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)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
184 C<isl> is released under the MIT license.
188 Permission is hereby granted, free of charge, to any person obtaining a copy of
189 this software and associated documentation files (the "Software"), to deal in
190 the Software without restriction, including without limitation the rights to
191 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
192 of the Software, and to permit persons to whom the Software is furnished to do
193 so, subject to the following conditions:
195 The above copyright notice and this permission notice shall be included in all
196 copies or substantial portions of the Software.
198 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
199 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
200 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
201 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
202 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
203 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
208 Note that C<isl> currently requires C<GMP>, which is released
209 under the GNU Lesser General Public License (LGPL). This means
210 that code linked against C<isl> is also linked against LGPL code.
214 The source of C<isl> can be obtained either as a tarball
215 or from the git repository. Both are available from
216 L<http://freshmeat.net/projects/isl/>.
217 The installation process depends on how you obtained
220 =head2 Installation from the git repository
224 =item 1 Clone or update the repository
226 The first time the source is obtained, you need to clone
229 git clone git://repo.or.cz/isl.git
231 To obtain updates, you need to pull in the latest changes
235 =item 2 Generate C<configure>
241 After performing the above steps, continue
242 with the L<Common installation instructions>.
244 =head2 Common installation instructions
248 =item 1 Obtain C<GMP>
250 Building C<isl> requires C<GMP>, including its headers files.
251 Your distribution may not provide these header files by default
252 and you may need to install a package called C<gmp-devel> or something
253 similar. Alternatively, C<GMP> can be built from
254 source, available from L<http://gmplib.org/>.
258 C<isl> uses the standard C<autoconf> C<configure> script.
263 optionally followed by some configure options.
264 A complete list of options can be obtained by running
268 Below we discuss some of the more common options.
270 C<isl> can optionally use C<piplib>, but no
271 C<piplib> functionality is currently used by default.
272 The C<--with-piplib> option can
273 be used to specify which C<piplib>
274 library to use, either an installed version (C<system>),
275 an externally built version (C<build>)
276 or no version (C<no>). The option C<build> is mostly useful
277 in C<configure> scripts of larger projects that bundle both C<isl>
284 Installation prefix for C<isl>
286 =item C<--with-gmp-prefix>
288 Installation prefix for C<GMP> (architecture-independent files).
290 =item C<--with-gmp-exec-prefix>
292 Installation prefix for C<GMP> (architecture-dependent files).
294 =item C<--with-piplib>
296 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
298 =item C<--with-piplib-prefix>
300 Installation prefix for C<system> C<piplib> (architecture-independent files).
302 =item C<--with-piplib-exec-prefix>
304 Installation prefix for C<system> C<piplib> (architecture-dependent files).
306 =item C<--with-piplib-builddir>
308 Location where C<build> C<piplib> was built.
316 =item 4 Install (optional)
324 =head2 Initialization
326 All manipulations of integer sets and relations occur within
327 the context of an C<isl_ctx>.
328 A given C<isl_ctx> can only be used within a single thread.
329 All arguments of a function are required to have been allocated
330 within the same context.
331 There are currently no functions available for moving an object
332 from one C<isl_ctx> to another C<isl_ctx>. This means that
333 there is currently no way of safely moving an object from one
334 thread to another, unless the whole C<isl_ctx> is moved.
336 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
337 freed using C<isl_ctx_free>.
338 All objects allocated within an C<isl_ctx> should be freed
339 before the C<isl_ctx> itself is freed.
341 isl_ctx *isl_ctx_alloc();
342 void isl_ctx_free(isl_ctx *ctx);
346 All operations on integers, mainly the coefficients
347 of the constraints describing the sets and relations,
348 are performed in exact integer arithmetic using C<GMP>.
349 However, to allow future versions of C<isl> to optionally
350 support fixed integer arithmetic, all calls to C<GMP>
351 are wrapped inside C<isl> specific macros.
352 The basic type is C<isl_int> and the operations below
353 are available on this type.
354 The meanings of these operations are essentially the same
355 as their C<GMP> C<mpz_> counterparts.
356 As always with C<GMP> types, C<isl_int>s need to be
357 initialized with C<isl_int_init> before they can be used
358 and they need to be released with C<isl_int_clear>
360 The user should not assume that an C<isl_int> is represented
361 as a C<mpz_t>, but should instead explicitly convert between
362 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
363 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
367 =item isl_int_init(i)
369 =item isl_int_clear(i)
371 =item isl_int_set(r,i)
373 =item isl_int_set_si(r,i)
375 =item isl_int_set_gmp(r,g)
377 =item isl_int_get_gmp(i,g)
379 =item isl_int_abs(r,i)
381 =item isl_int_neg(r,i)
383 =item isl_int_swap(i,j)
385 =item isl_int_swap_or_set(i,j)
387 =item isl_int_add_ui(r,i,j)
389 =item isl_int_sub_ui(r,i,j)
391 =item isl_int_add(r,i,j)
393 =item isl_int_sub(r,i,j)
395 =item isl_int_mul(r,i,j)
397 =item isl_int_mul_ui(r,i,j)
399 =item isl_int_addmul(r,i,j)
401 =item isl_int_submul(r,i,j)
403 =item isl_int_gcd(r,i,j)
405 =item isl_int_lcm(r,i,j)
407 =item isl_int_divexact(r,i,j)
409 =item isl_int_cdiv_q(r,i,j)
411 =item isl_int_fdiv_q(r,i,j)
413 =item isl_int_fdiv_r(r,i,j)
415 =item isl_int_fdiv_q_ui(r,i,j)
417 =item isl_int_read(r,s)
419 =item isl_int_print(out,i,width)
423 =item isl_int_cmp(i,j)
425 =item isl_int_cmp_si(i,si)
427 =item isl_int_eq(i,j)
429 =item isl_int_ne(i,j)
431 =item isl_int_lt(i,j)
433 =item isl_int_le(i,j)
435 =item isl_int_gt(i,j)
437 =item isl_int_ge(i,j)
439 =item isl_int_abs_eq(i,j)
441 =item isl_int_abs_ne(i,j)
443 =item isl_int_abs_lt(i,j)
445 =item isl_int_abs_gt(i,j)
447 =item isl_int_abs_ge(i,j)
449 =item isl_int_is_zero(i)
451 =item isl_int_is_one(i)
453 =item isl_int_is_negone(i)
455 =item isl_int_is_pos(i)
457 =item isl_int_is_neg(i)
459 =item isl_int_is_nonpos(i)
461 =item isl_int_is_nonneg(i)
463 =item isl_int_is_divisible_by(i,j)
467 =head2 Sets and Relations
469 C<isl> uses six types of objects for representing sets and relations,
470 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
471 C<isl_union_set> and C<isl_union_map>.
472 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
473 can be described as a conjunction of affine constraints, while
474 C<isl_set> and C<isl_map> represent unions of
475 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
476 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
477 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
478 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
479 where spaces are considered different if they have a different number
480 of dimensions and/or different names (see L<"Spaces">).
481 The difference between sets and relations (maps) is that sets have
482 one set of variables, while relations have two sets of variables,
483 input variables and output variables.
485 =head2 Memory Management
487 Since a high-level operation on sets and/or relations usually involves
488 several substeps and since the user is usually not interested in
489 the intermediate results, most functions that return a new object
490 will also release all the objects passed as arguments.
491 If the user still wants to use one or more of these arguments
492 after the function call, she should pass along a copy of the
493 object rather than the object itself.
494 The user is then responsible for making sure that the original
495 object gets used somewhere else or is explicitly freed.
497 The arguments and return values of all documented functions are
498 annotated to make clear which arguments are released and which
499 arguments are preserved. In particular, the following annotations
506 C<__isl_give> means that a new object is returned.
507 The user should make sure that the returned pointer is
508 used exactly once as a value for an C<__isl_take> argument.
509 In between, it can be used as a value for as many
510 C<__isl_keep> arguments as the user likes.
511 There is one exception, and that is the case where the
512 pointer returned is C<NULL>. Is this case, the user
513 is free to use it as an C<__isl_take> argument or not.
517 C<__isl_take> means that the object the argument points to
518 is taken over by the function and may no longer be used
519 by the user as an argument to any other function.
520 The pointer value must be one returned by a function
521 returning an C<__isl_give> pointer.
522 If the user passes in a C<NULL> value, then this will
523 be treated as an error in the sense that the function will
524 not perform its usual operation. However, it will still
525 make sure that all the other C<__isl_take> arguments
530 C<__isl_keep> means that the function will only use the object
531 temporarily. After the function has finished, the user
532 can still use it as an argument to other functions.
533 A C<NULL> value will be treated in the same way as
534 a C<NULL> value for an C<__isl_take> argument.
538 =head2 Error Handling
540 C<isl> supports different ways to react in case a runtime error is triggered.
541 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
542 with two maps that have incompatible spaces. There are three possible ways
543 to react on error: to warn, to continue or to abort.
545 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
546 the last error in the corresponding C<isl_ctx> and the function in which the
547 error was triggered returns C<NULL>. An error does not corrupt internal state,
548 such that isl can continue to be used. C<isl> also provides functions to
549 read the last error and to reset the memory that stores the last error. The
550 last error is only stored for information purposes. Its presence does not
551 change the behavior of C<isl>. Hence, resetting an error is not required to
552 continue to use isl, but only to observe new errors.
555 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
556 void isl_ctx_reset_error(isl_ctx *ctx);
558 Another option is to continue on error. This is similar to warn on error mode,
559 except that C<isl> does not print any warning. This allows a program to
560 implement its own error reporting.
562 The last option is to directly abort the execution of the program from within
563 the isl library. This makes it obviously impossible to recover from an error,
564 but it allows to directly spot the error location. By aborting on error,
565 debuggers break at the location the error occurred and can provide a stack
566 trace. Other tools that automatically provide stack traces on abort or that do
567 not want to continue execution after an error was triggered may also prefer to
570 The on error behavior of isl can be specified by calling
571 C<isl_options_set_on_error> or by setting the command line option
572 C<--isl-on-error>. Valid arguments for the function call are
573 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
574 choices for the command line option are C<warn>, C<continue> and C<abort>.
575 It is also possible to query the current error mode.
577 #include <isl/options.h>
578 int isl_options_set_on_error(isl_ctx *ctx, int val);
579 int isl_options_get_on_error(isl_ctx *ctx);
583 Identifiers are used to identify both individual dimensions
584 and tuples of dimensions. They consist of a name and an optional
585 pointer. Identifiers with the same name but different pointer values
586 are considered to be distinct.
587 Identifiers can be constructed, copied, freed, inspected and printed
588 using the following functions.
591 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
592 __isl_keep const char *name, void *user);
593 __isl_give isl_id *isl_id_copy(isl_id *id);
594 void *isl_id_free(__isl_take isl_id *id);
596 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
597 void *isl_id_get_user(__isl_keep isl_id *id);
598 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
600 __isl_give isl_printer *isl_printer_print_id(
601 __isl_take isl_printer *p, __isl_keep isl_id *id);
603 Note that C<isl_id_get_name> returns a pointer to some internal
604 data structure, so the result can only be used while the
605 corresponding C<isl_id> is alive.
609 Whenever a new set, relation or similiar object is created from scratch,
610 the space in which it lives needs to be specified using an C<isl_space>.
611 Each space involves zero or more parameters and zero, one or two
612 tuples of set or input/output dimensions. The parameters and dimensions
613 are identified by an C<isl_dim_type> and a position.
614 The type C<isl_dim_param> refers to parameters,
615 the type C<isl_dim_set> refers to set dimensions (for spaces
616 with a single tuple of dimensions) and the types C<isl_dim_in>
617 and C<isl_dim_out> refer to input and output dimensions
618 (for spaces with two tuples of dimensions).
619 Local spaces (see L</"Local Spaces">) also contain dimensions
620 of type C<isl_dim_div>.
621 Note that parameters are only identified by their position within
622 a given object. Across different objects, parameters are (usually)
623 identified by their names or identifiers. Only unnamed parameters
624 are identified by their positions across objects. The use of unnamed
625 parameters is discouraged.
627 #include <isl/space.h>
628 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
629 unsigned nparam, unsigned n_in, unsigned n_out);
630 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
632 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
633 unsigned nparam, unsigned dim);
634 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
635 void *isl_space_free(__isl_take isl_space *space);
636 unsigned isl_space_dim(__isl_keep isl_space *space,
637 enum isl_dim_type type);
639 The space used for creating a parameter domain
640 needs to be created using C<isl_space_params_alloc>.
641 For other sets, the space
642 needs to be created using C<isl_space_set_alloc>, while
643 for a relation, the space
644 needs to be created using C<isl_space_alloc>.
645 C<isl_space_dim> can be used
646 to find out the number of dimensions of each type in
647 a space, where type may be
648 C<isl_dim_param>, C<isl_dim_in> (only for relations),
649 C<isl_dim_out> (only for relations), C<isl_dim_set>
650 (only for sets) or C<isl_dim_all>.
652 To check whether a given space is that of a set or a map
653 or whether it is a parameter space, use these functions:
655 #include <isl/space.h>
656 int isl_space_is_params(__isl_keep isl_space *space);
657 int isl_space_is_set(__isl_keep isl_space *space);
658 int isl_space_is_map(__isl_keep isl_space *space);
660 Spaces can be compared using the following functions:
662 #include <isl/space.h>
663 int isl_space_is_equal(__isl_keep isl_space *space1,
664 __isl_keep isl_space *space2);
665 int isl_space_is_domain(__isl_keep isl_space *space1,
666 __isl_keep isl_space *space2);
667 int isl_space_is_range(__isl_keep isl_space *space1,
668 __isl_keep isl_space *space2);
670 C<isl_space_is_domain> checks whether the first argument is equal
671 to the domain of the second argument. This requires in particular that
672 the first argument is a set space and that the second argument
675 It is often useful to create objects that live in the
676 same space as some other object. This can be accomplished
677 by creating the new objects
678 (see L<Creating New Sets and Relations> or
679 L<Creating New (Piecewise) Quasipolynomials>) based on the space
680 of the original object.
683 __isl_give isl_space *isl_basic_set_get_space(
684 __isl_keep isl_basic_set *bset);
685 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
687 #include <isl/union_set.h>
688 __isl_give isl_space *isl_union_set_get_space(
689 __isl_keep isl_union_set *uset);
692 __isl_give isl_space *isl_basic_map_get_space(
693 __isl_keep isl_basic_map *bmap);
694 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
696 #include <isl/union_map.h>
697 __isl_give isl_space *isl_union_map_get_space(
698 __isl_keep isl_union_map *umap);
700 #include <isl/constraint.h>
701 __isl_give isl_space *isl_constraint_get_space(
702 __isl_keep isl_constraint *constraint);
704 #include <isl/polynomial.h>
705 __isl_give isl_space *isl_qpolynomial_get_domain_space(
706 __isl_keep isl_qpolynomial *qp);
707 __isl_give isl_space *isl_qpolynomial_get_space(
708 __isl_keep isl_qpolynomial *qp);
709 __isl_give isl_space *isl_qpolynomial_fold_get_space(
710 __isl_keep isl_qpolynomial_fold *fold);
711 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
712 __isl_keep isl_pw_qpolynomial *pwqp);
713 __isl_give isl_space *isl_pw_qpolynomial_get_space(
714 __isl_keep isl_pw_qpolynomial *pwqp);
715 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
716 __isl_keep isl_pw_qpolynomial_fold *pwf);
717 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
718 __isl_keep isl_pw_qpolynomial_fold *pwf);
719 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
720 __isl_keep isl_union_pw_qpolynomial *upwqp);
721 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
722 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
725 __isl_give isl_space *isl_aff_get_domain_space(
726 __isl_keep isl_aff *aff);
727 __isl_give isl_space *isl_aff_get_space(
728 __isl_keep isl_aff *aff);
729 __isl_give isl_space *isl_pw_aff_get_domain_space(
730 __isl_keep isl_pw_aff *pwaff);
731 __isl_give isl_space *isl_pw_aff_get_space(
732 __isl_keep isl_pw_aff *pwaff);
733 __isl_give isl_space *isl_multi_aff_get_domain_space(
734 __isl_keep isl_multi_aff *maff);
735 __isl_give isl_space *isl_multi_aff_get_space(
736 __isl_keep isl_multi_aff *maff);
737 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
738 __isl_keep isl_pw_multi_aff *pma);
739 __isl_give isl_space *isl_pw_multi_aff_get_space(
740 __isl_keep isl_pw_multi_aff *pma);
741 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
742 __isl_keep isl_union_pw_multi_aff *upma);
744 #include <isl/point.h>
745 __isl_give isl_space *isl_point_get_space(
746 __isl_keep isl_point *pnt);
748 The identifiers or names of the individual dimensions may be set or read off
749 using the following functions.
751 #include <isl/space.h>
752 __isl_give isl_space *isl_space_set_dim_id(
753 __isl_take isl_space *space,
754 enum isl_dim_type type, unsigned pos,
755 __isl_take isl_id *id);
756 int isl_space_has_dim_id(__isl_keep isl_space *space,
757 enum isl_dim_type type, unsigned pos);
758 __isl_give isl_id *isl_space_get_dim_id(
759 __isl_keep isl_space *space,
760 enum isl_dim_type type, unsigned pos);
761 __isl_give isl_space *isl_space_set_dim_name(
762 __isl_take isl_space *space,
763 enum isl_dim_type type, unsigned pos,
764 __isl_keep const char *name);
765 int isl_space_has_dim_name(__isl_keep isl_space *space,
766 enum isl_dim_type type, unsigned pos);
767 __isl_keep const char *isl_space_get_dim_name(
768 __isl_keep isl_space *space,
769 enum isl_dim_type type, unsigned pos);
771 Note that C<isl_space_get_name> returns a pointer to some internal
772 data structure, so the result can only be used while the
773 corresponding C<isl_space> is alive.
774 Also note that every function that operates on two sets or relations
775 requires that both arguments have the same parameters. This also
776 means that if one of the arguments has named parameters, then the
777 other needs to have named parameters too and the names need to match.
778 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
779 arguments may have different parameters (as long as they are named),
780 in which case the result will have as parameters the union of the parameters of
783 Given the identifier or name of a dimension (typically a parameter),
784 its position can be obtained from the following function.
786 #include <isl/space.h>
787 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
788 enum isl_dim_type type, __isl_keep isl_id *id);
789 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
790 enum isl_dim_type type, const char *name);
792 The identifiers or names of entire spaces may be set or read off
793 using the following functions.
795 #include <isl/space.h>
796 __isl_give isl_space *isl_space_set_tuple_id(
797 __isl_take isl_space *space,
798 enum isl_dim_type type, __isl_take isl_id *id);
799 __isl_give isl_space *isl_space_reset_tuple_id(
800 __isl_take isl_space *space, enum isl_dim_type type);
801 int isl_space_has_tuple_id(__isl_keep isl_space *space,
802 enum isl_dim_type type);
803 __isl_give isl_id *isl_space_get_tuple_id(
804 __isl_keep isl_space *space, enum isl_dim_type type);
805 __isl_give isl_space *isl_space_set_tuple_name(
806 __isl_take isl_space *space,
807 enum isl_dim_type type, const char *s);
808 int isl_space_has_tuple_name(__isl_keep isl_space *space,
809 enum isl_dim_type type);
810 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
811 enum isl_dim_type type);
813 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
814 or C<isl_dim_set>. As with C<isl_space_get_name>,
815 the C<isl_space_get_tuple_name> function returns a pointer to some internal
817 Binary operations require the corresponding spaces of their arguments
818 to have the same name.
820 Spaces can be nested. In particular, the domain of a set or
821 the domain or range of a relation can be a nested relation.
822 The following functions can be used to construct and deconstruct
825 #include <isl/space.h>
826 int isl_space_is_wrapping(__isl_keep isl_space *space);
827 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
828 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
830 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
831 be the space of a set, while that of
832 C<isl_space_wrap> should be the space of a relation.
833 Conversely, the output of C<isl_space_unwrap> is the space
834 of a relation, while that of C<isl_space_wrap> is the space of a set.
836 Spaces can be created from other spaces
837 using the following functions.
839 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
840 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
841 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
842 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
843 __isl_give isl_space *isl_space_params(
844 __isl_take isl_space *space);
845 __isl_give isl_space *isl_space_set_from_params(
846 __isl_take isl_space *space);
847 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
848 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
849 __isl_take isl_space *right);
850 __isl_give isl_space *isl_space_align_params(
851 __isl_take isl_space *space1, __isl_take isl_space *space2)
852 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
853 enum isl_dim_type type, unsigned pos, unsigned n);
854 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
855 enum isl_dim_type type, unsigned n);
856 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
857 enum isl_dim_type type, unsigned first, unsigned n);
858 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
859 enum isl_dim_type dst_type, unsigned dst_pos,
860 enum isl_dim_type src_type, unsigned src_pos,
862 __isl_give isl_space *isl_space_map_from_set(
863 __isl_take isl_space *space);
864 __isl_give isl_space *isl_space_map_from_domain_and_range(
865 __isl_take isl_space *domain,
866 __isl_take isl_space *range);
867 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
868 __isl_give isl_space *isl_space_curry(
869 __isl_take isl_space *space);
870 __isl_give isl_space *isl_space_uncurry(
871 __isl_take isl_space *space);
873 Note that if dimensions are added or removed from a space, then
874 the name and the internal structure are lost.
878 A local space is essentially a space with
879 zero or more existentially quantified variables.
880 The local space of a (constraint of a) basic set or relation can be obtained
881 using the following functions.
883 #include <isl/constraint.h>
884 __isl_give isl_local_space *isl_constraint_get_local_space(
885 __isl_keep isl_constraint *constraint);
888 __isl_give isl_local_space *isl_basic_set_get_local_space(
889 __isl_keep isl_basic_set *bset);
892 __isl_give isl_local_space *isl_basic_map_get_local_space(
893 __isl_keep isl_basic_map *bmap);
895 A new local space can be created from a space using
897 #include <isl/local_space.h>
898 __isl_give isl_local_space *isl_local_space_from_space(
899 __isl_take isl_space *space);
901 They can be inspected, modified, copied and freed using the following functions.
903 #include <isl/local_space.h>
904 isl_ctx *isl_local_space_get_ctx(
905 __isl_keep isl_local_space *ls);
906 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
907 int isl_local_space_dim(__isl_keep isl_local_space *ls,
908 enum isl_dim_type type);
909 int isl_local_space_has_dim_id(
910 __isl_keep isl_local_space *ls,
911 enum isl_dim_type type, unsigned pos);
912 __isl_give isl_id *isl_local_space_get_dim_id(
913 __isl_keep isl_local_space *ls,
914 enum isl_dim_type type, unsigned pos);
915 int isl_local_space_has_dim_name(
916 __isl_keep isl_local_space *ls,
917 enum isl_dim_type type, unsigned pos)
918 const char *isl_local_space_get_dim_name(
919 __isl_keep isl_local_space *ls,
920 enum isl_dim_type type, unsigned pos);
921 __isl_give isl_local_space *isl_local_space_set_dim_name(
922 __isl_take isl_local_space *ls,
923 enum isl_dim_type type, unsigned pos, const char *s);
924 __isl_give isl_local_space *isl_local_space_set_dim_id(
925 __isl_take isl_local_space *ls,
926 enum isl_dim_type type, unsigned pos,
927 __isl_take isl_id *id);
928 __isl_give isl_space *isl_local_space_get_space(
929 __isl_keep isl_local_space *ls);
930 __isl_give isl_aff *isl_local_space_get_div(
931 __isl_keep isl_local_space *ls, int pos);
932 __isl_give isl_local_space *isl_local_space_copy(
933 __isl_keep isl_local_space *ls);
934 void *isl_local_space_free(__isl_take isl_local_space *ls);
936 Two local spaces can be compared using
938 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
939 __isl_keep isl_local_space *ls2);
941 Local spaces can be created from other local spaces
942 using the following functions.
944 __isl_give isl_local_space *isl_local_space_domain(
945 __isl_take isl_local_space *ls);
946 __isl_give isl_local_space *isl_local_space_range(
947 __isl_take isl_local_space *ls);
948 __isl_give isl_local_space *isl_local_space_from_domain(
949 __isl_take isl_local_space *ls);
950 __isl_give isl_local_space *isl_local_space_intersect(
951 __isl_take isl_local_space *ls1,
952 __isl_take isl_local_space *ls2);
953 __isl_give isl_local_space *isl_local_space_add_dims(
954 __isl_take isl_local_space *ls,
955 enum isl_dim_type type, unsigned n);
956 __isl_give isl_local_space *isl_local_space_insert_dims(
957 __isl_take isl_local_space *ls,
958 enum isl_dim_type type, unsigned first, unsigned n);
959 __isl_give isl_local_space *isl_local_space_drop_dims(
960 __isl_take isl_local_space *ls,
961 enum isl_dim_type type, unsigned first, unsigned n);
963 =head2 Input and Output
965 C<isl> supports its own input/output format, which is similar
966 to the C<Omega> format, but also supports the C<PolyLib> format
971 The C<isl> format is similar to that of C<Omega>, but has a different
972 syntax for describing the parameters and allows for the definition
973 of an existentially quantified variable as the integer division
974 of an affine expression.
975 For example, the set of integers C<i> between C<0> and C<n>
976 such that C<i % 10 <= 6> can be described as
978 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
981 A set or relation can have several disjuncts, separated
982 by the keyword C<or>. Each disjunct is either a conjunction
983 of constraints or a projection (C<exists>) of a conjunction
984 of constraints. The constraints are separated by the keyword
987 =head3 C<PolyLib> format
989 If the represented set is a union, then the first line
990 contains a single number representing the number of disjuncts.
991 Otherwise, a line containing the number C<1> is optional.
993 Each disjunct is represented by a matrix of constraints.
994 The first line contains two numbers representing
995 the number of rows and columns,
996 where the number of rows is equal to the number of constraints
997 and the number of columns is equal to two plus the number of variables.
998 The following lines contain the actual rows of the constraint matrix.
999 In each row, the first column indicates whether the constraint
1000 is an equality (C<0>) or inequality (C<1>). The final column
1001 corresponds to the constant term.
1003 If the set is parametric, then the coefficients of the parameters
1004 appear in the last columns before the constant column.
1005 The coefficients of any existentially quantified variables appear
1006 between those of the set variables and those of the parameters.
1008 =head3 Extended C<PolyLib> format
1010 The extended C<PolyLib> format is nearly identical to the
1011 C<PolyLib> format. The only difference is that the line
1012 containing the number of rows and columns of a constraint matrix
1013 also contains four additional numbers:
1014 the number of output dimensions, the number of input dimensions,
1015 the number of local dimensions (i.e., the number of existentially
1016 quantified variables) and the number of parameters.
1017 For sets, the number of ``output'' dimensions is equal
1018 to the number of set dimensions, while the number of ``input''
1023 #include <isl/set.h>
1024 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1025 isl_ctx *ctx, FILE *input);
1026 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1027 isl_ctx *ctx, const char *str);
1028 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1030 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1033 #include <isl/map.h>
1034 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1035 isl_ctx *ctx, FILE *input);
1036 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1037 isl_ctx *ctx, const char *str);
1038 __isl_give isl_map *isl_map_read_from_file(
1039 isl_ctx *ctx, FILE *input);
1040 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1043 #include <isl/union_set.h>
1044 __isl_give isl_union_set *isl_union_set_read_from_file(
1045 isl_ctx *ctx, FILE *input);
1046 __isl_give isl_union_set *isl_union_set_read_from_str(
1047 isl_ctx *ctx, const char *str);
1049 #include <isl/union_map.h>
1050 __isl_give isl_union_map *isl_union_map_read_from_file(
1051 isl_ctx *ctx, FILE *input);
1052 __isl_give isl_union_map *isl_union_map_read_from_str(
1053 isl_ctx *ctx, const char *str);
1055 The input format is autodetected and may be either the C<PolyLib> format
1056 or the C<isl> format.
1060 Before anything can be printed, an C<isl_printer> needs to
1063 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1065 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1066 void *isl_printer_free(__isl_take isl_printer *printer);
1067 __isl_give char *isl_printer_get_str(
1068 __isl_keep isl_printer *printer);
1070 The printer can be inspected using the following functions.
1072 FILE *isl_printer_get_file(
1073 __isl_keep isl_printer *printer);
1074 int isl_printer_get_output_format(
1075 __isl_keep isl_printer *p);
1077 The behavior of the printer can be modified in various ways
1079 __isl_give isl_printer *isl_printer_set_output_format(
1080 __isl_take isl_printer *p, int output_format);
1081 __isl_give isl_printer *isl_printer_set_indent(
1082 __isl_take isl_printer *p, int indent);
1083 __isl_give isl_printer *isl_printer_indent(
1084 __isl_take isl_printer *p, int indent);
1085 __isl_give isl_printer *isl_printer_set_prefix(
1086 __isl_take isl_printer *p, const char *prefix);
1087 __isl_give isl_printer *isl_printer_set_suffix(
1088 __isl_take isl_printer *p, const char *suffix);
1090 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1091 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1092 and defaults to C<ISL_FORMAT_ISL>.
1093 Each line in the output is indented by C<indent> (set by
1094 C<isl_printer_set_indent>) spaces
1095 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1096 In the C<PolyLib> format output,
1097 the coefficients of the existentially quantified variables
1098 appear between those of the set variables and those
1100 The function C<isl_printer_indent> increases the indentation
1101 by the specified amount (which may be negative).
1103 To actually print something, use
1105 #include <isl/printer.h>
1106 __isl_give isl_printer *isl_printer_print_double(
1107 __isl_take isl_printer *p, double d);
1109 #include <isl/set.h>
1110 __isl_give isl_printer *isl_printer_print_basic_set(
1111 __isl_take isl_printer *printer,
1112 __isl_keep isl_basic_set *bset);
1113 __isl_give isl_printer *isl_printer_print_set(
1114 __isl_take isl_printer *printer,
1115 __isl_keep isl_set *set);
1117 #include <isl/map.h>
1118 __isl_give isl_printer *isl_printer_print_basic_map(
1119 __isl_take isl_printer *printer,
1120 __isl_keep isl_basic_map *bmap);
1121 __isl_give isl_printer *isl_printer_print_map(
1122 __isl_take isl_printer *printer,
1123 __isl_keep isl_map *map);
1125 #include <isl/union_set.h>
1126 __isl_give isl_printer *isl_printer_print_union_set(
1127 __isl_take isl_printer *p,
1128 __isl_keep isl_union_set *uset);
1130 #include <isl/union_map.h>
1131 __isl_give isl_printer *isl_printer_print_union_map(
1132 __isl_take isl_printer *p,
1133 __isl_keep isl_union_map *umap);
1135 When called on a file printer, the following function flushes
1136 the file. When called on a string printer, the buffer is cleared.
1138 __isl_give isl_printer *isl_printer_flush(
1139 __isl_take isl_printer *p);
1141 =head2 Creating New Sets and Relations
1143 C<isl> has functions for creating some standard sets and relations.
1147 =item * Empty sets and relations
1149 __isl_give isl_basic_set *isl_basic_set_empty(
1150 __isl_take isl_space *space);
1151 __isl_give isl_basic_map *isl_basic_map_empty(
1152 __isl_take isl_space *space);
1153 __isl_give isl_set *isl_set_empty(
1154 __isl_take isl_space *space);
1155 __isl_give isl_map *isl_map_empty(
1156 __isl_take isl_space *space);
1157 __isl_give isl_union_set *isl_union_set_empty(
1158 __isl_take isl_space *space);
1159 __isl_give isl_union_map *isl_union_map_empty(
1160 __isl_take isl_space *space);
1162 For C<isl_union_set>s and C<isl_union_map>s, the space
1163 is only used to specify the parameters.
1165 =item * Universe sets and relations
1167 __isl_give isl_basic_set *isl_basic_set_universe(
1168 __isl_take isl_space *space);
1169 __isl_give isl_basic_map *isl_basic_map_universe(
1170 __isl_take isl_space *space);
1171 __isl_give isl_set *isl_set_universe(
1172 __isl_take isl_space *space);
1173 __isl_give isl_map *isl_map_universe(
1174 __isl_take isl_space *space);
1175 __isl_give isl_union_set *isl_union_set_universe(
1176 __isl_take isl_union_set *uset);
1177 __isl_give isl_union_map *isl_union_map_universe(
1178 __isl_take isl_union_map *umap);
1180 The sets and relations constructed by the functions above
1181 contain all integer values, while those constructed by the
1182 functions below only contain non-negative values.
1184 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1185 __isl_take isl_space *space);
1186 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1187 __isl_take isl_space *space);
1188 __isl_give isl_set *isl_set_nat_universe(
1189 __isl_take isl_space *space);
1190 __isl_give isl_map *isl_map_nat_universe(
1191 __isl_take isl_space *space);
1193 =item * Identity relations
1195 __isl_give isl_basic_map *isl_basic_map_identity(
1196 __isl_take isl_space *space);
1197 __isl_give isl_map *isl_map_identity(
1198 __isl_take isl_space *space);
1200 The number of input and output dimensions in C<space> needs
1203 =item * Lexicographic order
1205 __isl_give isl_map *isl_map_lex_lt(
1206 __isl_take isl_space *set_space);
1207 __isl_give isl_map *isl_map_lex_le(
1208 __isl_take isl_space *set_space);
1209 __isl_give isl_map *isl_map_lex_gt(
1210 __isl_take isl_space *set_space);
1211 __isl_give isl_map *isl_map_lex_ge(
1212 __isl_take isl_space *set_space);
1213 __isl_give isl_map *isl_map_lex_lt_first(
1214 __isl_take isl_space *space, unsigned n);
1215 __isl_give isl_map *isl_map_lex_le_first(
1216 __isl_take isl_space *space, unsigned n);
1217 __isl_give isl_map *isl_map_lex_gt_first(
1218 __isl_take isl_space *space, unsigned n);
1219 __isl_give isl_map *isl_map_lex_ge_first(
1220 __isl_take isl_space *space, unsigned n);
1222 The first four functions take a space for a B<set>
1223 and return relations that express that the elements in the domain
1224 are lexicographically less
1225 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1226 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1227 than the elements in the range.
1228 The last four functions take a space for a map
1229 and return relations that express that the first C<n> dimensions
1230 in the domain are lexicographically less
1231 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1232 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1233 than the first C<n> dimensions in the range.
1237 A basic set or relation can be converted to a set or relation
1238 using the following functions.
1240 __isl_give isl_set *isl_set_from_basic_set(
1241 __isl_take isl_basic_set *bset);
1242 __isl_give isl_map *isl_map_from_basic_map(
1243 __isl_take isl_basic_map *bmap);
1245 Sets and relations can be converted to union sets and relations
1246 using the following functions.
1248 __isl_give isl_union_set *isl_union_set_from_basic_set(
1249 __isl_take isl_basic_set *bset);
1250 __isl_give isl_union_map *isl_union_map_from_basic_map(
1251 __isl_take isl_basic_map *bmap);
1252 __isl_give isl_union_set *isl_union_set_from_set(
1253 __isl_take isl_set *set);
1254 __isl_give isl_union_map *isl_union_map_from_map(
1255 __isl_take isl_map *map);
1257 The inverse conversions below can only be used if the input
1258 union set or relation is known to contain elements in exactly one
1261 __isl_give isl_set *isl_set_from_union_set(
1262 __isl_take isl_union_set *uset);
1263 __isl_give isl_map *isl_map_from_union_map(
1264 __isl_take isl_union_map *umap);
1266 A zero-dimensional set can be constructed on a given parameter domain
1267 using the following function.
1269 __isl_give isl_set *isl_set_from_params(
1270 __isl_take isl_set *set);
1272 Sets and relations can be copied and freed again using the following
1275 __isl_give isl_basic_set *isl_basic_set_copy(
1276 __isl_keep isl_basic_set *bset);
1277 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1278 __isl_give isl_union_set *isl_union_set_copy(
1279 __isl_keep isl_union_set *uset);
1280 __isl_give isl_basic_map *isl_basic_map_copy(
1281 __isl_keep isl_basic_map *bmap);
1282 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1283 __isl_give isl_union_map *isl_union_map_copy(
1284 __isl_keep isl_union_map *umap);
1285 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1286 void *isl_set_free(__isl_take isl_set *set);
1287 void *isl_union_set_free(__isl_take isl_union_set *uset);
1288 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1289 void *isl_map_free(__isl_take isl_map *map);
1290 void *isl_union_map_free(__isl_take isl_union_map *umap);
1292 Other sets and relations can be constructed by starting
1293 from a universe set or relation, adding equality and/or
1294 inequality constraints and then projecting out the
1295 existentially quantified variables, if any.
1296 Constraints can be constructed, manipulated and
1297 added to (or removed from) (basic) sets and relations
1298 using the following functions.
1300 #include <isl/constraint.h>
1301 __isl_give isl_constraint *isl_equality_alloc(
1302 __isl_take isl_local_space *ls);
1303 __isl_give isl_constraint *isl_inequality_alloc(
1304 __isl_take isl_local_space *ls);
1305 __isl_give isl_constraint *isl_constraint_set_constant(
1306 __isl_take isl_constraint *constraint, isl_int v);
1307 __isl_give isl_constraint *isl_constraint_set_constant_si(
1308 __isl_take isl_constraint *constraint, int v);
1309 __isl_give isl_constraint *isl_constraint_set_coefficient(
1310 __isl_take isl_constraint *constraint,
1311 enum isl_dim_type type, int pos, isl_int v);
1312 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1313 __isl_take isl_constraint *constraint,
1314 enum isl_dim_type type, int pos, int v);
1315 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1316 __isl_take isl_basic_map *bmap,
1317 __isl_take isl_constraint *constraint);
1318 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1319 __isl_take isl_basic_set *bset,
1320 __isl_take isl_constraint *constraint);
1321 __isl_give isl_map *isl_map_add_constraint(
1322 __isl_take isl_map *map,
1323 __isl_take isl_constraint *constraint);
1324 __isl_give isl_set *isl_set_add_constraint(
1325 __isl_take isl_set *set,
1326 __isl_take isl_constraint *constraint);
1327 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1328 __isl_take isl_basic_set *bset,
1329 __isl_take isl_constraint *constraint);
1331 For example, to create a set containing the even integers
1332 between 10 and 42, you would use the following code.
1335 isl_local_space *ls;
1337 isl_basic_set *bset;
1339 space = isl_space_set_alloc(ctx, 0, 2);
1340 bset = isl_basic_set_universe(isl_space_copy(space));
1341 ls = isl_local_space_from_space(space);
1343 c = isl_equality_alloc(isl_local_space_copy(ls));
1344 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1345 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1346 bset = isl_basic_set_add_constraint(bset, c);
1348 c = isl_inequality_alloc(isl_local_space_copy(ls));
1349 c = isl_constraint_set_constant_si(c, -10);
1350 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1351 bset = isl_basic_set_add_constraint(bset, c);
1353 c = isl_inequality_alloc(ls);
1354 c = isl_constraint_set_constant_si(c, 42);
1355 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1356 bset = isl_basic_set_add_constraint(bset, c);
1358 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1362 isl_basic_set *bset;
1363 bset = isl_basic_set_read_from_str(ctx,
1364 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1366 A basic set or relation can also be constructed from two matrices
1367 describing the equalities and the inequalities.
1369 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1370 __isl_take isl_space *space,
1371 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1372 enum isl_dim_type c1,
1373 enum isl_dim_type c2, enum isl_dim_type c3,
1374 enum isl_dim_type c4);
1375 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1376 __isl_take isl_space *space,
1377 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1378 enum isl_dim_type c1,
1379 enum isl_dim_type c2, enum isl_dim_type c3,
1380 enum isl_dim_type c4, enum isl_dim_type c5);
1382 The C<isl_dim_type> arguments indicate the order in which
1383 different kinds of variables appear in the input matrices
1384 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1385 C<isl_dim_set> and C<isl_dim_div> for sets and
1386 of C<isl_dim_cst>, C<isl_dim_param>,
1387 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1389 A (basic or union) set or relation can also be constructed from a
1390 (union) (piecewise) (multiple) affine expression
1391 or a list of affine expressions
1392 (See L<"Piecewise Quasi Affine Expressions"> and
1393 L<"Piecewise Multiple Quasi Affine Expressions">).
1395 __isl_give isl_basic_map *isl_basic_map_from_aff(
1396 __isl_take isl_aff *aff);
1397 __isl_give isl_map *isl_map_from_aff(
1398 __isl_take isl_aff *aff);
1399 __isl_give isl_set *isl_set_from_pw_aff(
1400 __isl_take isl_pw_aff *pwaff);
1401 __isl_give isl_map *isl_map_from_pw_aff(
1402 __isl_take isl_pw_aff *pwaff);
1403 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1404 __isl_take isl_space *domain_space,
1405 __isl_take isl_aff_list *list);
1406 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1407 __isl_take isl_multi_aff *maff)
1408 __isl_give isl_map *isl_map_from_multi_aff(
1409 __isl_take isl_multi_aff *maff)
1410 __isl_give isl_set *isl_set_from_pw_multi_aff(
1411 __isl_take isl_pw_multi_aff *pma);
1412 __isl_give isl_map *isl_map_from_pw_multi_aff(
1413 __isl_take isl_pw_multi_aff *pma);
1414 __isl_give isl_union_map *
1415 isl_union_map_from_union_pw_multi_aff(
1416 __isl_take isl_union_pw_multi_aff *upma);
1418 The C<domain_dim> argument describes the domain of the resulting
1419 basic relation. It is required because the C<list> may consist
1420 of zero affine expressions.
1422 =head2 Inspecting Sets and Relations
1424 Usually, the user should not have to care about the actual constraints
1425 of the sets and maps, but should instead apply the abstract operations
1426 explained in the following sections.
1427 Occasionally, however, it may be required to inspect the individual
1428 coefficients of the constraints. This section explains how to do so.
1429 In these cases, it may also be useful to have C<isl> compute
1430 an explicit representation of the existentially quantified variables.
1432 __isl_give isl_set *isl_set_compute_divs(
1433 __isl_take isl_set *set);
1434 __isl_give isl_map *isl_map_compute_divs(
1435 __isl_take isl_map *map);
1436 __isl_give isl_union_set *isl_union_set_compute_divs(
1437 __isl_take isl_union_set *uset);
1438 __isl_give isl_union_map *isl_union_map_compute_divs(
1439 __isl_take isl_union_map *umap);
1441 This explicit representation defines the existentially quantified
1442 variables as integer divisions of the other variables, possibly
1443 including earlier existentially quantified variables.
1444 An explicitly represented existentially quantified variable therefore
1445 has a unique value when the values of the other variables are known.
1446 If, furthermore, the same existentials, i.e., existentials
1447 with the same explicit representations, should appear in the
1448 same order in each of the disjuncts of a set or map, then the user should call
1449 either of the following functions.
1451 __isl_give isl_set *isl_set_align_divs(
1452 __isl_take isl_set *set);
1453 __isl_give isl_map *isl_map_align_divs(
1454 __isl_take isl_map *map);
1456 Alternatively, the existentially quantified variables can be removed
1457 using the following functions, which compute an overapproximation.
1459 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1460 __isl_take isl_basic_set *bset);
1461 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1462 __isl_take isl_basic_map *bmap);
1463 __isl_give isl_set *isl_set_remove_divs(
1464 __isl_take isl_set *set);
1465 __isl_give isl_map *isl_map_remove_divs(
1466 __isl_take isl_map *map);
1468 It is also possible to only remove those divs that are defined
1469 in terms of a given range of dimensions or only those for which
1470 no explicit representation is known.
1472 __isl_give isl_basic_set *
1473 isl_basic_set_remove_divs_involving_dims(
1474 __isl_take isl_basic_set *bset,
1475 enum isl_dim_type type,
1476 unsigned first, unsigned n);
1477 __isl_give isl_basic_map *
1478 isl_basic_map_remove_divs_involving_dims(
1479 __isl_take isl_basic_map *bmap,
1480 enum isl_dim_type type,
1481 unsigned first, unsigned n);
1482 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1483 __isl_take isl_set *set, enum isl_dim_type type,
1484 unsigned first, unsigned n);
1485 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1486 __isl_take isl_map *map, enum isl_dim_type type,
1487 unsigned first, unsigned n);
1489 __isl_give isl_basic_set *
1490 isl_basic_set_remove_unknown_divs(
1491 __isl_take isl_basic_set *bset);
1492 __isl_give isl_set *isl_set_remove_unknown_divs(
1493 __isl_take isl_set *set);
1494 __isl_give isl_map *isl_map_remove_unknown_divs(
1495 __isl_take isl_map *map);
1497 To iterate over all the sets or maps in a union set or map, use
1499 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1500 int (*fn)(__isl_take isl_set *set, void *user),
1502 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1503 int (*fn)(__isl_take isl_map *map, void *user),
1506 The number of sets or maps in a union set or map can be obtained
1509 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1510 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1512 To extract the set or map in a given space from a union, use
1514 __isl_give isl_set *isl_union_set_extract_set(
1515 __isl_keep isl_union_set *uset,
1516 __isl_take isl_space *space);
1517 __isl_give isl_map *isl_union_map_extract_map(
1518 __isl_keep isl_union_map *umap,
1519 __isl_take isl_space *space);
1521 To iterate over all the basic sets or maps in a set or map, use
1523 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1524 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1526 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1527 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1530 The callback function C<fn> should return 0 if successful and
1531 -1 if an error occurs. In the latter case, or if any other error
1532 occurs, the above functions will return -1.
1534 It should be noted that C<isl> does not guarantee that
1535 the basic sets or maps passed to C<fn> are disjoint.
1536 If this is required, then the user should call one of
1537 the following functions first.
1539 __isl_give isl_set *isl_set_make_disjoint(
1540 __isl_take isl_set *set);
1541 __isl_give isl_map *isl_map_make_disjoint(
1542 __isl_take isl_map *map);
1544 The number of basic sets in a set can be obtained
1547 int isl_set_n_basic_set(__isl_keep isl_set *set);
1549 To iterate over the constraints of a basic set or map, use
1551 #include <isl/constraint.h>
1553 int isl_basic_set_n_constraint(
1554 __isl_keep isl_basic_set *bset);
1555 int isl_basic_set_foreach_constraint(
1556 __isl_keep isl_basic_set *bset,
1557 int (*fn)(__isl_take isl_constraint *c, void *user),
1559 int isl_basic_map_foreach_constraint(
1560 __isl_keep isl_basic_map *bmap,
1561 int (*fn)(__isl_take isl_constraint *c, void *user),
1563 void *isl_constraint_free(__isl_take isl_constraint *c);
1565 Again, the callback function C<fn> should return 0 if successful and
1566 -1 if an error occurs. In the latter case, or if any other error
1567 occurs, the above functions will return -1.
1568 The constraint C<c> represents either an equality or an inequality.
1569 Use the following function to find out whether a constraint
1570 represents an equality. If not, it represents an inequality.
1572 int isl_constraint_is_equality(
1573 __isl_keep isl_constraint *constraint);
1575 The coefficients of the constraints can be inspected using
1576 the following functions.
1578 int isl_constraint_is_lower_bound(
1579 __isl_keep isl_constraint *constraint,
1580 enum isl_dim_type type, unsigned pos);
1581 int isl_constraint_is_upper_bound(
1582 __isl_keep isl_constraint *constraint,
1583 enum isl_dim_type type, unsigned pos);
1584 void isl_constraint_get_constant(
1585 __isl_keep isl_constraint *constraint, isl_int *v);
1586 void isl_constraint_get_coefficient(
1587 __isl_keep isl_constraint *constraint,
1588 enum isl_dim_type type, int pos, isl_int *v);
1589 int isl_constraint_involves_dims(
1590 __isl_keep isl_constraint *constraint,
1591 enum isl_dim_type type, unsigned first, unsigned n);
1593 The explicit representations of the existentially quantified
1594 variables can be inspected using the following function.
1595 Note that the user is only allowed to use this function
1596 if the inspected set or map is the result of a call
1597 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1598 The existentially quantified variable is equal to the floor
1599 of the returned affine expression. The affine expression
1600 itself can be inspected using the functions in
1601 L<"Piecewise Quasi Affine Expressions">.
1603 __isl_give isl_aff *isl_constraint_get_div(
1604 __isl_keep isl_constraint *constraint, int pos);
1606 To obtain the constraints of a basic set or map in matrix
1607 form, use the following functions.
1609 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1610 __isl_keep isl_basic_set *bset,
1611 enum isl_dim_type c1, enum isl_dim_type c2,
1612 enum isl_dim_type c3, enum isl_dim_type c4);
1613 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1614 __isl_keep isl_basic_set *bset,
1615 enum isl_dim_type c1, enum isl_dim_type c2,
1616 enum isl_dim_type c3, enum isl_dim_type c4);
1617 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1618 __isl_keep isl_basic_map *bmap,
1619 enum isl_dim_type c1,
1620 enum isl_dim_type c2, enum isl_dim_type c3,
1621 enum isl_dim_type c4, enum isl_dim_type c5);
1622 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1623 __isl_keep isl_basic_map *bmap,
1624 enum isl_dim_type c1,
1625 enum isl_dim_type c2, enum isl_dim_type c3,
1626 enum isl_dim_type c4, enum isl_dim_type c5);
1628 The C<isl_dim_type> arguments dictate the order in which
1629 different kinds of variables appear in the resulting matrix
1630 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1631 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1633 The number of parameters, input, output or set dimensions can
1634 be obtained using the following functions.
1636 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1637 enum isl_dim_type type);
1638 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1639 enum isl_dim_type type);
1640 unsigned isl_set_dim(__isl_keep isl_set *set,
1641 enum isl_dim_type type);
1642 unsigned isl_map_dim(__isl_keep isl_map *map,
1643 enum isl_dim_type type);
1645 To check whether the description of a set or relation depends
1646 on one or more given dimensions, it is not necessary to iterate over all
1647 constraints. Instead the following functions can be used.
1649 int isl_basic_set_involves_dims(
1650 __isl_keep isl_basic_set *bset,
1651 enum isl_dim_type type, unsigned first, unsigned n);
1652 int isl_set_involves_dims(__isl_keep isl_set *set,
1653 enum isl_dim_type type, unsigned first, unsigned n);
1654 int isl_basic_map_involves_dims(
1655 __isl_keep isl_basic_map *bmap,
1656 enum isl_dim_type type, unsigned first, unsigned n);
1657 int isl_map_involves_dims(__isl_keep isl_map *map,
1658 enum isl_dim_type type, unsigned first, unsigned n);
1660 Similarly, the following functions can be used to check whether
1661 a given dimension is involved in any lower or upper bound.
1663 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1664 enum isl_dim_type type, unsigned pos);
1665 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1666 enum isl_dim_type type, unsigned pos);
1668 The identifiers or names of the domain and range spaces of a set
1669 or relation can be read off or set using the following functions.
1671 __isl_give isl_set *isl_set_set_tuple_id(
1672 __isl_take isl_set *set, __isl_take isl_id *id);
1673 __isl_give isl_set *isl_set_reset_tuple_id(
1674 __isl_take isl_set *set);
1675 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1676 __isl_give isl_id *isl_set_get_tuple_id(
1677 __isl_keep isl_set *set);
1678 __isl_give isl_map *isl_map_set_tuple_id(
1679 __isl_take isl_map *map, enum isl_dim_type type,
1680 __isl_take isl_id *id);
1681 __isl_give isl_map *isl_map_reset_tuple_id(
1682 __isl_take isl_map *map, enum isl_dim_type type);
1683 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1684 enum isl_dim_type type);
1685 __isl_give isl_id *isl_map_get_tuple_id(
1686 __isl_keep isl_map *map, enum isl_dim_type type);
1688 const char *isl_basic_set_get_tuple_name(
1689 __isl_keep isl_basic_set *bset);
1690 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1691 __isl_take isl_basic_set *set, const char *s);
1692 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1693 const char *isl_set_get_tuple_name(
1694 __isl_keep isl_set *set);
1695 const char *isl_basic_map_get_tuple_name(
1696 __isl_keep isl_basic_map *bmap,
1697 enum isl_dim_type type);
1698 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1699 __isl_take isl_basic_map *bmap,
1700 enum isl_dim_type type, const char *s);
1701 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1702 enum isl_dim_type type);
1703 const char *isl_map_get_tuple_name(
1704 __isl_keep isl_map *map,
1705 enum isl_dim_type type);
1707 As with C<isl_space_get_tuple_name>, the value returned points to
1708 an internal data structure.
1709 The identifiers, positions or names of individual dimensions can be
1710 read off using the following functions.
1712 __isl_give isl_id *isl_basic_set_get_dim_id(
1713 __isl_keep isl_basic_set *bset,
1714 enum isl_dim_type type, unsigned pos);
1715 __isl_give isl_set *isl_set_set_dim_id(
1716 __isl_take isl_set *set, enum isl_dim_type type,
1717 unsigned pos, __isl_take isl_id *id);
1718 int isl_set_has_dim_id(__isl_keep isl_set *set,
1719 enum isl_dim_type type, unsigned pos);
1720 __isl_give isl_id *isl_set_get_dim_id(
1721 __isl_keep isl_set *set, enum isl_dim_type type,
1723 int isl_basic_map_has_dim_id(
1724 __isl_keep isl_basic_map *bmap,
1725 enum isl_dim_type type, unsigned pos);
1726 __isl_give isl_map *isl_map_set_dim_id(
1727 __isl_take isl_map *map, enum isl_dim_type type,
1728 unsigned pos, __isl_take isl_id *id);
1729 int isl_map_has_dim_id(__isl_keep isl_map *map,
1730 enum isl_dim_type type, unsigned pos);
1731 __isl_give isl_id *isl_map_get_dim_id(
1732 __isl_keep isl_map *map, enum isl_dim_type type,
1735 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1736 enum isl_dim_type type, __isl_keep isl_id *id);
1737 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1738 enum isl_dim_type type, __isl_keep isl_id *id);
1739 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1740 enum isl_dim_type type, const char *name);
1741 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1742 enum isl_dim_type type, const char *name);
1744 const char *isl_constraint_get_dim_name(
1745 __isl_keep isl_constraint *constraint,
1746 enum isl_dim_type type, unsigned pos);
1747 const char *isl_basic_set_get_dim_name(
1748 __isl_keep isl_basic_set *bset,
1749 enum isl_dim_type type, unsigned pos);
1750 int isl_set_has_dim_name(__isl_keep isl_set *set,
1751 enum isl_dim_type type, unsigned pos);
1752 const char *isl_set_get_dim_name(
1753 __isl_keep isl_set *set,
1754 enum isl_dim_type type, unsigned pos);
1755 const char *isl_basic_map_get_dim_name(
1756 __isl_keep isl_basic_map *bmap,
1757 enum isl_dim_type type, unsigned pos);
1758 int isl_map_has_dim_name(__isl_keep isl_map *map,
1759 enum isl_dim_type type, unsigned pos);
1760 const char *isl_map_get_dim_name(
1761 __isl_keep isl_map *map,
1762 enum isl_dim_type type, unsigned pos);
1764 These functions are mostly useful to obtain the identifiers, positions
1765 or names of the parameters. Identifiers of individual dimensions are
1766 essentially only useful for printing. They are ignored by all other
1767 operations and may not be preserved across those operations.
1771 =head3 Unary Properties
1777 The following functions test whether the given set or relation
1778 contains any integer points. The ``plain'' variants do not perform
1779 any computations, but simply check if the given set or relation
1780 is already known to be empty.
1782 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1783 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1784 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1785 int isl_set_is_empty(__isl_keep isl_set *set);
1786 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1787 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1788 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1789 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1790 int isl_map_is_empty(__isl_keep isl_map *map);
1791 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1793 =item * Universality
1795 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1796 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1797 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1799 =item * Single-valuedness
1801 int isl_basic_map_is_single_valued(
1802 __isl_keep isl_basic_map *bmap);
1803 int isl_map_plain_is_single_valued(
1804 __isl_keep isl_map *map);
1805 int isl_map_is_single_valued(__isl_keep isl_map *map);
1806 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1810 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1811 int isl_map_is_injective(__isl_keep isl_map *map);
1812 int isl_union_map_plain_is_injective(
1813 __isl_keep isl_union_map *umap);
1814 int isl_union_map_is_injective(
1815 __isl_keep isl_union_map *umap);
1819 int isl_map_is_bijective(__isl_keep isl_map *map);
1820 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1824 int isl_basic_map_plain_is_fixed(
1825 __isl_keep isl_basic_map *bmap,
1826 enum isl_dim_type type, unsigned pos,
1828 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1829 enum isl_dim_type type, unsigned pos,
1831 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1832 enum isl_dim_type type, unsigned pos,
1835 Check if the relation obviously lies on a hyperplane where the given dimension
1836 has a fixed value and if so, return that value in C<*val>.
1840 To check whether a set is a parameter domain, use this function:
1842 int isl_set_is_params(__isl_keep isl_set *set);
1843 int isl_union_set_is_params(
1844 __isl_keep isl_union_set *uset);
1848 The following functions check whether the domain of the given
1849 (basic) set is a wrapped relation.
1851 int isl_basic_set_is_wrapping(
1852 __isl_keep isl_basic_set *bset);
1853 int isl_set_is_wrapping(__isl_keep isl_set *set);
1855 =item * Internal Product
1857 int isl_basic_map_can_zip(
1858 __isl_keep isl_basic_map *bmap);
1859 int isl_map_can_zip(__isl_keep isl_map *map);
1861 Check whether the product of domain and range of the given relation
1863 i.e., whether both domain and range are nested relations.
1867 int isl_basic_map_can_curry(
1868 __isl_keep isl_basic_map *bmap);
1869 int isl_map_can_curry(__isl_keep isl_map *map);
1871 Check whether the domain of the (basic) relation is a wrapped relation.
1873 int isl_basic_map_can_uncurry(
1874 __isl_keep isl_basic_map *bmap);
1875 int isl_map_can_uncurry(__isl_keep isl_map *map);
1877 Check whether the range of the (basic) relation is a wrapped relation.
1881 =head3 Binary Properties
1887 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1888 __isl_keep isl_set *set2);
1889 int isl_set_is_equal(__isl_keep isl_set *set1,
1890 __isl_keep isl_set *set2);
1891 int isl_union_set_is_equal(
1892 __isl_keep isl_union_set *uset1,
1893 __isl_keep isl_union_set *uset2);
1894 int isl_basic_map_is_equal(
1895 __isl_keep isl_basic_map *bmap1,
1896 __isl_keep isl_basic_map *bmap2);
1897 int isl_map_is_equal(__isl_keep isl_map *map1,
1898 __isl_keep isl_map *map2);
1899 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1900 __isl_keep isl_map *map2);
1901 int isl_union_map_is_equal(
1902 __isl_keep isl_union_map *umap1,
1903 __isl_keep isl_union_map *umap2);
1905 =item * Disjointness
1907 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1908 __isl_keep isl_set *set2);
1909 int isl_set_is_disjoint(__isl_keep isl_set *set1,
1910 __isl_keep isl_set *set2);
1911 int isl_map_is_disjoint(__isl_keep isl_map *map1,
1912 __isl_keep isl_map *map2);
1916 int isl_basic_set_is_subset(
1917 __isl_keep isl_basic_set *bset1,
1918 __isl_keep isl_basic_set *bset2);
1919 int isl_set_is_subset(__isl_keep isl_set *set1,
1920 __isl_keep isl_set *set2);
1921 int isl_set_is_strict_subset(
1922 __isl_keep isl_set *set1,
1923 __isl_keep isl_set *set2);
1924 int isl_union_set_is_subset(
1925 __isl_keep isl_union_set *uset1,
1926 __isl_keep isl_union_set *uset2);
1927 int isl_union_set_is_strict_subset(
1928 __isl_keep isl_union_set *uset1,
1929 __isl_keep isl_union_set *uset2);
1930 int isl_basic_map_is_subset(
1931 __isl_keep isl_basic_map *bmap1,
1932 __isl_keep isl_basic_map *bmap2);
1933 int isl_basic_map_is_strict_subset(
1934 __isl_keep isl_basic_map *bmap1,
1935 __isl_keep isl_basic_map *bmap2);
1936 int isl_map_is_subset(
1937 __isl_keep isl_map *map1,
1938 __isl_keep isl_map *map2);
1939 int isl_map_is_strict_subset(
1940 __isl_keep isl_map *map1,
1941 __isl_keep isl_map *map2);
1942 int isl_union_map_is_subset(
1943 __isl_keep isl_union_map *umap1,
1944 __isl_keep isl_union_map *umap2);
1945 int isl_union_map_is_strict_subset(
1946 __isl_keep isl_union_map *umap1,
1947 __isl_keep isl_union_map *umap2);
1949 Check whether the first argument is a (strict) subset of the
1954 =head2 Unary Operations
1960 __isl_give isl_set *isl_set_complement(
1961 __isl_take isl_set *set);
1962 __isl_give isl_map *isl_map_complement(
1963 __isl_take isl_map *map);
1967 __isl_give isl_basic_map *isl_basic_map_reverse(
1968 __isl_take isl_basic_map *bmap);
1969 __isl_give isl_map *isl_map_reverse(
1970 __isl_take isl_map *map);
1971 __isl_give isl_union_map *isl_union_map_reverse(
1972 __isl_take isl_union_map *umap);
1976 __isl_give isl_basic_set *isl_basic_set_project_out(
1977 __isl_take isl_basic_set *bset,
1978 enum isl_dim_type type, unsigned first, unsigned n);
1979 __isl_give isl_basic_map *isl_basic_map_project_out(
1980 __isl_take isl_basic_map *bmap,
1981 enum isl_dim_type type, unsigned first, unsigned n);
1982 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1983 enum isl_dim_type type, unsigned first, unsigned n);
1984 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1985 enum isl_dim_type type, unsigned first, unsigned n);
1986 __isl_give isl_basic_set *isl_basic_set_params(
1987 __isl_take isl_basic_set *bset);
1988 __isl_give isl_basic_set *isl_basic_map_domain(
1989 __isl_take isl_basic_map *bmap);
1990 __isl_give isl_basic_set *isl_basic_map_range(
1991 __isl_take isl_basic_map *bmap);
1992 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1993 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1994 __isl_give isl_set *isl_map_domain(
1995 __isl_take isl_map *bmap);
1996 __isl_give isl_set *isl_map_range(
1997 __isl_take isl_map *map);
1998 __isl_give isl_set *isl_union_set_params(
1999 __isl_take isl_union_set *uset);
2000 __isl_give isl_set *isl_union_map_params(
2001 __isl_take isl_union_map *umap);
2002 __isl_give isl_union_set *isl_union_map_domain(
2003 __isl_take isl_union_map *umap);
2004 __isl_give isl_union_set *isl_union_map_range(
2005 __isl_take isl_union_map *umap);
2007 __isl_give isl_basic_map *isl_basic_map_domain_map(
2008 __isl_take isl_basic_map *bmap);
2009 __isl_give isl_basic_map *isl_basic_map_range_map(
2010 __isl_take isl_basic_map *bmap);
2011 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2012 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2013 __isl_give isl_union_map *isl_union_map_domain_map(
2014 __isl_take isl_union_map *umap);
2015 __isl_give isl_union_map *isl_union_map_range_map(
2016 __isl_take isl_union_map *umap);
2018 The functions above construct a (basic, regular or union) relation
2019 that maps (a wrapped version of) the input relation to its domain or range.
2023 __isl_give isl_basic_set *isl_basic_set_eliminate(
2024 __isl_take isl_basic_set *bset,
2025 enum isl_dim_type type,
2026 unsigned first, unsigned n);
2027 __isl_give isl_set *isl_set_eliminate(
2028 __isl_take isl_set *set, enum isl_dim_type type,
2029 unsigned first, unsigned n);
2030 __isl_give isl_basic_map *isl_basic_map_eliminate(
2031 __isl_take isl_basic_map *bmap,
2032 enum isl_dim_type type,
2033 unsigned first, unsigned n);
2034 __isl_give isl_map *isl_map_eliminate(
2035 __isl_take isl_map *map, enum isl_dim_type type,
2036 unsigned first, unsigned n);
2038 Eliminate the coefficients for the given dimensions from the constraints,
2039 without removing the dimensions.
2043 __isl_give isl_basic_set *isl_basic_set_fix(
2044 __isl_take isl_basic_set *bset,
2045 enum isl_dim_type type, unsigned pos,
2047 __isl_give isl_basic_set *isl_basic_set_fix_si(
2048 __isl_take isl_basic_set *bset,
2049 enum isl_dim_type type, unsigned pos, int value);
2050 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2051 enum isl_dim_type type, unsigned pos,
2053 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2054 enum isl_dim_type type, unsigned pos, int value);
2055 __isl_give isl_basic_map *isl_basic_map_fix_si(
2056 __isl_take isl_basic_map *bmap,
2057 enum isl_dim_type type, unsigned pos, int value);
2058 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
2059 enum isl_dim_type type, unsigned pos,
2061 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2062 enum isl_dim_type type, unsigned pos, int value);
2064 Intersect the set or relation with the hyperplane where the given
2065 dimension has the fixed given value.
2067 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2068 __isl_take isl_basic_map *bmap,
2069 enum isl_dim_type type, unsigned pos, int value);
2070 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2071 __isl_take isl_basic_map *bmap,
2072 enum isl_dim_type type, unsigned pos, int value);
2073 __isl_give isl_set *isl_set_lower_bound(
2074 __isl_take isl_set *set,
2075 enum isl_dim_type type, unsigned pos,
2077 __isl_give isl_set *isl_set_lower_bound_si(
2078 __isl_take isl_set *set,
2079 enum isl_dim_type type, unsigned pos, int value);
2080 __isl_give isl_map *isl_map_lower_bound_si(
2081 __isl_take isl_map *map,
2082 enum isl_dim_type type, unsigned pos, int value);
2083 __isl_give isl_set *isl_set_upper_bound(
2084 __isl_take isl_set *set,
2085 enum isl_dim_type type, unsigned pos,
2087 __isl_give isl_set *isl_set_upper_bound_si(
2088 __isl_take isl_set *set,
2089 enum isl_dim_type type, unsigned pos, int value);
2090 __isl_give isl_map *isl_map_upper_bound_si(
2091 __isl_take isl_map *map,
2092 enum isl_dim_type type, unsigned pos, int value);
2094 Intersect the set or relation with the half-space where the given
2095 dimension has a value bounded by the fixed given value.
2097 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2098 enum isl_dim_type type1, int pos1,
2099 enum isl_dim_type type2, int pos2);
2100 __isl_give isl_basic_map *isl_basic_map_equate(
2101 __isl_take isl_basic_map *bmap,
2102 enum isl_dim_type type1, int pos1,
2103 enum isl_dim_type type2, int pos2);
2104 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2105 enum isl_dim_type type1, int pos1,
2106 enum isl_dim_type type2, int pos2);
2108 Intersect the set or relation with the hyperplane where the given
2109 dimensions are equal to each other.
2111 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2112 enum isl_dim_type type1, int pos1,
2113 enum isl_dim_type type2, int pos2);
2115 Intersect the relation with the hyperplane where the given
2116 dimensions have opposite values.
2118 __isl_give isl_basic_map *isl_basic_map_order_ge(
2119 __isl_take isl_basic_map *bmap,
2120 enum isl_dim_type type1, int pos1,
2121 enum isl_dim_type type2, int pos2);
2122 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2123 enum isl_dim_type type1, int pos1,
2124 enum isl_dim_type type2, int pos2);
2125 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2126 enum isl_dim_type type1, int pos1,
2127 enum isl_dim_type type2, int pos2);
2129 Intersect the relation with the half-space where the given
2130 dimensions satisfy the given ordering.
2134 __isl_give isl_map *isl_set_identity(
2135 __isl_take isl_set *set);
2136 __isl_give isl_union_map *isl_union_set_identity(
2137 __isl_take isl_union_set *uset);
2139 Construct an identity relation on the given (union) set.
2143 __isl_give isl_basic_set *isl_basic_map_deltas(
2144 __isl_take isl_basic_map *bmap);
2145 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2146 __isl_give isl_union_set *isl_union_map_deltas(
2147 __isl_take isl_union_map *umap);
2149 These functions return a (basic) set containing the differences
2150 between image elements and corresponding domain elements in the input.
2152 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2153 __isl_take isl_basic_map *bmap);
2154 __isl_give isl_map *isl_map_deltas_map(
2155 __isl_take isl_map *map);
2156 __isl_give isl_union_map *isl_union_map_deltas_map(
2157 __isl_take isl_union_map *umap);
2159 The functions above construct a (basic, regular or union) relation
2160 that maps (a wrapped version of) the input relation to its delta set.
2164 Simplify the representation of a set or relation by trying
2165 to combine pairs of basic sets or relations into a single
2166 basic set or relation.
2168 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2169 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2170 __isl_give isl_union_set *isl_union_set_coalesce(
2171 __isl_take isl_union_set *uset);
2172 __isl_give isl_union_map *isl_union_map_coalesce(
2173 __isl_take isl_union_map *umap);
2175 One of the methods for combining pairs of basic sets or relations
2176 can result in coefficients that are much larger than those that appear
2177 in the constraints of the input. By default, the coefficients are
2178 not allowed to grow larger, but this can be changed by unsetting
2179 the following option.
2181 int isl_options_set_coalesce_bounded_wrapping(
2182 isl_ctx *ctx, int val);
2183 int isl_options_get_coalesce_bounded_wrapping(
2186 =item * Detecting equalities
2188 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2189 __isl_take isl_basic_set *bset);
2190 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2191 __isl_take isl_basic_map *bmap);
2192 __isl_give isl_set *isl_set_detect_equalities(
2193 __isl_take isl_set *set);
2194 __isl_give isl_map *isl_map_detect_equalities(
2195 __isl_take isl_map *map);
2196 __isl_give isl_union_set *isl_union_set_detect_equalities(
2197 __isl_take isl_union_set *uset);
2198 __isl_give isl_union_map *isl_union_map_detect_equalities(
2199 __isl_take isl_union_map *umap);
2201 Simplify the representation of a set or relation by detecting implicit
2204 =item * Removing redundant constraints
2206 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2207 __isl_take isl_basic_set *bset);
2208 __isl_give isl_set *isl_set_remove_redundancies(
2209 __isl_take isl_set *set);
2210 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2211 __isl_take isl_basic_map *bmap);
2212 __isl_give isl_map *isl_map_remove_redundancies(
2213 __isl_take isl_map *map);
2217 __isl_give isl_basic_set *isl_set_convex_hull(
2218 __isl_take isl_set *set);
2219 __isl_give isl_basic_map *isl_map_convex_hull(
2220 __isl_take isl_map *map);
2222 If the input set or relation has any existentially quantified
2223 variables, then the result of these operations is currently undefined.
2227 __isl_give isl_basic_set *isl_set_simple_hull(
2228 __isl_take isl_set *set);
2229 __isl_give isl_basic_map *isl_map_simple_hull(
2230 __isl_take isl_map *map);
2231 __isl_give isl_union_map *isl_union_map_simple_hull(
2232 __isl_take isl_union_map *umap);
2234 These functions compute a single basic set or relation
2235 that contains the whole input set or relation.
2236 In particular, the output is described by translates
2237 of the constraints describing the basic sets or relations in the input.
2241 (See \autoref{s:simple hull}.)
2247 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2248 __isl_take isl_basic_set *bset);
2249 __isl_give isl_basic_set *isl_set_affine_hull(
2250 __isl_take isl_set *set);
2251 __isl_give isl_union_set *isl_union_set_affine_hull(
2252 __isl_take isl_union_set *uset);
2253 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2254 __isl_take isl_basic_map *bmap);
2255 __isl_give isl_basic_map *isl_map_affine_hull(
2256 __isl_take isl_map *map);
2257 __isl_give isl_union_map *isl_union_map_affine_hull(
2258 __isl_take isl_union_map *umap);
2260 In case of union sets and relations, the affine hull is computed
2263 =item * Polyhedral hull
2265 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2266 __isl_take isl_set *set);
2267 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2268 __isl_take isl_map *map);
2269 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2270 __isl_take isl_union_set *uset);
2271 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2272 __isl_take isl_union_map *umap);
2274 These functions compute a single basic set or relation
2275 not involving any existentially quantified variables
2276 that contains the whole input set or relation.
2277 In case of union sets and relations, the polyhedral hull is computed
2282 __isl_give isl_basic_set *isl_basic_set_sample(
2283 __isl_take isl_basic_set *bset);
2284 __isl_give isl_basic_set *isl_set_sample(
2285 __isl_take isl_set *set);
2286 __isl_give isl_basic_map *isl_basic_map_sample(
2287 __isl_take isl_basic_map *bmap);
2288 __isl_give isl_basic_map *isl_map_sample(
2289 __isl_take isl_map *map);
2291 If the input (basic) set or relation is non-empty, then return
2292 a singleton subset of the input. Otherwise, return an empty set.
2294 =item * Optimization
2296 #include <isl/ilp.h>
2297 enum isl_lp_result isl_basic_set_max(
2298 __isl_keep isl_basic_set *bset,
2299 __isl_keep isl_aff *obj, isl_int *opt)
2300 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2301 __isl_keep isl_aff *obj, isl_int *opt);
2302 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2303 __isl_keep isl_aff *obj, isl_int *opt);
2305 Compute the minimum or maximum of the integer affine expression C<obj>
2306 over the points in C<set>, returning the result in C<opt>.
2307 The return value may be one of C<isl_lp_error>,
2308 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2310 =item * Parametric optimization
2312 __isl_give isl_pw_aff *isl_set_dim_min(
2313 __isl_take isl_set *set, int pos);
2314 __isl_give isl_pw_aff *isl_set_dim_max(
2315 __isl_take isl_set *set, int pos);
2316 __isl_give isl_pw_aff *isl_map_dim_max(
2317 __isl_take isl_map *map, int pos);
2319 Compute the minimum or maximum of the given set or output dimension
2320 as a function of the parameters (and input dimensions), but independently
2321 of the other set or output dimensions.
2322 For lexicographic optimization, see L<"Lexicographic Optimization">.
2326 The following functions compute either the set of (rational) coefficient
2327 values of valid constraints for the given set or the set of (rational)
2328 values satisfying the constraints with coefficients from the given set.
2329 Internally, these two sets of functions perform essentially the
2330 same operations, except that the set of coefficients is assumed to
2331 be a cone, while the set of values may be any polyhedron.
2332 The current implementation is based on the Farkas lemma and
2333 Fourier-Motzkin elimination, but this may change or be made optional
2334 in future. In particular, future implementations may use different
2335 dualization algorithms or skip the elimination step.
2337 __isl_give isl_basic_set *isl_basic_set_coefficients(
2338 __isl_take isl_basic_set *bset);
2339 __isl_give isl_basic_set *isl_set_coefficients(
2340 __isl_take isl_set *set);
2341 __isl_give isl_union_set *isl_union_set_coefficients(
2342 __isl_take isl_union_set *bset);
2343 __isl_give isl_basic_set *isl_basic_set_solutions(
2344 __isl_take isl_basic_set *bset);
2345 __isl_give isl_basic_set *isl_set_solutions(
2346 __isl_take isl_set *set);
2347 __isl_give isl_union_set *isl_union_set_solutions(
2348 __isl_take isl_union_set *bset);
2352 __isl_give isl_map *isl_map_fixed_power(
2353 __isl_take isl_map *map, isl_int exp);
2354 __isl_give isl_union_map *isl_union_map_fixed_power(
2355 __isl_take isl_union_map *umap, isl_int exp);
2357 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2358 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2359 of C<map> is computed.
2361 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2363 __isl_give isl_union_map *isl_union_map_power(
2364 __isl_take isl_union_map *umap, int *exact);
2366 Compute a parametric representation for all positive powers I<k> of C<map>.
2367 The result maps I<k> to a nested relation corresponding to the
2368 I<k>th power of C<map>.
2369 The result may be an overapproximation. If the result is known to be exact,
2370 then C<*exact> is set to C<1>.
2372 =item * Transitive closure
2374 __isl_give isl_map *isl_map_transitive_closure(
2375 __isl_take isl_map *map, int *exact);
2376 __isl_give isl_union_map *isl_union_map_transitive_closure(
2377 __isl_take isl_union_map *umap, int *exact);
2379 Compute the transitive closure of C<map>.
2380 The result may be an overapproximation. If the result is known to be exact,
2381 then C<*exact> is set to C<1>.
2383 =item * Reaching path lengths
2385 __isl_give isl_map *isl_map_reaching_path_lengths(
2386 __isl_take isl_map *map, int *exact);
2388 Compute a relation that maps each element in the range of C<map>
2389 to the lengths of all paths composed of edges in C<map> that
2390 end up in the given element.
2391 The result may be an overapproximation. If the result is known to be exact,
2392 then C<*exact> is set to C<1>.
2393 To compute the I<maximal> path length, the resulting relation
2394 should be postprocessed by C<isl_map_lexmax>.
2395 In particular, if the input relation is a dependence relation
2396 (mapping sources to sinks), then the maximal path length corresponds
2397 to the free schedule.
2398 Note, however, that C<isl_map_lexmax> expects the maximum to be
2399 finite, so if the path lengths are unbounded (possibly due to
2400 the overapproximation), then you will get an error message.
2404 __isl_give isl_basic_set *isl_basic_map_wrap(
2405 __isl_take isl_basic_map *bmap);
2406 __isl_give isl_set *isl_map_wrap(
2407 __isl_take isl_map *map);
2408 __isl_give isl_union_set *isl_union_map_wrap(
2409 __isl_take isl_union_map *umap);
2410 __isl_give isl_basic_map *isl_basic_set_unwrap(
2411 __isl_take isl_basic_set *bset);
2412 __isl_give isl_map *isl_set_unwrap(
2413 __isl_take isl_set *set);
2414 __isl_give isl_union_map *isl_union_set_unwrap(
2415 __isl_take isl_union_set *uset);
2419 Remove any internal structure of domain (and range) of the given
2420 set or relation. If there is any such internal structure in the input,
2421 then the name of the space is also removed.
2423 __isl_give isl_basic_set *isl_basic_set_flatten(
2424 __isl_take isl_basic_set *bset);
2425 __isl_give isl_set *isl_set_flatten(
2426 __isl_take isl_set *set);
2427 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2428 __isl_take isl_basic_map *bmap);
2429 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2430 __isl_take isl_basic_map *bmap);
2431 __isl_give isl_map *isl_map_flatten_range(
2432 __isl_take isl_map *map);
2433 __isl_give isl_map *isl_map_flatten_domain(
2434 __isl_take isl_map *map);
2435 __isl_give isl_basic_map *isl_basic_map_flatten(
2436 __isl_take isl_basic_map *bmap);
2437 __isl_give isl_map *isl_map_flatten(
2438 __isl_take isl_map *map);
2440 __isl_give isl_map *isl_set_flatten_map(
2441 __isl_take isl_set *set);
2443 The function above constructs a relation
2444 that maps the input set to a flattened version of the set.
2448 Lift the input set to a space with extra dimensions corresponding
2449 to the existentially quantified variables in the input.
2450 In particular, the result lives in a wrapped map where the domain
2451 is the original space and the range corresponds to the original
2452 existentially quantified variables.
2454 __isl_give isl_basic_set *isl_basic_set_lift(
2455 __isl_take isl_basic_set *bset);
2456 __isl_give isl_set *isl_set_lift(
2457 __isl_take isl_set *set);
2458 __isl_give isl_union_set *isl_union_set_lift(
2459 __isl_take isl_union_set *uset);
2461 Given a local space that contains the existentially quantified
2462 variables of a set, a basic relation that, when applied to
2463 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2464 can be constructed using the following function.
2466 #include <isl/local_space.h>
2467 __isl_give isl_basic_map *isl_local_space_lifting(
2468 __isl_take isl_local_space *ls);
2470 =item * Internal Product
2472 __isl_give isl_basic_map *isl_basic_map_zip(
2473 __isl_take isl_basic_map *bmap);
2474 __isl_give isl_map *isl_map_zip(
2475 __isl_take isl_map *map);
2476 __isl_give isl_union_map *isl_union_map_zip(
2477 __isl_take isl_union_map *umap);
2479 Given a relation with nested relations for domain and range,
2480 interchange the range of the domain with the domain of the range.
2484 __isl_give isl_basic_map *isl_basic_map_curry(
2485 __isl_take isl_basic_map *bmap);
2486 __isl_give isl_basic_map *isl_basic_map_uncurry(
2487 __isl_take isl_basic_map *bmap);
2488 __isl_give isl_map *isl_map_curry(
2489 __isl_take isl_map *map);
2490 __isl_give isl_map *isl_map_uncurry(
2491 __isl_take isl_map *map);
2492 __isl_give isl_union_map *isl_union_map_curry(
2493 __isl_take isl_union_map *umap);
2495 Given a relation with a nested relation for domain,
2496 the C<curry> functions
2497 move the range of the nested relation out of the domain
2498 and use it as the domain of a nested relation in the range,
2499 with the original range as range of this nested relation.
2500 The C<uncurry> functions perform the inverse operation.
2502 =item * Aligning parameters
2504 __isl_give isl_basic_set *isl_basic_set_align_params(
2505 __isl_take isl_basic_set *bset,
2506 __isl_take isl_space *model);
2507 __isl_give isl_set *isl_set_align_params(
2508 __isl_take isl_set *set,
2509 __isl_take isl_space *model);
2510 __isl_give isl_basic_map *isl_basic_map_align_params(
2511 __isl_take isl_basic_map *bmap,
2512 __isl_take isl_space *model);
2513 __isl_give isl_map *isl_map_align_params(
2514 __isl_take isl_map *map,
2515 __isl_take isl_space *model);
2517 Change the order of the parameters of the given set or relation
2518 such that the first parameters match those of C<model>.
2519 This may involve the introduction of extra parameters.
2520 All parameters need to be named.
2522 =item * Dimension manipulation
2524 __isl_give isl_set *isl_set_add_dims(
2525 __isl_take isl_set *set,
2526 enum isl_dim_type type, unsigned n);
2527 __isl_give isl_map *isl_map_add_dims(
2528 __isl_take isl_map *map,
2529 enum isl_dim_type type, unsigned n);
2530 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2531 __isl_take isl_basic_set *bset,
2532 enum isl_dim_type type, unsigned pos,
2534 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2535 __isl_take isl_basic_map *bmap,
2536 enum isl_dim_type type, unsigned pos,
2538 __isl_give isl_set *isl_set_insert_dims(
2539 __isl_take isl_set *set,
2540 enum isl_dim_type type, unsigned pos, unsigned n);
2541 __isl_give isl_map *isl_map_insert_dims(
2542 __isl_take isl_map *map,
2543 enum isl_dim_type type, unsigned pos, unsigned n);
2544 __isl_give isl_basic_set *isl_basic_set_move_dims(
2545 __isl_take isl_basic_set *bset,
2546 enum isl_dim_type dst_type, unsigned dst_pos,
2547 enum isl_dim_type src_type, unsigned src_pos,
2549 __isl_give isl_basic_map *isl_basic_map_move_dims(
2550 __isl_take isl_basic_map *bmap,
2551 enum isl_dim_type dst_type, unsigned dst_pos,
2552 enum isl_dim_type src_type, unsigned src_pos,
2554 __isl_give isl_set *isl_set_move_dims(
2555 __isl_take isl_set *set,
2556 enum isl_dim_type dst_type, unsigned dst_pos,
2557 enum isl_dim_type src_type, unsigned src_pos,
2559 __isl_give isl_map *isl_map_move_dims(
2560 __isl_take isl_map *map,
2561 enum isl_dim_type dst_type, unsigned dst_pos,
2562 enum isl_dim_type src_type, unsigned src_pos,
2565 It is usually not advisable to directly change the (input or output)
2566 space of a set or a relation as this removes the name and the internal
2567 structure of the space. However, the above functions can be useful
2568 to add new parameters, assuming
2569 C<isl_set_align_params> and C<isl_map_align_params>
2574 =head2 Binary Operations
2576 The two arguments of a binary operation not only need to live
2577 in the same C<isl_ctx>, they currently also need to have
2578 the same (number of) parameters.
2580 =head3 Basic Operations
2584 =item * Intersection
2586 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2587 __isl_take isl_basic_set *bset1,
2588 __isl_take isl_basic_set *bset2);
2589 __isl_give isl_basic_set *isl_basic_set_intersect(
2590 __isl_take isl_basic_set *bset1,
2591 __isl_take isl_basic_set *bset2);
2592 __isl_give isl_set *isl_set_intersect_params(
2593 __isl_take isl_set *set,
2594 __isl_take isl_set *params);
2595 __isl_give isl_set *isl_set_intersect(
2596 __isl_take isl_set *set1,
2597 __isl_take isl_set *set2);
2598 __isl_give isl_union_set *isl_union_set_intersect_params(
2599 __isl_take isl_union_set *uset,
2600 __isl_take isl_set *set);
2601 __isl_give isl_union_map *isl_union_map_intersect_params(
2602 __isl_take isl_union_map *umap,
2603 __isl_take isl_set *set);
2604 __isl_give isl_union_set *isl_union_set_intersect(
2605 __isl_take isl_union_set *uset1,
2606 __isl_take isl_union_set *uset2);
2607 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2608 __isl_take isl_basic_map *bmap,
2609 __isl_take isl_basic_set *bset);
2610 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2611 __isl_take isl_basic_map *bmap,
2612 __isl_take isl_basic_set *bset);
2613 __isl_give isl_basic_map *isl_basic_map_intersect(
2614 __isl_take isl_basic_map *bmap1,
2615 __isl_take isl_basic_map *bmap2);
2616 __isl_give isl_map *isl_map_intersect_params(
2617 __isl_take isl_map *map,
2618 __isl_take isl_set *params);
2619 __isl_give isl_map *isl_map_intersect_domain(
2620 __isl_take isl_map *map,
2621 __isl_take isl_set *set);
2622 __isl_give isl_map *isl_map_intersect_range(
2623 __isl_take isl_map *map,
2624 __isl_take isl_set *set);
2625 __isl_give isl_map *isl_map_intersect(
2626 __isl_take isl_map *map1,
2627 __isl_take isl_map *map2);
2628 __isl_give isl_union_map *isl_union_map_intersect_domain(
2629 __isl_take isl_union_map *umap,
2630 __isl_take isl_union_set *uset);
2631 __isl_give isl_union_map *isl_union_map_intersect_range(
2632 __isl_take isl_union_map *umap,
2633 __isl_take isl_union_set *uset);
2634 __isl_give isl_union_map *isl_union_map_intersect(
2635 __isl_take isl_union_map *umap1,
2636 __isl_take isl_union_map *umap2);
2638 The second argument to the C<_params> functions needs to be
2639 a parametric (basic) set. For the other functions, a parametric set
2640 for either argument is only allowed if the other argument is
2641 a parametric set as well.
2645 __isl_give isl_set *isl_basic_set_union(
2646 __isl_take isl_basic_set *bset1,
2647 __isl_take isl_basic_set *bset2);
2648 __isl_give isl_map *isl_basic_map_union(
2649 __isl_take isl_basic_map *bmap1,
2650 __isl_take isl_basic_map *bmap2);
2651 __isl_give isl_set *isl_set_union(
2652 __isl_take isl_set *set1,
2653 __isl_take isl_set *set2);
2654 __isl_give isl_map *isl_map_union(
2655 __isl_take isl_map *map1,
2656 __isl_take isl_map *map2);
2657 __isl_give isl_union_set *isl_union_set_union(
2658 __isl_take isl_union_set *uset1,
2659 __isl_take isl_union_set *uset2);
2660 __isl_give isl_union_map *isl_union_map_union(
2661 __isl_take isl_union_map *umap1,
2662 __isl_take isl_union_map *umap2);
2664 =item * Set difference
2666 __isl_give isl_set *isl_set_subtract(
2667 __isl_take isl_set *set1,
2668 __isl_take isl_set *set2);
2669 __isl_give isl_map *isl_map_subtract(
2670 __isl_take isl_map *map1,
2671 __isl_take isl_map *map2);
2672 __isl_give isl_map *isl_map_subtract_domain(
2673 __isl_take isl_map *map,
2674 __isl_take isl_set *dom);
2675 __isl_give isl_map *isl_map_subtract_range(
2676 __isl_take isl_map *map,
2677 __isl_take isl_set *dom);
2678 __isl_give isl_union_set *isl_union_set_subtract(
2679 __isl_take isl_union_set *uset1,
2680 __isl_take isl_union_set *uset2);
2681 __isl_give isl_union_map *isl_union_map_subtract(
2682 __isl_take isl_union_map *umap1,
2683 __isl_take isl_union_map *umap2);
2684 __isl_give isl_union_map *isl_union_map_subtract_domain(
2685 __isl_take isl_union_map *umap,
2686 __isl_take isl_union_set *dom);
2690 __isl_give isl_basic_set *isl_basic_set_apply(
2691 __isl_take isl_basic_set *bset,
2692 __isl_take isl_basic_map *bmap);
2693 __isl_give isl_set *isl_set_apply(
2694 __isl_take isl_set *set,
2695 __isl_take isl_map *map);
2696 __isl_give isl_union_set *isl_union_set_apply(
2697 __isl_take isl_union_set *uset,
2698 __isl_take isl_union_map *umap);
2699 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2700 __isl_take isl_basic_map *bmap1,
2701 __isl_take isl_basic_map *bmap2);
2702 __isl_give isl_basic_map *isl_basic_map_apply_range(
2703 __isl_take isl_basic_map *bmap1,
2704 __isl_take isl_basic_map *bmap2);
2705 __isl_give isl_map *isl_map_apply_domain(
2706 __isl_take isl_map *map1,
2707 __isl_take isl_map *map2);
2708 __isl_give isl_union_map *isl_union_map_apply_domain(
2709 __isl_take isl_union_map *umap1,
2710 __isl_take isl_union_map *umap2);
2711 __isl_give isl_map *isl_map_apply_range(
2712 __isl_take isl_map *map1,
2713 __isl_take isl_map *map2);
2714 __isl_give isl_union_map *isl_union_map_apply_range(
2715 __isl_take isl_union_map *umap1,
2716 __isl_take isl_union_map *umap2);
2718 =item * Cartesian Product
2720 __isl_give isl_set *isl_set_product(
2721 __isl_take isl_set *set1,
2722 __isl_take isl_set *set2);
2723 __isl_give isl_union_set *isl_union_set_product(
2724 __isl_take isl_union_set *uset1,
2725 __isl_take isl_union_set *uset2);
2726 __isl_give isl_basic_map *isl_basic_map_domain_product(
2727 __isl_take isl_basic_map *bmap1,
2728 __isl_take isl_basic_map *bmap2);
2729 __isl_give isl_basic_map *isl_basic_map_range_product(
2730 __isl_take isl_basic_map *bmap1,
2731 __isl_take isl_basic_map *bmap2);
2732 __isl_give isl_basic_map *isl_basic_map_product(
2733 __isl_take isl_basic_map *bmap1,
2734 __isl_take isl_basic_map *bmap2);
2735 __isl_give isl_map *isl_map_domain_product(
2736 __isl_take isl_map *map1,
2737 __isl_take isl_map *map2);
2738 __isl_give isl_map *isl_map_range_product(
2739 __isl_take isl_map *map1,
2740 __isl_take isl_map *map2);
2741 __isl_give isl_union_map *isl_union_map_domain_product(
2742 __isl_take isl_union_map *umap1,
2743 __isl_take isl_union_map *umap2);
2744 __isl_give isl_union_map *isl_union_map_range_product(
2745 __isl_take isl_union_map *umap1,
2746 __isl_take isl_union_map *umap2);
2747 __isl_give isl_map *isl_map_product(
2748 __isl_take isl_map *map1,
2749 __isl_take isl_map *map2);
2750 __isl_give isl_union_map *isl_union_map_product(
2751 __isl_take isl_union_map *umap1,
2752 __isl_take isl_union_map *umap2);
2754 The above functions compute the cross product of the given
2755 sets or relations. The domains and ranges of the results
2756 are wrapped maps between domains and ranges of the inputs.
2757 To obtain a ``flat'' product, use the following functions
2760 __isl_give isl_basic_set *isl_basic_set_flat_product(
2761 __isl_take isl_basic_set *bset1,
2762 __isl_take isl_basic_set *bset2);
2763 __isl_give isl_set *isl_set_flat_product(
2764 __isl_take isl_set *set1,
2765 __isl_take isl_set *set2);
2766 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2767 __isl_take isl_basic_map *bmap1,
2768 __isl_take isl_basic_map *bmap2);
2769 __isl_give isl_map *isl_map_flat_domain_product(
2770 __isl_take isl_map *map1,
2771 __isl_take isl_map *map2);
2772 __isl_give isl_map *isl_map_flat_range_product(
2773 __isl_take isl_map *map1,
2774 __isl_take isl_map *map2);
2775 __isl_give isl_union_map *isl_union_map_flat_range_product(
2776 __isl_take isl_union_map *umap1,
2777 __isl_take isl_union_map *umap2);
2778 __isl_give isl_basic_map *isl_basic_map_flat_product(
2779 __isl_take isl_basic_map *bmap1,
2780 __isl_take isl_basic_map *bmap2);
2781 __isl_give isl_map *isl_map_flat_product(
2782 __isl_take isl_map *map1,
2783 __isl_take isl_map *map2);
2785 =item * Simplification
2787 __isl_give isl_basic_set *isl_basic_set_gist(
2788 __isl_take isl_basic_set *bset,
2789 __isl_take isl_basic_set *context);
2790 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2791 __isl_take isl_set *context);
2792 __isl_give isl_set *isl_set_gist_params(
2793 __isl_take isl_set *set,
2794 __isl_take isl_set *context);
2795 __isl_give isl_union_set *isl_union_set_gist(
2796 __isl_take isl_union_set *uset,
2797 __isl_take isl_union_set *context);
2798 __isl_give isl_union_set *isl_union_set_gist_params(
2799 __isl_take isl_union_set *uset,
2800 __isl_take isl_set *set);
2801 __isl_give isl_basic_map *isl_basic_map_gist(
2802 __isl_take isl_basic_map *bmap,
2803 __isl_take isl_basic_map *context);
2804 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2805 __isl_take isl_map *context);
2806 __isl_give isl_map *isl_map_gist_params(
2807 __isl_take isl_map *map,
2808 __isl_take isl_set *context);
2809 __isl_give isl_map *isl_map_gist_domain(
2810 __isl_take isl_map *map,
2811 __isl_take isl_set *context);
2812 __isl_give isl_map *isl_map_gist_range(
2813 __isl_take isl_map *map,
2814 __isl_take isl_set *context);
2815 __isl_give isl_union_map *isl_union_map_gist(
2816 __isl_take isl_union_map *umap,
2817 __isl_take isl_union_map *context);
2818 __isl_give isl_union_map *isl_union_map_gist_params(
2819 __isl_take isl_union_map *umap,
2820 __isl_take isl_set *set);
2821 __isl_give isl_union_map *isl_union_map_gist_domain(
2822 __isl_take isl_union_map *umap,
2823 __isl_take isl_union_set *uset);
2824 __isl_give isl_union_map *isl_union_map_gist_range(
2825 __isl_take isl_union_map *umap,
2826 __isl_take isl_union_set *uset);
2828 The gist operation returns a set or relation that has the
2829 same intersection with the context as the input set or relation.
2830 Any implicit equality in the intersection is made explicit in the result,
2831 while all inequalities that are redundant with respect to the intersection
2833 In case of union sets and relations, the gist operation is performed
2838 =head3 Lexicographic Optimization
2840 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2841 the following functions
2842 compute a set that contains the lexicographic minimum or maximum
2843 of the elements in C<set> (or C<bset>) for those values of the parameters
2844 that satisfy C<dom>.
2845 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2846 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2848 In other words, the union of the parameter values
2849 for which the result is non-empty and of C<*empty>
2852 __isl_give isl_set *isl_basic_set_partial_lexmin(
2853 __isl_take isl_basic_set *bset,
2854 __isl_take isl_basic_set *dom,
2855 __isl_give isl_set **empty);
2856 __isl_give isl_set *isl_basic_set_partial_lexmax(
2857 __isl_take isl_basic_set *bset,
2858 __isl_take isl_basic_set *dom,
2859 __isl_give isl_set **empty);
2860 __isl_give isl_set *isl_set_partial_lexmin(
2861 __isl_take isl_set *set, __isl_take isl_set *dom,
2862 __isl_give isl_set **empty);
2863 __isl_give isl_set *isl_set_partial_lexmax(
2864 __isl_take isl_set *set, __isl_take isl_set *dom,
2865 __isl_give isl_set **empty);
2867 Given a (basic) set C<set> (or C<bset>), the following functions simply
2868 return a set containing the lexicographic minimum or maximum
2869 of the elements in C<set> (or C<bset>).
2870 In case of union sets, the optimum is computed per space.
2872 __isl_give isl_set *isl_basic_set_lexmin(
2873 __isl_take isl_basic_set *bset);
2874 __isl_give isl_set *isl_basic_set_lexmax(
2875 __isl_take isl_basic_set *bset);
2876 __isl_give isl_set *isl_set_lexmin(
2877 __isl_take isl_set *set);
2878 __isl_give isl_set *isl_set_lexmax(
2879 __isl_take isl_set *set);
2880 __isl_give isl_union_set *isl_union_set_lexmin(
2881 __isl_take isl_union_set *uset);
2882 __isl_give isl_union_set *isl_union_set_lexmax(
2883 __isl_take isl_union_set *uset);
2885 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2886 the following functions
2887 compute a relation that maps each element of C<dom>
2888 to the single lexicographic minimum or maximum
2889 of the elements that are associated to that same
2890 element in C<map> (or C<bmap>).
2891 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2892 that contains the elements in C<dom> that do not map
2893 to any elements in C<map> (or C<bmap>).
2894 In other words, the union of the domain of the result and of C<*empty>
2897 __isl_give isl_map *isl_basic_map_partial_lexmax(
2898 __isl_take isl_basic_map *bmap,
2899 __isl_take isl_basic_set *dom,
2900 __isl_give isl_set **empty);
2901 __isl_give isl_map *isl_basic_map_partial_lexmin(
2902 __isl_take isl_basic_map *bmap,
2903 __isl_take isl_basic_set *dom,
2904 __isl_give isl_set **empty);
2905 __isl_give isl_map *isl_map_partial_lexmax(
2906 __isl_take isl_map *map, __isl_take isl_set *dom,
2907 __isl_give isl_set **empty);
2908 __isl_give isl_map *isl_map_partial_lexmin(
2909 __isl_take isl_map *map, __isl_take isl_set *dom,
2910 __isl_give isl_set **empty);
2912 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2913 return a map mapping each element in the domain of
2914 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2915 of all elements associated to that element.
2916 In case of union relations, the optimum is computed per space.
2918 __isl_give isl_map *isl_basic_map_lexmin(
2919 __isl_take isl_basic_map *bmap);
2920 __isl_give isl_map *isl_basic_map_lexmax(
2921 __isl_take isl_basic_map *bmap);
2922 __isl_give isl_map *isl_map_lexmin(
2923 __isl_take isl_map *map);
2924 __isl_give isl_map *isl_map_lexmax(
2925 __isl_take isl_map *map);
2926 __isl_give isl_union_map *isl_union_map_lexmin(
2927 __isl_take isl_union_map *umap);
2928 __isl_give isl_union_map *isl_union_map_lexmax(
2929 __isl_take isl_union_map *umap);
2931 The following functions return their result in the form of
2932 a piecewise multi-affine expression
2933 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2934 but are otherwise equivalent to the corresponding functions
2935 returning a basic set or relation.
2937 __isl_give isl_pw_multi_aff *
2938 isl_basic_map_lexmin_pw_multi_aff(
2939 __isl_take isl_basic_map *bmap);
2940 __isl_give isl_pw_multi_aff *
2941 isl_basic_set_partial_lexmin_pw_multi_aff(
2942 __isl_take isl_basic_set *bset,
2943 __isl_take isl_basic_set *dom,
2944 __isl_give isl_set **empty);
2945 __isl_give isl_pw_multi_aff *
2946 isl_basic_set_partial_lexmax_pw_multi_aff(
2947 __isl_take isl_basic_set *bset,
2948 __isl_take isl_basic_set *dom,
2949 __isl_give isl_set **empty);
2950 __isl_give isl_pw_multi_aff *
2951 isl_basic_map_partial_lexmin_pw_multi_aff(
2952 __isl_take isl_basic_map *bmap,
2953 __isl_take isl_basic_set *dom,
2954 __isl_give isl_set **empty);
2955 __isl_give isl_pw_multi_aff *
2956 isl_basic_map_partial_lexmax_pw_multi_aff(
2957 __isl_take isl_basic_map *bmap,
2958 __isl_take isl_basic_set *dom,
2959 __isl_give isl_set **empty);
2960 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
2961 __isl_take isl_map *map);
2962 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
2963 __isl_take isl_map *map);
2967 Lists are defined over several element types, including
2968 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
2969 C<isl_basic_set> and C<isl_set>.
2970 Here we take lists of C<isl_set>s as an example.
2971 Lists can be created, copied, modified and freed using the following functions.
2973 #include <isl/list.h>
2974 __isl_give isl_set_list *isl_set_list_from_set(
2975 __isl_take isl_set *el);
2976 __isl_give isl_set_list *isl_set_list_alloc(
2977 isl_ctx *ctx, int n);
2978 __isl_give isl_set_list *isl_set_list_copy(
2979 __isl_keep isl_set_list *list);
2980 __isl_give isl_set_list *isl_set_list_insert(
2981 __isl_take isl_set_list *list, unsigned pos,
2982 __isl_take isl_set *el);
2983 __isl_give isl_set_list *isl_set_list_add(
2984 __isl_take isl_set_list *list,
2985 __isl_take isl_set *el);
2986 __isl_give isl_set_list *isl_set_list_drop(
2987 __isl_take isl_set_list *list,
2988 unsigned first, unsigned n);
2989 __isl_give isl_set_list *isl_set_list_set_set(
2990 __isl_take isl_set_list *list, int index,
2991 __isl_take isl_set *set);
2992 __isl_give isl_set_list *isl_set_list_concat(
2993 __isl_take isl_set_list *list1,
2994 __isl_take isl_set_list *list2);
2995 void *isl_set_list_free(__isl_take isl_set_list *list);
2997 C<isl_set_list_alloc> creates an empty list with a capacity for
2998 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3001 Lists can be inspected using the following functions.
3003 #include <isl/list.h>
3004 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3005 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3006 __isl_give isl_set *isl_set_list_get_set(
3007 __isl_keep isl_set_list *list, int index);
3008 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3009 int (*fn)(__isl_take isl_set *el, void *user),
3012 Lists can be printed using
3014 #include <isl/list.h>
3015 __isl_give isl_printer *isl_printer_print_set_list(
3016 __isl_take isl_printer *p,
3017 __isl_keep isl_set_list *list);
3021 Vectors can be created, copied and freed using the following functions.
3023 #include <isl/vec.h>
3024 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3026 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3027 void *isl_vec_free(__isl_take isl_vec *vec);
3029 Note that the elements of a newly created vector may have arbitrary values.
3030 The elements can be changed and inspected using the following functions.
3032 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3033 int isl_vec_size(__isl_keep isl_vec *vec);
3034 int isl_vec_get_element(__isl_keep isl_vec *vec,
3035 int pos, isl_int *v);
3036 __isl_give isl_vec *isl_vec_set_element(
3037 __isl_take isl_vec *vec, int pos, isl_int v);
3038 __isl_give isl_vec *isl_vec_set_element_si(
3039 __isl_take isl_vec *vec, int pos, int v);
3040 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3042 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3044 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3047 C<isl_vec_get_element> will return a negative value if anything went wrong.
3048 In that case, the value of C<*v> is undefined.
3050 The following function can be used to concatenate two vectors.
3052 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3053 __isl_take isl_vec *vec2);
3057 Matrices can be created, copied and freed using the following functions.
3059 #include <isl/mat.h>
3060 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3061 unsigned n_row, unsigned n_col);
3062 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3063 void isl_mat_free(__isl_take isl_mat *mat);
3065 Note that the elements of a newly created matrix may have arbitrary values.
3066 The elements can be changed and inspected using the following functions.
3068 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3069 int isl_mat_rows(__isl_keep isl_mat *mat);
3070 int isl_mat_cols(__isl_keep isl_mat *mat);
3071 int isl_mat_get_element(__isl_keep isl_mat *mat,
3072 int row, int col, isl_int *v);
3073 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3074 int row, int col, isl_int v);
3075 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3076 int row, int col, int v);
3078 C<isl_mat_get_element> will return a negative value if anything went wrong.
3079 In that case, the value of C<*v> is undefined.
3081 The following function can be used to compute the (right) inverse
3082 of a matrix, i.e., a matrix such that the product of the original
3083 and the inverse (in that order) is a multiple of the identity matrix.
3084 The input matrix is assumed to be of full row-rank.
3086 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3088 The following function can be used to compute the (right) kernel
3089 (or null space) of a matrix, i.e., a matrix such that the product of
3090 the original and the kernel (in that order) is the zero matrix.
3092 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3094 =head2 Piecewise Quasi Affine Expressions
3096 The zero quasi affine expression on a given domain can be created using
3098 __isl_give isl_aff *isl_aff_zero_on_domain(
3099 __isl_take isl_local_space *ls);
3101 Note that the space in which the resulting object lives is a map space
3102 with the given space as domain and a one-dimensional range.
3104 An empty piecewise quasi affine expression (one with no cells)
3105 or a piecewise quasi affine expression with a single cell can
3106 be created using the following functions.
3108 #include <isl/aff.h>
3109 __isl_give isl_pw_aff *isl_pw_aff_empty(
3110 __isl_take isl_space *space);
3111 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3112 __isl_take isl_set *set, __isl_take isl_aff *aff);
3113 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3114 __isl_take isl_aff *aff);
3116 A piecewise quasi affine expression that is equal to 1 on a set
3117 and 0 outside the set can be created using the following function.
3119 #include <isl/aff.h>
3120 __isl_give isl_pw_aff *isl_set_indicator_function(
3121 __isl_take isl_set *set);
3123 Quasi affine expressions can be copied and freed using
3125 #include <isl/aff.h>
3126 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3127 void *isl_aff_free(__isl_take isl_aff *aff);
3129 __isl_give isl_pw_aff *isl_pw_aff_copy(
3130 __isl_keep isl_pw_aff *pwaff);
3131 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3133 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3134 using the following function. The constraint is required to have
3135 a non-zero coefficient for the specified dimension.
3137 #include <isl/constraint.h>
3138 __isl_give isl_aff *isl_constraint_get_bound(
3139 __isl_keep isl_constraint *constraint,
3140 enum isl_dim_type type, int pos);
3142 The entire affine expression of the constraint can also be extracted
3143 using the following function.
3145 #include <isl/constraint.h>
3146 __isl_give isl_aff *isl_constraint_get_aff(
3147 __isl_keep isl_constraint *constraint);
3149 Conversely, an equality constraint equating
3150 the affine expression to zero or an inequality constraint enforcing
3151 the affine expression to be non-negative, can be constructed using
3153 __isl_give isl_constraint *isl_equality_from_aff(
3154 __isl_take isl_aff *aff);
3155 __isl_give isl_constraint *isl_inequality_from_aff(
3156 __isl_take isl_aff *aff);
3158 The expression can be inspected using
3160 #include <isl/aff.h>
3161 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3162 int isl_aff_dim(__isl_keep isl_aff *aff,
3163 enum isl_dim_type type);
3164 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3165 __isl_keep isl_aff *aff);
3166 __isl_give isl_local_space *isl_aff_get_local_space(
3167 __isl_keep isl_aff *aff);
3168 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3169 enum isl_dim_type type, unsigned pos);
3170 const char *isl_pw_aff_get_dim_name(
3171 __isl_keep isl_pw_aff *pa,
3172 enum isl_dim_type type, unsigned pos);
3173 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3174 enum isl_dim_type type, unsigned pos);
3175 __isl_give isl_id *isl_pw_aff_get_dim_id(
3176 __isl_keep isl_pw_aff *pa,
3177 enum isl_dim_type type, unsigned pos);
3178 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3179 __isl_keep isl_pw_aff *pa,
3180 enum isl_dim_type type);
3181 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3183 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3184 enum isl_dim_type type, int pos, isl_int *v);
3185 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3187 __isl_give isl_aff *isl_aff_get_div(
3188 __isl_keep isl_aff *aff, int pos);
3190 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3191 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3192 int (*fn)(__isl_take isl_set *set,
3193 __isl_take isl_aff *aff,
3194 void *user), void *user);
3196 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3197 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3199 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3200 enum isl_dim_type type, unsigned first, unsigned n);
3201 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3202 enum isl_dim_type type, unsigned first, unsigned n);
3204 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3205 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3206 enum isl_dim_type type);
3207 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3209 It can be modified using
3211 #include <isl/aff.h>
3212 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3213 __isl_take isl_pw_aff *pwaff,
3214 enum isl_dim_type type, __isl_take isl_id *id);
3215 __isl_give isl_aff *isl_aff_set_dim_name(
3216 __isl_take isl_aff *aff, enum isl_dim_type type,
3217 unsigned pos, const char *s);
3218 __isl_give isl_aff *isl_aff_set_dim_id(
3219 __isl_take isl_aff *aff, enum isl_dim_type type,
3220 unsigned pos, __isl_take isl_id *id);
3221 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3222 __isl_take isl_pw_aff *pma,
3223 enum isl_dim_type type, unsigned pos,
3224 __isl_take isl_id *id);
3225 __isl_give isl_aff *isl_aff_set_constant(
3226 __isl_take isl_aff *aff, isl_int v);
3227 __isl_give isl_aff *isl_aff_set_constant_si(
3228 __isl_take isl_aff *aff, int v);
3229 __isl_give isl_aff *isl_aff_set_coefficient(
3230 __isl_take isl_aff *aff,
3231 enum isl_dim_type type, int pos, isl_int v);
3232 __isl_give isl_aff *isl_aff_set_coefficient_si(
3233 __isl_take isl_aff *aff,
3234 enum isl_dim_type type, int pos, int v);
3235 __isl_give isl_aff *isl_aff_set_denominator(
3236 __isl_take isl_aff *aff, isl_int v);
3238 __isl_give isl_aff *isl_aff_add_constant(
3239 __isl_take isl_aff *aff, isl_int v);
3240 __isl_give isl_aff *isl_aff_add_constant_si(
3241 __isl_take isl_aff *aff, int v);
3242 __isl_give isl_aff *isl_aff_add_constant_num(
3243 __isl_take isl_aff *aff, isl_int v);
3244 __isl_give isl_aff *isl_aff_add_constant_num_si(
3245 __isl_take isl_aff *aff, int v);
3246 __isl_give isl_aff *isl_aff_add_coefficient(
3247 __isl_take isl_aff *aff,
3248 enum isl_dim_type type, int pos, isl_int v);
3249 __isl_give isl_aff *isl_aff_add_coefficient_si(
3250 __isl_take isl_aff *aff,
3251 enum isl_dim_type type, int pos, int v);
3253 __isl_give isl_aff *isl_aff_insert_dims(
3254 __isl_take isl_aff *aff,
3255 enum isl_dim_type type, unsigned first, unsigned n);
3256 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3257 __isl_take isl_pw_aff *pwaff,
3258 enum isl_dim_type type, unsigned first, unsigned n);
3259 __isl_give isl_aff *isl_aff_add_dims(
3260 __isl_take isl_aff *aff,
3261 enum isl_dim_type type, unsigned n);
3262 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3263 __isl_take isl_pw_aff *pwaff,
3264 enum isl_dim_type type, unsigned n);
3265 __isl_give isl_aff *isl_aff_drop_dims(
3266 __isl_take isl_aff *aff,
3267 enum isl_dim_type type, unsigned first, unsigned n);
3268 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3269 __isl_take isl_pw_aff *pwaff,
3270 enum isl_dim_type type, unsigned first, unsigned n);
3272 Note that the C<set_constant> and C<set_coefficient> functions
3273 set the I<numerator> of the constant or coefficient, while
3274 C<add_constant> and C<add_coefficient> add an integer value to
3275 the possibly rational constant or coefficient.
3276 The C<add_constant_num> functions add an integer value to
3279 To check whether an affine expressions is obviously zero
3280 or obviously equal to some other affine expression, use
3282 #include <isl/aff.h>
3283 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3284 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3285 __isl_keep isl_aff *aff2);
3286 int isl_pw_aff_plain_is_equal(
3287 __isl_keep isl_pw_aff *pwaff1,
3288 __isl_keep isl_pw_aff *pwaff2);
3292 #include <isl/aff.h>
3293 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3294 __isl_take isl_aff *aff2);
3295 __isl_give isl_pw_aff *isl_pw_aff_add(
3296 __isl_take isl_pw_aff *pwaff1,
3297 __isl_take isl_pw_aff *pwaff2);
3298 __isl_give isl_pw_aff *isl_pw_aff_min(
3299 __isl_take isl_pw_aff *pwaff1,
3300 __isl_take isl_pw_aff *pwaff2);
3301 __isl_give isl_pw_aff *isl_pw_aff_max(
3302 __isl_take isl_pw_aff *pwaff1,
3303 __isl_take isl_pw_aff *pwaff2);
3304 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3305 __isl_take isl_aff *aff2);
3306 __isl_give isl_pw_aff *isl_pw_aff_sub(
3307 __isl_take isl_pw_aff *pwaff1,
3308 __isl_take isl_pw_aff *pwaff2);
3309 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3310 __isl_give isl_pw_aff *isl_pw_aff_neg(
3311 __isl_take isl_pw_aff *pwaff);
3312 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3313 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3314 __isl_take isl_pw_aff *pwaff);
3315 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3316 __isl_give isl_pw_aff *isl_pw_aff_floor(
3317 __isl_take isl_pw_aff *pwaff);
3318 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3320 __isl_give isl_pw_aff *isl_pw_aff_mod(
3321 __isl_take isl_pw_aff *pwaff, isl_int mod);
3322 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3324 __isl_give isl_pw_aff *isl_pw_aff_scale(
3325 __isl_take isl_pw_aff *pwaff, isl_int f);
3326 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3328 __isl_give isl_aff *isl_aff_scale_down_ui(
3329 __isl_take isl_aff *aff, unsigned f);
3330 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3331 __isl_take isl_pw_aff *pwaff, isl_int f);
3333 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3334 __isl_take isl_pw_aff_list *list);
3335 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3336 __isl_take isl_pw_aff_list *list);
3338 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3339 __isl_take isl_pw_aff *pwqp);
3341 __isl_give isl_aff *isl_aff_align_params(
3342 __isl_take isl_aff *aff,
3343 __isl_take isl_space *model);
3344 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3345 __isl_take isl_pw_aff *pwaff,
3346 __isl_take isl_space *model);
3348 __isl_give isl_aff *isl_aff_project_domain_on_params(
3349 __isl_take isl_aff *aff);
3351 __isl_give isl_aff *isl_aff_gist_params(
3352 __isl_take isl_aff *aff,
3353 __isl_take isl_set *context);
3354 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3355 __isl_take isl_set *context);
3356 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3357 __isl_take isl_pw_aff *pwaff,
3358 __isl_take isl_set *context);
3359 __isl_give isl_pw_aff *isl_pw_aff_gist(
3360 __isl_take isl_pw_aff *pwaff,
3361 __isl_take isl_set *context);
3363 __isl_give isl_set *isl_pw_aff_domain(
3364 __isl_take isl_pw_aff *pwaff);
3365 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3366 __isl_take isl_pw_aff *pa,
3367 __isl_take isl_set *set);
3368 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3369 __isl_take isl_pw_aff *pa,
3370 __isl_take isl_set *set);
3372 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3373 __isl_take isl_aff *aff2);
3374 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3375 __isl_take isl_aff *aff2);
3376 __isl_give isl_pw_aff *isl_pw_aff_mul(
3377 __isl_take isl_pw_aff *pwaff1,
3378 __isl_take isl_pw_aff *pwaff2);
3379 __isl_give isl_pw_aff *isl_pw_aff_div(
3380 __isl_take isl_pw_aff *pa1,
3381 __isl_take isl_pw_aff *pa2);
3382 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3383 __isl_take isl_pw_aff *pa1,
3384 __isl_take isl_pw_aff *pa2);
3385 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3386 __isl_take isl_pw_aff *pa1,
3387 __isl_take isl_pw_aff *pa2);
3389 When multiplying two affine expressions, at least one of the two needs
3390 to be a constant. Similarly, when dividing an affine expression by another,
3391 the second expression needs to be a constant.
3392 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3393 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3396 #include <isl/aff.h>
3397 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3398 __isl_take isl_aff *aff);
3399 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3400 __isl_take isl_aff *aff);
3401 __isl_give isl_basic_set *isl_aff_le_basic_set(
3402 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3403 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3404 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3405 __isl_give isl_set *isl_pw_aff_eq_set(
3406 __isl_take isl_pw_aff *pwaff1,
3407 __isl_take isl_pw_aff *pwaff2);
3408 __isl_give isl_set *isl_pw_aff_ne_set(
3409 __isl_take isl_pw_aff *pwaff1,
3410 __isl_take isl_pw_aff *pwaff2);
3411 __isl_give isl_set *isl_pw_aff_le_set(
3412 __isl_take isl_pw_aff *pwaff1,
3413 __isl_take isl_pw_aff *pwaff2);
3414 __isl_give isl_set *isl_pw_aff_lt_set(
3415 __isl_take isl_pw_aff *pwaff1,
3416 __isl_take isl_pw_aff *pwaff2);
3417 __isl_give isl_set *isl_pw_aff_ge_set(
3418 __isl_take isl_pw_aff *pwaff1,
3419 __isl_take isl_pw_aff *pwaff2);
3420 __isl_give isl_set *isl_pw_aff_gt_set(
3421 __isl_take isl_pw_aff *pwaff1,
3422 __isl_take isl_pw_aff *pwaff2);
3424 __isl_give isl_set *isl_pw_aff_list_eq_set(
3425 __isl_take isl_pw_aff_list *list1,
3426 __isl_take isl_pw_aff_list *list2);
3427 __isl_give isl_set *isl_pw_aff_list_ne_set(
3428 __isl_take isl_pw_aff_list *list1,
3429 __isl_take isl_pw_aff_list *list2);
3430 __isl_give isl_set *isl_pw_aff_list_le_set(
3431 __isl_take isl_pw_aff_list *list1,
3432 __isl_take isl_pw_aff_list *list2);
3433 __isl_give isl_set *isl_pw_aff_list_lt_set(
3434 __isl_take isl_pw_aff_list *list1,
3435 __isl_take isl_pw_aff_list *list2);
3436 __isl_give isl_set *isl_pw_aff_list_ge_set(
3437 __isl_take isl_pw_aff_list *list1,
3438 __isl_take isl_pw_aff_list *list2);
3439 __isl_give isl_set *isl_pw_aff_list_gt_set(
3440 __isl_take isl_pw_aff_list *list1,
3441 __isl_take isl_pw_aff_list *list2);
3443 The function C<isl_aff_neg_basic_set> returns a basic set
3444 containing those elements in the domain space
3445 of C<aff> where C<aff> is negative.
3446 The function C<isl_aff_ge_basic_set> returns a basic set
3447 containing those elements in the shared space
3448 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3449 The function C<isl_pw_aff_ge_set> returns a set
3450 containing those elements in the shared domain
3451 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3452 The functions operating on C<isl_pw_aff_list> apply the corresponding
3453 C<isl_pw_aff> function to each pair of elements in the two lists.
3455 #include <isl/aff.h>
3456 __isl_give isl_set *isl_pw_aff_nonneg_set(
3457 __isl_take isl_pw_aff *pwaff);
3458 __isl_give isl_set *isl_pw_aff_zero_set(
3459 __isl_take isl_pw_aff *pwaff);
3460 __isl_give isl_set *isl_pw_aff_non_zero_set(
3461 __isl_take isl_pw_aff *pwaff);
3463 The function C<isl_pw_aff_nonneg_set> returns a set
3464 containing those elements in the domain
3465 of C<pwaff> where C<pwaff> is non-negative.
3467 #include <isl/aff.h>
3468 __isl_give isl_pw_aff *isl_pw_aff_cond(
3469 __isl_take isl_pw_aff *cond,
3470 __isl_take isl_pw_aff *pwaff_true,
3471 __isl_take isl_pw_aff *pwaff_false);
3473 The function C<isl_pw_aff_cond> performs a conditional operator
3474 and returns an expression that is equal to C<pwaff_true>
3475 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3476 where C<cond> is zero.
3478 #include <isl/aff.h>
3479 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3480 __isl_take isl_pw_aff *pwaff1,
3481 __isl_take isl_pw_aff *pwaff2);
3482 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3483 __isl_take isl_pw_aff *pwaff1,
3484 __isl_take isl_pw_aff *pwaff2);
3485 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3486 __isl_take isl_pw_aff *pwaff1,
3487 __isl_take isl_pw_aff *pwaff2);
3489 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3490 expression with a domain that is the union of those of C<pwaff1> and
3491 C<pwaff2> and such that on each cell, the quasi-affine expression is
3492 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3493 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3494 associated expression is the defined one.
3496 An expression can be read from input using
3498 #include <isl/aff.h>
3499 __isl_give isl_aff *isl_aff_read_from_str(
3500 isl_ctx *ctx, const char *str);
3501 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3502 isl_ctx *ctx, const char *str);
3504 An expression can be printed using
3506 #include <isl/aff.h>
3507 __isl_give isl_printer *isl_printer_print_aff(
3508 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3510 __isl_give isl_printer *isl_printer_print_pw_aff(
3511 __isl_take isl_printer *p,
3512 __isl_keep isl_pw_aff *pwaff);
3514 =head2 Piecewise Multiple Quasi Affine Expressions
3516 An C<isl_multi_aff> object represents a sequence of
3517 zero or more affine expressions, all defined on the same domain space.
3519 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3522 #include <isl/aff.h>
3523 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3524 __isl_take isl_space *space,
3525 __isl_take isl_aff_list *list);
3527 An empty piecewise multiple quasi affine expression (one with no cells),
3528 the zero piecewise multiple quasi affine expression (with value zero
3529 for each output dimension),
3530 a piecewise multiple quasi affine expression with a single cell (with
3531 either a universe or a specified domain) or
3532 a zero-dimensional piecewise multiple quasi affine expression
3534 can be created using the following functions.
3536 #include <isl/aff.h>
3537 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3538 __isl_take isl_space *space);
3539 __isl_give isl_multi_aff *isl_multi_aff_zero(
3540 __isl_take isl_space *space);
3541 __isl_give isl_multi_aff *isl_multi_aff_identity(
3542 __isl_take isl_space *space);
3543 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3544 __isl_take isl_space *space);
3545 __isl_give isl_pw_multi_aff *
3546 isl_pw_multi_aff_from_multi_aff(
3547 __isl_take isl_multi_aff *ma);
3548 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3549 __isl_take isl_set *set,
3550 __isl_take isl_multi_aff *maff);
3551 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3552 __isl_take isl_set *set);
3554 __isl_give isl_union_pw_multi_aff *
3555 isl_union_pw_multi_aff_empty(
3556 __isl_take isl_space *space);
3557 __isl_give isl_union_pw_multi_aff *
3558 isl_union_pw_multi_aff_add_pw_multi_aff(
3559 __isl_take isl_union_pw_multi_aff *upma,
3560 __isl_take isl_pw_multi_aff *pma);
3561 __isl_give isl_union_pw_multi_aff *
3562 isl_union_pw_multi_aff_from_domain(
3563 __isl_take isl_union_set *uset);
3565 A piecewise multiple quasi affine expression can also be initialized
3566 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3567 and the C<isl_map> is single-valued.
3569 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3570 __isl_take isl_set *set);
3571 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3572 __isl_take isl_map *map);
3574 Multiple quasi affine expressions can be copied and freed using
3576 #include <isl/aff.h>
3577 __isl_give isl_multi_aff *isl_multi_aff_copy(
3578 __isl_keep isl_multi_aff *maff);
3579 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3581 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3582 __isl_keep isl_pw_multi_aff *pma);
3583 void *isl_pw_multi_aff_free(
3584 __isl_take isl_pw_multi_aff *pma);
3586 __isl_give isl_union_pw_multi_aff *
3587 isl_union_pw_multi_aff_copy(
3588 __isl_keep isl_union_pw_multi_aff *upma);
3589 void *isl_union_pw_multi_aff_free(
3590 __isl_take isl_union_pw_multi_aff *upma);
3592 The expression can be inspected using
3594 #include <isl/aff.h>
3595 isl_ctx *isl_multi_aff_get_ctx(
3596 __isl_keep isl_multi_aff *maff);
3597 isl_ctx *isl_pw_multi_aff_get_ctx(
3598 __isl_keep isl_pw_multi_aff *pma);
3599 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3600 __isl_keep isl_union_pw_multi_aff *upma);
3601 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3602 enum isl_dim_type type);
3603 unsigned isl_pw_multi_aff_dim(
3604 __isl_keep isl_pw_multi_aff *pma,
3605 enum isl_dim_type type);
3606 __isl_give isl_aff *isl_multi_aff_get_aff(
3607 __isl_keep isl_multi_aff *multi, int pos);
3608 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3609 __isl_keep isl_pw_multi_aff *pma, int pos);
3610 const char *isl_pw_multi_aff_get_dim_name(
3611 __isl_keep isl_pw_multi_aff *pma,
3612 enum isl_dim_type type, unsigned pos);
3613 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3614 __isl_keep isl_pw_multi_aff *pma,
3615 enum isl_dim_type type, unsigned pos);
3616 const char *isl_multi_aff_get_tuple_name(
3617 __isl_keep isl_multi_aff *multi,
3618 enum isl_dim_type type);
3619 int isl_pw_multi_aff_has_tuple_name(
3620 __isl_keep isl_pw_multi_aff *pma,
3621 enum isl_dim_type type);
3622 const char *isl_pw_multi_aff_get_tuple_name(
3623 __isl_keep isl_pw_multi_aff *pma,
3624 enum isl_dim_type type);
3625 int isl_pw_multi_aff_has_tuple_id(
3626 __isl_keep isl_pw_multi_aff *pma,
3627 enum isl_dim_type type);
3628 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3629 __isl_keep isl_pw_multi_aff *pma,
3630 enum isl_dim_type type);
3632 int isl_pw_multi_aff_foreach_piece(
3633 __isl_keep isl_pw_multi_aff *pma,
3634 int (*fn)(__isl_take isl_set *set,
3635 __isl_take isl_multi_aff *maff,
3636 void *user), void *user);
3638 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3639 __isl_keep isl_union_pw_multi_aff *upma,
3640 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3641 void *user), void *user);
3643 It can be modified using
3645 #include <isl/aff.h>
3646 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3647 __isl_take isl_multi_aff *multi, int pos,
3648 __isl_take isl_aff *aff);
3649 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3650 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3651 __isl_take isl_pw_aff *pa);
3652 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3653 __isl_take isl_multi_aff *maff,
3654 enum isl_dim_type type, unsigned pos, const char *s);
3655 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3656 __isl_take isl_multi_aff *maff,
3657 enum isl_dim_type type, __isl_take isl_id *id);
3658 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3659 __isl_take isl_pw_multi_aff *pma,
3660 enum isl_dim_type type, __isl_take isl_id *id);
3662 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3663 __isl_take isl_multi_aff *maff,
3664 enum isl_dim_type type, unsigned first, unsigned n);
3665 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
3666 __isl_take isl_pw_multi_aff *pma,
3667 enum isl_dim_type type, unsigned first, unsigned n);
3669 To check whether two multiple affine expressions are
3670 obviously equal to each other, use
3672 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3673 __isl_keep isl_multi_aff *maff2);
3674 int isl_pw_multi_aff_plain_is_equal(
3675 __isl_keep isl_pw_multi_aff *pma1,
3676 __isl_keep isl_pw_multi_aff *pma2);
3680 #include <isl/aff.h>
3681 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3682 __isl_take isl_pw_multi_aff *pma1,
3683 __isl_take isl_pw_multi_aff *pma2);
3684 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3685 __isl_take isl_pw_multi_aff *pma1,
3686 __isl_take isl_pw_multi_aff *pma2);
3687 __isl_give isl_multi_aff *isl_multi_aff_add(
3688 __isl_take isl_multi_aff *maff1,
3689 __isl_take isl_multi_aff *maff2);
3690 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3691 __isl_take isl_pw_multi_aff *pma1,
3692 __isl_take isl_pw_multi_aff *pma2);
3693 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3694 __isl_take isl_union_pw_multi_aff *upma1,
3695 __isl_take isl_union_pw_multi_aff *upma2);
3696 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3697 __isl_take isl_pw_multi_aff *pma1,
3698 __isl_take isl_pw_multi_aff *pma2);
3699 __isl_give isl_multi_aff *isl_multi_aff_scale(
3700 __isl_take isl_multi_aff *maff,
3702 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3703 __isl_take isl_pw_multi_aff *pma,
3704 __isl_take isl_set *set);
3705 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3706 __isl_take isl_pw_multi_aff *pma,
3707 __isl_take isl_set *set);
3708 __isl_give isl_multi_aff *isl_multi_aff_lift(
3709 __isl_take isl_multi_aff *maff,
3710 __isl_give isl_local_space **ls);
3711 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3712 __isl_take isl_pw_multi_aff *pma);
3713 __isl_give isl_multi_aff *isl_multi_aff_align_params(
3714 __isl_take isl_multi_aff *multi,
3715 __isl_take isl_space *model);
3716 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
3717 __isl_take isl_pw_multi_aff *pma,
3718 __isl_take isl_space *model);
3719 __isl_give isl_pw_multi_aff *
3720 isl_pw_multi_aff_project_domain_on_params(
3721 __isl_take isl_pw_multi_aff *pma);
3722 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3723 __isl_take isl_multi_aff *maff,
3724 __isl_take isl_set *context);
3725 __isl_give isl_multi_aff *isl_multi_aff_gist(
3726 __isl_take isl_multi_aff *maff,
3727 __isl_take isl_set *context);
3728 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3729 __isl_take isl_pw_multi_aff *pma,
3730 __isl_take isl_set *set);
3731 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3732 __isl_take isl_pw_multi_aff *pma,
3733 __isl_take isl_set *set);
3734 __isl_give isl_set *isl_pw_multi_aff_domain(
3735 __isl_take isl_pw_multi_aff *pma);
3736 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3737 __isl_take isl_union_pw_multi_aff *upma);
3738 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3739 __isl_take isl_multi_aff *ma1,
3740 __isl_take isl_multi_aff *ma2);
3741 __isl_give isl_multi_aff *isl_multi_aff_product(
3742 __isl_take isl_multi_aff *ma1,
3743 __isl_take isl_multi_aff *ma2);
3744 __isl_give isl_pw_multi_aff *
3745 isl_pw_multi_aff_flat_range_product(
3746 __isl_take isl_pw_multi_aff *pma1,
3747 __isl_take isl_pw_multi_aff *pma2);
3748 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3749 __isl_take isl_pw_multi_aff *pma1,
3750 __isl_take isl_pw_multi_aff *pma2);
3751 __isl_give isl_union_pw_multi_aff *
3752 isl_union_pw_multi_aff_flat_range_product(
3753 __isl_take isl_union_pw_multi_aff *upma1,
3754 __isl_take isl_union_pw_multi_aff *upma2);
3756 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3757 then it is assigned the local space that lies at the basis of
3758 the lifting applied.
3760 __isl_give isl_set *isl_multi_aff_lex_le_set(
3761 __isl_take isl_multi_aff *ma1,
3762 __isl_take isl_multi_aff *ma2);
3763 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3764 __isl_take isl_multi_aff *ma1,
3765 __isl_take isl_multi_aff *ma2);
3767 The function C<isl_multi_aff_lex_le_set> returns a set
3768 containing those elements in the shared domain space
3769 where C<ma1> is lexicographically smaller than or
3772 An expression can be read from input using
3774 #include <isl/aff.h>
3775 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3776 isl_ctx *ctx, const char *str);
3777 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3778 isl_ctx *ctx, const char *str);
3780 An expression can be printed using
3782 #include <isl/aff.h>
3783 __isl_give isl_printer *isl_printer_print_multi_aff(
3784 __isl_take isl_printer *p,
3785 __isl_keep isl_multi_aff *maff);
3786 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3787 __isl_take isl_printer *p,
3788 __isl_keep isl_pw_multi_aff *pma);
3789 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3790 __isl_take isl_printer *p,
3791 __isl_keep isl_union_pw_multi_aff *upma);
3795 Points are elements of a set. They can be used to construct
3796 simple sets (boxes) or they can be used to represent the
3797 individual elements of a set.
3798 The zero point (the origin) can be created using
3800 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3802 The coordinates of a point can be inspected, set and changed
3805 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3806 enum isl_dim_type type, int pos, isl_int *v);
3807 __isl_give isl_point *isl_point_set_coordinate(
3808 __isl_take isl_point *pnt,
3809 enum isl_dim_type type, int pos, isl_int v);
3811 __isl_give isl_point *isl_point_add_ui(
3812 __isl_take isl_point *pnt,
3813 enum isl_dim_type type, int pos, unsigned val);
3814 __isl_give isl_point *isl_point_sub_ui(
3815 __isl_take isl_point *pnt,
3816 enum isl_dim_type type, int pos, unsigned val);
3818 Other properties can be obtained using
3820 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3822 Points can be copied or freed using
3824 __isl_give isl_point *isl_point_copy(
3825 __isl_keep isl_point *pnt);
3826 void isl_point_free(__isl_take isl_point *pnt);
3828 A singleton set can be created from a point using
3830 __isl_give isl_basic_set *isl_basic_set_from_point(
3831 __isl_take isl_point *pnt);
3832 __isl_give isl_set *isl_set_from_point(
3833 __isl_take isl_point *pnt);
3835 and a box can be created from two opposite extremal points using
3837 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3838 __isl_take isl_point *pnt1,
3839 __isl_take isl_point *pnt2);
3840 __isl_give isl_set *isl_set_box_from_points(
3841 __isl_take isl_point *pnt1,
3842 __isl_take isl_point *pnt2);
3844 All elements of a B<bounded> (union) set can be enumerated using
3845 the following functions.
3847 int isl_set_foreach_point(__isl_keep isl_set *set,
3848 int (*fn)(__isl_take isl_point *pnt, void *user),
3850 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3851 int (*fn)(__isl_take isl_point *pnt, void *user),
3854 The function C<fn> is called for each integer point in
3855 C<set> with as second argument the last argument of
3856 the C<isl_set_foreach_point> call. The function C<fn>
3857 should return C<0> on success and C<-1> on failure.
3858 In the latter case, C<isl_set_foreach_point> will stop
3859 enumerating and return C<-1> as well.
3860 If the enumeration is performed successfully and to completion,
3861 then C<isl_set_foreach_point> returns C<0>.
3863 To obtain a single point of a (basic) set, use
3865 __isl_give isl_point *isl_basic_set_sample_point(
3866 __isl_take isl_basic_set *bset);
3867 __isl_give isl_point *isl_set_sample_point(
3868 __isl_take isl_set *set);
3870 If C<set> does not contain any (integer) points, then the
3871 resulting point will be ``void'', a property that can be
3874 int isl_point_is_void(__isl_keep isl_point *pnt);
3876 =head2 Piecewise Quasipolynomials
3878 A piecewise quasipolynomial is a particular kind of function that maps
3879 a parametric point to a rational value.
3880 More specifically, a quasipolynomial is a polynomial expression in greatest
3881 integer parts of affine expressions of parameters and variables.
3882 A piecewise quasipolynomial is a subdivision of a given parametric
3883 domain into disjoint cells with a quasipolynomial associated to
3884 each cell. The value of the piecewise quasipolynomial at a given
3885 point is the value of the quasipolynomial associated to the cell
3886 that contains the point. Outside of the union of cells,
3887 the value is assumed to be zero.
3888 For example, the piecewise quasipolynomial
3890 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3892 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3893 A given piecewise quasipolynomial has a fixed domain dimension.
3894 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3895 defined over different domains.
3896 Piecewise quasipolynomials are mainly used by the C<barvinok>
3897 library for representing the number of elements in a parametric set or map.
3898 For example, the piecewise quasipolynomial above represents
3899 the number of points in the map
3901 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3903 =head3 Input and Output
3905 Piecewise quasipolynomials can be read from input using
3907 __isl_give isl_union_pw_qpolynomial *
3908 isl_union_pw_qpolynomial_read_from_str(
3909 isl_ctx *ctx, const char *str);
3911 Quasipolynomials and piecewise quasipolynomials can be printed
3912 using the following functions.
3914 __isl_give isl_printer *isl_printer_print_qpolynomial(
3915 __isl_take isl_printer *p,
3916 __isl_keep isl_qpolynomial *qp);
3918 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3919 __isl_take isl_printer *p,
3920 __isl_keep isl_pw_qpolynomial *pwqp);
3922 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3923 __isl_take isl_printer *p,
3924 __isl_keep isl_union_pw_qpolynomial *upwqp);
3926 The output format of the printer
3927 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3928 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3930 In case of printing in C<ISL_FORMAT_C>, the user may want
3931 to set the names of all dimensions
3933 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3934 __isl_take isl_qpolynomial *qp,
3935 enum isl_dim_type type, unsigned pos,
3937 __isl_give isl_pw_qpolynomial *
3938 isl_pw_qpolynomial_set_dim_name(
3939 __isl_take isl_pw_qpolynomial *pwqp,
3940 enum isl_dim_type type, unsigned pos,
3943 =head3 Creating New (Piecewise) Quasipolynomials
3945 Some simple quasipolynomials can be created using the following functions.
3946 More complicated quasipolynomials can be created by applying
3947 operations such as addition and multiplication
3948 on the resulting quasipolynomials
3950 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3951 __isl_take isl_space *domain);
3952 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3953 __isl_take isl_space *domain);
3954 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3955 __isl_take isl_space *domain);
3956 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3957 __isl_take isl_space *domain);
3958 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3959 __isl_take isl_space *domain);
3960 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3961 __isl_take isl_space *domain,
3962 const isl_int n, const isl_int d);
3963 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3964 __isl_take isl_space *domain,
3965 enum isl_dim_type type, unsigned pos);
3966 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3967 __isl_take isl_aff *aff);
3969 Note that the space in which a quasipolynomial lives is a map space
3970 with a one-dimensional range. The C<domain> argument in some of
3971 the functions above corresponds to the domain of this map space.
3973 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3974 with a single cell can be created using the following functions.
3975 Multiple of these single cell piecewise quasipolynomials can
3976 be combined to create more complicated piecewise quasipolynomials.
3978 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3979 __isl_take isl_space *space);
3980 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3981 __isl_take isl_set *set,
3982 __isl_take isl_qpolynomial *qp);
3983 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3984 __isl_take isl_qpolynomial *qp);
3985 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3986 __isl_take isl_pw_aff *pwaff);
3988 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3989 __isl_take isl_space *space);
3990 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3991 __isl_take isl_pw_qpolynomial *pwqp);
3992 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3993 __isl_take isl_union_pw_qpolynomial *upwqp,
3994 __isl_take isl_pw_qpolynomial *pwqp);
3996 Quasipolynomials can be copied and freed again using the following
3999 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4000 __isl_keep isl_qpolynomial *qp);
4001 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4003 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4004 __isl_keep isl_pw_qpolynomial *pwqp);
4005 void *isl_pw_qpolynomial_free(
4006 __isl_take isl_pw_qpolynomial *pwqp);
4008 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4009 __isl_keep isl_union_pw_qpolynomial *upwqp);
4010 void *isl_union_pw_qpolynomial_free(
4011 __isl_take isl_union_pw_qpolynomial *upwqp);
4013 =head3 Inspecting (Piecewise) Quasipolynomials
4015 To iterate over all piecewise quasipolynomials in a union
4016 piecewise quasipolynomial, use the following function
4018 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4019 __isl_keep isl_union_pw_qpolynomial *upwqp,
4020 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4023 To extract the piecewise quasipolynomial in a given space from a union, use
4025 __isl_give isl_pw_qpolynomial *
4026 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4027 __isl_keep isl_union_pw_qpolynomial *upwqp,
4028 __isl_take isl_space *space);
4030 To iterate over the cells in a piecewise quasipolynomial,
4031 use either of the following two functions
4033 int isl_pw_qpolynomial_foreach_piece(
4034 __isl_keep isl_pw_qpolynomial *pwqp,
4035 int (*fn)(__isl_take isl_set *set,
4036 __isl_take isl_qpolynomial *qp,
4037 void *user), void *user);
4038 int isl_pw_qpolynomial_foreach_lifted_piece(
4039 __isl_keep isl_pw_qpolynomial *pwqp,
4040 int (*fn)(__isl_take isl_set *set,
4041 __isl_take isl_qpolynomial *qp,
4042 void *user), void *user);
4044 As usual, the function C<fn> should return C<0> on success
4045 and C<-1> on failure. The difference between
4046 C<isl_pw_qpolynomial_foreach_piece> and
4047 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4048 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4049 compute unique representations for all existentially quantified
4050 variables and then turn these existentially quantified variables
4051 into extra set variables, adapting the associated quasipolynomial
4052 accordingly. This means that the C<set> passed to C<fn>
4053 will not have any existentially quantified variables, but that
4054 the dimensions of the sets may be different for different
4055 invocations of C<fn>.
4057 To iterate over all terms in a quasipolynomial,
4060 int isl_qpolynomial_foreach_term(
4061 __isl_keep isl_qpolynomial *qp,
4062 int (*fn)(__isl_take isl_term *term,
4063 void *user), void *user);
4065 The terms themselves can be inspected and freed using
4068 unsigned isl_term_dim(__isl_keep isl_term *term,
4069 enum isl_dim_type type);
4070 void isl_term_get_num(__isl_keep isl_term *term,
4072 void isl_term_get_den(__isl_keep isl_term *term,
4074 int isl_term_get_exp(__isl_keep isl_term *term,
4075 enum isl_dim_type type, unsigned pos);
4076 __isl_give isl_aff *isl_term_get_div(
4077 __isl_keep isl_term *term, unsigned pos);
4078 void isl_term_free(__isl_take isl_term *term);
4080 Each term is a product of parameters, set variables and
4081 integer divisions. The function C<isl_term_get_exp>
4082 returns the exponent of a given dimensions in the given term.
4083 The C<isl_int>s in the arguments of C<isl_term_get_num>
4084 and C<isl_term_get_den> need to have been initialized
4085 using C<isl_int_init> before calling these functions.
4087 =head3 Properties of (Piecewise) Quasipolynomials
4089 To check whether a quasipolynomial is actually a constant,
4090 use the following function.
4092 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4093 isl_int *n, isl_int *d);
4095 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4096 then the numerator and denominator of the constant
4097 are returned in C<*n> and C<*d>, respectively.
4099 To check whether two union piecewise quasipolynomials are
4100 obviously equal, use
4102 int isl_union_pw_qpolynomial_plain_is_equal(
4103 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4104 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4106 =head3 Operations on (Piecewise) Quasipolynomials
4108 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4109 __isl_take isl_qpolynomial *qp, isl_int v);
4110 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4111 __isl_take isl_qpolynomial *qp);
4112 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4113 __isl_take isl_qpolynomial *qp1,
4114 __isl_take isl_qpolynomial *qp2);
4115 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4116 __isl_take isl_qpolynomial *qp1,
4117 __isl_take isl_qpolynomial *qp2);
4118 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4119 __isl_take isl_qpolynomial *qp1,
4120 __isl_take isl_qpolynomial *qp2);
4121 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4122 __isl_take isl_qpolynomial *qp, unsigned exponent);
4124 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4125 __isl_take isl_pw_qpolynomial *pwqp1,
4126 __isl_take isl_pw_qpolynomial *pwqp2);
4127 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4128 __isl_take isl_pw_qpolynomial *pwqp1,
4129 __isl_take isl_pw_qpolynomial *pwqp2);
4130 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4131 __isl_take isl_pw_qpolynomial *pwqp1,
4132 __isl_take isl_pw_qpolynomial *pwqp2);
4133 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4134 __isl_take isl_pw_qpolynomial *pwqp);
4135 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4136 __isl_take isl_pw_qpolynomial *pwqp1,
4137 __isl_take isl_pw_qpolynomial *pwqp2);
4138 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4139 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4141 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4142 __isl_take isl_union_pw_qpolynomial *upwqp1,
4143 __isl_take isl_union_pw_qpolynomial *upwqp2);
4144 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4145 __isl_take isl_union_pw_qpolynomial *upwqp1,
4146 __isl_take isl_union_pw_qpolynomial *upwqp2);
4147 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4148 __isl_take isl_union_pw_qpolynomial *upwqp1,
4149 __isl_take isl_union_pw_qpolynomial *upwqp2);
4151 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4152 __isl_take isl_pw_qpolynomial *pwqp,
4153 __isl_take isl_point *pnt);
4155 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4156 __isl_take isl_union_pw_qpolynomial *upwqp,
4157 __isl_take isl_point *pnt);
4159 __isl_give isl_set *isl_pw_qpolynomial_domain(
4160 __isl_take isl_pw_qpolynomial *pwqp);
4161 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4162 __isl_take isl_pw_qpolynomial *pwpq,
4163 __isl_take isl_set *set);
4164 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4165 __isl_take isl_pw_qpolynomial *pwpq,
4166 __isl_take isl_set *set);
4168 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4169 __isl_take isl_union_pw_qpolynomial *upwqp);
4170 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4171 __isl_take isl_union_pw_qpolynomial *upwpq,
4172 __isl_take isl_union_set *uset);
4173 __isl_give isl_union_pw_qpolynomial *
4174 isl_union_pw_qpolynomial_intersect_params(
4175 __isl_take isl_union_pw_qpolynomial *upwpq,
4176 __isl_take isl_set *set);
4178 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4179 __isl_take isl_qpolynomial *qp,
4180 __isl_take isl_space *model);
4182 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4183 __isl_take isl_qpolynomial *qp);
4184 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4185 __isl_take isl_pw_qpolynomial *pwqp);
4187 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4188 __isl_take isl_union_pw_qpolynomial *upwqp);
4190 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4191 __isl_take isl_qpolynomial *qp,
4192 __isl_take isl_set *context);
4193 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4194 __isl_take isl_qpolynomial *qp,
4195 __isl_take isl_set *context);
4197 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4198 __isl_take isl_pw_qpolynomial *pwqp,
4199 __isl_take isl_set *context);
4200 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4201 __isl_take isl_pw_qpolynomial *pwqp,
4202 __isl_take isl_set *context);
4204 __isl_give isl_union_pw_qpolynomial *
4205 isl_union_pw_qpolynomial_gist_params(
4206 __isl_take isl_union_pw_qpolynomial *upwqp,
4207 __isl_take isl_set *context);
4208 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4209 __isl_take isl_union_pw_qpolynomial *upwqp,
4210 __isl_take isl_union_set *context);
4212 The gist operation applies the gist operation to each of
4213 the cells in the domain of the input piecewise quasipolynomial.
4214 The context is also exploited
4215 to simplify the quasipolynomials associated to each cell.
4217 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4218 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4219 __isl_give isl_union_pw_qpolynomial *
4220 isl_union_pw_qpolynomial_to_polynomial(
4221 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4223 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4224 the polynomial will be an overapproximation. If C<sign> is negative,
4225 it will be an underapproximation. If C<sign> is zero, the approximation
4226 will lie somewhere in between.
4228 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4230 A piecewise quasipolynomial reduction is a piecewise
4231 reduction (or fold) of quasipolynomials.
4232 In particular, the reduction can be maximum or a minimum.
4233 The objects are mainly used to represent the result of
4234 an upper or lower bound on a quasipolynomial over its domain,
4235 i.e., as the result of the following function.
4237 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4238 __isl_take isl_pw_qpolynomial *pwqp,
4239 enum isl_fold type, int *tight);
4241 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4242 __isl_take isl_union_pw_qpolynomial *upwqp,
4243 enum isl_fold type, int *tight);
4245 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4246 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4247 is the returned bound is known be tight, i.e., for each value
4248 of the parameters there is at least
4249 one element in the domain that reaches the bound.
4250 If the domain of C<pwqp> is not wrapping, then the bound is computed
4251 over all elements in that domain and the result has a purely parametric
4252 domain. If the domain of C<pwqp> is wrapping, then the bound is
4253 computed over the range of the wrapped relation. The domain of the
4254 wrapped relation becomes the domain of the result.
4256 A (piecewise) quasipolynomial reduction can be copied or freed using the
4257 following functions.
4259 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4260 __isl_keep isl_qpolynomial_fold *fold);
4261 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4262 __isl_keep isl_pw_qpolynomial_fold *pwf);
4263 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4264 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4265 void isl_qpolynomial_fold_free(
4266 __isl_take isl_qpolynomial_fold *fold);
4267 void *isl_pw_qpolynomial_fold_free(
4268 __isl_take isl_pw_qpolynomial_fold *pwf);
4269 void *isl_union_pw_qpolynomial_fold_free(
4270 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4272 =head3 Printing Piecewise Quasipolynomial Reductions
4274 Piecewise quasipolynomial reductions can be printed
4275 using the following function.
4277 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4278 __isl_take isl_printer *p,
4279 __isl_keep isl_pw_qpolynomial_fold *pwf);
4280 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4281 __isl_take isl_printer *p,
4282 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4284 For C<isl_printer_print_pw_qpolynomial_fold>,
4285 output format of the printer
4286 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4287 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4288 output format of the printer
4289 needs to be set to C<ISL_FORMAT_ISL>.
4290 In case of printing in C<ISL_FORMAT_C>, the user may want
4291 to set the names of all dimensions
4293 __isl_give isl_pw_qpolynomial_fold *
4294 isl_pw_qpolynomial_fold_set_dim_name(
4295 __isl_take isl_pw_qpolynomial_fold *pwf,
4296 enum isl_dim_type type, unsigned pos,
4299 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4301 To iterate over all piecewise quasipolynomial reductions in a union
4302 piecewise quasipolynomial reduction, use the following function
4304 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4305 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4306 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4307 void *user), void *user);
4309 To iterate over the cells in a piecewise quasipolynomial reduction,
4310 use either of the following two functions
4312 int isl_pw_qpolynomial_fold_foreach_piece(
4313 __isl_keep isl_pw_qpolynomial_fold *pwf,
4314 int (*fn)(__isl_take isl_set *set,
4315 __isl_take isl_qpolynomial_fold *fold,
4316 void *user), void *user);
4317 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4318 __isl_keep isl_pw_qpolynomial_fold *pwf,
4319 int (*fn)(__isl_take isl_set *set,
4320 __isl_take isl_qpolynomial_fold *fold,
4321 void *user), void *user);
4323 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4324 of the difference between these two functions.
4326 To iterate over all quasipolynomials in a reduction, use
4328 int isl_qpolynomial_fold_foreach_qpolynomial(
4329 __isl_keep isl_qpolynomial_fold *fold,
4330 int (*fn)(__isl_take isl_qpolynomial *qp,
4331 void *user), void *user);
4333 =head3 Properties of Piecewise Quasipolynomial Reductions
4335 To check whether two union piecewise quasipolynomial reductions are
4336 obviously equal, use
4338 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4339 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4340 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4342 =head3 Operations on Piecewise Quasipolynomial Reductions
4344 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4345 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4347 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4348 __isl_take isl_pw_qpolynomial_fold *pwf1,
4349 __isl_take isl_pw_qpolynomial_fold *pwf2);
4351 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4352 __isl_take isl_pw_qpolynomial_fold *pwf1,
4353 __isl_take isl_pw_qpolynomial_fold *pwf2);
4355 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4356 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4357 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4359 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4360 __isl_take isl_pw_qpolynomial_fold *pwf,
4361 __isl_take isl_point *pnt);
4363 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4364 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4365 __isl_take isl_point *pnt);
4367 __isl_give isl_pw_qpolynomial_fold *
4368 isl_pw_qpolynomial_fold_intersect_params(
4369 __isl_take isl_pw_qpolynomial_fold *pwf,
4370 __isl_take isl_set *set);
4372 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4373 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4374 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4375 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4376 __isl_take isl_union_set *uset);
4377 __isl_give isl_union_pw_qpolynomial_fold *
4378 isl_union_pw_qpolynomial_fold_intersect_params(
4379 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4380 __isl_take isl_set *set);
4382 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4383 __isl_take isl_pw_qpolynomial_fold *pwf);
4385 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4386 __isl_take isl_pw_qpolynomial_fold *pwf);
4388 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4389 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4391 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4392 __isl_take isl_qpolynomial_fold *fold,
4393 __isl_take isl_set *context);
4394 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4395 __isl_take isl_qpolynomial_fold *fold,
4396 __isl_take isl_set *context);
4398 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4399 __isl_take isl_pw_qpolynomial_fold *pwf,
4400 __isl_take isl_set *context);
4401 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4402 __isl_take isl_pw_qpolynomial_fold *pwf,
4403 __isl_take isl_set *context);
4405 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4406 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4407 __isl_take isl_union_set *context);
4408 __isl_give isl_union_pw_qpolynomial_fold *
4409 isl_union_pw_qpolynomial_fold_gist_params(
4410 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4411 __isl_take isl_set *context);
4413 The gist operation applies the gist operation to each of
4414 the cells in the domain of the input piecewise quasipolynomial reduction.
4415 In future, the operation will also exploit the context
4416 to simplify the quasipolynomial reductions associated to each cell.
4418 __isl_give isl_pw_qpolynomial_fold *
4419 isl_set_apply_pw_qpolynomial_fold(
4420 __isl_take isl_set *set,
4421 __isl_take isl_pw_qpolynomial_fold *pwf,
4423 __isl_give isl_pw_qpolynomial_fold *
4424 isl_map_apply_pw_qpolynomial_fold(
4425 __isl_take isl_map *map,
4426 __isl_take isl_pw_qpolynomial_fold *pwf,
4428 __isl_give isl_union_pw_qpolynomial_fold *
4429 isl_union_set_apply_union_pw_qpolynomial_fold(
4430 __isl_take isl_union_set *uset,
4431 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4433 __isl_give isl_union_pw_qpolynomial_fold *
4434 isl_union_map_apply_union_pw_qpolynomial_fold(
4435 __isl_take isl_union_map *umap,
4436 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4439 The functions taking a map
4440 compose the given map with the given piecewise quasipolynomial reduction.
4441 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4442 over all elements in the intersection of the range of the map
4443 and the domain of the piecewise quasipolynomial reduction
4444 as a function of an element in the domain of the map.
4445 The functions taking a set compute a bound over all elements in the
4446 intersection of the set and the domain of the
4447 piecewise quasipolynomial reduction.
4449 =head2 Dependence Analysis
4451 C<isl> contains specialized functionality for performing
4452 array dataflow analysis. That is, given a I<sink> access relation
4453 and a collection of possible I<source> access relations,
4454 C<isl> can compute relations that describe
4455 for each iteration of the sink access, which iteration
4456 of which of the source access relations was the last
4457 to access the same data element before the given iteration
4459 The resulting dependence relations map source iterations
4460 to the corresponding sink iterations.
4461 To compute standard flow dependences, the sink should be
4462 a read, while the sources should be writes.
4463 If any of the source accesses are marked as being I<may>
4464 accesses, then there will be a dependence from the last
4465 I<must> access B<and> from any I<may> access that follows
4466 this last I<must> access.
4467 In particular, if I<all> sources are I<may> accesses,
4468 then memory based dependence analysis is performed.
4469 If, on the other hand, all sources are I<must> accesses,
4470 then value based dependence analysis is performed.
4472 #include <isl/flow.h>
4474 typedef int (*isl_access_level_before)(void *first, void *second);
4476 __isl_give isl_access_info *isl_access_info_alloc(
4477 __isl_take isl_map *sink,
4478 void *sink_user, isl_access_level_before fn,
4480 __isl_give isl_access_info *isl_access_info_add_source(
4481 __isl_take isl_access_info *acc,
4482 __isl_take isl_map *source, int must,
4484 void *isl_access_info_free(__isl_take isl_access_info *acc);
4486 __isl_give isl_flow *isl_access_info_compute_flow(
4487 __isl_take isl_access_info *acc);
4489 int isl_flow_foreach(__isl_keep isl_flow *deps,
4490 int (*fn)(__isl_take isl_map *dep, int must,
4491 void *dep_user, void *user),
4493 __isl_give isl_map *isl_flow_get_no_source(
4494 __isl_keep isl_flow *deps, int must);
4495 void isl_flow_free(__isl_take isl_flow *deps);
4497 The function C<isl_access_info_compute_flow> performs the actual
4498 dependence analysis. The other functions are used to construct
4499 the input for this function or to read off the output.
4501 The input is collected in an C<isl_access_info>, which can
4502 be created through a call to C<isl_access_info_alloc>.
4503 The arguments to this functions are the sink access relation
4504 C<sink>, a token C<sink_user> used to identify the sink
4505 access to the user, a callback function for specifying the
4506 relative order of source and sink accesses, and the number
4507 of source access relations that will be added.
4508 The callback function has type C<int (*)(void *first, void *second)>.
4509 The function is called with two user supplied tokens identifying
4510 either a source or the sink and it should return the shared nesting
4511 level and the relative order of the two accesses.
4512 In particular, let I<n> be the number of loops shared by
4513 the two accesses. If C<first> precedes C<second> textually,
4514 then the function should return I<2 * n + 1>; otherwise,
4515 it should return I<2 * n>.
4516 The sources can be added to the C<isl_access_info> by performing
4517 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4518 C<must> indicates whether the source is a I<must> access
4519 or a I<may> access. Note that a multi-valued access relation
4520 should only be marked I<must> if every iteration in the domain
4521 of the relation accesses I<all> elements in its image.
4522 The C<source_user> token is again used to identify
4523 the source access. The range of the source access relation
4524 C<source> should have the same dimension as the range
4525 of the sink access relation.
4526 The C<isl_access_info_free> function should usually not be
4527 called explicitly, because it is called implicitly by
4528 C<isl_access_info_compute_flow>.
4530 The result of the dependence analysis is collected in an
4531 C<isl_flow>. There may be elements of
4532 the sink access for which no preceding source access could be
4533 found or for which all preceding sources are I<may> accesses.
4534 The relations containing these elements can be obtained through
4535 calls to C<isl_flow_get_no_source>, the first with C<must> set
4536 and the second with C<must> unset.
4537 In the case of standard flow dependence analysis,
4538 with the sink a read and the sources I<must> writes,
4539 the first relation corresponds to the reads from uninitialized
4540 array elements and the second relation is empty.
4541 The actual flow dependences can be extracted using
4542 C<isl_flow_foreach>. This function will call the user-specified
4543 callback function C<fn> for each B<non-empty> dependence between
4544 a source and the sink. The callback function is called
4545 with four arguments, the actual flow dependence relation
4546 mapping source iterations to sink iterations, a boolean that
4547 indicates whether it is a I<must> or I<may> dependence, a token
4548 identifying the source and an additional C<void *> with value
4549 equal to the third argument of the C<isl_flow_foreach> call.
4550 A dependence is marked I<must> if it originates from a I<must>
4551 source and if it is not followed by any I<may> sources.
4553 After finishing with an C<isl_flow>, the user should call
4554 C<isl_flow_free> to free all associated memory.
4556 A higher-level interface to dependence analysis is provided
4557 by the following function.
4559 #include <isl/flow.h>
4561 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4562 __isl_take isl_union_map *must_source,
4563 __isl_take isl_union_map *may_source,
4564 __isl_take isl_union_map *schedule,
4565 __isl_give isl_union_map **must_dep,
4566 __isl_give isl_union_map **may_dep,
4567 __isl_give isl_union_map **must_no_source,
4568 __isl_give isl_union_map **may_no_source);
4570 The arrays are identified by the tuple names of the ranges
4571 of the accesses. The iteration domains by the tuple names
4572 of the domains of the accesses and of the schedule.
4573 The relative order of the iteration domains is given by the
4574 schedule. The relations returned through C<must_no_source>
4575 and C<may_no_source> are subsets of C<sink>.
4576 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4577 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4578 any of the other arguments is treated as an error.
4580 =head3 Interaction with Dependence Analysis
4582 During the dependence analysis, we frequently need to perform
4583 the following operation. Given a relation between sink iterations
4584 and potential source iterations from a particular source domain,
4585 what is the last potential source iteration corresponding to each
4586 sink iteration. It can sometimes be convenient to adjust
4587 the set of potential source iterations before or after each such operation.
4588 The prototypical example is fuzzy array dataflow analysis,
4589 where we need to analyze if, based on data-dependent constraints,
4590 the sink iteration can ever be executed without one or more of
4591 the corresponding potential source iterations being executed.
4592 If so, we can introduce extra parameters and select an unknown
4593 but fixed source iteration from the potential source iterations.
4594 To be able to perform such manipulations, C<isl> provides the following
4597 #include <isl/flow.h>
4599 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4600 __isl_keep isl_map *source_map,
4601 __isl_keep isl_set *sink, void *source_user,
4603 __isl_give isl_access_info *isl_access_info_set_restrict(
4604 __isl_take isl_access_info *acc,
4605 isl_access_restrict fn, void *user);
4607 The function C<isl_access_info_set_restrict> should be called
4608 before calling C<isl_access_info_compute_flow> and registers a callback function
4609 that will be called any time C<isl> is about to compute the last
4610 potential source. The first argument is the (reverse) proto-dependence,
4611 mapping sink iterations to potential source iterations.
4612 The second argument represents the sink iterations for which
4613 we want to compute the last source iteration.
4614 The third argument is the token corresponding to the source
4615 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4616 The callback is expected to return a restriction on either the input or
4617 the output of the operation computing the last potential source.
4618 If the input needs to be restricted then restrictions are needed
4619 for both the source and the sink iterations. The sink iterations
4620 and the potential source iterations will be intersected with these sets.
4621 If the output needs to be restricted then only a restriction on the source
4622 iterations is required.
4623 If any error occurs, the callback should return C<NULL>.
4624 An C<isl_restriction> object can be created, freed and inspected
4625 using the following functions.
4627 #include <isl/flow.h>
4629 __isl_give isl_restriction *isl_restriction_input(
4630 __isl_take isl_set *source_restr,
4631 __isl_take isl_set *sink_restr);
4632 __isl_give isl_restriction *isl_restriction_output(
4633 __isl_take isl_set *source_restr);
4634 __isl_give isl_restriction *isl_restriction_none(
4635 __isl_take isl_map *source_map);
4636 __isl_give isl_restriction *isl_restriction_empty(
4637 __isl_take isl_map *source_map);
4638 void *isl_restriction_free(
4639 __isl_take isl_restriction *restr);
4640 isl_ctx *isl_restriction_get_ctx(
4641 __isl_keep isl_restriction *restr);
4643 C<isl_restriction_none> and C<isl_restriction_empty> are special
4644 cases of C<isl_restriction_input>. C<isl_restriction_none>
4645 is essentially equivalent to
4647 isl_restriction_input(isl_set_universe(
4648 isl_space_range(isl_map_get_space(source_map))),
4650 isl_space_domain(isl_map_get_space(source_map))));
4652 whereas C<isl_restriction_empty> is essentially equivalent to
4654 isl_restriction_input(isl_set_empty(
4655 isl_space_range(isl_map_get_space(source_map))),
4657 isl_space_domain(isl_map_get_space(source_map))));
4661 B<The functionality described in this section is fairly new
4662 and may be subject to change.>
4664 The following function can be used to compute a schedule
4665 for a union of domains.
4666 By default, the algorithm used to construct the schedule is similar
4667 to that of C<Pluto>.
4668 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4670 The generated schedule respects all C<validity> dependences.
4671 That is, all dependence distances over these dependences in the
4672 scheduled space are lexicographically positive.
4673 The default algorithm tries to minimize the dependence distances over
4674 C<proximity> dependences.
4675 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4676 for groups of domains where the dependence distances have only
4677 non-negative values.
4678 When using Feautrier's algorithm, the C<proximity> dependence
4679 distances are only minimized during the extension to a
4680 full-dimensional schedule.
4682 #include <isl/schedule.h>
4683 __isl_give isl_schedule *isl_union_set_compute_schedule(
4684 __isl_take isl_union_set *domain,
4685 __isl_take isl_union_map *validity,
4686 __isl_take isl_union_map *proximity);
4687 void *isl_schedule_free(__isl_take isl_schedule *sched);
4689 A mapping from the domains to the scheduled space can be obtained
4690 from an C<isl_schedule> using the following function.
4692 __isl_give isl_union_map *isl_schedule_get_map(
4693 __isl_keep isl_schedule *sched);
4695 A representation of the schedule can be printed using
4697 __isl_give isl_printer *isl_printer_print_schedule(
4698 __isl_take isl_printer *p,
4699 __isl_keep isl_schedule *schedule);
4701 A representation of the schedule as a forest of bands can be obtained
4702 using the following function.
4704 __isl_give isl_band_list *isl_schedule_get_band_forest(
4705 __isl_keep isl_schedule *schedule);
4707 The individual bands can be visited in depth-first post-order
4708 using the following function.
4710 #include <isl/schedule.h>
4711 int isl_schedule_foreach_band(
4712 __isl_keep isl_schedule *sched,
4713 int (*fn)(__isl_keep isl_band *band, void *user),
4716 The list can be manipulated as explained in L<"Lists">.
4717 The bands inside the list can be copied and freed using the following
4720 #include <isl/band.h>
4721 __isl_give isl_band *isl_band_copy(
4722 __isl_keep isl_band *band);
4723 void *isl_band_free(__isl_take isl_band *band);
4725 Each band contains zero or more scheduling dimensions.
4726 These are referred to as the members of the band.
4727 The section of the schedule that corresponds to the band is
4728 referred to as the partial schedule of the band.
4729 For those nodes that participate in a band, the outer scheduling
4730 dimensions form the prefix schedule, while the inner scheduling
4731 dimensions form the suffix schedule.
4732 That is, if we take a cut of the band forest, then the union of
4733 the concatenations of the prefix, partial and suffix schedules of
4734 each band in the cut is equal to the entire schedule (modulo
4735 some possible padding at the end with zero scheduling dimensions).
4736 The properties of a band can be inspected using the following functions.
4738 #include <isl/band.h>
4739 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4741 int isl_band_has_children(__isl_keep isl_band *band);
4742 __isl_give isl_band_list *isl_band_get_children(
4743 __isl_keep isl_band *band);
4745 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4746 __isl_keep isl_band *band);
4747 __isl_give isl_union_map *isl_band_get_partial_schedule(
4748 __isl_keep isl_band *band);
4749 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4750 __isl_keep isl_band *band);
4752 int isl_band_n_member(__isl_keep isl_band *band);
4753 int isl_band_member_is_zero_distance(
4754 __isl_keep isl_band *band, int pos);
4756 int isl_band_list_foreach_band(
4757 __isl_keep isl_band_list *list,
4758 int (*fn)(__isl_keep isl_band *band, void *user),
4761 Note that a scheduling dimension is considered to be ``zero
4762 distance'' if it does not carry any proximity dependences
4764 That is, if the dependence distances of the proximity
4765 dependences are all zero in that direction (for fixed
4766 iterations of outer bands).
4767 Like C<isl_schedule_foreach_band>,
4768 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4769 in depth-first post-order.
4771 A band can be tiled using the following function.
4773 #include <isl/band.h>
4774 int isl_band_tile(__isl_keep isl_band *band,
4775 __isl_take isl_vec *sizes);
4777 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4779 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4781 The C<isl_band_tile> function tiles the band using the given tile sizes
4782 inside its schedule.
4783 A new child band is created to represent the point loops and it is
4784 inserted between the modified band and its children.
4785 The C<tile_scale_tile_loops> option specifies whether the tile
4786 loops iterators should be scaled by the tile sizes.
4788 A representation of the band can be printed using
4790 #include <isl/band.h>
4791 __isl_give isl_printer *isl_printer_print_band(
4792 __isl_take isl_printer *p,
4793 __isl_keep isl_band *band);
4797 #include <isl/schedule.h>
4798 int isl_options_set_schedule_max_coefficient(
4799 isl_ctx *ctx, int val);
4800 int isl_options_get_schedule_max_coefficient(
4802 int isl_options_set_schedule_max_constant_term(
4803 isl_ctx *ctx, int val);
4804 int isl_options_get_schedule_max_constant_term(
4806 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4807 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4808 int isl_options_set_schedule_maximize_band_depth(
4809 isl_ctx *ctx, int val);
4810 int isl_options_get_schedule_maximize_band_depth(
4812 int isl_options_set_schedule_outer_zero_distance(
4813 isl_ctx *ctx, int val);
4814 int isl_options_get_schedule_outer_zero_distance(
4816 int isl_options_set_schedule_split_scaled(
4817 isl_ctx *ctx, int val);
4818 int isl_options_get_schedule_split_scaled(
4820 int isl_options_set_schedule_algorithm(
4821 isl_ctx *ctx, int val);
4822 int isl_options_get_schedule_algorithm(
4824 int isl_options_set_schedule_separate_components(
4825 isl_ctx *ctx, int val);
4826 int isl_options_get_schedule_separate_components(
4831 =item * schedule_max_coefficient
4833 This option enforces that the coefficients for variable and parameter
4834 dimensions in the calculated schedule are not larger than the specified value.
4835 This option can significantly increase the speed of the scheduling calculation
4836 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4837 this option does not introduce bounds on the variable or parameter
4840 =item * schedule_max_constant_term
4842 This option enforces that the constant coefficients in the calculated schedule
4843 are not larger than the maximal constant term. This option can significantly
4844 increase the speed of the scheduling calculation and may also prevent fusing of
4845 unrelated dimensions. A value of -1 means that this option does not introduce
4846 bounds on the constant coefficients.
4848 =item * schedule_fuse
4850 This option controls the level of fusion.
4851 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
4852 resulting schedule will be distributed as much as possible.
4853 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
4854 try to fuse loops in the resulting schedule.
4856 =item * schedule_maximize_band_depth
4858 If this option is set, we do not split bands at the point
4859 where we detect splitting is necessary. Instead, we
4860 backtrack and split bands as early as possible. This
4861 reduces the number of splits and maximizes the width of
4862 the bands. Wider bands give more possibilities for tiling.
4863 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
4864 then bands will be split as early as possible, even if there is no need.
4865 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
4867 =item * schedule_outer_zero_distance
4869 If this option is set, then we try to construct schedules
4870 where the outermost scheduling dimension in each band
4871 results in a zero dependence distance over the proximity
4874 =item * schedule_split_scaled
4876 If this option is set, then we try to construct schedules in which the
4877 constant term is split off from the linear part if the linear parts of
4878 the scheduling rows for all nodes in the graphs have a common non-trivial
4880 The constant term is then placed in a separate band and the linear
4883 =item * schedule_algorithm
4885 Selects the scheduling algorithm to be used.
4886 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4887 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4889 =item * schedule_separate_components
4891 If at any point the dependence graph contains any (weakly connected) components,
4892 then these components are scheduled separately.
4893 If this option is not set, then some iterations of the domains
4894 in these components may be scheduled together.
4895 If this option is set, then the components are given consecutive
4900 =head2 Parametric Vertex Enumeration
4902 The parametric vertex enumeration described in this section
4903 is mainly intended to be used internally and by the C<barvinok>
4906 #include <isl/vertices.h>
4907 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4908 __isl_keep isl_basic_set *bset);
4910 The function C<isl_basic_set_compute_vertices> performs the
4911 actual computation of the parametric vertices and the chamber
4912 decomposition and store the result in an C<isl_vertices> object.
4913 This information can be queried by either iterating over all
4914 the vertices or iterating over all the chambers or cells
4915 and then iterating over all vertices that are active on the chamber.
4917 int isl_vertices_foreach_vertex(
4918 __isl_keep isl_vertices *vertices,
4919 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4922 int isl_vertices_foreach_cell(
4923 __isl_keep isl_vertices *vertices,
4924 int (*fn)(__isl_take isl_cell *cell, void *user),
4926 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4927 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4930 Other operations that can be performed on an C<isl_vertices> object are
4933 isl_ctx *isl_vertices_get_ctx(
4934 __isl_keep isl_vertices *vertices);
4935 int isl_vertices_get_n_vertices(
4936 __isl_keep isl_vertices *vertices);
4937 void isl_vertices_free(__isl_take isl_vertices *vertices);
4939 Vertices can be inspected and destroyed using the following functions.
4941 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4942 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4943 __isl_give isl_basic_set *isl_vertex_get_domain(
4944 __isl_keep isl_vertex *vertex);
4945 __isl_give isl_basic_set *isl_vertex_get_expr(
4946 __isl_keep isl_vertex *vertex);
4947 void isl_vertex_free(__isl_take isl_vertex *vertex);
4949 C<isl_vertex_get_expr> returns a singleton parametric set describing
4950 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4952 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4953 B<rational> basic sets, so they should mainly be used for inspection
4954 and should not be mixed with integer sets.
4956 Chambers can be inspected and destroyed using the following functions.
4958 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4959 __isl_give isl_basic_set *isl_cell_get_domain(
4960 __isl_keep isl_cell *cell);
4961 void isl_cell_free(__isl_take isl_cell *cell);
4965 Although C<isl> is mainly meant to be used as a library,
4966 it also contains some basic applications that use some
4967 of the functionality of C<isl>.
4968 The input may be specified in either the L<isl format>
4969 or the L<PolyLib format>.
4971 =head2 C<isl_polyhedron_sample>
4973 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4974 an integer element of the polyhedron, if there is any.
4975 The first column in the output is the denominator and is always
4976 equal to 1. If the polyhedron contains no integer points,
4977 then a vector of length zero is printed.
4981 C<isl_pip> takes the same input as the C<example> program
4982 from the C<piplib> distribution, i.e., a set of constraints
4983 on the parameters, a line containing only -1 and finally a set
4984 of constraints on a parametric polyhedron.
4985 The coefficients of the parameters appear in the last columns
4986 (but before the final constant column).
4987 The output is the lexicographic minimum of the parametric polyhedron.
4988 As C<isl> currently does not have its own output format, the output
4989 is just a dump of the internal state.
4991 =head2 C<isl_polyhedron_minimize>
4993 C<isl_polyhedron_minimize> computes the minimum of some linear
4994 or affine objective function over the integer points in a polyhedron.
4995 If an affine objective function
4996 is given, then the constant should appear in the last column.
4998 =head2 C<isl_polytope_scan>
5000 Given a polytope, C<isl_polytope_scan> prints
5001 all integer points in the polytope.