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_set *isl_set_remove_unknown_divs(
1490 __isl_take isl_set *set);
1491 __isl_give isl_map *isl_map_remove_unknown_divs(
1492 __isl_take isl_map *map);
1494 To iterate over all the sets or maps in a union set or map, use
1496 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1497 int (*fn)(__isl_take isl_set *set, void *user),
1499 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1500 int (*fn)(__isl_take isl_map *map, void *user),
1503 The number of sets or maps in a union set or map can be obtained
1506 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1507 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1509 To extract the set or map in a given space from a union, use
1511 __isl_give isl_set *isl_union_set_extract_set(
1512 __isl_keep isl_union_set *uset,
1513 __isl_take isl_space *space);
1514 __isl_give isl_map *isl_union_map_extract_map(
1515 __isl_keep isl_union_map *umap,
1516 __isl_take isl_space *space);
1518 To iterate over all the basic sets or maps in a set or map, use
1520 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1521 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1523 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1524 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1527 The callback function C<fn> should return 0 if successful and
1528 -1 if an error occurs. In the latter case, or if any other error
1529 occurs, the above functions will return -1.
1531 It should be noted that C<isl> does not guarantee that
1532 the basic sets or maps passed to C<fn> are disjoint.
1533 If this is required, then the user should call one of
1534 the following functions first.
1536 __isl_give isl_set *isl_set_make_disjoint(
1537 __isl_take isl_set *set);
1538 __isl_give isl_map *isl_map_make_disjoint(
1539 __isl_take isl_map *map);
1541 The number of basic sets in a set can be obtained
1544 int isl_set_n_basic_set(__isl_keep isl_set *set);
1546 To iterate over the constraints of a basic set or map, use
1548 #include <isl/constraint.h>
1550 int isl_basic_set_n_constraint(
1551 __isl_keep isl_basic_set *bset);
1552 int isl_basic_set_foreach_constraint(
1553 __isl_keep isl_basic_set *bset,
1554 int (*fn)(__isl_take isl_constraint *c, void *user),
1556 int isl_basic_map_foreach_constraint(
1557 __isl_keep isl_basic_map *bmap,
1558 int (*fn)(__isl_take isl_constraint *c, void *user),
1560 void *isl_constraint_free(__isl_take isl_constraint *c);
1562 Again, the callback function C<fn> should return 0 if successful and
1563 -1 if an error occurs. In the latter case, or if any other error
1564 occurs, the above functions will return -1.
1565 The constraint C<c> represents either an equality or an inequality.
1566 Use the following function to find out whether a constraint
1567 represents an equality. If not, it represents an inequality.
1569 int isl_constraint_is_equality(
1570 __isl_keep isl_constraint *constraint);
1572 The coefficients of the constraints can be inspected using
1573 the following functions.
1575 int isl_constraint_is_lower_bound(
1576 __isl_keep isl_constraint *constraint,
1577 enum isl_dim_type type, unsigned pos);
1578 int isl_constraint_is_upper_bound(
1579 __isl_keep isl_constraint *constraint,
1580 enum isl_dim_type type, unsigned pos);
1581 void isl_constraint_get_constant(
1582 __isl_keep isl_constraint *constraint, isl_int *v);
1583 void isl_constraint_get_coefficient(
1584 __isl_keep isl_constraint *constraint,
1585 enum isl_dim_type type, int pos, isl_int *v);
1586 int isl_constraint_involves_dims(
1587 __isl_keep isl_constraint *constraint,
1588 enum isl_dim_type type, unsigned first, unsigned n);
1590 The explicit representations of the existentially quantified
1591 variables can be inspected using the following function.
1592 Note that the user is only allowed to use this function
1593 if the inspected set or map is the result of a call
1594 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1595 The existentially quantified variable is equal to the floor
1596 of the returned affine expression. The affine expression
1597 itself can be inspected using the functions in
1598 L<"Piecewise Quasi Affine Expressions">.
1600 __isl_give isl_aff *isl_constraint_get_div(
1601 __isl_keep isl_constraint *constraint, int pos);
1603 To obtain the constraints of a basic set or map in matrix
1604 form, use the following functions.
1606 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1607 __isl_keep isl_basic_set *bset,
1608 enum isl_dim_type c1, enum isl_dim_type c2,
1609 enum isl_dim_type c3, enum isl_dim_type c4);
1610 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1611 __isl_keep isl_basic_set *bset,
1612 enum isl_dim_type c1, enum isl_dim_type c2,
1613 enum isl_dim_type c3, enum isl_dim_type c4);
1614 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1615 __isl_keep isl_basic_map *bmap,
1616 enum isl_dim_type c1,
1617 enum isl_dim_type c2, enum isl_dim_type c3,
1618 enum isl_dim_type c4, enum isl_dim_type c5);
1619 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1620 __isl_keep isl_basic_map *bmap,
1621 enum isl_dim_type c1,
1622 enum isl_dim_type c2, enum isl_dim_type c3,
1623 enum isl_dim_type c4, enum isl_dim_type c5);
1625 The C<isl_dim_type> arguments dictate the order in which
1626 different kinds of variables appear in the resulting matrix
1627 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1628 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1630 The number of parameters, input, output or set dimensions can
1631 be obtained using the following functions.
1633 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1634 enum isl_dim_type type);
1635 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1636 enum isl_dim_type type);
1637 unsigned isl_set_dim(__isl_keep isl_set *set,
1638 enum isl_dim_type type);
1639 unsigned isl_map_dim(__isl_keep isl_map *map,
1640 enum isl_dim_type type);
1642 To check whether the description of a set or relation depends
1643 on one or more given dimensions, it is not necessary to iterate over all
1644 constraints. Instead the following functions can be used.
1646 int isl_basic_set_involves_dims(
1647 __isl_keep isl_basic_set *bset,
1648 enum isl_dim_type type, unsigned first, unsigned n);
1649 int isl_set_involves_dims(__isl_keep isl_set *set,
1650 enum isl_dim_type type, unsigned first, unsigned n);
1651 int isl_basic_map_involves_dims(
1652 __isl_keep isl_basic_map *bmap,
1653 enum isl_dim_type type, unsigned first, unsigned n);
1654 int isl_map_involves_dims(__isl_keep isl_map *map,
1655 enum isl_dim_type type, unsigned first, unsigned n);
1657 Similarly, the following functions can be used to check whether
1658 a given dimension is involved in any lower or upper bound.
1660 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1661 enum isl_dim_type type, unsigned pos);
1662 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1663 enum isl_dim_type type, unsigned pos);
1665 The identifiers or names of the domain and range spaces of a set
1666 or relation can be read off or set using the following functions.
1668 __isl_give isl_set *isl_set_set_tuple_id(
1669 __isl_take isl_set *set, __isl_take isl_id *id);
1670 __isl_give isl_set *isl_set_reset_tuple_id(
1671 __isl_take isl_set *set);
1672 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1673 __isl_give isl_id *isl_set_get_tuple_id(
1674 __isl_keep isl_set *set);
1675 __isl_give isl_map *isl_map_set_tuple_id(
1676 __isl_take isl_map *map, enum isl_dim_type type,
1677 __isl_take isl_id *id);
1678 __isl_give isl_map *isl_map_reset_tuple_id(
1679 __isl_take isl_map *map, enum isl_dim_type type);
1680 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1681 enum isl_dim_type type);
1682 __isl_give isl_id *isl_map_get_tuple_id(
1683 __isl_keep isl_map *map, enum isl_dim_type type);
1685 const char *isl_basic_set_get_tuple_name(
1686 __isl_keep isl_basic_set *bset);
1687 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1688 __isl_take isl_basic_set *set, const char *s);
1689 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1690 const char *isl_set_get_tuple_name(
1691 __isl_keep isl_set *set);
1692 const char *isl_basic_map_get_tuple_name(
1693 __isl_keep isl_basic_map *bmap,
1694 enum isl_dim_type type);
1695 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1696 __isl_take isl_basic_map *bmap,
1697 enum isl_dim_type type, const char *s);
1698 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1699 enum isl_dim_type type);
1700 const char *isl_map_get_tuple_name(
1701 __isl_keep isl_map *map,
1702 enum isl_dim_type type);
1704 As with C<isl_space_get_tuple_name>, the value returned points to
1705 an internal data structure.
1706 The identifiers, positions or names of individual dimensions can be
1707 read off using the following functions.
1709 __isl_give isl_id *isl_basic_set_get_dim_id(
1710 __isl_keep isl_basic_set *bset,
1711 enum isl_dim_type type, unsigned pos);
1712 __isl_give isl_set *isl_set_set_dim_id(
1713 __isl_take isl_set *set, enum isl_dim_type type,
1714 unsigned pos, __isl_take isl_id *id);
1715 int isl_set_has_dim_id(__isl_keep isl_set *set,
1716 enum isl_dim_type type, unsigned pos);
1717 __isl_give isl_id *isl_set_get_dim_id(
1718 __isl_keep isl_set *set, enum isl_dim_type type,
1720 int isl_basic_map_has_dim_id(
1721 __isl_keep isl_basic_map *bmap,
1722 enum isl_dim_type type, unsigned pos);
1723 __isl_give isl_map *isl_map_set_dim_id(
1724 __isl_take isl_map *map, enum isl_dim_type type,
1725 unsigned pos, __isl_take isl_id *id);
1726 int isl_map_has_dim_id(__isl_keep isl_map *map,
1727 enum isl_dim_type type, unsigned pos);
1728 __isl_give isl_id *isl_map_get_dim_id(
1729 __isl_keep isl_map *map, enum isl_dim_type type,
1732 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1733 enum isl_dim_type type, __isl_keep isl_id *id);
1734 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1735 enum isl_dim_type type, __isl_keep isl_id *id);
1736 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1737 enum isl_dim_type type, const char *name);
1738 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1739 enum isl_dim_type type, const char *name);
1741 const char *isl_constraint_get_dim_name(
1742 __isl_keep isl_constraint *constraint,
1743 enum isl_dim_type type, unsigned pos);
1744 const char *isl_basic_set_get_dim_name(
1745 __isl_keep isl_basic_set *bset,
1746 enum isl_dim_type type, unsigned pos);
1747 int isl_set_has_dim_name(__isl_keep isl_set *set,
1748 enum isl_dim_type type, unsigned pos);
1749 const char *isl_set_get_dim_name(
1750 __isl_keep isl_set *set,
1751 enum isl_dim_type type, unsigned pos);
1752 const char *isl_basic_map_get_dim_name(
1753 __isl_keep isl_basic_map *bmap,
1754 enum isl_dim_type type, unsigned pos);
1755 int isl_map_has_dim_name(__isl_keep isl_map *map,
1756 enum isl_dim_type type, unsigned pos);
1757 const char *isl_map_get_dim_name(
1758 __isl_keep isl_map *map,
1759 enum isl_dim_type type, unsigned pos);
1761 These functions are mostly useful to obtain the identifiers, positions
1762 or names of the parameters. Identifiers of individual dimensions are
1763 essentially only useful for printing. They are ignored by all other
1764 operations and may not be preserved across those operations.
1768 =head3 Unary Properties
1774 The following functions test whether the given set or relation
1775 contains any integer points. The ``plain'' variants do not perform
1776 any computations, but simply check if the given set or relation
1777 is already known to be empty.
1779 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1780 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1781 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1782 int isl_set_is_empty(__isl_keep isl_set *set);
1783 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1784 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1785 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1786 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1787 int isl_map_is_empty(__isl_keep isl_map *map);
1788 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1790 =item * Universality
1792 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1793 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1794 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1796 =item * Single-valuedness
1798 int isl_basic_map_is_single_valued(
1799 __isl_keep isl_basic_map *bmap);
1800 int isl_map_plain_is_single_valued(
1801 __isl_keep isl_map *map);
1802 int isl_map_is_single_valued(__isl_keep isl_map *map);
1803 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1807 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1808 int isl_map_is_injective(__isl_keep isl_map *map);
1809 int isl_union_map_plain_is_injective(
1810 __isl_keep isl_union_map *umap);
1811 int isl_union_map_is_injective(
1812 __isl_keep isl_union_map *umap);
1816 int isl_map_is_bijective(__isl_keep isl_map *map);
1817 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1821 int isl_basic_map_plain_is_fixed(
1822 __isl_keep isl_basic_map *bmap,
1823 enum isl_dim_type type, unsigned pos,
1825 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1826 enum isl_dim_type type, unsigned pos,
1828 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1829 enum isl_dim_type type, unsigned pos,
1832 Check if the relation obviously lies on a hyperplane where the given dimension
1833 has a fixed value and if so, return that value in C<*val>.
1837 To check whether a set is a parameter domain, use this function:
1839 int isl_set_is_params(__isl_keep isl_set *set);
1840 int isl_union_set_is_params(
1841 __isl_keep isl_union_set *uset);
1845 The following functions check whether the domain of the given
1846 (basic) set is a wrapped relation.
1848 int isl_basic_set_is_wrapping(
1849 __isl_keep isl_basic_set *bset);
1850 int isl_set_is_wrapping(__isl_keep isl_set *set);
1852 =item * Internal Product
1854 int isl_basic_map_can_zip(
1855 __isl_keep isl_basic_map *bmap);
1856 int isl_map_can_zip(__isl_keep isl_map *map);
1858 Check whether the product of domain and range of the given relation
1860 i.e., whether both domain and range are nested relations.
1864 int isl_basic_map_can_curry(
1865 __isl_keep isl_basic_map *bmap);
1866 int isl_map_can_curry(__isl_keep isl_map *map);
1868 Check whether the domain of the (basic) relation is a wrapped relation.
1870 int isl_basic_map_can_uncurry(
1871 __isl_keep isl_basic_map *bmap);
1872 int isl_map_can_uncurry(__isl_keep isl_map *map);
1874 Check whether the range of the (basic) relation is a wrapped relation.
1878 =head3 Binary Properties
1884 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1885 __isl_keep isl_set *set2);
1886 int isl_set_is_equal(__isl_keep isl_set *set1,
1887 __isl_keep isl_set *set2);
1888 int isl_union_set_is_equal(
1889 __isl_keep isl_union_set *uset1,
1890 __isl_keep isl_union_set *uset2);
1891 int isl_basic_map_is_equal(
1892 __isl_keep isl_basic_map *bmap1,
1893 __isl_keep isl_basic_map *bmap2);
1894 int isl_map_is_equal(__isl_keep isl_map *map1,
1895 __isl_keep isl_map *map2);
1896 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1897 __isl_keep isl_map *map2);
1898 int isl_union_map_is_equal(
1899 __isl_keep isl_union_map *umap1,
1900 __isl_keep isl_union_map *umap2);
1902 =item * Disjointness
1904 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1905 __isl_keep isl_set *set2);
1906 int isl_set_is_disjoint(__isl_keep isl_set *set1,
1907 __isl_keep isl_set *set2);
1908 int isl_map_is_disjoint(__isl_keep isl_map *map1,
1909 __isl_keep isl_map *map2);
1913 int isl_basic_set_is_subset(
1914 __isl_keep isl_basic_set *bset1,
1915 __isl_keep isl_basic_set *bset2);
1916 int isl_set_is_subset(__isl_keep isl_set *set1,
1917 __isl_keep isl_set *set2);
1918 int isl_set_is_strict_subset(
1919 __isl_keep isl_set *set1,
1920 __isl_keep isl_set *set2);
1921 int isl_union_set_is_subset(
1922 __isl_keep isl_union_set *uset1,
1923 __isl_keep isl_union_set *uset2);
1924 int isl_union_set_is_strict_subset(
1925 __isl_keep isl_union_set *uset1,
1926 __isl_keep isl_union_set *uset2);
1927 int isl_basic_map_is_subset(
1928 __isl_keep isl_basic_map *bmap1,
1929 __isl_keep isl_basic_map *bmap2);
1930 int isl_basic_map_is_strict_subset(
1931 __isl_keep isl_basic_map *bmap1,
1932 __isl_keep isl_basic_map *bmap2);
1933 int isl_map_is_subset(
1934 __isl_keep isl_map *map1,
1935 __isl_keep isl_map *map2);
1936 int isl_map_is_strict_subset(
1937 __isl_keep isl_map *map1,
1938 __isl_keep isl_map *map2);
1939 int isl_union_map_is_subset(
1940 __isl_keep isl_union_map *umap1,
1941 __isl_keep isl_union_map *umap2);
1942 int isl_union_map_is_strict_subset(
1943 __isl_keep isl_union_map *umap1,
1944 __isl_keep isl_union_map *umap2);
1946 Check whether the first argument is a (strict) subset of the
1951 =head2 Unary Operations
1957 __isl_give isl_set *isl_set_complement(
1958 __isl_take isl_set *set);
1959 __isl_give isl_map *isl_map_complement(
1960 __isl_take isl_map *map);
1964 __isl_give isl_basic_map *isl_basic_map_reverse(
1965 __isl_take isl_basic_map *bmap);
1966 __isl_give isl_map *isl_map_reverse(
1967 __isl_take isl_map *map);
1968 __isl_give isl_union_map *isl_union_map_reverse(
1969 __isl_take isl_union_map *umap);
1973 __isl_give isl_basic_set *isl_basic_set_project_out(
1974 __isl_take isl_basic_set *bset,
1975 enum isl_dim_type type, unsigned first, unsigned n);
1976 __isl_give isl_basic_map *isl_basic_map_project_out(
1977 __isl_take isl_basic_map *bmap,
1978 enum isl_dim_type type, unsigned first, unsigned n);
1979 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1980 enum isl_dim_type type, unsigned first, unsigned n);
1981 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1982 enum isl_dim_type type, unsigned first, unsigned n);
1983 __isl_give isl_basic_set *isl_basic_set_params(
1984 __isl_take isl_basic_set *bset);
1985 __isl_give isl_basic_set *isl_basic_map_domain(
1986 __isl_take isl_basic_map *bmap);
1987 __isl_give isl_basic_set *isl_basic_map_range(
1988 __isl_take isl_basic_map *bmap);
1989 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1990 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1991 __isl_give isl_set *isl_map_domain(
1992 __isl_take isl_map *bmap);
1993 __isl_give isl_set *isl_map_range(
1994 __isl_take isl_map *map);
1995 __isl_give isl_set *isl_union_set_params(
1996 __isl_take isl_union_set *uset);
1997 __isl_give isl_set *isl_union_map_params(
1998 __isl_take isl_union_map *umap);
1999 __isl_give isl_union_set *isl_union_map_domain(
2000 __isl_take isl_union_map *umap);
2001 __isl_give isl_union_set *isl_union_map_range(
2002 __isl_take isl_union_map *umap);
2004 __isl_give isl_basic_map *isl_basic_map_domain_map(
2005 __isl_take isl_basic_map *bmap);
2006 __isl_give isl_basic_map *isl_basic_map_range_map(
2007 __isl_take isl_basic_map *bmap);
2008 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2009 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2010 __isl_give isl_union_map *isl_union_map_domain_map(
2011 __isl_take isl_union_map *umap);
2012 __isl_give isl_union_map *isl_union_map_range_map(
2013 __isl_take isl_union_map *umap);
2015 The functions above construct a (basic, regular or union) relation
2016 that maps (a wrapped version of) the input relation to its domain or range.
2020 __isl_give isl_basic_set *isl_basic_set_eliminate(
2021 __isl_take isl_basic_set *bset,
2022 enum isl_dim_type type,
2023 unsigned first, unsigned n);
2024 __isl_give isl_set *isl_set_eliminate(
2025 __isl_take isl_set *set, enum isl_dim_type type,
2026 unsigned first, unsigned n);
2027 __isl_give isl_basic_map *isl_basic_map_eliminate(
2028 __isl_take isl_basic_map *bmap,
2029 enum isl_dim_type type,
2030 unsigned first, unsigned n);
2031 __isl_give isl_map *isl_map_eliminate(
2032 __isl_take isl_map *map, enum isl_dim_type type,
2033 unsigned first, unsigned n);
2035 Eliminate the coefficients for the given dimensions from the constraints,
2036 without removing the dimensions.
2040 __isl_give isl_basic_set *isl_basic_set_fix(
2041 __isl_take isl_basic_set *bset,
2042 enum isl_dim_type type, unsigned pos,
2044 __isl_give isl_basic_set *isl_basic_set_fix_si(
2045 __isl_take isl_basic_set *bset,
2046 enum isl_dim_type type, unsigned pos, int value);
2047 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2048 enum isl_dim_type type, unsigned pos,
2050 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2051 enum isl_dim_type type, unsigned pos, int value);
2052 __isl_give isl_basic_map *isl_basic_map_fix_si(
2053 __isl_take isl_basic_map *bmap,
2054 enum isl_dim_type type, unsigned pos, int value);
2055 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
2056 enum isl_dim_type type, unsigned pos,
2058 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2059 enum isl_dim_type type, unsigned pos, int value);
2061 Intersect the set or relation with the hyperplane where the given
2062 dimension has the fixed given value.
2064 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2065 __isl_take isl_basic_map *bmap,
2066 enum isl_dim_type type, unsigned pos, int value);
2067 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2068 __isl_take isl_basic_map *bmap,
2069 enum isl_dim_type type, unsigned pos, int value);
2070 __isl_give isl_set *isl_set_lower_bound(
2071 __isl_take isl_set *set,
2072 enum isl_dim_type type, unsigned pos,
2074 __isl_give isl_set *isl_set_lower_bound_si(
2075 __isl_take isl_set *set,
2076 enum isl_dim_type type, unsigned pos, int value);
2077 __isl_give isl_map *isl_map_lower_bound_si(
2078 __isl_take isl_map *map,
2079 enum isl_dim_type type, unsigned pos, int value);
2080 __isl_give isl_set *isl_set_upper_bound(
2081 __isl_take isl_set *set,
2082 enum isl_dim_type type, unsigned pos,
2084 __isl_give isl_set *isl_set_upper_bound_si(
2085 __isl_take isl_set *set,
2086 enum isl_dim_type type, unsigned pos, int value);
2087 __isl_give isl_map *isl_map_upper_bound_si(
2088 __isl_take isl_map *map,
2089 enum isl_dim_type type, unsigned pos, int value);
2091 Intersect the set or relation with the half-space where the given
2092 dimension has a value bounded by the fixed given value.
2094 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2095 enum isl_dim_type type1, int pos1,
2096 enum isl_dim_type type2, int pos2);
2097 __isl_give isl_basic_map *isl_basic_map_equate(
2098 __isl_take isl_basic_map *bmap,
2099 enum isl_dim_type type1, int pos1,
2100 enum isl_dim_type type2, int pos2);
2101 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2102 enum isl_dim_type type1, int pos1,
2103 enum isl_dim_type type2, int pos2);
2105 Intersect the set or relation with the hyperplane where the given
2106 dimensions are equal to each other.
2108 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2109 enum isl_dim_type type1, int pos1,
2110 enum isl_dim_type type2, int pos2);
2112 Intersect the relation with the hyperplane where the given
2113 dimensions have opposite values.
2115 __isl_give isl_basic_map *isl_basic_map_order_ge(
2116 __isl_take isl_basic_map *bmap,
2117 enum isl_dim_type type1, int pos1,
2118 enum isl_dim_type type2, int pos2);
2119 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2120 enum isl_dim_type type1, int pos1,
2121 enum isl_dim_type type2, int pos2);
2122 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2123 enum isl_dim_type type1, int pos1,
2124 enum isl_dim_type type2, int pos2);
2126 Intersect the relation with the half-space where the given
2127 dimensions satisfy the given ordering.
2131 __isl_give isl_map *isl_set_identity(
2132 __isl_take isl_set *set);
2133 __isl_give isl_union_map *isl_union_set_identity(
2134 __isl_take isl_union_set *uset);
2136 Construct an identity relation on the given (union) set.
2140 __isl_give isl_basic_set *isl_basic_map_deltas(
2141 __isl_take isl_basic_map *bmap);
2142 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2143 __isl_give isl_union_set *isl_union_map_deltas(
2144 __isl_take isl_union_map *umap);
2146 These functions return a (basic) set containing the differences
2147 between image elements and corresponding domain elements in the input.
2149 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2150 __isl_take isl_basic_map *bmap);
2151 __isl_give isl_map *isl_map_deltas_map(
2152 __isl_take isl_map *map);
2153 __isl_give isl_union_map *isl_union_map_deltas_map(
2154 __isl_take isl_union_map *umap);
2156 The functions above construct a (basic, regular or union) relation
2157 that maps (a wrapped version of) the input relation to its delta set.
2161 Simplify the representation of a set or relation by trying
2162 to combine pairs of basic sets or relations into a single
2163 basic set or relation.
2165 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2166 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2167 __isl_give isl_union_set *isl_union_set_coalesce(
2168 __isl_take isl_union_set *uset);
2169 __isl_give isl_union_map *isl_union_map_coalesce(
2170 __isl_take isl_union_map *umap);
2172 One of the methods for combining pairs of basic sets or relations
2173 can result in coefficients that are much larger than those that appear
2174 in the constraints of the input. By default, the coefficients are
2175 not allowed to grow larger, but this can be changed by unsetting
2176 the following option.
2178 int isl_options_set_coalesce_bounded_wrapping(
2179 isl_ctx *ctx, int val);
2180 int isl_options_get_coalesce_bounded_wrapping(
2183 =item * Detecting equalities
2185 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2186 __isl_take isl_basic_set *bset);
2187 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2188 __isl_take isl_basic_map *bmap);
2189 __isl_give isl_set *isl_set_detect_equalities(
2190 __isl_take isl_set *set);
2191 __isl_give isl_map *isl_map_detect_equalities(
2192 __isl_take isl_map *map);
2193 __isl_give isl_union_set *isl_union_set_detect_equalities(
2194 __isl_take isl_union_set *uset);
2195 __isl_give isl_union_map *isl_union_map_detect_equalities(
2196 __isl_take isl_union_map *umap);
2198 Simplify the representation of a set or relation by detecting implicit
2201 =item * Removing redundant constraints
2203 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2204 __isl_take isl_basic_set *bset);
2205 __isl_give isl_set *isl_set_remove_redundancies(
2206 __isl_take isl_set *set);
2207 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2208 __isl_take isl_basic_map *bmap);
2209 __isl_give isl_map *isl_map_remove_redundancies(
2210 __isl_take isl_map *map);
2214 __isl_give isl_basic_set *isl_set_convex_hull(
2215 __isl_take isl_set *set);
2216 __isl_give isl_basic_map *isl_map_convex_hull(
2217 __isl_take isl_map *map);
2219 If the input set or relation has any existentially quantified
2220 variables, then the result of these operations is currently undefined.
2224 __isl_give isl_basic_set *isl_set_simple_hull(
2225 __isl_take isl_set *set);
2226 __isl_give isl_basic_map *isl_map_simple_hull(
2227 __isl_take isl_map *map);
2228 __isl_give isl_union_map *isl_union_map_simple_hull(
2229 __isl_take isl_union_map *umap);
2231 These functions compute a single basic set or relation
2232 that contains the whole input set or relation.
2233 In particular, the output is described by translates
2234 of the constraints describing the basic sets or relations in the input.
2238 (See \autoref{s:simple hull}.)
2244 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2245 __isl_take isl_basic_set *bset);
2246 __isl_give isl_basic_set *isl_set_affine_hull(
2247 __isl_take isl_set *set);
2248 __isl_give isl_union_set *isl_union_set_affine_hull(
2249 __isl_take isl_union_set *uset);
2250 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2251 __isl_take isl_basic_map *bmap);
2252 __isl_give isl_basic_map *isl_map_affine_hull(
2253 __isl_take isl_map *map);
2254 __isl_give isl_union_map *isl_union_map_affine_hull(
2255 __isl_take isl_union_map *umap);
2257 In case of union sets and relations, the affine hull is computed
2260 =item * Polyhedral hull
2262 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2263 __isl_take isl_set *set);
2264 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2265 __isl_take isl_map *map);
2266 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2267 __isl_take isl_union_set *uset);
2268 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2269 __isl_take isl_union_map *umap);
2271 These functions compute a single basic set or relation
2272 not involving any existentially quantified variables
2273 that contains the whole input set or relation.
2274 In case of union sets and relations, the polyhedral hull is computed
2279 __isl_give isl_basic_set *isl_basic_set_sample(
2280 __isl_take isl_basic_set *bset);
2281 __isl_give isl_basic_set *isl_set_sample(
2282 __isl_take isl_set *set);
2283 __isl_give isl_basic_map *isl_basic_map_sample(
2284 __isl_take isl_basic_map *bmap);
2285 __isl_give isl_basic_map *isl_map_sample(
2286 __isl_take isl_map *map);
2288 If the input (basic) set or relation is non-empty, then return
2289 a singleton subset of the input. Otherwise, return an empty set.
2291 =item * Optimization
2293 #include <isl/ilp.h>
2294 enum isl_lp_result isl_basic_set_max(
2295 __isl_keep isl_basic_set *bset,
2296 __isl_keep isl_aff *obj, isl_int *opt)
2297 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2298 __isl_keep isl_aff *obj, isl_int *opt);
2299 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2300 __isl_keep isl_aff *obj, isl_int *opt);
2302 Compute the minimum or maximum of the integer affine expression C<obj>
2303 over the points in C<set>, returning the result in C<opt>.
2304 The return value may be one of C<isl_lp_error>,
2305 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2307 =item * Parametric optimization
2309 __isl_give isl_pw_aff *isl_set_dim_min(
2310 __isl_take isl_set *set, int pos);
2311 __isl_give isl_pw_aff *isl_set_dim_max(
2312 __isl_take isl_set *set, int pos);
2313 __isl_give isl_pw_aff *isl_map_dim_max(
2314 __isl_take isl_map *map, int pos);
2316 Compute the minimum or maximum of the given set or output dimension
2317 as a function of the parameters (and input dimensions), but independently
2318 of the other set or output dimensions.
2319 For lexicographic optimization, see L<"Lexicographic Optimization">.
2323 The following functions compute either the set of (rational) coefficient
2324 values of valid constraints for the given set or the set of (rational)
2325 values satisfying the constraints with coefficients from the given set.
2326 Internally, these two sets of functions perform essentially the
2327 same operations, except that the set of coefficients is assumed to
2328 be a cone, while the set of values may be any polyhedron.
2329 The current implementation is based on the Farkas lemma and
2330 Fourier-Motzkin elimination, but this may change or be made optional
2331 in future. In particular, future implementations may use different
2332 dualization algorithms or skip the elimination step.
2334 __isl_give isl_basic_set *isl_basic_set_coefficients(
2335 __isl_take isl_basic_set *bset);
2336 __isl_give isl_basic_set *isl_set_coefficients(
2337 __isl_take isl_set *set);
2338 __isl_give isl_union_set *isl_union_set_coefficients(
2339 __isl_take isl_union_set *bset);
2340 __isl_give isl_basic_set *isl_basic_set_solutions(
2341 __isl_take isl_basic_set *bset);
2342 __isl_give isl_basic_set *isl_set_solutions(
2343 __isl_take isl_set *set);
2344 __isl_give isl_union_set *isl_union_set_solutions(
2345 __isl_take isl_union_set *bset);
2349 __isl_give isl_map *isl_map_fixed_power(
2350 __isl_take isl_map *map, isl_int exp);
2351 __isl_give isl_union_map *isl_union_map_fixed_power(
2352 __isl_take isl_union_map *umap, isl_int exp);
2354 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2355 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2356 of C<map> is computed.
2358 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2360 __isl_give isl_union_map *isl_union_map_power(
2361 __isl_take isl_union_map *umap, int *exact);
2363 Compute a parametric representation for all positive powers I<k> of C<map>.
2364 The result maps I<k> to a nested relation corresponding to the
2365 I<k>th power of C<map>.
2366 The result may be an overapproximation. If the result is known to be exact,
2367 then C<*exact> is set to C<1>.
2369 =item * Transitive closure
2371 __isl_give isl_map *isl_map_transitive_closure(
2372 __isl_take isl_map *map, int *exact);
2373 __isl_give isl_union_map *isl_union_map_transitive_closure(
2374 __isl_take isl_union_map *umap, int *exact);
2376 Compute the transitive closure of C<map>.
2377 The result may be an overapproximation. If the result is known to be exact,
2378 then C<*exact> is set to C<1>.
2380 =item * Reaching path lengths
2382 __isl_give isl_map *isl_map_reaching_path_lengths(
2383 __isl_take isl_map *map, int *exact);
2385 Compute a relation that maps each element in the range of C<map>
2386 to the lengths of all paths composed of edges in C<map> that
2387 end up in the given element.
2388 The result may be an overapproximation. If the result is known to be exact,
2389 then C<*exact> is set to C<1>.
2390 To compute the I<maximal> path length, the resulting relation
2391 should be postprocessed by C<isl_map_lexmax>.
2392 In particular, if the input relation is a dependence relation
2393 (mapping sources to sinks), then the maximal path length corresponds
2394 to the free schedule.
2395 Note, however, that C<isl_map_lexmax> expects the maximum to be
2396 finite, so if the path lengths are unbounded (possibly due to
2397 the overapproximation), then you will get an error message.
2401 __isl_give isl_basic_set *isl_basic_map_wrap(
2402 __isl_take isl_basic_map *bmap);
2403 __isl_give isl_set *isl_map_wrap(
2404 __isl_take isl_map *map);
2405 __isl_give isl_union_set *isl_union_map_wrap(
2406 __isl_take isl_union_map *umap);
2407 __isl_give isl_basic_map *isl_basic_set_unwrap(
2408 __isl_take isl_basic_set *bset);
2409 __isl_give isl_map *isl_set_unwrap(
2410 __isl_take isl_set *set);
2411 __isl_give isl_union_map *isl_union_set_unwrap(
2412 __isl_take isl_union_set *uset);
2416 Remove any internal structure of domain (and range) of the given
2417 set or relation. If there is any such internal structure in the input,
2418 then the name of the space is also removed.
2420 __isl_give isl_basic_set *isl_basic_set_flatten(
2421 __isl_take isl_basic_set *bset);
2422 __isl_give isl_set *isl_set_flatten(
2423 __isl_take isl_set *set);
2424 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2425 __isl_take isl_basic_map *bmap);
2426 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2427 __isl_take isl_basic_map *bmap);
2428 __isl_give isl_map *isl_map_flatten_range(
2429 __isl_take isl_map *map);
2430 __isl_give isl_map *isl_map_flatten_domain(
2431 __isl_take isl_map *map);
2432 __isl_give isl_basic_map *isl_basic_map_flatten(
2433 __isl_take isl_basic_map *bmap);
2434 __isl_give isl_map *isl_map_flatten(
2435 __isl_take isl_map *map);
2437 __isl_give isl_map *isl_set_flatten_map(
2438 __isl_take isl_set *set);
2440 The function above constructs a relation
2441 that maps the input set to a flattened version of the set.
2445 Lift the input set to a space with extra dimensions corresponding
2446 to the existentially quantified variables in the input.
2447 In particular, the result lives in a wrapped map where the domain
2448 is the original space and the range corresponds to the original
2449 existentially quantified variables.
2451 __isl_give isl_basic_set *isl_basic_set_lift(
2452 __isl_take isl_basic_set *bset);
2453 __isl_give isl_set *isl_set_lift(
2454 __isl_take isl_set *set);
2455 __isl_give isl_union_set *isl_union_set_lift(
2456 __isl_take isl_union_set *uset);
2458 Given a local space that contains the existentially quantified
2459 variables of a set, a basic relation that, when applied to
2460 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2461 can be constructed using the following function.
2463 #include <isl/local_space.h>
2464 __isl_give isl_basic_map *isl_local_space_lifting(
2465 __isl_take isl_local_space *ls);
2467 =item * Internal Product
2469 __isl_give isl_basic_map *isl_basic_map_zip(
2470 __isl_take isl_basic_map *bmap);
2471 __isl_give isl_map *isl_map_zip(
2472 __isl_take isl_map *map);
2473 __isl_give isl_union_map *isl_union_map_zip(
2474 __isl_take isl_union_map *umap);
2476 Given a relation with nested relations for domain and range,
2477 interchange the range of the domain with the domain of the range.
2481 __isl_give isl_basic_map *isl_basic_map_curry(
2482 __isl_take isl_basic_map *bmap);
2483 __isl_give isl_basic_map *isl_basic_map_uncurry(
2484 __isl_take isl_basic_map *bmap);
2485 __isl_give isl_map *isl_map_curry(
2486 __isl_take isl_map *map);
2487 __isl_give isl_map *isl_map_uncurry(
2488 __isl_take isl_map *map);
2489 __isl_give isl_union_map *isl_union_map_curry(
2490 __isl_take isl_union_map *umap);
2492 Given a relation with a nested relation for domain,
2493 the C<curry> functions
2494 move the range of the nested relation out of the domain
2495 and use it as the domain of a nested relation in the range,
2496 with the original range as range of this nested relation.
2497 The C<uncurry> functions perform the inverse operation.
2499 =item * Aligning parameters
2501 __isl_give isl_basic_set *isl_basic_set_align_params(
2502 __isl_take isl_basic_set *bset,
2503 __isl_take isl_space *model);
2504 __isl_give isl_set *isl_set_align_params(
2505 __isl_take isl_set *set,
2506 __isl_take isl_space *model);
2507 __isl_give isl_basic_map *isl_basic_map_align_params(
2508 __isl_take isl_basic_map *bmap,
2509 __isl_take isl_space *model);
2510 __isl_give isl_map *isl_map_align_params(
2511 __isl_take isl_map *map,
2512 __isl_take isl_space *model);
2514 Change the order of the parameters of the given set or relation
2515 such that the first parameters match those of C<model>.
2516 This may involve the introduction of extra parameters.
2517 All parameters need to be named.
2519 =item * Dimension manipulation
2521 __isl_give isl_set *isl_set_add_dims(
2522 __isl_take isl_set *set,
2523 enum isl_dim_type type, unsigned n);
2524 __isl_give isl_map *isl_map_add_dims(
2525 __isl_take isl_map *map,
2526 enum isl_dim_type type, unsigned n);
2527 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2528 __isl_take isl_basic_set *bset,
2529 enum isl_dim_type type, unsigned pos,
2531 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2532 __isl_take isl_basic_map *bmap,
2533 enum isl_dim_type type, unsigned pos,
2535 __isl_give isl_set *isl_set_insert_dims(
2536 __isl_take isl_set *set,
2537 enum isl_dim_type type, unsigned pos, unsigned n);
2538 __isl_give isl_map *isl_map_insert_dims(
2539 __isl_take isl_map *map,
2540 enum isl_dim_type type, unsigned pos, unsigned n);
2541 __isl_give isl_basic_set *isl_basic_set_move_dims(
2542 __isl_take isl_basic_set *bset,
2543 enum isl_dim_type dst_type, unsigned dst_pos,
2544 enum isl_dim_type src_type, unsigned src_pos,
2546 __isl_give isl_basic_map *isl_basic_map_move_dims(
2547 __isl_take isl_basic_map *bmap,
2548 enum isl_dim_type dst_type, unsigned dst_pos,
2549 enum isl_dim_type src_type, unsigned src_pos,
2551 __isl_give isl_set *isl_set_move_dims(
2552 __isl_take isl_set *set,
2553 enum isl_dim_type dst_type, unsigned dst_pos,
2554 enum isl_dim_type src_type, unsigned src_pos,
2556 __isl_give isl_map *isl_map_move_dims(
2557 __isl_take isl_map *map,
2558 enum isl_dim_type dst_type, unsigned dst_pos,
2559 enum isl_dim_type src_type, unsigned src_pos,
2562 It is usually not advisable to directly change the (input or output)
2563 space of a set or a relation as this removes the name and the internal
2564 structure of the space. However, the above functions can be useful
2565 to add new parameters, assuming
2566 C<isl_set_align_params> and C<isl_map_align_params>
2571 =head2 Binary Operations
2573 The two arguments of a binary operation not only need to live
2574 in the same C<isl_ctx>, they currently also need to have
2575 the same (number of) parameters.
2577 =head3 Basic Operations
2581 =item * Intersection
2583 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2584 __isl_take isl_basic_set *bset1,
2585 __isl_take isl_basic_set *bset2);
2586 __isl_give isl_basic_set *isl_basic_set_intersect(
2587 __isl_take isl_basic_set *bset1,
2588 __isl_take isl_basic_set *bset2);
2589 __isl_give isl_set *isl_set_intersect_params(
2590 __isl_take isl_set *set,
2591 __isl_take isl_set *params);
2592 __isl_give isl_set *isl_set_intersect(
2593 __isl_take isl_set *set1,
2594 __isl_take isl_set *set2);
2595 __isl_give isl_union_set *isl_union_set_intersect_params(
2596 __isl_take isl_union_set *uset,
2597 __isl_take isl_set *set);
2598 __isl_give isl_union_map *isl_union_map_intersect_params(
2599 __isl_take isl_union_map *umap,
2600 __isl_take isl_set *set);
2601 __isl_give isl_union_set *isl_union_set_intersect(
2602 __isl_take isl_union_set *uset1,
2603 __isl_take isl_union_set *uset2);
2604 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2605 __isl_take isl_basic_map *bmap,
2606 __isl_take isl_basic_set *bset);
2607 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2608 __isl_take isl_basic_map *bmap,
2609 __isl_take isl_basic_set *bset);
2610 __isl_give isl_basic_map *isl_basic_map_intersect(
2611 __isl_take isl_basic_map *bmap1,
2612 __isl_take isl_basic_map *bmap2);
2613 __isl_give isl_map *isl_map_intersect_params(
2614 __isl_take isl_map *map,
2615 __isl_take isl_set *params);
2616 __isl_give isl_map *isl_map_intersect_domain(
2617 __isl_take isl_map *map,
2618 __isl_take isl_set *set);
2619 __isl_give isl_map *isl_map_intersect_range(
2620 __isl_take isl_map *map,
2621 __isl_take isl_set *set);
2622 __isl_give isl_map *isl_map_intersect(
2623 __isl_take isl_map *map1,
2624 __isl_take isl_map *map2);
2625 __isl_give isl_union_map *isl_union_map_intersect_domain(
2626 __isl_take isl_union_map *umap,
2627 __isl_take isl_union_set *uset);
2628 __isl_give isl_union_map *isl_union_map_intersect_range(
2629 __isl_take isl_union_map *umap,
2630 __isl_take isl_union_set *uset);
2631 __isl_give isl_union_map *isl_union_map_intersect(
2632 __isl_take isl_union_map *umap1,
2633 __isl_take isl_union_map *umap2);
2635 The second argument to the C<_params> functions needs to be
2636 a parametric (basic) set. For the other functions, a parametric set
2637 for either argument is only allowed if the other argument is
2638 a parametric set as well.
2642 __isl_give isl_set *isl_basic_set_union(
2643 __isl_take isl_basic_set *bset1,
2644 __isl_take isl_basic_set *bset2);
2645 __isl_give isl_map *isl_basic_map_union(
2646 __isl_take isl_basic_map *bmap1,
2647 __isl_take isl_basic_map *bmap2);
2648 __isl_give isl_set *isl_set_union(
2649 __isl_take isl_set *set1,
2650 __isl_take isl_set *set2);
2651 __isl_give isl_map *isl_map_union(
2652 __isl_take isl_map *map1,
2653 __isl_take isl_map *map2);
2654 __isl_give isl_union_set *isl_union_set_union(
2655 __isl_take isl_union_set *uset1,
2656 __isl_take isl_union_set *uset2);
2657 __isl_give isl_union_map *isl_union_map_union(
2658 __isl_take isl_union_map *umap1,
2659 __isl_take isl_union_map *umap2);
2661 =item * Set difference
2663 __isl_give isl_set *isl_set_subtract(
2664 __isl_take isl_set *set1,
2665 __isl_take isl_set *set2);
2666 __isl_give isl_map *isl_map_subtract(
2667 __isl_take isl_map *map1,
2668 __isl_take isl_map *map2);
2669 __isl_give isl_map *isl_map_subtract_domain(
2670 __isl_take isl_map *map,
2671 __isl_take isl_set *dom);
2672 __isl_give isl_map *isl_map_subtract_range(
2673 __isl_take isl_map *map,
2674 __isl_take isl_set *dom);
2675 __isl_give isl_union_set *isl_union_set_subtract(
2676 __isl_take isl_union_set *uset1,
2677 __isl_take isl_union_set *uset2);
2678 __isl_give isl_union_map *isl_union_map_subtract(
2679 __isl_take isl_union_map *umap1,
2680 __isl_take isl_union_map *umap2);
2681 __isl_give isl_union_map *isl_union_map_subtract_domain(
2682 __isl_take isl_union_map *umap,
2683 __isl_take isl_union_set *dom);
2687 __isl_give isl_basic_set *isl_basic_set_apply(
2688 __isl_take isl_basic_set *bset,
2689 __isl_take isl_basic_map *bmap);
2690 __isl_give isl_set *isl_set_apply(
2691 __isl_take isl_set *set,
2692 __isl_take isl_map *map);
2693 __isl_give isl_union_set *isl_union_set_apply(
2694 __isl_take isl_union_set *uset,
2695 __isl_take isl_union_map *umap);
2696 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2697 __isl_take isl_basic_map *bmap1,
2698 __isl_take isl_basic_map *bmap2);
2699 __isl_give isl_basic_map *isl_basic_map_apply_range(
2700 __isl_take isl_basic_map *bmap1,
2701 __isl_take isl_basic_map *bmap2);
2702 __isl_give isl_map *isl_map_apply_domain(
2703 __isl_take isl_map *map1,
2704 __isl_take isl_map *map2);
2705 __isl_give isl_union_map *isl_union_map_apply_domain(
2706 __isl_take isl_union_map *umap1,
2707 __isl_take isl_union_map *umap2);
2708 __isl_give isl_map *isl_map_apply_range(
2709 __isl_take isl_map *map1,
2710 __isl_take isl_map *map2);
2711 __isl_give isl_union_map *isl_union_map_apply_range(
2712 __isl_take isl_union_map *umap1,
2713 __isl_take isl_union_map *umap2);
2715 =item * Cartesian Product
2717 __isl_give isl_set *isl_set_product(
2718 __isl_take isl_set *set1,
2719 __isl_take isl_set *set2);
2720 __isl_give isl_union_set *isl_union_set_product(
2721 __isl_take isl_union_set *uset1,
2722 __isl_take isl_union_set *uset2);
2723 __isl_give isl_basic_map *isl_basic_map_domain_product(
2724 __isl_take isl_basic_map *bmap1,
2725 __isl_take isl_basic_map *bmap2);
2726 __isl_give isl_basic_map *isl_basic_map_range_product(
2727 __isl_take isl_basic_map *bmap1,
2728 __isl_take isl_basic_map *bmap2);
2729 __isl_give isl_basic_map *isl_basic_map_product(
2730 __isl_take isl_basic_map *bmap1,
2731 __isl_take isl_basic_map *bmap2);
2732 __isl_give isl_map *isl_map_domain_product(
2733 __isl_take isl_map *map1,
2734 __isl_take isl_map *map2);
2735 __isl_give isl_map *isl_map_range_product(
2736 __isl_take isl_map *map1,
2737 __isl_take isl_map *map2);
2738 __isl_give isl_union_map *isl_union_map_domain_product(
2739 __isl_take isl_union_map *umap1,
2740 __isl_take isl_union_map *umap2);
2741 __isl_give isl_union_map *isl_union_map_range_product(
2742 __isl_take isl_union_map *umap1,
2743 __isl_take isl_union_map *umap2);
2744 __isl_give isl_map *isl_map_product(
2745 __isl_take isl_map *map1,
2746 __isl_take isl_map *map2);
2747 __isl_give isl_union_map *isl_union_map_product(
2748 __isl_take isl_union_map *umap1,
2749 __isl_take isl_union_map *umap2);
2751 The above functions compute the cross product of the given
2752 sets or relations. The domains and ranges of the results
2753 are wrapped maps between domains and ranges of the inputs.
2754 To obtain a ``flat'' product, use the following functions
2757 __isl_give isl_basic_set *isl_basic_set_flat_product(
2758 __isl_take isl_basic_set *bset1,
2759 __isl_take isl_basic_set *bset2);
2760 __isl_give isl_set *isl_set_flat_product(
2761 __isl_take isl_set *set1,
2762 __isl_take isl_set *set2);
2763 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2764 __isl_take isl_basic_map *bmap1,
2765 __isl_take isl_basic_map *bmap2);
2766 __isl_give isl_map *isl_map_flat_domain_product(
2767 __isl_take isl_map *map1,
2768 __isl_take isl_map *map2);
2769 __isl_give isl_map *isl_map_flat_range_product(
2770 __isl_take isl_map *map1,
2771 __isl_take isl_map *map2);
2772 __isl_give isl_union_map *isl_union_map_flat_range_product(
2773 __isl_take isl_union_map *umap1,
2774 __isl_take isl_union_map *umap2);
2775 __isl_give isl_basic_map *isl_basic_map_flat_product(
2776 __isl_take isl_basic_map *bmap1,
2777 __isl_take isl_basic_map *bmap2);
2778 __isl_give isl_map *isl_map_flat_product(
2779 __isl_take isl_map *map1,
2780 __isl_take isl_map *map2);
2782 =item * Simplification
2784 __isl_give isl_basic_set *isl_basic_set_gist(
2785 __isl_take isl_basic_set *bset,
2786 __isl_take isl_basic_set *context);
2787 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2788 __isl_take isl_set *context);
2789 __isl_give isl_set *isl_set_gist_params(
2790 __isl_take isl_set *set,
2791 __isl_take isl_set *context);
2792 __isl_give isl_union_set *isl_union_set_gist(
2793 __isl_take isl_union_set *uset,
2794 __isl_take isl_union_set *context);
2795 __isl_give isl_union_set *isl_union_set_gist_params(
2796 __isl_take isl_union_set *uset,
2797 __isl_take isl_set *set);
2798 __isl_give isl_basic_map *isl_basic_map_gist(
2799 __isl_take isl_basic_map *bmap,
2800 __isl_take isl_basic_map *context);
2801 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2802 __isl_take isl_map *context);
2803 __isl_give isl_map *isl_map_gist_params(
2804 __isl_take isl_map *map,
2805 __isl_take isl_set *context);
2806 __isl_give isl_map *isl_map_gist_domain(
2807 __isl_take isl_map *map,
2808 __isl_take isl_set *context);
2809 __isl_give isl_map *isl_map_gist_range(
2810 __isl_take isl_map *map,
2811 __isl_take isl_set *context);
2812 __isl_give isl_union_map *isl_union_map_gist(
2813 __isl_take isl_union_map *umap,
2814 __isl_take isl_union_map *context);
2815 __isl_give isl_union_map *isl_union_map_gist_params(
2816 __isl_take isl_union_map *umap,
2817 __isl_take isl_set *set);
2818 __isl_give isl_union_map *isl_union_map_gist_domain(
2819 __isl_take isl_union_map *umap,
2820 __isl_take isl_union_set *uset);
2821 __isl_give isl_union_map *isl_union_map_gist_range(
2822 __isl_take isl_union_map *umap,
2823 __isl_take isl_union_set *uset);
2825 The gist operation returns a set or relation that has the
2826 same intersection with the context as the input set or relation.
2827 Any implicit equality in the intersection is made explicit in the result,
2828 while all inequalities that are redundant with respect to the intersection
2830 In case of union sets and relations, the gist operation is performed
2835 =head3 Lexicographic Optimization
2837 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2838 the following functions
2839 compute a set that contains the lexicographic minimum or maximum
2840 of the elements in C<set> (or C<bset>) for those values of the parameters
2841 that satisfy C<dom>.
2842 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2843 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2845 In other words, the union of the parameter values
2846 for which the result is non-empty and of C<*empty>
2849 __isl_give isl_set *isl_basic_set_partial_lexmin(
2850 __isl_take isl_basic_set *bset,
2851 __isl_take isl_basic_set *dom,
2852 __isl_give isl_set **empty);
2853 __isl_give isl_set *isl_basic_set_partial_lexmax(
2854 __isl_take isl_basic_set *bset,
2855 __isl_take isl_basic_set *dom,
2856 __isl_give isl_set **empty);
2857 __isl_give isl_set *isl_set_partial_lexmin(
2858 __isl_take isl_set *set, __isl_take isl_set *dom,
2859 __isl_give isl_set **empty);
2860 __isl_give isl_set *isl_set_partial_lexmax(
2861 __isl_take isl_set *set, __isl_take isl_set *dom,
2862 __isl_give isl_set **empty);
2864 Given a (basic) set C<set> (or C<bset>), the following functions simply
2865 return a set containing the lexicographic minimum or maximum
2866 of the elements in C<set> (or C<bset>).
2867 In case of union sets, the optimum is computed per space.
2869 __isl_give isl_set *isl_basic_set_lexmin(
2870 __isl_take isl_basic_set *bset);
2871 __isl_give isl_set *isl_basic_set_lexmax(
2872 __isl_take isl_basic_set *bset);
2873 __isl_give isl_set *isl_set_lexmin(
2874 __isl_take isl_set *set);
2875 __isl_give isl_set *isl_set_lexmax(
2876 __isl_take isl_set *set);
2877 __isl_give isl_union_set *isl_union_set_lexmin(
2878 __isl_take isl_union_set *uset);
2879 __isl_give isl_union_set *isl_union_set_lexmax(
2880 __isl_take isl_union_set *uset);
2882 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2883 the following functions
2884 compute a relation that maps each element of C<dom>
2885 to the single lexicographic minimum or maximum
2886 of the elements that are associated to that same
2887 element in C<map> (or C<bmap>).
2888 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2889 that contains the elements in C<dom> that do not map
2890 to any elements in C<map> (or C<bmap>).
2891 In other words, the union of the domain of the result and of C<*empty>
2894 __isl_give isl_map *isl_basic_map_partial_lexmax(
2895 __isl_take isl_basic_map *bmap,
2896 __isl_take isl_basic_set *dom,
2897 __isl_give isl_set **empty);
2898 __isl_give isl_map *isl_basic_map_partial_lexmin(
2899 __isl_take isl_basic_map *bmap,
2900 __isl_take isl_basic_set *dom,
2901 __isl_give isl_set **empty);
2902 __isl_give isl_map *isl_map_partial_lexmax(
2903 __isl_take isl_map *map, __isl_take isl_set *dom,
2904 __isl_give isl_set **empty);
2905 __isl_give isl_map *isl_map_partial_lexmin(
2906 __isl_take isl_map *map, __isl_take isl_set *dom,
2907 __isl_give isl_set **empty);
2909 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2910 return a map mapping each element in the domain of
2911 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2912 of all elements associated to that element.
2913 In case of union relations, the optimum is computed per space.
2915 __isl_give isl_map *isl_basic_map_lexmin(
2916 __isl_take isl_basic_map *bmap);
2917 __isl_give isl_map *isl_basic_map_lexmax(
2918 __isl_take isl_basic_map *bmap);
2919 __isl_give isl_map *isl_map_lexmin(
2920 __isl_take isl_map *map);
2921 __isl_give isl_map *isl_map_lexmax(
2922 __isl_take isl_map *map);
2923 __isl_give isl_union_map *isl_union_map_lexmin(
2924 __isl_take isl_union_map *umap);
2925 __isl_give isl_union_map *isl_union_map_lexmax(
2926 __isl_take isl_union_map *umap);
2928 The following functions return their result in the form of
2929 a piecewise multi-affine expression
2930 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2931 but are otherwise equivalent to the corresponding functions
2932 returning a basic set or relation.
2934 __isl_give isl_pw_multi_aff *
2935 isl_basic_map_lexmin_pw_multi_aff(
2936 __isl_take isl_basic_map *bmap);
2937 __isl_give isl_pw_multi_aff *
2938 isl_basic_set_partial_lexmin_pw_multi_aff(
2939 __isl_take isl_basic_set *bset,
2940 __isl_take isl_basic_set *dom,
2941 __isl_give isl_set **empty);
2942 __isl_give isl_pw_multi_aff *
2943 isl_basic_set_partial_lexmax_pw_multi_aff(
2944 __isl_take isl_basic_set *bset,
2945 __isl_take isl_basic_set *dom,
2946 __isl_give isl_set **empty);
2947 __isl_give isl_pw_multi_aff *
2948 isl_basic_map_partial_lexmin_pw_multi_aff(
2949 __isl_take isl_basic_map *bmap,
2950 __isl_take isl_basic_set *dom,
2951 __isl_give isl_set **empty);
2952 __isl_give isl_pw_multi_aff *
2953 isl_basic_map_partial_lexmax_pw_multi_aff(
2954 __isl_take isl_basic_map *bmap,
2955 __isl_take isl_basic_set *dom,
2956 __isl_give isl_set **empty);
2957 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
2958 __isl_take isl_map *map);
2959 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
2960 __isl_take isl_map *map);
2964 Lists are defined over several element types, including
2965 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
2966 C<isl_basic_set> and C<isl_set>.
2967 Here we take lists of C<isl_set>s as an example.
2968 Lists can be created, copied, modified and freed using the following functions.
2970 #include <isl/list.h>
2971 __isl_give isl_set_list *isl_set_list_from_set(
2972 __isl_take isl_set *el);
2973 __isl_give isl_set_list *isl_set_list_alloc(
2974 isl_ctx *ctx, int n);
2975 __isl_give isl_set_list *isl_set_list_copy(
2976 __isl_keep isl_set_list *list);
2977 __isl_give isl_set_list *isl_set_list_insert(
2978 __isl_take isl_set_list *list, unsigned pos,
2979 __isl_take isl_set *el);
2980 __isl_give isl_set_list *isl_set_list_add(
2981 __isl_take isl_set_list *list,
2982 __isl_take isl_set *el);
2983 __isl_give isl_set_list *isl_set_list_drop(
2984 __isl_take isl_set_list *list,
2985 unsigned first, unsigned n);
2986 __isl_give isl_set_list *isl_set_list_set_set(
2987 __isl_take isl_set_list *list, int index,
2988 __isl_take isl_set *set);
2989 __isl_give isl_set_list *isl_set_list_concat(
2990 __isl_take isl_set_list *list1,
2991 __isl_take isl_set_list *list2);
2992 void *isl_set_list_free(__isl_take isl_set_list *list);
2994 C<isl_set_list_alloc> creates an empty list with a capacity for
2995 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2998 Lists can be inspected using the following functions.
3000 #include <isl/list.h>
3001 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3002 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3003 __isl_give isl_set *isl_set_list_get_set(
3004 __isl_keep isl_set_list *list, int index);
3005 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3006 int (*fn)(__isl_take isl_set *el, void *user),
3009 Lists can be printed using
3011 #include <isl/list.h>
3012 __isl_give isl_printer *isl_printer_print_set_list(
3013 __isl_take isl_printer *p,
3014 __isl_keep isl_set_list *list);
3018 Vectors can be created, copied and freed using the following functions.
3020 #include <isl/vec.h>
3021 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3023 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3024 void *isl_vec_free(__isl_take isl_vec *vec);
3026 Note that the elements of a newly created vector may have arbitrary values.
3027 The elements can be changed and inspected using the following functions.
3029 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3030 int isl_vec_size(__isl_keep isl_vec *vec);
3031 int isl_vec_get_element(__isl_keep isl_vec *vec,
3032 int pos, isl_int *v);
3033 __isl_give isl_vec *isl_vec_set_element(
3034 __isl_take isl_vec *vec, int pos, isl_int v);
3035 __isl_give isl_vec *isl_vec_set_element_si(
3036 __isl_take isl_vec *vec, int pos, int v);
3037 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3039 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3041 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3044 C<isl_vec_get_element> will return a negative value if anything went wrong.
3045 In that case, the value of C<*v> is undefined.
3047 The following function can be used to concatenate two vectors.
3049 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3050 __isl_take isl_vec *vec2);
3054 Matrices can be created, copied and freed using the following functions.
3056 #include <isl/mat.h>
3057 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3058 unsigned n_row, unsigned n_col);
3059 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3060 void isl_mat_free(__isl_take isl_mat *mat);
3062 Note that the elements of a newly created matrix may have arbitrary values.
3063 The elements can be changed and inspected using the following functions.
3065 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3066 int isl_mat_rows(__isl_keep isl_mat *mat);
3067 int isl_mat_cols(__isl_keep isl_mat *mat);
3068 int isl_mat_get_element(__isl_keep isl_mat *mat,
3069 int row, int col, isl_int *v);
3070 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3071 int row, int col, isl_int v);
3072 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3073 int row, int col, int v);
3075 C<isl_mat_get_element> will return a negative value if anything went wrong.
3076 In that case, the value of C<*v> is undefined.
3078 The following function can be used to compute the (right) inverse
3079 of a matrix, i.e., a matrix such that the product of the original
3080 and the inverse (in that order) is a multiple of the identity matrix.
3081 The input matrix is assumed to be of full row-rank.
3083 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3085 The following function can be used to compute the (right) kernel
3086 (or null space) of a matrix, i.e., a matrix such that the product of
3087 the original and the kernel (in that order) is the zero matrix.
3089 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3091 =head2 Piecewise Quasi Affine Expressions
3093 The zero quasi affine expression on a given domain can be created using
3095 __isl_give isl_aff *isl_aff_zero_on_domain(
3096 __isl_take isl_local_space *ls);
3098 Note that the space in which the resulting object lives is a map space
3099 with the given space as domain and a one-dimensional range.
3101 An empty piecewise quasi affine expression (one with no cells)
3102 or a piecewise quasi affine expression with a single cell can
3103 be created using the following functions.
3105 #include <isl/aff.h>
3106 __isl_give isl_pw_aff *isl_pw_aff_empty(
3107 __isl_take isl_space *space);
3108 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3109 __isl_take isl_set *set, __isl_take isl_aff *aff);
3110 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3111 __isl_take isl_aff *aff);
3113 A piecewise quasi affine expression that is equal to 1 on a set
3114 and 0 outside the set can be created using the following function.
3116 #include <isl/aff.h>
3117 __isl_give isl_pw_aff *isl_set_indicator_function(
3118 __isl_take isl_set *set);
3120 Quasi affine expressions can be copied and freed using
3122 #include <isl/aff.h>
3123 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3124 void *isl_aff_free(__isl_take isl_aff *aff);
3126 __isl_give isl_pw_aff *isl_pw_aff_copy(
3127 __isl_keep isl_pw_aff *pwaff);
3128 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3130 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3131 using the following function. The constraint is required to have
3132 a non-zero coefficient for the specified dimension.
3134 #include <isl/constraint.h>
3135 __isl_give isl_aff *isl_constraint_get_bound(
3136 __isl_keep isl_constraint *constraint,
3137 enum isl_dim_type type, int pos);
3139 The entire affine expression of the constraint can also be extracted
3140 using the following function.
3142 #include <isl/constraint.h>
3143 __isl_give isl_aff *isl_constraint_get_aff(
3144 __isl_keep isl_constraint *constraint);
3146 Conversely, an equality constraint equating
3147 the affine expression to zero or an inequality constraint enforcing
3148 the affine expression to be non-negative, can be constructed using
3150 __isl_give isl_constraint *isl_equality_from_aff(
3151 __isl_take isl_aff *aff);
3152 __isl_give isl_constraint *isl_inequality_from_aff(
3153 __isl_take isl_aff *aff);
3155 The expression can be inspected using
3157 #include <isl/aff.h>
3158 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3159 int isl_aff_dim(__isl_keep isl_aff *aff,
3160 enum isl_dim_type type);
3161 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3162 __isl_keep isl_aff *aff);
3163 __isl_give isl_local_space *isl_aff_get_local_space(
3164 __isl_keep isl_aff *aff);
3165 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3166 enum isl_dim_type type, unsigned pos);
3167 const char *isl_pw_aff_get_dim_name(
3168 __isl_keep isl_pw_aff *pa,
3169 enum isl_dim_type type, unsigned pos);
3170 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3171 enum isl_dim_type type, unsigned pos);
3172 __isl_give isl_id *isl_pw_aff_get_dim_id(
3173 __isl_keep isl_pw_aff *pa,
3174 enum isl_dim_type type, unsigned pos);
3175 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3176 __isl_keep isl_pw_aff *pa,
3177 enum isl_dim_type type);
3178 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3180 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3181 enum isl_dim_type type, int pos, isl_int *v);
3182 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3184 __isl_give isl_aff *isl_aff_get_div(
3185 __isl_keep isl_aff *aff, int pos);
3187 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3188 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3189 int (*fn)(__isl_take isl_set *set,
3190 __isl_take isl_aff *aff,
3191 void *user), void *user);
3193 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3194 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3196 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3197 enum isl_dim_type type, unsigned first, unsigned n);
3198 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3199 enum isl_dim_type type, unsigned first, unsigned n);
3201 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3202 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3203 enum isl_dim_type type);
3204 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3206 It can be modified using
3208 #include <isl/aff.h>
3209 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3210 __isl_take isl_pw_aff *pwaff,
3211 enum isl_dim_type type, __isl_take isl_id *id);
3212 __isl_give isl_aff *isl_aff_set_dim_name(
3213 __isl_take isl_aff *aff, enum isl_dim_type type,
3214 unsigned pos, const char *s);
3215 __isl_give isl_aff *isl_aff_set_dim_id(
3216 __isl_take isl_aff *aff, enum isl_dim_type type,
3217 unsigned pos, __isl_take isl_id *id);
3218 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3219 __isl_take isl_pw_aff *pma,
3220 enum isl_dim_type type, unsigned pos,
3221 __isl_take isl_id *id);
3222 __isl_give isl_aff *isl_aff_set_constant(
3223 __isl_take isl_aff *aff, isl_int v);
3224 __isl_give isl_aff *isl_aff_set_constant_si(
3225 __isl_take isl_aff *aff, int v);
3226 __isl_give isl_aff *isl_aff_set_coefficient(
3227 __isl_take isl_aff *aff,
3228 enum isl_dim_type type, int pos, isl_int v);
3229 __isl_give isl_aff *isl_aff_set_coefficient_si(
3230 __isl_take isl_aff *aff,
3231 enum isl_dim_type type, int pos, int v);
3232 __isl_give isl_aff *isl_aff_set_denominator(
3233 __isl_take isl_aff *aff, isl_int v);
3235 __isl_give isl_aff *isl_aff_add_constant(
3236 __isl_take isl_aff *aff, isl_int v);
3237 __isl_give isl_aff *isl_aff_add_constant_si(
3238 __isl_take isl_aff *aff, int v);
3239 __isl_give isl_aff *isl_aff_add_constant_num(
3240 __isl_take isl_aff *aff, isl_int v);
3241 __isl_give isl_aff *isl_aff_add_constant_num_si(
3242 __isl_take isl_aff *aff, int v);
3243 __isl_give isl_aff *isl_aff_add_coefficient(
3244 __isl_take isl_aff *aff,
3245 enum isl_dim_type type, int pos, isl_int v);
3246 __isl_give isl_aff *isl_aff_add_coefficient_si(
3247 __isl_take isl_aff *aff,
3248 enum isl_dim_type type, int pos, int v);
3250 __isl_give isl_aff *isl_aff_insert_dims(
3251 __isl_take isl_aff *aff,
3252 enum isl_dim_type type, unsigned first, unsigned n);
3253 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3254 __isl_take isl_pw_aff *pwaff,
3255 enum isl_dim_type type, unsigned first, unsigned n);
3256 __isl_give isl_aff *isl_aff_add_dims(
3257 __isl_take isl_aff *aff,
3258 enum isl_dim_type type, unsigned n);
3259 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3260 __isl_take isl_pw_aff *pwaff,
3261 enum isl_dim_type type, unsigned n);
3262 __isl_give isl_aff *isl_aff_drop_dims(
3263 __isl_take isl_aff *aff,
3264 enum isl_dim_type type, unsigned first, unsigned n);
3265 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3266 __isl_take isl_pw_aff *pwaff,
3267 enum isl_dim_type type, unsigned first, unsigned n);
3269 Note that the C<set_constant> and C<set_coefficient> functions
3270 set the I<numerator> of the constant or coefficient, while
3271 C<add_constant> and C<add_coefficient> add an integer value to
3272 the possibly rational constant or coefficient.
3273 The C<add_constant_num> functions add an integer value to
3276 To check whether an affine expressions is obviously zero
3277 or obviously equal to some other affine expression, use
3279 #include <isl/aff.h>
3280 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3281 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3282 __isl_keep isl_aff *aff2);
3283 int isl_pw_aff_plain_is_equal(
3284 __isl_keep isl_pw_aff *pwaff1,
3285 __isl_keep isl_pw_aff *pwaff2);
3289 #include <isl/aff.h>
3290 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3291 __isl_take isl_aff *aff2);
3292 __isl_give isl_pw_aff *isl_pw_aff_add(
3293 __isl_take isl_pw_aff *pwaff1,
3294 __isl_take isl_pw_aff *pwaff2);
3295 __isl_give isl_pw_aff *isl_pw_aff_min(
3296 __isl_take isl_pw_aff *pwaff1,
3297 __isl_take isl_pw_aff *pwaff2);
3298 __isl_give isl_pw_aff *isl_pw_aff_max(
3299 __isl_take isl_pw_aff *pwaff1,
3300 __isl_take isl_pw_aff *pwaff2);
3301 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3302 __isl_take isl_aff *aff2);
3303 __isl_give isl_pw_aff *isl_pw_aff_sub(
3304 __isl_take isl_pw_aff *pwaff1,
3305 __isl_take isl_pw_aff *pwaff2);
3306 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3307 __isl_give isl_pw_aff *isl_pw_aff_neg(
3308 __isl_take isl_pw_aff *pwaff);
3309 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3310 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3311 __isl_take isl_pw_aff *pwaff);
3312 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3313 __isl_give isl_pw_aff *isl_pw_aff_floor(
3314 __isl_take isl_pw_aff *pwaff);
3315 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3317 __isl_give isl_pw_aff *isl_pw_aff_mod(
3318 __isl_take isl_pw_aff *pwaff, isl_int mod);
3319 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3321 __isl_give isl_pw_aff *isl_pw_aff_scale(
3322 __isl_take isl_pw_aff *pwaff, isl_int f);
3323 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3325 __isl_give isl_aff *isl_aff_scale_down_ui(
3326 __isl_take isl_aff *aff, unsigned f);
3327 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3328 __isl_take isl_pw_aff *pwaff, isl_int f);
3330 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3331 __isl_take isl_pw_aff_list *list);
3332 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3333 __isl_take isl_pw_aff_list *list);
3335 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3336 __isl_take isl_pw_aff *pwqp);
3338 __isl_give isl_aff *isl_aff_align_params(
3339 __isl_take isl_aff *aff,
3340 __isl_take isl_space *model);
3341 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3342 __isl_take isl_pw_aff *pwaff,
3343 __isl_take isl_space *model);
3345 __isl_give isl_aff *isl_aff_project_domain_on_params(
3346 __isl_take isl_aff *aff);
3348 __isl_give isl_aff *isl_aff_gist_params(
3349 __isl_take isl_aff *aff,
3350 __isl_take isl_set *context);
3351 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3352 __isl_take isl_set *context);
3353 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3354 __isl_take isl_pw_aff *pwaff,
3355 __isl_take isl_set *context);
3356 __isl_give isl_pw_aff *isl_pw_aff_gist(
3357 __isl_take isl_pw_aff *pwaff,
3358 __isl_take isl_set *context);
3360 __isl_give isl_set *isl_pw_aff_domain(
3361 __isl_take isl_pw_aff *pwaff);
3362 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3363 __isl_take isl_pw_aff *pa,
3364 __isl_take isl_set *set);
3365 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3366 __isl_take isl_pw_aff *pa,
3367 __isl_take isl_set *set);
3369 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3370 __isl_take isl_aff *aff2);
3371 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3372 __isl_take isl_aff *aff2);
3373 __isl_give isl_pw_aff *isl_pw_aff_mul(
3374 __isl_take isl_pw_aff *pwaff1,
3375 __isl_take isl_pw_aff *pwaff2);
3376 __isl_give isl_pw_aff *isl_pw_aff_div(
3377 __isl_take isl_pw_aff *pa1,
3378 __isl_take isl_pw_aff *pa2);
3380 When multiplying two affine expressions, at least one of the two needs
3381 to be a constant. Similarly, when dividing an affine expression by another,
3382 the second expression needs to be a constant.
3384 #include <isl/aff.h>
3385 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3386 __isl_take isl_aff *aff);
3387 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3388 __isl_take isl_aff *aff);
3389 __isl_give isl_basic_set *isl_aff_le_basic_set(
3390 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3391 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3392 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3393 __isl_give isl_set *isl_pw_aff_eq_set(
3394 __isl_take isl_pw_aff *pwaff1,
3395 __isl_take isl_pw_aff *pwaff2);
3396 __isl_give isl_set *isl_pw_aff_ne_set(
3397 __isl_take isl_pw_aff *pwaff1,
3398 __isl_take isl_pw_aff *pwaff2);
3399 __isl_give isl_set *isl_pw_aff_le_set(
3400 __isl_take isl_pw_aff *pwaff1,
3401 __isl_take isl_pw_aff *pwaff2);
3402 __isl_give isl_set *isl_pw_aff_lt_set(
3403 __isl_take isl_pw_aff *pwaff1,
3404 __isl_take isl_pw_aff *pwaff2);
3405 __isl_give isl_set *isl_pw_aff_ge_set(
3406 __isl_take isl_pw_aff *pwaff1,
3407 __isl_take isl_pw_aff *pwaff2);
3408 __isl_give isl_set *isl_pw_aff_gt_set(
3409 __isl_take isl_pw_aff *pwaff1,
3410 __isl_take isl_pw_aff *pwaff2);
3412 __isl_give isl_set *isl_pw_aff_list_eq_set(
3413 __isl_take isl_pw_aff_list *list1,
3414 __isl_take isl_pw_aff_list *list2);
3415 __isl_give isl_set *isl_pw_aff_list_ne_set(
3416 __isl_take isl_pw_aff_list *list1,
3417 __isl_take isl_pw_aff_list *list2);
3418 __isl_give isl_set *isl_pw_aff_list_le_set(
3419 __isl_take isl_pw_aff_list *list1,
3420 __isl_take isl_pw_aff_list *list2);
3421 __isl_give isl_set *isl_pw_aff_list_lt_set(
3422 __isl_take isl_pw_aff_list *list1,
3423 __isl_take isl_pw_aff_list *list2);
3424 __isl_give isl_set *isl_pw_aff_list_ge_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_gt_set(
3428 __isl_take isl_pw_aff_list *list1,
3429 __isl_take isl_pw_aff_list *list2);
3431 The function C<isl_aff_neg_basic_set> returns a basic set
3432 containing those elements in the domain space
3433 of C<aff> where C<aff> is negative.
3434 The function C<isl_aff_ge_basic_set> returns a basic set
3435 containing those elements in the shared space
3436 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3437 The function C<isl_pw_aff_ge_set> returns a set
3438 containing those elements in the shared domain
3439 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3440 The functions operating on C<isl_pw_aff_list> apply the corresponding
3441 C<isl_pw_aff> function to each pair of elements in the two lists.
3443 #include <isl/aff.h>
3444 __isl_give isl_set *isl_pw_aff_nonneg_set(
3445 __isl_take isl_pw_aff *pwaff);
3446 __isl_give isl_set *isl_pw_aff_zero_set(
3447 __isl_take isl_pw_aff *pwaff);
3448 __isl_give isl_set *isl_pw_aff_non_zero_set(
3449 __isl_take isl_pw_aff *pwaff);
3451 The function C<isl_pw_aff_nonneg_set> returns a set
3452 containing those elements in the domain
3453 of C<pwaff> where C<pwaff> is non-negative.
3455 #include <isl/aff.h>
3456 __isl_give isl_pw_aff *isl_pw_aff_cond(
3457 __isl_take isl_pw_aff *cond,
3458 __isl_take isl_pw_aff *pwaff_true,
3459 __isl_take isl_pw_aff *pwaff_false);
3461 The function C<isl_pw_aff_cond> performs a conditional operator
3462 and returns an expression that is equal to C<pwaff_true>
3463 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3464 where C<cond> is zero.
3466 #include <isl/aff.h>
3467 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3468 __isl_take isl_pw_aff *pwaff1,
3469 __isl_take isl_pw_aff *pwaff2);
3470 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3471 __isl_take isl_pw_aff *pwaff1,
3472 __isl_take isl_pw_aff *pwaff2);
3473 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3474 __isl_take isl_pw_aff *pwaff1,
3475 __isl_take isl_pw_aff *pwaff2);
3477 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3478 expression with a domain that is the union of those of C<pwaff1> and
3479 C<pwaff2> and such that on each cell, the quasi-affine expression is
3480 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3481 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3482 associated expression is the defined one.
3484 An expression can be read from input using
3486 #include <isl/aff.h>
3487 __isl_give isl_aff *isl_aff_read_from_str(
3488 isl_ctx *ctx, const char *str);
3489 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3490 isl_ctx *ctx, const char *str);
3492 An expression can be printed using
3494 #include <isl/aff.h>
3495 __isl_give isl_printer *isl_printer_print_aff(
3496 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3498 __isl_give isl_printer *isl_printer_print_pw_aff(
3499 __isl_take isl_printer *p,
3500 __isl_keep isl_pw_aff *pwaff);
3502 =head2 Piecewise Multiple Quasi Affine Expressions
3504 An C<isl_multi_aff> object represents a sequence of
3505 zero or more affine expressions, all defined on the same domain space.
3507 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3510 #include <isl/aff.h>
3511 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3512 __isl_take isl_space *space,
3513 __isl_take isl_aff_list *list);
3515 An empty piecewise multiple quasi affine expression (one with no cells),
3516 the zero piecewise multiple quasi affine expression (with value zero
3517 for each output dimension),
3518 a piecewise multiple quasi affine expression with a single cell (with
3519 either a universe or a specified domain) or
3520 a zero-dimensional piecewise multiple quasi affine expression
3522 can be created using the following functions.
3524 #include <isl/aff.h>
3525 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3526 __isl_take isl_space *space);
3527 __isl_give isl_multi_aff *isl_multi_aff_zero(
3528 __isl_take isl_space *space);
3529 __isl_give isl_multi_aff *isl_multi_aff_identity(
3530 __isl_take isl_space *space);
3531 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3532 __isl_take isl_space *space);
3533 __isl_give isl_pw_multi_aff *
3534 isl_pw_multi_aff_from_multi_aff(
3535 __isl_take isl_multi_aff *ma);
3536 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3537 __isl_take isl_set *set,
3538 __isl_take isl_multi_aff *maff);
3539 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3540 __isl_take isl_set *set);
3542 __isl_give isl_union_pw_multi_aff *
3543 isl_union_pw_multi_aff_empty(
3544 __isl_take isl_space *space);
3545 __isl_give isl_union_pw_multi_aff *
3546 isl_union_pw_multi_aff_add_pw_multi_aff(
3547 __isl_take isl_union_pw_multi_aff *upma,
3548 __isl_take isl_pw_multi_aff *pma);
3549 __isl_give isl_union_pw_multi_aff *
3550 isl_union_pw_multi_aff_from_domain(
3551 __isl_take isl_union_set *uset);
3553 A piecewise multiple quasi affine expression can also be initialized
3554 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3555 and the C<isl_map> is single-valued.
3557 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3558 __isl_take isl_set *set);
3559 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3560 __isl_take isl_map *map);
3562 Multiple quasi affine expressions can be copied and freed using
3564 #include <isl/aff.h>
3565 __isl_give isl_multi_aff *isl_multi_aff_copy(
3566 __isl_keep isl_multi_aff *maff);
3567 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3569 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3570 __isl_keep isl_pw_multi_aff *pma);
3571 void *isl_pw_multi_aff_free(
3572 __isl_take isl_pw_multi_aff *pma);
3574 __isl_give isl_union_pw_multi_aff *
3575 isl_union_pw_multi_aff_copy(
3576 __isl_keep isl_union_pw_multi_aff *upma);
3577 void *isl_union_pw_multi_aff_free(
3578 __isl_take isl_union_pw_multi_aff *upma);
3580 The expression can be inspected using
3582 #include <isl/aff.h>
3583 isl_ctx *isl_multi_aff_get_ctx(
3584 __isl_keep isl_multi_aff *maff);
3585 isl_ctx *isl_pw_multi_aff_get_ctx(
3586 __isl_keep isl_pw_multi_aff *pma);
3587 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3588 __isl_keep isl_union_pw_multi_aff *upma);
3589 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3590 enum isl_dim_type type);
3591 unsigned isl_pw_multi_aff_dim(
3592 __isl_keep isl_pw_multi_aff *pma,
3593 enum isl_dim_type type);
3594 __isl_give isl_aff *isl_multi_aff_get_aff(
3595 __isl_keep isl_multi_aff *multi, int pos);
3596 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3597 __isl_keep isl_pw_multi_aff *pma, int pos);
3598 const char *isl_pw_multi_aff_get_dim_name(
3599 __isl_keep isl_pw_multi_aff *pma,
3600 enum isl_dim_type type, unsigned pos);
3601 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3602 __isl_keep isl_pw_multi_aff *pma,
3603 enum isl_dim_type type, unsigned pos);
3604 const char *isl_multi_aff_get_tuple_name(
3605 __isl_keep isl_multi_aff *multi,
3606 enum isl_dim_type type);
3607 int isl_pw_multi_aff_has_tuple_name(
3608 __isl_keep isl_pw_multi_aff *pma,
3609 enum isl_dim_type type);
3610 const char *isl_pw_multi_aff_get_tuple_name(
3611 __isl_keep isl_pw_multi_aff *pma,
3612 enum isl_dim_type type);
3613 int isl_pw_multi_aff_has_tuple_id(
3614 __isl_keep isl_pw_multi_aff *pma,
3615 enum isl_dim_type type);
3616 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3617 __isl_keep isl_pw_multi_aff *pma,
3618 enum isl_dim_type type);
3620 int isl_pw_multi_aff_foreach_piece(
3621 __isl_keep isl_pw_multi_aff *pma,
3622 int (*fn)(__isl_take isl_set *set,
3623 __isl_take isl_multi_aff *maff,
3624 void *user), void *user);
3626 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3627 __isl_keep isl_union_pw_multi_aff *upma,
3628 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3629 void *user), void *user);
3631 It can be modified using
3633 #include <isl/aff.h>
3634 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3635 __isl_take isl_multi_aff *multi, int pos,
3636 __isl_take isl_aff *aff);
3637 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3638 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3639 __isl_take isl_pw_aff *pa);
3640 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3641 __isl_take isl_multi_aff *maff,
3642 enum isl_dim_type type, unsigned pos, const char *s);
3643 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3644 __isl_take isl_multi_aff *maff,
3645 enum isl_dim_type type, __isl_take isl_id *id);
3646 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3647 __isl_take isl_pw_multi_aff *pma,
3648 enum isl_dim_type type, __isl_take isl_id *id);
3650 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3651 __isl_take isl_multi_aff *maff,
3652 enum isl_dim_type type, unsigned first, unsigned n);
3653 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
3654 __isl_take isl_pw_multi_aff *pma,
3655 enum isl_dim_type type, unsigned first, unsigned n);
3657 To check whether two multiple affine expressions are
3658 obviously equal to each other, use
3660 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3661 __isl_keep isl_multi_aff *maff2);
3662 int isl_pw_multi_aff_plain_is_equal(
3663 __isl_keep isl_pw_multi_aff *pma1,
3664 __isl_keep isl_pw_multi_aff *pma2);
3668 #include <isl/aff.h>
3669 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3670 __isl_take isl_pw_multi_aff *pma1,
3671 __isl_take isl_pw_multi_aff *pma2);
3672 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3673 __isl_take isl_pw_multi_aff *pma1,
3674 __isl_take isl_pw_multi_aff *pma2);
3675 __isl_give isl_multi_aff *isl_multi_aff_add(
3676 __isl_take isl_multi_aff *maff1,
3677 __isl_take isl_multi_aff *maff2);
3678 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3679 __isl_take isl_pw_multi_aff *pma1,
3680 __isl_take isl_pw_multi_aff *pma2);
3681 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3682 __isl_take isl_union_pw_multi_aff *upma1,
3683 __isl_take isl_union_pw_multi_aff *upma2);
3684 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
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_scale(
3688 __isl_take isl_multi_aff *maff,
3690 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3691 __isl_take isl_pw_multi_aff *pma,
3692 __isl_take isl_set *set);
3693 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3694 __isl_take isl_pw_multi_aff *pma,
3695 __isl_take isl_set *set);
3696 __isl_give isl_multi_aff *isl_multi_aff_lift(
3697 __isl_take isl_multi_aff *maff,
3698 __isl_give isl_local_space **ls);
3699 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3700 __isl_take isl_pw_multi_aff *pma);
3701 __isl_give isl_multi_aff *isl_multi_aff_align_params(
3702 __isl_take isl_multi_aff *multi,
3703 __isl_take isl_space *model);
3704 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
3705 __isl_take isl_pw_multi_aff *pma,
3706 __isl_take isl_space *model);
3707 __isl_give isl_pw_multi_aff *
3708 isl_pw_multi_aff_project_domain_on_params(
3709 __isl_take isl_pw_multi_aff *pma);
3710 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3711 __isl_take isl_multi_aff *maff,
3712 __isl_take isl_set *context);
3713 __isl_give isl_multi_aff *isl_multi_aff_gist(
3714 __isl_take isl_multi_aff *maff,
3715 __isl_take isl_set *context);
3716 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3717 __isl_take isl_pw_multi_aff *pma,
3718 __isl_take isl_set *set);
3719 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3720 __isl_take isl_pw_multi_aff *pma,
3721 __isl_take isl_set *set);
3722 __isl_give isl_set *isl_pw_multi_aff_domain(
3723 __isl_take isl_pw_multi_aff *pma);
3724 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3725 __isl_take isl_union_pw_multi_aff *upma);
3726 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3727 __isl_take isl_multi_aff *ma1,
3728 __isl_take isl_multi_aff *ma2);
3729 __isl_give isl_multi_aff *isl_multi_aff_product(
3730 __isl_take isl_multi_aff *ma1,
3731 __isl_take isl_multi_aff *ma2);
3732 __isl_give isl_pw_multi_aff *
3733 isl_pw_multi_aff_flat_range_product(
3734 __isl_take isl_pw_multi_aff *pma1,
3735 __isl_take isl_pw_multi_aff *pma2);
3736 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3737 __isl_take isl_pw_multi_aff *pma1,
3738 __isl_take isl_pw_multi_aff *pma2);
3739 __isl_give isl_union_pw_multi_aff *
3740 isl_union_pw_multi_aff_flat_range_product(
3741 __isl_take isl_union_pw_multi_aff *upma1,
3742 __isl_take isl_union_pw_multi_aff *upma2);
3744 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3745 then it is assigned the local space that lies at the basis of
3746 the lifting applied.
3748 __isl_give isl_set *isl_multi_aff_lex_le_set(
3749 __isl_take isl_multi_aff *ma1,
3750 __isl_take isl_multi_aff *ma2);
3751 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3752 __isl_take isl_multi_aff *ma1,
3753 __isl_take isl_multi_aff *ma2);
3755 The function C<isl_multi_aff_lex_le_set> returns a set
3756 containing those elements in the shared domain space
3757 where C<ma1> is lexicographically smaller than or
3760 An expression can be read from input using
3762 #include <isl/aff.h>
3763 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3764 isl_ctx *ctx, const char *str);
3765 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3766 isl_ctx *ctx, const char *str);
3768 An expression can be printed using
3770 #include <isl/aff.h>
3771 __isl_give isl_printer *isl_printer_print_multi_aff(
3772 __isl_take isl_printer *p,
3773 __isl_keep isl_multi_aff *maff);
3774 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3775 __isl_take isl_printer *p,
3776 __isl_keep isl_pw_multi_aff *pma);
3777 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3778 __isl_take isl_printer *p,
3779 __isl_keep isl_union_pw_multi_aff *upma);
3783 Points are elements of a set. They can be used to construct
3784 simple sets (boxes) or they can be used to represent the
3785 individual elements of a set.
3786 The zero point (the origin) can be created using
3788 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3790 The coordinates of a point can be inspected, set and changed
3793 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3794 enum isl_dim_type type, int pos, isl_int *v);
3795 __isl_give isl_point *isl_point_set_coordinate(
3796 __isl_take isl_point *pnt,
3797 enum isl_dim_type type, int pos, isl_int v);
3799 __isl_give isl_point *isl_point_add_ui(
3800 __isl_take isl_point *pnt,
3801 enum isl_dim_type type, int pos, unsigned val);
3802 __isl_give isl_point *isl_point_sub_ui(
3803 __isl_take isl_point *pnt,
3804 enum isl_dim_type type, int pos, unsigned val);
3806 Other properties can be obtained using
3808 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3810 Points can be copied or freed using
3812 __isl_give isl_point *isl_point_copy(
3813 __isl_keep isl_point *pnt);
3814 void isl_point_free(__isl_take isl_point *pnt);
3816 A singleton set can be created from a point using
3818 __isl_give isl_basic_set *isl_basic_set_from_point(
3819 __isl_take isl_point *pnt);
3820 __isl_give isl_set *isl_set_from_point(
3821 __isl_take isl_point *pnt);
3823 and a box can be created from two opposite extremal points using
3825 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3826 __isl_take isl_point *pnt1,
3827 __isl_take isl_point *pnt2);
3828 __isl_give isl_set *isl_set_box_from_points(
3829 __isl_take isl_point *pnt1,
3830 __isl_take isl_point *pnt2);
3832 All elements of a B<bounded> (union) set can be enumerated using
3833 the following functions.
3835 int isl_set_foreach_point(__isl_keep isl_set *set,
3836 int (*fn)(__isl_take isl_point *pnt, void *user),
3838 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3839 int (*fn)(__isl_take isl_point *pnt, void *user),
3842 The function C<fn> is called for each integer point in
3843 C<set> with as second argument the last argument of
3844 the C<isl_set_foreach_point> call. The function C<fn>
3845 should return C<0> on success and C<-1> on failure.
3846 In the latter case, C<isl_set_foreach_point> will stop
3847 enumerating and return C<-1> as well.
3848 If the enumeration is performed successfully and to completion,
3849 then C<isl_set_foreach_point> returns C<0>.
3851 To obtain a single point of a (basic) set, use
3853 __isl_give isl_point *isl_basic_set_sample_point(
3854 __isl_take isl_basic_set *bset);
3855 __isl_give isl_point *isl_set_sample_point(
3856 __isl_take isl_set *set);
3858 If C<set> does not contain any (integer) points, then the
3859 resulting point will be ``void'', a property that can be
3862 int isl_point_is_void(__isl_keep isl_point *pnt);
3864 =head2 Piecewise Quasipolynomials
3866 A piecewise quasipolynomial is a particular kind of function that maps
3867 a parametric point to a rational value.
3868 More specifically, a quasipolynomial is a polynomial expression in greatest
3869 integer parts of affine expressions of parameters and variables.
3870 A piecewise quasipolynomial is a subdivision of a given parametric
3871 domain into disjoint cells with a quasipolynomial associated to
3872 each cell. The value of the piecewise quasipolynomial at a given
3873 point is the value of the quasipolynomial associated to the cell
3874 that contains the point. Outside of the union of cells,
3875 the value is assumed to be zero.
3876 For example, the piecewise quasipolynomial
3878 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3880 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3881 A given piecewise quasipolynomial has a fixed domain dimension.
3882 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3883 defined over different domains.
3884 Piecewise quasipolynomials are mainly used by the C<barvinok>
3885 library for representing the number of elements in a parametric set or map.
3886 For example, the piecewise quasipolynomial above represents
3887 the number of points in the map
3889 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3891 =head3 Input and Output
3893 Piecewise quasipolynomials can be read from input using
3895 __isl_give isl_union_pw_qpolynomial *
3896 isl_union_pw_qpolynomial_read_from_str(
3897 isl_ctx *ctx, const char *str);
3899 Quasipolynomials and piecewise quasipolynomials can be printed
3900 using the following functions.
3902 __isl_give isl_printer *isl_printer_print_qpolynomial(
3903 __isl_take isl_printer *p,
3904 __isl_keep isl_qpolynomial *qp);
3906 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3907 __isl_take isl_printer *p,
3908 __isl_keep isl_pw_qpolynomial *pwqp);
3910 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3911 __isl_take isl_printer *p,
3912 __isl_keep isl_union_pw_qpolynomial *upwqp);
3914 The output format of the printer
3915 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3916 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3918 In case of printing in C<ISL_FORMAT_C>, the user may want
3919 to set the names of all dimensions
3921 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3922 __isl_take isl_qpolynomial *qp,
3923 enum isl_dim_type type, unsigned pos,
3925 __isl_give isl_pw_qpolynomial *
3926 isl_pw_qpolynomial_set_dim_name(
3927 __isl_take isl_pw_qpolynomial *pwqp,
3928 enum isl_dim_type type, unsigned pos,
3931 =head3 Creating New (Piecewise) Quasipolynomials
3933 Some simple quasipolynomials can be created using the following functions.
3934 More complicated quasipolynomials can be created by applying
3935 operations such as addition and multiplication
3936 on the resulting quasipolynomials
3938 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3939 __isl_take isl_space *domain);
3940 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3941 __isl_take isl_space *domain);
3942 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3943 __isl_take isl_space *domain);
3944 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3945 __isl_take isl_space *domain);
3946 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3947 __isl_take isl_space *domain);
3948 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3949 __isl_take isl_space *domain,
3950 const isl_int n, const isl_int d);
3951 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3952 __isl_take isl_space *domain,
3953 enum isl_dim_type type, unsigned pos);
3954 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3955 __isl_take isl_aff *aff);
3957 Note that the space in which a quasipolynomial lives is a map space
3958 with a one-dimensional range. The C<domain> argument in some of
3959 the functions above corresponds to the domain of this map space.
3961 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3962 with a single cell can be created using the following functions.
3963 Multiple of these single cell piecewise quasipolynomials can
3964 be combined to create more complicated piecewise quasipolynomials.
3966 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3967 __isl_take isl_space *space);
3968 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3969 __isl_take isl_set *set,
3970 __isl_take isl_qpolynomial *qp);
3971 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3972 __isl_take isl_qpolynomial *qp);
3973 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3974 __isl_take isl_pw_aff *pwaff);
3976 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3977 __isl_take isl_space *space);
3978 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3979 __isl_take isl_pw_qpolynomial *pwqp);
3980 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3981 __isl_take isl_union_pw_qpolynomial *upwqp,
3982 __isl_take isl_pw_qpolynomial *pwqp);
3984 Quasipolynomials can be copied and freed again using the following
3987 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3988 __isl_keep isl_qpolynomial *qp);
3989 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3991 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3992 __isl_keep isl_pw_qpolynomial *pwqp);
3993 void *isl_pw_qpolynomial_free(
3994 __isl_take isl_pw_qpolynomial *pwqp);
3996 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3997 __isl_keep isl_union_pw_qpolynomial *upwqp);
3998 void *isl_union_pw_qpolynomial_free(
3999 __isl_take isl_union_pw_qpolynomial *upwqp);
4001 =head3 Inspecting (Piecewise) Quasipolynomials
4003 To iterate over all piecewise quasipolynomials in a union
4004 piecewise quasipolynomial, use the following function
4006 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4007 __isl_keep isl_union_pw_qpolynomial *upwqp,
4008 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4011 To extract the piecewise quasipolynomial in a given space from a union, use
4013 __isl_give isl_pw_qpolynomial *
4014 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4015 __isl_keep isl_union_pw_qpolynomial *upwqp,
4016 __isl_take isl_space *space);
4018 To iterate over the cells in a piecewise quasipolynomial,
4019 use either of the following two functions
4021 int isl_pw_qpolynomial_foreach_piece(
4022 __isl_keep isl_pw_qpolynomial *pwqp,
4023 int (*fn)(__isl_take isl_set *set,
4024 __isl_take isl_qpolynomial *qp,
4025 void *user), void *user);
4026 int isl_pw_qpolynomial_foreach_lifted_piece(
4027 __isl_keep isl_pw_qpolynomial *pwqp,
4028 int (*fn)(__isl_take isl_set *set,
4029 __isl_take isl_qpolynomial *qp,
4030 void *user), void *user);
4032 As usual, the function C<fn> should return C<0> on success
4033 and C<-1> on failure. The difference between
4034 C<isl_pw_qpolynomial_foreach_piece> and
4035 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4036 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4037 compute unique representations for all existentially quantified
4038 variables and then turn these existentially quantified variables
4039 into extra set variables, adapting the associated quasipolynomial
4040 accordingly. This means that the C<set> passed to C<fn>
4041 will not have any existentially quantified variables, but that
4042 the dimensions of the sets may be different for different
4043 invocations of C<fn>.
4045 To iterate over all terms in a quasipolynomial,
4048 int isl_qpolynomial_foreach_term(
4049 __isl_keep isl_qpolynomial *qp,
4050 int (*fn)(__isl_take isl_term *term,
4051 void *user), void *user);
4053 The terms themselves can be inspected and freed using
4056 unsigned isl_term_dim(__isl_keep isl_term *term,
4057 enum isl_dim_type type);
4058 void isl_term_get_num(__isl_keep isl_term *term,
4060 void isl_term_get_den(__isl_keep isl_term *term,
4062 int isl_term_get_exp(__isl_keep isl_term *term,
4063 enum isl_dim_type type, unsigned pos);
4064 __isl_give isl_aff *isl_term_get_div(
4065 __isl_keep isl_term *term, unsigned pos);
4066 void isl_term_free(__isl_take isl_term *term);
4068 Each term is a product of parameters, set variables and
4069 integer divisions. The function C<isl_term_get_exp>
4070 returns the exponent of a given dimensions in the given term.
4071 The C<isl_int>s in the arguments of C<isl_term_get_num>
4072 and C<isl_term_get_den> need to have been initialized
4073 using C<isl_int_init> before calling these functions.
4075 =head3 Properties of (Piecewise) Quasipolynomials
4077 To check whether a quasipolynomial is actually a constant,
4078 use the following function.
4080 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4081 isl_int *n, isl_int *d);
4083 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4084 then the numerator and denominator of the constant
4085 are returned in C<*n> and C<*d>, respectively.
4087 To check whether two union piecewise quasipolynomials are
4088 obviously equal, use
4090 int isl_union_pw_qpolynomial_plain_is_equal(
4091 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4092 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4094 =head3 Operations on (Piecewise) Quasipolynomials
4096 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4097 __isl_take isl_qpolynomial *qp, isl_int v);
4098 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4099 __isl_take isl_qpolynomial *qp);
4100 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4101 __isl_take isl_qpolynomial *qp1,
4102 __isl_take isl_qpolynomial *qp2);
4103 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4104 __isl_take isl_qpolynomial *qp1,
4105 __isl_take isl_qpolynomial *qp2);
4106 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4107 __isl_take isl_qpolynomial *qp1,
4108 __isl_take isl_qpolynomial *qp2);
4109 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4110 __isl_take isl_qpolynomial *qp, unsigned exponent);
4112 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4113 __isl_take isl_pw_qpolynomial *pwqp1,
4114 __isl_take isl_pw_qpolynomial *pwqp2);
4115 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4116 __isl_take isl_pw_qpolynomial *pwqp1,
4117 __isl_take isl_pw_qpolynomial *pwqp2);
4118 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4119 __isl_take isl_pw_qpolynomial *pwqp1,
4120 __isl_take isl_pw_qpolynomial *pwqp2);
4121 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4122 __isl_take isl_pw_qpolynomial *pwqp);
4123 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4124 __isl_take isl_pw_qpolynomial *pwqp1,
4125 __isl_take isl_pw_qpolynomial *pwqp2);
4126 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4127 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4129 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4130 __isl_take isl_union_pw_qpolynomial *upwqp1,
4131 __isl_take isl_union_pw_qpolynomial *upwqp2);
4132 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4133 __isl_take isl_union_pw_qpolynomial *upwqp1,
4134 __isl_take isl_union_pw_qpolynomial *upwqp2);
4135 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4136 __isl_take isl_union_pw_qpolynomial *upwqp1,
4137 __isl_take isl_union_pw_qpolynomial *upwqp2);
4139 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4140 __isl_take isl_pw_qpolynomial *pwqp,
4141 __isl_take isl_point *pnt);
4143 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4144 __isl_take isl_union_pw_qpolynomial *upwqp,
4145 __isl_take isl_point *pnt);
4147 __isl_give isl_set *isl_pw_qpolynomial_domain(
4148 __isl_take isl_pw_qpolynomial *pwqp);
4149 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4150 __isl_take isl_pw_qpolynomial *pwpq,
4151 __isl_take isl_set *set);
4152 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4153 __isl_take isl_pw_qpolynomial *pwpq,
4154 __isl_take isl_set *set);
4156 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4157 __isl_take isl_union_pw_qpolynomial *upwqp);
4158 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4159 __isl_take isl_union_pw_qpolynomial *upwpq,
4160 __isl_take isl_union_set *uset);
4161 __isl_give isl_union_pw_qpolynomial *
4162 isl_union_pw_qpolynomial_intersect_params(
4163 __isl_take isl_union_pw_qpolynomial *upwpq,
4164 __isl_take isl_set *set);
4166 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4167 __isl_take isl_qpolynomial *qp,
4168 __isl_take isl_space *model);
4170 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4171 __isl_take isl_qpolynomial *qp);
4172 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4173 __isl_take isl_pw_qpolynomial *pwqp);
4175 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4176 __isl_take isl_union_pw_qpolynomial *upwqp);
4178 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4179 __isl_take isl_qpolynomial *qp,
4180 __isl_take isl_set *context);
4181 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4182 __isl_take isl_qpolynomial *qp,
4183 __isl_take isl_set *context);
4185 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4186 __isl_take isl_pw_qpolynomial *pwqp,
4187 __isl_take isl_set *context);
4188 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4189 __isl_take isl_pw_qpolynomial *pwqp,
4190 __isl_take isl_set *context);
4192 __isl_give isl_union_pw_qpolynomial *
4193 isl_union_pw_qpolynomial_gist_params(
4194 __isl_take isl_union_pw_qpolynomial *upwqp,
4195 __isl_take isl_set *context);
4196 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4197 __isl_take isl_union_pw_qpolynomial *upwqp,
4198 __isl_take isl_union_set *context);
4200 The gist operation applies the gist operation to each of
4201 the cells in the domain of the input piecewise quasipolynomial.
4202 The context is also exploited
4203 to simplify the quasipolynomials associated to each cell.
4205 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4206 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4207 __isl_give isl_union_pw_qpolynomial *
4208 isl_union_pw_qpolynomial_to_polynomial(
4209 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4211 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4212 the polynomial will be an overapproximation. If C<sign> is negative,
4213 it will be an underapproximation. If C<sign> is zero, the approximation
4214 will lie somewhere in between.
4216 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4218 A piecewise quasipolynomial reduction is a piecewise
4219 reduction (or fold) of quasipolynomials.
4220 In particular, the reduction can be maximum or a minimum.
4221 The objects are mainly used to represent the result of
4222 an upper or lower bound on a quasipolynomial over its domain,
4223 i.e., as the result of the following function.
4225 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4226 __isl_take isl_pw_qpolynomial *pwqp,
4227 enum isl_fold type, int *tight);
4229 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4230 __isl_take isl_union_pw_qpolynomial *upwqp,
4231 enum isl_fold type, int *tight);
4233 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4234 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4235 is the returned bound is known be tight, i.e., for each value
4236 of the parameters there is at least
4237 one element in the domain that reaches the bound.
4238 If the domain of C<pwqp> is not wrapping, then the bound is computed
4239 over all elements in that domain and the result has a purely parametric
4240 domain. If the domain of C<pwqp> is wrapping, then the bound is
4241 computed over the range of the wrapped relation. The domain of the
4242 wrapped relation becomes the domain of the result.
4244 A (piecewise) quasipolynomial reduction can be copied or freed using the
4245 following functions.
4247 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4248 __isl_keep isl_qpolynomial_fold *fold);
4249 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4250 __isl_keep isl_pw_qpolynomial_fold *pwf);
4251 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4252 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4253 void isl_qpolynomial_fold_free(
4254 __isl_take isl_qpolynomial_fold *fold);
4255 void *isl_pw_qpolynomial_fold_free(
4256 __isl_take isl_pw_qpolynomial_fold *pwf);
4257 void *isl_union_pw_qpolynomial_fold_free(
4258 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4260 =head3 Printing Piecewise Quasipolynomial Reductions
4262 Piecewise quasipolynomial reductions can be printed
4263 using the following function.
4265 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4266 __isl_take isl_printer *p,
4267 __isl_keep isl_pw_qpolynomial_fold *pwf);
4268 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4269 __isl_take isl_printer *p,
4270 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4272 For C<isl_printer_print_pw_qpolynomial_fold>,
4273 output format of the printer
4274 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4275 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4276 output format of the printer
4277 needs to be set to C<ISL_FORMAT_ISL>.
4278 In case of printing in C<ISL_FORMAT_C>, the user may want
4279 to set the names of all dimensions
4281 __isl_give isl_pw_qpolynomial_fold *
4282 isl_pw_qpolynomial_fold_set_dim_name(
4283 __isl_take isl_pw_qpolynomial_fold *pwf,
4284 enum isl_dim_type type, unsigned pos,
4287 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4289 To iterate over all piecewise quasipolynomial reductions in a union
4290 piecewise quasipolynomial reduction, use the following function
4292 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4293 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4294 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4295 void *user), void *user);
4297 To iterate over the cells in a piecewise quasipolynomial reduction,
4298 use either of the following two functions
4300 int isl_pw_qpolynomial_fold_foreach_piece(
4301 __isl_keep isl_pw_qpolynomial_fold *pwf,
4302 int (*fn)(__isl_take isl_set *set,
4303 __isl_take isl_qpolynomial_fold *fold,
4304 void *user), void *user);
4305 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4306 __isl_keep isl_pw_qpolynomial_fold *pwf,
4307 int (*fn)(__isl_take isl_set *set,
4308 __isl_take isl_qpolynomial_fold *fold,
4309 void *user), void *user);
4311 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4312 of the difference between these two functions.
4314 To iterate over all quasipolynomials in a reduction, use
4316 int isl_qpolynomial_fold_foreach_qpolynomial(
4317 __isl_keep isl_qpolynomial_fold *fold,
4318 int (*fn)(__isl_take isl_qpolynomial *qp,
4319 void *user), void *user);
4321 =head3 Properties of Piecewise Quasipolynomial Reductions
4323 To check whether two union piecewise quasipolynomial reductions are
4324 obviously equal, use
4326 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4327 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4328 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4330 =head3 Operations on Piecewise Quasipolynomial Reductions
4332 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4333 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4335 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4336 __isl_take isl_pw_qpolynomial_fold *pwf1,
4337 __isl_take isl_pw_qpolynomial_fold *pwf2);
4339 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4340 __isl_take isl_pw_qpolynomial_fold *pwf1,
4341 __isl_take isl_pw_qpolynomial_fold *pwf2);
4343 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4344 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4345 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4347 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4348 __isl_take isl_pw_qpolynomial_fold *pwf,
4349 __isl_take isl_point *pnt);
4351 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4352 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4353 __isl_take isl_point *pnt);
4355 __isl_give isl_pw_qpolynomial_fold *
4356 isl_pw_qpolynomial_fold_intersect_params(
4357 __isl_take isl_pw_qpolynomial_fold *pwf,
4358 __isl_take isl_set *set);
4360 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4361 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4362 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4363 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4364 __isl_take isl_union_set *uset);
4365 __isl_give isl_union_pw_qpolynomial_fold *
4366 isl_union_pw_qpolynomial_fold_intersect_params(
4367 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4368 __isl_take isl_set *set);
4370 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4371 __isl_take isl_pw_qpolynomial_fold *pwf);
4373 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4374 __isl_take isl_pw_qpolynomial_fold *pwf);
4376 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4377 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4379 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4380 __isl_take isl_qpolynomial_fold *fold,
4381 __isl_take isl_set *context);
4382 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4383 __isl_take isl_qpolynomial_fold *fold,
4384 __isl_take isl_set *context);
4386 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4387 __isl_take isl_pw_qpolynomial_fold *pwf,
4388 __isl_take isl_set *context);
4389 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4390 __isl_take isl_pw_qpolynomial_fold *pwf,
4391 __isl_take isl_set *context);
4393 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4394 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4395 __isl_take isl_union_set *context);
4396 __isl_give isl_union_pw_qpolynomial_fold *
4397 isl_union_pw_qpolynomial_fold_gist_params(
4398 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4399 __isl_take isl_set *context);
4401 The gist operation applies the gist operation to each of
4402 the cells in the domain of the input piecewise quasipolynomial reduction.
4403 In future, the operation will also exploit the context
4404 to simplify the quasipolynomial reductions associated to each cell.
4406 __isl_give isl_pw_qpolynomial_fold *
4407 isl_set_apply_pw_qpolynomial_fold(
4408 __isl_take isl_set *set,
4409 __isl_take isl_pw_qpolynomial_fold *pwf,
4411 __isl_give isl_pw_qpolynomial_fold *
4412 isl_map_apply_pw_qpolynomial_fold(
4413 __isl_take isl_map *map,
4414 __isl_take isl_pw_qpolynomial_fold *pwf,
4416 __isl_give isl_union_pw_qpolynomial_fold *
4417 isl_union_set_apply_union_pw_qpolynomial_fold(
4418 __isl_take isl_union_set *uset,
4419 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4421 __isl_give isl_union_pw_qpolynomial_fold *
4422 isl_union_map_apply_union_pw_qpolynomial_fold(
4423 __isl_take isl_union_map *umap,
4424 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4427 The functions taking a map
4428 compose the given map with the given piecewise quasipolynomial reduction.
4429 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4430 over all elements in the intersection of the range of the map
4431 and the domain of the piecewise quasipolynomial reduction
4432 as a function of an element in the domain of the map.
4433 The functions taking a set compute a bound over all elements in the
4434 intersection of the set and the domain of the
4435 piecewise quasipolynomial reduction.
4437 =head2 Dependence Analysis
4439 C<isl> contains specialized functionality for performing
4440 array dataflow analysis. That is, given a I<sink> access relation
4441 and a collection of possible I<source> access relations,
4442 C<isl> can compute relations that describe
4443 for each iteration of the sink access, which iteration
4444 of which of the source access relations was the last
4445 to access the same data element before the given iteration
4447 The resulting dependence relations map source iterations
4448 to the corresponding sink iterations.
4449 To compute standard flow dependences, the sink should be
4450 a read, while the sources should be writes.
4451 If any of the source accesses are marked as being I<may>
4452 accesses, then there will be a dependence from the last
4453 I<must> access B<and> from any I<may> access that follows
4454 this last I<must> access.
4455 In particular, if I<all> sources are I<may> accesses,
4456 then memory based dependence analysis is performed.
4457 If, on the other hand, all sources are I<must> accesses,
4458 then value based dependence analysis is performed.
4460 #include <isl/flow.h>
4462 typedef int (*isl_access_level_before)(void *first, void *second);
4464 __isl_give isl_access_info *isl_access_info_alloc(
4465 __isl_take isl_map *sink,
4466 void *sink_user, isl_access_level_before fn,
4468 __isl_give isl_access_info *isl_access_info_add_source(
4469 __isl_take isl_access_info *acc,
4470 __isl_take isl_map *source, int must,
4472 void *isl_access_info_free(__isl_take isl_access_info *acc);
4474 __isl_give isl_flow *isl_access_info_compute_flow(
4475 __isl_take isl_access_info *acc);
4477 int isl_flow_foreach(__isl_keep isl_flow *deps,
4478 int (*fn)(__isl_take isl_map *dep, int must,
4479 void *dep_user, void *user),
4481 __isl_give isl_map *isl_flow_get_no_source(
4482 __isl_keep isl_flow *deps, int must);
4483 void isl_flow_free(__isl_take isl_flow *deps);
4485 The function C<isl_access_info_compute_flow> performs the actual
4486 dependence analysis. The other functions are used to construct
4487 the input for this function or to read off the output.
4489 The input is collected in an C<isl_access_info>, which can
4490 be created through a call to C<isl_access_info_alloc>.
4491 The arguments to this functions are the sink access relation
4492 C<sink>, a token C<sink_user> used to identify the sink
4493 access to the user, a callback function for specifying the
4494 relative order of source and sink accesses, and the number
4495 of source access relations that will be added.
4496 The callback function has type C<int (*)(void *first, void *second)>.
4497 The function is called with two user supplied tokens identifying
4498 either a source or the sink and it should return the shared nesting
4499 level and the relative order of the two accesses.
4500 In particular, let I<n> be the number of loops shared by
4501 the two accesses. If C<first> precedes C<second> textually,
4502 then the function should return I<2 * n + 1>; otherwise,
4503 it should return I<2 * n>.
4504 The sources can be added to the C<isl_access_info> by performing
4505 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4506 C<must> indicates whether the source is a I<must> access
4507 or a I<may> access. Note that a multi-valued access relation
4508 should only be marked I<must> if every iteration in the domain
4509 of the relation accesses I<all> elements in its image.
4510 The C<source_user> token is again used to identify
4511 the source access. The range of the source access relation
4512 C<source> should have the same dimension as the range
4513 of the sink access relation.
4514 The C<isl_access_info_free> function should usually not be
4515 called explicitly, because it is called implicitly by
4516 C<isl_access_info_compute_flow>.
4518 The result of the dependence analysis is collected in an
4519 C<isl_flow>. There may be elements of
4520 the sink access for which no preceding source access could be
4521 found or for which all preceding sources are I<may> accesses.
4522 The relations containing these elements can be obtained through
4523 calls to C<isl_flow_get_no_source>, the first with C<must> set
4524 and the second with C<must> unset.
4525 In the case of standard flow dependence analysis,
4526 with the sink a read and the sources I<must> writes,
4527 the first relation corresponds to the reads from uninitialized
4528 array elements and the second relation is empty.
4529 The actual flow dependences can be extracted using
4530 C<isl_flow_foreach>. This function will call the user-specified
4531 callback function C<fn> for each B<non-empty> dependence between
4532 a source and the sink. The callback function is called
4533 with four arguments, the actual flow dependence relation
4534 mapping source iterations to sink iterations, a boolean that
4535 indicates whether it is a I<must> or I<may> dependence, a token
4536 identifying the source and an additional C<void *> with value
4537 equal to the third argument of the C<isl_flow_foreach> call.
4538 A dependence is marked I<must> if it originates from a I<must>
4539 source and if it is not followed by any I<may> sources.
4541 After finishing with an C<isl_flow>, the user should call
4542 C<isl_flow_free> to free all associated memory.
4544 A higher-level interface to dependence analysis is provided
4545 by the following function.
4547 #include <isl/flow.h>
4549 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4550 __isl_take isl_union_map *must_source,
4551 __isl_take isl_union_map *may_source,
4552 __isl_take isl_union_map *schedule,
4553 __isl_give isl_union_map **must_dep,
4554 __isl_give isl_union_map **may_dep,
4555 __isl_give isl_union_map **must_no_source,
4556 __isl_give isl_union_map **may_no_source);
4558 The arrays are identified by the tuple names of the ranges
4559 of the accesses. The iteration domains by the tuple names
4560 of the domains of the accesses and of the schedule.
4561 The relative order of the iteration domains is given by the
4562 schedule. The relations returned through C<must_no_source>
4563 and C<may_no_source> are subsets of C<sink>.
4564 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4565 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4566 any of the other arguments is treated as an error.
4568 =head3 Interaction with Dependence Analysis
4570 During the dependence analysis, we frequently need to perform
4571 the following operation. Given a relation between sink iterations
4572 and potential source iterations from a particular source domain,
4573 what is the last potential source iteration corresponding to each
4574 sink iteration. It can sometimes be convenient to adjust
4575 the set of potential source iterations before or after each such operation.
4576 The prototypical example is fuzzy array dataflow analysis,
4577 where we need to analyze if, based on data-dependent constraints,
4578 the sink iteration can ever be executed without one or more of
4579 the corresponding potential source iterations being executed.
4580 If so, we can introduce extra parameters and select an unknown
4581 but fixed source iteration from the potential source iterations.
4582 To be able to perform such manipulations, C<isl> provides the following
4585 #include <isl/flow.h>
4587 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4588 __isl_keep isl_map *source_map,
4589 __isl_keep isl_set *sink, void *source_user,
4591 __isl_give isl_access_info *isl_access_info_set_restrict(
4592 __isl_take isl_access_info *acc,
4593 isl_access_restrict fn, void *user);
4595 The function C<isl_access_info_set_restrict> should be called
4596 before calling C<isl_access_info_compute_flow> and registers a callback function
4597 that will be called any time C<isl> is about to compute the last
4598 potential source. The first argument is the (reverse) proto-dependence,
4599 mapping sink iterations to potential source iterations.
4600 The second argument represents the sink iterations for which
4601 we want to compute the last source iteration.
4602 The third argument is the token corresponding to the source
4603 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4604 The callback is expected to return a restriction on either the input or
4605 the output of the operation computing the last potential source.
4606 If the input needs to be restricted then restrictions are needed
4607 for both the source and the sink iterations. The sink iterations
4608 and the potential source iterations will be intersected with these sets.
4609 If the output needs to be restricted then only a restriction on the source
4610 iterations is required.
4611 If any error occurs, the callback should return C<NULL>.
4612 An C<isl_restriction> object can be created, freed and inspected
4613 using the following functions.
4615 #include <isl/flow.h>
4617 __isl_give isl_restriction *isl_restriction_input(
4618 __isl_take isl_set *source_restr,
4619 __isl_take isl_set *sink_restr);
4620 __isl_give isl_restriction *isl_restriction_output(
4621 __isl_take isl_set *source_restr);
4622 __isl_give isl_restriction *isl_restriction_none(
4623 __isl_take isl_map *source_map);
4624 __isl_give isl_restriction *isl_restriction_empty(
4625 __isl_take isl_map *source_map);
4626 void *isl_restriction_free(
4627 __isl_take isl_restriction *restr);
4628 isl_ctx *isl_restriction_get_ctx(
4629 __isl_keep isl_restriction *restr);
4631 C<isl_restriction_none> and C<isl_restriction_empty> are special
4632 cases of C<isl_restriction_input>. C<isl_restriction_none>
4633 is essentially equivalent to
4635 isl_restriction_input(isl_set_universe(
4636 isl_space_range(isl_map_get_space(source_map))),
4638 isl_space_domain(isl_map_get_space(source_map))));
4640 whereas C<isl_restriction_empty> is essentially equivalent to
4642 isl_restriction_input(isl_set_empty(
4643 isl_space_range(isl_map_get_space(source_map))),
4645 isl_space_domain(isl_map_get_space(source_map))));
4649 B<The functionality described in this section is fairly new
4650 and may be subject to change.>
4652 The following function can be used to compute a schedule
4653 for a union of domains.
4654 By default, the algorithm used to construct the schedule is similar
4655 to that of C<Pluto>.
4656 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4658 The generated schedule respects all C<validity> dependences.
4659 That is, all dependence distances over these dependences in the
4660 scheduled space are lexicographically positive.
4661 The default algorithm tries to minimize the dependence distances over
4662 C<proximity> dependences.
4663 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4664 for groups of domains where the dependence distances have only
4665 non-negative values.
4666 When using Feautrier's algorithm, the C<proximity> dependence
4667 distances are only minimized during the extension to a
4668 full-dimensional schedule.
4670 #include <isl/schedule.h>
4671 __isl_give isl_schedule *isl_union_set_compute_schedule(
4672 __isl_take isl_union_set *domain,
4673 __isl_take isl_union_map *validity,
4674 __isl_take isl_union_map *proximity);
4675 void *isl_schedule_free(__isl_take isl_schedule *sched);
4677 A mapping from the domains to the scheduled space can be obtained
4678 from an C<isl_schedule> using the following function.
4680 __isl_give isl_union_map *isl_schedule_get_map(
4681 __isl_keep isl_schedule *sched);
4683 A representation of the schedule can be printed using
4685 __isl_give isl_printer *isl_printer_print_schedule(
4686 __isl_take isl_printer *p,
4687 __isl_keep isl_schedule *schedule);
4689 A representation of the schedule as a forest of bands can be obtained
4690 using the following function.
4692 __isl_give isl_band_list *isl_schedule_get_band_forest(
4693 __isl_keep isl_schedule *schedule);
4695 The individual bands can be visited in depth-first post-order
4696 using the following function.
4698 #include <isl/schedule.h>
4699 int isl_schedule_foreach_band(
4700 __isl_keep isl_schedule *sched,
4701 int (*fn)(__isl_keep isl_band *band, void *user),
4704 The list can be manipulated as explained in L<"Lists">.
4705 The bands inside the list can be copied and freed using the following
4708 #include <isl/band.h>
4709 __isl_give isl_band *isl_band_copy(
4710 __isl_keep isl_band *band);
4711 void *isl_band_free(__isl_take isl_band *band);
4713 Each band contains zero or more scheduling dimensions.
4714 These are referred to as the members of the band.
4715 The section of the schedule that corresponds to the band is
4716 referred to as the partial schedule of the band.
4717 For those nodes that participate in a band, the outer scheduling
4718 dimensions form the prefix schedule, while the inner scheduling
4719 dimensions form the suffix schedule.
4720 That is, if we take a cut of the band forest, then the union of
4721 the concatenations of the prefix, partial and suffix schedules of
4722 each band in the cut is equal to the entire schedule (modulo
4723 some possible padding at the end with zero scheduling dimensions).
4724 The properties of a band can be inspected using the following functions.
4726 #include <isl/band.h>
4727 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4729 int isl_band_has_children(__isl_keep isl_band *band);
4730 __isl_give isl_band_list *isl_band_get_children(
4731 __isl_keep isl_band *band);
4733 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4734 __isl_keep isl_band *band);
4735 __isl_give isl_union_map *isl_band_get_partial_schedule(
4736 __isl_keep isl_band *band);
4737 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4738 __isl_keep isl_band *band);
4740 int isl_band_n_member(__isl_keep isl_band *band);
4741 int isl_band_member_is_zero_distance(
4742 __isl_keep isl_band *band, int pos);
4744 int isl_band_list_foreach_band(
4745 __isl_keep isl_band_list *list,
4746 int (*fn)(__isl_keep isl_band *band, void *user),
4749 Note that a scheduling dimension is considered to be ``zero
4750 distance'' if it does not carry any proximity dependences
4752 That is, if the dependence distances of the proximity
4753 dependences are all zero in that direction (for fixed
4754 iterations of outer bands).
4755 Like C<isl_schedule_foreach_band>,
4756 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4757 in depth-first post-order.
4759 A band can be tiled using the following function.
4761 #include <isl/band.h>
4762 int isl_band_tile(__isl_keep isl_band *band,
4763 __isl_take isl_vec *sizes);
4765 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4767 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4769 The C<isl_band_tile> function tiles the band using the given tile sizes
4770 inside its schedule.
4771 A new child band is created to represent the point loops and it is
4772 inserted between the modified band and its children.
4773 The C<tile_scale_tile_loops> option specifies whether the tile
4774 loops iterators should be scaled by the tile sizes.
4776 A representation of the band can be printed using
4778 #include <isl/band.h>
4779 __isl_give isl_printer *isl_printer_print_band(
4780 __isl_take isl_printer *p,
4781 __isl_keep isl_band *band);
4785 #include <isl/schedule.h>
4786 int isl_options_set_schedule_max_coefficient(
4787 isl_ctx *ctx, int val);
4788 int isl_options_get_schedule_max_coefficient(
4790 int isl_options_set_schedule_max_constant_term(
4791 isl_ctx *ctx, int val);
4792 int isl_options_get_schedule_max_constant_term(
4794 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4795 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4796 int isl_options_set_schedule_maximize_band_depth(
4797 isl_ctx *ctx, int val);
4798 int isl_options_get_schedule_maximize_band_depth(
4800 int isl_options_set_schedule_outer_zero_distance(
4801 isl_ctx *ctx, int val);
4802 int isl_options_get_schedule_outer_zero_distance(
4804 int isl_options_set_schedule_split_scaled(
4805 isl_ctx *ctx, int val);
4806 int isl_options_get_schedule_split_scaled(
4808 int isl_options_set_schedule_algorithm(
4809 isl_ctx *ctx, int val);
4810 int isl_options_get_schedule_algorithm(
4812 int isl_options_set_schedule_separate_components(
4813 isl_ctx *ctx, int val);
4814 int isl_options_get_schedule_separate_components(
4819 =item * schedule_max_coefficient
4821 This option enforces that the coefficients for variable and parameter
4822 dimensions in the calculated schedule are not larger than the specified value.
4823 This option can significantly increase the speed of the scheduling calculation
4824 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4825 this option does not introduce bounds on the variable or parameter
4828 =item * schedule_max_constant_term
4830 This option enforces that the constant coefficients in the calculated schedule
4831 are not larger than the maximal constant term. This option can significantly
4832 increase the speed of the scheduling calculation and may also prevent fusing of
4833 unrelated dimensions. A value of -1 means that this option does not introduce
4834 bounds on the constant coefficients.
4836 =item * schedule_fuse
4838 This option controls the level of fusion.
4839 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
4840 resulting schedule will be distributed as much as possible.
4841 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
4842 try to fuse loops in the resulting schedule.
4844 =item * schedule_maximize_band_depth
4846 If this option is set, we do not split bands at the point
4847 where we detect splitting is necessary. Instead, we
4848 backtrack and split bands as early as possible. This
4849 reduces the number of splits and maximizes the width of
4850 the bands. Wider bands give more possibilities for tiling.
4851 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
4852 then bands will be split as early as possible, even if there is no need.
4853 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
4855 =item * schedule_outer_zero_distance
4857 If this option is set, then we try to construct schedules
4858 where the outermost scheduling dimension in each band
4859 results in a zero dependence distance over the proximity
4862 =item * schedule_split_scaled
4864 If this option is set, then we try to construct schedules in which the
4865 constant term is split off from the linear part if the linear parts of
4866 the scheduling rows for all nodes in the graphs have a common non-trivial
4868 The constant term is then placed in a separate band and the linear
4871 =item * schedule_algorithm
4873 Selects the scheduling algorithm to be used.
4874 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4875 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4877 =item * schedule_separate_components
4879 If at any point the dependence graph contains any (weakly connected) components,
4880 then these components are scheduled separately.
4881 If this option is not set, then some iterations of the domains
4882 in these components may be scheduled together.
4883 If this option is set, then the components are given consecutive
4888 =head2 Parametric Vertex Enumeration
4890 The parametric vertex enumeration described in this section
4891 is mainly intended to be used internally and by the C<barvinok>
4894 #include <isl/vertices.h>
4895 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4896 __isl_keep isl_basic_set *bset);
4898 The function C<isl_basic_set_compute_vertices> performs the
4899 actual computation of the parametric vertices and the chamber
4900 decomposition and store the result in an C<isl_vertices> object.
4901 This information can be queried by either iterating over all
4902 the vertices or iterating over all the chambers or cells
4903 and then iterating over all vertices that are active on the chamber.
4905 int isl_vertices_foreach_vertex(
4906 __isl_keep isl_vertices *vertices,
4907 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4910 int isl_vertices_foreach_cell(
4911 __isl_keep isl_vertices *vertices,
4912 int (*fn)(__isl_take isl_cell *cell, void *user),
4914 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4915 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4918 Other operations that can be performed on an C<isl_vertices> object are
4921 isl_ctx *isl_vertices_get_ctx(
4922 __isl_keep isl_vertices *vertices);
4923 int isl_vertices_get_n_vertices(
4924 __isl_keep isl_vertices *vertices);
4925 void isl_vertices_free(__isl_take isl_vertices *vertices);
4927 Vertices can be inspected and destroyed using the following functions.
4929 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4930 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4931 __isl_give isl_basic_set *isl_vertex_get_domain(
4932 __isl_keep isl_vertex *vertex);
4933 __isl_give isl_basic_set *isl_vertex_get_expr(
4934 __isl_keep isl_vertex *vertex);
4935 void isl_vertex_free(__isl_take isl_vertex *vertex);
4937 C<isl_vertex_get_expr> returns a singleton parametric set describing
4938 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4940 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4941 B<rational> basic sets, so they should mainly be used for inspection
4942 and should not be mixed with integer sets.
4944 Chambers can be inspected and destroyed using the following functions.
4946 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4947 __isl_give isl_basic_set *isl_cell_get_domain(
4948 __isl_keep isl_cell *cell);
4949 void isl_cell_free(__isl_take isl_cell *cell);
4953 Although C<isl> is mainly meant to be used as a library,
4954 it also contains some basic applications that use some
4955 of the functionality of C<isl>.
4956 The input may be specified in either the L<isl format>
4957 or the L<PolyLib format>.
4959 =head2 C<isl_polyhedron_sample>
4961 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4962 an integer element of the polyhedron, if there is any.
4963 The first column in the output is the denominator and is always
4964 equal to 1. If the polyhedron contains no integer points,
4965 then a vector of length zero is printed.
4969 C<isl_pip> takes the same input as the C<example> program
4970 from the C<piplib> distribution, i.e., a set of constraints
4971 on the parameters, a line containing only -1 and finally a set
4972 of constraints on a parametric polyhedron.
4973 The coefficients of the parameters appear in the last columns
4974 (but before the final constant column).
4975 The output is the lexicographic minimum of the parametric polyhedron.
4976 As C<isl> currently does not have its own output format, the output
4977 is just a dump of the internal state.
4979 =head2 C<isl_polyhedron_minimize>
4981 C<isl_polyhedron_minimize> computes the minimum of some linear
4982 or affine objective function over the integer points in a polyhedron.
4983 If an affine objective function
4984 is given, then the constant should appear in the last column.
4986 =head2 C<isl_polytope_scan>
4988 Given a polytope, C<isl_polytope_scan> prints
4989 all integer points in the polytope.