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);
871 Note that if dimensions are added or removed from a space, then
872 the name and the internal structure are lost.
876 A local space is essentially a space with
877 zero or more existentially quantified variables.
878 The local space of a (constraint of a) basic set or relation can be obtained
879 using the following functions.
881 #include <isl/constraint.h>
882 __isl_give isl_local_space *isl_constraint_get_local_space(
883 __isl_keep isl_constraint *constraint);
886 __isl_give isl_local_space *isl_basic_set_get_local_space(
887 __isl_keep isl_basic_set *bset);
890 __isl_give isl_local_space *isl_basic_map_get_local_space(
891 __isl_keep isl_basic_map *bmap);
893 A new local space can be created from a space using
895 #include <isl/local_space.h>
896 __isl_give isl_local_space *isl_local_space_from_space(
897 __isl_take isl_space *space);
899 They can be inspected, modified, copied and freed using the following functions.
901 #include <isl/local_space.h>
902 isl_ctx *isl_local_space_get_ctx(
903 __isl_keep isl_local_space *ls);
904 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
905 int isl_local_space_dim(__isl_keep isl_local_space *ls,
906 enum isl_dim_type type);
907 int isl_local_space_has_dim_id(
908 __isl_keep isl_local_space *ls,
909 enum isl_dim_type type, unsigned pos);
910 __isl_give isl_id *isl_local_space_get_dim_id(
911 __isl_keep isl_local_space *ls,
912 enum isl_dim_type type, unsigned pos);
913 int isl_local_space_has_dim_name(
914 __isl_keep isl_local_space *ls,
915 enum isl_dim_type type, unsigned pos)
916 const char *isl_local_space_get_dim_name(
917 __isl_keep isl_local_space *ls,
918 enum isl_dim_type type, unsigned pos);
919 __isl_give isl_local_space *isl_local_space_set_dim_name(
920 __isl_take isl_local_space *ls,
921 enum isl_dim_type type, unsigned pos, const char *s);
922 __isl_give isl_local_space *isl_local_space_set_dim_id(
923 __isl_take isl_local_space *ls,
924 enum isl_dim_type type, unsigned pos,
925 __isl_take isl_id *id);
926 __isl_give isl_space *isl_local_space_get_space(
927 __isl_keep isl_local_space *ls);
928 __isl_give isl_aff *isl_local_space_get_div(
929 __isl_keep isl_local_space *ls, int pos);
930 __isl_give isl_local_space *isl_local_space_copy(
931 __isl_keep isl_local_space *ls);
932 void *isl_local_space_free(__isl_take isl_local_space *ls);
934 Two local spaces can be compared using
936 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
937 __isl_keep isl_local_space *ls2);
939 Local spaces can be created from other local spaces
940 using the following functions.
942 __isl_give isl_local_space *isl_local_space_domain(
943 __isl_take isl_local_space *ls);
944 __isl_give isl_local_space *isl_local_space_range(
945 __isl_take isl_local_space *ls);
946 __isl_give isl_local_space *isl_local_space_from_domain(
947 __isl_take isl_local_space *ls);
948 __isl_give isl_local_space *isl_local_space_intersect(
949 __isl_take isl_local_space *ls1,
950 __isl_take isl_local_space *ls2);
951 __isl_give isl_local_space *isl_local_space_add_dims(
952 __isl_take isl_local_space *ls,
953 enum isl_dim_type type, unsigned n);
954 __isl_give isl_local_space *isl_local_space_insert_dims(
955 __isl_take isl_local_space *ls,
956 enum isl_dim_type type, unsigned first, unsigned n);
957 __isl_give isl_local_space *isl_local_space_drop_dims(
958 __isl_take isl_local_space *ls,
959 enum isl_dim_type type, unsigned first, unsigned n);
961 =head2 Input and Output
963 C<isl> supports its own input/output format, which is similar
964 to the C<Omega> format, but also supports the C<PolyLib> format
969 The C<isl> format is similar to that of C<Omega>, but has a different
970 syntax for describing the parameters and allows for the definition
971 of an existentially quantified variable as the integer division
972 of an affine expression.
973 For example, the set of integers C<i> between C<0> and C<n>
974 such that C<i % 10 <= 6> can be described as
976 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
979 A set or relation can have several disjuncts, separated
980 by the keyword C<or>. Each disjunct is either a conjunction
981 of constraints or a projection (C<exists>) of a conjunction
982 of constraints. The constraints are separated by the keyword
985 =head3 C<PolyLib> format
987 If the represented set is a union, then the first line
988 contains a single number representing the number of disjuncts.
989 Otherwise, a line containing the number C<1> is optional.
991 Each disjunct is represented by a matrix of constraints.
992 The first line contains two numbers representing
993 the number of rows and columns,
994 where the number of rows is equal to the number of constraints
995 and the number of columns is equal to two plus the number of variables.
996 The following lines contain the actual rows of the constraint matrix.
997 In each row, the first column indicates whether the constraint
998 is an equality (C<0>) or inequality (C<1>). The final column
999 corresponds to the constant term.
1001 If the set is parametric, then the coefficients of the parameters
1002 appear in the last columns before the constant column.
1003 The coefficients of any existentially quantified variables appear
1004 between those of the set variables and those of the parameters.
1006 =head3 Extended C<PolyLib> format
1008 The extended C<PolyLib> format is nearly identical to the
1009 C<PolyLib> format. The only difference is that the line
1010 containing the number of rows and columns of a constraint matrix
1011 also contains four additional numbers:
1012 the number of output dimensions, the number of input dimensions,
1013 the number of local dimensions (i.e., the number of existentially
1014 quantified variables) and the number of parameters.
1015 For sets, the number of ``output'' dimensions is equal
1016 to the number of set dimensions, while the number of ``input''
1021 #include <isl/set.h>
1022 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1023 isl_ctx *ctx, FILE *input);
1024 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1025 isl_ctx *ctx, const char *str);
1026 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1028 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1031 #include <isl/map.h>
1032 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1033 isl_ctx *ctx, FILE *input);
1034 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1035 isl_ctx *ctx, const char *str);
1036 __isl_give isl_map *isl_map_read_from_file(
1037 isl_ctx *ctx, FILE *input);
1038 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1041 #include <isl/union_set.h>
1042 __isl_give isl_union_set *isl_union_set_read_from_file(
1043 isl_ctx *ctx, FILE *input);
1044 __isl_give isl_union_set *isl_union_set_read_from_str(
1045 isl_ctx *ctx, const char *str);
1047 #include <isl/union_map.h>
1048 __isl_give isl_union_map *isl_union_map_read_from_file(
1049 isl_ctx *ctx, FILE *input);
1050 __isl_give isl_union_map *isl_union_map_read_from_str(
1051 isl_ctx *ctx, const char *str);
1053 The input format is autodetected and may be either the C<PolyLib> format
1054 or the C<isl> format.
1058 Before anything can be printed, an C<isl_printer> needs to
1061 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1063 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1064 void *isl_printer_free(__isl_take isl_printer *printer);
1065 __isl_give char *isl_printer_get_str(
1066 __isl_keep isl_printer *printer);
1068 The printer can be inspected using the following functions.
1070 FILE *isl_printer_get_file(
1071 __isl_keep isl_printer *printer);
1072 int isl_printer_get_output_format(
1073 __isl_keep isl_printer *p);
1075 The behavior of the printer can be modified in various ways
1077 __isl_give isl_printer *isl_printer_set_output_format(
1078 __isl_take isl_printer *p, int output_format);
1079 __isl_give isl_printer *isl_printer_set_indent(
1080 __isl_take isl_printer *p, int indent);
1081 __isl_give isl_printer *isl_printer_indent(
1082 __isl_take isl_printer *p, int indent);
1083 __isl_give isl_printer *isl_printer_set_prefix(
1084 __isl_take isl_printer *p, const char *prefix);
1085 __isl_give isl_printer *isl_printer_set_suffix(
1086 __isl_take isl_printer *p, const char *suffix);
1088 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1089 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1090 and defaults to C<ISL_FORMAT_ISL>.
1091 Each line in the output is indented by C<indent> (set by
1092 C<isl_printer_set_indent>) spaces
1093 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1094 In the C<PolyLib> format output,
1095 the coefficients of the existentially quantified variables
1096 appear between those of the set variables and those
1098 The function C<isl_printer_indent> increases the indentation
1099 by the specified amount (which may be negative).
1101 To actually print something, use
1103 #include <isl/printer.h>
1104 __isl_give isl_printer *isl_printer_print_double(
1105 __isl_take isl_printer *p, double d);
1107 #include <isl/set.h>
1108 __isl_give isl_printer *isl_printer_print_basic_set(
1109 __isl_take isl_printer *printer,
1110 __isl_keep isl_basic_set *bset);
1111 __isl_give isl_printer *isl_printer_print_set(
1112 __isl_take isl_printer *printer,
1113 __isl_keep isl_set *set);
1115 #include <isl/map.h>
1116 __isl_give isl_printer *isl_printer_print_basic_map(
1117 __isl_take isl_printer *printer,
1118 __isl_keep isl_basic_map *bmap);
1119 __isl_give isl_printer *isl_printer_print_map(
1120 __isl_take isl_printer *printer,
1121 __isl_keep isl_map *map);
1123 #include <isl/union_set.h>
1124 __isl_give isl_printer *isl_printer_print_union_set(
1125 __isl_take isl_printer *p,
1126 __isl_keep isl_union_set *uset);
1128 #include <isl/union_map.h>
1129 __isl_give isl_printer *isl_printer_print_union_map(
1130 __isl_take isl_printer *p,
1131 __isl_keep isl_union_map *umap);
1133 When called on a file printer, the following function flushes
1134 the file. When called on a string printer, the buffer is cleared.
1136 __isl_give isl_printer *isl_printer_flush(
1137 __isl_take isl_printer *p);
1139 =head2 Creating New Sets and Relations
1141 C<isl> has functions for creating some standard sets and relations.
1145 =item * Empty sets and relations
1147 __isl_give isl_basic_set *isl_basic_set_empty(
1148 __isl_take isl_space *space);
1149 __isl_give isl_basic_map *isl_basic_map_empty(
1150 __isl_take isl_space *space);
1151 __isl_give isl_set *isl_set_empty(
1152 __isl_take isl_space *space);
1153 __isl_give isl_map *isl_map_empty(
1154 __isl_take isl_space *space);
1155 __isl_give isl_union_set *isl_union_set_empty(
1156 __isl_take isl_space *space);
1157 __isl_give isl_union_map *isl_union_map_empty(
1158 __isl_take isl_space *space);
1160 For C<isl_union_set>s and C<isl_union_map>s, the space
1161 is only used to specify the parameters.
1163 =item * Universe sets and relations
1165 __isl_give isl_basic_set *isl_basic_set_universe(
1166 __isl_take isl_space *space);
1167 __isl_give isl_basic_map *isl_basic_map_universe(
1168 __isl_take isl_space *space);
1169 __isl_give isl_set *isl_set_universe(
1170 __isl_take isl_space *space);
1171 __isl_give isl_map *isl_map_universe(
1172 __isl_take isl_space *space);
1173 __isl_give isl_union_set *isl_union_set_universe(
1174 __isl_take isl_union_set *uset);
1175 __isl_give isl_union_map *isl_union_map_universe(
1176 __isl_take isl_union_map *umap);
1178 The sets and relations constructed by the functions above
1179 contain all integer values, while those constructed by the
1180 functions below only contain non-negative values.
1182 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1183 __isl_take isl_space *space);
1184 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1185 __isl_take isl_space *space);
1186 __isl_give isl_set *isl_set_nat_universe(
1187 __isl_take isl_space *space);
1188 __isl_give isl_map *isl_map_nat_universe(
1189 __isl_take isl_space *space);
1191 =item * Identity relations
1193 __isl_give isl_basic_map *isl_basic_map_identity(
1194 __isl_take isl_space *space);
1195 __isl_give isl_map *isl_map_identity(
1196 __isl_take isl_space *space);
1198 The number of input and output dimensions in C<space> needs
1201 =item * Lexicographic order
1203 __isl_give isl_map *isl_map_lex_lt(
1204 __isl_take isl_space *set_space);
1205 __isl_give isl_map *isl_map_lex_le(
1206 __isl_take isl_space *set_space);
1207 __isl_give isl_map *isl_map_lex_gt(
1208 __isl_take isl_space *set_space);
1209 __isl_give isl_map *isl_map_lex_ge(
1210 __isl_take isl_space *set_space);
1211 __isl_give isl_map *isl_map_lex_lt_first(
1212 __isl_take isl_space *space, unsigned n);
1213 __isl_give isl_map *isl_map_lex_le_first(
1214 __isl_take isl_space *space, unsigned n);
1215 __isl_give isl_map *isl_map_lex_gt_first(
1216 __isl_take isl_space *space, unsigned n);
1217 __isl_give isl_map *isl_map_lex_ge_first(
1218 __isl_take isl_space *space, unsigned n);
1220 The first four functions take a space for a B<set>
1221 and return relations that express that the elements in the domain
1222 are lexicographically less
1223 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1224 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1225 than the elements in the range.
1226 The last four functions take a space for a map
1227 and return relations that express that the first C<n> dimensions
1228 in the domain are lexicographically less
1229 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1230 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1231 than the first C<n> dimensions in the range.
1235 A basic set or relation can be converted to a set or relation
1236 using the following functions.
1238 __isl_give isl_set *isl_set_from_basic_set(
1239 __isl_take isl_basic_set *bset);
1240 __isl_give isl_map *isl_map_from_basic_map(
1241 __isl_take isl_basic_map *bmap);
1243 Sets and relations can be converted to union sets and relations
1244 using the following functions.
1246 __isl_give isl_union_set *isl_union_set_from_basic_set(
1247 __isl_take isl_basic_set *bset);
1248 __isl_give isl_union_map *isl_union_map_from_basic_map(
1249 __isl_take isl_basic_map *bmap);
1250 __isl_give isl_union_set *isl_union_set_from_set(
1251 __isl_take isl_set *set);
1252 __isl_give isl_union_map *isl_union_map_from_map(
1253 __isl_take isl_map *map);
1255 The inverse conversions below can only be used if the input
1256 union set or relation is known to contain elements in exactly one
1259 __isl_give isl_set *isl_set_from_union_set(
1260 __isl_take isl_union_set *uset);
1261 __isl_give isl_map *isl_map_from_union_map(
1262 __isl_take isl_union_map *umap);
1264 A zero-dimensional set can be constructed on a given parameter domain
1265 using the following function.
1267 __isl_give isl_set *isl_set_from_params(
1268 __isl_take isl_set *set);
1270 Sets and relations can be copied and freed again using the following
1273 __isl_give isl_basic_set *isl_basic_set_copy(
1274 __isl_keep isl_basic_set *bset);
1275 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1276 __isl_give isl_union_set *isl_union_set_copy(
1277 __isl_keep isl_union_set *uset);
1278 __isl_give isl_basic_map *isl_basic_map_copy(
1279 __isl_keep isl_basic_map *bmap);
1280 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1281 __isl_give isl_union_map *isl_union_map_copy(
1282 __isl_keep isl_union_map *umap);
1283 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1284 void *isl_set_free(__isl_take isl_set *set);
1285 void *isl_union_set_free(__isl_take isl_union_set *uset);
1286 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1287 void *isl_map_free(__isl_take isl_map *map);
1288 void *isl_union_map_free(__isl_take isl_union_map *umap);
1290 Other sets and relations can be constructed by starting
1291 from a universe set or relation, adding equality and/or
1292 inequality constraints and then projecting out the
1293 existentially quantified variables, if any.
1294 Constraints can be constructed, manipulated and
1295 added to (or removed from) (basic) sets and relations
1296 using the following functions.
1298 #include <isl/constraint.h>
1299 __isl_give isl_constraint *isl_equality_alloc(
1300 __isl_take isl_local_space *ls);
1301 __isl_give isl_constraint *isl_inequality_alloc(
1302 __isl_take isl_local_space *ls);
1303 __isl_give isl_constraint *isl_constraint_set_constant(
1304 __isl_take isl_constraint *constraint, isl_int v);
1305 __isl_give isl_constraint *isl_constraint_set_constant_si(
1306 __isl_take isl_constraint *constraint, int v);
1307 __isl_give isl_constraint *isl_constraint_set_coefficient(
1308 __isl_take isl_constraint *constraint,
1309 enum isl_dim_type type, int pos, isl_int v);
1310 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1311 __isl_take isl_constraint *constraint,
1312 enum isl_dim_type type, int pos, int v);
1313 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1314 __isl_take isl_basic_map *bmap,
1315 __isl_take isl_constraint *constraint);
1316 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1317 __isl_take isl_basic_set *bset,
1318 __isl_take isl_constraint *constraint);
1319 __isl_give isl_map *isl_map_add_constraint(
1320 __isl_take isl_map *map,
1321 __isl_take isl_constraint *constraint);
1322 __isl_give isl_set *isl_set_add_constraint(
1323 __isl_take isl_set *set,
1324 __isl_take isl_constraint *constraint);
1325 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1326 __isl_take isl_basic_set *bset,
1327 __isl_take isl_constraint *constraint);
1329 For example, to create a set containing the even integers
1330 between 10 and 42, you would use the following code.
1333 isl_local_space *ls;
1335 isl_basic_set *bset;
1337 space = isl_space_set_alloc(ctx, 0, 2);
1338 bset = isl_basic_set_universe(isl_space_copy(space));
1339 ls = isl_local_space_from_space(space);
1341 c = isl_equality_alloc(isl_local_space_copy(ls));
1342 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1343 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1344 bset = isl_basic_set_add_constraint(bset, c);
1346 c = isl_inequality_alloc(isl_local_space_copy(ls));
1347 c = isl_constraint_set_constant_si(c, -10);
1348 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1349 bset = isl_basic_set_add_constraint(bset, c);
1351 c = isl_inequality_alloc(ls);
1352 c = isl_constraint_set_constant_si(c, 42);
1353 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1354 bset = isl_basic_set_add_constraint(bset, c);
1356 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1360 isl_basic_set *bset;
1361 bset = isl_basic_set_read_from_str(ctx,
1362 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1364 A basic set or relation can also be constructed from two matrices
1365 describing the equalities and the inequalities.
1367 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1368 __isl_take isl_space *space,
1369 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1370 enum isl_dim_type c1,
1371 enum isl_dim_type c2, enum isl_dim_type c3,
1372 enum isl_dim_type c4);
1373 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1374 __isl_take isl_space *space,
1375 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1376 enum isl_dim_type c1,
1377 enum isl_dim_type c2, enum isl_dim_type c3,
1378 enum isl_dim_type c4, enum isl_dim_type c5);
1380 The C<isl_dim_type> arguments indicate the order in which
1381 different kinds of variables appear in the input matrices
1382 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1383 C<isl_dim_set> and C<isl_dim_div> for sets and
1384 of C<isl_dim_cst>, C<isl_dim_param>,
1385 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1387 A (basic or union) set or relation can also be constructed from a
1388 (union) (piecewise) (multiple) affine expression
1389 or a list of affine expressions
1390 (See L<"Piecewise Quasi Affine Expressions"> and
1391 L<"Piecewise Multiple Quasi Affine Expressions">).
1393 __isl_give isl_basic_map *isl_basic_map_from_aff(
1394 __isl_take isl_aff *aff);
1395 __isl_give isl_map *isl_map_from_aff(
1396 __isl_take isl_aff *aff);
1397 __isl_give isl_set *isl_set_from_pw_aff(
1398 __isl_take isl_pw_aff *pwaff);
1399 __isl_give isl_map *isl_map_from_pw_aff(
1400 __isl_take isl_pw_aff *pwaff);
1401 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1402 __isl_take isl_space *domain_space,
1403 __isl_take isl_aff_list *list);
1404 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1405 __isl_take isl_multi_aff *maff)
1406 __isl_give isl_map *isl_map_from_multi_aff(
1407 __isl_take isl_multi_aff *maff)
1408 __isl_give isl_set *isl_set_from_pw_multi_aff(
1409 __isl_take isl_pw_multi_aff *pma);
1410 __isl_give isl_map *isl_map_from_pw_multi_aff(
1411 __isl_take isl_pw_multi_aff *pma);
1412 __isl_give isl_union_map *
1413 isl_union_map_from_union_pw_multi_aff(
1414 __isl_take isl_union_pw_multi_aff *upma);
1416 The C<domain_dim> argument describes the domain of the resulting
1417 basic relation. It is required because the C<list> may consist
1418 of zero affine expressions.
1420 =head2 Inspecting Sets and Relations
1422 Usually, the user should not have to care about the actual constraints
1423 of the sets and maps, but should instead apply the abstract operations
1424 explained in the following sections.
1425 Occasionally, however, it may be required to inspect the individual
1426 coefficients of the constraints. This section explains how to do so.
1427 In these cases, it may also be useful to have C<isl> compute
1428 an explicit representation of the existentially quantified variables.
1430 __isl_give isl_set *isl_set_compute_divs(
1431 __isl_take isl_set *set);
1432 __isl_give isl_map *isl_map_compute_divs(
1433 __isl_take isl_map *map);
1434 __isl_give isl_union_set *isl_union_set_compute_divs(
1435 __isl_take isl_union_set *uset);
1436 __isl_give isl_union_map *isl_union_map_compute_divs(
1437 __isl_take isl_union_map *umap);
1439 This explicit representation defines the existentially quantified
1440 variables as integer divisions of the other variables, possibly
1441 including earlier existentially quantified variables.
1442 An explicitly represented existentially quantified variable therefore
1443 has a unique value when the values of the other variables are known.
1444 If, furthermore, the same existentials, i.e., existentials
1445 with the same explicit representations, should appear in the
1446 same order in each of the disjuncts of a set or map, then the user should call
1447 either of the following functions.
1449 __isl_give isl_set *isl_set_align_divs(
1450 __isl_take isl_set *set);
1451 __isl_give isl_map *isl_map_align_divs(
1452 __isl_take isl_map *map);
1454 Alternatively, the existentially quantified variables can be removed
1455 using the following functions, which compute an overapproximation.
1457 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1458 __isl_take isl_basic_set *bset);
1459 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1460 __isl_take isl_basic_map *bmap);
1461 __isl_give isl_set *isl_set_remove_divs(
1462 __isl_take isl_set *set);
1463 __isl_give isl_map *isl_map_remove_divs(
1464 __isl_take isl_map *map);
1466 It is also possible to only remove those divs that are defined
1467 in terms of a given range of dimensions or only those for which
1468 no explicit representation is known.
1470 __isl_give isl_basic_set *
1471 isl_basic_set_remove_divs_involving_dims(
1472 __isl_take isl_basic_set *bset,
1473 enum isl_dim_type type,
1474 unsigned first, unsigned n);
1475 __isl_give isl_basic_map *
1476 isl_basic_map_remove_divs_involving_dims(
1477 __isl_take isl_basic_map *bmap,
1478 enum isl_dim_type type,
1479 unsigned first, unsigned n);
1480 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1481 __isl_take isl_set *set, enum isl_dim_type type,
1482 unsigned first, unsigned n);
1483 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1484 __isl_take isl_map *map, enum isl_dim_type type,
1485 unsigned first, unsigned n);
1487 __isl_give isl_set *isl_set_remove_unknown_divs(
1488 __isl_take isl_set *set);
1489 __isl_give isl_map *isl_map_remove_unknown_divs(
1490 __isl_take isl_map *map);
1492 To iterate over all the sets or maps in a union set or map, use
1494 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1495 int (*fn)(__isl_take isl_set *set, void *user),
1497 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1498 int (*fn)(__isl_take isl_map *map, void *user),
1501 The number of sets or maps in a union set or map can be obtained
1504 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1505 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1507 To extract the set or map in a given space from a union, use
1509 __isl_give isl_set *isl_union_set_extract_set(
1510 __isl_keep isl_union_set *uset,
1511 __isl_take isl_space *space);
1512 __isl_give isl_map *isl_union_map_extract_map(
1513 __isl_keep isl_union_map *umap,
1514 __isl_take isl_space *space);
1516 To iterate over all the basic sets or maps in a set or map, use
1518 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1519 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1521 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1522 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1525 The callback function C<fn> should return 0 if successful and
1526 -1 if an error occurs. In the latter case, or if any other error
1527 occurs, the above functions will return -1.
1529 It should be noted that C<isl> does not guarantee that
1530 the basic sets or maps passed to C<fn> are disjoint.
1531 If this is required, then the user should call one of
1532 the following functions first.
1534 __isl_give isl_set *isl_set_make_disjoint(
1535 __isl_take isl_set *set);
1536 __isl_give isl_map *isl_map_make_disjoint(
1537 __isl_take isl_map *map);
1539 The number of basic sets in a set can be obtained
1542 int isl_set_n_basic_set(__isl_keep isl_set *set);
1544 To iterate over the constraints of a basic set or map, use
1546 #include <isl/constraint.h>
1548 int isl_basic_set_n_constraint(
1549 __isl_keep isl_basic_set *bset);
1550 int isl_basic_set_foreach_constraint(
1551 __isl_keep isl_basic_set *bset,
1552 int (*fn)(__isl_take isl_constraint *c, void *user),
1554 int isl_basic_map_foreach_constraint(
1555 __isl_keep isl_basic_map *bmap,
1556 int (*fn)(__isl_take isl_constraint *c, void *user),
1558 void *isl_constraint_free(__isl_take isl_constraint *c);
1560 Again, the callback function C<fn> should return 0 if successful and
1561 -1 if an error occurs. In the latter case, or if any other error
1562 occurs, the above functions will return -1.
1563 The constraint C<c> represents either an equality or an inequality.
1564 Use the following function to find out whether a constraint
1565 represents an equality. If not, it represents an inequality.
1567 int isl_constraint_is_equality(
1568 __isl_keep isl_constraint *constraint);
1570 The coefficients of the constraints can be inspected using
1571 the following functions.
1573 int isl_constraint_is_lower_bound(
1574 __isl_keep isl_constraint *constraint,
1575 enum isl_dim_type type, unsigned pos);
1576 int isl_constraint_is_upper_bound(
1577 __isl_keep isl_constraint *constraint,
1578 enum isl_dim_type type, unsigned pos);
1579 void isl_constraint_get_constant(
1580 __isl_keep isl_constraint *constraint, isl_int *v);
1581 void isl_constraint_get_coefficient(
1582 __isl_keep isl_constraint *constraint,
1583 enum isl_dim_type type, int pos, isl_int *v);
1584 int isl_constraint_involves_dims(
1585 __isl_keep isl_constraint *constraint,
1586 enum isl_dim_type type, unsigned first, unsigned n);
1588 The explicit representations of the existentially quantified
1589 variables can be inspected using the following function.
1590 Note that the user is only allowed to use this function
1591 if the inspected set or map is the result of a call
1592 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1593 The existentially quantified variable is equal to the floor
1594 of the returned affine expression. The affine expression
1595 itself can be inspected using the functions in
1596 L<"Piecewise Quasi Affine Expressions">.
1598 __isl_give isl_aff *isl_constraint_get_div(
1599 __isl_keep isl_constraint *constraint, int pos);
1601 To obtain the constraints of a basic set or map in matrix
1602 form, use the following functions.
1604 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1605 __isl_keep isl_basic_set *bset,
1606 enum isl_dim_type c1, enum isl_dim_type c2,
1607 enum isl_dim_type c3, enum isl_dim_type c4);
1608 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1609 __isl_keep isl_basic_set *bset,
1610 enum isl_dim_type c1, enum isl_dim_type c2,
1611 enum isl_dim_type c3, enum isl_dim_type c4);
1612 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1613 __isl_keep isl_basic_map *bmap,
1614 enum isl_dim_type c1,
1615 enum isl_dim_type c2, enum isl_dim_type c3,
1616 enum isl_dim_type c4, enum isl_dim_type c5);
1617 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1618 __isl_keep isl_basic_map *bmap,
1619 enum isl_dim_type c1,
1620 enum isl_dim_type c2, enum isl_dim_type c3,
1621 enum isl_dim_type c4, enum isl_dim_type c5);
1623 The C<isl_dim_type> arguments dictate the order in which
1624 different kinds of variables appear in the resulting matrix
1625 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1626 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1628 The number of parameters, input, output or set dimensions can
1629 be obtained using the following functions.
1631 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1632 enum isl_dim_type type);
1633 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1634 enum isl_dim_type type);
1635 unsigned isl_set_dim(__isl_keep isl_set *set,
1636 enum isl_dim_type type);
1637 unsigned isl_map_dim(__isl_keep isl_map *map,
1638 enum isl_dim_type type);
1640 To check whether the description of a set or relation depends
1641 on one or more given dimensions, it is not necessary to iterate over all
1642 constraints. Instead the following functions can be used.
1644 int isl_basic_set_involves_dims(
1645 __isl_keep isl_basic_set *bset,
1646 enum isl_dim_type type, unsigned first, unsigned n);
1647 int isl_set_involves_dims(__isl_keep isl_set *set,
1648 enum isl_dim_type type, unsigned first, unsigned n);
1649 int isl_basic_map_involves_dims(
1650 __isl_keep isl_basic_map *bmap,
1651 enum isl_dim_type type, unsigned first, unsigned n);
1652 int isl_map_involves_dims(__isl_keep isl_map *map,
1653 enum isl_dim_type type, unsigned first, unsigned n);
1655 Similarly, the following functions can be used to check whether
1656 a given dimension is involved in any lower or upper bound.
1658 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1659 enum isl_dim_type type, unsigned pos);
1660 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1661 enum isl_dim_type type, unsigned pos);
1663 The identifiers or names of the domain and range spaces of a set
1664 or relation can be read off or set using the following functions.
1666 __isl_give isl_set *isl_set_set_tuple_id(
1667 __isl_take isl_set *set, __isl_take isl_id *id);
1668 __isl_give isl_set *isl_set_reset_tuple_id(
1669 __isl_take isl_set *set);
1670 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1671 __isl_give isl_id *isl_set_get_tuple_id(
1672 __isl_keep isl_set *set);
1673 __isl_give isl_map *isl_map_set_tuple_id(
1674 __isl_take isl_map *map, enum isl_dim_type type,
1675 __isl_take isl_id *id);
1676 __isl_give isl_map *isl_map_reset_tuple_id(
1677 __isl_take isl_map *map, enum isl_dim_type type);
1678 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1679 enum isl_dim_type type);
1680 __isl_give isl_id *isl_map_get_tuple_id(
1681 __isl_keep isl_map *map, enum isl_dim_type type);
1683 const char *isl_basic_set_get_tuple_name(
1684 __isl_keep isl_basic_set *bset);
1685 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1686 __isl_take isl_basic_set *set, const char *s);
1687 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1688 const char *isl_set_get_tuple_name(
1689 __isl_keep isl_set *set);
1690 const char *isl_basic_map_get_tuple_name(
1691 __isl_keep isl_basic_map *bmap,
1692 enum isl_dim_type type);
1693 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1694 __isl_take isl_basic_map *bmap,
1695 enum isl_dim_type type, const char *s);
1696 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1697 enum isl_dim_type type);
1698 const char *isl_map_get_tuple_name(
1699 __isl_keep isl_map *map,
1700 enum isl_dim_type type);
1702 As with C<isl_space_get_tuple_name>, the value returned points to
1703 an internal data structure.
1704 The identifiers, positions or names of individual dimensions can be
1705 read off using the following functions.
1707 __isl_give isl_id *isl_basic_set_get_dim_id(
1708 __isl_keep isl_basic_set *bset,
1709 enum isl_dim_type type, unsigned pos);
1710 __isl_give isl_set *isl_set_set_dim_id(
1711 __isl_take isl_set *set, enum isl_dim_type type,
1712 unsigned pos, __isl_take isl_id *id);
1713 int isl_set_has_dim_id(__isl_keep isl_set *set,
1714 enum isl_dim_type type, unsigned pos);
1715 __isl_give isl_id *isl_set_get_dim_id(
1716 __isl_keep isl_set *set, enum isl_dim_type type,
1718 int isl_basic_map_has_dim_id(
1719 __isl_keep isl_basic_map *bmap,
1720 enum isl_dim_type type, unsigned pos);
1721 __isl_give isl_map *isl_map_set_dim_id(
1722 __isl_take isl_map *map, enum isl_dim_type type,
1723 unsigned pos, __isl_take isl_id *id);
1724 int isl_map_has_dim_id(__isl_keep isl_map *map,
1725 enum isl_dim_type type, unsigned pos);
1726 __isl_give isl_id *isl_map_get_dim_id(
1727 __isl_keep isl_map *map, enum isl_dim_type type,
1730 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1731 enum isl_dim_type type, __isl_keep isl_id *id);
1732 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1733 enum isl_dim_type type, __isl_keep isl_id *id);
1734 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1735 enum isl_dim_type type, const char *name);
1736 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1737 enum isl_dim_type type, const char *name);
1739 const char *isl_constraint_get_dim_name(
1740 __isl_keep isl_constraint *constraint,
1741 enum isl_dim_type type, unsigned pos);
1742 const char *isl_basic_set_get_dim_name(
1743 __isl_keep isl_basic_set *bset,
1744 enum isl_dim_type type, unsigned pos);
1745 int isl_set_has_dim_name(__isl_keep isl_set *set,
1746 enum isl_dim_type type, unsigned pos);
1747 const char *isl_set_get_dim_name(
1748 __isl_keep isl_set *set,
1749 enum isl_dim_type type, unsigned pos);
1750 const char *isl_basic_map_get_dim_name(
1751 __isl_keep isl_basic_map *bmap,
1752 enum isl_dim_type type, unsigned pos);
1753 int isl_map_has_dim_name(__isl_keep isl_map *map,
1754 enum isl_dim_type type, unsigned pos);
1755 const char *isl_map_get_dim_name(
1756 __isl_keep isl_map *map,
1757 enum isl_dim_type type, unsigned pos);
1759 These functions are mostly useful to obtain the identifiers, positions
1760 or names of the parameters. Identifiers of individual dimensions are
1761 essentially only useful for printing. They are ignored by all other
1762 operations and may not be preserved across those operations.
1766 =head3 Unary Properties
1772 The following functions test whether the given set or relation
1773 contains any integer points. The ``plain'' variants do not perform
1774 any computations, but simply check if the given set or relation
1775 is already known to be empty.
1777 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1778 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1779 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1780 int isl_set_is_empty(__isl_keep isl_set *set);
1781 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1782 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1783 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1784 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1785 int isl_map_is_empty(__isl_keep isl_map *map);
1786 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1788 =item * Universality
1790 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1791 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1792 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1794 =item * Single-valuedness
1796 int isl_basic_map_is_single_valued(
1797 __isl_keep isl_basic_map *bmap);
1798 int isl_map_plain_is_single_valued(
1799 __isl_keep isl_map *map);
1800 int isl_map_is_single_valued(__isl_keep isl_map *map);
1801 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1805 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1806 int isl_map_is_injective(__isl_keep isl_map *map);
1807 int isl_union_map_plain_is_injective(
1808 __isl_keep isl_union_map *umap);
1809 int isl_union_map_is_injective(
1810 __isl_keep isl_union_map *umap);
1814 int isl_map_is_bijective(__isl_keep isl_map *map);
1815 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1819 int isl_basic_map_plain_is_fixed(
1820 __isl_keep isl_basic_map *bmap,
1821 enum isl_dim_type type, unsigned pos,
1823 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1824 enum isl_dim_type type, unsigned pos,
1826 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1827 enum isl_dim_type type, unsigned pos,
1830 Check if the relation obviously lies on a hyperplane where the given dimension
1831 has a fixed value and if so, return that value in C<*val>.
1835 To check whether a set is a parameter domain, use this function:
1837 int isl_set_is_params(__isl_keep isl_set *set);
1838 int isl_union_set_is_params(
1839 __isl_keep isl_union_set *uset);
1843 The following functions check whether the domain of the given
1844 (basic) set is a wrapped relation.
1846 int isl_basic_set_is_wrapping(
1847 __isl_keep isl_basic_set *bset);
1848 int isl_set_is_wrapping(__isl_keep isl_set *set);
1850 =item * Internal Product
1852 int isl_basic_map_can_zip(
1853 __isl_keep isl_basic_map *bmap);
1854 int isl_map_can_zip(__isl_keep isl_map *map);
1856 Check whether the product of domain and range of the given relation
1858 i.e., whether both domain and range are nested relations.
1862 int isl_basic_map_can_curry(
1863 __isl_keep isl_basic_map *bmap);
1864 int isl_map_can_curry(__isl_keep isl_map *map);
1866 Check whether the domain of the (basic) relation is a wrapped relation.
1870 =head3 Binary Properties
1876 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1877 __isl_keep isl_set *set2);
1878 int isl_set_is_equal(__isl_keep isl_set *set1,
1879 __isl_keep isl_set *set2);
1880 int isl_union_set_is_equal(
1881 __isl_keep isl_union_set *uset1,
1882 __isl_keep isl_union_set *uset2);
1883 int isl_basic_map_is_equal(
1884 __isl_keep isl_basic_map *bmap1,
1885 __isl_keep isl_basic_map *bmap2);
1886 int isl_map_is_equal(__isl_keep isl_map *map1,
1887 __isl_keep isl_map *map2);
1888 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1889 __isl_keep isl_map *map2);
1890 int isl_union_map_is_equal(
1891 __isl_keep isl_union_map *umap1,
1892 __isl_keep isl_union_map *umap2);
1894 =item * Disjointness
1896 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1897 __isl_keep isl_set *set2);
1901 int isl_basic_set_is_subset(
1902 __isl_keep isl_basic_set *bset1,
1903 __isl_keep isl_basic_set *bset2);
1904 int isl_set_is_subset(__isl_keep isl_set *set1,
1905 __isl_keep isl_set *set2);
1906 int isl_set_is_strict_subset(
1907 __isl_keep isl_set *set1,
1908 __isl_keep isl_set *set2);
1909 int isl_union_set_is_subset(
1910 __isl_keep isl_union_set *uset1,
1911 __isl_keep isl_union_set *uset2);
1912 int isl_union_set_is_strict_subset(
1913 __isl_keep isl_union_set *uset1,
1914 __isl_keep isl_union_set *uset2);
1915 int isl_basic_map_is_subset(
1916 __isl_keep isl_basic_map *bmap1,
1917 __isl_keep isl_basic_map *bmap2);
1918 int isl_basic_map_is_strict_subset(
1919 __isl_keep isl_basic_map *bmap1,
1920 __isl_keep isl_basic_map *bmap2);
1921 int isl_map_is_subset(
1922 __isl_keep isl_map *map1,
1923 __isl_keep isl_map *map2);
1924 int isl_map_is_strict_subset(
1925 __isl_keep isl_map *map1,
1926 __isl_keep isl_map *map2);
1927 int isl_union_map_is_subset(
1928 __isl_keep isl_union_map *umap1,
1929 __isl_keep isl_union_map *umap2);
1930 int isl_union_map_is_strict_subset(
1931 __isl_keep isl_union_map *umap1,
1932 __isl_keep isl_union_map *umap2);
1934 Check whether the first argument is a (strict) subset of the
1939 =head2 Unary Operations
1945 __isl_give isl_set *isl_set_complement(
1946 __isl_take isl_set *set);
1947 __isl_give isl_map *isl_map_complement(
1948 __isl_take isl_map *map);
1952 __isl_give isl_basic_map *isl_basic_map_reverse(
1953 __isl_take isl_basic_map *bmap);
1954 __isl_give isl_map *isl_map_reverse(
1955 __isl_take isl_map *map);
1956 __isl_give isl_union_map *isl_union_map_reverse(
1957 __isl_take isl_union_map *umap);
1961 __isl_give isl_basic_set *isl_basic_set_project_out(
1962 __isl_take isl_basic_set *bset,
1963 enum isl_dim_type type, unsigned first, unsigned n);
1964 __isl_give isl_basic_map *isl_basic_map_project_out(
1965 __isl_take isl_basic_map *bmap,
1966 enum isl_dim_type type, unsigned first, unsigned n);
1967 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1968 enum isl_dim_type type, unsigned first, unsigned n);
1969 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1970 enum isl_dim_type type, unsigned first, unsigned n);
1971 __isl_give isl_basic_set *isl_basic_set_params(
1972 __isl_take isl_basic_set *bset);
1973 __isl_give isl_basic_set *isl_basic_map_domain(
1974 __isl_take isl_basic_map *bmap);
1975 __isl_give isl_basic_set *isl_basic_map_range(
1976 __isl_take isl_basic_map *bmap);
1977 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1978 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1979 __isl_give isl_set *isl_map_domain(
1980 __isl_take isl_map *bmap);
1981 __isl_give isl_set *isl_map_range(
1982 __isl_take isl_map *map);
1983 __isl_give isl_set *isl_union_set_params(
1984 __isl_take isl_union_set *uset);
1985 __isl_give isl_set *isl_union_map_params(
1986 __isl_take isl_union_map *umap);
1987 __isl_give isl_union_set *isl_union_map_domain(
1988 __isl_take isl_union_map *umap);
1989 __isl_give isl_union_set *isl_union_map_range(
1990 __isl_take isl_union_map *umap);
1992 __isl_give isl_basic_map *isl_basic_map_domain_map(
1993 __isl_take isl_basic_map *bmap);
1994 __isl_give isl_basic_map *isl_basic_map_range_map(
1995 __isl_take isl_basic_map *bmap);
1996 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1997 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1998 __isl_give isl_union_map *isl_union_map_domain_map(
1999 __isl_take isl_union_map *umap);
2000 __isl_give isl_union_map *isl_union_map_range_map(
2001 __isl_take isl_union_map *umap);
2003 The functions above construct a (basic, regular or union) relation
2004 that maps (a wrapped version of) the input relation to its domain or range.
2008 __isl_give isl_basic_set *isl_basic_set_eliminate(
2009 __isl_take isl_basic_set *bset,
2010 enum isl_dim_type type,
2011 unsigned first, unsigned n);
2012 __isl_give isl_set *isl_set_eliminate(
2013 __isl_take isl_set *set, enum isl_dim_type type,
2014 unsigned first, unsigned n);
2015 __isl_give isl_basic_map *isl_basic_map_eliminate(
2016 __isl_take isl_basic_map *bmap,
2017 enum isl_dim_type type,
2018 unsigned first, unsigned n);
2019 __isl_give isl_map *isl_map_eliminate(
2020 __isl_take isl_map *map, enum isl_dim_type type,
2021 unsigned first, unsigned n);
2023 Eliminate the coefficients for the given dimensions from the constraints,
2024 without removing the dimensions.
2028 __isl_give isl_basic_set *isl_basic_set_fix(
2029 __isl_take isl_basic_set *bset,
2030 enum isl_dim_type type, unsigned pos,
2032 __isl_give isl_basic_set *isl_basic_set_fix_si(
2033 __isl_take isl_basic_set *bset,
2034 enum isl_dim_type type, unsigned pos, int value);
2035 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2036 enum isl_dim_type type, unsigned pos,
2038 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2039 enum isl_dim_type type, unsigned pos, int value);
2040 __isl_give isl_basic_map *isl_basic_map_fix_si(
2041 __isl_take isl_basic_map *bmap,
2042 enum isl_dim_type type, unsigned pos, int value);
2043 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
2044 enum isl_dim_type type, unsigned pos,
2046 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2047 enum isl_dim_type type, unsigned pos, int value);
2049 Intersect the set or relation with the hyperplane where the given
2050 dimension has the fixed given value.
2052 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2053 __isl_take isl_basic_map *bmap,
2054 enum isl_dim_type type, unsigned pos, int value);
2055 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2056 __isl_take isl_basic_map *bmap,
2057 enum isl_dim_type type, unsigned pos, int value);
2058 __isl_give isl_set *isl_set_lower_bound(
2059 __isl_take isl_set *set,
2060 enum isl_dim_type type, unsigned pos,
2062 __isl_give isl_set *isl_set_lower_bound_si(
2063 __isl_take isl_set *set,
2064 enum isl_dim_type type, unsigned pos, int value);
2065 __isl_give isl_map *isl_map_lower_bound_si(
2066 __isl_take isl_map *map,
2067 enum isl_dim_type type, unsigned pos, int value);
2068 __isl_give isl_set *isl_set_upper_bound(
2069 __isl_take isl_set *set,
2070 enum isl_dim_type type, unsigned pos,
2072 __isl_give isl_set *isl_set_upper_bound_si(
2073 __isl_take isl_set *set,
2074 enum isl_dim_type type, unsigned pos, int value);
2075 __isl_give isl_map *isl_map_upper_bound_si(
2076 __isl_take isl_map *map,
2077 enum isl_dim_type type, unsigned pos, int value);
2079 Intersect the set or relation with the half-space where the given
2080 dimension has a value bounded by the fixed given value.
2082 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2083 enum isl_dim_type type1, int pos1,
2084 enum isl_dim_type type2, int pos2);
2085 __isl_give isl_basic_map *isl_basic_map_equate(
2086 __isl_take isl_basic_map *bmap,
2087 enum isl_dim_type type1, int pos1,
2088 enum isl_dim_type type2, int pos2);
2089 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2090 enum isl_dim_type type1, int pos1,
2091 enum isl_dim_type type2, int pos2);
2093 Intersect the set or relation with the hyperplane where the given
2094 dimensions are equal to each other.
2096 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2097 enum isl_dim_type type1, int pos1,
2098 enum isl_dim_type type2, int pos2);
2100 Intersect the relation with the hyperplane where the given
2101 dimensions have opposite values.
2103 __isl_give isl_basic_map *isl_basic_map_order_ge(
2104 __isl_take isl_basic_map *bmap,
2105 enum isl_dim_type type1, int pos1,
2106 enum isl_dim_type type2, int pos2);
2107 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2108 enum isl_dim_type type1, int pos1,
2109 enum isl_dim_type type2, int pos2);
2110 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2111 enum isl_dim_type type1, int pos1,
2112 enum isl_dim_type type2, int pos2);
2114 Intersect the relation with the half-space where the given
2115 dimensions satisfy the given ordering.
2119 __isl_give isl_map *isl_set_identity(
2120 __isl_take isl_set *set);
2121 __isl_give isl_union_map *isl_union_set_identity(
2122 __isl_take isl_union_set *uset);
2124 Construct an identity relation on the given (union) set.
2128 __isl_give isl_basic_set *isl_basic_map_deltas(
2129 __isl_take isl_basic_map *bmap);
2130 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2131 __isl_give isl_union_set *isl_union_map_deltas(
2132 __isl_take isl_union_map *umap);
2134 These functions return a (basic) set containing the differences
2135 between image elements and corresponding domain elements in the input.
2137 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2138 __isl_take isl_basic_map *bmap);
2139 __isl_give isl_map *isl_map_deltas_map(
2140 __isl_take isl_map *map);
2141 __isl_give isl_union_map *isl_union_map_deltas_map(
2142 __isl_take isl_union_map *umap);
2144 The functions above construct a (basic, regular or union) relation
2145 that maps (a wrapped version of) the input relation to its delta set.
2149 Simplify the representation of a set or relation by trying
2150 to combine pairs of basic sets or relations into a single
2151 basic set or relation.
2153 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2154 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2155 __isl_give isl_union_set *isl_union_set_coalesce(
2156 __isl_take isl_union_set *uset);
2157 __isl_give isl_union_map *isl_union_map_coalesce(
2158 __isl_take isl_union_map *umap);
2160 One of the methods for combining pairs of basic sets or relations
2161 can result in coefficients that are much larger than those that appear
2162 in the constraints of the input. By default, the coefficients are
2163 not allowed to grow larger, but this can be changed by unsetting
2164 the following option.
2166 int isl_options_set_coalesce_bounded_wrapping(
2167 isl_ctx *ctx, int val);
2168 int isl_options_get_coalesce_bounded_wrapping(
2171 =item * Detecting equalities
2173 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2174 __isl_take isl_basic_set *bset);
2175 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2176 __isl_take isl_basic_map *bmap);
2177 __isl_give isl_set *isl_set_detect_equalities(
2178 __isl_take isl_set *set);
2179 __isl_give isl_map *isl_map_detect_equalities(
2180 __isl_take isl_map *map);
2181 __isl_give isl_union_set *isl_union_set_detect_equalities(
2182 __isl_take isl_union_set *uset);
2183 __isl_give isl_union_map *isl_union_map_detect_equalities(
2184 __isl_take isl_union_map *umap);
2186 Simplify the representation of a set or relation by detecting implicit
2189 =item * Removing redundant constraints
2191 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2192 __isl_take isl_basic_set *bset);
2193 __isl_give isl_set *isl_set_remove_redundancies(
2194 __isl_take isl_set *set);
2195 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2196 __isl_take isl_basic_map *bmap);
2197 __isl_give isl_map *isl_map_remove_redundancies(
2198 __isl_take isl_map *map);
2202 __isl_give isl_basic_set *isl_set_convex_hull(
2203 __isl_take isl_set *set);
2204 __isl_give isl_basic_map *isl_map_convex_hull(
2205 __isl_take isl_map *map);
2207 If the input set or relation has any existentially quantified
2208 variables, then the result of these operations is currently undefined.
2212 __isl_give isl_basic_set *isl_set_simple_hull(
2213 __isl_take isl_set *set);
2214 __isl_give isl_basic_map *isl_map_simple_hull(
2215 __isl_take isl_map *map);
2216 __isl_give isl_union_map *isl_union_map_simple_hull(
2217 __isl_take isl_union_map *umap);
2219 These functions compute a single basic set or relation
2220 that contains the whole input set or relation.
2221 In particular, the output is described by translates
2222 of the constraints describing the basic sets or relations in the input.
2226 (See \autoref{s:simple hull}.)
2232 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2233 __isl_take isl_basic_set *bset);
2234 __isl_give isl_basic_set *isl_set_affine_hull(
2235 __isl_take isl_set *set);
2236 __isl_give isl_union_set *isl_union_set_affine_hull(
2237 __isl_take isl_union_set *uset);
2238 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2239 __isl_take isl_basic_map *bmap);
2240 __isl_give isl_basic_map *isl_map_affine_hull(
2241 __isl_take isl_map *map);
2242 __isl_give isl_union_map *isl_union_map_affine_hull(
2243 __isl_take isl_union_map *umap);
2245 In case of union sets and relations, the affine hull is computed
2248 =item * Polyhedral hull
2250 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2251 __isl_take isl_set *set);
2252 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2253 __isl_take isl_map *map);
2254 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2255 __isl_take isl_union_set *uset);
2256 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2257 __isl_take isl_union_map *umap);
2259 These functions compute a single basic set or relation
2260 not involving any existentially quantified variables
2261 that contains the whole input set or relation.
2262 In case of union sets and relations, the polyhedral hull is computed
2267 __isl_give isl_basic_set *isl_basic_set_sample(
2268 __isl_take isl_basic_set *bset);
2269 __isl_give isl_basic_set *isl_set_sample(
2270 __isl_take isl_set *set);
2271 __isl_give isl_basic_map *isl_basic_map_sample(
2272 __isl_take isl_basic_map *bmap);
2273 __isl_give isl_basic_map *isl_map_sample(
2274 __isl_take isl_map *map);
2276 If the input (basic) set or relation is non-empty, then return
2277 a singleton subset of the input. Otherwise, return an empty set.
2279 =item * Optimization
2281 #include <isl/ilp.h>
2282 enum isl_lp_result isl_basic_set_max(
2283 __isl_keep isl_basic_set *bset,
2284 __isl_keep isl_aff *obj, isl_int *opt)
2285 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2286 __isl_keep isl_aff *obj, isl_int *opt);
2287 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2288 __isl_keep isl_aff *obj, isl_int *opt);
2290 Compute the minimum or maximum of the integer affine expression C<obj>
2291 over the points in C<set>, returning the result in C<opt>.
2292 The return value may be one of C<isl_lp_error>,
2293 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2295 =item * Parametric optimization
2297 __isl_give isl_pw_aff *isl_set_dim_min(
2298 __isl_take isl_set *set, int pos);
2299 __isl_give isl_pw_aff *isl_set_dim_max(
2300 __isl_take isl_set *set, int pos);
2301 __isl_give isl_pw_aff *isl_map_dim_max(
2302 __isl_take isl_map *map, int pos);
2304 Compute the minimum or maximum of the given set or output dimension
2305 as a function of the parameters (and input dimensions), but independently
2306 of the other set or output dimensions.
2307 For lexicographic optimization, see L<"Lexicographic Optimization">.
2311 The following functions compute either the set of (rational) coefficient
2312 values of valid constraints for the given set or the set of (rational)
2313 values satisfying the constraints with coefficients from the given set.
2314 Internally, these two sets of functions perform essentially the
2315 same operations, except that the set of coefficients is assumed to
2316 be a cone, while the set of values may be any polyhedron.
2317 The current implementation is based on the Farkas lemma and
2318 Fourier-Motzkin elimination, but this may change or be made optional
2319 in future. In particular, future implementations may use different
2320 dualization algorithms or skip the elimination step.
2322 __isl_give isl_basic_set *isl_basic_set_coefficients(
2323 __isl_take isl_basic_set *bset);
2324 __isl_give isl_basic_set *isl_set_coefficients(
2325 __isl_take isl_set *set);
2326 __isl_give isl_union_set *isl_union_set_coefficients(
2327 __isl_take isl_union_set *bset);
2328 __isl_give isl_basic_set *isl_basic_set_solutions(
2329 __isl_take isl_basic_set *bset);
2330 __isl_give isl_basic_set *isl_set_solutions(
2331 __isl_take isl_set *set);
2332 __isl_give isl_union_set *isl_union_set_solutions(
2333 __isl_take isl_union_set *bset);
2337 __isl_give isl_map *isl_map_fixed_power(
2338 __isl_take isl_map *map, isl_int exp);
2339 __isl_give isl_union_map *isl_union_map_fixed_power(
2340 __isl_take isl_union_map *umap, isl_int exp);
2342 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2343 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2344 of C<map> is computed.
2346 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2348 __isl_give isl_union_map *isl_union_map_power(
2349 __isl_take isl_union_map *umap, int *exact);
2351 Compute a parametric representation for all positive powers I<k> of C<map>.
2352 The result maps I<k> to a nested relation corresponding to the
2353 I<k>th power of C<map>.
2354 The result may be an overapproximation. If the result is known to be exact,
2355 then C<*exact> is set to C<1>.
2357 =item * Transitive closure
2359 __isl_give isl_map *isl_map_transitive_closure(
2360 __isl_take isl_map *map, int *exact);
2361 __isl_give isl_union_map *isl_union_map_transitive_closure(
2362 __isl_take isl_union_map *umap, int *exact);
2364 Compute the transitive closure of C<map>.
2365 The result may be an overapproximation. If the result is known to be exact,
2366 then C<*exact> is set to C<1>.
2368 =item * Reaching path lengths
2370 __isl_give isl_map *isl_map_reaching_path_lengths(
2371 __isl_take isl_map *map, int *exact);
2373 Compute a relation that maps each element in the range of C<map>
2374 to the lengths of all paths composed of edges in C<map> that
2375 end up in the given element.
2376 The result may be an overapproximation. If the result is known to be exact,
2377 then C<*exact> is set to C<1>.
2378 To compute the I<maximal> path length, the resulting relation
2379 should be postprocessed by C<isl_map_lexmax>.
2380 In particular, if the input relation is a dependence relation
2381 (mapping sources to sinks), then the maximal path length corresponds
2382 to the free schedule.
2383 Note, however, that C<isl_map_lexmax> expects the maximum to be
2384 finite, so if the path lengths are unbounded (possibly due to
2385 the overapproximation), then you will get an error message.
2389 __isl_give isl_basic_set *isl_basic_map_wrap(
2390 __isl_take isl_basic_map *bmap);
2391 __isl_give isl_set *isl_map_wrap(
2392 __isl_take isl_map *map);
2393 __isl_give isl_union_set *isl_union_map_wrap(
2394 __isl_take isl_union_map *umap);
2395 __isl_give isl_basic_map *isl_basic_set_unwrap(
2396 __isl_take isl_basic_set *bset);
2397 __isl_give isl_map *isl_set_unwrap(
2398 __isl_take isl_set *set);
2399 __isl_give isl_union_map *isl_union_set_unwrap(
2400 __isl_take isl_union_set *uset);
2404 Remove any internal structure of domain (and range) of the given
2405 set or relation. If there is any such internal structure in the input,
2406 then the name of the space is also removed.
2408 __isl_give isl_basic_set *isl_basic_set_flatten(
2409 __isl_take isl_basic_set *bset);
2410 __isl_give isl_set *isl_set_flatten(
2411 __isl_take isl_set *set);
2412 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2413 __isl_take isl_basic_map *bmap);
2414 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2415 __isl_take isl_basic_map *bmap);
2416 __isl_give isl_map *isl_map_flatten_range(
2417 __isl_take isl_map *map);
2418 __isl_give isl_map *isl_map_flatten_domain(
2419 __isl_take isl_map *map);
2420 __isl_give isl_basic_map *isl_basic_map_flatten(
2421 __isl_take isl_basic_map *bmap);
2422 __isl_give isl_map *isl_map_flatten(
2423 __isl_take isl_map *map);
2425 __isl_give isl_map *isl_set_flatten_map(
2426 __isl_take isl_set *set);
2428 The function above constructs a relation
2429 that maps the input set to a flattened version of the set.
2433 Lift the input set to a space with extra dimensions corresponding
2434 to the existentially quantified variables in the input.
2435 In particular, the result lives in a wrapped map where the domain
2436 is the original space and the range corresponds to the original
2437 existentially quantified variables.
2439 __isl_give isl_basic_set *isl_basic_set_lift(
2440 __isl_take isl_basic_set *bset);
2441 __isl_give isl_set *isl_set_lift(
2442 __isl_take isl_set *set);
2443 __isl_give isl_union_set *isl_union_set_lift(
2444 __isl_take isl_union_set *uset);
2446 Given a local space that contains the existentially quantified
2447 variables of a set, a basic relation that, when applied to
2448 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2449 can be constructed using the following function.
2451 #include <isl/local_space.h>
2452 __isl_give isl_basic_map *isl_local_space_lifting(
2453 __isl_take isl_local_space *ls);
2455 =item * Internal Product
2457 __isl_give isl_basic_map *isl_basic_map_zip(
2458 __isl_take isl_basic_map *bmap);
2459 __isl_give isl_map *isl_map_zip(
2460 __isl_take isl_map *map);
2461 __isl_give isl_union_map *isl_union_map_zip(
2462 __isl_take isl_union_map *umap);
2464 Given a relation with nested relations for domain and range,
2465 interchange the range of the domain with the domain of the range.
2469 __isl_give isl_basic_map *isl_basic_map_curry(
2470 __isl_take isl_basic_map *bmap);
2471 __isl_give isl_map *isl_map_curry(
2472 __isl_take isl_map *map);
2473 __isl_give isl_union_map *isl_union_map_curry(
2474 __isl_take isl_union_map *umap);
2476 Given a relation with a nested relation for domain,
2477 move the range of the nested relation out of the domain
2478 and use it as the domain of a nested relation in the range,
2479 with the original range as range of this nested relation.
2481 =item * Aligning parameters
2483 __isl_give isl_basic_set *isl_basic_set_align_params(
2484 __isl_take isl_basic_set *bset,
2485 __isl_take isl_space *model);
2486 __isl_give isl_set *isl_set_align_params(
2487 __isl_take isl_set *set,
2488 __isl_take isl_space *model);
2489 __isl_give isl_basic_map *isl_basic_map_align_params(
2490 __isl_take isl_basic_map *bmap,
2491 __isl_take isl_space *model);
2492 __isl_give isl_map *isl_map_align_params(
2493 __isl_take isl_map *map,
2494 __isl_take isl_space *model);
2496 Change the order of the parameters of the given set or relation
2497 such that the first parameters match those of C<model>.
2498 This may involve the introduction of extra parameters.
2499 All parameters need to be named.
2501 =item * Dimension manipulation
2503 __isl_give isl_set *isl_set_add_dims(
2504 __isl_take isl_set *set,
2505 enum isl_dim_type type, unsigned n);
2506 __isl_give isl_map *isl_map_add_dims(
2507 __isl_take isl_map *map,
2508 enum isl_dim_type type, unsigned n);
2509 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2510 __isl_take isl_basic_set *bset,
2511 enum isl_dim_type type, unsigned pos,
2513 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2514 __isl_take isl_basic_map *bmap,
2515 enum isl_dim_type type, unsigned pos,
2517 __isl_give isl_set *isl_set_insert_dims(
2518 __isl_take isl_set *set,
2519 enum isl_dim_type type, unsigned pos, unsigned n);
2520 __isl_give isl_map *isl_map_insert_dims(
2521 __isl_take isl_map *map,
2522 enum isl_dim_type type, unsigned pos, unsigned n);
2523 __isl_give isl_basic_set *isl_basic_set_move_dims(
2524 __isl_take isl_basic_set *bset,
2525 enum isl_dim_type dst_type, unsigned dst_pos,
2526 enum isl_dim_type src_type, unsigned src_pos,
2528 __isl_give isl_basic_map *isl_basic_map_move_dims(
2529 __isl_take isl_basic_map *bmap,
2530 enum isl_dim_type dst_type, unsigned dst_pos,
2531 enum isl_dim_type src_type, unsigned src_pos,
2533 __isl_give isl_set *isl_set_move_dims(
2534 __isl_take isl_set *set,
2535 enum isl_dim_type dst_type, unsigned dst_pos,
2536 enum isl_dim_type src_type, unsigned src_pos,
2538 __isl_give isl_map *isl_map_move_dims(
2539 __isl_take isl_map *map,
2540 enum isl_dim_type dst_type, unsigned dst_pos,
2541 enum isl_dim_type src_type, unsigned src_pos,
2544 It is usually not advisable to directly change the (input or output)
2545 space of a set or a relation as this removes the name and the internal
2546 structure of the space. However, the above functions can be useful
2547 to add new parameters, assuming
2548 C<isl_set_align_params> and C<isl_map_align_params>
2553 =head2 Binary Operations
2555 The two arguments of a binary operation not only need to live
2556 in the same C<isl_ctx>, they currently also need to have
2557 the same (number of) parameters.
2559 =head3 Basic Operations
2563 =item * Intersection
2565 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2566 __isl_take isl_basic_set *bset1,
2567 __isl_take isl_basic_set *bset2);
2568 __isl_give isl_basic_set *isl_basic_set_intersect(
2569 __isl_take isl_basic_set *bset1,
2570 __isl_take isl_basic_set *bset2);
2571 __isl_give isl_set *isl_set_intersect_params(
2572 __isl_take isl_set *set,
2573 __isl_take isl_set *params);
2574 __isl_give isl_set *isl_set_intersect(
2575 __isl_take isl_set *set1,
2576 __isl_take isl_set *set2);
2577 __isl_give isl_union_set *isl_union_set_intersect_params(
2578 __isl_take isl_union_set *uset,
2579 __isl_take isl_set *set);
2580 __isl_give isl_union_map *isl_union_map_intersect_params(
2581 __isl_take isl_union_map *umap,
2582 __isl_take isl_set *set);
2583 __isl_give isl_union_set *isl_union_set_intersect(
2584 __isl_take isl_union_set *uset1,
2585 __isl_take isl_union_set *uset2);
2586 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2587 __isl_take isl_basic_map *bmap,
2588 __isl_take isl_basic_set *bset);
2589 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2590 __isl_take isl_basic_map *bmap,
2591 __isl_take isl_basic_set *bset);
2592 __isl_give isl_basic_map *isl_basic_map_intersect(
2593 __isl_take isl_basic_map *bmap1,
2594 __isl_take isl_basic_map *bmap2);
2595 __isl_give isl_map *isl_map_intersect_params(
2596 __isl_take isl_map *map,
2597 __isl_take isl_set *params);
2598 __isl_give isl_map *isl_map_intersect_domain(
2599 __isl_take isl_map *map,
2600 __isl_take isl_set *set);
2601 __isl_give isl_map *isl_map_intersect_range(
2602 __isl_take isl_map *map,
2603 __isl_take isl_set *set);
2604 __isl_give isl_map *isl_map_intersect(
2605 __isl_take isl_map *map1,
2606 __isl_take isl_map *map2);
2607 __isl_give isl_union_map *isl_union_map_intersect_domain(
2608 __isl_take isl_union_map *umap,
2609 __isl_take isl_union_set *uset);
2610 __isl_give isl_union_map *isl_union_map_intersect_range(
2611 __isl_take isl_union_map *umap,
2612 __isl_take isl_union_set *uset);
2613 __isl_give isl_union_map *isl_union_map_intersect(
2614 __isl_take isl_union_map *umap1,
2615 __isl_take isl_union_map *umap2);
2617 The second argument to the C<_params> functions needs to be
2618 a parametric (basic) set. For the other functions, a parametric set
2619 for either argument is only allowed if the other argument is
2620 a parametric set as well.
2624 __isl_give isl_set *isl_basic_set_union(
2625 __isl_take isl_basic_set *bset1,
2626 __isl_take isl_basic_set *bset2);
2627 __isl_give isl_map *isl_basic_map_union(
2628 __isl_take isl_basic_map *bmap1,
2629 __isl_take isl_basic_map *bmap2);
2630 __isl_give isl_set *isl_set_union(
2631 __isl_take isl_set *set1,
2632 __isl_take isl_set *set2);
2633 __isl_give isl_map *isl_map_union(
2634 __isl_take isl_map *map1,
2635 __isl_take isl_map *map2);
2636 __isl_give isl_union_set *isl_union_set_union(
2637 __isl_take isl_union_set *uset1,
2638 __isl_take isl_union_set *uset2);
2639 __isl_give isl_union_map *isl_union_map_union(
2640 __isl_take isl_union_map *umap1,
2641 __isl_take isl_union_map *umap2);
2643 =item * Set difference
2645 __isl_give isl_set *isl_set_subtract(
2646 __isl_take isl_set *set1,
2647 __isl_take isl_set *set2);
2648 __isl_give isl_map *isl_map_subtract(
2649 __isl_take isl_map *map1,
2650 __isl_take isl_map *map2);
2651 __isl_give isl_map *isl_map_subtract_domain(
2652 __isl_take isl_map *map,
2653 __isl_take isl_set *dom);
2654 __isl_give isl_map *isl_map_subtract_range(
2655 __isl_take isl_map *map,
2656 __isl_take isl_set *dom);
2657 __isl_give isl_union_set *isl_union_set_subtract(
2658 __isl_take isl_union_set *uset1,
2659 __isl_take isl_union_set *uset2);
2660 __isl_give isl_union_map *isl_union_map_subtract(
2661 __isl_take isl_union_map *umap1,
2662 __isl_take isl_union_map *umap2);
2663 __isl_give isl_union_map *isl_union_map_subtract_domain(
2664 __isl_take isl_union_map *umap,
2665 __isl_take isl_union_set *dom);
2669 __isl_give isl_basic_set *isl_basic_set_apply(
2670 __isl_take isl_basic_set *bset,
2671 __isl_take isl_basic_map *bmap);
2672 __isl_give isl_set *isl_set_apply(
2673 __isl_take isl_set *set,
2674 __isl_take isl_map *map);
2675 __isl_give isl_union_set *isl_union_set_apply(
2676 __isl_take isl_union_set *uset,
2677 __isl_take isl_union_map *umap);
2678 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2679 __isl_take isl_basic_map *bmap1,
2680 __isl_take isl_basic_map *bmap2);
2681 __isl_give isl_basic_map *isl_basic_map_apply_range(
2682 __isl_take isl_basic_map *bmap1,
2683 __isl_take isl_basic_map *bmap2);
2684 __isl_give isl_map *isl_map_apply_domain(
2685 __isl_take isl_map *map1,
2686 __isl_take isl_map *map2);
2687 __isl_give isl_union_map *isl_union_map_apply_domain(
2688 __isl_take isl_union_map *umap1,
2689 __isl_take isl_union_map *umap2);
2690 __isl_give isl_map *isl_map_apply_range(
2691 __isl_take isl_map *map1,
2692 __isl_take isl_map *map2);
2693 __isl_give isl_union_map *isl_union_map_apply_range(
2694 __isl_take isl_union_map *umap1,
2695 __isl_take isl_union_map *umap2);
2697 =item * Cartesian Product
2699 __isl_give isl_set *isl_set_product(
2700 __isl_take isl_set *set1,
2701 __isl_take isl_set *set2);
2702 __isl_give isl_union_set *isl_union_set_product(
2703 __isl_take isl_union_set *uset1,
2704 __isl_take isl_union_set *uset2);
2705 __isl_give isl_basic_map *isl_basic_map_domain_product(
2706 __isl_take isl_basic_map *bmap1,
2707 __isl_take isl_basic_map *bmap2);
2708 __isl_give isl_basic_map *isl_basic_map_range_product(
2709 __isl_take isl_basic_map *bmap1,
2710 __isl_take isl_basic_map *bmap2);
2711 __isl_give isl_basic_map *isl_basic_map_product(
2712 __isl_take isl_basic_map *bmap1,
2713 __isl_take isl_basic_map *bmap2);
2714 __isl_give isl_map *isl_map_domain_product(
2715 __isl_take isl_map *map1,
2716 __isl_take isl_map *map2);
2717 __isl_give isl_map *isl_map_range_product(
2718 __isl_take isl_map *map1,
2719 __isl_take isl_map *map2);
2720 __isl_give isl_union_map *isl_union_map_domain_product(
2721 __isl_take isl_union_map *umap1,
2722 __isl_take isl_union_map *umap2);
2723 __isl_give isl_union_map *isl_union_map_range_product(
2724 __isl_take isl_union_map *umap1,
2725 __isl_take isl_union_map *umap2);
2726 __isl_give isl_map *isl_map_product(
2727 __isl_take isl_map *map1,
2728 __isl_take isl_map *map2);
2729 __isl_give isl_union_map *isl_union_map_product(
2730 __isl_take isl_union_map *umap1,
2731 __isl_take isl_union_map *umap2);
2733 The above functions compute the cross product of the given
2734 sets or relations. The domains and ranges of the results
2735 are wrapped maps between domains and ranges of the inputs.
2736 To obtain a ``flat'' product, use the following functions
2739 __isl_give isl_basic_set *isl_basic_set_flat_product(
2740 __isl_take isl_basic_set *bset1,
2741 __isl_take isl_basic_set *bset2);
2742 __isl_give isl_set *isl_set_flat_product(
2743 __isl_take isl_set *set1,
2744 __isl_take isl_set *set2);
2745 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2746 __isl_take isl_basic_map *bmap1,
2747 __isl_take isl_basic_map *bmap2);
2748 __isl_give isl_map *isl_map_flat_domain_product(
2749 __isl_take isl_map *map1,
2750 __isl_take isl_map *map2);
2751 __isl_give isl_map *isl_map_flat_range_product(
2752 __isl_take isl_map *map1,
2753 __isl_take isl_map *map2);
2754 __isl_give isl_union_map *isl_union_map_flat_range_product(
2755 __isl_take isl_union_map *umap1,
2756 __isl_take isl_union_map *umap2);
2757 __isl_give isl_basic_map *isl_basic_map_flat_product(
2758 __isl_take isl_basic_map *bmap1,
2759 __isl_take isl_basic_map *bmap2);
2760 __isl_give isl_map *isl_map_flat_product(
2761 __isl_take isl_map *map1,
2762 __isl_take isl_map *map2);
2764 =item * Simplification
2766 __isl_give isl_basic_set *isl_basic_set_gist(
2767 __isl_take isl_basic_set *bset,
2768 __isl_take isl_basic_set *context);
2769 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2770 __isl_take isl_set *context);
2771 __isl_give isl_set *isl_set_gist_params(
2772 __isl_take isl_set *set,
2773 __isl_take isl_set *context);
2774 __isl_give isl_union_set *isl_union_set_gist(
2775 __isl_take isl_union_set *uset,
2776 __isl_take isl_union_set *context);
2777 __isl_give isl_union_set *isl_union_set_gist_params(
2778 __isl_take isl_union_set *uset,
2779 __isl_take isl_set *set);
2780 __isl_give isl_basic_map *isl_basic_map_gist(
2781 __isl_take isl_basic_map *bmap,
2782 __isl_take isl_basic_map *context);
2783 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2784 __isl_take isl_map *context);
2785 __isl_give isl_map *isl_map_gist_params(
2786 __isl_take isl_map *map,
2787 __isl_take isl_set *context);
2788 __isl_give isl_map *isl_map_gist_domain(
2789 __isl_take isl_map *map,
2790 __isl_take isl_set *context);
2791 __isl_give isl_map *isl_map_gist_range(
2792 __isl_take isl_map *map,
2793 __isl_take isl_set *context);
2794 __isl_give isl_union_map *isl_union_map_gist(
2795 __isl_take isl_union_map *umap,
2796 __isl_take isl_union_map *context);
2797 __isl_give isl_union_map *isl_union_map_gist_params(
2798 __isl_take isl_union_map *umap,
2799 __isl_take isl_set *set);
2800 __isl_give isl_union_map *isl_union_map_gist_domain(
2801 __isl_take isl_union_map *umap,
2802 __isl_take isl_union_set *uset);
2803 __isl_give isl_union_map *isl_union_map_gist_range(
2804 __isl_take isl_union_map *umap,
2805 __isl_take isl_union_set *uset);
2807 The gist operation returns a set or relation that has the
2808 same intersection with the context as the input set or relation.
2809 Any implicit equality in the intersection is made explicit in the result,
2810 while all inequalities that are redundant with respect to the intersection
2812 In case of union sets and relations, the gist operation is performed
2817 =head3 Lexicographic Optimization
2819 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2820 the following functions
2821 compute a set that contains the lexicographic minimum or maximum
2822 of the elements in C<set> (or C<bset>) for those values of the parameters
2823 that satisfy C<dom>.
2824 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2825 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2827 In other words, the union of the parameter values
2828 for which the result is non-empty and of C<*empty>
2831 __isl_give isl_set *isl_basic_set_partial_lexmin(
2832 __isl_take isl_basic_set *bset,
2833 __isl_take isl_basic_set *dom,
2834 __isl_give isl_set **empty);
2835 __isl_give isl_set *isl_basic_set_partial_lexmax(
2836 __isl_take isl_basic_set *bset,
2837 __isl_take isl_basic_set *dom,
2838 __isl_give isl_set **empty);
2839 __isl_give isl_set *isl_set_partial_lexmin(
2840 __isl_take isl_set *set, __isl_take isl_set *dom,
2841 __isl_give isl_set **empty);
2842 __isl_give isl_set *isl_set_partial_lexmax(
2843 __isl_take isl_set *set, __isl_take isl_set *dom,
2844 __isl_give isl_set **empty);
2846 Given a (basic) set C<set> (or C<bset>), the following functions simply
2847 return a set containing the lexicographic minimum or maximum
2848 of the elements in C<set> (or C<bset>).
2849 In case of union sets, the optimum is computed per space.
2851 __isl_give isl_set *isl_basic_set_lexmin(
2852 __isl_take isl_basic_set *bset);
2853 __isl_give isl_set *isl_basic_set_lexmax(
2854 __isl_take isl_basic_set *bset);
2855 __isl_give isl_set *isl_set_lexmin(
2856 __isl_take isl_set *set);
2857 __isl_give isl_set *isl_set_lexmax(
2858 __isl_take isl_set *set);
2859 __isl_give isl_union_set *isl_union_set_lexmin(
2860 __isl_take isl_union_set *uset);
2861 __isl_give isl_union_set *isl_union_set_lexmax(
2862 __isl_take isl_union_set *uset);
2864 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2865 the following functions
2866 compute a relation that maps each element of C<dom>
2867 to the single lexicographic minimum or maximum
2868 of the elements that are associated to that same
2869 element in C<map> (or C<bmap>).
2870 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2871 that contains the elements in C<dom> that do not map
2872 to any elements in C<map> (or C<bmap>).
2873 In other words, the union of the domain of the result and of C<*empty>
2876 __isl_give isl_map *isl_basic_map_partial_lexmax(
2877 __isl_take isl_basic_map *bmap,
2878 __isl_take isl_basic_set *dom,
2879 __isl_give isl_set **empty);
2880 __isl_give isl_map *isl_basic_map_partial_lexmin(
2881 __isl_take isl_basic_map *bmap,
2882 __isl_take isl_basic_set *dom,
2883 __isl_give isl_set **empty);
2884 __isl_give isl_map *isl_map_partial_lexmax(
2885 __isl_take isl_map *map, __isl_take isl_set *dom,
2886 __isl_give isl_set **empty);
2887 __isl_give isl_map *isl_map_partial_lexmin(
2888 __isl_take isl_map *map, __isl_take isl_set *dom,
2889 __isl_give isl_set **empty);
2891 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2892 return a map mapping each element in the domain of
2893 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2894 of all elements associated to that element.
2895 In case of union relations, the optimum is computed per space.
2897 __isl_give isl_map *isl_basic_map_lexmin(
2898 __isl_take isl_basic_map *bmap);
2899 __isl_give isl_map *isl_basic_map_lexmax(
2900 __isl_take isl_basic_map *bmap);
2901 __isl_give isl_map *isl_map_lexmin(
2902 __isl_take isl_map *map);
2903 __isl_give isl_map *isl_map_lexmax(
2904 __isl_take isl_map *map);
2905 __isl_give isl_union_map *isl_union_map_lexmin(
2906 __isl_take isl_union_map *umap);
2907 __isl_give isl_union_map *isl_union_map_lexmax(
2908 __isl_take isl_union_map *umap);
2910 The following functions return their result in the form of
2911 a piecewise multi-affine expression
2912 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2913 but are otherwise equivalent to the corresponding functions
2914 returning a basic set or relation.
2916 __isl_give isl_pw_multi_aff *
2917 isl_basic_map_lexmin_pw_multi_aff(
2918 __isl_take isl_basic_map *bmap);
2919 __isl_give isl_pw_multi_aff *
2920 isl_basic_set_partial_lexmin_pw_multi_aff(
2921 __isl_take isl_basic_set *bset,
2922 __isl_take isl_basic_set *dom,
2923 __isl_give isl_set **empty);
2924 __isl_give isl_pw_multi_aff *
2925 isl_basic_set_partial_lexmax_pw_multi_aff(
2926 __isl_take isl_basic_set *bset,
2927 __isl_take isl_basic_set *dom,
2928 __isl_give isl_set **empty);
2929 __isl_give isl_pw_multi_aff *
2930 isl_basic_map_partial_lexmin_pw_multi_aff(
2931 __isl_take isl_basic_map *bmap,
2932 __isl_take isl_basic_set *dom,
2933 __isl_give isl_set **empty);
2934 __isl_give isl_pw_multi_aff *
2935 isl_basic_map_partial_lexmax_pw_multi_aff(
2936 __isl_take isl_basic_map *bmap,
2937 __isl_take isl_basic_set *dom,
2938 __isl_give isl_set **empty);
2939 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
2940 __isl_take isl_map *map);
2941 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
2942 __isl_take isl_map *map);
2946 Lists are defined over several element types, including
2947 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
2948 C<isl_basic_set> and C<isl_set>.
2949 Here we take lists of C<isl_set>s as an example.
2950 Lists can be created, copied, modified and freed using the following functions.
2952 #include <isl/list.h>
2953 __isl_give isl_set_list *isl_set_list_from_set(
2954 __isl_take isl_set *el);
2955 __isl_give isl_set_list *isl_set_list_alloc(
2956 isl_ctx *ctx, int n);
2957 __isl_give isl_set_list *isl_set_list_copy(
2958 __isl_keep isl_set_list *list);
2959 __isl_give isl_set_list *isl_set_list_insert(
2960 __isl_take isl_set_list *list, unsigned pos,
2961 __isl_take isl_set *el);
2962 __isl_give isl_set_list *isl_set_list_add(
2963 __isl_take isl_set_list *list,
2964 __isl_take isl_set *el);
2965 __isl_give isl_set_list *isl_set_list_drop(
2966 __isl_take isl_set_list *list,
2967 unsigned first, unsigned n);
2968 __isl_give isl_set_list *isl_set_list_set_set(
2969 __isl_take isl_set_list *list, int index,
2970 __isl_take isl_set *set);
2971 __isl_give isl_set_list *isl_set_list_concat(
2972 __isl_take isl_set_list *list1,
2973 __isl_take isl_set_list *list2);
2974 void *isl_set_list_free(__isl_take isl_set_list *list);
2976 C<isl_set_list_alloc> creates an empty list with a capacity for
2977 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2980 Lists can be inspected using the following functions.
2982 #include <isl/list.h>
2983 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2984 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2985 __isl_give isl_set *isl_set_list_get_set(
2986 __isl_keep isl_set_list *list, int index);
2987 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2988 int (*fn)(__isl_take isl_set *el, void *user),
2991 Lists can be printed using
2993 #include <isl/list.h>
2994 __isl_give isl_printer *isl_printer_print_set_list(
2995 __isl_take isl_printer *p,
2996 __isl_keep isl_set_list *list);
3000 Vectors can be created, copied and freed using the following functions.
3002 #include <isl/vec.h>
3003 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3005 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3006 void *isl_vec_free(__isl_take isl_vec *vec);
3008 Note that the elements of a newly created vector may have arbitrary values.
3009 The elements can be changed and inspected using the following functions.
3011 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3012 int isl_vec_size(__isl_keep isl_vec *vec);
3013 int isl_vec_get_element(__isl_keep isl_vec *vec,
3014 int pos, isl_int *v);
3015 __isl_give isl_vec *isl_vec_set_element(
3016 __isl_take isl_vec *vec, int pos, isl_int v);
3017 __isl_give isl_vec *isl_vec_set_element_si(
3018 __isl_take isl_vec *vec, int pos, int v);
3019 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3021 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3023 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3026 C<isl_vec_get_element> will return a negative value if anything went wrong.
3027 In that case, the value of C<*v> is undefined.
3029 The following function can be used to concatenate two vectors.
3031 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3032 __isl_take isl_vec *vec2);
3036 Matrices can be created, copied and freed using the following functions.
3038 #include <isl/mat.h>
3039 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3040 unsigned n_row, unsigned n_col);
3041 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3042 void isl_mat_free(__isl_take isl_mat *mat);
3044 Note that the elements of a newly created matrix may have arbitrary values.
3045 The elements can be changed and inspected using the following functions.
3047 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3048 int isl_mat_rows(__isl_keep isl_mat *mat);
3049 int isl_mat_cols(__isl_keep isl_mat *mat);
3050 int isl_mat_get_element(__isl_keep isl_mat *mat,
3051 int row, int col, isl_int *v);
3052 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3053 int row, int col, isl_int v);
3054 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3055 int row, int col, int v);
3057 C<isl_mat_get_element> will return a negative value if anything went wrong.
3058 In that case, the value of C<*v> is undefined.
3060 The following function can be used to compute the (right) inverse
3061 of a matrix, i.e., a matrix such that the product of the original
3062 and the inverse (in that order) is a multiple of the identity matrix.
3063 The input matrix is assumed to be of full row-rank.
3065 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3067 The following function can be used to compute the (right) kernel
3068 (or null space) of a matrix, i.e., a matrix such that the product of
3069 the original and the kernel (in that order) is the zero matrix.
3071 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3073 =head2 Piecewise Quasi Affine Expressions
3075 The zero quasi affine expression on a given domain can be created using
3077 __isl_give isl_aff *isl_aff_zero_on_domain(
3078 __isl_take isl_local_space *ls);
3080 Note that the space in which the resulting object lives is a map space
3081 with the given space as domain and a one-dimensional range.
3083 An empty piecewise quasi affine expression (one with no cells)
3084 or a piecewise quasi affine expression with a single cell can
3085 be created using the following functions.
3087 #include <isl/aff.h>
3088 __isl_give isl_pw_aff *isl_pw_aff_empty(
3089 __isl_take isl_space *space);
3090 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3091 __isl_take isl_set *set, __isl_take isl_aff *aff);
3092 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3093 __isl_take isl_aff *aff);
3095 A piecewise quasi affine expression that is equal to 1 on a set
3096 and 0 outside the set can be created using the following function.
3098 #include <isl/aff.h>
3099 __isl_give isl_pw_aff *isl_set_indicator_function(
3100 __isl_take isl_set *set);
3102 Quasi affine expressions can be copied and freed using
3104 #include <isl/aff.h>
3105 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3106 void *isl_aff_free(__isl_take isl_aff *aff);
3108 __isl_give isl_pw_aff *isl_pw_aff_copy(
3109 __isl_keep isl_pw_aff *pwaff);
3110 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3112 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3113 using the following function. The constraint is required to have
3114 a non-zero coefficient for the specified dimension.
3116 #include <isl/constraint.h>
3117 __isl_give isl_aff *isl_constraint_get_bound(
3118 __isl_keep isl_constraint *constraint,
3119 enum isl_dim_type type, int pos);
3121 The entire affine expression of the constraint can also be extracted
3122 using the following function.
3124 #include <isl/constraint.h>
3125 __isl_give isl_aff *isl_constraint_get_aff(
3126 __isl_keep isl_constraint *constraint);
3128 Conversely, an equality constraint equating
3129 the affine expression to zero or an inequality constraint enforcing
3130 the affine expression to be non-negative, can be constructed using
3132 __isl_give isl_constraint *isl_equality_from_aff(
3133 __isl_take isl_aff *aff);
3134 __isl_give isl_constraint *isl_inequality_from_aff(
3135 __isl_take isl_aff *aff);
3137 The expression can be inspected using
3139 #include <isl/aff.h>
3140 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3141 int isl_aff_dim(__isl_keep isl_aff *aff,
3142 enum isl_dim_type type);
3143 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3144 __isl_keep isl_aff *aff);
3145 __isl_give isl_local_space *isl_aff_get_local_space(
3146 __isl_keep isl_aff *aff);
3147 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3148 enum isl_dim_type type, unsigned pos);
3149 const char *isl_pw_aff_get_dim_name(
3150 __isl_keep isl_pw_aff *pa,
3151 enum isl_dim_type type, unsigned pos);
3152 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3153 enum isl_dim_type type, unsigned pos);
3154 __isl_give isl_id *isl_pw_aff_get_dim_id(
3155 __isl_keep isl_pw_aff *pa,
3156 enum isl_dim_type type, unsigned pos);
3157 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3158 __isl_keep isl_pw_aff *pa,
3159 enum isl_dim_type type);
3160 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3162 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3163 enum isl_dim_type type, int pos, isl_int *v);
3164 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3166 __isl_give isl_aff *isl_aff_get_div(
3167 __isl_keep isl_aff *aff, int pos);
3169 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3170 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3171 int (*fn)(__isl_take isl_set *set,
3172 __isl_take isl_aff *aff,
3173 void *user), void *user);
3175 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3176 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3178 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3179 enum isl_dim_type type, unsigned first, unsigned n);
3180 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3181 enum isl_dim_type type, unsigned first, unsigned n);
3183 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3184 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3185 enum isl_dim_type type);
3186 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3188 It can be modified using
3190 #include <isl/aff.h>
3191 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3192 __isl_take isl_pw_aff *pwaff,
3193 enum isl_dim_type type, __isl_take isl_id *id);
3194 __isl_give isl_aff *isl_aff_set_dim_name(
3195 __isl_take isl_aff *aff, enum isl_dim_type type,
3196 unsigned pos, const char *s);
3197 __isl_give isl_aff *isl_aff_set_dim_id(
3198 __isl_take isl_aff *aff, enum isl_dim_type type,
3199 unsigned pos, __isl_take isl_id *id);
3200 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3201 __isl_take isl_pw_aff *pma,
3202 enum isl_dim_type type, unsigned pos,
3203 __isl_take isl_id *id);
3204 __isl_give isl_aff *isl_aff_set_constant(
3205 __isl_take isl_aff *aff, isl_int v);
3206 __isl_give isl_aff *isl_aff_set_constant_si(
3207 __isl_take isl_aff *aff, int v);
3208 __isl_give isl_aff *isl_aff_set_coefficient(
3209 __isl_take isl_aff *aff,
3210 enum isl_dim_type type, int pos, isl_int v);
3211 __isl_give isl_aff *isl_aff_set_coefficient_si(
3212 __isl_take isl_aff *aff,
3213 enum isl_dim_type type, int pos, int v);
3214 __isl_give isl_aff *isl_aff_set_denominator(
3215 __isl_take isl_aff *aff, isl_int v);
3217 __isl_give isl_aff *isl_aff_add_constant(
3218 __isl_take isl_aff *aff, isl_int v);
3219 __isl_give isl_aff *isl_aff_add_constant_si(
3220 __isl_take isl_aff *aff, int v);
3221 __isl_give isl_aff *isl_aff_add_constant_num(
3222 __isl_take isl_aff *aff, isl_int v);
3223 __isl_give isl_aff *isl_aff_add_constant_num_si(
3224 __isl_take isl_aff *aff, int v);
3225 __isl_give isl_aff *isl_aff_add_coefficient(
3226 __isl_take isl_aff *aff,
3227 enum isl_dim_type type, int pos, isl_int v);
3228 __isl_give isl_aff *isl_aff_add_coefficient_si(
3229 __isl_take isl_aff *aff,
3230 enum isl_dim_type type, int pos, int v);
3232 __isl_give isl_aff *isl_aff_insert_dims(
3233 __isl_take isl_aff *aff,
3234 enum isl_dim_type type, unsigned first, unsigned n);
3235 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3236 __isl_take isl_pw_aff *pwaff,
3237 enum isl_dim_type type, unsigned first, unsigned n);
3238 __isl_give isl_aff *isl_aff_add_dims(
3239 __isl_take isl_aff *aff,
3240 enum isl_dim_type type, unsigned n);
3241 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3242 __isl_take isl_pw_aff *pwaff,
3243 enum isl_dim_type type, unsigned n);
3244 __isl_give isl_aff *isl_aff_drop_dims(
3245 __isl_take isl_aff *aff,
3246 enum isl_dim_type type, unsigned first, unsigned n);
3247 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3248 __isl_take isl_pw_aff *pwaff,
3249 enum isl_dim_type type, unsigned first, unsigned n);
3251 Note that the C<set_constant> and C<set_coefficient> functions
3252 set the I<numerator> of the constant or coefficient, while
3253 C<add_constant> and C<add_coefficient> add an integer value to
3254 the possibly rational constant or coefficient.
3255 The C<add_constant_num> functions add an integer value to
3258 To check whether an affine expressions is obviously zero
3259 or obviously equal to some other affine expression, use
3261 #include <isl/aff.h>
3262 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3263 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3264 __isl_keep isl_aff *aff2);
3265 int isl_pw_aff_plain_is_equal(
3266 __isl_keep isl_pw_aff *pwaff1,
3267 __isl_keep isl_pw_aff *pwaff2);
3271 #include <isl/aff.h>
3272 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3273 __isl_take isl_aff *aff2);
3274 __isl_give isl_pw_aff *isl_pw_aff_add(
3275 __isl_take isl_pw_aff *pwaff1,
3276 __isl_take isl_pw_aff *pwaff2);
3277 __isl_give isl_pw_aff *isl_pw_aff_min(
3278 __isl_take isl_pw_aff *pwaff1,
3279 __isl_take isl_pw_aff *pwaff2);
3280 __isl_give isl_pw_aff *isl_pw_aff_max(
3281 __isl_take isl_pw_aff *pwaff1,
3282 __isl_take isl_pw_aff *pwaff2);
3283 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3284 __isl_take isl_aff *aff2);
3285 __isl_give isl_pw_aff *isl_pw_aff_sub(
3286 __isl_take isl_pw_aff *pwaff1,
3287 __isl_take isl_pw_aff *pwaff2);
3288 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3289 __isl_give isl_pw_aff *isl_pw_aff_neg(
3290 __isl_take isl_pw_aff *pwaff);
3291 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3292 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3293 __isl_take isl_pw_aff *pwaff);
3294 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3295 __isl_give isl_pw_aff *isl_pw_aff_floor(
3296 __isl_take isl_pw_aff *pwaff);
3297 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3299 __isl_give isl_pw_aff *isl_pw_aff_mod(
3300 __isl_take isl_pw_aff *pwaff, isl_int mod);
3301 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3303 __isl_give isl_pw_aff *isl_pw_aff_scale(
3304 __isl_take isl_pw_aff *pwaff, isl_int f);
3305 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3307 __isl_give isl_aff *isl_aff_scale_down_ui(
3308 __isl_take isl_aff *aff, unsigned f);
3309 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3310 __isl_take isl_pw_aff *pwaff, isl_int f);
3312 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3313 __isl_take isl_pw_aff_list *list);
3314 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3315 __isl_take isl_pw_aff_list *list);
3317 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3318 __isl_take isl_pw_aff *pwqp);
3320 __isl_give isl_aff *isl_aff_align_params(
3321 __isl_take isl_aff *aff,
3322 __isl_take isl_space *model);
3323 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3324 __isl_take isl_pw_aff *pwaff,
3325 __isl_take isl_space *model);
3327 __isl_give isl_aff *isl_aff_project_domain_on_params(
3328 __isl_take isl_aff *aff);
3330 __isl_give isl_aff *isl_aff_gist_params(
3331 __isl_take isl_aff *aff,
3332 __isl_take isl_set *context);
3333 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3334 __isl_take isl_set *context);
3335 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3336 __isl_take isl_pw_aff *pwaff,
3337 __isl_take isl_set *context);
3338 __isl_give isl_pw_aff *isl_pw_aff_gist(
3339 __isl_take isl_pw_aff *pwaff,
3340 __isl_take isl_set *context);
3342 __isl_give isl_set *isl_pw_aff_domain(
3343 __isl_take isl_pw_aff *pwaff);
3344 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3345 __isl_take isl_pw_aff *pa,
3346 __isl_take isl_set *set);
3347 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3348 __isl_take isl_pw_aff *pa,
3349 __isl_take isl_set *set);
3351 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3352 __isl_take isl_aff *aff2);
3353 __isl_give isl_pw_aff *isl_pw_aff_mul(
3354 __isl_take isl_pw_aff *pwaff1,
3355 __isl_take isl_pw_aff *pwaff2);
3357 When multiplying two affine expressions, at least one of the two needs
3360 #include <isl/aff.h>
3361 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3362 __isl_take isl_aff *aff);
3363 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3364 __isl_take isl_aff *aff);
3365 __isl_give isl_basic_set *isl_aff_le_basic_set(
3366 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3367 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3368 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3369 __isl_give isl_set *isl_pw_aff_eq_set(
3370 __isl_take isl_pw_aff *pwaff1,
3371 __isl_take isl_pw_aff *pwaff2);
3372 __isl_give isl_set *isl_pw_aff_ne_set(
3373 __isl_take isl_pw_aff *pwaff1,
3374 __isl_take isl_pw_aff *pwaff2);
3375 __isl_give isl_set *isl_pw_aff_le_set(
3376 __isl_take isl_pw_aff *pwaff1,
3377 __isl_take isl_pw_aff *pwaff2);
3378 __isl_give isl_set *isl_pw_aff_lt_set(
3379 __isl_take isl_pw_aff *pwaff1,
3380 __isl_take isl_pw_aff *pwaff2);
3381 __isl_give isl_set *isl_pw_aff_ge_set(
3382 __isl_take isl_pw_aff *pwaff1,
3383 __isl_take isl_pw_aff *pwaff2);
3384 __isl_give isl_set *isl_pw_aff_gt_set(
3385 __isl_take isl_pw_aff *pwaff1,
3386 __isl_take isl_pw_aff *pwaff2);
3388 __isl_give isl_set *isl_pw_aff_list_eq_set(
3389 __isl_take isl_pw_aff_list *list1,
3390 __isl_take isl_pw_aff_list *list2);
3391 __isl_give isl_set *isl_pw_aff_list_ne_set(
3392 __isl_take isl_pw_aff_list *list1,
3393 __isl_take isl_pw_aff_list *list2);
3394 __isl_give isl_set *isl_pw_aff_list_le_set(
3395 __isl_take isl_pw_aff_list *list1,
3396 __isl_take isl_pw_aff_list *list2);
3397 __isl_give isl_set *isl_pw_aff_list_lt_set(
3398 __isl_take isl_pw_aff_list *list1,
3399 __isl_take isl_pw_aff_list *list2);
3400 __isl_give isl_set *isl_pw_aff_list_ge_set(
3401 __isl_take isl_pw_aff_list *list1,
3402 __isl_take isl_pw_aff_list *list2);
3403 __isl_give isl_set *isl_pw_aff_list_gt_set(
3404 __isl_take isl_pw_aff_list *list1,
3405 __isl_take isl_pw_aff_list *list2);
3407 The function C<isl_aff_neg_basic_set> returns a basic set
3408 containing those elements in the domain space
3409 of C<aff> where C<aff> is negative.
3410 The function C<isl_aff_ge_basic_set> returns a basic set
3411 containing those elements in the shared space
3412 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3413 The function C<isl_pw_aff_ge_set> returns a set
3414 containing those elements in the shared domain
3415 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3416 The functions operating on C<isl_pw_aff_list> apply the corresponding
3417 C<isl_pw_aff> function to each pair of elements in the two lists.
3419 #include <isl/aff.h>
3420 __isl_give isl_set *isl_pw_aff_nonneg_set(
3421 __isl_take isl_pw_aff *pwaff);
3422 __isl_give isl_set *isl_pw_aff_zero_set(
3423 __isl_take isl_pw_aff *pwaff);
3424 __isl_give isl_set *isl_pw_aff_non_zero_set(
3425 __isl_take isl_pw_aff *pwaff);
3427 The function C<isl_pw_aff_nonneg_set> returns a set
3428 containing those elements in the domain
3429 of C<pwaff> where C<pwaff> is non-negative.
3431 #include <isl/aff.h>
3432 __isl_give isl_pw_aff *isl_pw_aff_cond(
3433 __isl_take isl_pw_aff *cond,
3434 __isl_take isl_pw_aff *pwaff_true,
3435 __isl_take isl_pw_aff *pwaff_false);
3437 The function C<isl_pw_aff_cond> performs a conditional operator
3438 and returns an expression that is equal to C<pwaff_true>
3439 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3440 where C<cond> is zero.
3442 #include <isl/aff.h>
3443 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3444 __isl_take isl_pw_aff *pwaff1,
3445 __isl_take isl_pw_aff *pwaff2);
3446 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3447 __isl_take isl_pw_aff *pwaff1,
3448 __isl_take isl_pw_aff *pwaff2);
3449 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3450 __isl_take isl_pw_aff *pwaff1,
3451 __isl_take isl_pw_aff *pwaff2);
3453 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3454 expression with a domain that is the union of those of C<pwaff1> and
3455 C<pwaff2> and such that on each cell, the quasi-affine expression is
3456 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3457 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3458 associated expression is the defined one.
3460 An expression can be read from input using
3462 #include <isl/aff.h>
3463 __isl_give isl_aff *isl_aff_read_from_str(
3464 isl_ctx *ctx, const char *str);
3465 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3466 isl_ctx *ctx, const char *str);
3468 An expression can be printed using
3470 #include <isl/aff.h>
3471 __isl_give isl_printer *isl_printer_print_aff(
3472 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3474 __isl_give isl_printer *isl_printer_print_pw_aff(
3475 __isl_take isl_printer *p,
3476 __isl_keep isl_pw_aff *pwaff);
3478 =head2 Piecewise Multiple Quasi Affine Expressions
3480 An C<isl_multi_aff> object represents a sequence of
3481 zero or more affine expressions, all defined on the same domain space.
3483 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3486 #include <isl/aff.h>
3487 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3488 __isl_take isl_space *space,
3489 __isl_take isl_aff_list *list);
3491 An empty piecewise multiple quasi affine expression (one with no cells),
3492 the zero piecewise multiple quasi affine expression (with value zero
3493 for each output dimension),
3494 a piecewise multiple quasi affine expression with a single cell (with
3495 either a universe or a specified domain) or
3496 a zero-dimensional piecewise multiple quasi affine expression
3498 can be created using the following functions.
3500 #include <isl/aff.h>
3501 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3502 __isl_take isl_space *space);
3503 __isl_give isl_multi_aff *isl_multi_aff_zero(
3504 __isl_take isl_space *space);
3505 __isl_give isl_multi_aff *isl_multi_aff_identity(
3506 __isl_take isl_space *space);
3507 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3508 __isl_take isl_space *space);
3509 __isl_give isl_pw_multi_aff *
3510 isl_pw_multi_aff_from_multi_aff(
3511 __isl_take isl_multi_aff *ma);
3512 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3513 __isl_take isl_set *set,
3514 __isl_take isl_multi_aff *maff);
3515 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3516 __isl_take isl_set *set);
3518 __isl_give isl_union_pw_multi_aff *
3519 isl_union_pw_multi_aff_empty(
3520 __isl_take isl_space *space);
3521 __isl_give isl_union_pw_multi_aff *
3522 isl_union_pw_multi_aff_add_pw_multi_aff(
3523 __isl_take isl_union_pw_multi_aff *upma,
3524 __isl_take isl_pw_multi_aff *pma);
3525 __isl_give isl_union_pw_multi_aff *
3526 isl_union_pw_multi_aff_from_domain(
3527 __isl_take isl_union_set *uset);
3529 A piecewise multiple quasi affine expression can also be initialized
3530 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3531 and the C<isl_map> is single-valued.
3533 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3534 __isl_take isl_set *set);
3535 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3536 __isl_take isl_map *map);
3538 Multiple quasi affine expressions can be copied and freed using
3540 #include <isl/aff.h>
3541 __isl_give isl_multi_aff *isl_multi_aff_copy(
3542 __isl_keep isl_multi_aff *maff);
3543 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3545 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3546 __isl_keep isl_pw_multi_aff *pma);
3547 void *isl_pw_multi_aff_free(
3548 __isl_take isl_pw_multi_aff *pma);
3550 __isl_give isl_union_pw_multi_aff *
3551 isl_union_pw_multi_aff_copy(
3552 __isl_keep isl_union_pw_multi_aff *upma);
3553 void *isl_union_pw_multi_aff_free(
3554 __isl_take isl_union_pw_multi_aff *upma);
3556 The expression can be inspected using
3558 #include <isl/aff.h>
3559 isl_ctx *isl_multi_aff_get_ctx(
3560 __isl_keep isl_multi_aff *maff);
3561 isl_ctx *isl_pw_multi_aff_get_ctx(
3562 __isl_keep isl_pw_multi_aff *pma);
3563 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3564 __isl_keep isl_union_pw_multi_aff *upma);
3565 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3566 enum isl_dim_type type);
3567 unsigned isl_pw_multi_aff_dim(
3568 __isl_keep isl_pw_multi_aff *pma,
3569 enum isl_dim_type type);
3570 __isl_give isl_aff *isl_multi_aff_get_aff(
3571 __isl_keep isl_multi_aff *multi, int pos);
3572 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3573 __isl_keep isl_pw_multi_aff *pma, int pos);
3574 const char *isl_pw_multi_aff_get_dim_name(
3575 __isl_keep isl_pw_multi_aff *pma,
3576 enum isl_dim_type type, unsigned pos);
3577 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3578 __isl_keep isl_pw_multi_aff *pma,
3579 enum isl_dim_type type, unsigned pos);
3580 const char *isl_multi_aff_get_tuple_name(
3581 __isl_keep isl_multi_aff *multi,
3582 enum isl_dim_type type);
3583 int isl_pw_multi_aff_has_tuple_name(
3584 __isl_keep isl_pw_multi_aff *pma,
3585 enum isl_dim_type type);
3586 const char *isl_pw_multi_aff_get_tuple_name(
3587 __isl_keep isl_pw_multi_aff *pma,
3588 enum isl_dim_type type);
3589 int isl_pw_multi_aff_has_tuple_id(
3590 __isl_keep isl_pw_multi_aff *pma,
3591 enum isl_dim_type type);
3592 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3593 __isl_keep isl_pw_multi_aff *pma,
3594 enum isl_dim_type type);
3596 int isl_pw_multi_aff_foreach_piece(
3597 __isl_keep isl_pw_multi_aff *pma,
3598 int (*fn)(__isl_take isl_set *set,
3599 __isl_take isl_multi_aff *maff,
3600 void *user), void *user);
3602 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3603 __isl_keep isl_union_pw_multi_aff *upma,
3604 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3605 void *user), void *user);
3607 It can be modified using
3609 #include <isl/aff.h>
3610 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3611 __isl_take isl_multi_aff *multi, int pos,
3612 __isl_take isl_aff *aff);
3613 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3614 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3615 __isl_take isl_pw_aff *pa);
3616 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3617 __isl_take isl_multi_aff *maff,
3618 enum isl_dim_type type, unsigned pos, const char *s);
3619 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3620 __isl_take isl_multi_aff *maff,
3621 enum isl_dim_type type, __isl_take isl_id *id);
3622 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3623 __isl_take isl_pw_multi_aff *pma,
3624 enum isl_dim_type type, __isl_take isl_id *id);
3626 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3627 __isl_take isl_multi_aff *maff,
3628 enum isl_dim_type type, unsigned first, unsigned n);
3629 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
3630 __isl_take isl_pw_multi_aff *pma,
3631 enum isl_dim_type type, unsigned first, unsigned n);
3633 To check whether two multiple affine expressions are
3634 obviously equal to each other, use
3636 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3637 __isl_keep isl_multi_aff *maff2);
3638 int isl_pw_multi_aff_plain_is_equal(
3639 __isl_keep isl_pw_multi_aff *pma1,
3640 __isl_keep isl_pw_multi_aff *pma2);
3644 #include <isl/aff.h>
3645 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3646 __isl_take isl_pw_multi_aff *pma1,
3647 __isl_take isl_pw_multi_aff *pma2);
3648 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3649 __isl_take isl_pw_multi_aff *pma1,
3650 __isl_take isl_pw_multi_aff *pma2);
3651 __isl_give isl_multi_aff *isl_multi_aff_add(
3652 __isl_take isl_multi_aff *maff1,
3653 __isl_take isl_multi_aff *maff2);
3654 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3655 __isl_take isl_pw_multi_aff *pma1,
3656 __isl_take isl_pw_multi_aff *pma2);
3657 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3658 __isl_take isl_union_pw_multi_aff *upma1,
3659 __isl_take isl_union_pw_multi_aff *upma2);
3660 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3661 __isl_take isl_pw_multi_aff *pma1,
3662 __isl_take isl_pw_multi_aff *pma2);
3663 __isl_give isl_multi_aff *isl_multi_aff_scale(
3664 __isl_take isl_multi_aff *maff,
3666 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3667 __isl_take isl_pw_multi_aff *pma,
3668 __isl_take isl_set *set);
3669 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3670 __isl_take isl_pw_multi_aff *pma,
3671 __isl_take isl_set *set);
3672 __isl_give isl_multi_aff *isl_multi_aff_lift(
3673 __isl_take isl_multi_aff *maff,
3674 __isl_give isl_local_space **ls);
3675 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3676 __isl_take isl_pw_multi_aff *pma);
3677 __isl_give isl_multi_aff *isl_multi_aff_align_params(
3678 __isl_take isl_multi_aff *multi,
3679 __isl_take isl_space *model);
3680 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
3681 __isl_take isl_pw_multi_aff *pma,
3682 __isl_take isl_space *model);
3683 __isl_give isl_pw_multi_aff *
3684 isl_pw_multi_aff_project_domain_on_params(
3685 __isl_take isl_pw_multi_aff *pma);
3686 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3687 __isl_take isl_multi_aff *maff,
3688 __isl_take isl_set *context);
3689 __isl_give isl_multi_aff *isl_multi_aff_gist(
3690 __isl_take isl_multi_aff *maff,
3691 __isl_take isl_set *context);
3692 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3693 __isl_take isl_pw_multi_aff *pma,
3694 __isl_take isl_set *set);
3695 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3696 __isl_take isl_pw_multi_aff *pma,
3697 __isl_take isl_set *set);
3698 __isl_give isl_set *isl_pw_multi_aff_domain(
3699 __isl_take isl_pw_multi_aff *pma);
3700 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3701 __isl_take isl_union_pw_multi_aff *upma);
3702 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3703 __isl_take isl_multi_aff *ma1,
3704 __isl_take isl_multi_aff *ma2);
3705 __isl_give isl_multi_aff *isl_multi_aff_product(
3706 __isl_take isl_multi_aff *ma1,
3707 __isl_take isl_multi_aff *ma2);
3708 __isl_give isl_pw_multi_aff *
3709 isl_pw_multi_aff_flat_range_product(
3710 __isl_take isl_pw_multi_aff *pma1,
3711 __isl_take isl_pw_multi_aff *pma2);
3712 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3713 __isl_take isl_pw_multi_aff *pma1,
3714 __isl_take isl_pw_multi_aff *pma2);
3715 __isl_give isl_union_pw_multi_aff *
3716 isl_union_pw_multi_aff_flat_range_product(
3717 __isl_take isl_union_pw_multi_aff *upma1,
3718 __isl_take isl_union_pw_multi_aff *upma2);
3720 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3721 then it is assigned the local space that lies at the basis of
3722 the lifting applied.
3724 __isl_give isl_set *isl_multi_aff_lex_le_set(
3725 __isl_take isl_multi_aff *ma1,
3726 __isl_take isl_multi_aff *ma2);
3727 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3728 __isl_take isl_multi_aff *ma1,
3729 __isl_take isl_multi_aff *ma2);
3731 The function C<isl_multi_aff_lex_le_set> returns a set
3732 containing those elements in the shared domain space
3733 where C<ma1> is lexicographically smaller than or
3736 An expression can be read from input using
3738 #include <isl/aff.h>
3739 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3740 isl_ctx *ctx, const char *str);
3741 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3742 isl_ctx *ctx, const char *str);
3744 An expression can be printed using
3746 #include <isl/aff.h>
3747 __isl_give isl_printer *isl_printer_print_multi_aff(
3748 __isl_take isl_printer *p,
3749 __isl_keep isl_multi_aff *maff);
3750 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3751 __isl_take isl_printer *p,
3752 __isl_keep isl_pw_multi_aff *pma);
3753 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3754 __isl_take isl_printer *p,
3755 __isl_keep isl_union_pw_multi_aff *upma);
3759 Points are elements of a set. They can be used to construct
3760 simple sets (boxes) or they can be used to represent the
3761 individual elements of a set.
3762 The zero point (the origin) can be created using
3764 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3766 The coordinates of a point can be inspected, set and changed
3769 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3770 enum isl_dim_type type, int pos, isl_int *v);
3771 __isl_give isl_point *isl_point_set_coordinate(
3772 __isl_take isl_point *pnt,
3773 enum isl_dim_type type, int pos, isl_int v);
3775 __isl_give isl_point *isl_point_add_ui(
3776 __isl_take isl_point *pnt,
3777 enum isl_dim_type type, int pos, unsigned val);
3778 __isl_give isl_point *isl_point_sub_ui(
3779 __isl_take isl_point *pnt,
3780 enum isl_dim_type type, int pos, unsigned val);
3782 Other properties can be obtained using
3784 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3786 Points can be copied or freed using
3788 __isl_give isl_point *isl_point_copy(
3789 __isl_keep isl_point *pnt);
3790 void isl_point_free(__isl_take isl_point *pnt);
3792 A singleton set can be created from a point using
3794 __isl_give isl_basic_set *isl_basic_set_from_point(
3795 __isl_take isl_point *pnt);
3796 __isl_give isl_set *isl_set_from_point(
3797 __isl_take isl_point *pnt);
3799 and a box can be created from two opposite extremal points using
3801 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3802 __isl_take isl_point *pnt1,
3803 __isl_take isl_point *pnt2);
3804 __isl_give isl_set *isl_set_box_from_points(
3805 __isl_take isl_point *pnt1,
3806 __isl_take isl_point *pnt2);
3808 All elements of a B<bounded> (union) set can be enumerated using
3809 the following functions.
3811 int isl_set_foreach_point(__isl_keep isl_set *set,
3812 int (*fn)(__isl_take isl_point *pnt, void *user),
3814 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3815 int (*fn)(__isl_take isl_point *pnt, void *user),
3818 The function C<fn> is called for each integer point in
3819 C<set> with as second argument the last argument of
3820 the C<isl_set_foreach_point> call. The function C<fn>
3821 should return C<0> on success and C<-1> on failure.
3822 In the latter case, C<isl_set_foreach_point> will stop
3823 enumerating and return C<-1> as well.
3824 If the enumeration is performed successfully and to completion,
3825 then C<isl_set_foreach_point> returns C<0>.
3827 To obtain a single point of a (basic) set, use
3829 __isl_give isl_point *isl_basic_set_sample_point(
3830 __isl_take isl_basic_set *bset);
3831 __isl_give isl_point *isl_set_sample_point(
3832 __isl_take isl_set *set);
3834 If C<set> does not contain any (integer) points, then the
3835 resulting point will be ``void'', a property that can be
3838 int isl_point_is_void(__isl_keep isl_point *pnt);
3840 =head2 Piecewise Quasipolynomials
3842 A piecewise quasipolynomial is a particular kind of function that maps
3843 a parametric point to a rational value.
3844 More specifically, a quasipolynomial is a polynomial expression in greatest
3845 integer parts of affine expressions of parameters and variables.
3846 A piecewise quasipolynomial is a subdivision of a given parametric
3847 domain into disjoint cells with a quasipolynomial associated to
3848 each cell. The value of the piecewise quasipolynomial at a given
3849 point is the value of the quasipolynomial associated to the cell
3850 that contains the point. Outside of the union of cells,
3851 the value is assumed to be zero.
3852 For example, the piecewise quasipolynomial
3854 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3856 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3857 A given piecewise quasipolynomial has a fixed domain dimension.
3858 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3859 defined over different domains.
3860 Piecewise quasipolynomials are mainly used by the C<barvinok>
3861 library for representing the number of elements in a parametric set or map.
3862 For example, the piecewise quasipolynomial above represents
3863 the number of points in the map
3865 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3867 =head3 Input and Output
3869 Piecewise quasipolynomials can be read from input using
3871 __isl_give isl_union_pw_qpolynomial *
3872 isl_union_pw_qpolynomial_read_from_str(
3873 isl_ctx *ctx, const char *str);
3875 Quasipolynomials and piecewise quasipolynomials can be printed
3876 using the following functions.
3878 __isl_give isl_printer *isl_printer_print_qpolynomial(
3879 __isl_take isl_printer *p,
3880 __isl_keep isl_qpolynomial *qp);
3882 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3883 __isl_take isl_printer *p,
3884 __isl_keep isl_pw_qpolynomial *pwqp);
3886 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3887 __isl_take isl_printer *p,
3888 __isl_keep isl_union_pw_qpolynomial *upwqp);
3890 The output format of the printer
3891 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3892 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3894 In case of printing in C<ISL_FORMAT_C>, the user may want
3895 to set the names of all dimensions
3897 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3898 __isl_take isl_qpolynomial *qp,
3899 enum isl_dim_type type, unsigned pos,
3901 __isl_give isl_pw_qpolynomial *
3902 isl_pw_qpolynomial_set_dim_name(
3903 __isl_take isl_pw_qpolynomial *pwqp,
3904 enum isl_dim_type type, unsigned pos,
3907 =head3 Creating New (Piecewise) Quasipolynomials
3909 Some simple quasipolynomials can be created using the following functions.
3910 More complicated quasipolynomials can be created by applying
3911 operations such as addition and multiplication
3912 on the resulting quasipolynomials
3914 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3915 __isl_take isl_space *domain);
3916 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3917 __isl_take isl_space *domain);
3918 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3919 __isl_take isl_space *domain);
3920 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3921 __isl_take isl_space *domain);
3922 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3923 __isl_take isl_space *domain);
3924 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3925 __isl_take isl_space *domain,
3926 const isl_int n, const isl_int d);
3927 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3928 __isl_take isl_space *domain,
3929 enum isl_dim_type type, unsigned pos);
3930 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3931 __isl_take isl_aff *aff);
3933 Note that the space in which a quasipolynomial lives is a map space
3934 with a one-dimensional range. The C<domain> argument in some of
3935 the functions above corresponds to the domain of this map space.
3937 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3938 with a single cell can be created using the following functions.
3939 Multiple of these single cell piecewise quasipolynomials can
3940 be combined to create more complicated piecewise quasipolynomials.
3942 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3943 __isl_take isl_space *space);
3944 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3945 __isl_take isl_set *set,
3946 __isl_take isl_qpolynomial *qp);
3947 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3948 __isl_take isl_qpolynomial *qp);
3949 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3950 __isl_take isl_pw_aff *pwaff);
3952 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3953 __isl_take isl_space *space);
3954 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3955 __isl_take isl_pw_qpolynomial *pwqp);
3956 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3957 __isl_take isl_union_pw_qpolynomial *upwqp,
3958 __isl_take isl_pw_qpolynomial *pwqp);
3960 Quasipolynomials can be copied and freed again using the following
3963 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3964 __isl_keep isl_qpolynomial *qp);
3965 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3967 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3968 __isl_keep isl_pw_qpolynomial *pwqp);
3969 void *isl_pw_qpolynomial_free(
3970 __isl_take isl_pw_qpolynomial *pwqp);
3972 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3973 __isl_keep isl_union_pw_qpolynomial *upwqp);
3974 void *isl_union_pw_qpolynomial_free(
3975 __isl_take isl_union_pw_qpolynomial *upwqp);
3977 =head3 Inspecting (Piecewise) Quasipolynomials
3979 To iterate over all piecewise quasipolynomials in a union
3980 piecewise quasipolynomial, use the following function
3982 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3983 __isl_keep isl_union_pw_qpolynomial *upwqp,
3984 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3987 To extract the piecewise quasipolynomial in a given space from a union, use
3989 __isl_give isl_pw_qpolynomial *
3990 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3991 __isl_keep isl_union_pw_qpolynomial *upwqp,
3992 __isl_take isl_space *space);
3994 To iterate over the cells in a piecewise quasipolynomial,
3995 use either of the following two functions
3997 int isl_pw_qpolynomial_foreach_piece(
3998 __isl_keep isl_pw_qpolynomial *pwqp,
3999 int (*fn)(__isl_take isl_set *set,
4000 __isl_take isl_qpolynomial *qp,
4001 void *user), void *user);
4002 int isl_pw_qpolynomial_foreach_lifted_piece(
4003 __isl_keep isl_pw_qpolynomial *pwqp,
4004 int (*fn)(__isl_take isl_set *set,
4005 __isl_take isl_qpolynomial *qp,
4006 void *user), void *user);
4008 As usual, the function C<fn> should return C<0> on success
4009 and C<-1> on failure. The difference between
4010 C<isl_pw_qpolynomial_foreach_piece> and
4011 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4012 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4013 compute unique representations for all existentially quantified
4014 variables and then turn these existentially quantified variables
4015 into extra set variables, adapting the associated quasipolynomial
4016 accordingly. This means that the C<set> passed to C<fn>
4017 will not have any existentially quantified variables, but that
4018 the dimensions of the sets may be different for different
4019 invocations of C<fn>.
4021 To iterate over all terms in a quasipolynomial,
4024 int isl_qpolynomial_foreach_term(
4025 __isl_keep isl_qpolynomial *qp,
4026 int (*fn)(__isl_take isl_term *term,
4027 void *user), void *user);
4029 The terms themselves can be inspected and freed using
4032 unsigned isl_term_dim(__isl_keep isl_term *term,
4033 enum isl_dim_type type);
4034 void isl_term_get_num(__isl_keep isl_term *term,
4036 void isl_term_get_den(__isl_keep isl_term *term,
4038 int isl_term_get_exp(__isl_keep isl_term *term,
4039 enum isl_dim_type type, unsigned pos);
4040 __isl_give isl_aff *isl_term_get_div(
4041 __isl_keep isl_term *term, unsigned pos);
4042 void isl_term_free(__isl_take isl_term *term);
4044 Each term is a product of parameters, set variables and
4045 integer divisions. The function C<isl_term_get_exp>
4046 returns the exponent of a given dimensions in the given term.
4047 The C<isl_int>s in the arguments of C<isl_term_get_num>
4048 and C<isl_term_get_den> need to have been initialized
4049 using C<isl_int_init> before calling these functions.
4051 =head3 Properties of (Piecewise) Quasipolynomials
4053 To check whether a quasipolynomial is actually a constant,
4054 use the following function.
4056 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4057 isl_int *n, isl_int *d);
4059 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4060 then the numerator and denominator of the constant
4061 are returned in C<*n> and C<*d>, respectively.
4063 To check whether two union piecewise quasipolynomials are
4064 obviously equal, use
4066 int isl_union_pw_qpolynomial_plain_is_equal(
4067 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4068 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4070 =head3 Operations on (Piecewise) Quasipolynomials
4072 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4073 __isl_take isl_qpolynomial *qp, isl_int v);
4074 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4075 __isl_take isl_qpolynomial *qp);
4076 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4077 __isl_take isl_qpolynomial *qp1,
4078 __isl_take isl_qpolynomial *qp2);
4079 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4080 __isl_take isl_qpolynomial *qp1,
4081 __isl_take isl_qpolynomial *qp2);
4082 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4083 __isl_take isl_qpolynomial *qp1,
4084 __isl_take isl_qpolynomial *qp2);
4085 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4086 __isl_take isl_qpolynomial *qp, unsigned exponent);
4088 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4089 __isl_take isl_pw_qpolynomial *pwqp1,
4090 __isl_take isl_pw_qpolynomial *pwqp2);
4091 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4092 __isl_take isl_pw_qpolynomial *pwqp1,
4093 __isl_take isl_pw_qpolynomial *pwqp2);
4094 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4095 __isl_take isl_pw_qpolynomial *pwqp1,
4096 __isl_take isl_pw_qpolynomial *pwqp2);
4097 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4098 __isl_take isl_pw_qpolynomial *pwqp);
4099 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4100 __isl_take isl_pw_qpolynomial *pwqp1,
4101 __isl_take isl_pw_qpolynomial *pwqp2);
4102 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4103 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4105 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4106 __isl_take isl_union_pw_qpolynomial *upwqp1,
4107 __isl_take isl_union_pw_qpolynomial *upwqp2);
4108 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4109 __isl_take isl_union_pw_qpolynomial *upwqp1,
4110 __isl_take isl_union_pw_qpolynomial *upwqp2);
4111 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4112 __isl_take isl_union_pw_qpolynomial *upwqp1,
4113 __isl_take isl_union_pw_qpolynomial *upwqp2);
4115 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4116 __isl_take isl_pw_qpolynomial *pwqp,
4117 __isl_take isl_point *pnt);
4119 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4120 __isl_take isl_union_pw_qpolynomial *upwqp,
4121 __isl_take isl_point *pnt);
4123 __isl_give isl_set *isl_pw_qpolynomial_domain(
4124 __isl_take isl_pw_qpolynomial *pwqp);
4125 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4126 __isl_take isl_pw_qpolynomial *pwpq,
4127 __isl_take isl_set *set);
4128 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4129 __isl_take isl_pw_qpolynomial *pwpq,
4130 __isl_take isl_set *set);
4132 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4133 __isl_take isl_union_pw_qpolynomial *upwqp);
4134 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4135 __isl_take isl_union_pw_qpolynomial *upwpq,
4136 __isl_take isl_union_set *uset);
4137 __isl_give isl_union_pw_qpolynomial *
4138 isl_union_pw_qpolynomial_intersect_params(
4139 __isl_take isl_union_pw_qpolynomial *upwpq,
4140 __isl_take isl_set *set);
4142 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4143 __isl_take isl_qpolynomial *qp,
4144 __isl_take isl_space *model);
4146 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4147 __isl_take isl_qpolynomial *qp);
4148 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4149 __isl_take isl_pw_qpolynomial *pwqp);
4151 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4152 __isl_take isl_union_pw_qpolynomial *upwqp);
4154 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4155 __isl_take isl_qpolynomial *qp,
4156 __isl_take isl_set *context);
4157 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4158 __isl_take isl_qpolynomial *qp,
4159 __isl_take isl_set *context);
4161 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4162 __isl_take isl_pw_qpolynomial *pwqp,
4163 __isl_take isl_set *context);
4164 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4165 __isl_take isl_pw_qpolynomial *pwqp,
4166 __isl_take isl_set *context);
4168 __isl_give isl_union_pw_qpolynomial *
4169 isl_union_pw_qpolynomial_gist_params(
4170 __isl_take isl_union_pw_qpolynomial *upwqp,
4171 __isl_take isl_set *context);
4172 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4173 __isl_take isl_union_pw_qpolynomial *upwqp,
4174 __isl_take isl_union_set *context);
4176 The gist operation applies the gist operation to each of
4177 the cells in the domain of the input piecewise quasipolynomial.
4178 The context is also exploited
4179 to simplify the quasipolynomials associated to each cell.
4181 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4182 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4183 __isl_give isl_union_pw_qpolynomial *
4184 isl_union_pw_qpolynomial_to_polynomial(
4185 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4187 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4188 the polynomial will be an overapproximation. If C<sign> is negative,
4189 it will be an underapproximation. If C<sign> is zero, the approximation
4190 will lie somewhere in between.
4192 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4194 A piecewise quasipolynomial reduction is a piecewise
4195 reduction (or fold) of quasipolynomials.
4196 In particular, the reduction can be maximum or a minimum.
4197 The objects are mainly used to represent the result of
4198 an upper or lower bound on a quasipolynomial over its domain,
4199 i.e., as the result of the following function.
4201 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4202 __isl_take isl_pw_qpolynomial *pwqp,
4203 enum isl_fold type, int *tight);
4205 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4206 __isl_take isl_union_pw_qpolynomial *upwqp,
4207 enum isl_fold type, int *tight);
4209 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4210 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4211 is the returned bound is known be tight, i.e., for each value
4212 of the parameters there is at least
4213 one element in the domain that reaches the bound.
4214 If the domain of C<pwqp> is not wrapping, then the bound is computed
4215 over all elements in that domain and the result has a purely parametric
4216 domain. If the domain of C<pwqp> is wrapping, then the bound is
4217 computed over the range of the wrapped relation. The domain of the
4218 wrapped relation becomes the domain of the result.
4220 A (piecewise) quasipolynomial reduction can be copied or freed using the
4221 following functions.
4223 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4224 __isl_keep isl_qpolynomial_fold *fold);
4225 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4226 __isl_keep isl_pw_qpolynomial_fold *pwf);
4227 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4228 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4229 void isl_qpolynomial_fold_free(
4230 __isl_take isl_qpolynomial_fold *fold);
4231 void *isl_pw_qpolynomial_fold_free(
4232 __isl_take isl_pw_qpolynomial_fold *pwf);
4233 void *isl_union_pw_qpolynomial_fold_free(
4234 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4236 =head3 Printing Piecewise Quasipolynomial Reductions
4238 Piecewise quasipolynomial reductions can be printed
4239 using the following function.
4241 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4242 __isl_take isl_printer *p,
4243 __isl_keep isl_pw_qpolynomial_fold *pwf);
4244 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4245 __isl_take isl_printer *p,
4246 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4248 For C<isl_printer_print_pw_qpolynomial_fold>,
4249 output format of the printer
4250 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4251 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4252 output format of the printer
4253 needs to be set to C<ISL_FORMAT_ISL>.
4254 In case of printing in C<ISL_FORMAT_C>, the user may want
4255 to set the names of all dimensions
4257 __isl_give isl_pw_qpolynomial_fold *
4258 isl_pw_qpolynomial_fold_set_dim_name(
4259 __isl_take isl_pw_qpolynomial_fold *pwf,
4260 enum isl_dim_type type, unsigned pos,
4263 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4265 To iterate over all piecewise quasipolynomial reductions in a union
4266 piecewise quasipolynomial reduction, use the following function
4268 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4269 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4270 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4271 void *user), void *user);
4273 To iterate over the cells in a piecewise quasipolynomial reduction,
4274 use either of the following two functions
4276 int isl_pw_qpolynomial_fold_foreach_piece(
4277 __isl_keep isl_pw_qpolynomial_fold *pwf,
4278 int (*fn)(__isl_take isl_set *set,
4279 __isl_take isl_qpolynomial_fold *fold,
4280 void *user), void *user);
4281 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4282 __isl_keep isl_pw_qpolynomial_fold *pwf,
4283 int (*fn)(__isl_take isl_set *set,
4284 __isl_take isl_qpolynomial_fold *fold,
4285 void *user), void *user);
4287 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4288 of the difference between these two functions.
4290 To iterate over all quasipolynomials in a reduction, use
4292 int isl_qpolynomial_fold_foreach_qpolynomial(
4293 __isl_keep isl_qpolynomial_fold *fold,
4294 int (*fn)(__isl_take isl_qpolynomial *qp,
4295 void *user), void *user);
4297 =head3 Properties of Piecewise Quasipolynomial Reductions
4299 To check whether two union piecewise quasipolynomial reductions are
4300 obviously equal, use
4302 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4303 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4304 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4306 =head3 Operations on Piecewise Quasipolynomial Reductions
4308 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4309 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4311 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4312 __isl_take isl_pw_qpolynomial_fold *pwf1,
4313 __isl_take isl_pw_qpolynomial_fold *pwf2);
4315 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4316 __isl_take isl_pw_qpolynomial_fold *pwf1,
4317 __isl_take isl_pw_qpolynomial_fold *pwf2);
4319 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4320 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4321 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4323 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4324 __isl_take isl_pw_qpolynomial_fold *pwf,
4325 __isl_take isl_point *pnt);
4327 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4328 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4329 __isl_take isl_point *pnt);
4331 __isl_give isl_pw_qpolynomial_fold *
4332 isl_pw_qpolynomial_fold_intersect_params(
4333 __isl_take isl_pw_qpolynomial_fold *pwf,
4334 __isl_take isl_set *set);
4336 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4337 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4338 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4339 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4340 __isl_take isl_union_set *uset);
4341 __isl_give isl_union_pw_qpolynomial_fold *
4342 isl_union_pw_qpolynomial_fold_intersect_params(
4343 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4344 __isl_take isl_set *set);
4346 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4347 __isl_take isl_pw_qpolynomial_fold *pwf);
4349 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4350 __isl_take isl_pw_qpolynomial_fold *pwf);
4352 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4353 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4355 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4356 __isl_take isl_qpolynomial_fold *fold,
4357 __isl_take isl_set *context);
4358 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4359 __isl_take isl_qpolynomial_fold *fold,
4360 __isl_take isl_set *context);
4362 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4363 __isl_take isl_pw_qpolynomial_fold *pwf,
4364 __isl_take isl_set *context);
4365 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4366 __isl_take isl_pw_qpolynomial_fold *pwf,
4367 __isl_take isl_set *context);
4369 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4370 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4371 __isl_take isl_union_set *context);
4372 __isl_give isl_union_pw_qpolynomial_fold *
4373 isl_union_pw_qpolynomial_fold_gist_params(
4374 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4375 __isl_take isl_set *context);
4377 The gist operation applies the gist operation to each of
4378 the cells in the domain of the input piecewise quasipolynomial reduction.
4379 In future, the operation will also exploit the context
4380 to simplify the quasipolynomial reductions associated to each cell.
4382 __isl_give isl_pw_qpolynomial_fold *
4383 isl_set_apply_pw_qpolynomial_fold(
4384 __isl_take isl_set *set,
4385 __isl_take isl_pw_qpolynomial_fold *pwf,
4387 __isl_give isl_pw_qpolynomial_fold *
4388 isl_map_apply_pw_qpolynomial_fold(
4389 __isl_take isl_map *map,
4390 __isl_take isl_pw_qpolynomial_fold *pwf,
4392 __isl_give isl_union_pw_qpolynomial_fold *
4393 isl_union_set_apply_union_pw_qpolynomial_fold(
4394 __isl_take isl_union_set *uset,
4395 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4397 __isl_give isl_union_pw_qpolynomial_fold *
4398 isl_union_map_apply_union_pw_qpolynomial_fold(
4399 __isl_take isl_union_map *umap,
4400 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4403 The functions taking a map
4404 compose the given map with the given piecewise quasipolynomial reduction.
4405 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4406 over all elements in the intersection of the range of the map
4407 and the domain of the piecewise quasipolynomial reduction
4408 as a function of an element in the domain of the map.
4409 The functions taking a set compute a bound over all elements in the
4410 intersection of the set and the domain of the
4411 piecewise quasipolynomial reduction.
4413 =head2 Dependence Analysis
4415 C<isl> contains specialized functionality for performing
4416 array dataflow analysis. That is, given a I<sink> access relation
4417 and a collection of possible I<source> access relations,
4418 C<isl> can compute relations that describe
4419 for each iteration of the sink access, which iteration
4420 of which of the source access relations was the last
4421 to access the same data element before the given iteration
4423 The resulting dependence relations map source iterations
4424 to the corresponding sink iterations.
4425 To compute standard flow dependences, the sink should be
4426 a read, while the sources should be writes.
4427 If any of the source accesses are marked as being I<may>
4428 accesses, then there will be a dependence from the last
4429 I<must> access B<and> from any I<may> access that follows
4430 this last I<must> access.
4431 In particular, if I<all> sources are I<may> accesses,
4432 then memory based dependence analysis is performed.
4433 If, on the other hand, all sources are I<must> accesses,
4434 then value based dependence analysis is performed.
4436 #include <isl/flow.h>
4438 typedef int (*isl_access_level_before)(void *first, void *second);
4440 __isl_give isl_access_info *isl_access_info_alloc(
4441 __isl_take isl_map *sink,
4442 void *sink_user, isl_access_level_before fn,
4444 __isl_give isl_access_info *isl_access_info_add_source(
4445 __isl_take isl_access_info *acc,
4446 __isl_take isl_map *source, int must,
4448 void *isl_access_info_free(__isl_take isl_access_info *acc);
4450 __isl_give isl_flow *isl_access_info_compute_flow(
4451 __isl_take isl_access_info *acc);
4453 int isl_flow_foreach(__isl_keep isl_flow *deps,
4454 int (*fn)(__isl_take isl_map *dep, int must,
4455 void *dep_user, void *user),
4457 __isl_give isl_map *isl_flow_get_no_source(
4458 __isl_keep isl_flow *deps, int must);
4459 void isl_flow_free(__isl_take isl_flow *deps);
4461 The function C<isl_access_info_compute_flow> performs the actual
4462 dependence analysis. The other functions are used to construct
4463 the input for this function or to read off the output.
4465 The input is collected in an C<isl_access_info>, which can
4466 be created through a call to C<isl_access_info_alloc>.
4467 The arguments to this functions are the sink access relation
4468 C<sink>, a token C<sink_user> used to identify the sink
4469 access to the user, a callback function for specifying the
4470 relative order of source and sink accesses, and the number
4471 of source access relations that will be added.
4472 The callback function has type C<int (*)(void *first, void *second)>.
4473 The function is called with two user supplied tokens identifying
4474 either a source or the sink and it should return the shared nesting
4475 level and the relative order of the two accesses.
4476 In particular, let I<n> be the number of loops shared by
4477 the two accesses. If C<first> precedes C<second> textually,
4478 then the function should return I<2 * n + 1>; otherwise,
4479 it should return I<2 * n>.
4480 The sources can be added to the C<isl_access_info> by performing
4481 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4482 C<must> indicates whether the source is a I<must> access
4483 or a I<may> access. Note that a multi-valued access relation
4484 should only be marked I<must> if every iteration in the domain
4485 of the relation accesses I<all> elements in its image.
4486 The C<source_user> token is again used to identify
4487 the source access. The range of the source access relation
4488 C<source> should have the same dimension as the range
4489 of the sink access relation.
4490 The C<isl_access_info_free> function should usually not be
4491 called explicitly, because it is called implicitly by
4492 C<isl_access_info_compute_flow>.
4494 The result of the dependence analysis is collected in an
4495 C<isl_flow>. There may be elements of
4496 the sink access for which no preceding source access could be
4497 found or for which all preceding sources are I<may> accesses.
4498 The relations containing these elements can be obtained through
4499 calls to C<isl_flow_get_no_source>, the first with C<must> set
4500 and the second with C<must> unset.
4501 In the case of standard flow dependence analysis,
4502 with the sink a read and the sources I<must> writes,
4503 the first relation corresponds to the reads from uninitialized
4504 array elements and the second relation is empty.
4505 The actual flow dependences can be extracted using
4506 C<isl_flow_foreach>. This function will call the user-specified
4507 callback function C<fn> for each B<non-empty> dependence between
4508 a source and the sink. The callback function is called
4509 with four arguments, the actual flow dependence relation
4510 mapping source iterations to sink iterations, a boolean that
4511 indicates whether it is a I<must> or I<may> dependence, a token
4512 identifying the source and an additional C<void *> with value
4513 equal to the third argument of the C<isl_flow_foreach> call.
4514 A dependence is marked I<must> if it originates from a I<must>
4515 source and if it is not followed by any I<may> sources.
4517 After finishing with an C<isl_flow>, the user should call
4518 C<isl_flow_free> to free all associated memory.
4520 A higher-level interface to dependence analysis is provided
4521 by the following function.
4523 #include <isl/flow.h>
4525 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4526 __isl_take isl_union_map *must_source,
4527 __isl_take isl_union_map *may_source,
4528 __isl_take isl_union_map *schedule,
4529 __isl_give isl_union_map **must_dep,
4530 __isl_give isl_union_map **may_dep,
4531 __isl_give isl_union_map **must_no_source,
4532 __isl_give isl_union_map **may_no_source);
4534 The arrays are identified by the tuple names of the ranges
4535 of the accesses. The iteration domains by the tuple names
4536 of the domains of the accesses and of the schedule.
4537 The relative order of the iteration domains is given by the
4538 schedule. The relations returned through C<must_no_source>
4539 and C<may_no_source> are subsets of C<sink>.
4540 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4541 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4542 any of the other arguments is treated as an error.
4544 =head3 Interaction with Dependence Analysis
4546 During the dependence analysis, we frequently need to perform
4547 the following operation. Given a relation between sink iterations
4548 and potential source iterations from a particular source domain,
4549 what is the last potential source iteration corresponding to each
4550 sink iteration. It can sometimes be convenient to adjust
4551 the set of potential source iterations before or after each such operation.
4552 The prototypical example is fuzzy array dataflow analysis,
4553 where we need to analyze if, based on data-dependent constraints,
4554 the sink iteration can ever be executed without one or more of
4555 the corresponding potential source iterations being executed.
4556 If so, we can introduce extra parameters and select an unknown
4557 but fixed source iteration from the potential source iterations.
4558 To be able to perform such manipulations, C<isl> provides the following
4561 #include <isl/flow.h>
4563 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4564 __isl_keep isl_map *source_map,
4565 __isl_keep isl_set *sink, void *source_user,
4567 __isl_give isl_access_info *isl_access_info_set_restrict(
4568 __isl_take isl_access_info *acc,
4569 isl_access_restrict fn, void *user);
4571 The function C<isl_access_info_set_restrict> should be called
4572 before calling C<isl_access_info_compute_flow> and registers a callback function
4573 that will be called any time C<isl> is about to compute the last
4574 potential source. The first argument is the (reverse) proto-dependence,
4575 mapping sink iterations to potential source iterations.
4576 The second argument represents the sink iterations for which
4577 we want to compute the last source iteration.
4578 The third argument is the token corresponding to the source
4579 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4580 The callback is expected to return a restriction on either the input or
4581 the output of the operation computing the last potential source.
4582 If the input needs to be restricted then restrictions are needed
4583 for both the source and the sink iterations. The sink iterations
4584 and the potential source iterations will be intersected with these sets.
4585 If the output needs to be restricted then only a restriction on the source
4586 iterations is required.
4587 If any error occurs, the callback should return C<NULL>.
4588 An C<isl_restriction> object can be created, freed and inspected
4589 using the following functions.
4591 #include <isl/flow.h>
4593 __isl_give isl_restriction *isl_restriction_input(
4594 __isl_take isl_set *source_restr,
4595 __isl_take isl_set *sink_restr);
4596 __isl_give isl_restriction *isl_restriction_output(
4597 __isl_take isl_set *source_restr);
4598 __isl_give isl_restriction *isl_restriction_none(
4599 __isl_take isl_map *source_map);
4600 __isl_give isl_restriction *isl_restriction_empty(
4601 __isl_take isl_map *source_map);
4602 void *isl_restriction_free(
4603 __isl_take isl_restriction *restr);
4604 isl_ctx *isl_restriction_get_ctx(
4605 __isl_keep isl_restriction *restr);
4607 C<isl_restriction_none> and C<isl_restriction_empty> are special
4608 cases of C<isl_restriction_input>. C<isl_restriction_none>
4609 is essentially equivalent to
4611 isl_restriction_input(isl_set_universe(
4612 isl_space_range(isl_map_get_space(source_map))),
4614 isl_space_domain(isl_map_get_space(source_map))));
4616 whereas C<isl_restriction_empty> is essentially equivalent to
4618 isl_restriction_input(isl_set_empty(
4619 isl_space_range(isl_map_get_space(source_map))),
4621 isl_space_domain(isl_map_get_space(source_map))));
4625 B<The functionality described in this section is fairly new
4626 and may be subject to change.>
4628 The following function can be used to compute a schedule
4629 for a union of domains.
4630 By default, the algorithm used to construct the schedule is similar
4631 to that of C<Pluto>.
4632 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4634 The generated schedule respects all C<validity> dependences.
4635 That is, all dependence distances over these dependences in the
4636 scheduled space are lexicographically positive.
4637 The default algorithm tries to minimize the dependence distances over
4638 C<proximity> dependences.
4639 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4640 for groups of domains where the dependence distances have only
4641 non-negative values.
4642 When using Feautrier's algorithm, the C<proximity> dependence
4643 distances are only minimized during the extension to a
4644 full-dimensional schedule.
4646 #include <isl/schedule.h>
4647 __isl_give isl_schedule *isl_union_set_compute_schedule(
4648 __isl_take isl_union_set *domain,
4649 __isl_take isl_union_map *validity,
4650 __isl_take isl_union_map *proximity);
4651 void *isl_schedule_free(__isl_take isl_schedule *sched);
4653 A mapping from the domains to the scheduled space can be obtained
4654 from an C<isl_schedule> using the following function.
4656 __isl_give isl_union_map *isl_schedule_get_map(
4657 __isl_keep isl_schedule *sched);
4659 A representation of the schedule can be printed using
4661 __isl_give isl_printer *isl_printer_print_schedule(
4662 __isl_take isl_printer *p,
4663 __isl_keep isl_schedule *schedule);
4665 A representation of the schedule as a forest of bands can be obtained
4666 using the following function.
4668 __isl_give isl_band_list *isl_schedule_get_band_forest(
4669 __isl_keep isl_schedule *schedule);
4671 The individual bands can be visited in depth-first post-order
4672 using the following function.
4674 #include <isl/schedule.h>
4675 int isl_schedule_foreach_band(
4676 __isl_keep isl_schedule *sched,
4677 int (*fn)(__isl_keep isl_band *band, void *user),
4680 The list can be manipulated as explained in L<"Lists">.
4681 The bands inside the list can be copied and freed using the following
4684 #include <isl/band.h>
4685 __isl_give isl_band *isl_band_copy(
4686 __isl_keep isl_band *band);
4687 void *isl_band_free(__isl_take isl_band *band);
4689 Each band contains zero or more scheduling dimensions.
4690 These are referred to as the members of the band.
4691 The section of the schedule that corresponds to the band is
4692 referred to as the partial schedule of the band.
4693 For those nodes that participate in a band, the outer scheduling
4694 dimensions form the prefix schedule, while the inner scheduling
4695 dimensions form the suffix schedule.
4696 That is, if we take a cut of the band forest, then the union of
4697 the concatenations of the prefix, partial and suffix schedules of
4698 each band in the cut is equal to the entire schedule (modulo
4699 some possible padding at the end with zero scheduling dimensions).
4700 The properties of a band can be inspected using the following functions.
4702 #include <isl/band.h>
4703 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4705 int isl_band_has_children(__isl_keep isl_band *band);
4706 __isl_give isl_band_list *isl_band_get_children(
4707 __isl_keep isl_band *band);
4709 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4710 __isl_keep isl_band *band);
4711 __isl_give isl_union_map *isl_band_get_partial_schedule(
4712 __isl_keep isl_band *band);
4713 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4714 __isl_keep isl_band *band);
4716 int isl_band_n_member(__isl_keep isl_band *band);
4717 int isl_band_member_is_zero_distance(
4718 __isl_keep isl_band *band, int pos);
4720 int isl_band_list_foreach_band(
4721 __isl_keep isl_band_list *list,
4722 int (*fn)(__isl_keep isl_band *band, void *user),
4725 Note that a scheduling dimension is considered to be ``zero
4726 distance'' if it does not carry any proximity dependences
4728 That is, if the dependence distances of the proximity
4729 dependences are all zero in that direction (for fixed
4730 iterations of outer bands).
4731 Like C<isl_schedule_foreach_band>,
4732 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4733 in depth-first post-order.
4735 A band can be tiled using the following function.
4737 #include <isl/band.h>
4738 int isl_band_tile(__isl_keep isl_band *band,
4739 __isl_take isl_vec *sizes);
4741 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4743 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4745 The C<isl_band_tile> function tiles the band using the given tile sizes
4746 inside its schedule.
4747 A new child band is created to represent the point loops and it is
4748 inserted between the modified band and its children.
4749 The C<tile_scale_tile_loops> option specifies whether the tile
4750 loops iterators should be scaled by the tile sizes.
4752 A representation of the band can be printed using
4754 #include <isl/band.h>
4755 __isl_give isl_printer *isl_printer_print_band(
4756 __isl_take isl_printer *p,
4757 __isl_keep isl_band *band);
4761 #include <isl/schedule.h>
4762 int isl_options_set_schedule_max_coefficient(
4763 isl_ctx *ctx, int val);
4764 int isl_options_get_schedule_max_coefficient(
4766 int isl_options_set_schedule_max_constant_term(
4767 isl_ctx *ctx, int val);
4768 int isl_options_get_schedule_max_constant_term(
4770 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4771 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4772 int isl_options_set_schedule_maximize_band_depth(
4773 isl_ctx *ctx, int val);
4774 int isl_options_get_schedule_maximize_band_depth(
4776 int isl_options_set_schedule_outer_zero_distance(
4777 isl_ctx *ctx, int val);
4778 int isl_options_get_schedule_outer_zero_distance(
4780 int isl_options_set_schedule_split_scaled(
4781 isl_ctx *ctx, int val);
4782 int isl_options_get_schedule_split_scaled(
4784 int isl_options_set_schedule_algorithm(
4785 isl_ctx *ctx, int val);
4786 int isl_options_get_schedule_algorithm(
4788 int isl_options_set_schedule_separate_components(
4789 isl_ctx *ctx, int val);
4790 int isl_options_get_schedule_separate_components(
4795 =item * schedule_max_coefficient
4797 This option enforces that the coefficients for variable and parameter
4798 dimensions in the calculated schedule are not larger than the specified value.
4799 This option can significantly increase the speed of the scheduling calculation
4800 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4801 this option does not introduce bounds on the variable or parameter
4804 =item * schedule_max_constant_term
4806 This option enforces that the constant coefficients in the calculated schedule
4807 are not larger than the maximal constant term. This option can significantly
4808 increase the speed of the scheduling calculation and may also prevent fusing of
4809 unrelated dimensions. A value of -1 means that this option does not introduce
4810 bounds on the constant coefficients.
4812 =item * schedule_fuse
4814 This option controls the level of fusion.
4815 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
4816 resulting schedule will be distributed as much as possible.
4817 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
4818 try to fuse loops in the resulting schedule.
4820 =item * schedule_maximize_band_depth
4822 If this option is set, we do not split bands at the point
4823 where we detect splitting is necessary. Instead, we
4824 backtrack and split bands as early as possible. This
4825 reduces the number of splits and maximizes the width of
4826 the bands. Wider bands give more possibilities for tiling.
4827 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
4828 then bands will be split as early as possible, even if there is no need.
4829 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
4831 =item * schedule_outer_zero_distance
4833 If this option is set, then we try to construct schedules
4834 where the outermost scheduling dimension in each band
4835 results in a zero dependence distance over the proximity
4838 =item * schedule_split_scaled
4840 If this option is set, then we try to construct schedules in which the
4841 constant term is split off from the linear part if the linear parts of
4842 the scheduling rows for all nodes in the graphs have a common non-trivial
4844 The constant term is then placed in a separate band and the linear
4847 =item * schedule_algorithm
4849 Selects the scheduling algorithm to be used.
4850 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4851 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4853 =item * schedule_separate_components
4855 If at any point the dependence graph contains any (weakly connected) components,
4856 then these components are scheduled separately.
4857 If this option is not set, then some iterations of the domains
4858 in these components may be scheduled together.
4859 If this option is set, then the components are given consecutive
4864 =head2 Parametric Vertex Enumeration
4866 The parametric vertex enumeration described in this section
4867 is mainly intended to be used internally and by the C<barvinok>
4870 #include <isl/vertices.h>
4871 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4872 __isl_keep isl_basic_set *bset);
4874 The function C<isl_basic_set_compute_vertices> performs the
4875 actual computation of the parametric vertices and the chamber
4876 decomposition and store the result in an C<isl_vertices> object.
4877 This information can be queried by either iterating over all
4878 the vertices or iterating over all the chambers or cells
4879 and then iterating over all vertices that are active on the chamber.
4881 int isl_vertices_foreach_vertex(
4882 __isl_keep isl_vertices *vertices,
4883 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4886 int isl_vertices_foreach_cell(
4887 __isl_keep isl_vertices *vertices,
4888 int (*fn)(__isl_take isl_cell *cell, void *user),
4890 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4891 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4894 Other operations that can be performed on an C<isl_vertices> object are
4897 isl_ctx *isl_vertices_get_ctx(
4898 __isl_keep isl_vertices *vertices);
4899 int isl_vertices_get_n_vertices(
4900 __isl_keep isl_vertices *vertices);
4901 void isl_vertices_free(__isl_take isl_vertices *vertices);
4903 Vertices can be inspected and destroyed using the following functions.
4905 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4906 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4907 __isl_give isl_basic_set *isl_vertex_get_domain(
4908 __isl_keep isl_vertex *vertex);
4909 __isl_give isl_basic_set *isl_vertex_get_expr(
4910 __isl_keep isl_vertex *vertex);
4911 void isl_vertex_free(__isl_take isl_vertex *vertex);
4913 C<isl_vertex_get_expr> returns a singleton parametric set describing
4914 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4916 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4917 B<rational> basic sets, so they should mainly be used for inspection
4918 and should not be mixed with integer sets.
4920 Chambers can be inspected and destroyed using the following functions.
4922 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4923 __isl_give isl_basic_set *isl_cell_get_domain(
4924 __isl_keep isl_cell *cell);
4925 void isl_cell_free(__isl_take isl_cell *cell);
4929 Although C<isl> is mainly meant to be used as a library,
4930 it also contains some basic applications that use some
4931 of the functionality of C<isl>.
4932 The input may be specified in either the L<isl format>
4933 or the L<PolyLib format>.
4935 =head2 C<isl_polyhedron_sample>
4937 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4938 an integer element of the polyhedron, if there is any.
4939 The first column in the output is the denominator and is always
4940 equal to 1. If the polyhedron contains no integer points,
4941 then a vector of length zero is printed.
4945 C<isl_pip> takes the same input as the C<example> program
4946 from the C<piplib> distribution, i.e., a set of constraints
4947 on the parameters, a line containing only -1 and finally a set
4948 of constraints on a parametric polyhedron.
4949 The coefficients of the parameters appear in the last columns
4950 (but before the final constant column).
4951 The output is the lexicographic minimum of the parametric polyhedron.
4952 As C<isl> currently does not have its own output format, the output
4953 is just a dump of the internal state.
4955 =head2 C<isl_polyhedron_minimize>
4957 C<isl_polyhedron_minimize> computes the minimum of some linear
4958 or affine objective function over the integer points in a polyhedron.
4959 If an affine objective function
4960 is given, then the constant should appear in the last column.
4962 =head2 C<isl_polytope_scan>
4964 Given a polytope, C<isl_polytope_scan> prints
4965 all integer points in the polytope.