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>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
186 C<isl> is released under the MIT license.
190 Permission is hereby granted, free of charge, to any person obtaining a copy of
191 this software and associated documentation files (the "Software"), to deal in
192 the Software without restriction, including without limitation the rights to
193 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
194 of the Software, and to permit persons to whom the Software is furnished to do
195 so, subject to the following conditions:
197 The above copyright notice and this permission notice shall be included in all
198 copies or substantial portions of the Software.
200 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
201 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
202 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
203 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
204 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
205 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
210 Note that C<isl> currently requires C<GMP>, which is released
211 under the GNU Lesser General Public License (LGPL). This means
212 that code linked against C<isl> is also linked against LGPL code.
216 The source of C<isl> can be obtained either as a tarball
217 or from the git repository. Both are available from
218 L<http://freshmeat.net/projects/isl/>.
219 The installation process depends on how you obtained
222 =head2 Installation from the git repository
226 =item 1 Clone or update the repository
228 The first time the source is obtained, you need to clone
231 git clone git://repo.or.cz/isl.git
233 To obtain updates, you need to pull in the latest changes
237 =item 2 Generate C<configure>
243 After performing the above steps, continue
244 with the L<Common installation instructions>.
246 =head2 Common installation instructions
250 =item 1 Obtain C<GMP>
252 Building C<isl> requires C<GMP>, including its headers files.
253 Your distribution may not provide these header files by default
254 and you may need to install a package called C<gmp-devel> or something
255 similar. Alternatively, C<GMP> can be built from
256 source, available from L<http://gmplib.org/>.
260 C<isl> uses the standard C<autoconf> C<configure> script.
265 optionally followed by some configure options.
266 A complete list of options can be obtained by running
270 Below we discuss some of the more common options.
272 C<isl> can optionally use C<piplib>, but no
273 C<piplib> functionality is currently used by default.
274 The C<--with-piplib> option can
275 be used to specify which C<piplib>
276 library to use, either an installed version (C<system>),
277 an externally built version (C<build>)
278 or no version (C<no>). The option C<build> is mostly useful
279 in C<configure> scripts of larger projects that bundle both C<isl>
286 Installation prefix for C<isl>
288 =item C<--with-gmp-prefix>
290 Installation prefix for C<GMP> (architecture-independent files).
292 =item C<--with-gmp-exec-prefix>
294 Installation prefix for C<GMP> (architecture-dependent files).
296 =item C<--with-piplib>
298 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
300 =item C<--with-piplib-prefix>
302 Installation prefix for C<system> C<piplib> (architecture-independent files).
304 =item C<--with-piplib-exec-prefix>
306 Installation prefix for C<system> C<piplib> (architecture-dependent files).
308 =item C<--with-piplib-builddir>
310 Location where C<build> C<piplib> was built.
318 =item 4 Install (optional)
324 =head1 Integer Set Library
326 =head2 Initialization
328 All manipulations of integer sets and relations occur within
329 the context of an C<isl_ctx>.
330 A given C<isl_ctx> can only be used within a single thread.
331 All arguments of a function are required to have been allocated
332 within the same context.
333 There are currently no functions available for moving an object
334 from one C<isl_ctx> to another C<isl_ctx>. This means that
335 there is currently no way of safely moving an object from one
336 thread to another, unless the whole C<isl_ctx> is moved.
338 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
339 freed using C<isl_ctx_free>.
340 All objects allocated within an C<isl_ctx> should be freed
341 before the C<isl_ctx> itself is freed.
343 isl_ctx *isl_ctx_alloc();
344 void isl_ctx_free(isl_ctx *ctx);
348 All operations on integers, mainly the coefficients
349 of the constraints describing the sets and relations,
350 are performed in exact integer arithmetic using C<GMP>.
351 However, to allow future versions of C<isl> to optionally
352 support fixed integer arithmetic, all calls to C<GMP>
353 are wrapped inside C<isl> specific macros.
354 The basic type is C<isl_int> and the operations below
355 are available on this type.
356 The meanings of these operations are essentially the same
357 as their C<GMP> C<mpz_> counterparts.
358 As always with C<GMP> types, C<isl_int>s need to be
359 initialized with C<isl_int_init> before they can be used
360 and they need to be released with C<isl_int_clear>
362 The user should not assume that an C<isl_int> is represented
363 as a C<mpz_t>, but should instead explicitly convert between
364 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
365 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
369 =item isl_int_init(i)
371 =item isl_int_clear(i)
373 =item isl_int_set(r,i)
375 =item isl_int_set_si(r,i)
377 =item isl_int_set_gmp(r,g)
379 =item isl_int_get_gmp(i,g)
381 =item isl_int_abs(r,i)
383 =item isl_int_neg(r,i)
385 =item isl_int_swap(i,j)
387 =item isl_int_swap_or_set(i,j)
389 =item isl_int_add_ui(r,i,j)
391 =item isl_int_sub_ui(r,i,j)
393 =item isl_int_add(r,i,j)
395 =item isl_int_sub(r,i,j)
397 =item isl_int_mul(r,i,j)
399 =item isl_int_mul_ui(r,i,j)
401 =item isl_int_addmul(r,i,j)
403 =item isl_int_submul(r,i,j)
405 =item isl_int_gcd(r,i,j)
407 =item isl_int_lcm(r,i,j)
409 =item isl_int_divexact(r,i,j)
411 =item isl_int_cdiv_q(r,i,j)
413 =item isl_int_fdiv_q(r,i,j)
415 =item isl_int_fdiv_r(r,i,j)
417 =item isl_int_fdiv_q_ui(r,i,j)
419 =item isl_int_read(r,s)
421 =item isl_int_print(out,i,width)
425 =item isl_int_cmp(i,j)
427 =item isl_int_cmp_si(i,si)
429 =item isl_int_eq(i,j)
431 =item isl_int_ne(i,j)
433 =item isl_int_lt(i,j)
435 =item isl_int_le(i,j)
437 =item isl_int_gt(i,j)
439 =item isl_int_ge(i,j)
441 =item isl_int_abs_eq(i,j)
443 =item isl_int_abs_ne(i,j)
445 =item isl_int_abs_lt(i,j)
447 =item isl_int_abs_gt(i,j)
449 =item isl_int_abs_ge(i,j)
451 =item isl_int_is_zero(i)
453 =item isl_int_is_one(i)
455 =item isl_int_is_negone(i)
457 =item isl_int_is_pos(i)
459 =item isl_int_is_neg(i)
461 =item isl_int_is_nonpos(i)
463 =item isl_int_is_nonneg(i)
465 =item isl_int_is_divisible_by(i,j)
469 =head2 Sets and Relations
471 C<isl> uses six types of objects for representing sets and relations,
472 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
473 C<isl_union_set> and C<isl_union_map>.
474 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
475 can be described as a conjunction of affine constraints, while
476 C<isl_set> and C<isl_map> represent unions of
477 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
478 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
479 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
480 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
481 where spaces are considered different if they have a different number
482 of dimensions and/or different names (see L<"Spaces">).
483 The difference between sets and relations (maps) is that sets have
484 one set of variables, while relations have two sets of variables,
485 input variables and output variables.
487 =head2 Memory Management
489 Since a high-level operation on sets and/or relations usually involves
490 several substeps and since the user is usually not interested in
491 the intermediate results, most functions that return a new object
492 will also release all the objects passed as arguments.
493 If the user still wants to use one or more of these arguments
494 after the function call, she should pass along a copy of the
495 object rather than the object itself.
496 The user is then responsible for making sure that the original
497 object gets used somewhere else or is explicitly freed.
499 The arguments and return values of all documented functions are
500 annotated to make clear which arguments are released and which
501 arguments are preserved. In particular, the following annotations
508 C<__isl_give> means that a new object is returned.
509 The user should make sure that the returned pointer is
510 used exactly once as a value for an C<__isl_take> argument.
511 In between, it can be used as a value for as many
512 C<__isl_keep> arguments as the user likes.
513 There is one exception, and that is the case where the
514 pointer returned is C<NULL>. Is this case, the user
515 is free to use it as an C<__isl_take> argument or not.
519 C<__isl_take> means that the object the argument points to
520 is taken over by the function and may no longer be used
521 by the user as an argument to any other function.
522 The pointer value must be one returned by a function
523 returning an C<__isl_give> pointer.
524 If the user passes in a C<NULL> value, then this will
525 be treated as an error in the sense that the function will
526 not perform its usual operation. However, it will still
527 make sure that all the other C<__isl_take> arguments
532 C<__isl_keep> means that the function will only use the object
533 temporarily. After the function has finished, the user
534 can still use it as an argument to other functions.
535 A C<NULL> value will be treated in the same way as
536 a C<NULL> value for an C<__isl_take> argument.
540 =head2 Error Handling
542 C<isl> supports different ways to react in case a runtime error is triggered.
543 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
544 with two maps that have incompatible spaces. There are three possible ways
545 to react on error: to warn, to continue or to abort.
547 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
548 the last error in the corresponding C<isl_ctx> and the function in which the
549 error was triggered returns C<NULL>. An error does not corrupt internal state,
550 such that isl can continue to be used. C<isl> also provides functions to
551 read the last error and to reset the memory that stores the last error. The
552 last error is only stored for information purposes. Its presence does not
553 change the behavior of C<isl>. Hence, resetting an error is not required to
554 continue to use isl, but only to observe new errors.
557 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
558 void isl_ctx_reset_error(isl_ctx *ctx);
560 Another option is to continue on error. This is similar to warn on error mode,
561 except that C<isl> does not print any warning. This allows a program to
562 implement its own error reporting.
564 The last option is to directly abort the execution of the program from within
565 the isl library. This makes it obviously impossible to recover from an error,
566 but it allows to directly spot the error location. By aborting on error,
567 debuggers break at the location the error occurred and can provide a stack
568 trace. Other tools that automatically provide stack traces on abort or that do
569 not want to continue execution after an error was triggered may also prefer to
572 The on error behavior of isl can be specified by calling
573 C<isl_options_set_on_error> or by setting the command line option
574 C<--isl-on-error>. Valid arguments for the function call are
575 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
576 choices for the command line option are C<warn>, C<continue> and C<abort>.
577 It is also possible to query the current error mode.
579 #include <isl/options.h>
580 int isl_options_set_on_error(isl_ctx *ctx, int val);
581 int isl_options_get_on_error(isl_ctx *ctx);
585 Identifiers are used to identify both individual dimensions
586 and tuples of dimensions. They consist of an optional name and an optional
587 user pointer. The name and the user pointer cannot both be C<NULL>, however.
588 Identifiers with the same name but different pointer values
589 are considered to be distinct.
590 Similarly, identifiers with different names but the same pointer value
591 are also considered to be distinct.
592 Equal identifiers are represented using the same object.
593 Pairs of identifiers can therefore be tested for equality using the
595 Identifiers can be constructed, copied, freed, inspected and printed
596 using the following functions.
599 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
600 __isl_keep const char *name, void *user);
601 __isl_give isl_id *isl_id_copy(isl_id *id);
602 void *isl_id_free(__isl_take isl_id *id);
604 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
605 void *isl_id_get_user(__isl_keep isl_id *id);
606 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
608 __isl_give isl_printer *isl_printer_print_id(
609 __isl_take isl_printer *p, __isl_keep isl_id *id);
611 Note that C<isl_id_get_name> returns a pointer to some internal
612 data structure, so the result can only be used while the
613 corresponding C<isl_id> is alive.
617 Whenever a new set, relation or similiar object is created from scratch,
618 the space in which it lives needs to be specified using an C<isl_space>.
619 Each space involves zero or more parameters and zero, one or two
620 tuples of set or input/output dimensions. The parameters and dimensions
621 are identified by an C<isl_dim_type> and a position.
622 The type C<isl_dim_param> refers to parameters,
623 the type C<isl_dim_set> refers to set dimensions (for spaces
624 with a single tuple of dimensions) and the types C<isl_dim_in>
625 and C<isl_dim_out> refer to input and output dimensions
626 (for spaces with two tuples of dimensions).
627 Local spaces (see L</"Local Spaces">) also contain dimensions
628 of type C<isl_dim_div>.
629 Note that parameters are only identified by their position within
630 a given object. Across different objects, parameters are (usually)
631 identified by their names or identifiers. Only unnamed parameters
632 are identified by their positions across objects. The use of unnamed
633 parameters is discouraged.
635 #include <isl/space.h>
636 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
637 unsigned nparam, unsigned n_in, unsigned n_out);
638 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
640 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
641 unsigned nparam, unsigned dim);
642 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
643 void *isl_space_free(__isl_take isl_space *space);
644 unsigned isl_space_dim(__isl_keep isl_space *space,
645 enum isl_dim_type type);
647 The space used for creating a parameter domain
648 needs to be created using C<isl_space_params_alloc>.
649 For other sets, the space
650 needs to be created using C<isl_space_set_alloc>, while
651 for a relation, the space
652 needs to be created using C<isl_space_alloc>.
653 C<isl_space_dim> can be used
654 to find out the number of dimensions of each type in
655 a space, where type may be
656 C<isl_dim_param>, C<isl_dim_in> (only for relations),
657 C<isl_dim_out> (only for relations), C<isl_dim_set>
658 (only for sets) or C<isl_dim_all>.
660 To check whether a given space is that of a set or a map
661 or whether it is a parameter space, use these functions:
663 #include <isl/space.h>
664 int isl_space_is_params(__isl_keep isl_space *space);
665 int isl_space_is_set(__isl_keep isl_space *space);
666 int isl_space_is_map(__isl_keep isl_space *space);
668 Spaces can be compared using the following functions:
670 #include <isl/space.h>
671 int isl_space_is_equal(__isl_keep isl_space *space1,
672 __isl_keep isl_space *space2);
673 int isl_space_is_domain(__isl_keep isl_space *space1,
674 __isl_keep isl_space *space2);
675 int isl_space_is_range(__isl_keep isl_space *space1,
676 __isl_keep isl_space *space2);
678 C<isl_space_is_domain> checks whether the first argument is equal
679 to the domain of the second argument. This requires in particular that
680 the first argument is a set space and that the second argument
683 It is often useful to create objects that live in the
684 same space as some other object. This can be accomplished
685 by creating the new objects
686 (see L<Creating New Sets and Relations> or
687 L<Creating New (Piecewise) Quasipolynomials>) based on the space
688 of the original object.
691 __isl_give isl_space *isl_basic_set_get_space(
692 __isl_keep isl_basic_set *bset);
693 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
695 #include <isl/union_set.h>
696 __isl_give isl_space *isl_union_set_get_space(
697 __isl_keep isl_union_set *uset);
700 __isl_give isl_space *isl_basic_map_get_space(
701 __isl_keep isl_basic_map *bmap);
702 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
704 #include <isl/union_map.h>
705 __isl_give isl_space *isl_union_map_get_space(
706 __isl_keep isl_union_map *umap);
708 #include <isl/constraint.h>
709 __isl_give isl_space *isl_constraint_get_space(
710 __isl_keep isl_constraint *constraint);
712 #include <isl/polynomial.h>
713 __isl_give isl_space *isl_qpolynomial_get_domain_space(
714 __isl_keep isl_qpolynomial *qp);
715 __isl_give isl_space *isl_qpolynomial_get_space(
716 __isl_keep isl_qpolynomial *qp);
717 __isl_give isl_space *isl_qpolynomial_fold_get_space(
718 __isl_keep isl_qpolynomial_fold *fold);
719 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
720 __isl_keep isl_pw_qpolynomial *pwqp);
721 __isl_give isl_space *isl_pw_qpolynomial_get_space(
722 __isl_keep isl_pw_qpolynomial *pwqp);
723 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
724 __isl_keep isl_pw_qpolynomial_fold *pwf);
725 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
726 __isl_keep isl_pw_qpolynomial_fold *pwf);
727 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
728 __isl_keep isl_union_pw_qpolynomial *upwqp);
729 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
730 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
733 __isl_give isl_space *isl_aff_get_domain_space(
734 __isl_keep isl_aff *aff);
735 __isl_give isl_space *isl_aff_get_space(
736 __isl_keep isl_aff *aff);
737 __isl_give isl_space *isl_pw_aff_get_domain_space(
738 __isl_keep isl_pw_aff *pwaff);
739 __isl_give isl_space *isl_pw_aff_get_space(
740 __isl_keep isl_pw_aff *pwaff);
741 __isl_give isl_space *isl_multi_aff_get_domain_space(
742 __isl_keep isl_multi_aff *maff);
743 __isl_give isl_space *isl_multi_aff_get_space(
744 __isl_keep isl_multi_aff *maff);
745 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
746 __isl_keep isl_pw_multi_aff *pma);
747 __isl_give isl_space *isl_pw_multi_aff_get_space(
748 __isl_keep isl_pw_multi_aff *pma);
749 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
750 __isl_keep isl_union_pw_multi_aff *upma);
751 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
752 __isl_keep isl_multi_pw_aff *mpa);
753 __isl_give isl_space *isl_multi_pw_aff_get_space(
754 __isl_keep isl_multi_pw_aff *mpa);
756 #include <isl/point.h>
757 __isl_give isl_space *isl_point_get_space(
758 __isl_keep isl_point *pnt);
760 The identifiers or names of the individual dimensions may be set or read off
761 using the following functions.
763 #include <isl/space.h>
764 __isl_give isl_space *isl_space_set_dim_id(
765 __isl_take isl_space *space,
766 enum isl_dim_type type, unsigned pos,
767 __isl_take isl_id *id);
768 int isl_space_has_dim_id(__isl_keep isl_space *space,
769 enum isl_dim_type type, unsigned pos);
770 __isl_give isl_id *isl_space_get_dim_id(
771 __isl_keep isl_space *space,
772 enum isl_dim_type type, unsigned pos);
773 __isl_give isl_space *isl_space_set_dim_name(
774 __isl_take isl_space *space,
775 enum isl_dim_type type, unsigned pos,
776 __isl_keep const char *name);
777 int isl_space_has_dim_name(__isl_keep isl_space *space,
778 enum isl_dim_type type, unsigned pos);
779 __isl_keep const char *isl_space_get_dim_name(
780 __isl_keep isl_space *space,
781 enum isl_dim_type type, unsigned pos);
783 Note that C<isl_space_get_name> returns a pointer to some internal
784 data structure, so the result can only be used while the
785 corresponding C<isl_space> is alive.
786 Also note that every function that operates on two sets or relations
787 requires that both arguments have the same parameters. This also
788 means that if one of the arguments has named parameters, then the
789 other needs to have named parameters too and the names need to match.
790 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
791 arguments may have different parameters (as long as they are named),
792 in which case the result will have as parameters the union of the parameters of
795 Given the identifier or name of a dimension (typically a parameter),
796 its position can be obtained from the following function.
798 #include <isl/space.h>
799 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
800 enum isl_dim_type type, __isl_keep isl_id *id);
801 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
802 enum isl_dim_type type, const char *name);
804 The identifiers or names of entire spaces may be set or read off
805 using the following functions.
807 #include <isl/space.h>
808 __isl_give isl_space *isl_space_set_tuple_id(
809 __isl_take isl_space *space,
810 enum isl_dim_type type, __isl_take isl_id *id);
811 __isl_give isl_space *isl_space_reset_tuple_id(
812 __isl_take isl_space *space, enum isl_dim_type type);
813 int isl_space_has_tuple_id(__isl_keep isl_space *space,
814 enum isl_dim_type type);
815 __isl_give isl_id *isl_space_get_tuple_id(
816 __isl_keep isl_space *space, enum isl_dim_type type);
817 __isl_give isl_space *isl_space_set_tuple_name(
818 __isl_take isl_space *space,
819 enum isl_dim_type type, const char *s);
820 int isl_space_has_tuple_name(__isl_keep isl_space *space,
821 enum isl_dim_type type);
822 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
823 enum isl_dim_type type);
825 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
826 or C<isl_dim_set>. As with C<isl_space_get_name>,
827 the C<isl_space_get_tuple_name> function returns a pointer to some internal
829 Binary operations require the corresponding spaces of their arguments
830 to have the same name.
832 Spaces can be nested. In particular, the domain of a set or
833 the domain or range of a relation can be a nested relation.
834 The following functions can be used to construct and deconstruct
837 #include <isl/space.h>
838 int isl_space_is_wrapping(__isl_keep isl_space *space);
839 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
840 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
842 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
843 be the space of a set, while that of
844 C<isl_space_wrap> should be the space of a relation.
845 Conversely, the output of C<isl_space_unwrap> is the space
846 of a relation, while that of C<isl_space_wrap> is the space of a set.
848 Spaces can be created from other spaces
849 using the following functions.
851 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
852 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
853 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
854 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
855 __isl_give isl_space *isl_space_params(
856 __isl_take isl_space *space);
857 __isl_give isl_space *isl_space_set_from_params(
858 __isl_take isl_space *space);
859 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
860 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
861 __isl_take isl_space *right);
862 __isl_give isl_space *isl_space_align_params(
863 __isl_take isl_space *space1, __isl_take isl_space *space2)
864 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
865 enum isl_dim_type type, unsigned pos, unsigned n);
866 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
867 enum isl_dim_type type, unsigned n);
868 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
869 enum isl_dim_type type, unsigned first, unsigned n);
870 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
871 enum isl_dim_type dst_type, unsigned dst_pos,
872 enum isl_dim_type src_type, unsigned src_pos,
874 __isl_give isl_space *isl_space_map_from_set(
875 __isl_take isl_space *space);
876 __isl_give isl_space *isl_space_map_from_domain_and_range(
877 __isl_take isl_space *domain,
878 __isl_take isl_space *range);
879 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
880 __isl_give isl_space *isl_space_curry(
881 __isl_take isl_space *space);
882 __isl_give isl_space *isl_space_uncurry(
883 __isl_take isl_space *space);
885 Note that if dimensions are added or removed from a space, then
886 the name and the internal structure are lost.
890 A local space is essentially a space with
891 zero or more existentially quantified variables.
892 The local space of a (constraint of a) basic set or relation can be obtained
893 using the following functions.
895 #include <isl/constraint.h>
896 __isl_give isl_local_space *isl_constraint_get_local_space(
897 __isl_keep isl_constraint *constraint);
900 __isl_give isl_local_space *isl_basic_set_get_local_space(
901 __isl_keep isl_basic_set *bset);
904 __isl_give isl_local_space *isl_basic_map_get_local_space(
905 __isl_keep isl_basic_map *bmap);
907 A new local space can be created from a space using
909 #include <isl/local_space.h>
910 __isl_give isl_local_space *isl_local_space_from_space(
911 __isl_take isl_space *space);
913 They can be inspected, modified, copied and freed using the following functions.
915 #include <isl/local_space.h>
916 isl_ctx *isl_local_space_get_ctx(
917 __isl_keep isl_local_space *ls);
918 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
919 int isl_local_space_dim(__isl_keep isl_local_space *ls,
920 enum isl_dim_type type);
921 int isl_local_space_has_dim_id(
922 __isl_keep isl_local_space *ls,
923 enum isl_dim_type type, unsigned pos);
924 __isl_give isl_id *isl_local_space_get_dim_id(
925 __isl_keep isl_local_space *ls,
926 enum isl_dim_type type, unsigned pos);
927 int isl_local_space_has_dim_name(
928 __isl_keep isl_local_space *ls,
929 enum isl_dim_type type, unsigned pos)
930 const char *isl_local_space_get_dim_name(
931 __isl_keep isl_local_space *ls,
932 enum isl_dim_type type, unsigned pos);
933 __isl_give isl_local_space *isl_local_space_set_dim_name(
934 __isl_take isl_local_space *ls,
935 enum isl_dim_type type, unsigned pos, const char *s);
936 __isl_give isl_local_space *isl_local_space_set_dim_id(
937 __isl_take isl_local_space *ls,
938 enum isl_dim_type type, unsigned pos,
939 __isl_take isl_id *id);
940 __isl_give isl_space *isl_local_space_get_space(
941 __isl_keep isl_local_space *ls);
942 __isl_give isl_aff *isl_local_space_get_div(
943 __isl_keep isl_local_space *ls, int pos);
944 __isl_give isl_local_space *isl_local_space_copy(
945 __isl_keep isl_local_space *ls);
946 void *isl_local_space_free(__isl_take isl_local_space *ls);
948 Two local spaces can be compared using
950 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
951 __isl_keep isl_local_space *ls2);
953 Local spaces can be created from other local spaces
954 using the following functions.
956 __isl_give isl_local_space *isl_local_space_domain(
957 __isl_take isl_local_space *ls);
958 __isl_give isl_local_space *isl_local_space_range(
959 __isl_take isl_local_space *ls);
960 __isl_give isl_local_space *isl_local_space_from_domain(
961 __isl_take isl_local_space *ls);
962 __isl_give isl_local_space *isl_local_space_intersect(
963 __isl_take isl_local_space *ls1,
964 __isl_take isl_local_space *ls2);
965 __isl_give isl_local_space *isl_local_space_add_dims(
966 __isl_take isl_local_space *ls,
967 enum isl_dim_type type, unsigned n);
968 __isl_give isl_local_space *isl_local_space_insert_dims(
969 __isl_take isl_local_space *ls,
970 enum isl_dim_type type, unsigned first, unsigned n);
971 __isl_give isl_local_space *isl_local_space_drop_dims(
972 __isl_take isl_local_space *ls,
973 enum isl_dim_type type, unsigned first, unsigned n);
975 =head2 Input and Output
977 C<isl> supports its own input/output format, which is similar
978 to the C<Omega> format, but also supports the C<PolyLib> format
983 The C<isl> format is similar to that of C<Omega>, but has a different
984 syntax for describing the parameters and allows for the definition
985 of an existentially quantified variable as the integer division
986 of an affine expression.
987 For example, the set of integers C<i> between C<0> and C<n>
988 such that C<i % 10 <= 6> can be described as
990 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
993 A set or relation can have several disjuncts, separated
994 by the keyword C<or>. Each disjunct is either a conjunction
995 of constraints or a projection (C<exists>) of a conjunction
996 of constraints. The constraints are separated by the keyword
999 =head3 C<PolyLib> format
1001 If the represented set is a union, then the first line
1002 contains a single number representing the number of disjuncts.
1003 Otherwise, a line containing the number C<1> is optional.
1005 Each disjunct is represented by a matrix of constraints.
1006 The first line contains two numbers representing
1007 the number of rows and columns,
1008 where the number of rows is equal to the number of constraints
1009 and the number of columns is equal to two plus the number of variables.
1010 The following lines contain the actual rows of the constraint matrix.
1011 In each row, the first column indicates whether the constraint
1012 is an equality (C<0>) or inequality (C<1>). The final column
1013 corresponds to the constant term.
1015 If the set is parametric, then the coefficients of the parameters
1016 appear in the last columns before the constant column.
1017 The coefficients of any existentially quantified variables appear
1018 between those of the set variables and those of the parameters.
1020 =head3 Extended C<PolyLib> format
1022 The extended C<PolyLib> format is nearly identical to the
1023 C<PolyLib> format. The only difference is that the line
1024 containing the number of rows and columns of a constraint matrix
1025 also contains four additional numbers:
1026 the number of output dimensions, the number of input dimensions,
1027 the number of local dimensions (i.e., the number of existentially
1028 quantified variables) and the number of parameters.
1029 For sets, the number of ``output'' dimensions is equal
1030 to the number of set dimensions, while the number of ``input''
1035 #include <isl/set.h>
1036 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1037 isl_ctx *ctx, FILE *input);
1038 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1039 isl_ctx *ctx, const char *str);
1040 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1042 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1045 #include <isl/map.h>
1046 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1047 isl_ctx *ctx, FILE *input);
1048 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1049 isl_ctx *ctx, const char *str);
1050 __isl_give isl_map *isl_map_read_from_file(
1051 isl_ctx *ctx, FILE *input);
1052 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1055 #include <isl/union_set.h>
1056 __isl_give isl_union_set *isl_union_set_read_from_file(
1057 isl_ctx *ctx, FILE *input);
1058 __isl_give isl_union_set *isl_union_set_read_from_str(
1059 isl_ctx *ctx, const char *str);
1061 #include <isl/union_map.h>
1062 __isl_give isl_union_map *isl_union_map_read_from_file(
1063 isl_ctx *ctx, FILE *input);
1064 __isl_give isl_union_map *isl_union_map_read_from_str(
1065 isl_ctx *ctx, const char *str);
1067 The input format is autodetected and may be either the C<PolyLib> format
1068 or the C<isl> format.
1072 Before anything can be printed, an C<isl_printer> needs to
1075 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1077 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1078 void *isl_printer_free(__isl_take isl_printer *printer);
1079 __isl_give char *isl_printer_get_str(
1080 __isl_keep isl_printer *printer);
1082 The printer can be inspected using the following functions.
1084 FILE *isl_printer_get_file(
1085 __isl_keep isl_printer *printer);
1086 int isl_printer_get_output_format(
1087 __isl_keep isl_printer *p);
1089 The behavior of the printer can be modified in various ways
1091 __isl_give isl_printer *isl_printer_set_output_format(
1092 __isl_take isl_printer *p, int output_format);
1093 __isl_give isl_printer *isl_printer_set_indent(
1094 __isl_take isl_printer *p, int indent);
1095 __isl_give isl_printer *isl_printer_indent(
1096 __isl_take isl_printer *p, int indent);
1097 __isl_give isl_printer *isl_printer_set_prefix(
1098 __isl_take isl_printer *p, const char *prefix);
1099 __isl_give isl_printer *isl_printer_set_suffix(
1100 __isl_take isl_printer *p, const char *suffix);
1102 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1103 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1104 and defaults to C<ISL_FORMAT_ISL>.
1105 Each line in the output is indented by C<indent> (set by
1106 C<isl_printer_set_indent>) spaces
1107 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1108 In the C<PolyLib> format output,
1109 the coefficients of the existentially quantified variables
1110 appear between those of the set variables and those
1112 The function C<isl_printer_indent> increases the indentation
1113 by the specified amount (which may be negative).
1115 To actually print something, use
1117 #include <isl/printer.h>
1118 __isl_give isl_printer *isl_printer_print_double(
1119 __isl_take isl_printer *p, double d);
1121 #include <isl/set.h>
1122 __isl_give isl_printer *isl_printer_print_basic_set(
1123 __isl_take isl_printer *printer,
1124 __isl_keep isl_basic_set *bset);
1125 __isl_give isl_printer *isl_printer_print_set(
1126 __isl_take isl_printer *printer,
1127 __isl_keep isl_set *set);
1129 #include <isl/map.h>
1130 __isl_give isl_printer *isl_printer_print_basic_map(
1131 __isl_take isl_printer *printer,
1132 __isl_keep isl_basic_map *bmap);
1133 __isl_give isl_printer *isl_printer_print_map(
1134 __isl_take isl_printer *printer,
1135 __isl_keep isl_map *map);
1137 #include <isl/union_set.h>
1138 __isl_give isl_printer *isl_printer_print_union_set(
1139 __isl_take isl_printer *p,
1140 __isl_keep isl_union_set *uset);
1142 #include <isl/union_map.h>
1143 __isl_give isl_printer *isl_printer_print_union_map(
1144 __isl_take isl_printer *p,
1145 __isl_keep isl_union_map *umap);
1147 When called on a file printer, the following function flushes
1148 the file. When called on a string printer, the buffer is cleared.
1150 __isl_give isl_printer *isl_printer_flush(
1151 __isl_take isl_printer *p);
1153 =head2 Creating New Sets and Relations
1155 C<isl> has functions for creating some standard sets and relations.
1159 =item * Empty sets and relations
1161 __isl_give isl_basic_set *isl_basic_set_empty(
1162 __isl_take isl_space *space);
1163 __isl_give isl_basic_map *isl_basic_map_empty(
1164 __isl_take isl_space *space);
1165 __isl_give isl_set *isl_set_empty(
1166 __isl_take isl_space *space);
1167 __isl_give isl_map *isl_map_empty(
1168 __isl_take isl_space *space);
1169 __isl_give isl_union_set *isl_union_set_empty(
1170 __isl_take isl_space *space);
1171 __isl_give isl_union_map *isl_union_map_empty(
1172 __isl_take isl_space *space);
1174 For C<isl_union_set>s and C<isl_union_map>s, the space
1175 is only used to specify the parameters.
1177 =item * Universe sets and relations
1179 __isl_give isl_basic_set *isl_basic_set_universe(
1180 __isl_take isl_space *space);
1181 __isl_give isl_basic_map *isl_basic_map_universe(
1182 __isl_take isl_space *space);
1183 __isl_give isl_set *isl_set_universe(
1184 __isl_take isl_space *space);
1185 __isl_give isl_map *isl_map_universe(
1186 __isl_take isl_space *space);
1187 __isl_give isl_union_set *isl_union_set_universe(
1188 __isl_take isl_union_set *uset);
1189 __isl_give isl_union_map *isl_union_map_universe(
1190 __isl_take isl_union_map *umap);
1192 The sets and relations constructed by the functions above
1193 contain all integer values, while those constructed by the
1194 functions below only contain non-negative values.
1196 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1197 __isl_take isl_space *space);
1198 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1199 __isl_take isl_space *space);
1200 __isl_give isl_set *isl_set_nat_universe(
1201 __isl_take isl_space *space);
1202 __isl_give isl_map *isl_map_nat_universe(
1203 __isl_take isl_space *space);
1205 =item * Identity relations
1207 __isl_give isl_basic_map *isl_basic_map_identity(
1208 __isl_take isl_space *space);
1209 __isl_give isl_map *isl_map_identity(
1210 __isl_take isl_space *space);
1212 The number of input and output dimensions in C<space> needs
1215 =item * Lexicographic order
1217 __isl_give isl_map *isl_map_lex_lt(
1218 __isl_take isl_space *set_space);
1219 __isl_give isl_map *isl_map_lex_le(
1220 __isl_take isl_space *set_space);
1221 __isl_give isl_map *isl_map_lex_gt(
1222 __isl_take isl_space *set_space);
1223 __isl_give isl_map *isl_map_lex_ge(
1224 __isl_take isl_space *set_space);
1225 __isl_give isl_map *isl_map_lex_lt_first(
1226 __isl_take isl_space *space, unsigned n);
1227 __isl_give isl_map *isl_map_lex_le_first(
1228 __isl_take isl_space *space, unsigned n);
1229 __isl_give isl_map *isl_map_lex_gt_first(
1230 __isl_take isl_space *space, unsigned n);
1231 __isl_give isl_map *isl_map_lex_ge_first(
1232 __isl_take isl_space *space, unsigned n);
1234 The first four functions take a space for a B<set>
1235 and return relations that express that the elements in the domain
1236 are lexicographically less
1237 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1238 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1239 than the elements in the range.
1240 The last four functions take a space for a map
1241 and return relations that express that the first C<n> dimensions
1242 in the domain are lexicographically less
1243 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1244 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1245 than the first C<n> dimensions in the range.
1249 A basic set or relation can be converted to a set or relation
1250 using the following functions.
1252 __isl_give isl_set *isl_set_from_basic_set(
1253 __isl_take isl_basic_set *bset);
1254 __isl_give isl_map *isl_map_from_basic_map(
1255 __isl_take isl_basic_map *bmap);
1257 Sets and relations can be converted to union sets and relations
1258 using the following functions.
1260 __isl_give isl_union_set *isl_union_set_from_basic_set(
1261 __isl_take isl_basic_set *bset);
1262 __isl_give isl_union_map *isl_union_map_from_basic_map(
1263 __isl_take isl_basic_map *bmap);
1264 __isl_give isl_union_set *isl_union_set_from_set(
1265 __isl_take isl_set *set);
1266 __isl_give isl_union_map *isl_union_map_from_map(
1267 __isl_take isl_map *map);
1269 The inverse conversions below can only be used if the input
1270 union set or relation is known to contain elements in exactly one
1273 __isl_give isl_set *isl_set_from_union_set(
1274 __isl_take isl_union_set *uset);
1275 __isl_give isl_map *isl_map_from_union_map(
1276 __isl_take isl_union_map *umap);
1278 A zero-dimensional set can be constructed on a given parameter domain
1279 using the following function.
1281 __isl_give isl_set *isl_set_from_params(
1282 __isl_take isl_set *set);
1284 Sets and relations can be copied and freed again using the following
1287 __isl_give isl_basic_set *isl_basic_set_copy(
1288 __isl_keep isl_basic_set *bset);
1289 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1290 __isl_give isl_union_set *isl_union_set_copy(
1291 __isl_keep isl_union_set *uset);
1292 __isl_give isl_basic_map *isl_basic_map_copy(
1293 __isl_keep isl_basic_map *bmap);
1294 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1295 __isl_give isl_union_map *isl_union_map_copy(
1296 __isl_keep isl_union_map *umap);
1297 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1298 void *isl_set_free(__isl_take isl_set *set);
1299 void *isl_union_set_free(__isl_take isl_union_set *uset);
1300 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1301 void *isl_map_free(__isl_take isl_map *map);
1302 void *isl_union_map_free(__isl_take isl_union_map *umap);
1304 Other sets and relations can be constructed by starting
1305 from a universe set or relation, adding equality and/or
1306 inequality constraints and then projecting out the
1307 existentially quantified variables, if any.
1308 Constraints can be constructed, manipulated and
1309 added to (or removed from) (basic) sets and relations
1310 using the following functions.
1312 #include <isl/constraint.h>
1313 __isl_give isl_constraint *isl_equality_alloc(
1314 __isl_take isl_local_space *ls);
1315 __isl_give isl_constraint *isl_inequality_alloc(
1316 __isl_take isl_local_space *ls);
1317 __isl_give isl_constraint *isl_constraint_set_constant(
1318 __isl_take isl_constraint *constraint, isl_int v);
1319 __isl_give isl_constraint *isl_constraint_set_constant_si(
1320 __isl_take isl_constraint *constraint, int v);
1321 __isl_give isl_constraint *isl_constraint_set_coefficient(
1322 __isl_take isl_constraint *constraint,
1323 enum isl_dim_type type, int pos, isl_int v);
1324 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1325 __isl_take isl_constraint *constraint,
1326 enum isl_dim_type type, int pos, int v);
1327 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1328 __isl_take isl_basic_map *bmap,
1329 __isl_take isl_constraint *constraint);
1330 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1331 __isl_take isl_basic_set *bset,
1332 __isl_take isl_constraint *constraint);
1333 __isl_give isl_map *isl_map_add_constraint(
1334 __isl_take isl_map *map,
1335 __isl_take isl_constraint *constraint);
1336 __isl_give isl_set *isl_set_add_constraint(
1337 __isl_take isl_set *set,
1338 __isl_take isl_constraint *constraint);
1339 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1340 __isl_take isl_basic_set *bset,
1341 __isl_take isl_constraint *constraint);
1343 For example, to create a set containing the even integers
1344 between 10 and 42, you would use the following code.
1347 isl_local_space *ls;
1349 isl_basic_set *bset;
1351 space = isl_space_set_alloc(ctx, 0, 2);
1352 bset = isl_basic_set_universe(isl_space_copy(space));
1353 ls = isl_local_space_from_space(space);
1355 c = isl_equality_alloc(isl_local_space_copy(ls));
1356 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1357 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1358 bset = isl_basic_set_add_constraint(bset, c);
1360 c = isl_inequality_alloc(isl_local_space_copy(ls));
1361 c = isl_constraint_set_constant_si(c, -10);
1362 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1363 bset = isl_basic_set_add_constraint(bset, c);
1365 c = isl_inequality_alloc(ls);
1366 c = isl_constraint_set_constant_si(c, 42);
1367 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1368 bset = isl_basic_set_add_constraint(bset, c);
1370 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1374 isl_basic_set *bset;
1375 bset = isl_basic_set_read_from_str(ctx,
1376 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1378 A basic set or relation can also be constructed from two matrices
1379 describing the equalities and the inequalities.
1381 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1382 __isl_take isl_space *space,
1383 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1384 enum isl_dim_type c1,
1385 enum isl_dim_type c2, enum isl_dim_type c3,
1386 enum isl_dim_type c4);
1387 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1388 __isl_take isl_space *space,
1389 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1390 enum isl_dim_type c1,
1391 enum isl_dim_type c2, enum isl_dim_type c3,
1392 enum isl_dim_type c4, enum isl_dim_type c5);
1394 The C<isl_dim_type> arguments indicate the order in which
1395 different kinds of variables appear in the input matrices
1396 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1397 C<isl_dim_set> and C<isl_dim_div> for sets and
1398 of C<isl_dim_cst>, C<isl_dim_param>,
1399 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1401 A (basic or union) set or relation can also be constructed from a
1402 (union) (piecewise) (multiple) affine expression
1403 or a list of affine expressions
1404 (See L<"Piecewise Quasi Affine Expressions"> and
1405 L<"Piecewise Multiple Quasi Affine Expressions">).
1407 __isl_give isl_basic_map *isl_basic_map_from_aff(
1408 __isl_take isl_aff *aff);
1409 __isl_give isl_map *isl_map_from_aff(
1410 __isl_take isl_aff *aff);
1411 __isl_give isl_set *isl_set_from_pw_aff(
1412 __isl_take isl_pw_aff *pwaff);
1413 __isl_give isl_map *isl_map_from_pw_aff(
1414 __isl_take isl_pw_aff *pwaff);
1415 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1416 __isl_take isl_space *domain_space,
1417 __isl_take isl_aff_list *list);
1418 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1419 __isl_take isl_multi_aff *maff)
1420 __isl_give isl_map *isl_map_from_multi_aff(
1421 __isl_take isl_multi_aff *maff)
1422 __isl_give isl_set *isl_set_from_pw_multi_aff(
1423 __isl_take isl_pw_multi_aff *pma);
1424 __isl_give isl_map *isl_map_from_pw_multi_aff(
1425 __isl_take isl_pw_multi_aff *pma);
1426 __isl_give isl_union_map *
1427 isl_union_map_from_union_pw_multi_aff(
1428 __isl_take isl_union_pw_multi_aff *upma);
1430 The C<domain_dim> argument describes the domain of the resulting
1431 basic relation. It is required because the C<list> may consist
1432 of zero affine expressions.
1434 =head2 Inspecting Sets and Relations
1436 Usually, the user should not have to care about the actual constraints
1437 of the sets and maps, but should instead apply the abstract operations
1438 explained in the following sections.
1439 Occasionally, however, it may be required to inspect the individual
1440 coefficients of the constraints. This section explains how to do so.
1441 In these cases, it may also be useful to have C<isl> compute
1442 an explicit representation of the existentially quantified variables.
1444 __isl_give isl_set *isl_set_compute_divs(
1445 __isl_take isl_set *set);
1446 __isl_give isl_map *isl_map_compute_divs(
1447 __isl_take isl_map *map);
1448 __isl_give isl_union_set *isl_union_set_compute_divs(
1449 __isl_take isl_union_set *uset);
1450 __isl_give isl_union_map *isl_union_map_compute_divs(
1451 __isl_take isl_union_map *umap);
1453 This explicit representation defines the existentially quantified
1454 variables as integer divisions of the other variables, possibly
1455 including earlier existentially quantified variables.
1456 An explicitly represented existentially quantified variable therefore
1457 has a unique value when the values of the other variables are known.
1458 If, furthermore, the same existentials, i.e., existentials
1459 with the same explicit representations, should appear in the
1460 same order in each of the disjuncts of a set or map, then the user should call
1461 either of the following functions.
1463 __isl_give isl_set *isl_set_align_divs(
1464 __isl_take isl_set *set);
1465 __isl_give isl_map *isl_map_align_divs(
1466 __isl_take isl_map *map);
1468 Alternatively, the existentially quantified variables can be removed
1469 using the following functions, which compute an overapproximation.
1471 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1472 __isl_take isl_basic_set *bset);
1473 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1474 __isl_take isl_basic_map *bmap);
1475 __isl_give isl_set *isl_set_remove_divs(
1476 __isl_take isl_set *set);
1477 __isl_give isl_map *isl_map_remove_divs(
1478 __isl_take isl_map *map);
1480 It is also possible to only remove those divs that are defined
1481 in terms of a given range of dimensions or only those for which
1482 no explicit representation is known.
1484 __isl_give isl_basic_set *
1485 isl_basic_set_remove_divs_involving_dims(
1486 __isl_take isl_basic_set *bset,
1487 enum isl_dim_type type,
1488 unsigned first, unsigned n);
1489 __isl_give isl_basic_map *
1490 isl_basic_map_remove_divs_involving_dims(
1491 __isl_take isl_basic_map *bmap,
1492 enum isl_dim_type type,
1493 unsigned first, unsigned n);
1494 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1495 __isl_take isl_set *set, enum isl_dim_type type,
1496 unsigned first, unsigned n);
1497 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1498 __isl_take isl_map *map, enum isl_dim_type type,
1499 unsigned first, unsigned n);
1501 __isl_give isl_basic_set *
1502 isl_basic_set_remove_unknown_divs(
1503 __isl_take isl_basic_set *bset);
1504 __isl_give isl_set *isl_set_remove_unknown_divs(
1505 __isl_take isl_set *set);
1506 __isl_give isl_map *isl_map_remove_unknown_divs(
1507 __isl_take isl_map *map);
1509 To iterate over all the sets or maps in a union set or map, use
1511 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1512 int (*fn)(__isl_take isl_set *set, void *user),
1514 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1515 int (*fn)(__isl_take isl_map *map, void *user),
1518 The number of sets or maps in a union set or map can be obtained
1521 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1522 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1524 To extract the set or map in a given space from a union, use
1526 __isl_give isl_set *isl_union_set_extract_set(
1527 __isl_keep isl_union_set *uset,
1528 __isl_take isl_space *space);
1529 __isl_give isl_map *isl_union_map_extract_map(
1530 __isl_keep isl_union_map *umap,
1531 __isl_take isl_space *space);
1533 To iterate over all the basic sets or maps in a set or map, use
1535 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1536 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1538 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1539 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1542 The callback function C<fn> should return 0 if successful and
1543 -1 if an error occurs. In the latter case, or if any other error
1544 occurs, the above functions will return -1.
1546 It should be noted that C<isl> does not guarantee that
1547 the basic sets or maps passed to C<fn> are disjoint.
1548 If this is required, then the user should call one of
1549 the following functions first.
1551 __isl_give isl_set *isl_set_make_disjoint(
1552 __isl_take isl_set *set);
1553 __isl_give isl_map *isl_map_make_disjoint(
1554 __isl_take isl_map *map);
1556 The number of basic sets in a set can be obtained
1559 int isl_set_n_basic_set(__isl_keep isl_set *set);
1561 To iterate over the constraints of a basic set or map, use
1563 #include <isl/constraint.h>
1565 int isl_basic_set_n_constraint(
1566 __isl_keep isl_basic_set *bset);
1567 int isl_basic_set_foreach_constraint(
1568 __isl_keep isl_basic_set *bset,
1569 int (*fn)(__isl_take isl_constraint *c, void *user),
1571 int isl_basic_map_foreach_constraint(
1572 __isl_keep isl_basic_map *bmap,
1573 int (*fn)(__isl_take isl_constraint *c, void *user),
1575 void *isl_constraint_free(__isl_take isl_constraint *c);
1577 Again, the callback function C<fn> should return 0 if successful and
1578 -1 if an error occurs. In the latter case, or if any other error
1579 occurs, the above functions will return -1.
1580 The constraint C<c> represents either an equality or an inequality.
1581 Use the following function to find out whether a constraint
1582 represents an equality. If not, it represents an inequality.
1584 int isl_constraint_is_equality(
1585 __isl_keep isl_constraint *constraint);
1587 The coefficients of the constraints can be inspected using
1588 the following functions.
1590 int isl_constraint_is_lower_bound(
1591 __isl_keep isl_constraint *constraint,
1592 enum isl_dim_type type, unsigned pos);
1593 int isl_constraint_is_upper_bound(
1594 __isl_keep isl_constraint *constraint,
1595 enum isl_dim_type type, unsigned pos);
1596 void isl_constraint_get_constant(
1597 __isl_keep isl_constraint *constraint, isl_int *v);
1598 void isl_constraint_get_coefficient(
1599 __isl_keep isl_constraint *constraint,
1600 enum isl_dim_type type, int pos, isl_int *v);
1601 int isl_constraint_involves_dims(
1602 __isl_keep isl_constraint *constraint,
1603 enum isl_dim_type type, unsigned first, unsigned n);
1605 The explicit representations of the existentially quantified
1606 variables can be inspected using the following function.
1607 Note that the user is only allowed to use this function
1608 if the inspected set or map is the result of a call
1609 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1610 The existentially quantified variable is equal to the floor
1611 of the returned affine expression. The affine expression
1612 itself can be inspected using the functions in
1613 L<"Piecewise Quasi Affine Expressions">.
1615 __isl_give isl_aff *isl_constraint_get_div(
1616 __isl_keep isl_constraint *constraint, int pos);
1618 To obtain the constraints of a basic set or map in matrix
1619 form, use the following functions.
1621 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1622 __isl_keep isl_basic_set *bset,
1623 enum isl_dim_type c1, enum isl_dim_type c2,
1624 enum isl_dim_type c3, enum isl_dim_type c4);
1625 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1626 __isl_keep isl_basic_set *bset,
1627 enum isl_dim_type c1, enum isl_dim_type c2,
1628 enum isl_dim_type c3, enum isl_dim_type c4);
1629 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1630 __isl_keep isl_basic_map *bmap,
1631 enum isl_dim_type c1,
1632 enum isl_dim_type c2, enum isl_dim_type c3,
1633 enum isl_dim_type c4, enum isl_dim_type c5);
1634 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1635 __isl_keep isl_basic_map *bmap,
1636 enum isl_dim_type c1,
1637 enum isl_dim_type c2, enum isl_dim_type c3,
1638 enum isl_dim_type c4, enum isl_dim_type c5);
1640 The C<isl_dim_type> arguments dictate the order in which
1641 different kinds of variables appear in the resulting matrix
1642 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1643 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1645 The number of parameters, input, output or set dimensions can
1646 be obtained using the following functions.
1648 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1649 enum isl_dim_type type);
1650 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1651 enum isl_dim_type type);
1652 unsigned isl_set_dim(__isl_keep isl_set *set,
1653 enum isl_dim_type type);
1654 unsigned isl_map_dim(__isl_keep isl_map *map,
1655 enum isl_dim_type type);
1657 To check whether the description of a set or relation depends
1658 on one or more given dimensions, it is not necessary to iterate over all
1659 constraints. Instead the following functions can be used.
1661 int isl_basic_set_involves_dims(
1662 __isl_keep isl_basic_set *bset,
1663 enum isl_dim_type type, unsigned first, unsigned n);
1664 int isl_set_involves_dims(__isl_keep isl_set *set,
1665 enum isl_dim_type type, unsigned first, unsigned n);
1666 int isl_basic_map_involves_dims(
1667 __isl_keep isl_basic_map *bmap,
1668 enum isl_dim_type type, unsigned first, unsigned n);
1669 int isl_map_involves_dims(__isl_keep isl_map *map,
1670 enum isl_dim_type type, unsigned first, unsigned n);
1672 Similarly, the following functions can be used to check whether
1673 a given dimension is involved in any lower or upper bound.
1675 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1676 enum isl_dim_type type, unsigned pos);
1677 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1678 enum isl_dim_type type, unsigned pos);
1680 Note that these functions return true even if there is a bound on
1681 the dimension on only some of the basic sets of C<set>.
1682 To check if they have a bound for all of the basic sets in C<set>,
1683 use the following functions instead.
1685 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1686 enum isl_dim_type type, unsigned pos);
1687 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1688 enum isl_dim_type type, unsigned pos);
1690 The identifiers or names of the domain and range spaces of a set
1691 or relation can be read off or set using the following functions.
1693 __isl_give isl_set *isl_set_set_tuple_id(
1694 __isl_take isl_set *set, __isl_take isl_id *id);
1695 __isl_give isl_set *isl_set_reset_tuple_id(
1696 __isl_take isl_set *set);
1697 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1698 __isl_give isl_id *isl_set_get_tuple_id(
1699 __isl_keep isl_set *set);
1700 __isl_give isl_map *isl_map_set_tuple_id(
1701 __isl_take isl_map *map, enum isl_dim_type type,
1702 __isl_take isl_id *id);
1703 __isl_give isl_map *isl_map_reset_tuple_id(
1704 __isl_take isl_map *map, enum isl_dim_type type);
1705 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1706 enum isl_dim_type type);
1707 __isl_give isl_id *isl_map_get_tuple_id(
1708 __isl_keep isl_map *map, enum isl_dim_type type);
1710 const char *isl_basic_set_get_tuple_name(
1711 __isl_keep isl_basic_set *bset);
1712 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1713 __isl_take isl_basic_set *set, const char *s);
1714 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1715 const char *isl_set_get_tuple_name(
1716 __isl_keep isl_set *set);
1717 const char *isl_basic_map_get_tuple_name(
1718 __isl_keep isl_basic_map *bmap,
1719 enum isl_dim_type type);
1720 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1721 __isl_take isl_basic_map *bmap,
1722 enum isl_dim_type type, const char *s);
1723 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1724 enum isl_dim_type type);
1725 const char *isl_map_get_tuple_name(
1726 __isl_keep isl_map *map,
1727 enum isl_dim_type type);
1729 As with C<isl_space_get_tuple_name>, the value returned points to
1730 an internal data structure.
1731 The identifiers, positions or names of individual dimensions can be
1732 read off using the following functions.
1734 __isl_give isl_id *isl_basic_set_get_dim_id(
1735 __isl_keep isl_basic_set *bset,
1736 enum isl_dim_type type, unsigned pos);
1737 __isl_give isl_set *isl_set_set_dim_id(
1738 __isl_take isl_set *set, enum isl_dim_type type,
1739 unsigned pos, __isl_take isl_id *id);
1740 int isl_set_has_dim_id(__isl_keep isl_set *set,
1741 enum isl_dim_type type, unsigned pos);
1742 __isl_give isl_id *isl_set_get_dim_id(
1743 __isl_keep isl_set *set, enum isl_dim_type type,
1745 int isl_basic_map_has_dim_id(
1746 __isl_keep isl_basic_map *bmap,
1747 enum isl_dim_type type, unsigned pos);
1748 __isl_give isl_map *isl_map_set_dim_id(
1749 __isl_take isl_map *map, enum isl_dim_type type,
1750 unsigned pos, __isl_take isl_id *id);
1751 int isl_map_has_dim_id(__isl_keep isl_map *map,
1752 enum isl_dim_type type, unsigned pos);
1753 __isl_give isl_id *isl_map_get_dim_id(
1754 __isl_keep isl_map *map, enum isl_dim_type type,
1757 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1758 enum isl_dim_type type, __isl_keep isl_id *id);
1759 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1760 enum isl_dim_type type, __isl_keep isl_id *id);
1761 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1762 enum isl_dim_type type, const char *name);
1763 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1764 enum isl_dim_type type, const char *name);
1766 const char *isl_constraint_get_dim_name(
1767 __isl_keep isl_constraint *constraint,
1768 enum isl_dim_type type, unsigned pos);
1769 const char *isl_basic_set_get_dim_name(
1770 __isl_keep isl_basic_set *bset,
1771 enum isl_dim_type type, unsigned pos);
1772 int isl_set_has_dim_name(__isl_keep isl_set *set,
1773 enum isl_dim_type type, unsigned pos);
1774 const char *isl_set_get_dim_name(
1775 __isl_keep isl_set *set,
1776 enum isl_dim_type type, unsigned pos);
1777 const char *isl_basic_map_get_dim_name(
1778 __isl_keep isl_basic_map *bmap,
1779 enum isl_dim_type type, unsigned pos);
1780 int isl_map_has_dim_name(__isl_keep isl_map *map,
1781 enum isl_dim_type type, unsigned pos);
1782 const char *isl_map_get_dim_name(
1783 __isl_keep isl_map *map,
1784 enum isl_dim_type type, unsigned pos);
1786 These functions are mostly useful to obtain the identifiers, positions
1787 or names of the parameters. Identifiers of individual dimensions are
1788 essentially only useful for printing. They are ignored by all other
1789 operations and may not be preserved across those operations.
1793 =head3 Unary Properties
1799 The following functions test whether the given set or relation
1800 contains any integer points. The ``plain'' variants do not perform
1801 any computations, but simply check if the given set or relation
1802 is already known to be empty.
1804 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1805 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1806 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1807 int isl_set_is_empty(__isl_keep isl_set *set);
1808 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1809 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1810 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1811 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1812 int isl_map_is_empty(__isl_keep isl_map *map);
1813 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1815 =item * Universality
1817 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1818 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1819 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1821 =item * Single-valuedness
1823 int isl_basic_map_is_single_valued(
1824 __isl_keep isl_basic_map *bmap);
1825 int isl_map_plain_is_single_valued(
1826 __isl_keep isl_map *map);
1827 int isl_map_is_single_valued(__isl_keep isl_map *map);
1828 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1832 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1833 int isl_map_is_injective(__isl_keep isl_map *map);
1834 int isl_union_map_plain_is_injective(
1835 __isl_keep isl_union_map *umap);
1836 int isl_union_map_is_injective(
1837 __isl_keep isl_union_map *umap);
1841 int isl_map_is_bijective(__isl_keep isl_map *map);
1842 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1846 int isl_basic_map_plain_is_fixed(
1847 __isl_keep isl_basic_map *bmap,
1848 enum isl_dim_type type, unsigned pos,
1850 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1851 enum isl_dim_type type, unsigned pos,
1853 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1854 enum isl_dim_type type, unsigned pos,
1857 Check if the relation obviously lies on a hyperplane where the given dimension
1858 has a fixed value and if so, return that value in C<*val>.
1862 To check whether a set is a parameter domain, use this function:
1864 int isl_set_is_params(__isl_keep isl_set *set);
1865 int isl_union_set_is_params(
1866 __isl_keep isl_union_set *uset);
1870 The following functions check whether the domain of the given
1871 (basic) set is a wrapped relation.
1873 int isl_basic_set_is_wrapping(
1874 __isl_keep isl_basic_set *bset);
1875 int isl_set_is_wrapping(__isl_keep isl_set *set);
1877 =item * Internal Product
1879 int isl_basic_map_can_zip(
1880 __isl_keep isl_basic_map *bmap);
1881 int isl_map_can_zip(__isl_keep isl_map *map);
1883 Check whether the product of domain and range of the given relation
1885 i.e., whether both domain and range are nested relations.
1889 int isl_basic_map_can_curry(
1890 __isl_keep isl_basic_map *bmap);
1891 int isl_map_can_curry(__isl_keep isl_map *map);
1893 Check whether the domain of the (basic) relation is a wrapped relation.
1895 int isl_basic_map_can_uncurry(
1896 __isl_keep isl_basic_map *bmap);
1897 int isl_map_can_uncurry(__isl_keep isl_map *map);
1899 Check whether the range of the (basic) relation is a wrapped relation.
1903 =head3 Binary Properties
1909 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1910 __isl_keep isl_set *set2);
1911 int isl_set_is_equal(__isl_keep isl_set *set1,
1912 __isl_keep isl_set *set2);
1913 int isl_union_set_is_equal(
1914 __isl_keep isl_union_set *uset1,
1915 __isl_keep isl_union_set *uset2);
1916 int isl_basic_map_is_equal(
1917 __isl_keep isl_basic_map *bmap1,
1918 __isl_keep isl_basic_map *bmap2);
1919 int isl_map_is_equal(__isl_keep isl_map *map1,
1920 __isl_keep isl_map *map2);
1921 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1922 __isl_keep isl_map *map2);
1923 int isl_union_map_is_equal(
1924 __isl_keep isl_union_map *umap1,
1925 __isl_keep isl_union_map *umap2);
1927 =item * Disjointness
1929 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1930 __isl_keep isl_set *set2);
1931 int isl_set_is_disjoint(__isl_keep isl_set *set1,
1932 __isl_keep isl_set *set2);
1933 int isl_map_is_disjoint(__isl_keep isl_map *map1,
1934 __isl_keep isl_map *map2);
1938 int isl_basic_set_is_subset(
1939 __isl_keep isl_basic_set *bset1,
1940 __isl_keep isl_basic_set *bset2);
1941 int isl_set_is_subset(__isl_keep isl_set *set1,
1942 __isl_keep isl_set *set2);
1943 int isl_set_is_strict_subset(
1944 __isl_keep isl_set *set1,
1945 __isl_keep isl_set *set2);
1946 int isl_union_set_is_subset(
1947 __isl_keep isl_union_set *uset1,
1948 __isl_keep isl_union_set *uset2);
1949 int isl_union_set_is_strict_subset(
1950 __isl_keep isl_union_set *uset1,
1951 __isl_keep isl_union_set *uset2);
1952 int isl_basic_map_is_subset(
1953 __isl_keep isl_basic_map *bmap1,
1954 __isl_keep isl_basic_map *bmap2);
1955 int isl_basic_map_is_strict_subset(
1956 __isl_keep isl_basic_map *bmap1,
1957 __isl_keep isl_basic_map *bmap2);
1958 int isl_map_is_subset(
1959 __isl_keep isl_map *map1,
1960 __isl_keep isl_map *map2);
1961 int isl_map_is_strict_subset(
1962 __isl_keep isl_map *map1,
1963 __isl_keep isl_map *map2);
1964 int isl_union_map_is_subset(
1965 __isl_keep isl_union_map *umap1,
1966 __isl_keep isl_union_map *umap2);
1967 int isl_union_map_is_strict_subset(
1968 __isl_keep isl_union_map *umap1,
1969 __isl_keep isl_union_map *umap2);
1971 Check whether the first argument is a (strict) subset of the
1976 int isl_set_plain_cmp(__isl_keep isl_set *set1,
1977 __isl_keep isl_set *set2);
1979 This function is useful for sorting C<isl_set>s.
1980 The order depends on the internal representation of the inputs.
1981 The order is fixed over different calls to the function (assuming
1982 the internal representation of the inputs has not changed), but may
1983 change over different versions of C<isl>.
1987 =head2 Unary Operations
1993 __isl_give isl_set *isl_set_complement(
1994 __isl_take isl_set *set);
1995 __isl_give isl_map *isl_map_complement(
1996 __isl_take isl_map *map);
2000 __isl_give isl_basic_map *isl_basic_map_reverse(
2001 __isl_take isl_basic_map *bmap);
2002 __isl_give isl_map *isl_map_reverse(
2003 __isl_take isl_map *map);
2004 __isl_give isl_union_map *isl_union_map_reverse(
2005 __isl_take isl_union_map *umap);
2009 __isl_give isl_basic_set *isl_basic_set_project_out(
2010 __isl_take isl_basic_set *bset,
2011 enum isl_dim_type type, unsigned first, unsigned n);
2012 __isl_give isl_basic_map *isl_basic_map_project_out(
2013 __isl_take isl_basic_map *bmap,
2014 enum isl_dim_type type, unsigned first, unsigned n);
2015 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2016 enum isl_dim_type type, unsigned first, unsigned n);
2017 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2018 enum isl_dim_type type, unsigned first, unsigned n);
2019 __isl_give isl_basic_set *isl_basic_set_params(
2020 __isl_take isl_basic_set *bset);
2021 __isl_give isl_basic_set *isl_basic_map_domain(
2022 __isl_take isl_basic_map *bmap);
2023 __isl_give isl_basic_set *isl_basic_map_range(
2024 __isl_take isl_basic_map *bmap);
2025 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2026 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2027 __isl_give isl_set *isl_map_domain(
2028 __isl_take isl_map *bmap);
2029 __isl_give isl_set *isl_map_range(
2030 __isl_take isl_map *map);
2031 __isl_give isl_set *isl_union_set_params(
2032 __isl_take isl_union_set *uset);
2033 __isl_give isl_set *isl_union_map_params(
2034 __isl_take isl_union_map *umap);
2035 __isl_give isl_union_set *isl_union_map_domain(
2036 __isl_take isl_union_map *umap);
2037 __isl_give isl_union_set *isl_union_map_range(
2038 __isl_take isl_union_map *umap);
2040 __isl_give isl_basic_map *isl_basic_map_domain_map(
2041 __isl_take isl_basic_map *bmap);
2042 __isl_give isl_basic_map *isl_basic_map_range_map(
2043 __isl_take isl_basic_map *bmap);
2044 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2045 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2046 __isl_give isl_union_map *isl_union_map_domain_map(
2047 __isl_take isl_union_map *umap);
2048 __isl_give isl_union_map *isl_union_map_range_map(
2049 __isl_take isl_union_map *umap);
2051 The functions above construct a (basic, regular or union) relation
2052 that maps (a wrapped version of) the input relation to its domain or range.
2056 __isl_give isl_basic_set *isl_basic_set_eliminate(
2057 __isl_take isl_basic_set *bset,
2058 enum isl_dim_type type,
2059 unsigned first, unsigned n);
2060 __isl_give isl_set *isl_set_eliminate(
2061 __isl_take isl_set *set, enum isl_dim_type type,
2062 unsigned first, unsigned n);
2063 __isl_give isl_basic_map *isl_basic_map_eliminate(
2064 __isl_take isl_basic_map *bmap,
2065 enum isl_dim_type type,
2066 unsigned first, unsigned n);
2067 __isl_give isl_map *isl_map_eliminate(
2068 __isl_take isl_map *map, enum isl_dim_type type,
2069 unsigned first, unsigned n);
2071 Eliminate the coefficients for the given dimensions from the constraints,
2072 without removing the dimensions.
2076 __isl_give isl_basic_set *isl_basic_set_fix(
2077 __isl_take isl_basic_set *bset,
2078 enum isl_dim_type type, unsigned pos,
2080 __isl_give isl_basic_set *isl_basic_set_fix_si(
2081 __isl_take isl_basic_set *bset,
2082 enum isl_dim_type type, unsigned pos, int value);
2083 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2084 enum isl_dim_type type, unsigned pos,
2086 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2087 enum isl_dim_type type, unsigned pos, int value);
2088 __isl_give isl_basic_map *isl_basic_map_fix_si(
2089 __isl_take isl_basic_map *bmap,
2090 enum isl_dim_type type, unsigned pos, int value);
2091 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
2092 enum isl_dim_type type, unsigned pos,
2094 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2095 enum isl_dim_type type, unsigned pos, int value);
2097 Intersect the set or relation with the hyperplane where the given
2098 dimension has the fixed given value.
2100 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2101 __isl_take isl_basic_map *bmap,
2102 enum isl_dim_type type, unsigned pos, int value);
2103 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2104 __isl_take isl_basic_map *bmap,
2105 enum isl_dim_type type, unsigned pos, int value);
2106 __isl_give isl_set *isl_set_lower_bound(
2107 __isl_take isl_set *set,
2108 enum isl_dim_type type, unsigned pos,
2110 __isl_give isl_set *isl_set_lower_bound_si(
2111 __isl_take isl_set *set,
2112 enum isl_dim_type type, unsigned pos, int value);
2113 __isl_give isl_map *isl_map_lower_bound_si(
2114 __isl_take isl_map *map,
2115 enum isl_dim_type type, unsigned pos, int value);
2116 __isl_give isl_set *isl_set_upper_bound(
2117 __isl_take isl_set *set,
2118 enum isl_dim_type type, unsigned pos,
2120 __isl_give isl_set *isl_set_upper_bound_si(
2121 __isl_take isl_set *set,
2122 enum isl_dim_type type, unsigned pos, int value);
2123 __isl_give isl_map *isl_map_upper_bound_si(
2124 __isl_take isl_map *map,
2125 enum isl_dim_type type, unsigned pos, int value);
2127 Intersect the set or relation with the half-space where the given
2128 dimension has a value bounded by the fixed given value.
2130 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2131 enum isl_dim_type type1, int pos1,
2132 enum isl_dim_type type2, int pos2);
2133 __isl_give isl_basic_map *isl_basic_map_equate(
2134 __isl_take isl_basic_map *bmap,
2135 enum isl_dim_type type1, int pos1,
2136 enum isl_dim_type type2, int pos2);
2137 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2138 enum isl_dim_type type1, int pos1,
2139 enum isl_dim_type type2, int pos2);
2141 Intersect the set or relation with the hyperplane where the given
2142 dimensions are equal to each other.
2144 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2145 enum isl_dim_type type1, int pos1,
2146 enum isl_dim_type type2, int pos2);
2148 Intersect the relation with the hyperplane where the given
2149 dimensions have opposite values.
2151 __isl_give isl_basic_map *isl_basic_map_order_ge(
2152 __isl_take isl_basic_map *bmap,
2153 enum isl_dim_type type1, int pos1,
2154 enum isl_dim_type type2, int pos2);
2155 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2156 enum isl_dim_type type1, int pos1,
2157 enum isl_dim_type type2, int pos2);
2158 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2159 enum isl_dim_type type1, int pos1,
2160 enum isl_dim_type type2, int pos2);
2162 Intersect the relation with the half-space where the given
2163 dimensions satisfy the given ordering.
2167 __isl_give isl_map *isl_set_identity(
2168 __isl_take isl_set *set);
2169 __isl_give isl_union_map *isl_union_set_identity(
2170 __isl_take isl_union_set *uset);
2172 Construct an identity relation on the given (union) set.
2176 __isl_give isl_basic_set *isl_basic_map_deltas(
2177 __isl_take isl_basic_map *bmap);
2178 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2179 __isl_give isl_union_set *isl_union_map_deltas(
2180 __isl_take isl_union_map *umap);
2182 These functions return a (basic) set containing the differences
2183 between image elements and corresponding domain elements in the input.
2185 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2186 __isl_take isl_basic_map *bmap);
2187 __isl_give isl_map *isl_map_deltas_map(
2188 __isl_take isl_map *map);
2189 __isl_give isl_union_map *isl_union_map_deltas_map(
2190 __isl_take isl_union_map *umap);
2192 The functions above construct a (basic, regular or union) relation
2193 that maps (a wrapped version of) the input relation to its delta set.
2197 Simplify the representation of a set or relation by trying
2198 to combine pairs of basic sets or relations into a single
2199 basic set or relation.
2201 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2202 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2203 __isl_give isl_union_set *isl_union_set_coalesce(
2204 __isl_take isl_union_set *uset);
2205 __isl_give isl_union_map *isl_union_map_coalesce(
2206 __isl_take isl_union_map *umap);
2208 One of the methods for combining pairs of basic sets or relations
2209 can result in coefficients that are much larger than those that appear
2210 in the constraints of the input. By default, the coefficients are
2211 not allowed to grow larger, but this can be changed by unsetting
2212 the following option.
2214 int isl_options_set_coalesce_bounded_wrapping(
2215 isl_ctx *ctx, int val);
2216 int isl_options_get_coalesce_bounded_wrapping(
2219 =item * Detecting equalities
2221 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2222 __isl_take isl_basic_set *bset);
2223 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2224 __isl_take isl_basic_map *bmap);
2225 __isl_give isl_set *isl_set_detect_equalities(
2226 __isl_take isl_set *set);
2227 __isl_give isl_map *isl_map_detect_equalities(
2228 __isl_take isl_map *map);
2229 __isl_give isl_union_set *isl_union_set_detect_equalities(
2230 __isl_take isl_union_set *uset);
2231 __isl_give isl_union_map *isl_union_map_detect_equalities(
2232 __isl_take isl_union_map *umap);
2234 Simplify the representation of a set or relation by detecting implicit
2237 =item * Removing redundant constraints
2239 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2240 __isl_take isl_basic_set *bset);
2241 __isl_give isl_set *isl_set_remove_redundancies(
2242 __isl_take isl_set *set);
2243 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2244 __isl_take isl_basic_map *bmap);
2245 __isl_give isl_map *isl_map_remove_redundancies(
2246 __isl_take isl_map *map);
2250 __isl_give isl_basic_set *isl_set_convex_hull(
2251 __isl_take isl_set *set);
2252 __isl_give isl_basic_map *isl_map_convex_hull(
2253 __isl_take isl_map *map);
2255 If the input set or relation has any existentially quantified
2256 variables, then the result of these operations is currently undefined.
2260 __isl_give isl_basic_set *
2261 isl_set_unshifted_simple_hull(
2262 __isl_take isl_set *set);
2263 __isl_give isl_basic_map *
2264 isl_map_unshifted_simple_hull(
2265 __isl_take isl_map *map);
2266 __isl_give isl_basic_set *isl_set_simple_hull(
2267 __isl_take isl_set *set);
2268 __isl_give isl_basic_map *isl_map_simple_hull(
2269 __isl_take isl_map *map);
2270 __isl_give isl_union_map *isl_union_map_simple_hull(
2271 __isl_take isl_union_map *umap);
2273 These functions compute a single basic set or relation
2274 that contains the whole input set or relation.
2275 In particular, the output is described by translates
2276 of the constraints describing the basic sets or relations in the input.
2277 In case of C<isl_set_unshifted_simple_hull>, only the original
2278 constraints are used, without any translation.
2282 (See \autoref{s:simple hull}.)
2288 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2289 __isl_take isl_basic_set *bset);
2290 __isl_give isl_basic_set *isl_set_affine_hull(
2291 __isl_take isl_set *set);
2292 __isl_give isl_union_set *isl_union_set_affine_hull(
2293 __isl_take isl_union_set *uset);
2294 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2295 __isl_take isl_basic_map *bmap);
2296 __isl_give isl_basic_map *isl_map_affine_hull(
2297 __isl_take isl_map *map);
2298 __isl_give isl_union_map *isl_union_map_affine_hull(
2299 __isl_take isl_union_map *umap);
2301 In case of union sets and relations, the affine hull is computed
2304 =item * Polyhedral hull
2306 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2307 __isl_take isl_set *set);
2308 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2309 __isl_take isl_map *map);
2310 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2311 __isl_take isl_union_set *uset);
2312 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2313 __isl_take isl_union_map *umap);
2315 These functions compute a single basic set or relation
2316 not involving any existentially quantified variables
2317 that contains the whole input set or relation.
2318 In case of union sets and relations, the polyhedral hull is computed
2321 =item * Other approximations
2323 __isl_give isl_basic_set *
2324 isl_basic_set_drop_constraints_involving_dims(
2325 __isl_take isl_basic_set *bset,
2326 enum isl_dim_type type,
2327 unsigned first, unsigned n);
2328 __isl_give isl_basic_set *
2329 isl_basic_set_drop_constraints_not_involving_dims(
2330 __isl_take isl_basic_set *bset,
2331 enum isl_dim_type type,
2332 unsigned first, unsigned n);
2333 __isl_give isl_set *
2334 isl_set_drop_constraints_involving_dims(
2335 __isl_take isl_set *set,
2336 enum isl_dim_type type,
2337 unsigned first, unsigned n);
2338 __isl_give isl_map *
2339 isl_map_drop_constraints_involving_dims(
2340 __isl_take isl_map *map,
2341 enum isl_dim_type type,
2342 unsigned first, unsigned n);
2344 These functions drop any constraints (not) involving the specified dimensions.
2345 Note that the result depends on the representation of the input.
2349 __isl_give isl_basic_set *isl_basic_set_sample(
2350 __isl_take isl_basic_set *bset);
2351 __isl_give isl_basic_set *isl_set_sample(
2352 __isl_take isl_set *set);
2353 __isl_give isl_basic_map *isl_basic_map_sample(
2354 __isl_take isl_basic_map *bmap);
2355 __isl_give isl_basic_map *isl_map_sample(
2356 __isl_take isl_map *map);
2358 If the input (basic) set or relation is non-empty, then return
2359 a singleton subset of the input. Otherwise, return an empty set.
2361 =item * Optimization
2363 #include <isl/ilp.h>
2364 enum isl_lp_result isl_basic_set_max(
2365 __isl_keep isl_basic_set *bset,
2366 __isl_keep isl_aff *obj, isl_int *opt)
2367 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2368 __isl_keep isl_aff *obj, isl_int *opt);
2369 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2370 __isl_keep isl_aff *obj, isl_int *opt);
2372 Compute the minimum or maximum of the integer affine expression C<obj>
2373 over the points in C<set>, returning the result in C<opt>.
2374 The return value may be one of C<isl_lp_error>,
2375 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2377 =item * Parametric optimization
2379 __isl_give isl_pw_aff *isl_set_dim_min(
2380 __isl_take isl_set *set, int pos);
2381 __isl_give isl_pw_aff *isl_set_dim_max(
2382 __isl_take isl_set *set, int pos);
2383 __isl_give isl_pw_aff *isl_map_dim_max(
2384 __isl_take isl_map *map, int pos);
2386 Compute the minimum or maximum of the given set or output dimension
2387 as a function of the parameters (and input dimensions), but independently
2388 of the other set or output dimensions.
2389 For lexicographic optimization, see L<"Lexicographic Optimization">.
2393 The following functions compute either the set of (rational) coefficient
2394 values of valid constraints for the given set or the set of (rational)
2395 values satisfying the constraints with coefficients from the given set.
2396 Internally, these two sets of functions perform essentially the
2397 same operations, except that the set of coefficients is assumed to
2398 be a cone, while the set of values may be any polyhedron.
2399 The current implementation is based on the Farkas lemma and
2400 Fourier-Motzkin elimination, but this may change or be made optional
2401 in future. In particular, future implementations may use different
2402 dualization algorithms or skip the elimination step.
2404 __isl_give isl_basic_set *isl_basic_set_coefficients(
2405 __isl_take isl_basic_set *bset);
2406 __isl_give isl_basic_set *isl_set_coefficients(
2407 __isl_take isl_set *set);
2408 __isl_give isl_union_set *isl_union_set_coefficients(
2409 __isl_take isl_union_set *bset);
2410 __isl_give isl_basic_set *isl_basic_set_solutions(
2411 __isl_take isl_basic_set *bset);
2412 __isl_give isl_basic_set *isl_set_solutions(
2413 __isl_take isl_set *set);
2414 __isl_give isl_union_set *isl_union_set_solutions(
2415 __isl_take isl_union_set *bset);
2419 __isl_give isl_map *isl_map_fixed_power(
2420 __isl_take isl_map *map, isl_int exp);
2421 __isl_give isl_union_map *isl_union_map_fixed_power(
2422 __isl_take isl_union_map *umap, isl_int exp);
2424 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2425 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2426 of C<map> is computed.
2428 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2430 __isl_give isl_union_map *isl_union_map_power(
2431 __isl_take isl_union_map *umap, int *exact);
2433 Compute a parametric representation for all positive powers I<k> of C<map>.
2434 The result maps I<k> to a nested relation corresponding to the
2435 I<k>th power of C<map>.
2436 The result may be an overapproximation. If the result is known to be exact,
2437 then C<*exact> is set to C<1>.
2439 =item * Transitive closure
2441 __isl_give isl_map *isl_map_transitive_closure(
2442 __isl_take isl_map *map, int *exact);
2443 __isl_give isl_union_map *isl_union_map_transitive_closure(
2444 __isl_take isl_union_map *umap, int *exact);
2446 Compute the transitive closure of C<map>.
2447 The result may be an overapproximation. If the result is known to be exact,
2448 then C<*exact> is set to C<1>.
2450 =item * Reaching path lengths
2452 __isl_give isl_map *isl_map_reaching_path_lengths(
2453 __isl_take isl_map *map, int *exact);
2455 Compute a relation that maps each element in the range of C<map>
2456 to the lengths of all paths composed of edges in C<map> that
2457 end up in the given element.
2458 The result may be an overapproximation. If the result is known to be exact,
2459 then C<*exact> is set to C<1>.
2460 To compute the I<maximal> path length, the resulting relation
2461 should be postprocessed by C<isl_map_lexmax>.
2462 In particular, if the input relation is a dependence relation
2463 (mapping sources to sinks), then the maximal path length corresponds
2464 to the free schedule.
2465 Note, however, that C<isl_map_lexmax> expects the maximum to be
2466 finite, so if the path lengths are unbounded (possibly due to
2467 the overapproximation), then you will get an error message.
2471 __isl_give isl_basic_set *isl_basic_map_wrap(
2472 __isl_take isl_basic_map *bmap);
2473 __isl_give isl_set *isl_map_wrap(
2474 __isl_take isl_map *map);
2475 __isl_give isl_union_set *isl_union_map_wrap(
2476 __isl_take isl_union_map *umap);
2477 __isl_give isl_basic_map *isl_basic_set_unwrap(
2478 __isl_take isl_basic_set *bset);
2479 __isl_give isl_map *isl_set_unwrap(
2480 __isl_take isl_set *set);
2481 __isl_give isl_union_map *isl_union_set_unwrap(
2482 __isl_take isl_union_set *uset);
2486 Remove any internal structure of domain (and range) of the given
2487 set or relation. If there is any such internal structure in the input,
2488 then the name of the space is also removed.
2490 __isl_give isl_basic_set *isl_basic_set_flatten(
2491 __isl_take isl_basic_set *bset);
2492 __isl_give isl_set *isl_set_flatten(
2493 __isl_take isl_set *set);
2494 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2495 __isl_take isl_basic_map *bmap);
2496 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2497 __isl_take isl_basic_map *bmap);
2498 __isl_give isl_map *isl_map_flatten_range(
2499 __isl_take isl_map *map);
2500 __isl_give isl_map *isl_map_flatten_domain(
2501 __isl_take isl_map *map);
2502 __isl_give isl_basic_map *isl_basic_map_flatten(
2503 __isl_take isl_basic_map *bmap);
2504 __isl_give isl_map *isl_map_flatten(
2505 __isl_take isl_map *map);
2507 __isl_give isl_map *isl_set_flatten_map(
2508 __isl_take isl_set *set);
2510 The function above constructs a relation
2511 that maps the input set to a flattened version of the set.
2515 Lift the input set to a space with extra dimensions corresponding
2516 to the existentially quantified variables in the input.
2517 In particular, the result lives in a wrapped map where the domain
2518 is the original space and the range corresponds to the original
2519 existentially quantified variables.
2521 __isl_give isl_basic_set *isl_basic_set_lift(
2522 __isl_take isl_basic_set *bset);
2523 __isl_give isl_set *isl_set_lift(
2524 __isl_take isl_set *set);
2525 __isl_give isl_union_set *isl_union_set_lift(
2526 __isl_take isl_union_set *uset);
2528 Given a local space that contains the existentially quantified
2529 variables of a set, a basic relation that, when applied to
2530 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2531 can be constructed using the following function.
2533 #include <isl/local_space.h>
2534 __isl_give isl_basic_map *isl_local_space_lifting(
2535 __isl_take isl_local_space *ls);
2537 =item * Internal Product
2539 __isl_give isl_basic_map *isl_basic_map_zip(
2540 __isl_take isl_basic_map *bmap);
2541 __isl_give isl_map *isl_map_zip(
2542 __isl_take isl_map *map);
2543 __isl_give isl_union_map *isl_union_map_zip(
2544 __isl_take isl_union_map *umap);
2546 Given a relation with nested relations for domain and range,
2547 interchange the range of the domain with the domain of the range.
2551 __isl_give isl_basic_map *isl_basic_map_curry(
2552 __isl_take isl_basic_map *bmap);
2553 __isl_give isl_basic_map *isl_basic_map_uncurry(
2554 __isl_take isl_basic_map *bmap);
2555 __isl_give isl_map *isl_map_curry(
2556 __isl_take isl_map *map);
2557 __isl_give isl_map *isl_map_uncurry(
2558 __isl_take isl_map *map);
2559 __isl_give isl_union_map *isl_union_map_curry(
2560 __isl_take isl_union_map *umap);
2562 Given a relation with a nested relation for domain,
2563 the C<curry> functions
2564 move the range of the nested relation out of the domain
2565 and use it as the domain of a nested relation in the range,
2566 with the original range as range of this nested relation.
2567 The C<uncurry> functions perform the inverse operation.
2569 =item * Aligning parameters
2571 __isl_give isl_basic_set *isl_basic_set_align_params(
2572 __isl_take isl_basic_set *bset,
2573 __isl_take isl_space *model);
2574 __isl_give isl_set *isl_set_align_params(
2575 __isl_take isl_set *set,
2576 __isl_take isl_space *model);
2577 __isl_give isl_basic_map *isl_basic_map_align_params(
2578 __isl_take isl_basic_map *bmap,
2579 __isl_take isl_space *model);
2580 __isl_give isl_map *isl_map_align_params(
2581 __isl_take isl_map *map,
2582 __isl_take isl_space *model);
2584 Change the order of the parameters of the given set or relation
2585 such that the first parameters match those of C<model>.
2586 This may involve the introduction of extra parameters.
2587 All parameters need to be named.
2589 =item * Dimension manipulation
2591 __isl_give isl_set *isl_set_add_dims(
2592 __isl_take isl_set *set,
2593 enum isl_dim_type type, unsigned n);
2594 __isl_give isl_map *isl_map_add_dims(
2595 __isl_take isl_map *map,
2596 enum isl_dim_type type, unsigned n);
2597 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2598 __isl_take isl_basic_set *bset,
2599 enum isl_dim_type type, unsigned pos,
2601 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2602 __isl_take isl_basic_map *bmap,
2603 enum isl_dim_type type, unsigned pos,
2605 __isl_give isl_set *isl_set_insert_dims(
2606 __isl_take isl_set *set,
2607 enum isl_dim_type type, unsigned pos, unsigned n);
2608 __isl_give isl_map *isl_map_insert_dims(
2609 __isl_take isl_map *map,
2610 enum isl_dim_type type, unsigned pos, unsigned n);
2611 __isl_give isl_basic_set *isl_basic_set_move_dims(
2612 __isl_take isl_basic_set *bset,
2613 enum isl_dim_type dst_type, unsigned dst_pos,
2614 enum isl_dim_type src_type, unsigned src_pos,
2616 __isl_give isl_basic_map *isl_basic_map_move_dims(
2617 __isl_take isl_basic_map *bmap,
2618 enum isl_dim_type dst_type, unsigned dst_pos,
2619 enum isl_dim_type src_type, unsigned src_pos,
2621 __isl_give isl_set *isl_set_move_dims(
2622 __isl_take isl_set *set,
2623 enum isl_dim_type dst_type, unsigned dst_pos,
2624 enum isl_dim_type src_type, unsigned src_pos,
2626 __isl_give isl_map *isl_map_move_dims(
2627 __isl_take isl_map *map,
2628 enum isl_dim_type dst_type, unsigned dst_pos,
2629 enum isl_dim_type src_type, unsigned src_pos,
2632 It is usually not advisable to directly change the (input or output)
2633 space of a set or a relation as this removes the name and the internal
2634 structure of the space. However, the above functions can be useful
2635 to add new parameters, assuming
2636 C<isl_set_align_params> and C<isl_map_align_params>
2641 =head2 Binary Operations
2643 The two arguments of a binary operation not only need to live
2644 in the same C<isl_ctx>, they currently also need to have
2645 the same (number of) parameters.
2647 =head3 Basic Operations
2651 =item * Intersection
2653 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2654 __isl_take isl_basic_set *bset1,
2655 __isl_take isl_basic_set *bset2);
2656 __isl_give isl_basic_set *isl_basic_set_intersect(
2657 __isl_take isl_basic_set *bset1,
2658 __isl_take isl_basic_set *bset2);
2659 __isl_give isl_set *isl_set_intersect_params(
2660 __isl_take isl_set *set,
2661 __isl_take isl_set *params);
2662 __isl_give isl_set *isl_set_intersect(
2663 __isl_take isl_set *set1,
2664 __isl_take isl_set *set2);
2665 __isl_give isl_union_set *isl_union_set_intersect_params(
2666 __isl_take isl_union_set *uset,
2667 __isl_take isl_set *set);
2668 __isl_give isl_union_map *isl_union_map_intersect_params(
2669 __isl_take isl_union_map *umap,
2670 __isl_take isl_set *set);
2671 __isl_give isl_union_set *isl_union_set_intersect(
2672 __isl_take isl_union_set *uset1,
2673 __isl_take isl_union_set *uset2);
2674 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2675 __isl_take isl_basic_map *bmap,
2676 __isl_take isl_basic_set *bset);
2677 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2678 __isl_take isl_basic_map *bmap,
2679 __isl_take isl_basic_set *bset);
2680 __isl_give isl_basic_map *isl_basic_map_intersect(
2681 __isl_take isl_basic_map *bmap1,
2682 __isl_take isl_basic_map *bmap2);
2683 __isl_give isl_map *isl_map_intersect_params(
2684 __isl_take isl_map *map,
2685 __isl_take isl_set *params);
2686 __isl_give isl_map *isl_map_intersect_domain(
2687 __isl_take isl_map *map,
2688 __isl_take isl_set *set);
2689 __isl_give isl_map *isl_map_intersect_range(
2690 __isl_take isl_map *map,
2691 __isl_take isl_set *set);
2692 __isl_give isl_map *isl_map_intersect(
2693 __isl_take isl_map *map1,
2694 __isl_take isl_map *map2);
2695 __isl_give isl_union_map *isl_union_map_intersect_domain(
2696 __isl_take isl_union_map *umap,
2697 __isl_take isl_union_set *uset);
2698 __isl_give isl_union_map *isl_union_map_intersect_range(
2699 __isl_take isl_union_map *umap,
2700 __isl_take isl_union_set *uset);
2701 __isl_give isl_union_map *isl_union_map_intersect(
2702 __isl_take isl_union_map *umap1,
2703 __isl_take isl_union_map *umap2);
2705 The second argument to the C<_params> functions needs to be
2706 a parametric (basic) set. For the other functions, a parametric set
2707 for either argument is only allowed if the other argument is
2708 a parametric set as well.
2712 __isl_give isl_set *isl_basic_set_union(
2713 __isl_take isl_basic_set *bset1,
2714 __isl_take isl_basic_set *bset2);
2715 __isl_give isl_map *isl_basic_map_union(
2716 __isl_take isl_basic_map *bmap1,
2717 __isl_take isl_basic_map *bmap2);
2718 __isl_give isl_set *isl_set_union(
2719 __isl_take isl_set *set1,
2720 __isl_take isl_set *set2);
2721 __isl_give isl_map *isl_map_union(
2722 __isl_take isl_map *map1,
2723 __isl_take isl_map *map2);
2724 __isl_give isl_union_set *isl_union_set_union(
2725 __isl_take isl_union_set *uset1,
2726 __isl_take isl_union_set *uset2);
2727 __isl_give isl_union_map *isl_union_map_union(
2728 __isl_take isl_union_map *umap1,
2729 __isl_take isl_union_map *umap2);
2731 =item * Set difference
2733 __isl_give isl_set *isl_set_subtract(
2734 __isl_take isl_set *set1,
2735 __isl_take isl_set *set2);
2736 __isl_give isl_map *isl_map_subtract(
2737 __isl_take isl_map *map1,
2738 __isl_take isl_map *map2);
2739 __isl_give isl_map *isl_map_subtract_domain(
2740 __isl_take isl_map *map,
2741 __isl_take isl_set *dom);
2742 __isl_give isl_map *isl_map_subtract_range(
2743 __isl_take isl_map *map,
2744 __isl_take isl_set *dom);
2745 __isl_give isl_union_set *isl_union_set_subtract(
2746 __isl_take isl_union_set *uset1,
2747 __isl_take isl_union_set *uset2);
2748 __isl_give isl_union_map *isl_union_map_subtract(
2749 __isl_take isl_union_map *umap1,
2750 __isl_take isl_union_map *umap2);
2751 __isl_give isl_union_map *isl_union_map_subtract_domain(
2752 __isl_take isl_union_map *umap,
2753 __isl_take isl_union_set *dom);
2754 __isl_give isl_union_map *isl_union_map_subtract_range(
2755 __isl_take isl_union_map *umap,
2756 __isl_take isl_union_set *dom);
2760 __isl_give isl_basic_set *isl_basic_set_apply(
2761 __isl_take isl_basic_set *bset,
2762 __isl_take isl_basic_map *bmap);
2763 __isl_give isl_set *isl_set_apply(
2764 __isl_take isl_set *set,
2765 __isl_take isl_map *map);
2766 __isl_give isl_union_set *isl_union_set_apply(
2767 __isl_take isl_union_set *uset,
2768 __isl_take isl_union_map *umap);
2769 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2770 __isl_take isl_basic_map *bmap1,
2771 __isl_take isl_basic_map *bmap2);
2772 __isl_give isl_basic_map *isl_basic_map_apply_range(
2773 __isl_take isl_basic_map *bmap1,
2774 __isl_take isl_basic_map *bmap2);
2775 __isl_give isl_map *isl_map_apply_domain(
2776 __isl_take isl_map *map1,
2777 __isl_take isl_map *map2);
2778 __isl_give isl_union_map *isl_union_map_apply_domain(
2779 __isl_take isl_union_map *umap1,
2780 __isl_take isl_union_map *umap2);
2781 __isl_give isl_map *isl_map_apply_range(
2782 __isl_take isl_map *map1,
2783 __isl_take isl_map *map2);
2784 __isl_give isl_union_map *isl_union_map_apply_range(
2785 __isl_take isl_union_map *umap1,
2786 __isl_take isl_union_map *umap2);
2790 __isl_give isl_basic_set *
2791 isl_basic_set_preimage_multi_aff(
2792 __isl_take isl_basic_set *bset,
2793 __isl_take isl_multi_aff *ma);
2794 __isl_give isl_set *isl_set_preimage_multi_aff(
2795 __isl_take isl_set *set,
2796 __isl_take isl_multi_aff *ma);
2797 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
2798 __isl_take isl_set *set,
2799 __isl_take isl_pw_multi_aff *pma);
2801 These functions compute the preimage of the given set under
2802 the given function. In other words, the expression is plugged
2803 into the set description.
2804 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
2805 L</"Piecewise Multiple Quasi Affine Expressions">.
2807 =item * Cartesian Product
2809 __isl_give isl_set *isl_set_product(
2810 __isl_take isl_set *set1,
2811 __isl_take isl_set *set2);
2812 __isl_give isl_union_set *isl_union_set_product(
2813 __isl_take isl_union_set *uset1,
2814 __isl_take isl_union_set *uset2);
2815 __isl_give isl_basic_map *isl_basic_map_domain_product(
2816 __isl_take isl_basic_map *bmap1,
2817 __isl_take isl_basic_map *bmap2);
2818 __isl_give isl_basic_map *isl_basic_map_range_product(
2819 __isl_take isl_basic_map *bmap1,
2820 __isl_take isl_basic_map *bmap2);
2821 __isl_give isl_basic_map *isl_basic_map_product(
2822 __isl_take isl_basic_map *bmap1,
2823 __isl_take isl_basic_map *bmap2);
2824 __isl_give isl_map *isl_map_domain_product(
2825 __isl_take isl_map *map1,
2826 __isl_take isl_map *map2);
2827 __isl_give isl_map *isl_map_range_product(
2828 __isl_take isl_map *map1,
2829 __isl_take isl_map *map2);
2830 __isl_give isl_union_map *isl_union_map_domain_product(
2831 __isl_take isl_union_map *umap1,
2832 __isl_take isl_union_map *umap2);
2833 __isl_give isl_union_map *isl_union_map_range_product(
2834 __isl_take isl_union_map *umap1,
2835 __isl_take isl_union_map *umap2);
2836 __isl_give isl_map *isl_map_product(
2837 __isl_take isl_map *map1,
2838 __isl_take isl_map *map2);
2839 __isl_give isl_union_map *isl_union_map_product(
2840 __isl_take isl_union_map *umap1,
2841 __isl_take isl_union_map *umap2);
2843 The above functions compute the cross product of the given
2844 sets or relations. The domains and ranges of the results
2845 are wrapped maps between domains and ranges of the inputs.
2846 To obtain a ``flat'' product, use the following functions
2849 __isl_give isl_basic_set *isl_basic_set_flat_product(
2850 __isl_take isl_basic_set *bset1,
2851 __isl_take isl_basic_set *bset2);
2852 __isl_give isl_set *isl_set_flat_product(
2853 __isl_take isl_set *set1,
2854 __isl_take isl_set *set2);
2855 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2856 __isl_take isl_basic_map *bmap1,
2857 __isl_take isl_basic_map *bmap2);
2858 __isl_give isl_map *isl_map_flat_domain_product(
2859 __isl_take isl_map *map1,
2860 __isl_take isl_map *map2);
2861 __isl_give isl_map *isl_map_flat_range_product(
2862 __isl_take isl_map *map1,
2863 __isl_take isl_map *map2);
2864 __isl_give isl_union_map *isl_union_map_flat_range_product(
2865 __isl_take isl_union_map *umap1,
2866 __isl_take isl_union_map *umap2);
2867 __isl_give isl_basic_map *isl_basic_map_flat_product(
2868 __isl_take isl_basic_map *bmap1,
2869 __isl_take isl_basic_map *bmap2);
2870 __isl_give isl_map *isl_map_flat_product(
2871 __isl_take isl_map *map1,
2872 __isl_take isl_map *map2);
2874 =item * Simplification
2876 __isl_give isl_basic_set *isl_basic_set_gist(
2877 __isl_take isl_basic_set *bset,
2878 __isl_take isl_basic_set *context);
2879 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2880 __isl_take isl_set *context);
2881 __isl_give isl_set *isl_set_gist_params(
2882 __isl_take isl_set *set,
2883 __isl_take isl_set *context);
2884 __isl_give isl_union_set *isl_union_set_gist(
2885 __isl_take isl_union_set *uset,
2886 __isl_take isl_union_set *context);
2887 __isl_give isl_union_set *isl_union_set_gist_params(
2888 __isl_take isl_union_set *uset,
2889 __isl_take isl_set *set);
2890 __isl_give isl_basic_map *isl_basic_map_gist(
2891 __isl_take isl_basic_map *bmap,
2892 __isl_take isl_basic_map *context);
2893 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2894 __isl_take isl_map *context);
2895 __isl_give isl_map *isl_map_gist_params(
2896 __isl_take isl_map *map,
2897 __isl_take isl_set *context);
2898 __isl_give isl_map *isl_map_gist_domain(
2899 __isl_take isl_map *map,
2900 __isl_take isl_set *context);
2901 __isl_give isl_map *isl_map_gist_range(
2902 __isl_take isl_map *map,
2903 __isl_take isl_set *context);
2904 __isl_give isl_union_map *isl_union_map_gist(
2905 __isl_take isl_union_map *umap,
2906 __isl_take isl_union_map *context);
2907 __isl_give isl_union_map *isl_union_map_gist_params(
2908 __isl_take isl_union_map *umap,
2909 __isl_take isl_set *set);
2910 __isl_give isl_union_map *isl_union_map_gist_domain(
2911 __isl_take isl_union_map *umap,
2912 __isl_take isl_union_set *uset);
2913 __isl_give isl_union_map *isl_union_map_gist_range(
2914 __isl_take isl_union_map *umap,
2915 __isl_take isl_union_set *uset);
2917 The gist operation returns a set or relation that has the
2918 same intersection with the context as the input set or relation.
2919 Any implicit equality in the intersection is made explicit in the result,
2920 while all inequalities that are redundant with respect to the intersection
2922 In case of union sets and relations, the gist operation is performed
2927 =head3 Lexicographic Optimization
2929 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2930 the following functions
2931 compute a set that contains the lexicographic minimum or maximum
2932 of the elements in C<set> (or C<bset>) for those values of the parameters
2933 that satisfy C<dom>.
2934 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2935 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2937 In other words, the union of the parameter values
2938 for which the result is non-empty and of C<*empty>
2941 __isl_give isl_set *isl_basic_set_partial_lexmin(
2942 __isl_take isl_basic_set *bset,
2943 __isl_take isl_basic_set *dom,
2944 __isl_give isl_set **empty);
2945 __isl_give isl_set *isl_basic_set_partial_lexmax(
2946 __isl_take isl_basic_set *bset,
2947 __isl_take isl_basic_set *dom,
2948 __isl_give isl_set **empty);
2949 __isl_give isl_set *isl_set_partial_lexmin(
2950 __isl_take isl_set *set, __isl_take isl_set *dom,
2951 __isl_give isl_set **empty);
2952 __isl_give isl_set *isl_set_partial_lexmax(
2953 __isl_take isl_set *set, __isl_take isl_set *dom,
2954 __isl_give isl_set **empty);
2956 Given a (basic) set C<set> (or C<bset>), the following functions simply
2957 return a set containing the lexicographic minimum or maximum
2958 of the elements in C<set> (or C<bset>).
2959 In case of union sets, the optimum is computed per space.
2961 __isl_give isl_set *isl_basic_set_lexmin(
2962 __isl_take isl_basic_set *bset);
2963 __isl_give isl_set *isl_basic_set_lexmax(
2964 __isl_take isl_basic_set *bset);
2965 __isl_give isl_set *isl_set_lexmin(
2966 __isl_take isl_set *set);
2967 __isl_give isl_set *isl_set_lexmax(
2968 __isl_take isl_set *set);
2969 __isl_give isl_union_set *isl_union_set_lexmin(
2970 __isl_take isl_union_set *uset);
2971 __isl_give isl_union_set *isl_union_set_lexmax(
2972 __isl_take isl_union_set *uset);
2974 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2975 the following functions
2976 compute a relation that maps each element of C<dom>
2977 to the single lexicographic minimum or maximum
2978 of the elements that are associated to that same
2979 element in C<map> (or C<bmap>).
2980 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2981 that contains the elements in C<dom> that do not map
2982 to any elements in C<map> (or C<bmap>).
2983 In other words, the union of the domain of the result and of C<*empty>
2986 __isl_give isl_map *isl_basic_map_partial_lexmax(
2987 __isl_take isl_basic_map *bmap,
2988 __isl_take isl_basic_set *dom,
2989 __isl_give isl_set **empty);
2990 __isl_give isl_map *isl_basic_map_partial_lexmin(
2991 __isl_take isl_basic_map *bmap,
2992 __isl_take isl_basic_set *dom,
2993 __isl_give isl_set **empty);
2994 __isl_give isl_map *isl_map_partial_lexmax(
2995 __isl_take isl_map *map, __isl_take isl_set *dom,
2996 __isl_give isl_set **empty);
2997 __isl_give isl_map *isl_map_partial_lexmin(
2998 __isl_take isl_map *map, __isl_take isl_set *dom,
2999 __isl_give isl_set **empty);
3001 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3002 return a map mapping each element in the domain of
3003 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3004 of all elements associated to that element.
3005 In case of union relations, the optimum is computed per space.
3007 __isl_give isl_map *isl_basic_map_lexmin(
3008 __isl_take isl_basic_map *bmap);
3009 __isl_give isl_map *isl_basic_map_lexmax(
3010 __isl_take isl_basic_map *bmap);
3011 __isl_give isl_map *isl_map_lexmin(
3012 __isl_take isl_map *map);
3013 __isl_give isl_map *isl_map_lexmax(
3014 __isl_take isl_map *map);
3015 __isl_give isl_union_map *isl_union_map_lexmin(
3016 __isl_take isl_union_map *umap);
3017 __isl_give isl_union_map *isl_union_map_lexmax(
3018 __isl_take isl_union_map *umap);
3020 The following functions return their result in the form of
3021 a piecewise multi-affine expression
3022 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3023 but are otherwise equivalent to the corresponding functions
3024 returning a basic set or relation.
3026 __isl_give isl_pw_multi_aff *
3027 isl_basic_map_lexmin_pw_multi_aff(
3028 __isl_take isl_basic_map *bmap);
3029 __isl_give isl_pw_multi_aff *
3030 isl_basic_set_partial_lexmin_pw_multi_aff(
3031 __isl_take isl_basic_set *bset,
3032 __isl_take isl_basic_set *dom,
3033 __isl_give isl_set **empty);
3034 __isl_give isl_pw_multi_aff *
3035 isl_basic_set_partial_lexmax_pw_multi_aff(
3036 __isl_take isl_basic_set *bset,
3037 __isl_take isl_basic_set *dom,
3038 __isl_give isl_set **empty);
3039 __isl_give isl_pw_multi_aff *
3040 isl_basic_map_partial_lexmin_pw_multi_aff(
3041 __isl_take isl_basic_map *bmap,
3042 __isl_take isl_basic_set *dom,
3043 __isl_give isl_set **empty);
3044 __isl_give isl_pw_multi_aff *
3045 isl_basic_map_partial_lexmax_pw_multi_aff(
3046 __isl_take isl_basic_map *bmap,
3047 __isl_take isl_basic_set *dom,
3048 __isl_give isl_set **empty);
3049 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3050 __isl_take isl_map *map);
3051 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3052 __isl_take isl_map *map);
3056 Lists are defined over several element types, including
3057 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3058 C<isl_basic_set> and C<isl_set>.
3059 Here we take lists of C<isl_set>s as an example.
3060 Lists can be created, copied, modified and freed using the following functions.
3062 #include <isl/list.h>
3063 __isl_give isl_set_list *isl_set_list_from_set(
3064 __isl_take isl_set *el);
3065 __isl_give isl_set_list *isl_set_list_alloc(
3066 isl_ctx *ctx, int n);
3067 __isl_give isl_set_list *isl_set_list_copy(
3068 __isl_keep isl_set_list *list);
3069 __isl_give isl_set_list *isl_set_list_insert(
3070 __isl_take isl_set_list *list, unsigned pos,
3071 __isl_take isl_set *el);
3072 __isl_give isl_set_list *isl_set_list_add(
3073 __isl_take isl_set_list *list,
3074 __isl_take isl_set *el);
3075 __isl_give isl_set_list *isl_set_list_drop(
3076 __isl_take isl_set_list *list,
3077 unsigned first, unsigned n);
3078 __isl_give isl_set_list *isl_set_list_set_set(
3079 __isl_take isl_set_list *list, int index,
3080 __isl_take isl_set *set);
3081 __isl_give isl_set_list *isl_set_list_concat(
3082 __isl_take isl_set_list *list1,
3083 __isl_take isl_set_list *list2);
3084 void *isl_set_list_free(__isl_take isl_set_list *list);
3086 C<isl_set_list_alloc> creates an empty list with a capacity for
3087 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3090 Lists can be inspected using the following functions.
3092 #include <isl/list.h>
3093 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3094 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3095 __isl_give isl_set *isl_set_list_get_set(
3096 __isl_keep isl_set_list *list, int index);
3097 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3098 int (*fn)(__isl_take isl_set *el, void *user),
3101 Lists can be printed using
3103 #include <isl/list.h>
3104 __isl_give isl_printer *isl_printer_print_set_list(
3105 __isl_take isl_printer *p,
3106 __isl_keep isl_set_list *list);
3110 Vectors can be created, copied and freed using the following functions.
3112 #include <isl/vec.h>
3113 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3115 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3116 void *isl_vec_free(__isl_take isl_vec *vec);
3118 Note that the elements of a newly created vector may have arbitrary values.
3119 The elements can be changed and inspected using the following functions.
3121 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3122 int isl_vec_size(__isl_keep isl_vec *vec);
3123 int isl_vec_get_element(__isl_keep isl_vec *vec,
3124 int pos, isl_int *v);
3125 __isl_give isl_vec *isl_vec_set_element(
3126 __isl_take isl_vec *vec, int pos, isl_int v);
3127 __isl_give isl_vec *isl_vec_set_element_si(
3128 __isl_take isl_vec *vec, int pos, int v);
3129 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3131 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3133 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3136 C<isl_vec_get_element> will return a negative value if anything went wrong.
3137 In that case, the value of C<*v> is undefined.
3139 The following function can be used to concatenate two vectors.
3141 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3142 __isl_take isl_vec *vec2);
3146 Matrices can be created, copied and freed using the following functions.
3148 #include <isl/mat.h>
3149 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3150 unsigned n_row, unsigned n_col);
3151 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3152 void isl_mat_free(__isl_take isl_mat *mat);
3154 Note that the elements of a newly created matrix may have arbitrary values.
3155 The elements can be changed and inspected using the following functions.
3157 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3158 int isl_mat_rows(__isl_keep isl_mat *mat);
3159 int isl_mat_cols(__isl_keep isl_mat *mat);
3160 int isl_mat_get_element(__isl_keep isl_mat *mat,
3161 int row, int col, isl_int *v);
3162 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3163 int row, int col, isl_int v);
3164 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3165 int row, int col, int v);
3167 C<isl_mat_get_element> will return a negative value if anything went wrong.
3168 In that case, the value of C<*v> is undefined.
3170 The following function can be used to compute the (right) inverse
3171 of a matrix, i.e., a matrix such that the product of the original
3172 and the inverse (in that order) is a multiple of the identity matrix.
3173 The input matrix is assumed to be of full row-rank.
3175 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3177 The following function can be used to compute the (right) kernel
3178 (or null space) of a matrix, i.e., a matrix such that the product of
3179 the original and the kernel (in that order) is the zero matrix.
3181 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3183 =head2 Piecewise Quasi Affine Expressions
3185 The zero quasi affine expression or the quasi affine expression
3186 that is equal to a specified dimension on a given domain can be created using
3188 __isl_give isl_aff *isl_aff_zero_on_domain(
3189 __isl_take isl_local_space *ls);
3190 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3191 __isl_take isl_local_space *ls);
3192 __isl_give isl_aff *isl_aff_var_on_domain(
3193 __isl_take isl_local_space *ls,
3194 enum isl_dim_type type, unsigned pos);
3195 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3196 __isl_take isl_local_space *ls,
3197 enum isl_dim_type type, unsigned pos);
3199 Note that the space in which the resulting objects live is a map space
3200 with the given space as domain and a one-dimensional range.
3202 An empty piecewise quasi affine expression (one with no cells)
3203 or a piecewise quasi affine expression with a single cell can
3204 be created using the following functions.
3206 #include <isl/aff.h>
3207 __isl_give isl_pw_aff *isl_pw_aff_empty(
3208 __isl_take isl_space *space);
3209 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3210 __isl_take isl_set *set, __isl_take isl_aff *aff);
3211 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3212 __isl_take isl_aff *aff);
3214 A piecewise quasi affine expression that is equal to 1 on a set
3215 and 0 outside the set can be created using the following function.
3217 #include <isl/aff.h>
3218 __isl_give isl_pw_aff *isl_set_indicator_function(
3219 __isl_take isl_set *set);
3221 Quasi affine expressions can be copied and freed using
3223 #include <isl/aff.h>
3224 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3225 void *isl_aff_free(__isl_take isl_aff *aff);
3227 __isl_give isl_pw_aff *isl_pw_aff_copy(
3228 __isl_keep isl_pw_aff *pwaff);
3229 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3231 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3232 using the following function. The constraint is required to have
3233 a non-zero coefficient for the specified dimension.
3235 #include <isl/constraint.h>
3236 __isl_give isl_aff *isl_constraint_get_bound(
3237 __isl_keep isl_constraint *constraint,
3238 enum isl_dim_type type, int pos);
3240 The entire affine expression of the constraint can also be extracted
3241 using the following function.
3243 #include <isl/constraint.h>
3244 __isl_give isl_aff *isl_constraint_get_aff(
3245 __isl_keep isl_constraint *constraint);
3247 Conversely, an equality constraint equating
3248 the affine expression to zero or an inequality constraint enforcing
3249 the affine expression to be non-negative, can be constructed using
3251 __isl_give isl_constraint *isl_equality_from_aff(
3252 __isl_take isl_aff *aff);
3253 __isl_give isl_constraint *isl_inequality_from_aff(
3254 __isl_take isl_aff *aff);
3256 The expression can be inspected using
3258 #include <isl/aff.h>
3259 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3260 int isl_aff_dim(__isl_keep isl_aff *aff,
3261 enum isl_dim_type type);
3262 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3263 __isl_keep isl_aff *aff);
3264 __isl_give isl_local_space *isl_aff_get_local_space(
3265 __isl_keep isl_aff *aff);
3266 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3267 enum isl_dim_type type, unsigned pos);
3268 const char *isl_pw_aff_get_dim_name(
3269 __isl_keep isl_pw_aff *pa,
3270 enum isl_dim_type type, unsigned pos);
3271 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3272 enum isl_dim_type type, unsigned pos);
3273 __isl_give isl_id *isl_pw_aff_get_dim_id(
3274 __isl_keep isl_pw_aff *pa,
3275 enum isl_dim_type type, unsigned pos);
3276 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3277 __isl_keep isl_pw_aff *pa,
3278 enum isl_dim_type type);
3279 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3281 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3282 enum isl_dim_type type, int pos, isl_int *v);
3283 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3285 __isl_give isl_aff *isl_aff_get_div(
3286 __isl_keep isl_aff *aff, int pos);
3288 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3289 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3290 int (*fn)(__isl_take isl_set *set,
3291 __isl_take isl_aff *aff,
3292 void *user), void *user);
3294 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3295 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3297 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3298 enum isl_dim_type type, unsigned first, unsigned n);
3299 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3300 enum isl_dim_type type, unsigned first, unsigned n);
3302 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3303 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3304 enum isl_dim_type type);
3305 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3307 It can be modified using
3309 #include <isl/aff.h>
3310 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3311 __isl_take isl_pw_aff *pwaff,
3312 enum isl_dim_type type, __isl_take isl_id *id);
3313 __isl_give isl_aff *isl_aff_set_dim_name(
3314 __isl_take isl_aff *aff, enum isl_dim_type type,
3315 unsigned pos, const char *s);
3316 __isl_give isl_aff *isl_aff_set_dim_id(
3317 __isl_take isl_aff *aff, enum isl_dim_type type,
3318 unsigned pos, __isl_take isl_id *id);
3319 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3320 __isl_take isl_pw_aff *pma,
3321 enum isl_dim_type type, unsigned pos,
3322 __isl_take isl_id *id);
3323 __isl_give isl_aff *isl_aff_set_constant(
3324 __isl_take isl_aff *aff, isl_int v);
3325 __isl_give isl_aff *isl_aff_set_constant_si(
3326 __isl_take isl_aff *aff, int v);
3327 __isl_give isl_aff *isl_aff_set_coefficient(
3328 __isl_take isl_aff *aff,
3329 enum isl_dim_type type, int pos, isl_int v);
3330 __isl_give isl_aff *isl_aff_set_coefficient_si(
3331 __isl_take isl_aff *aff,
3332 enum isl_dim_type type, int pos, int v);
3333 __isl_give isl_aff *isl_aff_set_denominator(
3334 __isl_take isl_aff *aff, isl_int v);
3336 __isl_give isl_aff *isl_aff_add_constant(
3337 __isl_take isl_aff *aff, isl_int v);
3338 __isl_give isl_aff *isl_aff_add_constant_si(
3339 __isl_take isl_aff *aff, int v);
3340 __isl_give isl_aff *isl_aff_add_constant_num(
3341 __isl_take isl_aff *aff, isl_int v);
3342 __isl_give isl_aff *isl_aff_add_constant_num_si(
3343 __isl_take isl_aff *aff, int v);
3344 __isl_give isl_aff *isl_aff_add_coefficient(
3345 __isl_take isl_aff *aff,
3346 enum isl_dim_type type, int pos, isl_int v);
3347 __isl_give isl_aff *isl_aff_add_coefficient_si(
3348 __isl_take isl_aff *aff,
3349 enum isl_dim_type type, int pos, int v);
3351 __isl_give isl_aff *isl_aff_insert_dims(
3352 __isl_take isl_aff *aff,
3353 enum isl_dim_type type, unsigned first, unsigned n);
3354 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3355 __isl_take isl_pw_aff *pwaff,
3356 enum isl_dim_type type, unsigned first, unsigned n);
3357 __isl_give isl_aff *isl_aff_add_dims(
3358 __isl_take isl_aff *aff,
3359 enum isl_dim_type type, unsigned n);
3360 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3361 __isl_take isl_pw_aff *pwaff,
3362 enum isl_dim_type type, unsigned n);
3363 __isl_give isl_aff *isl_aff_drop_dims(
3364 __isl_take isl_aff *aff,
3365 enum isl_dim_type type, unsigned first, unsigned n);
3366 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3367 __isl_take isl_pw_aff *pwaff,
3368 enum isl_dim_type type, unsigned first, unsigned n);
3370 Note that the C<set_constant> and C<set_coefficient> functions
3371 set the I<numerator> of the constant or coefficient, while
3372 C<add_constant> and C<add_coefficient> add an integer value to
3373 the possibly rational constant or coefficient.
3374 The C<add_constant_num> functions add an integer value to
3377 To check whether an affine expressions is obviously zero
3378 or obviously equal to some other affine expression, use
3380 #include <isl/aff.h>
3381 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3382 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3383 __isl_keep isl_aff *aff2);
3384 int isl_pw_aff_plain_is_equal(
3385 __isl_keep isl_pw_aff *pwaff1,
3386 __isl_keep isl_pw_aff *pwaff2);
3390 #include <isl/aff.h>
3391 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3392 __isl_take isl_aff *aff2);
3393 __isl_give isl_pw_aff *isl_pw_aff_add(
3394 __isl_take isl_pw_aff *pwaff1,
3395 __isl_take isl_pw_aff *pwaff2);
3396 __isl_give isl_pw_aff *isl_pw_aff_min(
3397 __isl_take isl_pw_aff *pwaff1,
3398 __isl_take isl_pw_aff *pwaff2);
3399 __isl_give isl_pw_aff *isl_pw_aff_max(
3400 __isl_take isl_pw_aff *pwaff1,
3401 __isl_take isl_pw_aff *pwaff2);
3402 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3403 __isl_take isl_aff *aff2);
3404 __isl_give isl_pw_aff *isl_pw_aff_sub(
3405 __isl_take isl_pw_aff *pwaff1,
3406 __isl_take isl_pw_aff *pwaff2);
3407 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3408 __isl_give isl_pw_aff *isl_pw_aff_neg(
3409 __isl_take isl_pw_aff *pwaff);
3410 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3411 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3412 __isl_take isl_pw_aff *pwaff);
3413 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3414 __isl_give isl_pw_aff *isl_pw_aff_floor(
3415 __isl_take isl_pw_aff *pwaff);
3416 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3418 __isl_give isl_pw_aff *isl_pw_aff_mod(
3419 __isl_take isl_pw_aff *pwaff, isl_int mod);
3420 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3422 __isl_give isl_pw_aff *isl_pw_aff_scale(
3423 __isl_take isl_pw_aff *pwaff, isl_int f);
3424 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3426 __isl_give isl_aff *isl_aff_scale_down_ui(
3427 __isl_take isl_aff *aff, unsigned f);
3428 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3429 __isl_take isl_pw_aff *pwaff, isl_int f);
3431 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3432 __isl_take isl_pw_aff_list *list);
3433 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3434 __isl_take isl_pw_aff_list *list);
3436 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3437 __isl_take isl_pw_aff *pwqp);
3439 __isl_give isl_aff *isl_aff_align_params(
3440 __isl_take isl_aff *aff,
3441 __isl_take isl_space *model);
3442 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3443 __isl_take isl_pw_aff *pwaff,
3444 __isl_take isl_space *model);
3446 __isl_give isl_aff *isl_aff_project_domain_on_params(
3447 __isl_take isl_aff *aff);
3449 __isl_give isl_aff *isl_aff_gist_params(
3450 __isl_take isl_aff *aff,
3451 __isl_take isl_set *context);
3452 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3453 __isl_take isl_set *context);
3454 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3455 __isl_take isl_pw_aff *pwaff,
3456 __isl_take isl_set *context);
3457 __isl_give isl_pw_aff *isl_pw_aff_gist(
3458 __isl_take isl_pw_aff *pwaff,
3459 __isl_take isl_set *context);
3461 __isl_give isl_set *isl_pw_aff_domain(
3462 __isl_take isl_pw_aff *pwaff);
3463 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3464 __isl_take isl_pw_aff *pa,
3465 __isl_take isl_set *set);
3466 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3467 __isl_take isl_pw_aff *pa,
3468 __isl_take isl_set *set);
3470 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3471 __isl_take isl_aff *aff2);
3472 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3473 __isl_take isl_aff *aff2);
3474 __isl_give isl_pw_aff *isl_pw_aff_mul(
3475 __isl_take isl_pw_aff *pwaff1,
3476 __isl_take isl_pw_aff *pwaff2);
3477 __isl_give isl_pw_aff *isl_pw_aff_div(
3478 __isl_take isl_pw_aff *pa1,
3479 __isl_take isl_pw_aff *pa2);
3480 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3481 __isl_take isl_pw_aff *pa1,
3482 __isl_take isl_pw_aff *pa2);
3483 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3484 __isl_take isl_pw_aff *pa1,
3485 __isl_take isl_pw_aff *pa2);
3487 When multiplying two affine expressions, at least one of the two needs
3488 to be a constant. Similarly, when dividing an affine expression by another,
3489 the second expression needs to be a constant.
3490 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3491 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3494 #include <isl/aff.h>
3495 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3496 __isl_take isl_aff *aff,
3497 __isl_take isl_multi_aff *ma);
3498 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3499 __isl_take isl_pw_aff *pa,
3500 __isl_take isl_multi_aff *ma);
3501 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3502 __isl_take isl_pw_aff *pa,
3503 __isl_take isl_pw_multi_aff *pma);
3505 These functions precompose the input expression by the given
3506 C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3507 the C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3508 into the (piecewise) affine expression.
3509 Objects of type C<isl_multi_aff> are described in
3510 L</"Piecewise Multiple Quasi Affine Expressions">.
3512 #include <isl/aff.h>
3513 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3514 __isl_take isl_aff *aff);
3515 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3516 __isl_take isl_aff *aff);
3517 __isl_give isl_basic_set *isl_aff_le_basic_set(
3518 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3519 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3520 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3521 __isl_give isl_set *isl_pw_aff_eq_set(
3522 __isl_take isl_pw_aff *pwaff1,
3523 __isl_take isl_pw_aff *pwaff2);
3524 __isl_give isl_set *isl_pw_aff_ne_set(
3525 __isl_take isl_pw_aff *pwaff1,
3526 __isl_take isl_pw_aff *pwaff2);
3527 __isl_give isl_set *isl_pw_aff_le_set(
3528 __isl_take isl_pw_aff *pwaff1,
3529 __isl_take isl_pw_aff *pwaff2);
3530 __isl_give isl_set *isl_pw_aff_lt_set(
3531 __isl_take isl_pw_aff *pwaff1,
3532 __isl_take isl_pw_aff *pwaff2);
3533 __isl_give isl_set *isl_pw_aff_ge_set(
3534 __isl_take isl_pw_aff *pwaff1,
3535 __isl_take isl_pw_aff *pwaff2);
3536 __isl_give isl_set *isl_pw_aff_gt_set(
3537 __isl_take isl_pw_aff *pwaff1,
3538 __isl_take isl_pw_aff *pwaff2);
3540 __isl_give isl_set *isl_pw_aff_list_eq_set(
3541 __isl_take isl_pw_aff_list *list1,
3542 __isl_take isl_pw_aff_list *list2);
3543 __isl_give isl_set *isl_pw_aff_list_ne_set(
3544 __isl_take isl_pw_aff_list *list1,
3545 __isl_take isl_pw_aff_list *list2);
3546 __isl_give isl_set *isl_pw_aff_list_le_set(
3547 __isl_take isl_pw_aff_list *list1,
3548 __isl_take isl_pw_aff_list *list2);
3549 __isl_give isl_set *isl_pw_aff_list_lt_set(
3550 __isl_take isl_pw_aff_list *list1,
3551 __isl_take isl_pw_aff_list *list2);
3552 __isl_give isl_set *isl_pw_aff_list_ge_set(
3553 __isl_take isl_pw_aff_list *list1,
3554 __isl_take isl_pw_aff_list *list2);
3555 __isl_give isl_set *isl_pw_aff_list_gt_set(
3556 __isl_take isl_pw_aff_list *list1,
3557 __isl_take isl_pw_aff_list *list2);
3559 The function C<isl_aff_neg_basic_set> returns a basic set
3560 containing those elements in the domain space
3561 of C<aff> where C<aff> is negative.
3562 The function C<isl_aff_ge_basic_set> returns a basic set
3563 containing those elements in the shared space
3564 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3565 The function C<isl_pw_aff_ge_set> returns a set
3566 containing those elements in the shared domain
3567 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3568 The functions operating on C<isl_pw_aff_list> apply the corresponding
3569 C<isl_pw_aff> function to each pair of elements in the two lists.
3571 #include <isl/aff.h>
3572 __isl_give isl_set *isl_pw_aff_nonneg_set(
3573 __isl_take isl_pw_aff *pwaff);
3574 __isl_give isl_set *isl_pw_aff_zero_set(
3575 __isl_take isl_pw_aff *pwaff);
3576 __isl_give isl_set *isl_pw_aff_non_zero_set(
3577 __isl_take isl_pw_aff *pwaff);
3579 The function C<isl_pw_aff_nonneg_set> returns a set
3580 containing those elements in the domain
3581 of C<pwaff> where C<pwaff> is non-negative.
3583 #include <isl/aff.h>
3584 __isl_give isl_pw_aff *isl_pw_aff_cond(
3585 __isl_take isl_pw_aff *cond,
3586 __isl_take isl_pw_aff *pwaff_true,
3587 __isl_take isl_pw_aff *pwaff_false);
3589 The function C<isl_pw_aff_cond> performs a conditional operator
3590 and returns an expression that is equal to C<pwaff_true>
3591 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3592 where C<cond> is zero.
3594 #include <isl/aff.h>
3595 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3596 __isl_take isl_pw_aff *pwaff1,
3597 __isl_take isl_pw_aff *pwaff2);
3598 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3599 __isl_take isl_pw_aff *pwaff1,
3600 __isl_take isl_pw_aff *pwaff2);
3601 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3602 __isl_take isl_pw_aff *pwaff1,
3603 __isl_take isl_pw_aff *pwaff2);
3605 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3606 expression with a domain that is the union of those of C<pwaff1> and
3607 C<pwaff2> and such that on each cell, the quasi-affine expression is
3608 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3609 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3610 associated expression is the defined one.
3612 An expression can be read from input using
3614 #include <isl/aff.h>
3615 __isl_give isl_aff *isl_aff_read_from_str(
3616 isl_ctx *ctx, const char *str);
3617 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3618 isl_ctx *ctx, const char *str);
3620 An expression can be printed using
3622 #include <isl/aff.h>
3623 __isl_give isl_printer *isl_printer_print_aff(
3624 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3626 __isl_give isl_printer *isl_printer_print_pw_aff(
3627 __isl_take isl_printer *p,
3628 __isl_keep isl_pw_aff *pwaff);
3630 =head2 Piecewise Multiple Quasi Affine Expressions
3632 An C<isl_multi_aff> object represents a sequence of
3633 zero or more affine expressions, all defined on the same domain space.
3634 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
3635 zero or more piecewise affine expressions.
3637 An C<isl_multi_aff> can be constructed from a single
3638 C<isl_aff> or an C<isl_aff_list> using the
3639 following functions. Similarly for C<isl_multi_pw_aff>.
3641 #include <isl/aff.h>
3642 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
3643 __isl_take isl_aff *aff);
3644 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
3645 __isl_take isl_pw_aff *pa);
3646 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3647 __isl_take isl_space *space,
3648 __isl_take isl_aff_list *list);
3650 An empty piecewise multiple quasi affine expression (one with no cells),
3651 the zero piecewise multiple quasi affine expression (with value zero
3652 for each output dimension),
3653 a piecewise multiple quasi affine expression with a single cell (with
3654 either a universe or a specified domain) or
3655 a zero-dimensional piecewise multiple quasi affine expression
3657 can be created using the following functions.
3659 #include <isl/aff.h>
3660 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3661 __isl_take isl_space *space);
3662 __isl_give isl_multi_aff *isl_multi_aff_zero(
3663 __isl_take isl_space *space);
3664 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
3665 __isl_take isl_space *space);
3666 __isl_give isl_multi_aff *isl_multi_aff_identity(
3667 __isl_take isl_space *space);
3668 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3669 __isl_take isl_space *space);
3670 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
3671 __isl_take isl_space *space);
3672 __isl_give isl_pw_multi_aff *
3673 isl_pw_multi_aff_from_multi_aff(
3674 __isl_take isl_multi_aff *ma);
3675 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3676 __isl_take isl_set *set,
3677 __isl_take isl_multi_aff *maff);
3678 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3679 __isl_take isl_set *set);
3681 __isl_give isl_union_pw_multi_aff *
3682 isl_union_pw_multi_aff_empty(
3683 __isl_take isl_space *space);
3684 __isl_give isl_union_pw_multi_aff *
3685 isl_union_pw_multi_aff_add_pw_multi_aff(
3686 __isl_take isl_union_pw_multi_aff *upma,
3687 __isl_take isl_pw_multi_aff *pma);
3688 __isl_give isl_union_pw_multi_aff *
3689 isl_union_pw_multi_aff_from_domain(
3690 __isl_take isl_union_set *uset);
3692 A piecewise multiple quasi affine expression can also be initialized
3693 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3694 and the C<isl_map> is single-valued.
3696 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3697 __isl_take isl_set *set);
3698 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3699 __isl_take isl_map *map);
3701 Multiple quasi affine expressions can be copied and freed using
3703 #include <isl/aff.h>
3704 __isl_give isl_multi_aff *isl_multi_aff_copy(
3705 __isl_keep isl_multi_aff *maff);
3706 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3708 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3709 __isl_keep isl_pw_multi_aff *pma);
3710 void *isl_pw_multi_aff_free(
3711 __isl_take isl_pw_multi_aff *pma);
3713 __isl_give isl_union_pw_multi_aff *
3714 isl_union_pw_multi_aff_copy(
3715 __isl_keep isl_union_pw_multi_aff *upma);
3716 void *isl_union_pw_multi_aff_free(
3717 __isl_take isl_union_pw_multi_aff *upma);
3719 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
3720 __isl_keep isl_multi_pw_aff *mpa);
3721 void *isl_multi_pw_aff_free(
3722 __isl_take isl_multi_pw_aff *mpa);
3724 The expression can be inspected using
3726 #include <isl/aff.h>
3727 isl_ctx *isl_multi_aff_get_ctx(
3728 __isl_keep isl_multi_aff *maff);
3729 isl_ctx *isl_pw_multi_aff_get_ctx(
3730 __isl_keep isl_pw_multi_aff *pma);
3731 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3732 __isl_keep isl_union_pw_multi_aff *upma);
3733 isl_ctx *isl_multi_pw_aff_get_ctx(
3734 __isl_keep isl_multi_pw_aff *mpa);
3735 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3736 enum isl_dim_type type);
3737 unsigned isl_pw_multi_aff_dim(
3738 __isl_keep isl_pw_multi_aff *pma,
3739 enum isl_dim_type type);
3740 unsigned isl_multi_pw_aff_dim(
3741 __isl_keep isl_multi_pw_aff *mpa,
3742 enum isl_dim_type type);
3743 __isl_give isl_aff *isl_multi_aff_get_aff(
3744 __isl_keep isl_multi_aff *multi, int pos);
3745 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3746 __isl_keep isl_pw_multi_aff *pma, int pos);
3747 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
3748 __isl_keep isl_multi_pw_aff *mpa, int pos);
3749 const char *isl_pw_multi_aff_get_dim_name(
3750 __isl_keep isl_pw_multi_aff *pma,
3751 enum isl_dim_type type, unsigned pos);
3752 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3753 __isl_keep isl_pw_multi_aff *pma,
3754 enum isl_dim_type type, unsigned pos);
3755 const char *isl_multi_aff_get_tuple_name(
3756 __isl_keep isl_multi_aff *multi,
3757 enum isl_dim_type type);
3758 int isl_pw_multi_aff_has_tuple_name(
3759 __isl_keep isl_pw_multi_aff *pma,
3760 enum isl_dim_type type);
3761 const char *isl_pw_multi_aff_get_tuple_name(
3762 __isl_keep isl_pw_multi_aff *pma,
3763 enum isl_dim_type type);
3764 int isl_pw_multi_aff_has_tuple_id(
3765 __isl_keep isl_pw_multi_aff *pma,
3766 enum isl_dim_type type);
3767 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3768 __isl_keep isl_pw_multi_aff *pma,
3769 enum isl_dim_type type);
3771 int isl_pw_multi_aff_foreach_piece(
3772 __isl_keep isl_pw_multi_aff *pma,
3773 int (*fn)(__isl_take isl_set *set,
3774 __isl_take isl_multi_aff *maff,
3775 void *user), void *user);
3777 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3778 __isl_keep isl_union_pw_multi_aff *upma,
3779 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3780 void *user), void *user);
3782 It can be modified using
3784 #include <isl/aff.h>
3785 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3786 __isl_take isl_multi_aff *multi, int pos,
3787 __isl_take isl_aff *aff);
3788 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3789 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3790 __isl_take isl_pw_aff *pa);
3791 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3792 __isl_take isl_multi_aff *maff,
3793 enum isl_dim_type type, unsigned pos, const char *s);
3794 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
3795 __isl_take isl_multi_aff *maff,
3796 enum isl_dim_type type, const char *s);
3797 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3798 __isl_take isl_multi_aff *maff,
3799 enum isl_dim_type type, __isl_take isl_id *id);
3800 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3801 __isl_take isl_pw_multi_aff *pma,
3802 enum isl_dim_type type, __isl_take isl_id *id);
3804 __isl_give isl_multi_pw_aff *
3805 isl_multi_pw_aff_set_dim_name(
3806 __isl_take isl_multi_pw_aff *mpa,
3807 enum isl_dim_type type, unsigned pos, const char *s);
3808 __isl_give isl_multi_pw_aff *
3809 isl_multi_pw_aff_set_tuple_name(
3810 __isl_take isl_multi_pw_aff *mpa,
3811 enum isl_dim_type type, const char *s);
3813 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
3814 __isl_take isl_multi_aff *ma,
3815 enum isl_dim_type type, unsigned first, unsigned n);
3816 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
3817 __isl_take isl_multi_aff *ma,
3818 enum isl_dim_type type, unsigned n);
3819 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3820 __isl_take isl_multi_aff *maff,
3821 enum isl_dim_type type, unsigned first, unsigned n);
3822 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
3823 __isl_take isl_pw_multi_aff *pma,
3824 enum isl_dim_type type, unsigned first, unsigned n);
3826 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
3827 __isl_take isl_multi_pw_aff *mpa,
3828 enum isl_dim_type type, unsigned first, unsigned n);
3829 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
3830 __isl_take isl_multi_pw_aff *mpa,
3831 enum isl_dim_type type, unsigned n);
3833 To check whether two multiple affine expressions are
3834 obviously equal to each other, use
3836 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3837 __isl_keep isl_multi_aff *maff2);
3838 int isl_pw_multi_aff_plain_is_equal(
3839 __isl_keep isl_pw_multi_aff *pma1,
3840 __isl_keep isl_pw_multi_aff *pma2);
3844 #include <isl/aff.h>
3845 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3846 __isl_take isl_pw_multi_aff *pma1,
3847 __isl_take isl_pw_multi_aff *pma2);
3848 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3849 __isl_take isl_pw_multi_aff *pma1,
3850 __isl_take isl_pw_multi_aff *pma2);
3851 __isl_give isl_multi_aff *isl_multi_aff_add(
3852 __isl_take isl_multi_aff *maff1,
3853 __isl_take isl_multi_aff *maff2);
3854 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3855 __isl_take isl_pw_multi_aff *pma1,
3856 __isl_take isl_pw_multi_aff *pma2);
3857 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3858 __isl_take isl_union_pw_multi_aff *upma1,
3859 __isl_take isl_union_pw_multi_aff *upma2);
3860 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3861 __isl_take isl_pw_multi_aff *pma1,
3862 __isl_take isl_pw_multi_aff *pma2);
3863 __isl_give isl_multi_aff *isl_multi_aff_scale(
3864 __isl_take isl_multi_aff *maff,
3866 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3867 __isl_take isl_pw_multi_aff *pma,
3868 __isl_take isl_set *set);
3869 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3870 __isl_take isl_pw_multi_aff *pma,
3871 __isl_take isl_set *set);
3872 __isl_give isl_multi_aff *isl_multi_aff_lift(
3873 __isl_take isl_multi_aff *maff,
3874 __isl_give isl_local_space **ls);
3875 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3876 __isl_take isl_pw_multi_aff *pma);
3877 __isl_give isl_multi_aff *isl_multi_aff_align_params(
3878 __isl_take isl_multi_aff *multi,
3879 __isl_take isl_space *model);
3880 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
3881 __isl_take isl_pw_multi_aff *pma,
3882 __isl_take isl_space *model);
3883 __isl_give isl_pw_multi_aff *
3884 isl_pw_multi_aff_project_domain_on_params(
3885 __isl_take isl_pw_multi_aff *pma);
3886 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3887 __isl_take isl_multi_aff *maff,
3888 __isl_take isl_set *context);
3889 __isl_give isl_multi_aff *isl_multi_aff_gist(
3890 __isl_take isl_multi_aff *maff,
3891 __isl_take isl_set *context);
3892 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3893 __isl_take isl_pw_multi_aff *pma,
3894 __isl_take isl_set *set);
3895 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3896 __isl_take isl_pw_multi_aff *pma,
3897 __isl_take isl_set *set);
3898 __isl_give isl_set *isl_pw_multi_aff_domain(
3899 __isl_take isl_pw_multi_aff *pma);
3900 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3901 __isl_take isl_union_pw_multi_aff *upma);
3902 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
3903 __isl_take isl_multi_aff *ma1, unsigned pos,
3904 __isl_take isl_multi_aff *ma2);
3905 __isl_give isl_multi_aff *isl_multi_aff_splice(
3906 __isl_take isl_multi_aff *ma1,
3907 unsigned in_pos, unsigned out_pos,
3908 __isl_take isl_multi_aff *ma2);
3909 __isl_give isl_multi_aff *isl_multi_aff_range_product(
3910 __isl_take isl_multi_aff *ma1,
3911 __isl_take isl_multi_aff *ma2);
3912 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3913 __isl_take isl_multi_aff *ma1,
3914 __isl_take isl_multi_aff *ma2);
3915 __isl_give isl_multi_aff *isl_multi_aff_product(
3916 __isl_take isl_multi_aff *ma1,
3917 __isl_take isl_multi_aff *ma2);
3918 __isl_give isl_pw_multi_aff *
3919 isl_pw_multi_aff_range_product(
3920 __isl_take isl_pw_multi_aff *pma1,
3921 __isl_take isl_pw_multi_aff *pma2);
3922 __isl_give isl_pw_multi_aff *
3923 isl_pw_multi_aff_flat_range_product(
3924 __isl_take isl_pw_multi_aff *pma1,
3925 __isl_take isl_pw_multi_aff *pma2);
3926 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3927 __isl_take isl_pw_multi_aff *pma1,
3928 __isl_take isl_pw_multi_aff *pma2);
3929 __isl_give isl_union_pw_multi_aff *
3930 isl_union_pw_multi_aff_flat_range_product(
3931 __isl_take isl_union_pw_multi_aff *upma1,
3932 __isl_take isl_union_pw_multi_aff *upma2);
3933 __isl_give isl_multi_pw_aff *
3934 isl_multi_pw_aff_range_splice(
3935 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
3936 __isl_take isl_multi_pw_aff *mpa2);
3937 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
3938 __isl_take isl_multi_pw_aff *mpa1,
3939 unsigned in_pos, unsigned out_pos,
3940 __isl_take isl_multi_pw_aff *mpa2);
3941 __isl_give isl_multi_pw_aff *
3942 isl_multi_pw_aff_range_product(
3943 __isl_take isl_multi_pw_aff *mpa1,
3944 __isl_take isl_multi_pw_aff *mpa2);
3945 __isl_give isl_multi_pw_aff *
3946 isl_multi_pw_aff_flat_range_product(
3947 __isl_take isl_multi_pw_aff *mpa1,
3948 __isl_take isl_multi_pw_aff *mpa2);
3950 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3951 then it is assigned the local space that lies at the basis of
3952 the lifting applied.
3954 #include <isl/aff.h>
3955 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
3956 __isl_take isl_multi_aff *ma1,
3957 __isl_take isl_multi_aff *ma2);
3958 __isl_give isl_pw_multi_aff *
3959 isl_pw_multi_aff_pullback_multi_aff(
3960 __isl_take isl_pw_multi_aff *pma,
3961 __isl_take isl_multi_aff *ma);
3962 __isl_give isl_pw_multi_aff *
3963 isl_pw_multi_aff_pullback_pw_multi_aff(
3964 __isl_take isl_pw_multi_aff *pma1,
3965 __isl_take isl_pw_multi_aff *pma2);
3967 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
3968 In other words, C<ma2> is plugged
3971 __isl_give isl_set *isl_multi_aff_lex_le_set(
3972 __isl_take isl_multi_aff *ma1,
3973 __isl_take isl_multi_aff *ma2);
3974 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3975 __isl_take isl_multi_aff *ma1,
3976 __isl_take isl_multi_aff *ma2);
3978 The function C<isl_multi_aff_lex_le_set> returns a set
3979 containing those elements in the shared domain space
3980 where C<ma1> is lexicographically smaller than or
3983 An expression can be read from input using
3985 #include <isl/aff.h>
3986 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3987 isl_ctx *ctx, const char *str);
3988 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3989 isl_ctx *ctx, const char *str);
3991 An expression can be printed using
3993 #include <isl/aff.h>
3994 __isl_give isl_printer *isl_printer_print_multi_aff(
3995 __isl_take isl_printer *p,
3996 __isl_keep isl_multi_aff *maff);
3997 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3998 __isl_take isl_printer *p,
3999 __isl_keep isl_pw_multi_aff *pma);
4000 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4001 __isl_take isl_printer *p,
4002 __isl_keep isl_union_pw_multi_aff *upma);
4003 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4004 __isl_take isl_printer *p,
4005 __isl_keep isl_multi_pw_aff *mpa);
4009 Points are elements of a set. They can be used to construct
4010 simple sets (boxes) or they can be used to represent the
4011 individual elements of a set.
4012 The zero point (the origin) can be created using
4014 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4016 The coordinates of a point can be inspected, set and changed
4019 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
4020 enum isl_dim_type type, int pos, isl_int *v);
4021 __isl_give isl_point *isl_point_set_coordinate(
4022 __isl_take isl_point *pnt,
4023 enum isl_dim_type type, int pos, isl_int v);
4025 __isl_give isl_point *isl_point_add_ui(
4026 __isl_take isl_point *pnt,
4027 enum isl_dim_type type, int pos, unsigned val);
4028 __isl_give isl_point *isl_point_sub_ui(
4029 __isl_take isl_point *pnt,
4030 enum isl_dim_type type, int pos, unsigned val);
4032 Other properties can be obtained using
4034 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4036 Points can be copied or freed using
4038 __isl_give isl_point *isl_point_copy(
4039 __isl_keep isl_point *pnt);
4040 void isl_point_free(__isl_take isl_point *pnt);
4042 A singleton set can be created from a point using
4044 __isl_give isl_basic_set *isl_basic_set_from_point(
4045 __isl_take isl_point *pnt);
4046 __isl_give isl_set *isl_set_from_point(
4047 __isl_take isl_point *pnt);
4049 and a box can be created from two opposite extremal points using
4051 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4052 __isl_take isl_point *pnt1,
4053 __isl_take isl_point *pnt2);
4054 __isl_give isl_set *isl_set_box_from_points(
4055 __isl_take isl_point *pnt1,
4056 __isl_take isl_point *pnt2);
4058 All elements of a B<bounded> (union) set can be enumerated using
4059 the following functions.
4061 int isl_set_foreach_point(__isl_keep isl_set *set,
4062 int (*fn)(__isl_take isl_point *pnt, void *user),
4064 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4065 int (*fn)(__isl_take isl_point *pnt, void *user),
4068 The function C<fn> is called for each integer point in
4069 C<set> with as second argument the last argument of
4070 the C<isl_set_foreach_point> call. The function C<fn>
4071 should return C<0> on success and C<-1> on failure.
4072 In the latter case, C<isl_set_foreach_point> will stop
4073 enumerating and return C<-1> as well.
4074 If the enumeration is performed successfully and to completion,
4075 then C<isl_set_foreach_point> returns C<0>.
4077 To obtain a single point of a (basic) set, use
4079 __isl_give isl_point *isl_basic_set_sample_point(
4080 __isl_take isl_basic_set *bset);
4081 __isl_give isl_point *isl_set_sample_point(
4082 __isl_take isl_set *set);
4084 If C<set> does not contain any (integer) points, then the
4085 resulting point will be ``void'', a property that can be
4088 int isl_point_is_void(__isl_keep isl_point *pnt);
4090 =head2 Piecewise Quasipolynomials
4092 A piecewise quasipolynomial is a particular kind of function that maps
4093 a parametric point to a rational value.
4094 More specifically, a quasipolynomial is a polynomial expression in greatest
4095 integer parts of affine expressions of parameters and variables.
4096 A piecewise quasipolynomial is a subdivision of a given parametric
4097 domain into disjoint cells with a quasipolynomial associated to
4098 each cell. The value of the piecewise quasipolynomial at a given
4099 point is the value of the quasipolynomial associated to the cell
4100 that contains the point. Outside of the union of cells,
4101 the value is assumed to be zero.
4102 For example, the piecewise quasipolynomial
4104 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4106 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4107 A given piecewise quasipolynomial has a fixed domain dimension.
4108 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4109 defined over different domains.
4110 Piecewise quasipolynomials are mainly used by the C<barvinok>
4111 library for representing the number of elements in a parametric set or map.
4112 For example, the piecewise quasipolynomial above represents
4113 the number of points in the map
4115 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4117 =head3 Input and Output
4119 Piecewise quasipolynomials can be read from input using
4121 __isl_give isl_union_pw_qpolynomial *
4122 isl_union_pw_qpolynomial_read_from_str(
4123 isl_ctx *ctx, const char *str);
4125 Quasipolynomials and piecewise quasipolynomials can be printed
4126 using the following functions.
4128 __isl_give isl_printer *isl_printer_print_qpolynomial(
4129 __isl_take isl_printer *p,
4130 __isl_keep isl_qpolynomial *qp);
4132 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4133 __isl_take isl_printer *p,
4134 __isl_keep isl_pw_qpolynomial *pwqp);
4136 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4137 __isl_take isl_printer *p,
4138 __isl_keep isl_union_pw_qpolynomial *upwqp);
4140 The output format of the printer
4141 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4142 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4144 In case of printing in C<ISL_FORMAT_C>, the user may want
4145 to set the names of all dimensions
4147 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4148 __isl_take isl_qpolynomial *qp,
4149 enum isl_dim_type type, unsigned pos,
4151 __isl_give isl_pw_qpolynomial *
4152 isl_pw_qpolynomial_set_dim_name(
4153 __isl_take isl_pw_qpolynomial *pwqp,
4154 enum isl_dim_type type, unsigned pos,
4157 =head3 Creating New (Piecewise) Quasipolynomials
4159 Some simple quasipolynomials can be created using the following functions.
4160 More complicated quasipolynomials can be created by applying
4161 operations such as addition and multiplication
4162 on the resulting quasipolynomials
4164 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4165 __isl_take isl_space *domain);
4166 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4167 __isl_take isl_space *domain);
4168 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4169 __isl_take isl_space *domain);
4170 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4171 __isl_take isl_space *domain);
4172 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4173 __isl_take isl_space *domain);
4174 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
4175 __isl_take isl_space *domain,
4176 const isl_int n, const isl_int d);
4177 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4178 __isl_take isl_space *domain,
4179 enum isl_dim_type type, unsigned pos);
4180 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4181 __isl_take isl_aff *aff);
4183 Note that the space in which a quasipolynomial lives is a map space
4184 with a one-dimensional range. The C<domain> argument in some of
4185 the functions above corresponds to the domain of this map space.
4187 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4188 with a single cell can be created using the following functions.
4189 Multiple of these single cell piecewise quasipolynomials can
4190 be combined to create more complicated piecewise quasipolynomials.
4192 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4193 __isl_take isl_space *space);
4194 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4195 __isl_take isl_set *set,
4196 __isl_take isl_qpolynomial *qp);
4197 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4198 __isl_take isl_qpolynomial *qp);
4199 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4200 __isl_take isl_pw_aff *pwaff);
4202 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4203 __isl_take isl_space *space);
4204 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4205 __isl_take isl_pw_qpolynomial *pwqp);
4206 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4207 __isl_take isl_union_pw_qpolynomial *upwqp,
4208 __isl_take isl_pw_qpolynomial *pwqp);
4210 Quasipolynomials can be copied and freed again using the following
4213 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4214 __isl_keep isl_qpolynomial *qp);
4215 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4217 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4218 __isl_keep isl_pw_qpolynomial *pwqp);
4219 void *isl_pw_qpolynomial_free(
4220 __isl_take isl_pw_qpolynomial *pwqp);
4222 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4223 __isl_keep isl_union_pw_qpolynomial *upwqp);
4224 void *isl_union_pw_qpolynomial_free(
4225 __isl_take isl_union_pw_qpolynomial *upwqp);
4227 =head3 Inspecting (Piecewise) Quasipolynomials
4229 To iterate over all piecewise quasipolynomials in a union
4230 piecewise quasipolynomial, use the following function
4232 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4233 __isl_keep isl_union_pw_qpolynomial *upwqp,
4234 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4237 To extract the piecewise quasipolynomial in a given space from a union, use
4239 __isl_give isl_pw_qpolynomial *
4240 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4241 __isl_keep isl_union_pw_qpolynomial *upwqp,
4242 __isl_take isl_space *space);
4244 To iterate over the cells in a piecewise quasipolynomial,
4245 use either of the following two functions
4247 int isl_pw_qpolynomial_foreach_piece(
4248 __isl_keep isl_pw_qpolynomial *pwqp,
4249 int (*fn)(__isl_take isl_set *set,
4250 __isl_take isl_qpolynomial *qp,
4251 void *user), void *user);
4252 int isl_pw_qpolynomial_foreach_lifted_piece(
4253 __isl_keep isl_pw_qpolynomial *pwqp,
4254 int (*fn)(__isl_take isl_set *set,
4255 __isl_take isl_qpolynomial *qp,
4256 void *user), void *user);
4258 As usual, the function C<fn> should return C<0> on success
4259 and C<-1> on failure. The difference between
4260 C<isl_pw_qpolynomial_foreach_piece> and
4261 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4262 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4263 compute unique representations for all existentially quantified
4264 variables and then turn these existentially quantified variables
4265 into extra set variables, adapting the associated quasipolynomial
4266 accordingly. This means that the C<set> passed to C<fn>
4267 will not have any existentially quantified variables, but that
4268 the dimensions of the sets may be different for different
4269 invocations of C<fn>.
4271 To iterate over all terms in a quasipolynomial,
4274 int isl_qpolynomial_foreach_term(
4275 __isl_keep isl_qpolynomial *qp,
4276 int (*fn)(__isl_take isl_term *term,
4277 void *user), void *user);
4279 The terms themselves can be inspected and freed using
4282 unsigned isl_term_dim(__isl_keep isl_term *term,
4283 enum isl_dim_type type);
4284 void isl_term_get_num(__isl_keep isl_term *term,
4286 void isl_term_get_den(__isl_keep isl_term *term,
4288 int isl_term_get_exp(__isl_keep isl_term *term,
4289 enum isl_dim_type type, unsigned pos);
4290 __isl_give isl_aff *isl_term_get_div(
4291 __isl_keep isl_term *term, unsigned pos);
4292 void isl_term_free(__isl_take isl_term *term);
4294 Each term is a product of parameters, set variables and
4295 integer divisions. The function C<isl_term_get_exp>
4296 returns the exponent of a given dimensions in the given term.
4297 The C<isl_int>s in the arguments of C<isl_term_get_num>
4298 and C<isl_term_get_den> need to have been initialized
4299 using C<isl_int_init> before calling these functions.
4301 =head3 Properties of (Piecewise) Quasipolynomials
4303 To check whether a quasipolynomial is actually a constant,
4304 use the following function.
4306 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4307 isl_int *n, isl_int *d);
4309 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4310 then the numerator and denominator of the constant
4311 are returned in C<*n> and C<*d>, respectively.
4313 To check whether two union piecewise quasipolynomials are
4314 obviously equal, use
4316 int isl_union_pw_qpolynomial_plain_is_equal(
4317 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4318 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4320 =head3 Operations on (Piecewise) Quasipolynomials
4322 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4323 __isl_take isl_qpolynomial *qp, isl_int v);
4324 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4325 __isl_take isl_qpolynomial *qp);
4326 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4327 __isl_take isl_qpolynomial *qp1,
4328 __isl_take isl_qpolynomial *qp2);
4329 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4330 __isl_take isl_qpolynomial *qp1,
4331 __isl_take isl_qpolynomial *qp2);
4332 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4333 __isl_take isl_qpolynomial *qp1,
4334 __isl_take isl_qpolynomial *qp2);
4335 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4336 __isl_take isl_qpolynomial *qp, unsigned exponent);
4338 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4339 __isl_take isl_pw_qpolynomial *pwqp1,
4340 __isl_take isl_pw_qpolynomial *pwqp2);
4341 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4342 __isl_take isl_pw_qpolynomial *pwqp1,
4343 __isl_take isl_pw_qpolynomial *pwqp2);
4344 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4345 __isl_take isl_pw_qpolynomial *pwqp1,
4346 __isl_take isl_pw_qpolynomial *pwqp2);
4347 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4348 __isl_take isl_pw_qpolynomial *pwqp);
4349 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4350 __isl_take isl_pw_qpolynomial *pwqp1,
4351 __isl_take isl_pw_qpolynomial *pwqp2);
4352 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4353 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4355 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4356 __isl_take isl_union_pw_qpolynomial *upwqp1,
4357 __isl_take isl_union_pw_qpolynomial *upwqp2);
4358 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4359 __isl_take isl_union_pw_qpolynomial *upwqp1,
4360 __isl_take isl_union_pw_qpolynomial *upwqp2);
4361 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4362 __isl_take isl_union_pw_qpolynomial *upwqp1,
4363 __isl_take isl_union_pw_qpolynomial *upwqp2);
4365 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4366 __isl_take isl_pw_qpolynomial *pwqp,
4367 __isl_take isl_point *pnt);
4369 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4370 __isl_take isl_union_pw_qpolynomial *upwqp,
4371 __isl_take isl_point *pnt);
4373 __isl_give isl_set *isl_pw_qpolynomial_domain(
4374 __isl_take isl_pw_qpolynomial *pwqp);
4375 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4376 __isl_take isl_pw_qpolynomial *pwpq,
4377 __isl_take isl_set *set);
4378 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4379 __isl_take isl_pw_qpolynomial *pwpq,
4380 __isl_take isl_set *set);
4382 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4383 __isl_take isl_union_pw_qpolynomial *upwqp);
4384 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4385 __isl_take isl_union_pw_qpolynomial *upwpq,
4386 __isl_take isl_union_set *uset);
4387 __isl_give isl_union_pw_qpolynomial *
4388 isl_union_pw_qpolynomial_intersect_params(
4389 __isl_take isl_union_pw_qpolynomial *upwpq,
4390 __isl_take isl_set *set);
4392 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4393 __isl_take isl_qpolynomial *qp,
4394 __isl_take isl_space *model);
4396 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4397 __isl_take isl_qpolynomial *qp);
4398 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4399 __isl_take isl_pw_qpolynomial *pwqp);
4401 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4402 __isl_take isl_union_pw_qpolynomial *upwqp);
4404 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4405 __isl_take isl_qpolynomial *qp,
4406 __isl_take isl_set *context);
4407 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4408 __isl_take isl_qpolynomial *qp,
4409 __isl_take isl_set *context);
4411 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4412 __isl_take isl_pw_qpolynomial *pwqp,
4413 __isl_take isl_set *context);
4414 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4415 __isl_take isl_pw_qpolynomial *pwqp,
4416 __isl_take isl_set *context);
4418 __isl_give isl_union_pw_qpolynomial *
4419 isl_union_pw_qpolynomial_gist_params(
4420 __isl_take isl_union_pw_qpolynomial *upwqp,
4421 __isl_take isl_set *context);
4422 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4423 __isl_take isl_union_pw_qpolynomial *upwqp,
4424 __isl_take isl_union_set *context);
4426 The gist operation applies the gist operation to each of
4427 the cells in the domain of the input piecewise quasipolynomial.
4428 The context is also exploited
4429 to simplify the quasipolynomials associated to each cell.
4431 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4432 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4433 __isl_give isl_union_pw_qpolynomial *
4434 isl_union_pw_qpolynomial_to_polynomial(
4435 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4437 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4438 the polynomial will be an overapproximation. If C<sign> is negative,
4439 it will be an underapproximation. If C<sign> is zero, the approximation
4440 will lie somewhere in between.
4442 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4444 A piecewise quasipolynomial reduction is a piecewise
4445 reduction (or fold) of quasipolynomials.
4446 In particular, the reduction can be maximum or a minimum.
4447 The objects are mainly used to represent the result of
4448 an upper or lower bound on a quasipolynomial over its domain,
4449 i.e., as the result of the following function.
4451 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4452 __isl_take isl_pw_qpolynomial *pwqp,
4453 enum isl_fold type, int *tight);
4455 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4456 __isl_take isl_union_pw_qpolynomial *upwqp,
4457 enum isl_fold type, int *tight);
4459 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4460 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4461 is the returned bound is known be tight, i.e., for each value
4462 of the parameters there is at least
4463 one element in the domain that reaches the bound.
4464 If the domain of C<pwqp> is not wrapping, then the bound is computed
4465 over all elements in that domain and the result has a purely parametric
4466 domain. If the domain of C<pwqp> is wrapping, then the bound is
4467 computed over the range of the wrapped relation. The domain of the
4468 wrapped relation becomes the domain of the result.
4470 A (piecewise) quasipolynomial reduction can be copied or freed using the
4471 following functions.
4473 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4474 __isl_keep isl_qpolynomial_fold *fold);
4475 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4476 __isl_keep isl_pw_qpolynomial_fold *pwf);
4477 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4478 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4479 void isl_qpolynomial_fold_free(
4480 __isl_take isl_qpolynomial_fold *fold);
4481 void *isl_pw_qpolynomial_fold_free(
4482 __isl_take isl_pw_qpolynomial_fold *pwf);
4483 void *isl_union_pw_qpolynomial_fold_free(
4484 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4486 =head3 Printing Piecewise Quasipolynomial Reductions
4488 Piecewise quasipolynomial reductions can be printed
4489 using the following function.
4491 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4492 __isl_take isl_printer *p,
4493 __isl_keep isl_pw_qpolynomial_fold *pwf);
4494 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4495 __isl_take isl_printer *p,
4496 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4498 For C<isl_printer_print_pw_qpolynomial_fold>,
4499 output format of the printer
4500 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4501 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4502 output format of the printer
4503 needs to be set to C<ISL_FORMAT_ISL>.
4504 In case of printing in C<ISL_FORMAT_C>, the user may want
4505 to set the names of all dimensions
4507 __isl_give isl_pw_qpolynomial_fold *
4508 isl_pw_qpolynomial_fold_set_dim_name(
4509 __isl_take isl_pw_qpolynomial_fold *pwf,
4510 enum isl_dim_type type, unsigned pos,
4513 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4515 To iterate over all piecewise quasipolynomial reductions in a union
4516 piecewise quasipolynomial reduction, use the following function
4518 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4519 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4520 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4521 void *user), void *user);
4523 To iterate over the cells in a piecewise quasipolynomial reduction,
4524 use either of the following two functions
4526 int isl_pw_qpolynomial_fold_foreach_piece(
4527 __isl_keep isl_pw_qpolynomial_fold *pwf,
4528 int (*fn)(__isl_take isl_set *set,
4529 __isl_take isl_qpolynomial_fold *fold,
4530 void *user), void *user);
4531 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4532 __isl_keep isl_pw_qpolynomial_fold *pwf,
4533 int (*fn)(__isl_take isl_set *set,
4534 __isl_take isl_qpolynomial_fold *fold,
4535 void *user), void *user);
4537 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4538 of the difference between these two functions.
4540 To iterate over all quasipolynomials in a reduction, use
4542 int isl_qpolynomial_fold_foreach_qpolynomial(
4543 __isl_keep isl_qpolynomial_fold *fold,
4544 int (*fn)(__isl_take isl_qpolynomial *qp,
4545 void *user), void *user);
4547 =head3 Properties of Piecewise Quasipolynomial Reductions
4549 To check whether two union piecewise quasipolynomial reductions are
4550 obviously equal, use
4552 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4553 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4554 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4556 =head3 Operations on Piecewise Quasipolynomial Reductions
4558 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4559 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4561 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4562 __isl_take isl_pw_qpolynomial_fold *pwf1,
4563 __isl_take isl_pw_qpolynomial_fold *pwf2);
4565 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4566 __isl_take isl_pw_qpolynomial_fold *pwf1,
4567 __isl_take isl_pw_qpolynomial_fold *pwf2);
4569 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4570 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4571 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4573 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4574 __isl_take isl_pw_qpolynomial_fold *pwf,
4575 __isl_take isl_point *pnt);
4577 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4578 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4579 __isl_take isl_point *pnt);
4581 __isl_give isl_pw_qpolynomial_fold *
4582 isl_pw_qpolynomial_fold_intersect_params(
4583 __isl_take isl_pw_qpolynomial_fold *pwf,
4584 __isl_take isl_set *set);
4586 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4587 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4588 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4589 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4590 __isl_take isl_union_set *uset);
4591 __isl_give isl_union_pw_qpolynomial_fold *
4592 isl_union_pw_qpolynomial_fold_intersect_params(
4593 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4594 __isl_take isl_set *set);
4596 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4597 __isl_take isl_pw_qpolynomial_fold *pwf);
4599 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4600 __isl_take isl_pw_qpolynomial_fold *pwf);
4602 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4603 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4605 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4606 __isl_take isl_qpolynomial_fold *fold,
4607 __isl_take isl_set *context);
4608 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4609 __isl_take isl_qpolynomial_fold *fold,
4610 __isl_take isl_set *context);
4612 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4613 __isl_take isl_pw_qpolynomial_fold *pwf,
4614 __isl_take isl_set *context);
4615 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4616 __isl_take isl_pw_qpolynomial_fold *pwf,
4617 __isl_take isl_set *context);
4619 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4620 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4621 __isl_take isl_union_set *context);
4622 __isl_give isl_union_pw_qpolynomial_fold *
4623 isl_union_pw_qpolynomial_fold_gist_params(
4624 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4625 __isl_take isl_set *context);
4627 The gist operation applies the gist operation to each of
4628 the cells in the domain of the input piecewise quasipolynomial reduction.
4629 In future, the operation will also exploit the context
4630 to simplify the quasipolynomial reductions associated to each cell.
4632 __isl_give isl_pw_qpolynomial_fold *
4633 isl_set_apply_pw_qpolynomial_fold(
4634 __isl_take isl_set *set,
4635 __isl_take isl_pw_qpolynomial_fold *pwf,
4637 __isl_give isl_pw_qpolynomial_fold *
4638 isl_map_apply_pw_qpolynomial_fold(
4639 __isl_take isl_map *map,
4640 __isl_take isl_pw_qpolynomial_fold *pwf,
4642 __isl_give isl_union_pw_qpolynomial_fold *
4643 isl_union_set_apply_union_pw_qpolynomial_fold(
4644 __isl_take isl_union_set *uset,
4645 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4647 __isl_give isl_union_pw_qpolynomial_fold *
4648 isl_union_map_apply_union_pw_qpolynomial_fold(
4649 __isl_take isl_union_map *umap,
4650 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4653 The functions taking a map
4654 compose the given map with the given piecewise quasipolynomial reduction.
4655 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4656 over all elements in the intersection of the range of the map
4657 and the domain of the piecewise quasipolynomial reduction
4658 as a function of an element in the domain of the map.
4659 The functions taking a set compute a bound over all elements in the
4660 intersection of the set and the domain of the
4661 piecewise quasipolynomial reduction.
4663 =head2 Parametric Vertex Enumeration
4665 The parametric vertex enumeration described in this section
4666 is mainly intended to be used internally and by the C<barvinok>
4669 #include <isl/vertices.h>
4670 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4671 __isl_keep isl_basic_set *bset);
4673 The function C<isl_basic_set_compute_vertices> performs the
4674 actual computation of the parametric vertices and the chamber
4675 decomposition and store the result in an C<isl_vertices> object.
4676 This information can be queried by either iterating over all
4677 the vertices or iterating over all the chambers or cells
4678 and then iterating over all vertices that are active on the chamber.
4680 int isl_vertices_foreach_vertex(
4681 __isl_keep isl_vertices *vertices,
4682 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4685 int isl_vertices_foreach_cell(
4686 __isl_keep isl_vertices *vertices,
4687 int (*fn)(__isl_take isl_cell *cell, void *user),
4689 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4690 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4693 Other operations that can be performed on an C<isl_vertices> object are
4696 isl_ctx *isl_vertices_get_ctx(
4697 __isl_keep isl_vertices *vertices);
4698 int isl_vertices_get_n_vertices(
4699 __isl_keep isl_vertices *vertices);
4700 void isl_vertices_free(__isl_take isl_vertices *vertices);
4702 Vertices can be inspected and destroyed using the following functions.
4704 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4705 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4706 __isl_give isl_basic_set *isl_vertex_get_domain(
4707 __isl_keep isl_vertex *vertex);
4708 __isl_give isl_basic_set *isl_vertex_get_expr(
4709 __isl_keep isl_vertex *vertex);
4710 void isl_vertex_free(__isl_take isl_vertex *vertex);
4712 C<isl_vertex_get_expr> returns a singleton parametric set describing
4713 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4715 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4716 B<rational> basic sets, so they should mainly be used for inspection
4717 and should not be mixed with integer sets.
4719 Chambers can be inspected and destroyed using the following functions.
4721 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4722 __isl_give isl_basic_set *isl_cell_get_domain(
4723 __isl_keep isl_cell *cell);
4724 void isl_cell_free(__isl_take isl_cell *cell);
4726 =head1 Polyhedral Compilation Library
4728 This section collects functionality in C<isl> that has been specifically
4729 designed for use during polyhedral compilation.
4731 =head2 Dependence Analysis
4733 C<isl> contains specialized functionality for performing
4734 array dataflow analysis. That is, given a I<sink> access relation
4735 and a collection of possible I<source> access relations,
4736 C<isl> can compute relations that describe
4737 for each iteration of the sink access, which iteration
4738 of which of the source access relations was the last
4739 to access the same data element before the given iteration
4741 The resulting dependence relations map source iterations
4742 to the corresponding sink iterations.
4743 To compute standard flow dependences, the sink should be
4744 a read, while the sources should be writes.
4745 If any of the source accesses are marked as being I<may>
4746 accesses, then there will be a dependence from the last
4747 I<must> access B<and> from any I<may> access that follows
4748 this last I<must> access.
4749 In particular, if I<all> sources are I<may> accesses,
4750 then memory based dependence analysis is performed.
4751 If, on the other hand, all sources are I<must> accesses,
4752 then value based dependence analysis is performed.
4754 #include <isl/flow.h>
4756 typedef int (*isl_access_level_before)(void *first, void *second);
4758 __isl_give isl_access_info *isl_access_info_alloc(
4759 __isl_take isl_map *sink,
4760 void *sink_user, isl_access_level_before fn,
4762 __isl_give isl_access_info *isl_access_info_add_source(
4763 __isl_take isl_access_info *acc,
4764 __isl_take isl_map *source, int must,
4766 void *isl_access_info_free(__isl_take isl_access_info *acc);
4768 __isl_give isl_flow *isl_access_info_compute_flow(
4769 __isl_take isl_access_info *acc);
4771 int isl_flow_foreach(__isl_keep isl_flow *deps,
4772 int (*fn)(__isl_take isl_map *dep, int must,
4773 void *dep_user, void *user),
4775 __isl_give isl_map *isl_flow_get_no_source(
4776 __isl_keep isl_flow *deps, int must);
4777 void isl_flow_free(__isl_take isl_flow *deps);
4779 The function C<isl_access_info_compute_flow> performs the actual
4780 dependence analysis. The other functions are used to construct
4781 the input for this function or to read off the output.
4783 The input is collected in an C<isl_access_info>, which can
4784 be created through a call to C<isl_access_info_alloc>.
4785 The arguments to this functions are the sink access relation
4786 C<sink>, a token C<sink_user> used to identify the sink
4787 access to the user, a callback function for specifying the
4788 relative order of source and sink accesses, and the number
4789 of source access relations that will be added.
4790 The callback function has type C<int (*)(void *first, void *second)>.
4791 The function is called with two user supplied tokens identifying
4792 either a source or the sink and it should return the shared nesting
4793 level and the relative order of the two accesses.
4794 In particular, let I<n> be the number of loops shared by
4795 the two accesses. If C<first> precedes C<second> textually,
4796 then the function should return I<2 * n + 1>; otherwise,
4797 it should return I<2 * n>.
4798 The sources can be added to the C<isl_access_info> by performing
4799 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4800 C<must> indicates whether the source is a I<must> access
4801 or a I<may> access. Note that a multi-valued access relation
4802 should only be marked I<must> if every iteration in the domain
4803 of the relation accesses I<all> elements in its image.
4804 The C<source_user> token is again used to identify
4805 the source access. The range of the source access relation
4806 C<source> should have the same dimension as the range
4807 of the sink access relation.
4808 The C<isl_access_info_free> function should usually not be
4809 called explicitly, because it is called implicitly by
4810 C<isl_access_info_compute_flow>.
4812 The result of the dependence analysis is collected in an
4813 C<isl_flow>. There may be elements of
4814 the sink access for which no preceding source access could be
4815 found or for which all preceding sources are I<may> accesses.
4816 The relations containing these elements can be obtained through
4817 calls to C<isl_flow_get_no_source>, the first with C<must> set
4818 and the second with C<must> unset.
4819 In the case of standard flow dependence analysis,
4820 with the sink a read and the sources I<must> writes,
4821 the first relation corresponds to the reads from uninitialized
4822 array elements and the second relation is empty.
4823 The actual flow dependences can be extracted using
4824 C<isl_flow_foreach>. This function will call the user-specified
4825 callback function C<fn> for each B<non-empty> dependence between
4826 a source and the sink. The callback function is called
4827 with four arguments, the actual flow dependence relation
4828 mapping source iterations to sink iterations, a boolean that
4829 indicates whether it is a I<must> or I<may> dependence, a token
4830 identifying the source and an additional C<void *> with value
4831 equal to the third argument of the C<isl_flow_foreach> call.
4832 A dependence is marked I<must> if it originates from a I<must>
4833 source and if it is not followed by any I<may> sources.
4835 After finishing with an C<isl_flow>, the user should call
4836 C<isl_flow_free> to free all associated memory.
4838 A higher-level interface to dependence analysis is provided
4839 by the following function.
4841 #include <isl/flow.h>
4843 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4844 __isl_take isl_union_map *must_source,
4845 __isl_take isl_union_map *may_source,
4846 __isl_take isl_union_map *schedule,
4847 __isl_give isl_union_map **must_dep,
4848 __isl_give isl_union_map **may_dep,
4849 __isl_give isl_union_map **must_no_source,
4850 __isl_give isl_union_map **may_no_source);
4852 The arrays are identified by the tuple names of the ranges
4853 of the accesses. The iteration domains by the tuple names
4854 of the domains of the accesses and of the schedule.
4855 The relative order of the iteration domains is given by the
4856 schedule. The relations returned through C<must_no_source>
4857 and C<may_no_source> are subsets of C<sink>.
4858 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4859 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4860 any of the other arguments is treated as an error.
4862 =head3 Interaction with Dependence Analysis
4864 During the dependence analysis, we frequently need to perform
4865 the following operation. Given a relation between sink iterations
4866 and potential source iterations from a particular source domain,
4867 what is the last potential source iteration corresponding to each
4868 sink iteration. It can sometimes be convenient to adjust
4869 the set of potential source iterations before or after each such operation.
4870 The prototypical example is fuzzy array dataflow analysis,
4871 where we need to analyze if, based on data-dependent constraints,
4872 the sink iteration can ever be executed without one or more of
4873 the corresponding potential source iterations being executed.
4874 If so, we can introduce extra parameters and select an unknown
4875 but fixed source iteration from the potential source iterations.
4876 To be able to perform such manipulations, C<isl> provides the following
4879 #include <isl/flow.h>
4881 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4882 __isl_keep isl_map *source_map,
4883 __isl_keep isl_set *sink, void *source_user,
4885 __isl_give isl_access_info *isl_access_info_set_restrict(
4886 __isl_take isl_access_info *acc,
4887 isl_access_restrict fn, void *user);
4889 The function C<isl_access_info_set_restrict> should be called
4890 before calling C<isl_access_info_compute_flow> and registers a callback function
4891 that will be called any time C<isl> is about to compute the last
4892 potential source. The first argument is the (reverse) proto-dependence,
4893 mapping sink iterations to potential source iterations.
4894 The second argument represents the sink iterations for which
4895 we want to compute the last source iteration.
4896 The third argument is the token corresponding to the source
4897 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4898 The callback is expected to return a restriction on either the input or
4899 the output of the operation computing the last potential source.
4900 If the input needs to be restricted then restrictions are needed
4901 for both the source and the sink iterations. The sink iterations
4902 and the potential source iterations will be intersected with these sets.
4903 If the output needs to be restricted then only a restriction on the source
4904 iterations is required.
4905 If any error occurs, the callback should return C<NULL>.
4906 An C<isl_restriction> object can be created, freed and inspected
4907 using the following functions.
4909 #include <isl/flow.h>
4911 __isl_give isl_restriction *isl_restriction_input(
4912 __isl_take isl_set *source_restr,
4913 __isl_take isl_set *sink_restr);
4914 __isl_give isl_restriction *isl_restriction_output(
4915 __isl_take isl_set *source_restr);
4916 __isl_give isl_restriction *isl_restriction_none(
4917 __isl_take isl_map *source_map);
4918 __isl_give isl_restriction *isl_restriction_empty(
4919 __isl_take isl_map *source_map);
4920 void *isl_restriction_free(
4921 __isl_take isl_restriction *restr);
4922 isl_ctx *isl_restriction_get_ctx(
4923 __isl_keep isl_restriction *restr);
4925 C<isl_restriction_none> and C<isl_restriction_empty> are special
4926 cases of C<isl_restriction_input>. C<isl_restriction_none>
4927 is essentially equivalent to
4929 isl_restriction_input(isl_set_universe(
4930 isl_space_range(isl_map_get_space(source_map))),
4932 isl_space_domain(isl_map_get_space(source_map))));
4934 whereas C<isl_restriction_empty> is essentially equivalent to
4936 isl_restriction_input(isl_set_empty(
4937 isl_space_range(isl_map_get_space(source_map))),
4939 isl_space_domain(isl_map_get_space(source_map))));
4943 B<The functionality described in this section is fairly new
4944 and may be subject to change.>
4946 The following function can be used to compute a schedule
4947 for a union of domains.
4948 By default, the algorithm used to construct the schedule is similar
4949 to that of C<Pluto>.
4950 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4952 The generated schedule respects all C<validity> dependences.
4953 That is, all dependence distances over these dependences in the
4954 scheduled space are lexicographically positive.
4955 The default algorithm tries to minimize the dependence distances over
4956 C<proximity> dependences.
4957 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4958 for groups of domains where the dependence distances have only
4959 non-negative values.
4960 When using Feautrier's algorithm, the C<proximity> dependence
4961 distances are only minimized during the extension to a
4962 full-dimensional schedule.
4964 #include <isl/schedule.h>
4965 __isl_give isl_schedule *isl_union_set_compute_schedule(
4966 __isl_take isl_union_set *domain,
4967 __isl_take isl_union_map *validity,
4968 __isl_take isl_union_map *proximity);
4969 void *isl_schedule_free(__isl_take isl_schedule *sched);
4971 A mapping from the domains to the scheduled space can be obtained
4972 from an C<isl_schedule> using the following function.
4974 __isl_give isl_union_map *isl_schedule_get_map(
4975 __isl_keep isl_schedule *sched);
4977 A representation of the schedule can be printed using
4979 __isl_give isl_printer *isl_printer_print_schedule(
4980 __isl_take isl_printer *p,
4981 __isl_keep isl_schedule *schedule);
4983 A representation of the schedule as a forest of bands can be obtained
4984 using the following function.
4986 __isl_give isl_band_list *isl_schedule_get_band_forest(
4987 __isl_keep isl_schedule *schedule);
4989 The individual bands can be visited in depth-first post-order
4990 using the following function.
4992 #include <isl/schedule.h>
4993 int isl_schedule_foreach_band(
4994 __isl_keep isl_schedule *sched,
4995 int (*fn)(__isl_keep isl_band *band, void *user),
4998 The list can be manipulated as explained in L<"Lists">.
4999 The bands inside the list can be copied and freed using the following
5002 #include <isl/band.h>
5003 __isl_give isl_band *isl_band_copy(
5004 __isl_keep isl_band *band);
5005 void *isl_band_free(__isl_take isl_band *band);
5007 Each band contains zero or more scheduling dimensions.
5008 These are referred to as the members of the band.
5009 The section of the schedule that corresponds to the band is
5010 referred to as the partial schedule of the band.
5011 For those nodes that participate in a band, the outer scheduling
5012 dimensions form the prefix schedule, while the inner scheduling
5013 dimensions form the suffix schedule.
5014 That is, if we take a cut of the band forest, then the union of
5015 the concatenations of the prefix, partial and suffix schedules of
5016 each band in the cut is equal to the entire schedule (modulo
5017 some possible padding at the end with zero scheduling dimensions).
5018 The properties of a band can be inspected using the following functions.
5020 #include <isl/band.h>
5021 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5023 int isl_band_has_children(__isl_keep isl_band *band);
5024 __isl_give isl_band_list *isl_band_get_children(
5025 __isl_keep isl_band *band);
5027 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5028 __isl_keep isl_band *band);
5029 __isl_give isl_union_map *isl_band_get_partial_schedule(
5030 __isl_keep isl_band *band);
5031 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5032 __isl_keep isl_band *band);
5034 int isl_band_n_member(__isl_keep isl_band *band);
5035 int isl_band_member_is_zero_distance(
5036 __isl_keep isl_band *band, int pos);
5038 int isl_band_list_foreach_band(
5039 __isl_keep isl_band_list *list,
5040 int (*fn)(__isl_keep isl_band *band, void *user),
5043 Note that a scheduling dimension is considered to be ``zero
5044 distance'' if it does not carry any proximity dependences
5046 That is, if the dependence distances of the proximity
5047 dependences are all zero in that direction (for fixed
5048 iterations of outer bands).
5049 Like C<isl_schedule_foreach_band>,
5050 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5051 in depth-first post-order.
5053 A band can be tiled using the following function.
5055 #include <isl/band.h>
5056 int isl_band_tile(__isl_keep isl_band *band,
5057 __isl_take isl_vec *sizes);
5059 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5061 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5063 The C<isl_band_tile> function tiles the band using the given tile sizes
5064 inside its schedule.
5065 A new child band is created to represent the point loops and it is
5066 inserted between the modified band and its children.
5067 The C<tile_scale_tile_loops> option specifies whether the tile
5068 loops iterators should be scaled by the tile sizes.
5070 A representation of the band can be printed using
5072 #include <isl/band.h>
5073 __isl_give isl_printer *isl_printer_print_band(
5074 __isl_take isl_printer *p,
5075 __isl_keep isl_band *band);
5079 #include <isl/schedule.h>
5080 int isl_options_set_schedule_max_coefficient(
5081 isl_ctx *ctx, int val);
5082 int isl_options_get_schedule_max_coefficient(
5084 int isl_options_set_schedule_max_constant_term(
5085 isl_ctx *ctx, int val);
5086 int isl_options_get_schedule_max_constant_term(
5088 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5089 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5090 int isl_options_set_schedule_maximize_band_depth(
5091 isl_ctx *ctx, int val);
5092 int isl_options_get_schedule_maximize_band_depth(
5094 int isl_options_set_schedule_outer_zero_distance(
5095 isl_ctx *ctx, int val);
5096 int isl_options_get_schedule_outer_zero_distance(
5098 int isl_options_set_schedule_split_scaled(
5099 isl_ctx *ctx, int val);
5100 int isl_options_get_schedule_split_scaled(
5102 int isl_options_set_schedule_algorithm(
5103 isl_ctx *ctx, int val);
5104 int isl_options_get_schedule_algorithm(
5106 int isl_options_set_schedule_separate_components(
5107 isl_ctx *ctx, int val);
5108 int isl_options_get_schedule_separate_components(
5113 =item * schedule_max_coefficient
5115 This option enforces that the coefficients for variable and parameter
5116 dimensions in the calculated schedule are not larger than the specified value.
5117 This option can significantly increase the speed of the scheduling calculation
5118 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5119 this option does not introduce bounds on the variable or parameter
5122 =item * schedule_max_constant_term
5124 This option enforces that the constant coefficients in the calculated schedule
5125 are not larger than the maximal constant term. This option can significantly
5126 increase the speed of the scheduling calculation and may also prevent fusing of
5127 unrelated dimensions. A value of -1 means that this option does not introduce
5128 bounds on the constant coefficients.
5130 =item * schedule_fuse
5132 This option controls the level of fusion.
5133 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5134 resulting schedule will be distributed as much as possible.
5135 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5136 try to fuse loops in the resulting schedule.
5138 =item * schedule_maximize_band_depth
5140 If this option is set, we do not split bands at the point
5141 where we detect splitting is necessary. Instead, we
5142 backtrack and split bands as early as possible. This
5143 reduces the number of splits and maximizes the width of
5144 the bands. Wider bands give more possibilities for tiling.
5145 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5146 then bands will be split as early as possible, even if there is no need.
5147 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5149 =item * schedule_outer_zero_distance
5151 If this option is set, then we try to construct schedules
5152 where the outermost scheduling dimension in each band
5153 results in a zero dependence distance over the proximity
5156 =item * schedule_split_scaled
5158 If this option is set, then we try to construct schedules in which the
5159 constant term is split off from the linear part if the linear parts of
5160 the scheduling rows for all nodes in the graphs have a common non-trivial
5162 The constant term is then placed in a separate band and the linear
5165 =item * schedule_algorithm
5167 Selects the scheduling algorithm to be used.
5168 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5169 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5171 =item * schedule_separate_components
5173 If at any point the dependence graph contains any (weakly connected) components,
5174 then these components are scheduled separately.
5175 If this option is not set, then some iterations of the domains
5176 in these components may be scheduled together.
5177 If this option is set, then the components are given consecutive
5184 Although C<isl> is mainly meant to be used as a library,
5185 it also contains some basic applications that use some
5186 of the functionality of C<isl>.
5187 The input may be specified in either the L<isl format>
5188 or the L<PolyLib format>.
5190 =head2 C<isl_polyhedron_sample>
5192 C<isl_polyhedron_sample> takes a polyhedron as input and prints
5193 an integer element of the polyhedron, if there is any.
5194 The first column in the output is the denominator and is always
5195 equal to 1. If the polyhedron contains no integer points,
5196 then a vector of length zero is printed.
5200 C<isl_pip> takes the same input as the C<example> program
5201 from the C<piplib> distribution, i.e., a set of constraints
5202 on the parameters, a line containing only -1 and finally a set
5203 of constraints on a parametric polyhedron.
5204 The coefficients of the parameters appear in the last columns
5205 (but before the final constant column).
5206 The output is the lexicographic minimum of the parametric polyhedron.
5207 As C<isl> currently does not have its own output format, the output
5208 is just a dump of the internal state.
5210 =head2 C<isl_polyhedron_minimize>
5212 C<isl_polyhedron_minimize> computes the minimum of some linear
5213 or affine objective function over the integer points in a polyhedron.
5214 If an affine objective function
5215 is given, then the constant should appear in the last column.
5217 =head2 C<isl_polytope_scan>
5219 Given a polytope, C<isl_polytope_scan> prints
5220 all integer points in the polytope.