl_pw_multi_aff *pma,
3447 enum isl_dim_type type, __isl_take isl_id *id);
3449 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3450 __isl_take isl_multi_aff *maff,
3451 enum isl_dim_type type, unsigned first, unsigned n);
3453 To check whether two multiple affine expressions are
3454 obviously equal to each other, use
3456 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3457 __isl_keep isl_multi_aff *maff2);
3458 int isl_pw_multi_aff_plain_is_equal(
3459 __isl_keep isl_pw_multi_aff *pma1,
3460 __isl_keep isl_pw_multi_aff *pma2);
3464 #include <isl/aff.h>
3465 __isl_give isl_multi_aff *isl_multi_aff_add(
3466 __isl_take isl_multi_aff *maff1,
3467 __isl_take isl_multi_aff *maff2);
3468 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3469 __isl_take isl_pw_multi_aff *pma1,
3470 __isl_take isl_pw_multi_aff *pma2);
3471 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3472 __isl_take isl_union_pw_multi_aff *upma1,
3473 __isl_take isl_union_pw_multi_aff *upma2);
3474 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3475 __isl_take isl_pw_multi_aff *pma1,
3476 __isl_take isl_pw_multi_aff *pma2);
3477 __isl_give isl_multi_aff *isl_multi_aff_scale(
3478 __isl_take isl_multi_aff *maff,
3480 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3481 __isl_take isl_pw_multi_aff *pma,
3482 __isl_take isl_set *set);
3483 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3484 __isl_take isl_pw_multi_aff *pma,
3485 __isl_take isl_set *set);
3486 __isl_give isl_multi_aff *isl_multi_aff_lift(
3487 __isl_take isl_multi_aff *maff,
3488 __isl_give isl_local_space **ls);
3489 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3490 __isl_take isl_pw_multi_aff *pma);
3491 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3492 __isl_take isl_multi_aff *maff,
3493 __isl_take isl_set *context);
3494 __isl_give isl_multi_aff *isl_multi_aff_gist(
3495 __isl_take isl_multi_aff *maff,
3496 __isl_take isl_set *context);
3497 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3498 __isl_take isl_pw_multi_aff *pma,
3499 __isl_take isl_set *set);
3500 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3501 __isl_take isl_pw_multi_aff *pma,
3502 __isl_take isl_set *set);
3503 __isl_give isl_set *isl_pw_multi_aff_domain(
3504 __isl_take isl_pw_multi_aff *pma);
3505 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3506 __isl_take isl_union_pw_multi_aff *upma);
3507 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3508 __isl_take isl_multi_aff *ma1,
3509 __isl_take isl_multi_aff *ma2);
3510 __isl_give isl_pw_multi_aff *
3511 isl_pw_multi_aff_flat_range_product(
3512 __isl_take isl_pw_multi_aff *pma1,
3513 __isl_take isl_pw_multi_aff *pma2);
3514 __isl_give isl_union_pw_multi_aff *
3515 isl_union_pw_multi_aff_flat_range_product(
3516 __isl_take isl_union_pw_multi_aff *upma1,
3517 __isl_take isl_union_pw_multi_aff *upma2);
3519 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3520 then it is assigned the local space that lies at the basis of
3521 the lifting applied.
3523 An expression can be read from input using
3525 #include <isl/aff.h>
3526 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3527 isl_ctx *ctx, const char *str);
3528 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3529 isl_ctx *ctx, const char *str);
3531 An expression can be printed using
3533 #include <isl/aff.h>
3534 __isl_give isl_printer *isl_printer_print_multi_aff(
3535 __isl_take isl_printer *p,
3536 __isl_keep isl_multi_aff *maff);
3537 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3538 __isl_take isl_printer *p,
3539 __isl_keep isl_pw_multi_aff *pma);
3540 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3541 __isl_take isl_printer *p,
3542 __isl_keep isl_union_pw_multi_aff *upma);
3546 Points are elements of a set. They can be used to construct
3547 simple sets (boxes) or they can be used to represent the
3548 individual elements of a set.
3549 The zero point (the origin) can be created using
3551 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3553 The coordinates of a point can be inspected, set and changed
3556 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3557 enum isl_dim_type type, int pos, isl_int *v);
3558 __isl_give isl_point *isl_point_set_coordinate(
3559 __isl_take isl_point *pnt,
3560 enum isl_dim_type type, int pos, isl_int v);
3562 __isl_give isl_point *isl_point_add_ui(
3563 __isl_take isl_point *pnt,
3564 enum isl_dim_type type, int pos, unsigned val);
3565 __isl_give isl_point *isl_point_sub_ui(
3566 __isl_take isl_point *pnt,
3567 enum isl_dim_type type, int pos, unsigned val);
3569 Other properties can be obtained using
3571 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3573 Points can be copied or freed using
3575 __isl_give isl_point *isl_point_copy(
3576 __isl_keep isl_point *pnt);
3577 void isl_point_free(__isl_take isl_point *pnt);
3579 A singleton set can be created from a point using
3581 __isl_give isl_basic_set *isl_basic_set_from_point(
3582 __isl_take isl_point *pnt);
3583 __isl_give isl_set *isl_set_from_point(
3584 __isl_take isl_point *pnt);
3586 and a box can be created from two opposite extremal points using
3588 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3589 __isl_take isl_point *pnt1,
3590 __isl_take isl_point *pnt2);
3591 __isl_give isl_set *isl_set_box_from_points(
3592 __isl_take isl_point *pnt1,
3593 __isl_take isl_point *pnt2);
3595 All elements of a B<bounded> (union) set can be enumerated using
3596 the following functions.
3598 int isl_set_foreach_point(__isl_keep isl_set *set,
3599 int (*fn)(__isl_take isl_point *pnt, void *user),
3601 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3602 int (*fn)(__isl_take isl_point *pnt, void *user),
3605 The function C<fn> is called for each integer point in
3606 C<set> with as second argument the last argument of
3607 the C<isl_set_foreach_point> call. The function C<fn>
3608 should return C<0> on success and C<-1> on failure.
3609 In the latter case, C<isl_set_foreach_point> will stop
3610 enumerating and return C<-1> as well.
3611 If the enumeration is performed successfully and to completion,
3612 then C<isl_set_foreach_point> returns C<0>.
3614 To obtain a single point of a (basic) set, use
3616 __isl_give isl_point *isl_basic_set_sample_point(
3617 __isl_take isl_basic_set *bset);
3618 __isl_give isl_point *isl_set_sample_point(
3619 __isl_take isl_set *set);
3621 If C<set> does not contain any (integer) points, then the
3622 resulting point will be ``void'', a property that can be
3625 int isl_point_is_void(__isl_keep isl_point *pnt);
3627 =head2 Piecewise Quasipolynomials
3629 A piecewise quasipolynomial is a particular kind of function that maps
3630 a parametric point to a rational value.
3631 More specifically, a quasipolynomial is a polynomial expression in greatest
3632 integer parts of affine expressions of parameters and variables.
3633 A piecewise quasipolynomial is a subdivision of a given parametric
3634 domain into disjoint cells with a quasipolynomial associated to
3635 each cell. The value of the piecewise quasipolynomial at a given
3636 point is the value of the quasipolynomial associated to the cell
3637 that contains the point. Outside of the union of cells,
3638 the value is assumed to be zero.
3639 For example, the piecewise quasipolynomial
3641 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3643 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3644 A given piecewise quasipolynomial has a fixed domain dimension.
3645 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3646 defined over different domains.
3647 Piecewise quasipolynomials are mainly used by the C<barvinok>
3648 library for representing the number of elements in a parametric set or map.
3649 For example, the piecewise quasipolynomial above represents
3650 the number of points in the map
3652 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3654 =head3 Input and Output
3656 Piecewise quasipolynomials can be read from input using
3658 __isl_give isl_union_pw_qpolynomial *
3659 isl_union_pw_qpolynomial_read_from_str(
3660 isl_ctx *ctx, const char *str);
3662 Quasipolynomials and piecewise quasipolynomials can be printed
3663 using the following functions.
3665 __isl_give isl_printer *isl_printer_print_qpolynomial(
3666 __isl_take isl_printer *p,
3667 __isl_keep isl_qpolynomial *qp);
3669 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3670 __isl_take isl_printer *p,
3671 __isl_keep isl_pw_qpolynomial *pwqp);
3673 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3674 __isl_take isl_printer *p,
3675 __isl_keep isl_union_pw_qpolynomial *upwqp);
3677 The output format of the printer
3678 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3679 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3681 In case of printing in C<ISL_FORMAT_C>, the user may want
3682 to set the names of all dimensions
3684 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3685 __isl_take isl_qpolynomial *qp,
3686 enum isl_dim_type type, unsigned pos,
3688 __isl_give isl_pw_qpolynomial *
3689 isl_pw_qpolynomial_set_dim_name(
3690 __isl_take isl_pw_qpolynomial *pwqp,
3691 enum isl_dim_type type, unsigned pos,
3694 =head3 Creating New (Piecewise) Quasipolynomials
3696 Some simple quasipolynomials can be created using the following functions.
3697 More complicated quasipolynomials can be created by applying
3698 operations such as addition and multiplication
3699 on the resulting quasipolynomials
3701 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3702 __isl_take isl_space *domain);
3703 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3704 __isl_take isl_space *domain);
3705 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3706 __isl_take isl_space *domain);
3707 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3708 __isl_take isl_space *domain);
3709 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3710 __isl_take isl_space *domain);
3711 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3712 __isl_take isl_space *domain,
3713 const isl_int n, const isl_int d);
3714 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3715 __isl_take isl_space *domain,
3716 enum isl_dim_type type, unsigned pos);
3717 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3718 __isl_take isl_aff *aff);
3720 Note that the space in which a quasipolynomial lives is a map space
3721 with a one-dimensional range. The C<domain> argument in some of
3722 the functions above corresponds to the domain of this map space.
3724 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3725 with a single cell can be created using the following functions.
3726 Multiple of these single cell piecewise quasipolynomials can
3727 be combined to create more complicated piecewise quasipolynomials.
3729 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3730 __isl_take isl_space *space);
3731 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3732 __isl_take isl_set *set,
3733 __isl_take isl_qpolynomial *qp);
3734 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3735 __isl_take isl_qpolynomial *qp);
3736 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3737 __isl_take isl_pw_aff *pwaff);
3739 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3740 __isl_take isl_space *space);
3741 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3742 __isl_take isl_pw_qpolynomial *pwqp);
3743 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3744 __isl_take isl_union_pw_qpolynomial *upwqp,
3745 __isl_take isl_pw_qpolynomial *pwqp);
3747 Quasipolynomials can be copied and freed again using the following
3750 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3751 __isl_keep isl_qpolynomial *qp);
3752 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3754 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3755 __isl_keep isl_pw_qpolynomial *pwqp);
3756 void *isl_pw_qpolynomial_free(
3757 __isl_take isl_pw_qpolynomial *pwqp);
3759 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3760 __isl_keep isl_union_pw_qpolynomial *upwqp);
3761 void *isl_union_pw_qpolynomial_free(
3762 __isl_take isl_union_pw_qpolynomial *upwqp);
3764 =head3 Inspecting (Piecewise) Quasipolynomials
3766 To iterate over all piecewise quasipolynomials in a union
3767 piecewise quasipolynomial, use the following function
3769 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3770 __isl_keep isl_union_pw_qpolynomial *upwqp,
3771 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3774 To extract the piecewise quasipolynomial in a given space from a union, use
3776 __isl_give isl_pw_qpolynomial *
3777 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3778 __isl_keep isl_union_pw_qpolynomial *upwqp,
3779 __isl_take isl_space *space);
3781 To iterate over the cells in a piecewise quasipolynomial,
3782 use either of the following two functions
3784 int isl_pw_qpolynomial_foreach_piece(
3785 __isl_keep isl_pw_qpolynomial *pwqp,
3786 int (*fn)(__isl_take isl_set *set,
3787 __isl_take isl_qpolynomial *qp,
3788 void *user), void *user);
3789 int isl_pw_qpolynomial_foreach_lifted_piece(
3790 __isl_keep isl_pw_qpolynomial *pwqp,
3791 int (*fn)(__isl_take isl_set *set,
3792 __isl_take isl_qpolynomial *qp,
3793 void *user), void *user);
3795 As usual, the function C<fn> should return C<0> on success
3796 and C<-1> on failure. The difference between
3797 C<isl_pw_qpolynomial_foreach_piece> and
3798 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3799 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3800 compute unique representations for all existentially quantified
3801 variables and then turn these existentially quantified variables
3802 into extra set variables, adapting the associated quasipolynomial
3803 accordingly. This means that the C<set> passed to C<fn>
3804 will not have any existentially quantified variables, but that
3805 the dimensions of the sets may be different for different
3806 invocations of C<fn>.
3808 To iterate over all terms in a quasipolynomial,
3811 int isl_qpolynomial_foreach_term(
3812 __isl_keep isl_qpolynomial *qp,
3813 int (*fn)(__isl_take isl_term *term,
3814 void *user), void *user);
3816 The terms themselves can be inspected and freed using
3819 unsigned isl_term_dim(__isl_keep isl_term *term,
3820 enum isl_dim_type type);
3821 void isl_term_get_num(__isl_keep isl_term *term,
3823 void isl_term_get_den(__isl_keep isl_term *term,
3825 int isl_term_get_exp(__isl_keep isl_term *term,
3826 enum isl_dim_type type, unsigned pos);
3827 __isl_give isl_aff *isl_term_get_div(
3828 __isl_keep isl_term *term, unsigned pos);
3829 void isl_term_free(__isl_take isl_term *term);
3831 Each term is a product of parameters, set variables and
3832 integer divisions. The function C<isl_term_get_exp>
3833 returns the exponent of a given dimensions in the given term.
3834 The C<isl_int>s in the arguments of C<isl_term_get_num>
3835 and C<isl_term_get_den> need to have been initialized
3836 using C<isl_int_init> before calling these functions.
3838 =head3 Properties of (Piecewise) Quasipolynomials
3840 To check whether a quasipolynomial is actually a constant,
3841 use the following function.
3843 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3844 isl_int *n, isl_int *d);
3846 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3847 then the numerator and denominator of the constant
3848 are returned in C<*n> and C<*d>, respectively.
3850 To check whether two union piecewise quasipolynomials are
3851 obviously equal, use
3853 int isl_union_pw_qpolynomial_plain_is_equal(
3854 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3855 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3857 =head3 Operations on (Piecewise) Quasipolynomials
3859 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3860 __isl_take isl_qpolynomial *qp, isl_int v);
3861 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3862 __isl_take isl_qpolynomial *qp);
3863 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3864 __isl_take isl_qpolynomial *qp1,
3865 __isl_take isl_qpolynomial *qp2);
3866 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3867 __isl_take isl_qpolynomial *qp1,
3868 __isl_take isl_qpolynomial *qp2);
3869 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3870 __isl_take isl_qpolynomial *qp1,
3871 __isl_take isl_qpolynomial *qp2);
3872 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3873 __isl_take isl_qpolynomial *qp, unsigned exponent);
3875 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3876 __isl_take isl_pw_qpolynomial *pwqp1,
3877 __isl_take isl_pw_qpolynomial *pwqp2);
3878 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3879 __isl_take isl_pw_qpolynomial *pwqp1,
3880 __isl_take isl_pw_qpolynomial *pwqp2);
3881 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3882 __isl_take isl_pw_qpolynomial *pwqp1,
3883 __isl_take isl_pw_qpolynomial *pwqp2);
3884 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3885 __isl_take isl_pw_qpolynomial *pwqp);
3886 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3887 __isl_take isl_pw_qpolynomial *pwqp1,
3888 __isl_take isl_pw_qpolynomial *pwqp2);
3889 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3890 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3892 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3893 __isl_take isl_union_pw_qpolynomial *upwqp1,
3894 __isl_take isl_union_pw_qpolynomial *upwqp2);
3895 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3896 __isl_take isl_union_pw_qpolynomial *upwqp1,
3897 __isl_take isl_union_pw_qpolynomial *upwqp2);
3898 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3899 __isl_take isl_union_pw_qpolynomial *upwqp1,
3900 __isl_take isl_union_pw_qpolynomial *upwqp2);
3902 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3903 __isl_take isl_pw_qpolynomial *pwqp,
3904 __isl_take isl_point *pnt);
3906 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3907 __isl_take isl_union_pw_qpolynomial *upwqp,
3908 __isl_take isl_point *pnt);
3910 __isl_give isl_set *isl_pw_qpolynomial_domain(
3911 __isl_take isl_pw_qpolynomial *pwqp);
3912 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3913 __isl_take isl_pw_qpolynomial *pwpq,
3914 __isl_take isl_set *set);
3915 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3916 __isl_take isl_pw_qpolynomial *pwpq,
3917 __isl_take isl_set *set);
3919 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3920 __isl_take isl_union_pw_qpolynomial *upwqp);
3921 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3922 __isl_take isl_union_pw_qpolynomial *upwpq,
3923 __isl_take isl_union_set *uset);
3924 __isl_give isl_union_pw_qpolynomial *
3925 isl_union_pw_qpolynomial_intersect_params(
3926 __isl_take isl_union_pw_qpolynomial *upwpq,
3927 __isl_take isl_set *set);
3929 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3930 __isl_take isl_qpolynomial *qp,
3931 __isl_take isl_space *model);
3933 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3934 __isl_take isl_qpolynomial *qp);
3935 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3936 __isl_take isl_pw_qpolynomial *pwqp);
3938 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3939 __isl_take isl_union_pw_qpolynomial *upwqp);
3941 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3942 __isl_take isl_qpolynomial *qp,
3943 __isl_take isl_set *context);
3944 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3945 __isl_take isl_qpolynomial *qp,
3946 __isl_take isl_set *context);
3948 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
3949 __isl_take isl_pw_qpolynomial *pwqp,
3950 __isl_take isl_set *context);
3951 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3952 __isl_take isl_pw_qpolynomial *pwqp,
3953 __isl_take isl_set *context);
3955 __isl_give isl_union_pw_qpolynomial *
3956 isl_union_pw_qpolynomial_gist_params(
3957 __isl_take isl_union_pw_qpolynomial *upwqp,
3958 __isl_take isl_set *context);
3959 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3960 __isl_take isl_union_pw_qpolynomial *upwqp,
3961 __isl_take isl_union_set *context);
3963 The gist operation applies the gist operation to each of
3964 the cells in the domain of the input piecewise quasipolynomial.
3965 The context is also exploited
3966 to simplify the quasipolynomials associated to each cell.
3968 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3969 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3970 __isl_give isl_union_pw_qpolynomial *
3971 isl_union_pw_qpolynomial_to_polynomial(
3972 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3974 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3975 the polynomial will be an overapproximation. If C<sign> is negative,
3976 it will be an underapproximation. If C<sign> is zero, the approximation
3977 will lie somewhere in between.
3979 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3981 A piecewise quasipolynomial reduction is a piecewise
3982 reduction (or fold) of quasipolynomials.
3983 In particular, the reduction can be maximum or a minimum.
3984 The objects are mainly used to represent the result of
3985 an upper or lower bound on a quasipolynomial over its domain,
3986 i.e., as the result of the following function.
3988 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3989 __isl_take isl_pw_qpolynomial *pwqp,
3990 enum isl_fold type, int *tight);
3992 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3993 __isl_take isl_union_pw_qpolynomial *upwqp,
3994 enum isl_fold type, int *tight);
3996 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3997 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3998 is the returned bound is known be tight, i.e., for each value
3999 of the parameters there is at least
4000 one element in the domain that reaches the bound.
4001 If the domain of C<pwqp> is not wrapping, then the bound is computed
4002 over all elements in that domain and the result has a purely parametric
4003 domain. If the domain of C<pwqp> is wrapping, then the bound is
4004 computed over the range of the wrapped relation. The domain of the
4005 wrapped relation becomes the domain of the result.
4007 A (piecewise) quasipolynomial reduction can be copied or freed using the
4008 following functions.
4010 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4011 __isl_keep isl_qpolynomial_fold *fold);
4012 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4013 __isl_keep isl_pw_qpolynomial_fold *pwf);
4014 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4015 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4016 void isl_qpolynomial_fold_free(
4017 __isl_take isl_qpolynomial_fold *fold);
4018 void *isl_pw_qpolynomial_fold_free(
4019 __isl_take isl_pw_qpolynomial_fold *pwf);
4020 void *isl_union_pw_qpolynomial_fold_free(
4021 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4023 =head3 Printing Piecewise Quasipolynomial Reductions
4025 Piecewise quasipolynomial reductions can be printed
4026 using the following function.
4028 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4029 __isl_take isl_printer *p,
4030 __isl_keep isl_pw_qpolynomial_fold *pwf);
4031 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4032 __isl_take isl_printer *p,
4033 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4035 For C<isl_printer_print_pw_qpolynomial_fold>,
4036 output format of the printer
4037 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4038 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4039 output format of the printer
4040 needs to be set to C<ISL_FORMAT_ISL>.
4041 In case of printing in C<ISL_FORMAT_C>, the user may want
4042 to set the names of all dimensions
4044 __isl_give isl_pw_qpolynomial_fold *
4045 isl_pw_qpolynomial_fold_set_dim_name(
4046 __isl_take isl_pw_qpolynomial_fold *pwf,
4047 enum isl_dim_type type, unsigned pos,
4050 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4052 To iterate over all piecewise quasipolynomial reductions in a union
4053 piecewise quasipolynomial reduction, use the following function
4055 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4056 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4057 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4058 void *user), void *user);
4060 To iterate over the cells in a piecewise quasipolynomial reduction,
4061 use either of the following two functions
4063 int isl_pw_qpolynomial_fold_foreach_piece(
4064 __isl_keep isl_pw_qpolynomial_fold *pwf,
4065 int (*fn)(__isl_take isl_set *set,
4066 __isl_take isl_qpolynomial_fold *fold,
4067 void *user), void *user);
4068 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4069 __isl_keep isl_pw_qpolynomial_fold *pwf,
4070 int (*fn)(__isl_take isl_set *set,
4071 __isl_take isl_qpolynomial_fold *fold,
4072 void *user), void *user);
4074 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4075 of the difference between these two functions.
4077 To iterate over all quasipolynomials in a reduction, use
4079 int isl_qpolynomial_fold_foreach_qpolynomial(
4080 __isl_keep isl_qpolynomial_fold *fold,
4081 int (*fn)(__isl_take isl_qpolynomial *qp,
4082 void *user), void *user);
4084 =head3 Properties of Piecewise Quasipolynomial Reductions
4086 To check whether two union piecewise quasipolynomial reductions are
4087 obviously equal, use
4089 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4090 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4091 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4093 =head3 Operations on Piecewise Quasipolynomial Reductions
4095 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4096 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4098 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4099 __isl_take isl_pw_qpolynomial_fold *pwf1,
4100 __isl_take isl_pw_qpolynomial_fold *pwf2);
4102 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4103 __isl_take isl_pw_qpolynomial_fold *pwf1,
4104 __isl_take isl_pw_qpolynomial_fold *pwf2);
4106 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4107 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4108 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4110 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4111 __isl_take isl_pw_qpolynomial_fold *pwf,
4112 __isl_take isl_point *pnt);
4114 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4115 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4116 __isl_take isl_point *pnt);
4118 __isl_give isl_pw_qpolynomial_fold *
4119 isl_pw_qpolynomial_fold_intersect_params(
4120 __isl_take isl_pw_qpolynomial_fold *pwf,
4121 __isl_take isl_set *set);
4123 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4124 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4125 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4126 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4127 __isl_take isl_union_set *uset);
4128 __isl_give isl_union_pw_qpolynomial_fold *
4129 isl_union_pw_qpolynomial_fold_intersect_params(
4130 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4131 __isl_take isl_set *set);
4133 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4134 __isl_take isl_pw_qpolynomial_fold *pwf);
4136 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4137 __isl_take isl_pw_qpolynomial_fold *pwf);
4139 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4140 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4142 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4143 __isl_take isl_qpolynomial_fold *fold,
4144 __isl_take isl_set *context);
4145 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4146 __isl_take isl_qpolynomial_fold *fold,
4147 __isl_take isl_set *context);
4149 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4150 __isl_take isl_pw_qpolynomial_fold *pwf,
4151 __isl_take isl_set *context);
4152 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4153 __isl_take isl_pw_qpolynomial_fold *pwf,
4154 __isl_take isl_set *context);
4156 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4157 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4158 __isl_take isl_union_set *context);
4159 __isl_give isl_union_pw_qpolynomial_fold *
4160 isl_union_pw_qpolynomial_fold_gist_params(
4161 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4162 __isl_take isl_set *context);
4164 The gist operation applies the gist operation to each of
4165 the cells in the domain of the input piecewise quasipolynomial reduction.
4166 In future, the operation will also exploit the context
4167 to simplify the quasipolynomial reductions associated to each cell.
4169 __isl_give isl_pw_qpolynomial_fold *
4170 isl_set_apply_pw_qpolynomial_fold(
4171 __isl_take isl_set *set,
4172 __isl_take isl_pw_qpolynomial_fold *pwf,
4174 __isl_give isl_pw_qpolynomial_fold *
4175 isl_map_apply_pw_qpolynomial_fold(
4176 __isl_take isl_map *map,
4177 __isl_take isl_pw_qpolynomial_fold *pwf,
4179 __isl_give isl_union_pw_qpolynomial_fold *
4180 isl_union_set_apply_union_pw_qpolynomial_fold(
4181 __isl_take isl_union_set *uset,
4182 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4184 __isl_give isl_union_pw_qpolynomial_fold *
4185 isl_union_map_apply_union_pw_qpolynomial_fold(
4186 __isl_take isl_union_map *umap,
4187 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4190 The functions taking a map
4191 compose the given map with the given piecewise quasipolynomial reduction.
4192 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4193 over all elements in the intersection of the range of the map
4194 and the domain of the piecewise quasipolynomial reduction
4195 as a function of an element in the domain of the map.
4196 The functions taking a set compute a bound over all elements in the
4197 intersection of the set and the domain of the
4198 piecewise quasipolynomial reduction.
4200 =head2 Dependence Analysis
4202 C<isl> contains specialized functionality for performing
4203 array dataflow analysis. That is, given a I<sink> access relation
4204 and a collection of possible I<source> access relations,
4205 C<isl> can compute relations that describe
4206 for each iteration of the sink access, which iteration
4207 of which of the source access relations was the last
4208 to access the same data element before the given iteration
4210 The resulting dependence relations map source iterations
4211 to the corresponding sink iterations.
4212 To compute standard flow dependences, the sink should be
4213 a read, while the sources should be writes.
4214 If any of the source accesses are marked as being I<may>
4215 accesses, then there will be a dependence from the last
4216 I<must> access B<and> from any I<may> access that follows
4217 this last I<must> access.
4218 In particular, if I<all> sources are I<may> accesses,
4219 then memory based dependence analysis is performed.
4220 If, on the other hand, all sources are I<must> accesses,
4221 then value based dependence analysis is performed.
4223 #include <isl/flow.h>
4225 typedef int (*isl_access_level_before)(void *first, void *second);
4227 __isl_give isl_access_info *isl_access_info_alloc(
4228 __isl_take isl_map *sink,
4229 void *sink_user, isl_access_level_before fn,
4231 __isl_give isl_access_info *isl_access_info_add_source(
4232 __isl_take isl_access_info *acc,
4233 __isl_take isl_map *source, int must,
4235 void *isl_access_info_free(__isl_take isl_access_info *acc);
4237 __isl_give isl_flow *isl_access_info_compute_flow(
4238 __isl_take isl_access_info *acc);
4240 int isl_flow_foreach(__isl_keep isl_flow *deps,
4241 int (*fn)(__isl_take isl_map *dep, int must,
4242 void *dep_user, void *user),
4244 __isl_give isl_map *isl_flow_get_no_source(
4245 __isl_keep isl_flow *deps, int must);
4246 void isl_flow_free(__isl_take isl_flow *deps);
4248 The function C<isl_access_info_compute_flow> performs the actual
4249 dependence analysis. The other functions are used to construct
4250 the input for this function or to read off the output.
4252 The input is collected in an C<isl_access_info>, which can
4253 be created through a call to C<isl_access_info_alloc>.
4254 The arguments to this functions are the sink access relation
4255 C<sink>, a token C<sink_user> used to identify the sink
4256 access to the user, a callback function for specifying the
4257 relative order of source and sink accesses, and the number
4258 of source access relations that will be added.
4259 The callback function has type C<int (*)(void *first, void *second)>.
4260 The function is called with two user supplied tokens identifying
4261 either a source or the sink and it should return the shared nesting
4262 level and the relative order of the two accesses.
4263 In particular, let I<n> be the number of loops shared by
4264 the two accesses. If C<first> precedes C<second> textually,
4265 then the function should return I<2 * n + 1>; otherwise,
4266 it should return I<2 * n>.
4267 The sources can be added to the C<isl_access_info> by performing
4268 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4269 C<must> indicates whether the source is a I<must> access
4270 or a I<may> access. Note that a multi-valued access relation
4271 should only be marked I<must> if every iteration in the domain
4272 of the relation accesses I<all> elements in its image.
4273 The C<source_user> token is again used to identify
4274 the source access. The range of the source access relation
4275 C<source> should have the same dimension as the range
4276 of the sink access relation.
4277 The C<isl_access_info_free> function should usually not be
4278 called explicitly, because it is called implicitly by
4279 C<isl_access_info_compute_flow>.
4281 The result of the dependence analysis is collected in an
4282 C<isl_flow>. There may be elements of
4283 the sink access for which no preceding source access could be
4284 found or for which all preceding sources are I<may> accesses.
4285 The relations containing these elements can be obtained through
4286 calls to C<isl_flow_get_no_source>, the first with C<must> set
4287 and the second with C<must> unset.
4288 In the case of standard flow dependence analysis,
4289 with the sink a read and the sources I<must> writes,
4290 the first relation corresponds to the reads from uninitialized
4291 array elements and the second relation is empty.
4292 The actual flow dependences can be extracted using
4293 C<isl_flow_foreach>. This function will call the user-specified
4294 callback function C<fn> for each B<non-empty> dependence between
4295 a source and the sink. The callback function is called
4296 with four arguments, the actual flow dependence relation
4297 mapping source iterations to sink iterations, a boolean that
4298 indicates whether it is a I<must> or I<may> dependence, a token
4299 identifying the source and an additional C<void *> with value
4300 equal to the third argument of the C<isl_flow_foreach> call.
4301 A dependence is marked I<must> if it originates from a I<must>
4302 source and if it is not followed by any I<may> sources.
4304 After finishing with an C<isl_flow>, the user should call
4305 C<isl_flow_free> to free all associated memory.
4307 A higher-level interface to dependence analysis is provided
4308 by the following function.
4310 #include <isl/flow.h>
4312 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4313 __isl_take isl_union_map *must_source,
4314 __isl_take isl_union_map *may_source,
4315 __isl_take isl_union_map *schedule,
4316 __isl_give isl_union_map **must_dep,
4317 __isl_give isl_union_map **may_dep,
4318 __isl_give isl_union_map **must_no_source,
4319 __isl_give isl_union_map **may_no_source);
4321 The arrays are identified by the tuple names of the ranges
4322 of the accesses. The iteration domains by the tuple names
4323 of the domains of the accesses and of the schedule.
4324 The relative order of the iteration domains is given by the
4325 schedule. The relations returned through C<must_no_source>
4326 and C<may_no_source> are subsets of C<sink>.
4327 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4328 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4329 any of the other arguments is treated as an error.
4331 =head3 Interaction with Dependence Analysis
4333 During the dependence analysis, we frequently need to perform
4334 the following operation. Given a relation between sink iterations
4335 and potential source iterations from a particular source domain,
4336 what is the last potential source iteration corresponding to each
4337 sink iteration. It can sometimes be convenient to adjust
4338 the set of potential source iterations before or after each such operation.
4339 The prototypical example is fuzzy array dataflow analysis,
4340 where we need to analyze if, based on data-dependent constraints,
4341 the sink iteration can ever be executed without one or more of
4342 the corresponding potential source iterations being executed.
4343 If so, we can introduce extra parameters and select an unknown
4344 but fixed source iteration from the potential source iterations.
4345 To be able to perform such manipulations, C<isl> provides the following
4348 #include <isl/flow.h>
4350 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4351 __isl_keep isl_map *source_map,
4352 __isl_keep isl_set *sink, void *source_user,
4354 __isl_give isl_access_info *isl_access_info_set_restrict(
4355 __isl_take isl_access_info *acc,
4356 isl_access_restrict fn, void *user);
4358 The function C<isl_access_info_set_restrict> should be called
4359 before calling C<isl_access_info_compute_flow> and registers a callback function
4360 that will be called any time C<isl> is about to compute the last
4361 potential source. The first argument is the (reverse) proto-dependence,
4362 mapping sink iterations to potential source iterations.
4363 The second argument represents the sink iterations for which
4364 we want to compute the last source iteration.
4365 The third argument is the token corresponding to the source
4366 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4367 The callback is expected to return a restriction on either the input or
4368 the output of the operation computing the last potential source.
4369 If the input needs to be restricted then restrictions are needed
4370 for both the source and the sink iterations. The sink iterations
4371 and the potential source iterations will be intersected with these sets.
4372 If the output needs to be restricted then only a restriction on the source
4373 iterations is required.
4374 If any error occurs, the callback should return C<NULL>.
4375 An C<isl_restriction> object can be created, freed and inspected
4376 using the following functions.
4378 #include <isl/flow.h>
4380 __isl_give isl_restriction *isl_restriction_input(
4381 __isl_take isl_set *source_restr,
4382 __isl_take isl_set *sink_restr);
4383 __isl_give isl_restriction *isl_restriction_output(
4384 __isl_take isl_set *source_restr);
4385 __isl_give isl_restriction *isl_restriction_none(
4386 __isl_take isl_map *source_map);
4387 __isl_give isl_restriction *isl_restriction_empty(
4388 __isl_take isl_map *source_map);
4389 void *isl_restriction_free(
4390 __isl_take isl_restriction *restr);
4391 isl_ctx *isl_restriction_get_ctx(
4392 __isl_keep isl_restriction *restr);
4394 C<isl_restriction_none> and C<isl_restriction_empty> are special
4395 cases of C<isl_restriction_input>. C<isl_restriction_none>
4396 is essentially equivalent to
4398 isl_restriction_input(isl_set_universe(
4399 isl_space_range(isl_map_get_space(source_map))),
4401 isl_space_domain(isl_map_get_space(source_map))));
4403 whereas C<isl_restriction_empty> is essentially equivalent to
4405 isl_restriction_input(isl_set_empty(
4406 isl_space_range(isl_map_get_space(source_map))),
4408 isl_space_domain(isl_map_get_space(source_map))));
4412 B<The functionality described in this section is fairly new
4413 and may be subject to change.>
4415 The following function can be used to compute a schedule
4416 for a union of domains.
4417 By default, the algorithm used to construct the schedule is similar
4418 to that of C<Pluto>.
4419 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4421 The generated schedule respects all C<validity> dependences.
4422 That is, all dependence distances over these dependences in the
4423 scheduled space are lexicographically positive.
4424 The default algorithm tries to minimize the dependence distances over
4425 C<proximity> dependences.
4426 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4427 for groups of domains where the dependence distances have only
4428 non-negative values.
4429 When using Feautrier's algorithm, the C<proximity> dependence
4430 distances are only minimized during the extension to a
4431 full-dimensional schedule.
4433 #include <isl/schedule.h>
4434 __isl_give isl_schedule *isl_union_set_compute_schedule(
4435 __isl_take isl_union_set *domain,
4436 __isl_take isl_union_map *validity,
4437 __isl_take isl_union_map *proximity);
4438 void *isl_schedule_free(__isl_take isl_schedule *sched);
4440 A mapping from the domains to the scheduled space can be obtained
4441 from an C<isl_schedule> using the following function.
4443 __isl_give isl_union_map *isl_schedule_get_map(
4444 __isl_keep isl_schedule *sched);
4446 A representation of the schedule can be printed using
4448 __isl_give isl_printer *isl_printer_print_schedule(
4449 __isl_take isl_printer *p,
4450 __isl_keep isl_schedule *schedule);
4452 A representation of the schedule as a forest of bands can be obtained
4453 using the following function.
4455 __isl_give isl_band_list *isl_schedule_get_band_forest(
4456 __isl_keep isl_schedule *schedule);
4458 The individual bands can be visited in depth-first post-order
4459 using the following function.
4461 #include <isl/schedule.h>
4462 int isl_schedule_foreach_band(
4463 __isl_keep isl_schedule *sched,
4464 int (*fn)(__isl_keep isl_band *band, void *user),
4467 The list can be manipulated as explained in L<"Lists">.
4468 The bands inside the list can be copied and freed using the following
4471 #include <isl/band.h>
4472 __isl_give isl_band *isl_band_copy(
4473 __isl_keep isl_band *band);
4474 void *isl_band_free(__isl_take isl_band *band);
4476 Each band contains zero or more scheduling dimensions.
4477 These are referred to as the members of the band.
4478 The section of the schedule that corresponds to the band is
4479 referred to as the partial schedule of the band.
4480 For those nodes that participate in a band, the outer scheduling
4481 dimensions form the prefix schedule, while the inner scheduling
4482 dimensions form the suffix schedule.
4483 That is, if we take a cut of the band forest, then the union of
4484 the concatenations of the prefix, partial and suffix schedules of
4485 each band in the cut is equal to the entire schedule (modulo
4486 some possible padding at the end with zero scheduling dimensions).
4487 The properties of a band can be inspected using the following functions.
4489 #include <isl/band.h>
4490 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4492 int isl_band_has_children(__isl_keep isl_band *band);
4493 __isl_give isl_band_list *isl_band_get_children(
4494 __isl_keep isl_band *band);
4496 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4497 __isl_keep isl_band *band);
4498 __isl_give isl_union_map *isl_band_get_partial_schedule(
4499 __isl_keep isl_band *band);
4500 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4501 __isl_keep isl_band *band);
4503 int isl_band_n_member(__isl_keep isl_band *band);
4504 int isl_band_member_is_zero_distance(
4505 __isl_keep isl_band *band, int pos);
4507 int isl_band_list_foreach_band(
4508 __isl_keep isl_band_list *list,
4509 int (*fn)(__isl_keep isl_band *band, void *user),
4512 Note that a scheduling dimension is considered to be ``zero
4513 distance'' if it does not carry any proximity dependences
4515 That is, if the dependence distances of the proximity
4516 dependences are all zero in that direction (for fixed
4517 iterations of outer bands).
4518 Like C<isl_schedule_foreach_band>,
4519 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4520 in depth-first post-order.
4522 A band can be tiled using the following function.
4524 #include <isl/band.h>
4525 int isl_band_tile(__isl_keep isl_band *band,
4526 __isl_take isl_vec *sizes);
4528 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4530 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4532 The C<isl_band_tile> function tiles the band using the given tile sizes
4533 inside its schedule.
4534 A new child band is created to represent the point loops and it is
4535 inserted between the modified band and its children.
4536 The C<tile_scale_tile_loops> option specifies whether the tile
4537 loops iterators should be scaled by the tile sizes.
4539 A representation of the band can be printed using
4541 #include <isl/band.h>
4542 __isl_give isl_printer *isl_printer_print_band(
4543 __isl_take isl_printer *p,
4544 __isl_keep isl_band *band);
4548 #include <isl/schedule.h>
4549 int isl_options_set_schedule_max_coefficient(
4550 isl_ctx *ctx, int val);
4551 int isl_options_get_schedule_max_coefficient(
4553 int isl_options_set_schedule_max_constant_term(
4554 isl_ctx *ctx, int val);
4555 int isl_options_get_schedule_max_constant_term(
4557 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4558 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4559 int isl_options_set_schedule_maximize_band_depth(
4560 isl_ctx *ctx, int val);
4561 int isl_options_get_schedule_maximize_band_depth(
4563 int isl_options_set_schedule_outer_zero_distance(
4564 isl_ctx *ctx, int val);
4565 int isl_options_get_schedule_outer_zero_distance(
4567 int isl_options_set_schedule_split_scaled(
4568 isl_ctx *ctx, int val);
4569 int isl_options_get_schedule_split_scaled(
4571 int isl_options_set_schedule_algorithm(
4572 isl_ctx *ctx, int val);
4573 int isl_options_get_schedule_algorithm(
4575 int isl_options_set_schedule_separate_components(
4576 isl_ctx *ctx, int val);
4577 int isl_options_get_schedule_separate_components(
4582 =item * schedule_max_coefficient
4584 This option enforces that the coefficients for variable and parameter
4585 dimensions in the calculated schedule are not larger than the specified value.
4586 This option can significantly increase the speed of the scheduling calculation
4587 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4588 this option does not introduce bounds on the variable or parameter
4591 =item * schedule_max_constant_term
4593 This option enforces that the constant coefficients in the calculated schedule
4594 are not larger than the maximal constant term. This option can significantly
4595 increase the speed of the scheduling calculation and may also prevent fusing of
4596 unrelated dimensions. A value of -1 means that this option does not introduce
4597 bounds on the constant coefficients.
4599 =item * schedule_fuse
4601 This option controls the level of fusion.
4602 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
4603 resulting schedule will be distributed as much as possible.
4604 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
4605 try to fuse loops in the resulting schedule.
4607 =item * schedule_maximize_band_depth
4609 If this option is set, we do not split bands at the point
4610 where we detect splitting is necessary. Instead, we
4611 backtrack and split bands as early as possible. This
4612 reduces the number of splits and maximizes the width of
4613 the bands. Wider bands give more possibilities for tiling.
4614 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
4615 then bands will be split as early as possible, even if there is no need.
4616 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
4618 =item * schedule_outer_zero_distance
4620 If this option is set, then we try to construct schedules
4621 where the outermost scheduling dimension in each band
4622 results in a zero dependence distance over the proximity
4625 =item * schedule_split_scaled
4627 If this option is set, then we try to construct schedules in which the
4628 constant term is split off from the linear part if the linear parts of
4629 the scheduling rows for all nodes in the graphs have a common non-trivial
4631 The constant term is then placed in a separate band and the linear
4634 =item * schedule_algorithm
4636 Selects the scheduling algorithm to be used.
4637 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4638 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4640 =item * schedule_separate_components
4642 If at any point the dependence graph contains any (weakly connected) components,
4643 then these components are scheduled separately.
4644 If this option is not set, then some iterations of the domains
4645 in these components may be scheduled together.
4646 If this option is set, then the components are given consecutive
4651 =head2 Parametric Vertex Enumeration
4653 The parametric vertex enumeration described in this section
4654 is mainly intended to be used internally and by the C<barvinok>
4657 #include <isl/vertices.h>
4658 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4659 __isl_keep isl_basic_set *bset);
4661 The function C<isl_basic_set_compute_vertices> performs the
4662 actual computation of the parametric vertices and the chamber
4663 decomposition and store the result in an C<isl_vertices> object.
4664 This information can be queried by either iterating over all
4665 the vertices or iterating over all the chambers or cells
4666 and then iterating over all vertices that are active on the chamber.
4668 int isl_vertices_foreach_vertex(
4669 __isl_keep isl_vertices *vertices,
4670 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4673 int isl_vertices_foreach_cell(
4674 __isl_keep isl_vertices *vertices,
4675 int (*fn)(__isl_take isl_cell *cell, void *user),
4677 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4678 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4681 Other operations that can be performed on an C<isl_vertices> object are
4684 isl_ctx *isl_vertices_get_ctx(
4685 __isl_keep isl_vertices *vertices);
4686 int isl_vertices_get_n_vertices(
4687 __isl_keep isl_vertices *vertices);
4688 void isl_vertices_free(__isl_take isl_vertices *vertices);
4690 Vertices can be inspected and destroyed using the following functions.
4692 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4693 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4694 __isl_give isl_basic_set *isl_vertex_get_domain(
4695 __isl_keep isl_vertex *vertex);
4696 __isl_give isl_basic_set *isl_vertex_get_expr(
4697 __isl_keep isl_vertex *vertex);
4698 void isl_vertex_free(__isl_take isl_vertex *vertex);
4700 C<isl_vertex_get_expr> returns a singleton parametric set describing
4701 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4703 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4704 B<rational> basic sets, so they should mainly be used for inspection
4705 and should not be mixed with integer sets.
4707 Chambers can be inspected and destroyed using the following functions.
4709 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4710 __isl_give isl_basic_set *isl_cell_get_domain(
4711 __isl_keep isl_cell *cell);
4712 void isl_cell_free(__isl_take isl_cell *cell);
4716 Although C<isl> is mainly meant to be used as a library,
4717 it also contains some basic applications that use some
4718 of the functionality of C<isl>.
4719 The input may be specified in either the L<isl format>
4720 or the L<PolyLib format>.
4722 =head2 C<isl_polyhedron_sample>
4724 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4725 an integer element of the polyhedron, if there is any.
4726 The first column in the output is the denominator and is always
4727 equal to 1. If the polyhedron contains no integer points,
4728 then a vector of length zero is printed.
4732 C<isl_pip> takes the same input as the C<example> program
4733 from the C<piplib> distribution, i.e., a set of constraints
4734 on the parameters, a line containing only -1 and finally a set
4735 of constraints on a parametric polyhedron.
4736 The coefficients of the parameters appear in the last columns
4737 (but before the final constant column).
4738 The output is the lexicographic minimum of the parametric polyhedron.
4739 As C<isl> currently does not have its own output format, the output
4740 is just a dump of the internal state.
4742 =head2 C<isl_polyhedron_minimize>
4744 C<isl_polyhedron_minimize> computes the minimum of some linear
4745 or affine objective function over the integer points in a polyhedron.
4746 If an affine objective function
4747 is given, then the constant should appear in the last column.
4749 =head2 C<isl_polytope_scan>
4751 Given a polytope, C<isl_polytope_scan> prints
4752 all integer points in the polytope.