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_set_free_user(
602 __isl_take isl_id *id,
603 __isl_give void (*free_user)(void *user));
604 __isl_give isl_id *isl_id_copy(isl_id *id);
605 void *isl_id_free(__isl_take isl_id *id);
607 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
608 void *isl_id_get_user(__isl_keep isl_id *id);
609 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
611 __isl_give isl_printer *isl_printer_print_id(
612 __isl_take isl_printer *p, __isl_keep isl_id *id);
614 The callback set by C<isl_id_set_free_user> is called on the user
615 pointer when the last reference to the C<isl_id> is freed.
616 Note that C<isl_id_get_name> returns a pointer to some internal
617 data structure, so the result can only be used while the
618 corresponding C<isl_id> is alive.
622 Whenever a new set, relation or similiar object is created from scratch,
623 the space in which it lives needs to be specified using an C<isl_space>.
624 Each space involves zero or more parameters and zero, one or two
625 tuples of set or input/output dimensions. The parameters and dimensions
626 are identified by an C<isl_dim_type> and a position.
627 The type C<isl_dim_param> refers to parameters,
628 the type C<isl_dim_set> refers to set dimensions (for spaces
629 with a single tuple of dimensions) and the types C<isl_dim_in>
630 and C<isl_dim_out> refer to input and output dimensions
631 (for spaces with two tuples of dimensions).
632 Local spaces (see L</"Local Spaces">) also contain dimensions
633 of type C<isl_dim_div>.
634 Note that parameters are only identified by their position within
635 a given object. Across different objects, parameters are (usually)
636 identified by their names or identifiers. Only unnamed parameters
637 are identified by their positions across objects. The use of unnamed
638 parameters is discouraged.
640 #include <isl/space.h>
641 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
642 unsigned nparam, unsigned n_in, unsigned n_out);
643 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
645 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
646 unsigned nparam, unsigned dim);
647 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
648 void *isl_space_free(__isl_take isl_space *space);
649 unsigned isl_space_dim(__isl_keep isl_space *space,
650 enum isl_dim_type type);
652 The space used for creating a parameter domain
653 needs to be created using C<isl_space_params_alloc>.
654 For other sets, the space
655 needs to be created using C<isl_space_set_alloc>, while
656 for a relation, the space
657 needs to be created using C<isl_space_alloc>.
658 C<isl_space_dim> can be used
659 to find out the number of dimensions of each type in
660 a space, where type may be
661 C<isl_dim_param>, C<isl_dim_in> (only for relations),
662 C<isl_dim_out> (only for relations), C<isl_dim_set>
663 (only for sets) or C<isl_dim_all>.
665 To check whether a given space is that of a set or a map
666 or whether it is a parameter space, use these functions:
668 #include <isl/space.h>
669 int isl_space_is_params(__isl_keep isl_space *space);
670 int isl_space_is_set(__isl_keep isl_space *space);
671 int isl_space_is_map(__isl_keep isl_space *space);
673 Spaces can be compared using the following functions:
675 #include <isl/space.h>
676 int isl_space_is_equal(__isl_keep isl_space *space1,
677 __isl_keep isl_space *space2);
678 int isl_space_is_domain(__isl_keep isl_space *space1,
679 __isl_keep isl_space *space2);
680 int isl_space_is_range(__isl_keep isl_space *space1,
681 __isl_keep isl_space *space2);
683 C<isl_space_is_domain> checks whether the first argument is equal
684 to the domain of the second argument. This requires in particular that
685 the first argument is a set space and that the second argument
688 It is often useful to create objects that live in the
689 same space as some other object. This can be accomplished
690 by creating the new objects
691 (see L<Creating New Sets and Relations> or
692 L<Creating New (Piecewise) Quasipolynomials>) based on the space
693 of the original object.
696 __isl_give isl_space *isl_basic_set_get_space(
697 __isl_keep isl_basic_set *bset);
698 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
700 #include <isl/union_set.h>
701 __isl_give isl_space *isl_union_set_get_space(
702 __isl_keep isl_union_set *uset);
705 __isl_give isl_space *isl_basic_map_get_space(
706 __isl_keep isl_basic_map *bmap);
707 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
709 #include <isl/union_map.h>
710 __isl_give isl_space *isl_union_map_get_space(
711 __isl_keep isl_union_map *umap);
713 #include <isl/constraint.h>
714 __isl_give isl_space *isl_constraint_get_space(
715 __isl_keep isl_constraint *constraint);
717 #include <isl/polynomial.h>
718 __isl_give isl_space *isl_qpolynomial_get_domain_space(
719 __isl_keep isl_qpolynomial *qp);
720 __isl_give isl_space *isl_qpolynomial_get_space(
721 __isl_keep isl_qpolynomial *qp);
722 __isl_give isl_space *isl_qpolynomial_fold_get_space(
723 __isl_keep isl_qpolynomial_fold *fold);
724 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
725 __isl_keep isl_pw_qpolynomial *pwqp);
726 __isl_give isl_space *isl_pw_qpolynomial_get_space(
727 __isl_keep isl_pw_qpolynomial *pwqp);
728 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
729 __isl_keep isl_pw_qpolynomial_fold *pwf);
730 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
731 __isl_keep isl_pw_qpolynomial_fold *pwf);
732 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
733 __isl_keep isl_union_pw_qpolynomial *upwqp);
734 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
735 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
738 __isl_give isl_space *isl_aff_get_domain_space(
739 __isl_keep isl_aff *aff);
740 __isl_give isl_space *isl_aff_get_space(
741 __isl_keep isl_aff *aff);
742 __isl_give isl_space *isl_pw_aff_get_domain_space(
743 __isl_keep isl_pw_aff *pwaff);
744 __isl_give isl_space *isl_pw_aff_get_space(
745 __isl_keep isl_pw_aff *pwaff);
746 __isl_give isl_space *isl_multi_aff_get_domain_space(
747 __isl_keep isl_multi_aff *maff);
748 __isl_give isl_space *isl_multi_aff_get_space(
749 __isl_keep isl_multi_aff *maff);
750 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
751 __isl_keep isl_pw_multi_aff *pma);
752 __isl_give isl_space *isl_pw_multi_aff_get_space(
753 __isl_keep isl_pw_multi_aff *pma);
754 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
755 __isl_keep isl_union_pw_multi_aff *upma);
756 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
757 __isl_keep isl_multi_pw_aff *mpa);
758 __isl_give isl_space *isl_multi_pw_aff_get_space(
759 __isl_keep isl_multi_pw_aff *mpa);
761 #include <isl/point.h>
762 __isl_give isl_space *isl_point_get_space(
763 __isl_keep isl_point *pnt);
765 The identifiers or names of the individual dimensions may be set or read off
766 using the following functions.
768 #include <isl/space.h>
769 __isl_give isl_space *isl_space_set_dim_id(
770 __isl_take isl_space *space,
771 enum isl_dim_type type, unsigned pos,
772 __isl_take isl_id *id);
773 int isl_space_has_dim_id(__isl_keep isl_space *space,
774 enum isl_dim_type type, unsigned pos);
775 __isl_give isl_id *isl_space_get_dim_id(
776 __isl_keep isl_space *space,
777 enum isl_dim_type type, unsigned pos);
778 __isl_give isl_space *isl_space_set_dim_name(
779 __isl_take isl_space *space,
780 enum isl_dim_type type, unsigned pos,
781 __isl_keep const char *name);
782 int isl_space_has_dim_name(__isl_keep isl_space *space,
783 enum isl_dim_type type, unsigned pos);
784 __isl_keep const char *isl_space_get_dim_name(
785 __isl_keep isl_space *space,
786 enum isl_dim_type type, unsigned pos);
788 Note that C<isl_space_get_name> returns a pointer to some internal
789 data structure, so the result can only be used while the
790 corresponding C<isl_space> is alive.
791 Also note that every function that operates on two sets or relations
792 requires that both arguments have the same parameters. This also
793 means that if one of the arguments has named parameters, then the
794 other needs to have named parameters too and the names need to match.
795 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
796 arguments may have different parameters (as long as they are named),
797 in which case the result will have as parameters the union of the parameters of
800 Given the identifier or name of a dimension (typically a parameter),
801 its position can be obtained from the following function.
803 #include <isl/space.h>
804 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
805 enum isl_dim_type type, __isl_keep isl_id *id);
806 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
807 enum isl_dim_type type, const char *name);
809 The identifiers or names of entire spaces may be set or read off
810 using the following functions.
812 #include <isl/space.h>
813 __isl_give isl_space *isl_space_set_tuple_id(
814 __isl_take isl_space *space,
815 enum isl_dim_type type, __isl_take isl_id *id);
816 __isl_give isl_space *isl_space_reset_tuple_id(
817 __isl_take isl_space *space, enum isl_dim_type type);
818 int isl_space_has_tuple_id(__isl_keep isl_space *space,
819 enum isl_dim_type type);
820 __isl_give isl_id *isl_space_get_tuple_id(
821 __isl_keep isl_space *space, enum isl_dim_type type);
822 __isl_give isl_space *isl_space_set_tuple_name(
823 __isl_take isl_space *space,
824 enum isl_dim_type type, const char *s);
825 int isl_space_has_tuple_name(__isl_keep isl_space *space,
826 enum isl_dim_type type);
827 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
828 enum isl_dim_type type);
830 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
831 or C<isl_dim_set>. As with C<isl_space_get_name>,
832 the C<isl_space_get_tuple_name> function returns a pointer to some internal
834 Binary operations require the corresponding spaces of their arguments
835 to have the same name.
837 Spaces can be nested. In particular, the domain of a set or
838 the domain or range of a relation can be a nested relation.
839 The following functions can be used to construct and deconstruct
842 #include <isl/space.h>
843 int isl_space_is_wrapping(__isl_keep isl_space *space);
844 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
845 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
847 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
848 be the space of a set, while that of
849 C<isl_space_wrap> should be the space of a relation.
850 Conversely, the output of C<isl_space_unwrap> is the space
851 of a relation, while that of C<isl_space_wrap> is the space of a set.
853 Spaces can be created from other spaces
854 using the following functions.
856 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
857 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
858 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
859 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
860 __isl_give isl_space *isl_space_params(
861 __isl_take isl_space *space);
862 __isl_give isl_space *isl_space_set_from_params(
863 __isl_take isl_space *space);
864 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
865 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
866 __isl_take isl_space *right);
867 __isl_give isl_space *isl_space_align_params(
868 __isl_take isl_space *space1, __isl_take isl_space *space2)
869 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
870 enum isl_dim_type type, unsigned pos, unsigned n);
871 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
872 enum isl_dim_type type, unsigned n);
873 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
874 enum isl_dim_type type, unsigned first, unsigned n);
875 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
876 enum isl_dim_type dst_type, unsigned dst_pos,
877 enum isl_dim_type src_type, unsigned src_pos,
879 __isl_give isl_space *isl_space_map_from_set(
880 __isl_take isl_space *space);
881 __isl_give isl_space *isl_space_map_from_domain_and_range(
882 __isl_take isl_space *domain,
883 __isl_take isl_space *range);
884 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
885 __isl_give isl_space *isl_space_curry(
886 __isl_take isl_space *space);
887 __isl_give isl_space *isl_space_uncurry(
888 __isl_take isl_space *space);
890 Note that if dimensions are added or removed from a space, then
891 the name and the internal structure are lost.
895 A local space is essentially a space with
896 zero or more existentially quantified variables.
897 The local space of a (constraint of a) basic set or relation can be obtained
898 using the following functions.
900 #include <isl/constraint.h>
901 __isl_give isl_local_space *isl_constraint_get_local_space(
902 __isl_keep isl_constraint *constraint);
905 __isl_give isl_local_space *isl_basic_set_get_local_space(
906 __isl_keep isl_basic_set *bset);
909 __isl_give isl_local_space *isl_basic_map_get_local_space(
910 __isl_keep isl_basic_map *bmap);
912 A new local space can be created from a space using
914 #include <isl/local_space.h>
915 __isl_give isl_local_space *isl_local_space_from_space(
916 __isl_take isl_space *space);
918 They can be inspected, modified, copied and freed using the following functions.
920 #include <isl/local_space.h>
921 isl_ctx *isl_local_space_get_ctx(
922 __isl_keep isl_local_space *ls);
923 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
924 int isl_local_space_dim(__isl_keep isl_local_space *ls,
925 enum isl_dim_type type);
926 int isl_local_space_has_dim_id(
927 __isl_keep isl_local_space *ls,
928 enum isl_dim_type type, unsigned pos);
929 __isl_give isl_id *isl_local_space_get_dim_id(
930 __isl_keep isl_local_space *ls,
931 enum isl_dim_type type, unsigned pos);
932 int isl_local_space_has_dim_name(
933 __isl_keep isl_local_space *ls,
934 enum isl_dim_type type, unsigned pos)
935 const char *isl_local_space_get_dim_name(
936 __isl_keep isl_local_space *ls,
937 enum isl_dim_type type, unsigned pos);
938 __isl_give isl_local_space *isl_local_space_set_dim_name(
939 __isl_take isl_local_space *ls,
940 enum isl_dim_type type, unsigned pos, const char *s);
941 __isl_give isl_local_space *isl_local_space_set_dim_id(
942 __isl_take isl_local_space *ls,
943 enum isl_dim_type type, unsigned pos,
944 __isl_take isl_id *id);
945 __isl_give isl_space *isl_local_space_get_space(
946 __isl_keep isl_local_space *ls);
947 __isl_give isl_aff *isl_local_space_get_div(
948 __isl_keep isl_local_space *ls, int pos);
949 __isl_give isl_local_space *isl_local_space_copy(
950 __isl_keep isl_local_space *ls);
951 void *isl_local_space_free(__isl_take isl_local_space *ls);
953 Two local spaces can be compared using
955 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
956 __isl_keep isl_local_space *ls2);
958 Local spaces can be created from other local spaces
959 using the following functions.
961 __isl_give isl_local_space *isl_local_space_domain(
962 __isl_take isl_local_space *ls);
963 __isl_give isl_local_space *isl_local_space_range(
964 __isl_take isl_local_space *ls);
965 __isl_give isl_local_space *isl_local_space_from_domain(
966 __isl_take isl_local_space *ls);
967 __isl_give isl_local_space *isl_local_space_intersect(
968 __isl_take isl_local_space *ls1,
969 __isl_take isl_local_space *ls2);
970 __isl_give isl_local_space *isl_local_space_add_dims(
971 __isl_take isl_local_space *ls,
972 enum isl_dim_type type, unsigned n);
973 __isl_give isl_local_space *isl_local_space_insert_dims(
974 __isl_take isl_local_space *ls,
975 enum isl_dim_type type, unsigned first, unsigned n);
976 __isl_give isl_local_space *isl_local_space_drop_dims(
977 __isl_take isl_local_space *ls,
978 enum isl_dim_type type, unsigned first, unsigned n);
980 =head2 Input and Output
982 C<isl> supports its own input/output format, which is similar
983 to the C<Omega> format, but also supports the C<PolyLib> format
988 The C<isl> format is similar to that of C<Omega>, but has a different
989 syntax for describing the parameters and allows for the definition
990 of an existentially quantified variable as the integer division
991 of an affine expression.
992 For example, the set of integers C<i> between C<0> and C<n>
993 such that C<i % 10 <= 6> can be described as
995 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
998 A set or relation can have several disjuncts, separated
999 by the keyword C<or>. Each disjunct is either a conjunction
1000 of constraints or a projection (C<exists>) of a conjunction
1001 of constraints. The constraints are separated by the keyword
1004 =head3 C<PolyLib> format
1006 If the represented set is a union, then the first line
1007 contains a single number representing the number of disjuncts.
1008 Otherwise, a line containing the number C<1> is optional.
1010 Each disjunct is represented by a matrix of constraints.
1011 The first line contains two numbers representing
1012 the number of rows and columns,
1013 where the number of rows is equal to the number of constraints
1014 and the number of columns is equal to two plus the number of variables.
1015 The following lines contain the actual rows of the constraint matrix.
1016 In each row, the first column indicates whether the constraint
1017 is an equality (C<0>) or inequality (C<1>). The final column
1018 corresponds to the constant term.
1020 If the set is parametric, then the coefficients of the parameters
1021 appear in the last columns before the constant column.
1022 The coefficients of any existentially quantified variables appear
1023 between those of the set variables and those of the parameters.
1025 =head3 Extended C<PolyLib> format
1027 The extended C<PolyLib> format is nearly identical to the
1028 C<PolyLib> format. The only difference is that the line
1029 containing the number of rows and columns of a constraint matrix
1030 also contains four additional numbers:
1031 the number of output dimensions, the number of input dimensions,
1032 the number of local dimensions (i.e., the number of existentially
1033 quantified variables) and the number of parameters.
1034 For sets, the number of ``output'' dimensions is equal
1035 to the number of set dimensions, while the number of ``input''
1040 #include <isl/set.h>
1041 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1042 isl_ctx *ctx, FILE *input);
1043 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1044 isl_ctx *ctx, const char *str);
1045 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1047 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1050 #include <isl/map.h>
1051 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1052 isl_ctx *ctx, FILE *input);
1053 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1054 isl_ctx *ctx, const char *str);
1055 __isl_give isl_map *isl_map_read_from_file(
1056 isl_ctx *ctx, FILE *input);
1057 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1060 #include <isl/union_set.h>
1061 __isl_give isl_union_set *isl_union_set_read_from_file(
1062 isl_ctx *ctx, FILE *input);
1063 __isl_give isl_union_set *isl_union_set_read_from_str(
1064 isl_ctx *ctx, const char *str);
1066 #include <isl/union_map.h>
1067 __isl_give isl_union_map *isl_union_map_read_from_file(
1068 isl_ctx *ctx, FILE *input);
1069 __isl_give isl_union_map *isl_union_map_read_from_str(
1070 isl_ctx *ctx, const char *str);
1072 The input format is autodetected and may be either the C<PolyLib> format
1073 or the C<isl> format.
1077 Before anything can be printed, an C<isl_printer> needs to
1080 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1082 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1083 void *isl_printer_free(__isl_take isl_printer *printer);
1084 __isl_give char *isl_printer_get_str(
1085 __isl_keep isl_printer *printer);
1087 The printer can be inspected using the following functions.
1089 FILE *isl_printer_get_file(
1090 __isl_keep isl_printer *printer);
1091 int isl_printer_get_output_format(
1092 __isl_keep isl_printer *p);
1094 The behavior of the printer can be modified in various ways
1096 __isl_give isl_printer *isl_printer_set_output_format(
1097 __isl_take isl_printer *p, int output_format);
1098 __isl_give isl_printer *isl_printer_set_indent(
1099 __isl_take isl_printer *p, int indent);
1100 __isl_give isl_printer *isl_printer_indent(
1101 __isl_take isl_printer *p, int indent);
1102 __isl_give isl_printer *isl_printer_set_prefix(
1103 __isl_take isl_printer *p, const char *prefix);
1104 __isl_give isl_printer *isl_printer_set_suffix(
1105 __isl_take isl_printer *p, const char *suffix);
1107 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1108 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1109 and defaults to C<ISL_FORMAT_ISL>.
1110 Each line in the output is indented by C<indent> (set by
1111 C<isl_printer_set_indent>) spaces
1112 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1113 In the C<PolyLib> format output,
1114 the coefficients of the existentially quantified variables
1115 appear between those of the set variables and those
1117 The function C<isl_printer_indent> increases the indentation
1118 by the specified amount (which may be negative).
1120 To actually print something, use
1122 #include <isl/printer.h>
1123 __isl_give isl_printer *isl_printer_print_double(
1124 __isl_take isl_printer *p, double d);
1126 #include <isl/set.h>
1127 __isl_give isl_printer *isl_printer_print_basic_set(
1128 __isl_take isl_printer *printer,
1129 __isl_keep isl_basic_set *bset);
1130 __isl_give isl_printer *isl_printer_print_set(
1131 __isl_take isl_printer *printer,
1132 __isl_keep isl_set *set);
1134 #include <isl/map.h>
1135 __isl_give isl_printer *isl_printer_print_basic_map(
1136 __isl_take isl_printer *printer,
1137 __isl_keep isl_basic_map *bmap);
1138 __isl_give isl_printer *isl_printer_print_map(
1139 __isl_take isl_printer *printer,
1140 __isl_keep isl_map *map);
1142 #include <isl/union_set.h>
1143 __isl_give isl_printer *isl_printer_print_union_set(
1144 __isl_take isl_printer *p,
1145 __isl_keep isl_union_set *uset);
1147 #include <isl/union_map.h>
1148 __isl_give isl_printer *isl_printer_print_union_map(
1149 __isl_take isl_printer *p,
1150 __isl_keep isl_union_map *umap);
1152 When called on a file printer, the following function flushes
1153 the file. When called on a string printer, the buffer is cleared.
1155 __isl_give isl_printer *isl_printer_flush(
1156 __isl_take isl_printer *p);
1158 =head2 Creating New Sets and Relations
1160 C<isl> has functions for creating some standard sets and relations.
1164 =item * Empty sets and relations
1166 __isl_give isl_basic_set *isl_basic_set_empty(
1167 __isl_take isl_space *space);
1168 __isl_give isl_basic_map *isl_basic_map_empty(
1169 __isl_take isl_space *space);
1170 __isl_give isl_set *isl_set_empty(
1171 __isl_take isl_space *space);
1172 __isl_give isl_map *isl_map_empty(
1173 __isl_take isl_space *space);
1174 __isl_give isl_union_set *isl_union_set_empty(
1175 __isl_take isl_space *space);
1176 __isl_give isl_union_map *isl_union_map_empty(
1177 __isl_take isl_space *space);
1179 For C<isl_union_set>s and C<isl_union_map>s, the space
1180 is only used to specify the parameters.
1182 =item * Universe sets and relations
1184 __isl_give isl_basic_set *isl_basic_set_universe(
1185 __isl_take isl_space *space);
1186 __isl_give isl_basic_map *isl_basic_map_universe(
1187 __isl_take isl_space *space);
1188 __isl_give isl_set *isl_set_universe(
1189 __isl_take isl_space *space);
1190 __isl_give isl_map *isl_map_universe(
1191 __isl_take isl_space *space);
1192 __isl_give isl_union_set *isl_union_set_universe(
1193 __isl_take isl_union_set *uset);
1194 __isl_give isl_union_map *isl_union_map_universe(
1195 __isl_take isl_union_map *umap);
1197 The sets and relations constructed by the functions above
1198 contain all integer values, while those constructed by the
1199 functions below only contain non-negative values.
1201 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1202 __isl_take isl_space *space);
1203 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1204 __isl_take isl_space *space);
1205 __isl_give isl_set *isl_set_nat_universe(
1206 __isl_take isl_space *space);
1207 __isl_give isl_map *isl_map_nat_universe(
1208 __isl_take isl_space *space);
1210 =item * Identity relations
1212 __isl_give isl_basic_map *isl_basic_map_identity(
1213 __isl_take isl_space *space);
1214 __isl_give isl_map *isl_map_identity(
1215 __isl_take isl_space *space);
1217 The number of input and output dimensions in C<space> needs
1220 =item * Lexicographic order
1222 __isl_give isl_map *isl_map_lex_lt(
1223 __isl_take isl_space *set_space);
1224 __isl_give isl_map *isl_map_lex_le(
1225 __isl_take isl_space *set_space);
1226 __isl_give isl_map *isl_map_lex_gt(
1227 __isl_take isl_space *set_space);
1228 __isl_give isl_map *isl_map_lex_ge(
1229 __isl_take isl_space *set_space);
1230 __isl_give isl_map *isl_map_lex_lt_first(
1231 __isl_take isl_space *space, unsigned n);
1232 __isl_give isl_map *isl_map_lex_le_first(
1233 __isl_take isl_space *space, unsigned n);
1234 __isl_give isl_map *isl_map_lex_gt_first(
1235 __isl_take isl_space *space, unsigned n);
1236 __isl_give isl_map *isl_map_lex_ge_first(
1237 __isl_take isl_space *space, unsigned n);
1239 The first four functions take a space for a B<set>
1240 and return relations that express that the elements in the domain
1241 are lexicographically less
1242 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1243 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1244 than the elements in the range.
1245 The last four functions take a space for a map
1246 and return relations that express that the first C<n> dimensions
1247 in the domain are lexicographically less
1248 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1249 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1250 than the first C<n> dimensions in the range.
1254 A basic set or relation can be converted to a set or relation
1255 using the following functions.
1257 __isl_give isl_set *isl_set_from_basic_set(
1258 __isl_take isl_basic_set *bset);
1259 __isl_give isl_map *isl_map_from_basic_map(
1260 __isl_take isl_basic_map *bmap);
1262 Sets and relations can be converted to union sets and relations
1263 using the following functions.
1265 __isl_give isl_union_set *isl_union_set_from_basic_set(
1266 __isl_take isl_basic_set *bset);
1267 __isl_give isl_union_map *isl_union_map_from_basic_map(
1268 __isl_take isl_basic_map *bmap);
1269 __isl_give isl_union_set *isl_union_set_from_set(
1270 __isl_take isl_set *set);
1271 __isl_give isl_union_map *isl_union_map_from_map(
1272 __isl_take isl_map *map);
1274 The inverse conversions below can only be used if the input
1275 union set or relation is known to contain elements in exactly one
1278 __isl_give isl_set *isl_set_from_union_set(
1279 __isl_take isl_union_set *uset);
1280 __isl_give isl_map *isl_map_from_union_map(
1281 __isl_take isl_union_map *umap);
1283 A zero-dimensional (basic) set can be constructed on a given parameter domain
1284 using the following function.
1286 __isl_give isl_basic_set *isl_basic_set_from_params(
1287 __isl_take isl_basic_set *bset);
1288 __isl_give isl_set *isl_set_from_params(
1289 __isl_take isl_set *set);
1291 Sets and relations can be copied and freed again using the following
1294 __isl_give isl_basic_set *isl_basic_set_copy(
1295 __isl_keep isl_basic_set *bset);
1296 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1297 __isl_give isl_union_set *isl_union_set_copy(
1298 __isl_keep isl_union_set *uset);
1299 __isl_give isl_basic_map *isl_basic_map_copy(
1300 __isl_keep isl_basic_map *bmap);
1301 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1302 __isl_give isl_union_map *isl_union_map_copy(
1303 __isl_keep isl_union_map *umap);
1304 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1305 void *isl_set_free(__isl_take isl_set *set);
1306 void *isl_union_set_free(__isl_take isl_union_set *uset);
1307 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1308 void *isl_map_free(__isl_take isl_map *map);
1309 void *isl_union_map_free(__isl_take isl_union_map *umap);
1311 Other sets and relations can be constructed by starting
1312 from a universe set or relation, adding equality and/or
1313 inequality constraints and then projecting out the
1314 existentially quantified variables, if any.
1315 Constraints can be constructed, manipulated and
1316 added to (or removed from) (basic) sets and relations
1317 using the following functions.
1319 #include <isl/constraint.h>
1320 __isl_give isl_constraint *isl_equality_alloc(
1321 __isl_take isl_local_space *ls);
1322 __isl_give isl_constraint *isl_inequality_alloc(
1323 __isl_take isl_local_space *ls);
1324 __isl_give isl_constraint *isl_constraint_set_constant(
1325 __isl_take isl_constraint *constraint, isl_int v);
1326 __isl_give isl_constraint *isl_constraint_set_constant_si(
1327 __isl_take isl_constraint *constraint, int v);
1328 __isl_give isl_constraint *isl_constraint_set_coefficient(
1329 __isl_take isl_constraint *constraint,
1330 enum isl_dim_type type, int pos, isl_int v);
1331 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1332 __isl_take isl_constraint *constraint,
1333 enum isl_dim_type type, int pos, int v);
1334 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1335 __isl_take isl_basic_map *bmap,
1336 __isl_take isl_constraint *constraint);
1337 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1338 __isl_take isl_basic_set *bset,
1339 __isl_take isl_constraint *constraint);
1340 __isl_give isl_map *isl_map_add_constraint(
1341 __isl_take isl_map *map,
1342 __isl_take isl_constraint *constraint);
1343 __isl_give isl_set *isl_set_add_constraint(
1344 __isl_take isl_set *set,
1345 __isl_take isl_constraint *constraint);
1346 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1347 __isl_take isl_basic_set *bset,
1348 __isl_take isl_constraint *constraint);
1350 For example, to create a set containing the even integers
1351 between 10 and 42, you would use the following code.
1354 isl_local_space *ls;
1356 isl_basic_set *bset;
1358 space = isl_space_set_alloc(ctx, 0, 2);
1359 bset = isl_basic_set_universe(isl_space_copy(space));
1360 ls = isl_local_space_from_space(space);
1362 c = isl_equality_alloc(isl_local_space_copy(ls));
1363 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1364 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1365 bset = isl_basic_set_add_constraint(bset, c);
1367 c = isl_inequality_alloc(isl_local_space_copy(ls));
1368 c = isl_constraint_set_constant_si(c, -10);
1369 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1370 bset = isl_basic_set_add_constraint(bset, c);
1372 c = isl_inequality_alloc(ls);
1373 c = isl_constraint_set_constant_si(c, 42);
1374 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1375 bset = isl_basic_set_add_constraint(bset, c);
1377 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1381 isl_basic_set *bset;
1382 bset = isl_basic_set_read_from_str(ctx,
1383 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1385 A basic set or relation can also be constructed from two matrices
1386 describing the equalities and the inequalities.
1388 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1389 __isl_take isl_space *space,
1390 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1391 enum isl_dim_type c1,
1392 enum isl_dim_type c2, enum isl_dim_type c3,
1393 enum isl_dim_type c4);
1394 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1395 __isl_take isl_space *space,
1396 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1397 enum isl_dim_type c1,
1398 enum isl_dim_type c2, enum isl_dim_type c3,
1399 enum isl_dim_type c4, enum isl_dim_type c5);
1401 The C<isl_dim_type> arguments indicate the order in which
1402 different kinds of variables appear in the input matrices
1403 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1404 C<isl_dim_set> and C<isl_dim_div> for sets and
1405 of C<isl_dim_cst>, C<isl_dim_param>,
1406 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1408 A (basic or union) set or relation can also be constructed from a
1409 (union) (piecewise) (multiple) affine expression
1410 or a list of affine expressions
1411 (See L<"Piecewise Quasi Affine Expressions"> and
1412 L<"Piecewise Multiple Quasi Affine Expressions">).
1414 __isl_give isl_basic_map *isl_basic_map_from_aff(
1415 __isl_take isl_aff *aff);
1416 __isl_give isl_map *isl_map_from_aff(
1417 __isl_take isl_aff *aff);
1418 __isl_give isl_set *isl_set_from_pw_aff(
1419 __isl_take isl_pw_aff *pwaff);
1420 __isl_give isl_map *isl_map_from_pw_aff(
1421 __isl_take isl_pw_aff *pwaff);
1422 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1423 __isl_take isl_space *domain_space,
1424 __isl_take isl_aff_list *list);
1425 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1426 __isl_take isl_multi_aff *maff)
1427 __isl_give isl_map *isl_map_from_multi_aff(
1428 __isl_take isl_multi_aff *maff)
1429 __isl_give isl_set *isl_set_from_pw_multi_aff(
1430 __isl_take isl_pw_multi_aff *pma);
1431 __isl_give isl_map *isl_map_from_pw_multi_aff(
1432 __isl_take isl_pw_multi_aff *pma);
1433 __isl_give isl_union_map *
1434 isl_union_map_from_union_pw_multi_aff(
1435 __isl_take isl_union_pw_multi_aff *upma);
1437 The C<domain_dim> argument describes the domain of the resulting
1438 basic relation. It is required because the C<list> may consist
1439 of zero affine expressions.
1441 =head2 Inspecting Sets and Relations
1443 Usually, the user should not have to care about the actual constraints
1444 of the sets and maps, but should instead apply the abstract operations
1445 explained in the following sections.
1446 Occasionally, however, it may be required to inspect the individual
1447 coefficients of the constraints. This section explains how to do so.
1448 In these cases, it may also be useful to have C<isl> compute
1449 an explicit representation of the existentially quantified variables.
1451 __isl_give isl_set *isl_set_compute_divs(
1452 __isl_take isl_set *set);
1453 __isl_give isl_map *isl_map_compute_divs(
1454 __isl_take isl_map *map);
1455 __isl_give isl_union_set *isl_union_set_compute_divs(
1456 __isl_take isl_union_set *uset);
1457 __isl_give isl_union_map *isl_union_map_compute_divs(
1458 __isl_take isl_union_map *umap);
1460 This explicit representation defines the existentially quantified
1461 variables as integer divisions of the other variables, possibly
1462 including earlier existentially quantified variables.
1463 An explicitly represented existentially quantified variable therefore
1464 has a unique value when the values of the other variables are known.
1465 If, furthermore, the same existentials, i.e., existentials
1466 with the same explicit representations, should appear in the
1467 same order in each of the disjuncts of a set or map, then the user should call
1468 either of the following functions.
1470 __isl_give isl_set *isl_set_align_divs(
1471 __isl_take isl_set *set);
1472 __isl_give isl_map *isl_map_align_divs(
1473 __isl_take isl_map *map);
1475 Alternatively, the existentially quantified variables can be removed
1476 using the following functions, which compute an overapproximation.
1478 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1479 __isl_take isl_basic_set *bset);
1480 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1481 __isl_take isl_basic_map *bmap);
1482 __isl_give isl_set *isl_set_remove_divs(
1483 __isl_take isl_set *set);
1484 __isl_give isl_map *isl_map_remove_divs(
1485 __isl_take isl_map *map);
1487 It is also possible to only remove those divs that are defined
1488 in terms of a given range of dimensions or only those for which
1489 no explicit representation is known.
1491 __isl_give isl_basic_set *
1492 isl_basic_set_remove_divs_involving_dims(
1493 __isl_take isl_basic_set *bset,
1494 enum isl_dim_type type,
1495 unsigned first, unsigned n);
1496 __isl_give isl_basic_map *
1497 isl_basic_map_remove_divs_involving_dims(
1498 __isl_take isl_basic_map *bmap,
1499 enum isl_dim_type type,
1500 unsigned first, unsigned n);
1501 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1502 __isl_take isl_set *set, enum isl_dim_type type,
1503 unsigned first, unsigned n);
1504 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1505 __isl_take isl_map *map, enum isl_dim_type type,
1506 unsigned first, unsigned n);
1508 __isl_give isl_basic_set *
1509 isl_basic_set_remove_unknown_divs(
1510 __isl_take isl_basic_set *bset);
1511 __isl_give isl_set *isl_set_remove_unknown_divs(
1512 __isl_take isl_set *set);
1513 __isl_give isl_map *isl_map_remove_unknown_divs(
1514 __isl_take isl_map *map);
1516 To iterate over all the sets or maps in a union set or map, use
1518 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1519 int (*fn)(__isl_take isl_set *set, void *user),
1521 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1522 int (*fn)(__isl_take isl_map *map, void *user),
1525 The number of sets or maps in a union set or map can be obtained
1528 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1529 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1531 To extract the set or map in a given space from a union, use
1533 __isl_give isl_set *isl_union_set_extract_set(
1534 __isl_keep isl_union_set *uset,
1535 __isl_take isl_space *space);
1536 __isl_give isl_map *isl_union_map_extract_map(
1537 __isl_keep isl_union_map *umap,
1538 __isl_take isl_space *space);
1540 To iterate over all the basic sets or maps in a set or map, use
1542 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1543 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1545 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1546 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1549 The callback function C<fn> should return 0 if successful and
1550 -1 if an error occurs. In the latter case, or if any other error
1551 occurs, the above functions will return -1.
1553 It should be noted that C<isl> does not guarantee that
1554 the basic sets or maps passed to C<fn> are disjoint.
1555 If this is required, then the user should call one of
1556 the following functions first.
1558 __isl_give isl_set *isl_set_make_disjoint(
1559 __isl_take isl_set *set);
1560 __isl_give isl_map *isl_map_make_disjoint(
1561 __isl_take isl_map *map);
1563 The number of basic sets in a set can be obtained
1566 int isl_set_n_basic_set(__isl_keep isl_set *set);
1568 To iterate over the constraints of a basic set or map, use
1570 #include <isl/constraint.h>
1572 int isl_basic_set_n_constraint(
1573 __isl_keep isl_basic_set *bset);
1574 int isl_basic_set_foreach_constraint(
1575 __isl_keep isl_basic_set *bset,
1576 int (*fn)(__isl_take isl_constraint *c, void *user),
1578 int isl_basic_map_foreach_constraint(
1579 __isl_keep isl_basic_map *bmap,
1580 int (*fn)(__isl_take isl_constraint *c, void *user),
1582 void *isl_constraint_free(__isl_take isl_constraint *c);
1584 Again, the callback function C<fn> should return 0 if successful and
1585 -1 if an error occurs. In the latter case, or if any other error
1586 occurs, the above functions will return -1.
1587 The constraint C<c> represents either an equality or an inequality.
1588 Use the following function to find out whether a constraint
1589 represents an equality. If not, it represents an inequality.
1591 int isl_constraint_is_equality(
1592 __isl_keep isl_constraint *constraint);
1594 The coefficients of the constraints can be inspected using
1595 the following functions.
1597 int isl_constraint_is_lower_bound(
1598 __isl_keep isl_constraint *constraint,
1599 enum isl_dim_type type, unsigned pos);
1600 int isl_constraint_is_upper_bound(
1601 __isl_keep isl_constraint *constraint,
1602 enum isl_dim_type type, unsigned pos);
1603 void isl_constraint_get_constant(
1604 __isl_keep isl_constraint *constraint, isl_int *v);
1605 void isl_constraint_get_coefficient(
1606 __isl_keep isl_constraint *constraint,
1607 enum isl_dim_type type, int pos, isl_int *v);
1608 int isl_constraint_involves_dims(
1609 __isl_keep isl_constraint *constraint,
1610 enum isl_dim_type type, unsigned first, unsigned n);
1612 The explicit representations of the existentially quantified
1613 variables can be inspected using the following function.
1614 Note that the user is only allowed to use this function
1615 if the inspected set or map is the result of a call
1616 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1617 The existentially quantified variable is equal to the floor
1618 of the returned affine expression. The affine expression
1619 itself can be inspected using the functions in
1620 L<"Piecewise Quasi Affine Expressions">.
1622 __isl_give isl_aff *isl_constraint_get_div(
1623 __isl_keep isl_constraint *constraint, int pos);
1625 To obtain the constraints of a basic set or map in matrix
1626 form, use the following functions.
1628 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1629 __isl_keep isl_basic_set *bset,
1630 enum isl_dim_type c1, enum isl_dim_type c2,
1631 enum isl_dim_type c3, enum isl_dim_type c4);
1632 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1633 __isl_keep isl_basic_set *bset,
1634 enum isl_dim_type c1, enum isl_dim_type c2,
1635 enum isl_dim_type c3, enum isl_dim_type c4);
1636 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1637 __isl_keep isl_basic_map *bmap,
1638 enum isl_dim_type c1,
1639 enum isl_dim_type c2, enum isl_dim_type c3,
1640 enum isl_dim_type c4, enum isl_dim_type c5);
1641 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1642 __isl_keep isl_basic_map *bmap,
1643 enum isl_dim_type c1,
1644 enum isl_dim_type c2, enum isl_dim_type c3,
1645 enum isl_dim_type c4, enum isl_dim_type c5);
1647 The C<isl_dim_type> arguments dictate the order in which
1648 different kinds of variables appear in the resulting matrix
1649 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1650 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1652 The number of parameters, input, output or set dimensions can
1653 be obtained using the following functions.
1655 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1656 enum isl_dim_type type);
1657 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1658 enum isl_dim_type type);
1659 unsigned isl_set_dim(__isl_keep isl_set *set,
1660 enum isl_dim_type type);
1661 unsigned isl_map_dim(__isl_keep isl_map *map,
1662 enum isl_dim_type type);
1664 To check whether the description of a set or relation depends
1665 on one or more given dimensions, it is not necessary to iterate over all
1666 constraints. Instead the following functions can be used.
1668 int isl_basic_set_involves_dims(
1669 __isl_keep isl_basic_set *bset,
1670 enum isl_dim_type type, unsigned first, unsigned n);
1671 int isl_set_involves_dims(__isl_keep isl_set *set,
1672 enum isl_dim_type type, unsigned first, unsigned n);
1673 int isl_basic_map_involves_dims(
1674 __isl_keep isl_basic_map *bmap,
1675 enum isl_dim_type type, unsigned first, unsigned n);
1676 int isl_map_involves_dims(__isl_keep isl_map *map,
1677 enum isl_dim_type type, unsigned first, unsigned n);
1679 Similarly, the following functions can be used to check whether
1680 a given dimension is involved in any lower or upper bound.
1682 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1683 enum isl_dim_type type, unsigned pos);
1684 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1685 enum isl_dim_type type, unsigned pos);
1687 Note that these functions return true even if there is a bound on
1688 the dimension on only some of the basic sets of C<set>.
1689 To check if they have a bound for all of the basic sets in C<set>,
1690 use the following functions instead.
1692 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1693 enum isl_dim_type type, unsigned pos);
1694 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1695 enum isl_dim_type type, unsigned pos);
1697 The identifiers or names of the domain and range spaces of a set
1698 or relation can be read off or set using the following functions.
1700 __isl_give isl_set *isl_set_set_tuple_id(
1701 __isl_take isl_set *set, __isl_take isl_id *id);
1702 __isl_give isl_set *isl_set_reset_tuple_id(
1703 __isl_take isl_set *set);
1704 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1705 __isl_give isl_id *isl_set_get_tuple_id(
1706 __isl_keep isl_set *set);
1707 __isl_give isl_map *isl_map_set_tuple_id(
1708 __isl_take isl_map *map, enum isl_dim_type type,
1709 __isl_take isl_id *id);
1710 __isl_give isl_map *isl_map_reset_tuple_id(
1711 __isl_take isl_map *map, enum isl_dim_type type);
1712 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1713 enum isl_dim_type type);
1714 __isl_give isl_id *isl_map_get_tuple_id(
1715 __isl_keep isl_map *map, enum isl_dim_type type);
1717 const char *isl_basic_set_get_tuple_name(
1718 __isl_keep isl_basic_set *bset);
1719 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1720 __isl_take isl_basic_set *set, const char *s);
1721 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1722 const char *isl_set_get_tuple_name(
1723 __isl_keep isl_set *set);
1724 const char *isl_basic_map_get_tuple_name(
1725 __isl_keep isl_basic_map *bmap,
1726 enum isl_dim_type type);
1727 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1728 __isl_take isl_basic_map *bmap,
1729 enum isl_dim_type type, const char *s);
1730 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1731 enum isl_dim_type type);
1732 const char *isl_map_get_tuple_name(
1733 __isl_keep isl_map *map,
1734 enum isl_dim_type type);
1736 As with C<isl_space_get_tuple_name>, the value returned points to
1737 an internal data structure.
1738 The identifiers, positions or names of individual dimensions can be
1739 read off using the following functions.
1741 __isl_give isl_id *isl_basic_set_get_dim_id(
1742 __isl_keep isl_basic_set *bset,
1743 enum isl_dim_type type, unsigned pos);
1744 __isl_give isl_set *isl_set_set_dim_id(
1745 __isl_take isl_set *set, enum isl_dim_type type,
1746 unsigned pos, __isl_take isl_id *id);
1747 int isl_set_has_dim_id(__isl_keep isl_set *set,
1748 enum isl_dim_type type, unsigned pos);
1749 __isl_give isl_id *isl_set_get_dim_id(
1750 __isl_keep isl_set *set, enum isl_dim_type type,
1752 int isl_basic_map_has_dim_id(
1753 __isl_keep isl_basic_map *bmap,
1754 enum isl_dim_type type, unsigned pos);
1755 __isl_give isl_map *isl_map_set_dim_id(
1756 __isl_take isl_map *map, enum isl_dim_type type,
1757 unsigned pos, __isl_take isl_id *id);
1758 int isl_map_has_dim_id(__isl_keep isl_map *map,
1759 enum isl_dim_type type, unsigned pos);
1760 __isl_give isl_id *isl_map_get_dim_id(
1761 __isl_keep isl_map *map, enum isl_dim_type type,
1764 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1765 enum isl_dim_type type, __isl_keep isl_id *id);
1766 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1767 enum isl_dim_type type, __isl_keep isl_id *id);
1768 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1769 enum isl_dim_type type, const char *name);
1770 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1771 enum isl_dim_type type, const char *name);
1773 const char *isl_constraint_get_dim_name(
1774 __isl_keep isl_constraint *constraint,
1775 enum isl_dim_type type, unsigned pos);
1776 const char *isl_basic_set_get_dim_name(
1777 __isl_keep isl_basic_set *bset,
1778 enum isl_dim_type type, unsigned pos);
1779 int isl_set_has_dim_name(__isl_keep isl_set *set,
1780 enum isl_dim_type type, unsigned pos);
1781 const char *isl_set_get_dim_name(
1782 __isl_keep isl_set *set,
1783 enum isl_dim_type type, unsigned pos);
1784 const char *isl_basic_map_get_dim_name(
1785 __isl_keep isl_basic_map *bmap,
1786 enum isl_dim_type type, unsigned pos);
1787 int isl_map_has_dim_name(__isl_keep isl_map *map,
1788 enum isl_dim_type type, unsigned pos);
1789 const char *isl_map_get_dim_name(
1790 __isl_keep isl_map *map,
1791 enum isl_dim_type type, unsigned pos);
1793 These functions are mostly useful to obtain the identifiers, positions
1794 or names of the parameters. Identifiers of individual dimensions are
1795 essentially only useful for printing. They are ignored by all other
1796 operations and may not be preserved across those operations.
1800 =head3 Unary Properties
1806 The following functions test whether the given set or relation
1807 contains any integer points. The ``plain'' variants do not perform
1808 any computations, but simply check if the given set or relation
1809 is already known to be empty.
1811 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1812 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1813 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1814 int isl_set_is_empty(__isl_keep isl_set *set);
1815 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1816 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1817 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1818 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1819 int isl_map_is_empty(__isl_keep isl_map *map);
1820 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1822 =item * Universality
1824 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1825 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1826 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1828 =item * Single-valuedness
1830 int isl_basic_map_is_single_valued(
1831 __isl_keep isl_basic_map *bmap);
1832 int isl_map_plain_is_single_valued(
1833 __isl_keep isl_map *map);
1834 int isl_map_is_single_valued(__isl_keep isl_map *map);
1835 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1839 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1840 int isl_map_is_injective(__isl_keep isl_map *map);
1841 int isl_union_map_plain_is_injective(
1842 __isl_keep isl_union_map *umap);
1843 int isl_union_map_is_injective(
1844 __isl_keep isl_union_map *umap);
1848 int isl_map_is_bijective(__isl_keep isl_map *map);
1849 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1853 int isl_basic_map_plain_is_fixed(
1854 __isl_keep isl_basic_map *bmap,
1855 enum isl_dim_type type, unsigned pos,
1857 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1858 enum isl_dim_type type, unsigned pos,
1860 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1861 enum isl_dim_type type, unsigned pos,
1864 Check if the relation obviously lies on a hyperplane where the given dimension
1865 has a fixed value and if so, return that value in C<*val>.
1869 To check whether a set is a parameter domain, use this function:
1871 int isl_set_is_params(__isl_keep isl_set *set);
1872 int isl_union_set_is_params(
1873 __isl_keep isl_union_set *uset);
1877 The following functions check whether the domain of the given
1878 (basic) set is a wrapped relation.
1880 int isl_basic_set_is_wrapping(
1881 __isl_keep isl_basic_set *bset);
1882 int isl_set_is_wrapping(__isl_keep isl_set *set);
1884 =item * Internal Product
1886 int isl_basic_map_can_zip(
1887 __isl_keep isl_basic_map *bmap);
1888 int isl_map_can_zip(__isl_keep isl_map *map);
1890 Check whether the product of domain and range of the given relation
1892 i.e., whether both domain and range are nested relations.
1896 int isl_basic_map_can_curry(
1897 __isl_keep isl_basic_map *bmap);
1898 int isl_map_can_curry(__isl_keep isl_map *map);
1900 Check whether the domain of the (basic) relation is a wrapped relation.
1902 int isl_basic_map_can_uncurry(
1903 __isl_keep isl_basic_map *bmap);
1904 int isl_map_can_uncurry(__isl_keep isl_map *map);
1906 Check whether the range of the (basic) relation is a wrapped relation.
1910 =head3 Binary Properties
1916 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1917 __isl_keep isl_set *set2);
1918 int isl_set_is_equal(__isl_keep isl_set *set1,
1919 __isl_keep isl_set *set2);
1920 int isl_union_set_is_equal(
1921 __isl_keep isl_union_set *uset1,
1922 __isl_keep isl_union_set *uset2);
1923 int isl_basic_map_is_equal(
1924 __isl_keep isl_basic_map *bmap1,
1925 __isl_keep isl_basic_map *bmap2);
1926 int isl_map_is_equal(__isl_keep isl_map *map1,
1927 __isl_keep isl_map *map2);
1928 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1929 __isl_keep isl_map *map2);
1930 int isl_union_map_is_equal(
1931 __isl_keep isl_union_map *umap1,
1932 __isl_keep isl_union_map *umap2);
1934 =item * Disjointness
1936 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1937 __isl_keep isl_set *set2);
1938 int isl_set_is_disjoint(__isl_keep isl_set *set1,
1939 __isl_keep isl_set *set2);
1940 int isl_map_is_disjoint(__isl_keep isl_map *map1,
1941 __isl_keep isl_map *map2);
1945 int isl_basic_set_is_subset(
1946 __isl_keep isl_basic_set *bset1,
1947 __isl_keep isl_basic_set *bset2);
1948 int isl_set_is_subset(__isl_keep isl_set *set1,
1949 __isl_keep isl_set *set2);
1950 int isl_set_is_strict_subset(
1951 __isl_keep isl_set *set1,
1952 __isl_keep isl_set *set2);
1953 int isl_union_set_is_subset(
1954 __isl_keep isl_union_set *uset1,
1955 __isl_keep isl_union_set *uset2);
1956 int isl_union_set_is_strict_subset(
1957 __isl_keep isl_union_set *uset1,
1958 __isl_keep isl_union_set *uset2);
1959 int isl_basic_map_is_subset(
1960 __isl_keep isl_basic_map *bmap1,
1961 __isl_keep isl_basic_map *bmap2);
1962 int isl_basic_map_is_strict_subset(
1963 __isl_keep isl_basic_map *bmap1,
1964 __isl_keep isl_basic_map *bmap2);
1965 int isl_map_is_subset(
1966 __isl_keep isl_map *map1,
1967 __isl_keep isl_map *map2);
1968 int isl_map_is_strict_subset(
1969 __isl_keep isl_map *map1,
1970 __isl_keep isl_map *map2);
1971 int isl_union_map_is_subset(
1972 __isl_keep isl_union_map *umap1,
1973 __isl_keep isl_union_map *umap2);
1974 int isl_union_map_is_strict_subset(
1975 __isl_keep isl_union_map *umap1,
1976 __isl_keep isl_union_map *umap2);
1978 Check whether the first argument is a (strict) subset of the
1983 int isl_set_plain_cmp(__isl_keep isl_set *set1,
1984 __isl_keep isl_set *set2);
1986 This function is useful for sorting C<isl_set>s.
1987 The order depends on the internal representation of the inputs.
1988 The order is fixed over different calls to the function (assuming
1989 the internal representation of the inputs has not changed), but may
1990 change over different versions of C<isl>.
1994 =head2 Unary Operations
2000 __isl_give isl_set *isl_set_complement(
2001 __isl_take isl_set *set);
2002 __isl_give isl_map *isl_map_complement(
2003 __isl_take isl_map *map);
2007 __isl_give isl_basic_map *isl_basic_map_reverse(
2008 __isl_take isl_basic_map *bmap);
2009 __isl_give isl_map *isl_map_reverse(
2010 __isl_take isl_map *map);
2011 __isl_give isl_union_map *isl_union_map_reverse(
2012 __isl_take isl_union_map *umap);
2016 __isl_give isl_basic_set *isl_basic_set_project_out(
2017 __isl_take isl_basic_set *bset,
2018 enum isl_dim_type type, unsigned first, unsigned n);
2019 __isl_give isl_basic_map *isl_basic_map_project_out(
2020 __isl_take isl_basic_map *bmap,
2021 enum isl_dim_type type, unsigned first, unsigned n);
2022 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2023 enum isl_dim_type type, unsigned first, unsigned n);
2024 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2025 enum isl_dim_type type, unsigned first, unsigned n);
2026 __isl_give isl_basic_set *isl_basic_set_params(
2027 __isl_take isl_basic_set *bset);
2028 __isl_give isl_basic_set *isl_basic_map_domain(
2029 __isl_take isl_basic_map *bmap);
2030 __isl_give isl_basic_set *isl_basic_map_range(
2031 __isl_take isl_basic_map *bmap);
2032 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2033 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2034 __isl_give isl_set *isl_map_domain(
2035 __isl_take isl_map *bmap);
2036 __isl_give isl_set *isl_map_range(
2037 __isl_take isl_map *map);
2038 __isl_give isl_set *isl_union_set_params(
2039 __isl_take isl_union_set *uset);
2040 __isl_give isl_set *isl_union_map_params(
2041 __isl_take isl_union_map *umap);
2042 __isl_give isl_union_set *isl_union_map_domain(
2043 __isl_take isl_union_map *umap);
2044 __isl_give isl_union_set *isl_union_map_range(
2045 __isl_take isl_union_map *umap);
2047 __isl_give isl_basic_map *isl_basic_map_domain_map(
2048 __isl_take isl_basic_map *bmap);
2049 __isl_give isl_basic_map *isl_basic_map_range_map(
2050 __isl_take isl_basic_map *bmap);
2051 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2052 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2053 __isl_give isl_union_map *isl_union_map_domain_map(
2054 __isl_take isl_union_map *umap);
2055 __isl_give isl_union_map *isl_union_map_range_map(
2056 __isl_take isl_union_map *umap);
2058 The functions above construct a (basic, regular or union) relation
2059 that maps (a wrapped version of) the input relation to its domain or range.
2063 __isl_give isl_basic_set *isl_basic_set_eliminate(
2064 __isl_take isl_basic_set *bset,
2065 enum isl_dim_type type,
2066 unsigned first, unsigned n);
2067 __isl_give isl_set *isl_set_eliminate(
2068 __isl_take isl_set *set, enum isl_dim_type type,
2069 unsigned first, unsigned n);
2070 __isl_give isl_basic_map *isl_basic_map_eliminate(
2071 __isl_take isl_basic_map *bmap,
2072 enum isl_dim_type type,
2073 unsigned first, unsigned n);
2074 __isl_give isl_map *isl_map_eliminate(
2075 __isl_take isl_map *map, enum isl_dim_type type,
2076 unsigned first, unsigned n);
2078 Eliminate the coefficients for the given dimensions from the constraints,
2079 without removing the dimensions.
2083 __isl_give isl_basic_set *isl_basic_set_fix(
2084 __isl_take isl_basic_set *bset,
2085 enum isl_dim_type type, unsigned pos,
2087 __isl_give isl_basic_set *isl_basic_set_fix_si(
2088 __isl_take isl_basic_set *bset,
2089 enum isl_dim_type type, unsigned pos, int value);
2090 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2091 enum isl_dim_type type, unsigned pos,
2093 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2094 enum isl_dim_type type, unsigned pos, int value);
2095 __isl_give isl_basic_map *isl_basic_map_fix_si(
2096 __isl_take isl_basic_map *bmap,
2097 enum isl_dim_type type, unsigned pos, int value);
2098 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
2099 enum isl_dim_type type, unsigned pos,
2101 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2102 enum isl_dim_type type, unsigned pos, int value);
2104 Intersect the set or relation with the hyperplane where the given
2105 dimension has the fixed given value.
2107 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2108 __isl_take isl_basic_map *bmap,
2109 enum isl_dim_type type, unsigned pos, int value);
2110 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2111 __isl_take isl_basic_map *bmap,
2112 enum isl_dim_type type, unsigned pos, int value);
2113 __isl_give isl_set *isl_set_lower_bound(
2114 __isl_take isl_set *set,
2115 enum isl_dim_type type, unsigned pos,
2117 __isl_give isl_set *isl_set_lower_bound_si(
2118 __isl_take isl_set *set,
2119 enum isl_dim_type type, unsigned pos, int value);
2120 __isl_give isl_map *isl_map_lower_bound_si(
2121 __isl_take isl_map *map,
2122 enum isl_dim_type type, unsigned pos, int value);
2123 __isl_give isl_set *isl_set_upper_bound(
2124 __isl_take isl_set *set,
2125 enum isl_dim_type type, unsigned pos,
2127 __isl_give isl_set *isl_set_upper_bound_si(
2128 __isl_take isl_set *set,
2129 enum isl_dim_type type, unsigned pos, int value);
2130 __isl_give isl_map *isl_map_upper_bound_si(
2131 __isl_take isl_map *map,
2132 enum isl_dim_type type, unsigned pos, int value);
2134 Intersect the set or relation with the half-space where the given
2135 dimension has a value bounded by the fixed given value.
2137 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2138 enum isl_dim_type type1, int pos1,
2139 enum isl_dim_type type2, int pos2);
2140 __isl_give isl_basic_map *isl_basic_map_equate(
2141 __isl_take isl_basic_map *bmap,
2142 enum isl_dim_type type1, int pos1,
2143 enum isl_dim_type type2, int pos2);
2144 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2145 enum isl_dim_type type1, int pos1,
2146 enum isl_dim_type type2, int pos2);
2148 Intersect the set or relation with the hyperplane where the given
2149 dimensions are equal to each other.
2151 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2152 enum isl_dim_type type1, int pos1,
2153 enum isl_dim_type type2, int pos2);
2155 Intersect the relation with the hyperplane where the given
2156 dimensions have opposite values.
2158 __isl_give isl_basic_map *isl_basic_map_order_ge(
2159 __isl_take isl_basic_map *bmap,
2160 enum isl_dim_type type1, int pos1,
2161 enum isl_dim_type type2, int pos2);
2162 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2163 enum isl_dim_type type1, int pos1,
2164 enum isl_dim_type type2, int pos2);
2165 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2166 enum isl_dim_type type1, int pos1,
2167 enum isl_dim_type type2, int pos2);
2169 Intersect the relation with the half-space where the given
2170 dimensions satisfy the given ordering.
2174 __isl_give isl_map *isl_set_identity(
2175 __isl_take isl_set *set);
2176 __isl_give isl_union_map *isl_union_set_identity(
2177 __isl_take isl_union_set *uset);
2179 Construct an identity relation on the given (union) set.
2183 __isl_give isl_basic_set *isl_basic_map_deltas(
2184 __isl_take isl_basic_map *bmap);
2185 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2186 __isl_give isl_union_set *isl_union_map_deltas(
2187 __isl_take isl_union_map *umap);
2189 These functions return a (basic) set containing the differences
2190 between image elements and corresponding domain elements in the input.
2192 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2193 __isl_take isl_basic_map *bmap);
2194 __isl_give isl_map *isl_map_deltas_map(
2195 __isl_take isl_map *map);
2196 __isl_give isl_union_map *isl_union_map_deltas_map(
2197 __isl_take isl_union_map *umap);
2199 The functions above construct a (basic, regular or union) relation
2200 that maps (a wrapped version of) the input relation to its delta set.
2204 Simplify the representation of a set or relation by trying
2205 to combine pairs of basic sets or relations into a single
2206 basic set or relation.
2208 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2209 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2210 __isl_give isl_union_set *isl_union_set_coalesce(
2211 __isl_take isl_union_set *uset);
2212 __isl_give isl_union_map *isl_union_map_coalesce(
2213 __isl_take isl_union_map *umap);
2215 One of the methods for combining pairs of basic sets or relations
2216 can result in coefficients that are much larger than those that appear
2217 in the constraints of the input. By default, the coefficients are
2218 not allowed to grow larger, but this can be changed by unsetting
2219 the following option.
2221 int isl_options_set_coalesce_bounded_wrapping(
2222 isl_ctx *ctx, int val);
2223 int isl_options_get_coalesce_bounded_wrapping(
2226 =item * Detecting equalities
2228 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2229 __isl_take isl_basic_set *bset);
2230 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2231 __isl_take isl_basic_map *bmap);
2232 __isl_give isl_set *isl_set_detect_equalities(
2233 __isl_take isl_set *set);
2234 __isl_give isl_map *isl_map_detect_equalities(
2235 __isl_take isl_map *map);
2236 __isl_give isl_union_set *isl_union_set_detect_equalities(
2237 __isl_take isl_union_set *uset);
2238 __isl_give isl_union_map *isl_union_map_detect_equalities(
2239 __isl_take isl_union_map *umap);
2241 Simplify the representation of a set or relation by detecting implicit
2244 =item * Removing redundant constraints
2246 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2247 __isl_take isl_basic_set *bset);
2248 __isl_give isl_set *isl_set_remove_redundancies(
2249 __isl_take isl_set *set);
2250 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2251 __isl_take isl_basic_map *bmap);
2252 __isl_give isl_map *isl_map_remove_redundancies(
2253 __isl_take isl_map *map);
2257 __isl_give isl_basic_set *isl_set_convex_hull(
2258 __isl_take isl_set *set);
2259 __isl_give isl_basic_map *isl_map_convex_hull(
2260 __isl_take isl_map *map);
2262 If the input set or relation has any existentially quantified
2263 variables, then the result of these operations is currently undefined.
2267 __isl_give isl_basic_set *
2268 isl_set_unshifted_simple_hull(
2269 __isl_take isl_set *set);
2270 __isl_give isl_basic_map *
2271 isl_map_unshifted_simple_hull(
2272 __isl_take isl_map *map);
2273 __isl_give isl_basic_set *isl_set_simple_hull(
2274 __isl_take isl_set *set);
2275 __isl_give isl_basic_map *isl_map_simple_hull(
2276 __isl_take isl_map *map);
2277 __isl_give isl_union_map *isl_union_map_simple_hull(
2278 __isl_take isl_union_map *umap);
2280 These functions compute a single basic set or relation
2281 that contains the whole input set or relation.
2282 In particular, the output is described by translates
2283 of the constraints describing the basic sets or relations in the input.
2284 In case of C<isl_set_unshifted_simple_hull>, only the original
2285 constraints are used, without any translation.
2289 (See \autoref{s:simple hull}.)
2295 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2296 __isl_take isl_basic_set *bset);
2297 __isl_give isl_basic_set *isl_set_affine_hull(
2298 __isl_take isl_set *set);
2299 __isl_give isl_union_set *isl_union_set_affine_hull(
2300 __isl_take isl_union_set *uset);
2301 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2302 __isl_take isl_basic_map *bmap);
2303 __isl_give isl_basic_map *isl_map_affine_hull(
2304 __isl_take isl_map *map);
2305 __isl_give isl_union_map *isl_union_map_affine_hull(
2306 __isl_take isl_union_map *umap);
2308 In case of union sets and relations, the affine hull is computed
2311 =item * Polyhedral hull
2313 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2314 __isl_take isl_set *set);
2315 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2316 __isl_take isl_map *map);
2317 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2318 __isl_take isl_union_set *uset);
2319 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2320 __isl_take isl_union_map *umap);
2322 These functions compute a single basic set or relation
2323 not involving any existentially quantified variables
2324 that contains the whole input set or relation.
2325 In case of union sets and relations, the polyhedral hull is computed
2328 =item * Other approximations
2330 __isl_give isl_basic_set *
2331 isl_basic_set_drop_constraints_involving_dims(
2332 __isl_take isl_basic_set *bset,
2333 enum isl_dim_type type,
2334 unsigned first, unsigned n);
2335 __isl_give isl_basic_set *
2336 isl_basic_set_drop_constraints_not_involving_dims(
2337 __isl_take isl_basic_set *bset,
2338 enum isl_dim_type type,
2339 unsigned first, unsigned n);
2340 __isl_give isl_set *
2341 isl_set_drop_constraints_involving_dims(
2342 __isl_take isl_set *set,
2343 enum isl_dim_type type,
2344 unsigned first, unsigned n);
2345 __isl_give isl_map *
2346 isl_map_drop_constraints_involving_dims(
2347 __isl_take isl_map *map,
2348 enum isl_dim_type type,
2349 unsigned first, unsigned n);
2351 These functions drop any constraints (not) involving the specified dimensions.
2352 Note that the result depends on the representation of the input.
2356 __isl_give isl_basic_set *isl_basic_set_sample(
2357 __isl_take isl_basic_set *bset);
2358 __isl_give isl_basic_set *isl_set_sample(
2359 __isl_take isl_set *set);
2360 __isl_give isl_basic_map *isl_basic_map_sample(
2361 __isl_take isl_basic_map *bmap);
2362 __isl_give isl_basic_map *isl_map_sample(
2363 __isl_take isl_map *map);
2365 If the input (basic) set or relation is non-empty, then return
2366 a singleton subset of the input. Otherwise, return an empty set.
2368 =item * Optimization
2370 #include <isl/ilp.h>
2371 enum isl_lp_result isl_basic_set_max(
2372 __isl_keep isl_basic_set *bset,
2373 __isl_keep isl_aff *obj, isl_int *opt)
2374 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2375 __isl_keep isl_aff *obj, isl_int *opt);
2376 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2377 __isl_keep isl_aff *obj, isl_int *opt);
2379 Compute the minimum or maximum of the integer affine expression C<obj>
2380 over the points in C<set>, returning the result in C<opt>.
2381 The return value may be one of C<isl_lp_error>,
2382 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2384 =item * Parametric optimization
2386 __isl_give isl_pw_aff *isl_set_dim_min(
2387 __isl_take isl_set *set, int pos);
2388 __isl_give isl_pw_aff *isl_set_dim_max(
2389 __isl_take isl_set *set, int pos);
2390 __isl_give isl_pw_aff *isl_map_dim_max(
2391 __isl_take isl_map *map, int pos);
2393 Compute the minimum or maximum of the given set or output dimension
2394 as a function of the parameters (and input dimensions), but independently
2395 of the other set or output dimensions.
2396 For lexicographic optimization, see L<"Lexicographic Optimization">.
2400 The following functions compute either the set of (rational) coefficient
2401 values of valid constraints for the given set or the set of (rational)
2402 values satisfying the constraints with coefficients from the given set.
2403 Internally, these two sets of functions perform essentially the
2404 same operations, except that the set of coefficients is assumed to
2405 be a cone, while the set of values may be any polyhedron.
2406 The current implementation is based on the Farkas lemma and
2407 Fourier-Motzkin elimination, but this may change or be made optional
2408 in future. In particular, future implementations may use different
2409 dualization algorithms or skip the elimination step.
2411 __isl_give isl_basic_set *isl_basic_set_coefficients(
2412 __isl_take isl_basic_set *bset);
2413 __isl_give isl_basic_set *isl_set_coefficients(
2414 __isl_take isl_set *set);
2415 __isl_give isl_union_set *isl_union_set_coefficients(
2416 __isl_take isl_union_set *bset);
2417 __isl_give isl_basic_set *isl_basic_set_solutions(
2418 __isl_take isl_basic_set *bset);
2419 __isl_give isl_basic_set *isl_set_solutions(
2420 __isl_take isl_set *set);
2421 __isl_give isl_union_set *isl_union_set_solutions(
2422 __isl_take isl_union_set *bset);
2426 __isl_give isl_map *isl_map_fixed_power(
2427 __isl_take isl_map *map, isl_int exp);
2428 __isl_give isl_union_map *isl_union_map_fixed_power(
2429 __isl_take isl_union_map *umap, isl_int exp);
2431 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2432 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2433 of C<map> is computed.
2435 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2437 __isl_give isl_union_map *isl_union_map_power(
2438 __isl_take isl_union_map *umap, int *exact);
2440 Compute a parametric representation for all positive powers I<k> of C<map>.
2441 The result maps I<k> to a nested relation corresponding to the
2442 I<k>th power of C<map>.
2443 The result may be an overapproximation. If the result is known to be exact,
2444 then C<*exact> is set to C<1>.
2446 =item * Transitive closure
2448 __isl_give isl_map *isl_map_transitive_closure(
2449 __isl_take isl_map *map, int *exact);
2450 __isl_give isl_union_map *isl_union_map_transitive_closure(
2451 __isl_take isl_union_map *umap, int *exact);
2453 Compute the transitive closure of C<map>.
2454 The result may be an overapproximation. If the result is known to be exact,
2455 then C<*exact> is set to C<1>.
2457 =item * Reaching path lengths
2459 __isl_give isl_map *isl_map_reaching_path_lengths(
2460 __isl_take isl_map *map, int *exact);
2462 Compute a relation that maps each element in the range of C<map>
2463 to the lengths of all paths composed of edges in C<map> that
2464 end up in the given element.
2465 The result may be an overapproximation. If the result is known to be exact,
2466 then C<*exact> is set to C<1>.
2467 To compute the I<maximal> path length, the resulting relation
2468 should be postprocessed by C<isl_map_lexmax>.
2469 In particular, if the input relation is a dependence relation
2470 (mapping sources to sinks), then the maximal path length corresponds
2471 to the free schedule.
2472 Note, however, that C<isl_map_lexmax> expects the maximum to be
2473 finite, so if the path lengths are unbounded (possibly due to
2474 the overapproximation), then you will get an error message.
2478 __isl_give isl_basic_set *isl_basic_map_wrap(
2479 __isl_take isl_basic_map *bmap);
2480 __isl_give isl_set *isl_map_wrap(
2481 __isl_take isl_map *map);
2482 __isl_give isl_union_set *isl_union_map_wrap(
2483 __isl_take isl_union_map *umap);
2484 __isl_give isl_basic_map *isl_basic_set_unwrap(
2485 __isl_take isl_basic_set *bset);
2486 __isl_give isl_map *isl_set_unwrap(
2487 __isl_take isl_set *set);
2488 __isl_give isl_union_map *isl_union_set_unwrap(
2489 __isl_take isl_union_set *uset);
2493 Remove any internal structure of domain (and range) of the given
2494 set or relation. If there is any such internal structure in the input,
2495 then the name of the space is also removed.
2497 __isl_give isl_basic_set *isl_basic_set_flatten(
2498 __isl_take isl_basic_set *bset);
2499 __isl_give isl_set *isl_set_flatten(
2500 __isl_take isl_set *set);
2501 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2502 __isl_take isl_basic_map *bmap);
2503 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2504 __isl_take isl_basic_map *bmap);
2505 __isl_give isl_map *isl_map_flatten_range(
2506 __isl_take isl_map *map);
2507 __isl_give isl_map *isl_map_flatten_domain(
2508 __isl_take isl_map *map);
2509 __isl_give isl_basic_map *isl_basic_map_flatten(
2510 __isl_take isl_basic_map *bmap);
2511 __isl_give isl_map *isl_map_flatten(
2512 __isl_take isl_map *map);
2514 __isl_give isl_map *isl_set_flatten_map(
2515 __isl_take isl_set *set);
2517 The function above constructs a relation
2518 that maps the input set to a flattened version of the set.
2522 Lift the input set to a space with extra dimensions corresponding
2523 to the existentially quantified variables in the input.
2524 In particular, the result lives in a wrapped map where the domain
2525 is the original space and the range corresponds to the original
2526 existentially quantified variables.
2528 __isl_give isl_basic_set *isl_basic_set_lift(
2529 __isl_take isl_basic_set *bset);
2530 __isl_give isl_set *isl_set_lift(
2531 __isl_take isl_set *set);
2532 __isl_give isl_union_set *isl_union_set_lift(
2533 __isl_take isl_union_set *uset);
2535 Given a local space that contains the existentially quantified
2536 variables of a set, a basic relation that, when applied to
2537 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2538 can be constructed using the following function.
2540 #include <isl/local_space.h>
2541 __isl_give isl_basic_map *isl_local_space_lifting(
2542 __isl_take isl_local_space *ls);
2544 =item * Internal Product
2546 __isl_give isl_basic_map *isl_basic_map_zip(
2547 __isl_take isl_basic_map *bmap);
2548 __isl_give isl_map *isl_map_zip(
2549 __isl_take isl_map *map);
2550 __isl_give isl_union_map *isl_union_map_zip(
2551 __isl_take isl_union_map *umap);
2553 Given a relation with nested relations for domain and range,
2554 interchange the range of the domain with the domain of the range.
2558 __isl_give isl_basic_map *isl_basic_map_curry(
2559 __isl_take isl_basic_map *bmap);
2560 __isl_give isl_basic_map *isl_basic_map_uncurry(
2561 __isl_take isl_basic_map *bmap);
2562 __isl_give isl_map *isl_map_curry(
2563 __isl_take isl_map *map);
2564 __isl_give isl_map *isl_map_uncurry(
2565 __isl_take isl_map *map);
2566 __isl_give isl_union_map *isl_union_map_curry(
2567 __isl_take isl_union_map *umap);
2568 __isl_give isl_union_map *isl_union_map_uncurry(
2569 __isl_take isl_union_map *umap);
2571 Given a relation with a nested relation for domain,
2572 the C<curry> functions
2573 move the range of the nested relation out of the domain
2574 and use it as the domain of a nested relation in the range,
2575 with the original range as range of this nested relation.
2576 The C<uncurry> functions perform the inverse operation.
2578 =item * Aligning parameters
2580 __isl_give isl_basic_set *isl_basic_set_align_params(
2581 __isl_take isl_basic_set *bset,
2582 __isl_take isl_space *model);
2583 __isl_give isl_set *isl_set_align_params(
2584 __isl_take isl_set *set,
2585 __isl_take isl_space *model);
2586 __isl_give isl_basic_map *isl_basic_map_align_params(
2587 __isl_take isl_basic_map *bmap,
2588 __isl_take isl_space *model);
2589 __isl_give isl_map *isl_map_align_params(
2590 __isl_take isl_map *map,
2591 __isl_take isl_space *model);
2593 Change the order of the parameters of the given set or relation
2594 such that the first parameters match those of C<model>.
2595 This may involve the introduction of extra parameters.
2596 All parameters need to be named.
2598 =item * Dimension manipulation
2600 __isl_give isl_basic_set *isl_basic_set_add_dims(
2601 __isl_take isl_basic_set *bset,
2602 enum isl_dim_type type, unsigned n);
2603 __isl_give isl_set *isl_set_add_dims(
2604 __isl_take isl_set *set,
2605 enum isl_dim_type type, unsigned n);
2606 __isl_give isl_map *isl_map_add_dims(
2607 __isl_take isl_map *map,
2608 enum isl_dim_type type, unsigned n);
2609 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2610 __isl_take isl_basic_set *bset,
2611 enum isl_dim_type type, unsigned pos,
2613 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2614 __isl_take isl_basic_map *bmap,
2615 enum isl_dim_type type, unsigned pos,
2617 __isl_give isl_set *isl_set_insert_dims(
2618 __isl_take isl_set *set,
2619 enum isl_dim_type type, unsigned pos, unsigned n);
2620 __isl_give isl_map *isl_map_insert_dims(
2621 __isl_take isl_map *map,
2622 enum isl_dim_type type, unsigned pos, unsigned n);
2623 __isl_give isl_basic_set *isl_basic_set_move_dims(
2624 __isl_take isl_basic_set *bset,
2625 enum isl_dim_type dst_type, unsigned dst_pos,
2626 enum isl_dim_type src_type, unsigned src_pos,
2628 __isl_give isl_basic_map *isl_basic_map_move_dims(
2629 __isl_take isl_basic_map *bmap,
2630 enum isl_dim_type dst_type, unsigned dst_pos,
2631 enum isl_dim_type src_type, unsigned src_pos,
2633 __isl_give isl_set *isl_set_move_dims(
2634 __isl_take isl_set *set,
2635 enum isl_dim_type dst_type, unsigned dst_pos,
2636 enum isl_dim_type src_type, unsigned src_pos,
2638 __isl_give isl_map *isl_map_move_dims(
2639 __isl_take isl_map *map,
2640 enum isl_dim_type dst_type, unsigned dst_pos,
2641 enum isl_dim_type src_type, unsigned src_pos,
2644 It is usually not advisable to directly change the (input or output)
2645 space of a set or a relation as this removes the name and the internal
2646 structure of the space. However, the above functions can be useful
2647 to add new parameters, assuming
2648 C<isl_set_align_params> and C<isl_map_align_params>
2653 =head2 Binary Operations
2655 The two arguments of a binary operation not only need to live
2656 in the same C<isl_ctx>, they currently also need to have
2657 the same (number of) parameters.
2659 =head3 Basic Operations
2663 =item * Intersection
2665 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2666 __isl_take isl_basic_set *bset1,
2667 __isl_take isl_basic_set *bset2);
2668 __isl_give isl_basic_set *isl_basic_set_intersect(
2669 __isl_take isl_basic_set *bset1,
2670 __isl_take isl_basic_set *bset2);
2671 __isl_give isl_set *isl_set_intersect_params(
2672 __isl_take isl_set *set,
2673 __isl_take isl_set *params);
2674 __isl_give isl_set *isl_set_intersect(
2675 __isl_take isl_set *set1,
2676 __isl_take isl_set *set2);
2677 __isl_give isl_union_set *isl_union_set_intersect_params(
2678 __isl_take isl_union_set *uset,
2679 __isl_take isl_set *set);
2680 __isl_give isl_union_map *isl_union_map_intersect_params(
2681 __isl_take isl_union_map *umap,
2682 __isl_take isl_set *set);
2683 __isl_give isl_union_set *isl_union_set_intersect(
2684 __isl_take isl_union_set *uset1,
2685 __isl_take isl_union_set *uset2);
2686 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2687 __isl_take isl_basic_map *bmap,
2688 __isl_take isl_basic_set *bset);
2689 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2690 __isl_take isl_basic_map *bmap,
2691 __isl_take isl_basic_set *bset);
2692 __isl_give isl_basic_map *isl_basic_map_intersect(
2693 __isl_take isl_basic_map *bmap1,
2694 __isl_take isl_basic_map *bmap2);
2695 __isl_give isl_map *isl_map_intersect_params(
2696 __isl_take isl_map *map,
2697 __isl_take isl_set *params);
2698 __isl_give isl_map *isl_map_intersect_domain(
2699 __isl_take isl_map *map,
2700 __isl_take isl_set *set);
2701 __isl_give isl_map *isl_map_intersect_range(
2702 __isl_take isl_map *map,
2703 __isl_take isl_set *set);
2704 __isl_give isl_map *isl_map_intersect(
2705 __isl_take isl_map *map1,
2706 __isl_take isl_map *map2);
2707 __isl_give isl_union_map *isl_union_map_intersect_domain(
2708 __isl_take isl_union_map *umap,
2709 __isl_take isl_union_set *uset);
2710 __isl_give isl_union_map *isl_union_map_intersect_range(
2711 __isl_take isl_union_map *umap,
2712 __isl_take isl_union_set *uset);
2713 __isl_give isl_union_map *isl_union_map_intersect(
2714 __isl_take isl_union_map *umap1,
2715 __isl_take isl_union_map *umap2);
2717 The second argument to the C<_params> functions needs to be
2718 a parametric (basic) set. For the other functions, a parametric set
2719 for either argument is only allowed if the other argument is
2720 a parametric set as well.
2724 __isl_give isl_set *isl_basic_set_union(
2725 __isl_take isl_basic_set *bset1,
2726 __isl_take isl_basic_set *bset2);
2727 __isl_give isl_map *isl_basic_map_union(
2728 __isl_take isl_basic_map *bmap1,
2729 __isl_take isl_basic_map *bmap2);
2730 __isl_give isl_set *isl_set_union(
2731 __isl_take isl_set *set1,
2732 __isl_take isl_set *set2);
2733 __isl_give isl_map *isl_map_union(
2734 __isl_take isl_map *map1,
2735 __isl_take isl_map *map2);
2736 __isl_give isl_union_set *isl_union_set_union(
2737 __isl_take isl_union_set *uset1,
2738 __isl_take isl_union_set *uset2);
2739 __isl_give isl_union_map *isl_union_map_union(
2740 __isl_take isl_union_map *umap1,
2741 __isl_take isl_union_map *umap2);
2743 =item * Set difference
2745 __isl_give isl_set *isl_set_subtract(
2746 __isl_take isl_set *set1,
2747 __isl_take isl_set *set2);
2748 __isl_give isl_map *isl_map_subtract(
2749 __isl_take isl_map *map1,
2750 __isl_take isl_map *map2);
2751 __isl_give isl_map *isl_map_subtract_domain(
2752 __isl_take isl_map *map,
2753 __isl_take isl_set *dom);
2754 __isl_give isl_map *isl_map_subtract_range(
2755 __isl_take isl_map *map,
2756 __isl_take isl_set *dom);
2757 __isl_give isl_union_set *isl_union_set_subtract(
2758 __isl_take isl_union_set *uset1,
2759 __isl_take isl_union_set *uset2);
2760 __isl_give isl_union_map *isl_union_map_subtract(
2761 __isl_take isl_union_map *umap1,
2762 __isl_take isl_union_map *umap2);
2763 __isl_give isl_union_map *isl_union_map_subtract_domain(
2764 __isl_take isl_union_map *umap,
2765 __isl_take isl_union_set *dom);
2766 __isl_give isl_union_map *isl_union_map_subtract_range(
2767 __isl_take isl_union_map *umap,
2768 __isl_take isl_union_set *dom);
2772 __isl_give isl_basic_set *isl_basic_set_apply(
2773 __isl_take isl_basic_set *bset,
2774 __isl_take isl_basic_map *bmap);
2775 __isl_give isl_set *isl_set_apply(
2776 __isl_take isl_set *set,
2777 __isl_take isl_map *map);
2778 __isl_give isl_union_set *isl_union_set_apply(
2779 __isl_take isl_union_set *uset,
2780 __isl_take isl_union_map *umap);
2781 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2782 __isl_take isl_basic_map *bmap1,
2783 __isl_take isl_basic_map *bmap2);
2784 __isl_give isl_basic_map *isl_basic_map_apply_range(
2785 __isl_take isl_basic_map *bmap1,
2786 __isl_take isl_basic_map *bmap2);
2787 __isl_give isl_map *isl_map_apply_domain(
2788 __isl_take isl_map *map1,
2789 __isl_take isl_map *map2);
2790 __isl_give isl_union_map *isl_union_map_apply_domain(
2791 __isl_take isl_union_map *umap1,
2792 __isl_take isl_union_map *umap2);
2793 __isl_give isl_map *isl_map_apply_range(
2794 __isl_take isl_map *map1,
2795 __isl_take isl_map *map2);
2796 __isl_give isl_union_map *isl_union_map_apply_range(
2797 __isl_take isl_union_map *umap1,
2798 __isl_take isl_union_map *umap2);
2802 __isl_give isl_basic_set *
2803 isl_basic_set_preimage_multi_aff(
2804 __isl_take isl_basic_set *bset,
2805 __isl_take isl_multi_aff *ma);
2806 __isl_give isl_set *isl_set_preimage_multi_aff(
2807 __isl_take isl_set *set,
2808 __isl_take isl_multi_aff *ma);
2809 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
2810 __isl_take isl_set *set,
2811 __isl_take isl_pw_multi_aff *pma);
2813 These functions compute the preimage of the given set under
2814 the given function. In other words, the expression is plugged
2815 into the set description.
2816 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
2817 L</"Piecewise Multiple Quasi Affine Expressions">.
2819 =item * Cartesian Product
2821 __isl_give isl_set *isl_set_product(
2822 __isl_take isl_set *set1,
2823 __isl_take isl_set *set2);
2824 __isl_give isl_union_set *isl_union_set_product(
2825 __isl_take isl_union_set *uset1,
2826 __isl_take isl_union_set *uset2);
2827 __isl_give isl_basic_map *isl_basic_map_domain_product(
2828 __isl_take isl_basic_map *bmap1,
2829 __isl_take isl_basic_map *bmap2);
2830 __isl_give isl_basic_map *isl_basic_map_range_product(
2831 __isl_take isl_basic_map *bmap1,
2832 __isl_take isl_basic_map *bmap2);
2833 __isl_give isl_basic_map *isl_basic_map_product(
2834 __isl_take isl_basic_map *bmap1,
2835 __isl_take isl_basic_map *bmap2);
2836 __isl_give isl_map *isl_map_domain_product(
2837 __isl_take isl_map *map1,
2838 __isl_take isl_map *map2);
2839 __isl_give isl_map *isl_map_range_product(
2840 __isl_take isl_map *map1,
2841 __isl_take isl_map *map2);
2842 __isl_give isl_union_map *isl_union_map_domain_product(
2843 __isl_take isl_union_map *umap1,
2844 __isl_take isl_union_map *umap2);
2845 __isl_give isl_union_map *isl_union_map_range_product(
2846 __isl_take isl_union_map *umap1,
2847 __isl_take isl_union_map *umap2);
2848 __isl_give isl_map *isl_map_product(
2849 __isl_take isl_map *map1,
2850 __isl_take isl_map *map2);
2851 __isl_give isl_union_map *isl_union_map_product(
2852 __isl_take isl_union_map *umap1,
2853 __isl_take isl_union_map *umap2);
2855 The above functions compute the cross product of the given
2856 sets or relations. The domains and ranges of the results
2857 are wrapped maps between domains and ranges of the inputs.
2858 To obtain a ``flat'' product, use the following functions
2861 __isl_give isl_basic_set *isl_basic_set_flat_product(
2862 __isl_take isl_basic_set *bset1,
2863 __isl_take isl_basic_set *bset2);
2864 __isl_give isl_set *isl_set_flat_product(
2865 __isl_take isl_set *set1,
2866 __isl_take isl_set *set2);
2867 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2868 __isl_take isl_basic_map *bmap1,
2869 __isl_take isl_basic_map *bmap2);
2870 __isl_give isl_map *isl_map_flat_domain_product(
2871 __isl_take isl_map *map1,
2872 __isl_take isl_map *map2);
2873 __isl_give isl_map *isl_map_flat_range_product(
2874 __isl_take isl_map *map1,
2875 __isl_take isl_map *map2);
2876 __isl_give isl_union_map *isl_union_map_flat_range_product(
2877 __isl_take isl_union_map *umap1,
2878 __isl_take isl_union_map *umap2);
2879 __isl_give isl_basic_map *isl_basic_map_flat_product(
2880 __isl_take isl_basic_map *bmap1,
2881 __isl_take isl_basic_map *bmap2);
2882 __isl_give isl_map *isl_map_flat_product(
2883 __isl_take isl_map *map1,
2884 __isl_take isl_map *map2);
2886 =item * Simplification
2888 __isl_give isl_basic_set *isl_basic_set_gist(
2889 __isl_take isl_basic_set *bset,
2890 __isl_take isl_basic_set *context);
2891 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2892 __isl_take isl_set *context);
2893 __isl_give isl_set *isl_set_gist_params(
2894 __isl_take isl_set *set,
2895 __isl_take isl_set *context);
2896 __isl_give isl_union_set *isl_union_set_gist(
2897 __isl_take isl_union_set *uset,
2898 __isl_take isl_union_set *context);
2899 __isl_give isl_union_set *isl_union_set_gist_params(
2900 __isl_take isl_union_set *uset,
2901 __isl_take isl_set *set);
2902 __isl_give isl_basic_map *isl_basic_map_gist(
2903 __isl_take isl_basic_map *bmap,
2904 __isl_take isl_basic_map *context);
2905 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2906 __isl_take isl_map *context);
2907 __isl_give isl_map *isl_map_gist_params(
2908 __isl_take isl_map *map,
2909 __isl_take isl_set *context);
2910 __isl_give isl_map *isl_map_gist_domain(
2911 __isl_take isl_map *map,
2912 __isl_take isl_set *context);
2913 __isl_give isl_map *isl_map_gist_range(
2914 __isl_take isl_map *map,
2915 __isl_take isl_set *context);
2916 __isl_give isl_union_map *isl_union_map_gist(
2917 __isl_take isl_union_map *umap,
2918 __isl_take isl_union_map *context);
2919 __isl_give isl_union_map *isl_union_map_gist_params(
2920 __isl_take isl_union_map *umap,
2921 __isl_take isl_set *set);
2922 __isl_give isl_union_map *isl_union_map_gist_domain(
2923 __isl_take isl_union_map *umap,
2924 __isl_take isl_union_set *uset);
2925 __isl_give isl_union_map *isl_union_map_gist_range(
2926 __isl_take isl_union_map *umap,
2927 __isl_take isl_union_set *uset);
2929 The gist operation returns a set or relation that has the
2930 same intersection with the context as the input set or relation.
2931 Any implicit equality in the intersection is made explicit in the result,
2932 while all inequalities that are redundant with respect to the intersection
2934 In case of union sets and relations, the gist operation is performed
2939 =head3 Lexicographic Optimization
2941 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2942 the following functions
2943 compute a set that contains the lexicographic minimum or maximum
2944 of the elements in C<set> (or C<bset>) for those values of the parameters
2945 that satisfy C<dom>.
2946 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2947 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2949 In other words, the union of the parameter values
2950 for which the result is non-empty and of C<*empty>
2953 __isl_give isl_set *isl_basic_set_partial_lexmin(
2954 __isl_take isl_basic_set *bset,
2955 __isl_take isl_basic_set *dom,
2956 __isl_give isl_set **empty);
2957 __isl_give isl_set *isl_basic_set_partial_lexmax(
2958 __isl_take isl_basic_set *bset,
2959 __isl_take isl_basic_set *dom,
2960 __isl_give isl_set **empty);
2961 __isl_give isl_set *isl_set_partial_lexmin(
2962 __isl_take isl_set *set, __isl_take isl_set *dom,
2963 __isl_give isl_set **empty);
2964 __isl_give isl_set *isl_set_partial_lexmax(
2965 __isl_take isl_set *set, __isl_take isl_set *dom,
2966 __isl_give isl_set **empty);
2968 Given a (basic) set C<set> (or C<bset>), the following functions simply
2969 return a set containing the lexicographic minimum or maximum
2970 of the elements in C<set> (or C<bset>).
2971 In case of union sets, the optimum is computed per space.
2973 __isl_give isl_set *isl_basic_set_lexmin(
2974 __isl_take isl_basic_set *bset);
2975 __isl_give isl_set *isl_basic_set_lexmax(
2976 __isl_take isl_basic_set *bset);
2977 __isl_give isl_set *isl_set_lexmin(
2978 __isl_take isl_set *set);
2979 __isl_give isl_set *isl_set_lexmax(
2980 __isl_take isl_set *set);
2981 __isl_give isl_union_set *isl_union_set_lexmin(
2982 __isl_take isl_union_set *uset);
2983 __isl_give isl_union_set *isl_union_set_lexmax(
2984 __isl_take isl_union_set *uset);
2986 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2987 the following functions
2988 compute a relation that maps each element of C<dom>
2989 to the single lexicographic minimum or maximum
2990 of the elements that are associated to that same
2991 element in C<map> (or C<bmap>).
2992 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2993 that contains the elements in C<dom> that do not map
2994 to any elements in C<map> (or C<bmap>).
2995 In other words, the union of the domain of the result and of C<*empty>
2998 __isl_give isl_map *isl_basic_map_partial_lexmax(
2999 __isl_take isl_basic_map *bmap,
3000 __isl_take isl_basic_set *dom,
3001 __isl_give isl_set **empty);
3002 __isl_give isl_map *isl_basic_map_partial_lexmin(
3003 __isl_take isl_basic_map *bmap,
3004 __isl_take isl_basic_set *dom,
3005 __isl_give isl_set **empty);
3006 __isl_give isl_map *isl_map_partial_lexmax(
3007 __isl_take isl_map *map, __isl_take isl_set *dom,
3008 __isl_give isl_set **empty);
3009 __isl_give isl_map *isl_map_partial_lexmin(
3010 __isl_take isl_map *map, __isl_take isl_set *dom,
3011 __isl_give isl_set **empty);
3013 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3014 return a map mapping each element in the domain of
3015 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3016 of all elements associated to that element.
3017 In case of union relations, the optimum is computed per space.
3019 __isl_give isl_map *isl_basic_map_lexmin(
3020 __isl_take isl_basic_map *bmap);
3021 __isl_give isl_map *isl_basic_map_lexmax(
3022 __isl_take isl_basic_map *bmap);
3023 __isl_give isl_map *isl_map_lexmin(
3024 __isl_take isl_map *map);
3025 __isl_give isl_map *isl_map_lexmax(
3026 __isl_take isl_map *map);
3027 __isl_give isl_union_map *isl_union_map_lexmin(
3028 __isl_take isl_union_map *umap);
3029 __isl_give isl_union_map *isl_union_map_lexmax(
3030 __isl_take isl_union_map *umap);
3032 The following functions return their result in the form of
3033 a piecewise multi-affine expression
3034 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3035 but are otherwise equivalent to the corresponding functions
3036 returning a basic set or relation.
3038 __isl_give isl_pw_multi_aff *
3039 isl_basic_map_lexmin_pw_multi_aff(
3040 __isl_take isl_basic_map *bmap);
3041 __isl_give isl_pw_multi_aff *
3042 isl_basic_set_partial_lexmin_pw_multi_aff(
3043 __isl_take isl_basic_set *bset,
3044 __isl_take isl_basic_set *dom,
3045 __isl_give isl_set **empty);
3046 __isl_give isl_pw_multi_aff *
3047 isl_basic_set_partial_lexmax_pw_multi_aff(
3048 __isl_take isl_basic_set *bset,
3049 __isl_take isl_basic_set *dom,
3050 __isl_give isl_set **empty);
3051 __isl_give isl_pw_multi_aff *
3052 isl_basic_map_partial_lexmin_pw_multi_aff(
3053 __isl_take isl_basic_map *bmap,
3054 __isl_take isl_basic_set *dom,
3055 __isl_give isl_set **empty);
3056 __isl_give isl_pw_multi_aff *
3057 isl_basic_map_partial_lexmax_pw_multi_aff(
3058 __isl_take isl_basic_map *bmap,
3059 __isl_take isl_basic_set *dom,
3060 __isl_give isl_set **empty);
3061 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3062 __isl_take isl_map *map);
3063 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3064 __isl_take isl_map *map);
3068 Lists are defined over several element types, including
3069 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3070 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3071 Here we take lists of C<isl_set>s as an example.
3072 Lists can be created, copied, modified and freed using the following functions.
3074 #include <isl/list.h>
3075 __isl_give isl_set_list *isl_set_list_from_set(
3076 __isl_take isl_set *el);
3077 __isl_give isl_set_list *isl_set_list_alloc(
3078 isl_ctx *ctx, int n);
3079 __isl_give isl_set_list *isl_set_list_copy(
3080 __isl_keep isl_set_list *list);
3081 __isl_give isl_set_list *isl_set_list_insert(
3082 __isl_take isl_set_list *list, unsigned pos,
3083 __isl_take isl_set *el);
3084 __isl_give isl_set_list *isl_set_list_add(
3085 __isl_take isl_set_list *list,
3086 __isl_take isl_set *el);
3087 __isl_give isl_set_list *isl_set_list_drop(
3088 __isl_take isl_set_list *list,
3089 unsigned first, unsigned n);
3090 __isl_give isl_set_list *isl_set_list_set_set(
3091 __isl_take isl_set_list *list, int index,
3092 __isl_take isl_set *set);
3093 __isl_give isl_set_list *isl_set_list_concat(
3094 __isl_take isl_set_list *list1,
3095 __isl_take isl_set_list *list2);
3096 void *isl_set_list_free(__isl_take isl_set_list *list);
3098 C<isl_set_list_alloc> creates an empty list with a capacity for
3099 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3102 Lists can be inspected using the following functions.
3104 #include <isl/list.h>
3105 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3106 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3107 __isl_give isl_set *isl_set_list_get_set(
3108 __isl_keep isl_set_list *list, int index);
3109 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3110 int (*fn)(__isl_take isl_set *el, void *user),
3113 Lists can be printed using
3115 #include <isl/list.h>
3116 __isl_give isl_printer *isl_printer_print_set_list(
3117 __isl_take isl_printer *p,
3118 __isl_keep isl_set_list *list);
3122 Vectors can be created, copied and freed using the following functions.
3124 #include <isl/vec.h>
3125 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3127 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3128 void *isl_vec_free(__isl_take isl_vec *vec);
3130 Note that the elements of a newly created vector may have arbitrary values.
3131 The elements can be changed and inspected using the following functions.
3133 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3134 int isl_vec_size(__isl_keep isl_vec *vec);
3135 int isl_vec_get_element(__isl_keep isl_vec *vec,
3136 int pos, isl_int *v);
3137 __isl_give isl_vec *isl_vec_set_element(
3138 __isl_take isl_vec *vec, int pos, isl_int v);
3139 __isl_give isl_vec *isl_vec_set_element_si(
3140 __isl_take isl_vec *vec, int pos, int v);
3141 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3143 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3145 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3148 C<isl_vec_get_element> will return a negative value if anything went wrong.
3149 In that case, the value of C<*v> is undefined.
3151 The following function can be used to concatenate two vectors.
3153 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3154 __isl_take isl_vec *vec2);
3158 Matrices can be created, copied and freed using the following functions.
3160 #include <isl/mat.h>
3161 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3162 unsigned n_row, unsigned n_col);
3163 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3164 void isl_mat_free(__isl_take isl_mat *mat);
3166 Note that the elements of a newly created matrix may have arbitrary values.
3167 The elements can be changed and inspected using the following functions.
3169 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3170 int isl_mat_rows(__isl_keep isl_mat *mat);
3171 int isl_mat_cols(__isl_keep isl_mat *mat);
3172 int isl_mat_get_element(__isl_keep isl_mat *mat,
3173 int row, int col, isl_int *v);
3174 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3175 int row, int col, isl_int v);
3176 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3177 int row, int col, int v);
3179 C<isl_mat_get_element> will return a negative value if anything went wrong.
3180 In that case, the value of C<*v> is undefined.
3182 The following function can be used to compute the (right) inverse
3183 of a matrix, i.e., a matrix such that the product of the original
3184 and the inverse (in that order) is a multiple of the identity matrix.
3185 The input matrix is assumed to be of full row-rank.
3187 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3189 The following function can be used to compute the (right) kernel
3190 (or null space) of a matrix, i.e., a matrix such that the product of
3191 the original and the kernel (in that order) is the zero matrix.
3193 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3195 =head2 Piecewise Quasi Affine Expressions
3197 The zero quasi affine expression or the quasi affine expression
3198 that is equal to a specified dimension on a given domain can be created using
3200 __isl_give isl_aff *isl_aff_zero_on_domain(
3201 __isl_take isl_local_space *ls);
3202 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3203 __isl_take isl_local_space *ls);
3204 __isl_give isl_aff *isl_aff_var_on_domain(
3205 __isl_take isl_local_space *ls,
3206 enum isl_dim_type type, unsigned pos);
3207 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3208 __isl_take isl_local_space *ls,
3209 enum isl_dim_type type, unsigned pos);
3211 Note that the space in which the resulting objects live is a map space
3212 with the given space as domain and a one-dimensional range.
3214 An empty piecewise quasi affine expression (one with no cells)
3215 or a piecewise quasi affine expression with a single cell can
3216 be created using the following functions.
3218 #include <isl/aff.h>
3219 __isl_give isl_pw_aff *isl_pw_aff_empty(
3220 __isl_take isl_space *space);
3221 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3222 __isl_take isl_set *set, __isl_take isl_aff *aff);
3223 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3224 __isl_take isl_aff *aff);
3226 A piecewise quasi affine expression that is equal to 1 on a set
3227 and 0 outside the set can be created using the following function.
3229 #include <isl/aff.h>
3230 __isl_give isl_pw_aff *isl_set_indicator_function(
3231 __isl_take isl_set *set);
3233 Quasi affine expressions can be copied and freed using
3235 #include <isl/aff.h>
3236 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3237 void *isl_aff_free(__isl_take isl_aff *aff);
3239 __isl_give isl_pw_aff *isl_pw_aff_copy(
3240 __isl_keep isl_pw_aff *pwaff);
3241 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3243 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3244 using the following function. The constraint is required to have
3245 a non-zero coefficient for the specified dimension.
3247 #include <isl/constraint.h>
3248 __isl_give isl_aff *isl_constraint_get_bound(
3249 __isl_keep isl_constraint *constraint,
3250 enum isl_dim_type type, int pos);
3252 The entire affine expression of the constraint can also be extracted
3253 using the following function.
3255 #include <isl/constraint.h>
3256 __isl_give isl_aff *isl_constraint_get_aff(
3257 __isl_keep isl_constraint *constraint);
3259 Conversely, an equality constraint equating
3260 the affine expression to zero or an inequality constraint enforcing
3261 the affine expression to be non-negative, can be constructed using
3263 __isl_give isl_constraint *isl_equality_from_aff(
3264 __isl_take isl_aff *aff);
3265 __isl_give isl_constraint *isl_inequality_from_aff(
3266 __isl_take isl_aff *aff);
3268 The expression can be inspected using
3270 #include <isl/aff.h>
3271 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3272 int isl_aff_dim(__isl_keep isl_aff *aff,
3273 enum isl_dim_type type);
3274 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3275 __isl_keep isl_aff *aff);
3276 __isl_give isl_local_space *isl_aff_get_local_space(
3277 __isl_keep isl_aff *aff);
3278 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3279 enum isl_dim_type type, unsigned pos);
3280 const char *isl_pw_aff_get_dim_name(
3281 __isl_keep isl_pw_aff *pa,
3282 enum isl_dim_type type, unsigned pos);
3283 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3284 enum isl_dim_type type, unsigned pos);
3285 __isl_give isl_id *isl_pw_aff_get_dim_id(
3286 __isl_keep isl_pw_aff *pa,
3287 enum isl_dim_type type, unsigned pos);
3288 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3289 __isl_keep isl_pw_aff *pa,
3290 enum isl_dim_type type);
3291 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3293 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3294 enum isl_dim_type type, int pos, isl_int *v);
3295 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3297 __isl_give isl_aff *isl_aff_get_div(
3298 __isl_keep isl_aff *aff, int pos);
3300 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3301 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3302 int (*fn)(__isl_take isl_set *set,
3303 __isl_take isl_aff *aff,
3304 void *user), void *user);
3306 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3307 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3309 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3310 enum isl_dim_type type, unsigned first, unsigned n);
3311 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3312 enum isl_dim_type type, unsigned first, unsigned n);
3314 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3315 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3316 enum isl_dim_type type);
3317 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3319 It can be modified using
3321 #include <isl/aff.h>
3322 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3323 __isl_take isl_pw_aff *pwaff,
3324 enum isl_dim_type type, __isl_take isl_id *id);
3325 __isl_give isl_aff *isl_aff_set_dim_name(
3326 __isl_take isl_aff *aff, enum isl_dim_type type,
3327 unsigned pos, const char *s);
3328 __isl_give isl_aff *isl_aff_set_dim_id(
3329 __isl_take isl_aff *aff, enum isl_dim_type type,
3330 unsigned pos, __isl_take isl_id *id);
3331 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3332 __isl_take isl_pw_aff *pma,
3333 enum isl_dim_type type, unsigned pos,
3334 __isl_take isl_id *id);
3335 __isl_give isl_aff *isl_aff_set_constant(
3336 __isl_take isl_aff *aff, isl_int v);
3337 __isl_give isl_aff *isl_aff_set_constant_si(
3338 __isl_take isl_aff *aff, int v);
3339 __isl_give isl_aff *isl_aff_set_coefficient(
3340 __isl_take isl_aff *aff,
3341 enum isl_dim_type type, int pos, isl_int v);
3342 __isl_give isl_aff *isl_aff_set_coefficient_si(
3343 __isl_take isl_aff *aff,
3344 enum isl_dim_type type, int pos, int v);
3345 __isl_give isl_aff *isl_aff_set_denominator(
3346 __isl_take isl_aff *aff, isl_int v);
3348 __isl_give isl_aff *isl_aff_add_constant(
3349 __isl_take isl_aff *aff, isl_int v);
3350 __isl_give isl_aff *isl_aff_add_constant_si(
3351 __isl_take isl_aff *aff, int v);
3352 __isl_give isl_aff *isl_aff_add_constant_num(
3353 __isl_take isl_aff *aff, isl_int v);
3354 __isl_give isl_aff *isl_aff_add_constant_num_si(
3355 __isl_take isl_aff *aff, int v);
3356 __isl_give isl_aff *isl_aff_add_coefficient(
3357 __isl_take isl_aff *aff,
3358 enum isl_dim_type type, int pos, isl_int v);
3359 __isl_give isl_aff *isl_aff_add_coefficient_si(
3360 __isl_take isl_aff *aff,
3361 enum isl_dim_type type, int pos, int v);
3363 __isl_give isl_aff *isl_aff_insert_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_insert_dims(
3367 __isl_take isl_pw_aff *pwaff,
3368 enum isl_dim_type type, unsigned first, unsigned n);
3369 __isl_give isl_aff *isl_aff_add_dims(
3370 __isl_take isl_aff *aff,
3371 enum isl_dim_type type, unsigned n);
3372 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3373 __isl_take isl_pw_aff *pwaff,
3374 enum isl_dim_type type, unsigned n);
3375 __isl_give isl_aff *isl_aff_drop_dims(
3376 __isl_take isl_aff *aff,
3377 enum isl_dim_type type, unsigned first, unsigned n);
3378 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3379 __isl_take isl_pw_aff *pwaff,
3380 enum isl_dim_type type, unsigned first, unsigned n);
3382 Note that the C<set_constant> and C<set_coefficient> functions
3383 set the I<numerator> of the constant or coefficient, while
3384 C<add_constant> and C<add_coefficient> add an integer value to
3385 the possibly rational constant or coefficient.
3386 The C<add_constant_num> functions add an integer value to
3389 To check whether an affine expressions is obviously zero
3390 or obviously equal to some other affine expression, use
3392 #include <isl/aff.h>
3393 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3394 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3395 __isl_keep isl_aff *aff2);
3396 int isl_pw_aff_plain_is_equal(
3397 __isl_keep isl_pw_aff *pwaff1,
3398 __isl_keep isl_pw_aff *pwaff2);
3402 #include <isl/aff.h>
3403 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3404 __isl_take isl_aff *aff2);
3405 __isl_give isl_pw_aff *isl_pw_aff_add(
3406 __isl_take isl_pw_aff *pwaff1,
3407 __isl_take isl_pw_aff *pwaff2);
3408 __isl_give isl_pw_aff *isl_pw_aff_min(
3409 __isl_take isl_pw_aff *pwaff1,
3410 __isl_take isl_pw_aff *pwaff2);
3411 __isl_give isl_pw_aff *isl_pw_aff_max(
3412 __isl_take isl_pw_aff *pwaff1,
3413 __isl_take isl_pw_aff *pwaff2);
3414 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3415 __isl_take isl_aff *aff2);
3416 __isl_give isl_pw_aff *isl_pw_aff_sub(
3417 __isl_take isl_pw_aff *pwaff1,
3418 __isl_take isl_pw_aff *pwaff2);
3419 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3420 __isl_give isl_pw_aff *isl_pw_aff_neg(
3421 __isl_take isl_pw_aff *pwaff);
3422 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3423 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3424 __isl_take isl_pw_aff *pwaff);
3425 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3426 __isl_give isl_pw_aff *isl_pw_aff_floor(
3427 __isl_take isl_pw_aff *pwaff);
3428 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3430 __isl_give isl_pw_aff *isl_pw_aff_mod(
3431 __isl_take isl_pw_aff *pwaff, isl_int mod);
3432 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3434 __isl_give isl_pw_aff *isl_pw_aff_scale(
3435 __isl_take isl_pw_aff *pwaff, isl_int f);
3436 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3438 __isl_give isl_aff *isl_aff_scale_down_ui(
3439 __isl_take isl_aff *aff, unsigned f);
3440 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3441 __isl_take isl_pw_aff *pwaff, isl_int f);
3443 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3444 __isl_take isl_pw_aff_list *list);
3445 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3446 __isl_take isl_pw_aff_list *list);
3448 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3449 __isl_take isl_pw_aff *pwqp);
3451 __isl_give isl_aff *isl_aff_align_params(
3452 __isl_take isl_aff *aff,
3453 __isl_take isl_space *model);
3454 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3455 __isl_take isl_pw_aff *pwaff,
3456 __isl_take isl_space *model);
3458 __isl_give isl_aff *isl_aff_project_domain_on_params(
3459 __isl_take isl_aff *aff);
3461 __isl_give isl_aff *isl_aff_gist_params(
3462 __isl_take isl_aff *aff,
3463 __isl_take isl_set *context);
3464 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3465 __isl_take isl_set *context);
3466 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3467 __isl_take isl_pw_aff *pwaff,
3468 __isl_take isl_set *context);
3469 __isl_give isl_pw_aff *isl_pw_aff_gist(
3470 __isl_take isl_pw_aff *pwaff,
3471 __isl_take isl_set *context);
3473 __isl_give isl_set *isl_pw_aff_domain(
3474 __isl_take isl_pw_aff *pwaff);
3475 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3476 __isl_take isl_pw_aff *pa,
3477 __isl_take isl_set *set);
3478 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3479 __isl_take isl_pw_aff *pa,
3480 __isl_take isl_set *set);
3482 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3483 __isl_take isl_aff *aff2);
3484 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3485 __isl_take isl_aff *aff2);
3486 __isl_give isl_pw_aff *isl_pw_aff_mul(
3487 __isl_take isl_pw_aff *pwaff1,
3488 __isl_take isl_pw_aff *pwaff2);
3489 __isl_give isl_pw_aff *isl_pw_aff_div(
3490 __isl_take isl_pw_aff *pa1,
3491 __isl_take isl_pw_aff *pa2);
3492 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3493 __isl_take isl_pw_aff *pa1,
3494 __isl_take isl_pw_aff *pa2);
3495 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3496 __isl_take isl_pw_aff *pa1,
3497 __isl_take isl_pw_aff *pa2);
3499 When multiplying two affine expressions, at least one of the two needs
3500 to be a constant. Similarly, when dividing an affine expression by another,
3501 the second expression needs to be a constant.
3502 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3503 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3506 #include <isl/aff.h>
3507 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3508 __isl_take isl_aff *aff,
3509 __isl_take isl_multi_aff *ma);
3510 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3511 __isl_take isl_pw_aff *pa,
3512 __isl_take isl_multi_aff *ma);
3513 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3514 __isl_take isl_pw_aff *pa,
3515 __isl_take isl_pw_multi_aff *pma);
3517 These functions precompose the input expression by the given
3518 C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3519 the C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3520 into the (piecewise) affine expression.
3521 Objects of type C<isl_multi_aff> are described in
3522 L</"Piecewise Multiple Quasi Affine Expressions">.
3524 #include <isl/aff.h>
3525 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3526 __isl_take isl_aff *aff);
3527 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3528 __isl_take isl_aff *aff);
3529 __isl_give isl_basic_set *isl_aff_le_basic_set(
3530 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3531 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3532 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3533 __isl_give isl_set *isl_pw_aff_eq_set(
3534 __isl_take isl_pw_aff *pwaff1,
3535 __isl_take isl_pw_aff *pwaff2);
3536 __isl_give isl_set *isl_pw_aff_ne_set(
3537 __isl_take isl_pw_aff *pwaff1,
3538 __isl_take isl_pw_aff *pwaff2);
3539 __isl_give isl_set *isl_pw_aff_le_set(
3540 __isl_take isl_pw_aff *pwaff1,
3541 __isl_take isl_pw_aff *pwaff2);
3542 __isl_give isl_set *isl_pw_aff_lt_set(
3543 __isl_take isl_pw_aff *pwaff1,
3544 __isl_take isl_pw_aff *pwaff2);
3545 __isl_give isl_set *isl_pw_aff_ge_set(
3546 __isl_take isl_pw_aff *pwaff1,
3547 __isl_take isl_pw_aff *pwaff2);
3548 __isl_give isl_set *isl_pw_aff_gt_set(
3549 __isl_take isl_pw_aff *pwaff1,
3550 __isl_take isl_pw_aff *pwaff2);
3552 __isl_give isl_set *isl_pw_aff_list_eq_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_ne_set(
3556 __isl_take isl_pw_aff_list *list1,
3557 __isl_take isl_pw_aff_list *list2);
3558 __isl_give isl_set *isl_pw_aff_list_le_set(
3559 __isl_take isl_pw_aff_list *list1,
3560 __isl_take isl_pw_aff_list *list2);
3561 __isl_give isl_set *isl_pw_aff_list_lt_set(
3562 __isl_take isl_pw_aff_list *list1,
3563 __isl_take isl_pw_aff_list *list2);
3564 __isl_give isl_set *isl_pw_aff_list_ge_set(
3565 __isl_take isl_pw_aff_list *list1,
3566 __isl_take isl_pw_aff_list *list2);
3567 __isl_give isl_set *isl_pw_aff_list_gt_set(
3568 __isl_take isl_pw_aff_list *list1,
3569 __isl_take isl_pw_aff_list *list2);
3571 The function C<isl_aff_neg_basic_set> returns a basic set
3572 containing those elements in the domain space
3573 of C<aff> where C<aff> is negative.
3574 The function C<isl_aff_ge_basic_set> returns a basic set
3575 containing those elements in the shared space
3576 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3577 The function C<isl_pw_aff_ge_set> returns a set
3578 containing those elements in the shared domain
3579 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3580 The functions operating on C<isl_pw_aff_list> apply the corresponding
3581 C<isl_pw_aff> function to each pair of elements in the two lists.
3583 #include <isl/aff.h>
3584 __isl_give isl_set *isl_pw_aff_nonneg_set(
3585 __isl_take isl_pw_aff *pwaff);
3586 __isl_give isl_set *isl_pw_aff_zero_set(
3587 __isl_take isl_pw_aff *pwaff);
3588 __isl_give isl_set *isl_pw_aff_non_zero_set(
3589 __isl_take isl_pw_aff *pwaff);
3591 The function C<isl_pw_aff_nonneg_set> returns a set
3592 containing those elements in the domain
3593 of C<pwaff> where C<pwaff> is non-negative.
3595 #include <isl/aff.h>
3596 __isl_give isl_pw_aff *isl_pw_aff_cond(
3597 __isl_take isl_pw_aff *cond,
3598 __isl_take isl_pw_aff *pwaff_true,
3599 __isl_take isl_pw_aff *pwaff_false);
3601 The function C<isl_pw_aff_cond> performs a conditional operator
3602 and returns an expression that is equal to C<pwaff_true>
3603 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3604 where C<cond> is zero.
3606 #include <isl/aff.h>
3607 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3608 __isl_take isl_pw_aff *pwaff1,
3609 __isl_take isl_pw_aff *pwaff2);
3610 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3611 __isl_take isl_pw_aff *pwaff1,
3612 __isl_take isl_pw_aff *pwaff2);
3613 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3614 __isl_take isl_pw_aff *pwaff1,
3615 __isl_take isl_pw_aff *pwaff2);
3617 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3618 expression with a domain that is the union of those of C<pwaff1> and
3619 C<pwaff2> and such that on each cell, the quasi-affine expression is
3620 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3621 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3622 associated expression is the defined one.
3624 An expression can be read from input using
3626 #include <isl/aff.h>
3627 __isl_give isl_aff *isl_aff_read_from_str(
3628 isl_ctx *ctx, const char *str);
3629 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3630 isl_ctx *ctx, const char *str);
3632 An expression can be printed using
3634 #include <isl/aff.h>
3635 __isl_give isl_printer *isl_printer_print_aff(
3636 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3638 __isl_give isl_printer *isl_printer_print_pw_aff(
3639 __isl_take isl_printer *p,
3640 __isl_keep isl_pw_aff *pwaff);
3642 =head2 Piecewise Multiple Quasi Affine Expressions
3644 An C<isl_multi_aff> object represents a sequence of
3645 zero or more affine expressions, all defined on the same domain space.
3646 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
3647 zero or more piecewise affine expressions.
3649 An C<isl_multi_aff> can be constructed from a single
3650 C<isl_aff> or an C<isl_aff_list> using the
3651 following functions. Similarly for C<isl_multi_pw_aff>.
3653 #include <isl/aff.h>
3654 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
3655 __isl_take isl_aff *aff);
3656 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
3657 __isl_take isl_pw_aff *pa);
3658 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3659 __isl_take isl_space *space,
3660 __isl_take isl_aff_list *list);
3662 An empty piecewise multiple quasi affine expression (one with no cells),
3663 the zero piecewise multiple quasi affine expression (with value zero
3664 for each output dimension),
3665 a piecewise multiple quasi affine expression with a single cell (with
3666 either a universe or a specified domain) or
3667 a zero-dimensional piecewise multiple quasi affine expression
3669 can be created using the following functions.
3671 #include <isl/aff.h>
3672 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3673 __isl_take isl_space *space);
3674 __isl_give isl_multi_aff *isl_multi_aff_zero(
3675 __isl_take isl_space *space);
3676 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
3677 __isl_take isl_space *space);
3678 __isl_give isl_multi_aff *isl_multi_aff_identity(
3679 __isl_take isl_space *space);
3680 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3681 __isl_take isl_space *space);
3682 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
3683 __isl_take isl_space *space);
3684 __isl_give isl_pw_multi_aff *
3685 isl_pw_multi_aff_from_multi_aff(
3686 __isl_take isl_multi_aff *ma);
3687 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3688 __isl_take isl_set *set,
3689 __isl_take isl_multi_aff *maff);
3690 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3691 __isl_take isl_set *set);
3693 __isl_give isl_union_pw_multi_aff *
3694 isl_union_pw_multi_aff_empty(
3695 __isl_take isl_space *space);
3696 __isl_give isl_union_pw_multi_aff *
3697 isl_union_pw_multi_aff_add_pw_multi_aff(
3698 __isl_take isl_union_pw_multi_aff *upma,
3699 __isl_take isl_pw_multi_aff *pma);
3700 __isl_give isl_union_pw_multi_aff *
3701 isl_union_pw_multi_aff_from_domain(
3702 __isl_take isl_union_set *uset);
3704 A piecewise multiple quasi affine expression can also be initialized
3705 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3706 and the C<isl_map> is single-valued.
3707 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
3708 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
3710 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3711 __isl_take isl_set *set);
3712 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3713 __isl_take isl_map *map);
3715 __isl_give isl_union_pw_multi_aff *
3716 isl_union_pw_multi_aff_from_union_set(
3717 __isl_take isl_union_set *uset);
3718 __isl_give isl_union_pw_multi_aff *
3719 isl_union_pw_multi_aff_from_union_map(
3720 __isl_take isl_union_map *umap);
3722 Multiple quasi affine expressions can be copied and freed using
3724 #include <isl/aff.h>
3725 __isl_give isl_multi_aff *isl_multi_aff_copy(
3726 __isl_keep isl_multi_aff *maff);
3727 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3729 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3730 __isl_keep isl_pw_multi_aff *pma);
3731 void *isl_pw_multi_aff_free(
3732 __isl_take isl_pw_multi_aff *pma);
3734 __isl_give isl_union_pw_multi_aff *
3735 isl_union_pw_multi_aff_copy(
3736 __isl_keep isl_union_pw_multi_aff *upma);
3737 void *isl_union_pw_multi_aff_free(
3738 __isl_take isl_union_pw_multi_aff *upma);
3740 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
3741 __isl_keep isl_multi_pw_aff *mpa);
3742 void *isl_multi_pw_aff_free(
3743 __isl_take isl_multi_pw_aff *mpa);
3745 The expression can be inspected using
3747 #include <isl/aff.h>
3748 isl_ctx *isl_multi_aff_get_ctx(
3749 __isl_keep isl_multi_aff *maff);
3750 isl_ctx *isl_pw_multi_aff_get_ctx(
3751 __isl_keep isl_pw_multi_aff *pma);
3752 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3753 __isl_keep isl_union_pw_multi_aff *upma);
3754 isl_ctx *isl_multi_pw_aff_get_ctx(
3755 __isl_keep isl_multi_pw_aff *mpa);
3756 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3757 enum isl_dim_type type);
3758 unsigned isl_pw_multi_aff_dim(
3759 __isl_keep isl_pw_multi_aff *pma,
3760 enum isl_dim_type type);
3761 unsigned isl_multi_pw_aff_dim(
3762 __isl_keep isl_multi_pw_aff *mpa,
3763 enum isl_dim_type type);
3764 __isl_give isl_aff *isl_multi_aff_get_aff(
3765 __isl_keep isl_multi_aff *multi, int pos);
3766 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3767 __isl_keep isl_pw_multi_aff *pma, int pos);
3768 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
3769 __isl_keep isl_multi_pw_aff *mpa, int pos);
3770 const char *isl_pw_multi_aff_get_dim_name(
3771 __isl_keep isl_pw_multi_aff *pma,
3772 enum isl_dim_type type, unsigned pos);
3773 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3774 __isl_keep isl_pw_multi_aff *pma,
3775 enum isl_dim_type type, unsigned pos);
3776 const char *isl_multi_aff_get_tuple_name(
3777 __isl_keep isl_multi_aff *multi,
3778 enum isl_dim_type type);
3779 int isl_pw_multi_aff_has_tuple_name(
3780 __isl_keep isl_pw_multi_aff *pma,
3781 enum isl_dim_type type);
3782 const char *isl_pw_multi_aff_get_tuple_name(
3783 __isl_keep isl_pw_multi_aff *pma,
3784 enum isl_dim_type type);
3785 int isl_pw_multi_aff_has_tuple_id(
3786 __isl_keep isl_pw_multi_aff *pma,
3787 enum isl_dim_type type);
3788 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3789 __isl_keep isl_pw_multi_aff *pma,
3790 enum isl_dim_type type);
3792 int isl_pw_multi_aff_foreach_piece(
3793 __isl_keep isl_pw_multi_aff *pma,
3794 int (*fn)(__isl_take isl_set *set,
3795 __isl_take isl_multi_aff *maff,
3796 void *user), void *user);
3798 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3799 __isl_keep isl_union_pw_multi_aff *upma,
3800 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3801 void *user), void *user);
3803 It can be modified using
3805 #include <isl/aff.h>
3806 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3807 __isl_take isl_multi_aff *multi, int pos,
3808 __isl_take isl_aff *aff);
3809 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3810 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3811 __isl_take isl_pw_aff *pa);
3812 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3813 __isl_take isl_multi_aff *maff,
3814 enum isl_dim_type type, unsigned pos, const char *s);
3815 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
3816 __isl_take isl_multi_aff *maff,
3817 enum isl_dim_type type, const char *s);
3818 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3819 __isl_take isl_multi_aff *maff,
3820 enum isl_dim_type type, __isl_take isl_id *id);
3821 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3822 __isl_take isl_pw_multi_aff *pma,
3823 enum isl_dim_type type, __isl_take isl_id *id);
3825 __isl_give isl_multi_pw_aff *
3826 isl_multi_pw_aff_set_dim_name(
3827 __isl_take isl_multi_pw_aff *mpa,
3828 enum isl_dim_type type, unsigned pos, const char *s);
3829 __isl_give isl_multi_pw_aff *
3830 isl_multi_pw_aff_set_tuple_name(
3831 __isl_take isl_multi_pw_aff *mpa,
3832 enum isl_dim_type type, const char *s);
3834 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
3835 __isl_take isl_multi_aff *ma,
3836 enum isl_dim_type type, unsigned first, unsigned n);
3837 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
3838 __isl_take isl_multi_aff *ma,
3839 enum isl_dim_type type, unsigned n);
3840 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3841 __isl_take isl_multi_aff *maff,
3842 enum isl_dim_type type, unsigned first, unsigned n);
3843 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
3844 __isl_take isl_pw_multi_aff *pma,
3845 enum isl_dim_type type, unsigned first, unsigned n);
3847 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
3848 __isl_take isl_multi_pw_aff *mpa,
3849 enum isl_dim_type type, unsigned first, unsigned n);
3850 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
3851 __isl_take isl_multi_pw_aff *mpa,
3852 enum isl_dim_type type, unsigned n);
3854 To check whether two multiple affine expressions are
3855 obviously equal to each other, use
3857 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3858 __isl_keep isl_multi_aff *maff2);
3859 int isl_pw_multi_aff_plain_is_equal(
3860 __isl_keep isl_pw_multi_aff *pma1,
3861 __isl_keep isl_pw_multi_aff *pma2);
3865 #include <isl/aff.h>
3866 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3867 __isl_take isl_pw_multi_aff *pma1,
3868 __isl_take isl_pw_multi_aff *pma2);
3869 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3870 __isl_take isl_pw_multi_aff *pma1,
3871 __isl_take isl_pw_multi_aff *pma2);
3872 __isl_give isl_multi_aff *isl_multi_aff_add(
3873 __isl_take isl_multi_aff *maff1,
3874 __isl_take isl_multi_aff *maff2);
3875 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3876 __isl_take isl_pw_multi_aff *pma1,
3877 __isl_take isl_pw_multi_aff *pma2);
3878 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3879 __isl_take isl_union_pw_multi_aff *upma1,
3880 __isl_take isl_union_pw_multi_aff *upma2);
3881 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3882 __isl_take isl_pw_multi_aff *pma1,
3883 __isl_take isl_pw_multi_aff *pma2);
3884 __isl_give isl_multi_aff *isl_multi_aff_scale(
3885 __isl_take isl_multi_aff *maff,
3887 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3888 __isl_take isl_pw_multi_aff *pma,
3889 __isl_take isl_set *set);
3890 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3891 __isl_take isl_pw_multi_aff *pma,
3892 __isl_take isl_set *set);
3893 __isl_give isl_multi_aff *isl_multi_aff_lift(
3894 __isl_take isl_multi_aff *maff,
3895 __isl_give isl_local_space **ls);
3896 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3897 __isl_take isl_pw_multi_aff *pma);
3898 __isl_give isl_multi_aff *isl_multi_aff_align_params(
3899 __isl_take isl_multi_aff *multi,
3900 __isl_take isl_space *model);
3901 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
3902 __isl_take isl_pw_multi_aff *pma,
3903 __isl_take isl_space *model);
3904 __isl_give isl_pw_multi_aff *
3905 isl_pw_multi_aff_project_domain_on_params(
3906 __isl_take isl_pw_multi_aff *pma);
3907 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3908 __isl_take isl_multi_aff *maff,
3909 __isl_take isl_set *context);
3910 __isl_give isl_multi_aff *isl_multi_aff_gist(
3911 __isl_take isl_multi_aff *maff,
3912 __isl_take isl_set *context);
3913 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3914 __isl_take isl_pw_multi_aff *pma,
3915 __isl_take isl_set *set);
3916 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3917 __isl_take isl_pw_multi_aff *pma,
3918 __isl_take isl_set *set);
3919 __isl_give isl_set *isl_pw_multi_aff_domain(
3920 __isl_take isl_pw_multi_aff *pma);
3921 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3922 __isl_take isl_union_pw_multi_aff *upma);
3923 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
3924 __isl_take isl_multi_aff *ma1, unsigned pos,
3925 __isl_take isl_multi_aff *ma2);
3926 __isl_give isl_multi_aff *isl_multi_aff_splice(
3927 __isl_take isl_multi_aff *ma1,
3928 unsigned in_pos, unsigned out_pos,
3929 __isl_take isl_multi_aff *ma2);
3930 __isl_give isl_multi_aff *isl_multi_aff_range_product(
3931 __isl_take isl_multi_aff *ma1,
3932 __isl_take isl_multi_aff *ma2);
3933 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3934 __isl_take isl_multi_aff *ma1,
3935 __isl_take isl_multi_aff *ma2);
3936 __isl_give isl_multi_aff *isl_multi_aff_product(
3937 __isl_take isl_multi_aff *ma1,
3938 __isl_take isl_multi_aff *ma2);
3939 __isl_give isl_pw_multi_aff *
3940 isl_pw_multi_aff_range_product(
3941 __isl_take isl_pw_multi_aff *pma1,
3942 __isl_take isl_pw_multi_aff *pma2);
3943 __isl_give isl_pw_multi_aff *
3944 isl_pw_multi_aff_flat_range_product(
3945 __isl_take isl_pw_multi_aff *pma1,
3946 __isl_take isl_pw_multi_aff *pma2);
3947 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3948 __isl_take isl_pw_multi_aff *pma1,
3949 __isl_take isl_pw_multi_aff *pma2);
3950 __isl_give isl_union_pw_multi_aff *
3951 isl_union_pw_multi_aff_flat_range_product(
3952 __isl_take isl_union_pw_multi_aff *upma1,
3953 __isl_take isl_union_pw_multi_aff *upma2);
3954 __isl_give isl_multi_pw_aff *
3955 isl_multi_pw_aff_range_splice(
3956 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
3957 __isl_take isl_multi_pw_aff *mpa2);
3958 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
3959 __isl_take isl_multi_pw_aff *mpa1,
3960 unsigned in_pos, unsigned out_pos,
3961 __isl_take isl_multi_pw_aff *mpa2);
3962 __isl_give isl_multi_pw_aff *
3963 isl_multi_pw_aff_range_product(
3964 __isl_take isl_multi_pw_aff *mpa1,
3965 __isl_take isl_multi_pw_aff *mpa2);
3966 __isl_give isl_multi_pw_aff *
3967 isl_multi_pw_aff_flat_range_product(
3968 __isl_take isl_multi_pw_aff *mpa1,
3969 __isl_take isl_multi_pw_aff *mpa2);
3971 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3972 then it is assigned the local space that lies at the basis of
3973 the lifting applied.
3975 #include <isl/aff.h>
3976 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
3977 __isl_take isl_multi_aff *ma1,
3978 __isl_take isl_multi_aff *ma2);
3979 __isl_give isl_pw_multi_aff *
3980 isl_pw_multi_aff_pullback_multi_aff(
3981 __isl_take isl_pw_multi_aff *pma,
3982 __isl_take isl_multi_aff *ma);
3983 __isl_give isl_pw_multi_aff *
3984 isl_pw_multi_aff_pullback_pw_multi_aff(
3985 __isl_take isl_pw_multi_aff *pma1,
3986 __isl_take isl_pw_multi_aff *pma2);
3988 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
3989 In other words, C<ma2> is plugged
3992 __isl_give isl_set *isl_multi_aff_lex_le_set(
3993 __isl_take isl_multi_aff *ma1,
3994 __isl_take isl_multi_aff *ma2);
3995 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3996 __isl_take isl_multi_aff *ma1,
3997 __isl_take isl_multi_aff *ma2);
3999 The function C<isl_multi_aff_lex_le_set> returns a set
4000 containing those elements in the shared domain space
4001 where C<ma1> is lexicographically smaller than or
4004 An expression can be read from input using
4006 #include <isl/aff.h>
4007 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4008 isl_ctx *ctx, const char *str);
4009 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4010 isl_ctx *ctx, const char *str);
4011 __isl_give isl_union_pw_multi_aff *
4012 isl_union_pw_multi_aff_read_from_str(
4013 isl_ctx *ctx, const char *str);
4015 An expression can be printed using
4017 #include <isl/aff.h>
4018 __isl_give isl_printer *isl_printer_print_multi_aff(
4019 __isl_take isl_printer *p,
4020 __isl_keep isl_multi_aff *maff);
4021 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4022 __isl_take isl_printer *p,
4023 __isl_keep isl_pw_multi_aff *pma);
4024 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4025 __isl_take isl_printer *p,
4026 __isl_keep isl_union_pw_multi_aff *upma);
4027 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4028 __isl_take isl_printer *p,
4029 __isl_keep isl_multi_pw_aff *mpa);
4033 Points are elements of a set. They can be used to construct
4034 simple sets (boxes) or they can be used to represent the
4035 individual elements of a set.
4036 The zero point (the origin) can be created using
4038 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4040 The coordinates of a point can be inspected, set and changed
4043 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
4044 enum isl_dim_type type, int pos, isl_int *v);
4045 __isl_give isl_point *isl_point_set_coordinate(
4046 __isl_take isl_point *pnt,
4047 enum isl_dim_type type, int pos, isl_int v);
4049 __isl_give isl_point *isl_point_add_ui(
4050 __isl_take isl_point *pnt,
4051 enum isl_dim_type type, int pos, unsigned val);
4052 __isl_give isl_point *isl_point_sub_ui(
4053 __isl_take isl_point *pnt,
4054 enum isl_dim_type type, int pos, unsigned val);
4056 Other properties can be obtained using
4058 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4060 Points can be copied or freed using
4062 __isl_give isl_point *isl_point_copy(
4063 __isl_keep isl_point *pnt);
4064 void isl_point_free(__isl_take isl_point *pnt);
4066 A singleton set can be created from a point using
4068 __isl_give isl_basic_set *isl_basic_set_from_point(
4069 __isl_take isl_point *pnt);
4070 __isl_give isl_set *isl_set_from_point(
4071 __isl_take isl_point *pnt);
4073 and a box can be created from two opposite extremal points using
4075 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4076 __isl_take isl_point *pnt1,
4077 __isl_take isl_point *pnt2);
4078 __isl_give isl_set *isl_set_box_from_points(
4079 __isl_take isl_point *pnt1,
4080 __isl_take isl_point *pnt2);
4082 All elements of a B<bounded> (union) set can be enumerated using
4083 the following functions.
4085 int isl_set_foreach_point(__isl_keep isl_set *set,
4086 int (*fn)(__isl_take isl_point *pnt, void *user),
4088 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4089 int (*fn)(__isl_take isl_point *pnt, void *user),
4092 The function C<fn> is called for each integer point in
4093 C<set> with as second argument the last argument of
4094 the C<isl_set_foreach_point> call. The function C<fn>
4095 should return C<0> on success and C<-1> on failure.
4096 In the latter case, C<isl_set_foreach_point> will stop
4097 enumerating and return C<-1> as well.
4098 If the enumeration is performed successfully and to completion,
4099 then C<isl_set_foreach_point> returns C<0>.
4101 To obtain a single point of a (basic) set, use
4103 __isl_give isl_point *isl_basic_set_sample_point(
4104 __isl_take isl_basic_set *bset);
4105 __isl_give isl_point *isl_set_sample_point(
4106 __isl_take isl_set *set);
4108 If C<set> does not contain any (integer) points, then the
4109 resulting point will be ``void'', a property that can be
4112 int isl_point_is_void(__isl_keep isl_point *pnt);
4114 =head2 Piecewise Quasipolynomials
4116 A piecewise quasipolynomial is a particular kind of function that maps
4117 a parametric point to a rational value.
4118 More specifically, a quasipolynomial is a polynomial expression in greatest
4119 integer parts of affine expressions of parameters and variables.
4120 A piecewise quasipolynomial is a subdivision of a given parametric
4121 domain into disjoint cells with a quasipolynomial associated to
4122 each cell. The value of the piecewise quasipolynomial at a given
4123 point is the value of the quasipolynomial associated to the cell
4124 that contains the point. Outside of the union of cells,
4125 the value is assumed to be zero.
4126 For example, the piecewise quasipolynomial
4128 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4130 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4131 A given piecewise quasipolynomial has a fixed domain dimension.
4132 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4133 defined over different domains.
4134 Piecewise quasipolynomials are mainly used by the C<barvinok>
4135 library for representing the number of elements in a parametric set or map.
4136 For example, the piecewise quasipolynomial above represents
4137 the number of points in the map
4139 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4141 =head3 Input and Output
4143 Piecewise quasipolynomials can be read from input using
4145 __isl_give isl_union_pw_qpolynomial *
4146 isl_union_pw_qpolynomial_read_from_str(
4147 isl_ctx *ctx, const char *str);
4149 Quasipolynomials and piecewise quasipolynomials can be printed
4150 using the following functions.
4152 __isl_give isl_printer *isl_printer_print_qpolynomial(
4153 __isl_take isl_printer *p,
4154 __isl_keep isl_qpolynomial *qp);
4156 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4157 __isl_take isl_printer *p,
4158 __isl_keep isl_pw_qpolynomial *pwqp);
4160 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4161 __isl_take isl_printer *p,
4162 __isl_keep isl_union_pw_qpolynomial *upwqp);
4164 The output format of the printer
4165 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4166 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4168 In case of printing in C<ISL_FORMAT_C>, the user may want
4169 to set the names of all dimensions
4171 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4172 __isl_take isl_qpolynomial *qp,
4173 enum isl_dim_type type, unsigned pos,
4175 __isl_give isl_pw_qpolynomial *
4176 isl_pw_qpolynomial_set_dim_name(
4177 __isl_take isl_pw_qpolynomial *pwqp,
4178 enum isl_dim_type type, unsigned pos,
4181 =head3 Creating New (Piecewise) Quasipolynomials
4183 Some simple quasipolynomials can be created using the following functions.
4184 More complicated quasipolynomials can be created by applying
4185 operations such as addition and multiplication
4186 on the resulting quasipolynomials
4188 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4189 __isl_take isl_space *domain);
4190 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4191 __isl_take isl_space *domain);
4192 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4193 __isl_take isl_space *domain);
4194 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4195 __isl_take isl_space *domain);
4196 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4197 __isl_take isl_space *domain);
4198 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
4199 __isl_take isl_space *domain,
4200 const isl_int n, const isl_int d);
4201 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4202 __isl_take isl_space *domain,
4203 enum isl_dim_type type, unsigned pos);
4204 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4205 __isl_take isl_aff *aff);
4207 Note that the space in which a quasipolynomial lives is a map space
4208 with a one-dimensional range. The C<domain> argument in some of
4209 the functions above corresponds to the domain of this map space.
4211 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4212 with a single cell can be created using the following functions.
4213 Multiple of these single cell piecewise quasipolynomials can
4214 be combined to create more complicated piecewise quasipolynomials.
4216 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4217 __isl_take isl_space *space);
4218 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4219 __isl_take isl_set *set,
4220 __isl_take isl_qpolynomial *qp);
4221 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4222 __isl_take isl_qpolynomial *qp);
4223 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4224 __isl_take isl_pw_aff *pwaff);
4226 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4227 __isl_take isl_space *space);
4228 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4229 __isl_take isl_pw_qpolynomial *pwqp);
4230 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4231 __isl_take isl_union_pw_qpolynomial *upwqp,
4232 __isl_take isl_pw_qpolynomial *pwqp);
4234 Quasipolynomials can be copied and freed again using the following
4237 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4238 __isl_keep isl_qpolynomial *qp);
4239 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4241 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4242 __isl_keep isl_pw_qpolynomial *pwqp);
4243 void *isl_pw_qpolynomial_free(
4244 __isl_take isl_pw_qpolynomial *pwqp);
4246 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4247 __isl_keep isl_union_pw_qpolynomial *upwqp);
4248 void *isl_union_pw_qpolynomial_free(
4249 __isl_take isl_union_pw_qpolynomial *upwqp);
4251 =head3 Inspecting (Piecewise) Quasipolynomials
4253 To iterate over all piecewise quasipolynomials in a union
4254 piecewise quasipolynomial, use the following function
4256 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4257 __isl_keep isl_union_pw_qpolynomial *upwqp,
4258 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4261 To extract the piecewise quasipolynomial in a given space from a union, use
4263 __isl_give isl_pw_qpolynomial *
4264 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4265 __isl_keep isl_union_pw_qpolynomial *upwqp,
4266 __isl_take isl_space *space);
4268 To iterate over the cells in a piecewise quasipolynomial,
4269 use either of the following two functions
4271 int isl_pw_qpolynomial_foreach_piece(
4272 __isl_keep isl_pw_qpolynomial *pwqp,
4273 int (*fn)(__isl_take isl_set *set,
4274 __isl_take isl_qpolynomial *qp,
4275 void *user), void *user);
4276 int isl_pw_qpolynomial_foreach_lifted_piece(
4277 __isl_keep isl_pw_qpolynomial *pwqp,
4278 int (*fn)(__isl_take isl_set *set,
4279 __isl_take isl_qpolynomial *qp,
4280 void *user), void *user);
4282 As usual, the function C<fn> should return C<0> on success
4283 and C<-1> on failure. The difference between
4284 C<isl_pw_qpolynomial_foreach_piece> and
4285 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4286 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4287 compute unique representations for all existentially quantified
4288 variables and then turn these existentially quantified variables
4289 into extra set variables, adapting the associated quasipolynomial
4290 accordingly. This means that the C<set> passed to C<fn>
4291 will not have any existentially quantified variables, but that
4292 the dimensions of the sets may be different for different
4293 invocations of C<fn>.
4295 To iterate over all terms in a quasipolynomial,
4298 int isl_qpolynomial_foreach_term(
4299 __isl_keep isl_qpolynomial *qp,
4300 int (*fn)(__isl_take isl_term *term,
4301 void *user), void *user);
4303 The terms themselves can be inspected and freed using
4306 unsigned isl_term_dim(__isl_keep isl_term *term,
4307 enum isl_dim_type type);
4308 void isl_term_get_num(__isl_keep isl_term *term,
4310 void isl_term_get_den(__isl_keep isl_term *term,
4312 int isl_term_get_exp(__isl_keep isl_term *term,
4313 enum isl_dim_type type, unsigned pos);
4314 __isl_give isl_aff *isl_term_get_div(
4315 __isl_keep isl_term *term, unsigned pos);
4316 void isl_term_free(__isl_take isl_term *term);
4318 Each term is a product of parameters, set variables and
4319 integer divisions. The function C<isl_term_get_exp>
4320 returns the exponent of a given dimensions in the given term.
4321 The C<isl_int>s in the arguments of C<isl_term_get_num>
4322 and C<isl_term_get_den> need to have been initialized
4323 using C<isl_int_init> before calling these functions.
4325 =head3 Properties of (Piecewise) Quasipolynomials
4327 To check whether a quasipolynomial is actually a constant,
4328 use the following function.
4330 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4331 isl_int *n, isl_int *d);
4333 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4334 then the numerator and denominator of the constant
4335 are returned in C<*n> and C<*d>, respectively.
4337 To check whether two union piecewise quasipolynomials are
4338 obviously equal, use
4340 int isl_union_pw_qpolynomial_plain_is_equal(
4341 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4342 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4344 =head3 Operations on (Piecewise) Quasipolynomials
4346 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4347 __isl_take isl_qpolynomial *qp, isl_int v);
4348 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4349 __isl_take isl_qpolynomial *qp);
4350 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4351 __isl_take isl_qpolynomial *qp1,
4352 __isl_take isl_qpolynomial *qp2);
4353 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4354 __isl_take isl_qpolynomial *qp1,
4355 __isl_take isl_qpolynomial *qp2);
4356 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4357 __isl_take isl_qpolynomial *qp1,
4358 __isl_take isl_qpolynomial *qp2);
4359 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4360 __isl_take isl_qpolynomial *qp, unsigned exponent);
4362 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4363 __isl_take isl_pw_qpolynomial *pwqp1,
4364 __isl_take isl_pw_qpolynomial *pwqp2);
4365 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4366 __isl_take isl_pw_qpolynomial *pwqp1,
4367 __isl_take isl_pw_qpolynomial *pwqp2);
4368 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4369 __isl_take isl_pw_qpolynomial *pwqp1,
4370 __isl_take isl_pw_qpolynomial *pwqp2);
4371 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4372 __isl_take isl_pw_qpolynomial *pwqp);
4373 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4374 __isl_take isl_pw_qpolynomial *pwqp1,
4375 __isl_take isl_pw_qpolynomial *pwqp2);
4376 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4377 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4379 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4380 __isl_take isl_union_pw_qpolynomial *upwqp1,
4381 __isl_take isl_union_pw_qpolynomial *upwqp2);
4382 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4383 __isl_take isl_union_pw_qpolynomial *upwqp1,
4384 __isl_take isl_union_pw_qpolynomial *upwqp2);
4385 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4386 __isl_take isl_union_pw_qpolynomial *upwqp1,
4387 __isl_take isl_union_pw_qpolynomial *upwqp2);
4389 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4390 __isl_take isl_pw_qpolynomial *pwqp,
4391 __isl_take isl_point *pnt);
4393 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4394 __isl_take isl_union_pw_qpolynomial *upwqp,
4395 __isl_take isl_point *pnt);
4397 __isl_give isl_set *isl_pw_qpolynomial_domain(
4398 __isl_take isl_pw_qpolynomial *pwqp);
4399 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4400 __isl_take isl_pw_qpolynomial *pwpq,
4401 __isl_take isl_set *set);
4402 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4403 __isl_take isl_pw_qpolynomial *pwpq,
4404 __isl_take isl_set *set);
4406 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4407 __isl_take isl_union_pw_qpolynomial *upwqp);
4408 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4409 __isl_take isl_union_pw_qpolynomial *upwpq,
4410 __isl_take isl_union_set *uset);
4411 __isl_give isl_union_pw_qpolynomial *
4412 isl_union_pw_qpolynomial_intersect_params(
4413 __isl_take isl_union_pw_qpolynomial *upwpq,
4414 __isl_take isl_set *set);
4416 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4417 __isl_take isl_qpolynomial *qp,
4418 __isl_take isl_space *model);
4420 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4421 __isl_take isl_qpolynomial *qp);
4422 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4423 __isl_take isl_pw_qpolynomial *pwqp);
4425 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4426 __isl_take isl_union_pw_qpolynomial *upwqp);
4428 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4429 __isl_take isl_qpolynomial *qp,
4430 __isl_take isl_set *context);
4431 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4432 __isl_take isl_qpolynomial *qp,
4433 __isl_take isl_set *context);
4435 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4436 __isl_take isl_pw_qpolynomial *pwqp,
4437 __isl_take isl_set *context);
4438 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4439 __isl_take isl_pw_qpolynomial *pwqp,
4440 __isl_take isl_set *context);
4442 __isl_give isl_union_pw_qpolynomial *
4443 isl_union_pw_qpolynomial_gist_params(
4444 __isl_take isl_union_pw_qpolynomial *upwqp,
4445 __isl_take isl_set *context);
4446 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4447 __isl_take isl_union_pw_qpolynomial *upwqp,
4448 __isl_take isl_union_set *context);
4450 The gist operation applies the gist operation to each of
4451 the cells in the domain of the input piecewise quasipolynomial.
4452 The context is also exploited
4453 to simplify the quasipolynomials associated to each cell.
4455 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4456 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4457 __isl_give isl_union_pw_qpolynomial *
4458 isl_union_pw_qpolynomial_to_polynomial(
4459 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4461 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4462 the polynomial will be an overapproximation. If C<sign> is negative,
4463 it will be an underapproximation. If C<sign> is zero, the approximation
4464 will lie somewhere in between.
4466 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4468 A piecewise quasipolynomial reduction is a piecewise
4469 reduction (or fold) of quasipolynomials.
4470 In particular, the reduction can be maximum or a minimum.
4471 The objects are mainly used to represent the result of
4472 an upper or lower bound on a quasipolynomial over its domain,
4473 i.e., as the result of the following function.
4475 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4476 __isl_take isl_pw_qpolynomial *pwqp,
4477 enum isl_fold type, int *tight);
4479 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4480 __isl_take isl_union_pw_qpolynomial *upwqp,
4481 enum isl_fold type, int *tight);
4483 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4484 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4485 is the returned bound is known be tight, i.e., for each value
4486 of the parameters there is at least
4487 one element in the domain that reaches the bound.
4488 If the domain of C<pwqp> is not wrapping, then the bound is computed
4489 over all elements in that domain and the result has a purely parametric
4490 domain. If the domain of C<pwqp> is wrapping, then the bound is
4491 computed over the range of the wrapped relation. The domain of the
4492 wrapped relation becomes the domain of the result.
4494 A (piecewise) quasipolynomial reduction can be copied or freed using the
4495 following functions.
4497 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4498 __isl_keep isl_qpolynomial_fold *fold);
4499 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4500 __isl_keep isl_pw_qpolynomial_fold *pwf);
4501 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4502 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4503 void isl_qpolynomial_fold_free(
4504 __isl_take isl_qpolynomial_fold *fold);
4505 void *isl_pw_qpolynomial_fold_free(
4506 __isl_take isl_pw_qpolynomial_fold *pwf);
4507 void *isl_union_pw_qpolynomial_fold_free(
4508 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4510 =head3 Printing Piecewise Quasipolynomial Reductions
4512 Piecewise quasipolynomial reductions can be printed
4513 using the following function.
4515 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4516 __isl_take isl_printer *p,
4517 __isl_keep isl_pw_qpolynomial_fold *pwf);
4518 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4519 __isl_take isl_printer *p,
4520 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4522 For C<isl_printer_print_pw_qpolynomial_fold>,
4523 output format of the printer
4524 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4525 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4526 output format of the printer
4527 needs to be set to C<ISL_FORMAT_ISL>.
4528 In case of printing in C<ISL_FORMAT_C>, the user may want
4529 to set the names of all dimensions
4531 __isl_give isl_pw_qpolynomial_fold *
4532 isl_pw_qpolynomial_fold_set_dim_name(
4533 __isl_take isl_pw_qpolynomial_fold *pwf,
4534 enum isl_dim_type type, unsigned pos,
4537 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4539 To iterate over all piecewise quasipolynomial reductions in a union
4540 piecewise quasipolynomial reduction, use the following function
4542 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4543 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4544 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4545 void *user), void *user);
4547 To iterate over the cells in a piecewise quasipolynomial reduction,
4548 use either of the following two functions
4550 int isl_pw_qpolynomial_fold_foreach_piece(
4551 __isl_keep isl_pw_qpolynomial_fold *pwf,
4552 int (*fn)(__isl_take isl_set *set,
4553 __isl_take isl_qpolynomial_fold *fold,
4554 void *user), void *user);
4555 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4556 __isl_keep isl_pw_qpolynomial_fold *pwf,
4557 int (*fn)(__isl_take isl_set *set,
4558 __isl_take isl_qpolynomial_fold *fold,
4559 void *user), void *user);
4561 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4562 of the difference between these two functions.
4564 To iterate over all quasipolynomials in a reduction, use
4566 int isl_qpolynomial_fold_foreach_qpolynomial(
4567 __isl_keep isl_qpolynomial_fold *fold,
4568 int (*fn)(__isl_take isl_qpolynomial *qp,
4569 void *user), void *user);
4571 =head3 Properties of Piecewise Quasipolynomial Reductions
4573 To check whether two union piecewise quasipolynomial reductions are
4574 obviously equal, use
4576 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4577 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4578 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4580 =head3 Operations on Piecewise Quasipolynomial Reductions
4582 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4583 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4585 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4586 __isl_take isl_pw_qpolynomial_fold *pwf1,
4587 __isl_take isl_pw_qpolynomial_fold *pwf2);
4589 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4590 __isl_take isl_pw_qpolynomial_fold *pwf1,
4591 __isl_take isl_pw_qpolynomial_fold *pwf2);
4593 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4594 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4595 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4597 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4598 __isl_take isl_pw_qpolynomial_fold *pwf,
4599 __isl_take isl_point *pnt);
4601 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4602 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4603 __isl_take isl_point *pnt);
4605 __isl_give isl_pw_qpolynomial_fold *
4606 isl_pw_qpolynomial_fold_intersect_params(
4607 __isl_take isl_pw_qpolynomial_fold *pwf,
4608 __isl_take isl_set *set);
4610 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4611 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4612 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4613 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4614 __isl_take isl_union_set *uset);
4615 __isl_give isl_union_pw_qpolynomial_fold *
4616 isl_union_pw_qpolynomial_fold_intersect_params(
4617 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4618 __isl_take isl_set *set);
4620 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4621 __isl_take isl_pw_qpolynomial_fold *pwf);
4623 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4624 __isl_take isl_pw_qpolynomial_fold *pwf);
4626 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4627 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4629 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4630 __isl_take isl_qpolynomial_fold *fold,
4631 __isl_take isl_set *context);
4632 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4633 __isl_take isl_qpolynomial_fold *fold,
4634 __isl_take isl_set *context);
4636 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4637 __isl_take isl_pw_qpolynomial_fold *pwf,
4638 __isl_take isl_set *context);
4639 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4640 __isl_take isl_pw_qpolynomial_fold *pwf,
4641 __isl_take isl_set *context);
4643 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4644 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4645 __isl_take isl_union_set *context);
4646 __isl_give isl_union_pw_qpolynomial_fold *
4647 isl_union_pw_qpolynomial_fold_gist_params(
4648 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4649 __isl_take isl_set *context);
4651 The gist operation applies the gist operation to each of
4652 the cells in the domain of the input piecewise quasipolynomial reduction.
4653 In future, the operation will also exploit the context
4654 to simplify the quasipolynomial reductions associated to each cell.
4656 __isl_give isl_pw_qpolynomial_fold *
4657 isl_set_apply_pw_qpolynomial_fold(
4658 __isl_take isl_set *set,
4659 __isl_take isl_pw_qpolynomial_fold *pwf,
4661 __isl_give isl_pw_qpolynomial_fold *
4662 isl_map_apply_pw_qpolynomial_fold(
4663 __isl_take isl_map *map,
4664 __isl_take isl_pw_qpolynomial_fold *pwf,
4666 __isl_give isl_union_pw_qpolynomial_fold *
4667 isl_union_set_apply_union_pw_qpolynomial_fold(
4668 __isl_take isl_union_set *uset,
4669 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4671 __isl_give isl_union_pw_qpolynomial_fold *
4672 isl_union_map_apply_union_pw_qpolynomial_fold(
4673 __isl_take isl_union_map *umap,
4674 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4677 The functions taking a map
4678 compose the given map with the given piecewise quasipolynomial reduction.
4679 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4680 over all elements in the intersection of the range of the map
4681 and the domain of the piecewise quasipolynomial reduction
4682 as a function of an element in the domain of the map.
4683 The functions taking a set compute a bound over all elements in the
4684 intersection of the set and the domain of the
4685 piecewise quasipolynomial reduction.
4687 =head2 Parametric Vertex Enumeration
4689 The parametric vertex enumeration described in this section
4690 is mainly intended to be used internally and by the C<barvinok>
4693 #include <isl/vertices.h>
4694 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4695 __isl_keep isl_basic_set *bset);
4697 The function C<isl_basic_set_compute_vertices> performs the
4698 actual computation of the parametric vertices and the chamber
4699 decomposition and store the result in an C<isl_vertices> object.
4700 This information can be queried by either iterating over all
4701 the vertices or iterating over all the chambers or cells
4702 and then iterating over all vertices that are active on the chamber.
4704 int isl_vertices_foreach_vertex(
4705 __isl_keep isl_vertices *vertices,
4706 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4709 int isl_vertices_foreach_cell(
4710 __isl_keep isl_vertices *vertices,
4711 int (*fn)(__isl_take isl_cell *cell, void *user),
4713 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4714 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4717 Other operations that can be performed on an C<isl_vertices> object are
4720 isl_ctx *isl_vertices_get_ctx(
4721 __isl_keep isl_vertices *vertices);
4722 int isl_vertices_get_n_vertices(
4723 __isl_keep isl_vertices *vertices);
4724 void isl_vertices_free(__isl_take isl_vertices *vertices);
4726 Vertices can be inspected and destroyed using the following functions.
4728 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4729 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4730 __isl_give isl_basic_set *isl_vertex_get_domain(
4731 __isl_keep isl_vertex *vertex);
4732 __isl_give isl_basic_set *isl_vertex_get_expr(
4733 __isl_keep isl_vertex *vertex);
4734 void isl_vertex_free(__isl_take isl_vertex *vertex);
4736 C<isl_vertex_get_expr> returns a singleton parametric set describing
4737 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4739 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4740 B<rational> basic sets, so they should mainly be used for inspection
4741 and should not be mixed with integer sets.
4743 Chambers can be inspected and destroyed using the following functions.
4745 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4746 __isl_give isl_basic_set *isl_cell_get_domain(
4747 __isl_keep isl_cell *cell);
4748 void isl_cell_free(__isl_take isl_cell *cell);
4750 =head1 Polyhedral Compilation Library
4752 This section collects functionality in C<isl> that has been specifically
4753 designed for use during polyhedral compilation.
4755 =head2 Dependence Analysis
4757 C<isl> contains specialized functionality for performing
4758 array dataflow analysis. That is, given a I<sink> access relation
4759 and a collection of possible I<source> access relations,
4760 C<isl> can compute relations that describe
4761 for each iteration of the sink access, which iteration
4762 of which of the source access relations was the last
4763 to access the same data element before the given iteration
4765 The resulting dependence relations map source iterations
4766 to the corresponding sink iterations.
4767 To compute standard flow dependences, the sink should be
4768 a read, while the sources should be writes.
4769 If any of the source accesses are marked as being I<may>
4770 accesses, then there will be a dependence from the last
4771 I<must> access B<and> from any I<may> access that follows
4772 this last I<must> access.
4773 In particular, if I<all> sources are I<may> accesses,
4774 then memory based dependence analysis is performed.
4775 If, on the other hand, all sources are I<must> accesses,
4776 then value based dependence analysis is performed.
4778 #include <isl/flow.h>
4780 typedef int (*isl_access_level_before)(void *first, void *second);
4782 __isl_give isl_access_info *isl_access_info_alloc(
4783 __isl_take isl_map *sink,
4784 void *sink_user, isl_access_level_before fn,
4786 __isl_give isl_access_info *isl_access_info_add_source(
4787 __isl_take isl_access_info *acc,
4788 __isl_take isl_map *source, int must,
4790 void *isl_access_info_free(__isl_take isl_access_info *acc);
4792 __isl_give isl_flow *isl_access_info_compute_flow(
4793 __isl_take isl_access_info *acc);
4795 int isl_flow_foreach(__isl_keep isl_flow *deps,
4796 int (*fn)(__isl_take isl_map *dep, int must,
4797 void *dep_user, void *user),
4799 __isl_give isl_map *isl_flow_get_no_source(
4800 __isl_keep isl_flow *deps, int must);
4801 void isl_flow_free(__isl_take isl_flow *deps);
4803 The function C<isl_access_info_compute_flow> performs the actual
4804 dependence analysis. The other functions are used to construct
4805 the input for this function or to read off the output.
4807 The input is collected in an C<isl_access_info>, which can
4808 be created through a call to C<isl_access_info_alloc>.
4809 The arguments to this functions are the sink access relation
4810 C<sink>, a token C<sink_user> used to identify the sink
4811 access to the user, a callback function for specifying the
4812 relative order of source and sink accesses, and the number
4813 of source access relations that will be added.
4814 The callback function has type C<int (*)(void *first, void *second)>.
4815 The function is called with two user supplied tokens identifying
4816 either a source or the sink and it should return the shared nesting
4817 level and the relative order of the two accesses.
4818 In particular, let I<n> be the number of loops shared by
4819 the two accesses. If C<first> precedes C<second> textually,
4820 then the function should return I<2 * n + 1>; otherwise,
4821 it should return I<2 * n>.
4822 The sources can be added to the C<isl_access_info> by performing
4823 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4824 C<must> indicates whether the source is a I<must> access
4825 or a I<may> access. Note that a multi-valued access relation
4826 should only be marked I<must> if every iteration in the domain
4827 of the relation accesses I<all> elements in its image.
4828 The C<source_user> token is again used to identify
4829 the source access. The range of the source access relation
4830 C<source> should have the same dimension as the range
4831 of the sink access relation.
4832 The C<isl_access_info_free> function should usually not be
4833 called explicitly, because it is called implicitly by
4834 C<isl_access_info_compute_flow>.
4836 The result of the dependence analysis is collected in an
4837 C<isl_flow>. There may be elements of
4838 the sink access for which no preceding source access could be
4839 found or for which all preceding sources are I<may> accesses.
4840 The relations containing these elements can be obtained through
4841 calls to C<isl_flow_get_no_source>, the first with C<must> set
4842 and the second with C<must> unset.
4843 In the case of standard flow dependence analysis,
4844 with the sink a read and the sources I<must> writes,
4845 the first relation corresponds to the reads from uninitialized
4846 array elements and the second relation is empty.
4847 The actual flow dependences can be extracted using
4848 C<isl_flow_foreach>. This function will call the user-specified
4849 callback function C<fn> for each B<non-empty> dependence between
4850 a source and the sink. The callback function is called
4851 with four arguments, the actual flow dependence relation
4852 mapping source iterations to sink iterations, a boolean that
4853 indicates whether it is a I<must> or I<may> dependence, a token
4854 identifying the source and an additional C<void *> with value
4855 equal to the third argument of the C<isl_flow_foreach> call.
4856 A dependence is marked I<must> if it originates from a I<must>
4857 source and if it is not followed by any I<may> sources.
4859 After finishing with an C<isl_flow>, the user should call
4860 C<isl_flow_free> to free all associated memory.
4862 A higher-level interface to dependence analysis is provided
4863 by the following function.
4865 #include <isl/flow.h>
4867 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4868 __isl_take isl_union_map *must_source,
4869 __isl_take isl_union_map *may_source,
4870 __isl_take isl_union_map *schedule,
4871 __isl_give isl_union_map **must_dep,
4872 __isl_give isl_union_map **may_dep,
4873 __isl_give isl_union_map **must_no_source,
4874 __isl_give isl_union_map **may_no_source);
4876 The arrays are identified by the tuple names of the ranges
4877 of the accesses. The iteration domains by the tuple names
4878 of the domains of the accesses and of the schedule.
4879 The relative order of the iteration domains is given by the
4880 schedule. The relations returned through C<must_no_source>
4881 and C<may_no_source> are subsets of C<sink>.
4882 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4883 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4884 any of the other arguments is treated as an error.
4886 =head3 Interaction with Dependence Analysis
4888 During the dependence analysis, we frequently need to perform
4889 the following operation. Given a relation between sink iterations
4890 and potential source iterations from a particular source domain,
4891 what is the last potential source iteration corresponding to each
4892 sink iteration. It can sometimes be convenient to adjust
4893 the set of potential source iterations before or after each such operation.
4894 The prototypical example is fuzzy array dataflow analysis,
4895 where we need to analyze if, based on data-dependent constraints,
4896 the sink iteration can ever be executed without one or more of
4897 the corresponding potential source iterations being executed.
4898 If so, we can introduce extra parameters and select an unknown
4899 but fixed source iteration from the potential source iterations.
4900 To be able to perform such manipulations, C<isl> provides the following
4903 #include <isl/flow.h>
4905 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4906 __isl_keep isl_map *source_map,
4907 __isl_keep isl_set *sink, void *source_user,
4909 __isl_give isl_access_info *isl_access_info_set_restrict(
4910 __isl_take isl_access_info *acc,
4911 isl_access_restrict fn, void *user);
4913 The function C<isl_access_info_set_restrict> should be called
4914 before calling C<isl_access_info_compute_flow> and registers a callback function
4915 that will be called any time C<isl> is about to compute the last
4916 potential source. The first argument is the (reverse) proto-dependence,
4917 mapping sink iterations to potential source iterations.
4918 The second argument represents the sink iterations for which
4919 we want to compute the last source iteration.
4920 The third argument is the token corresponding to the source
4921 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4922 The callback is expected to return a restriction on either the input or
4923 the output of the operation computing the last potential source.
4924 If the input needs to be restricted then restrictions are needed
4925 for both the source and the sink iterations. The sink iterations
4926 and the potential source iterations will be intersected with these sets.
4927 If the output needs to be restricted then only a restriction on the source
4928 iterations is required.
4929 If any error occurs, the callback should return C<NULL>.
4930 An C<isl_restriction> object can be created, freed and inspected
4931 using the following functions.
4933 #include <isl/flow.h>
4935 __isl_give isl_restriction *isl_restriction_input(
4936 __isl_take isl_set *source_restr,
4937 __isl_take isl_set *sink_restr);
4938 __isl_give isl_restriction *isl_restriction_output(
4939 __isl_take isl_set *source_restr);
4940 __isl_give isl_restriction *isl_restriction_none(
4941 __isl_take isl_map *source_map);
4942 __isl_give isl_restriction *isl_restriction_empty(
4943 __isl_take isl_map *source_map);
4944 void *isl_restriction_free(
4945 __isl_take isl_restriction *restr);
4946 isl_ctx *isl_restriction_get_ctx(
4947 __isl_keep isl_restriction *restr);
4949 C<isl_restriction_none> and C<isl_restriction_empty> are special
4950 cases of C<isl_restriction_input>. C<isl_restriction_none>
4951 is essentially equivalent to
4953 isl_restriction_input(isl_set_universe(
4954 isl_space_range(isl_map_get_space(source_map))),
4956 isl_space_domain(isl_map_get_space(source_map))));
4958 whereas C<isl_restriction_empty> is essentially equivalent to
4960 isl_restriction_input(isl_set_empty(
4961 isl_space_range(isl_map_get_space(source_map))),
4963 isl_space_domain(isl_map_get_space(source_map))));
4967 B<The functionality described in this section is fairly new
4968 and may be subject to change.>
4970 The following function can be used to compute a schedule
4971 for a union of domains.
4972 By default, the algorithm used to construct the schedule is similar
4973 to that of C<Pluto>.
4974 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4976 The generated schedule respects all C<validity> dependences.
4977 That is, all dependence distances over these dependences in the
4978 scheduled space are lexicographically positive.
4979 The default algorithm tries to minimize the dependence distances over
4980 C<proximity> dependences.
4981 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4982 for groups of domains where the dependence distances have only
4983 non-negative values.
4984 When using Feautrier's algorithm, the C<proximity> dependence
4985 distances are only minimized during the extension to a
4986 full-dimensional schedule.
4988 #include <isl/schedule.h>
4989 __isl_give isl_schedule *isl_union_set_compute_schedule(
4990 __isl_take isl_union_set *domain,
4991 __isl_take isl_union_map *validity,
4992 __isl_take isl_union_map *proximity);
4993 void *isl_schedule_free(__isl_take isl_schedule *sched);
4995 A mapping from the domains to the scheduled space can be obtained
4996 from an C<isl_schedule> using the following function.
4998 __isl_give isl_union_map *isl_schedule_get_map(
4999 __isl_keep isl_schedule *sched);
5001 A representation of the schedule can be printed using
5003 __isl_give isl_printer *isl_printer_print_schedule(
5004 __isl_take isl_printer *p,
5005 __isl_keep isl_schedule *schedule);
5007 A representation of the schedule as a forest of bands can be obtained
5008 using the following function.
5010 __isl_give isl_band_list *isl_schedule_get_band_forest(
5011 __isl_keep isl_schedule *schedule);
5013 The individual bands can be visited in depth-first post-order
5014 using the following function.
5016 #include <isl/schedule.h>
5017 int isl_schedule_foreach_band(
5018 __isl_keep isl_schedule *sched,
5019 int (*fn)(__isl_keep isl_band *band, void *user),
5022 The list can be manipulated as explained in L<"Lists">.
5023 The bands inside the list can be copied and freed using the following
5026 #include <isl/band.h>
5027 __isl_give isl_band *isl_band_copy(
5028 __isl_keep isl_band *band);
5029 void *isl_band_free(__isl_take isl_band *band);
5031 Each band contains zero or more scheduling dimensions.
5032 These are referred to as the members of the band.
5033 The section of the schedule that corresponds to the band is
5034 referred to as the partial schedule of the band.
5035 For those nodes that participate in a band, the outer scheduling
5036 dimensions form the prefix schedule, while the inner scheduling
5037 dimensions form the suffix schedule.
5038 That is, if we take a cut of the band forest, then the union of
5039 the concatenations of the prefix, partial and suffix schedules of
5040 each band in the cut is equal to the entire schedule (modulo
5041 some possible padding at the end with zero scheduling dimensions).
5042 The properties of a band can be inspected using the following functions.
5044 #include <isl/band.h>
5045 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5047 int isl_band_has_children(__isl_keep isl_band *band);
5048 __isl_give isl_band_list *isl_band_get_children(
5049 __isl_keep isl_band *band);
5051 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5052 __isl_keep isl_band *band);
5053 __isl_give isl_union_map *isl_band_get_partial_schedule(
5054 __isl_keep isl_band *band);
5055 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5056 __isl_keep isl_band *band);
5058 int isl_band_n_member(__isl_keep isl_band *band);
5059 int isl_band_member_is_zero_distance(
5060 __isl_keep isl_band *band, int pos);
5062 int isl_band_list_foreach_band(
5063 __isl_keep isl_band_list *list,
5064 int (*fn)(__isl_keep isl_band *band, void *user),
5067 Note that a scheduling dimension is considered to be ``zero
5068 distance'' if it does not carry any proximity dependences
5070 That is, if the dependence distances of the proximity
5071 dependences are all zero in that direction (for fixed
5072 iterations of outer bands).
5073 Like C<isl_schedule_foreach_band>,
5074 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5075 in depth-first post-order.
5077 A band can be tiled using the following function.
5079 #include <isl/band.h>
5080 int isl_band_tile(__isl_keep isl_band *band,
5081 __isl_take isl_vec *sizes);
5083 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5085 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5087 The C<isl_band_tile> function tiles the band using the given tile sizes
5088 inside its schedule.
5089 A new child band is created to represent the point loops and it is
5090 inserted between the modified band and its children.
5091 The C<tile_scale_tile_loops> option specifies whether the tile
5092 loops iterators should be scaled by the tile sizes.
5094 A representation of the band can be printed using
5096 #include <isl/band.h>
5097 __isl_give isl_printer *isl_printer_print_band(
5098 __isl_take isl_printer *p,
5099 __isl_keep isl_band *band);
5103 #include <isl/schedule.h>
5104 int isl_options_set_schedule_max_coefficient(
5105 isl_ctx *ctx, int val);
5106 int isl_options_get_schedule_max_coefficient(
5108 int isl_options_set_schedule_max_constant_term(
5109 isl_ctx *ctx, int val);
5110 int isl_options_get_schedule_max_constant_term(
5112 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5113 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5114 int isl_options_set_schedule_maximize_band_depth(
5115 isl_ctx *ctx, int val);
5116 int isl_options_get_schedule_maximize_band_depth(
5118 int isl_options_set_schedule_outer_zero_distance(
5119 isl_ctx *ctx, int val);
5120 int isl_options_get_schedule_outer_zero_distance(
5122 int isl_options_set_schedule_split_scaled(
5123 isl_ctx *ctx, int val);
5124 int isl_options_get_schedule_split_scaled(
5126 int isl_options_set_schedule_algorithm(
5127 isl_ctx *ctx, int val);
5128 int isl_options_get_schedule_algorithm(
5130 int isl_options_set_schedule_separate_components(
5131 isl_ctx *ctx, int val);
5132 int isl_options_get_schedule_separate_components(
5137 =item * schedule_max_coefficient
5139 This option enforces that the coefficients for variable and parameter
5140 dimensions in the calculated schedule are not larger than the specified value.
5141 This option can significantly increase the speed of the scheduling calculation
5142 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5143 this option does not introduce bounds on the variable or parameter
5146 =item * schedule_max_constant_term
5148 This option enforces that the constant coefficients in the calculated schedule
5149 are not larger than the maximal constant term. This option can significantly
5150 increase the speed of the scheduling calculation and may also prevent fusing of
5151 unrelated dimensions. A value of -1 means that this option does not introduce
5152 bounds on the constant coefficients.
5154 =item * schedule_fuse
5156 This option controls the level of fusion.
5157 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5158 resulting schedule will be distributed as much as possible.
5159 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5160 try to fuse loops in the resulting schedule.
5162 =item * schedule_maximize_band_depth
5164 If this option is set, we do not split bands at the point
5165 where we detect splitting is necessary. Instead, we
5166 backtrack and split bands as early as possible. This
5167 reduces the number of splits and maximizes the width of
5168 the bands. Wider bands give more possibilities for tiling.
5169 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5170 then bands will be split as early as possible, even if there is no need.
5171 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5173 =item * schedule_outer_zero_distance
5175 If this option is set, then we try to construct schedules
5176 where the outermost scheduling dimension in each band
5177 results in a zero dependence distance over the proximity
5180 =item * schedule_split_scaled
5182 If this option is set, then we try to construct schedules in which the
5183 constant term is split off from the linear part if the linear parts of
5184 the scheduling rows for all nodes in the graphs have a common non-trivial
5186 The constant term is then placed in a separate band and the linear
5189 =item * schedule_algorithm
5191 Selects the scheduling algorithm to be used.
5192 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5193 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5195 =item * schedule_separate_components
5197 If at any point the dependence graph contains any (weakly connected) components,
5198 then these components are scheduled separately.
5199 If this option is not set, then some iterations of the domains
5200 in these components may be scheduled together.
5201 If this option is set, then the components are given consecutive
5206 =head2 AST Generation
5208 This section describes the C<isl> functionality for generating
5209 ASTs that visit all the elements
5210 in a domain in an order specified by a schedule.
5211 In particular, given a C<isl_union_map>, an AST is generated
5212 that visits all the elements in the domain of the C<isl_union_map>
5213 according to the lexicographic order of the corresponding image
5214 element(s). If the range of the C<isl_union_map> consists of
5215 elements in more than one space, then each of these spaces is handled
5216 separately in an arbitrary order.
5217 It should be noted that the image elements only specify the I<order>
5218 in which the corresponding domain elements should be visited.
5219 No direct relation between the image elements and the loop iterators
5220 in the generated AST should be assumed.
5222 Each AST is generated within a build. The initial build
5223 simply specifies the constraints on the parameters (if any)
5224 and can be created, inspected, copied and freed using the following functions.
5226 #include <isl/ast_build.h>
5227 __isl_give isl_ast_build *isl_ast_build_from_context(
5228 __isl_take isl_set *set);
5229 isl_ctx *isl_ast_build_get_ctx(
5230 __isl_keep isl_ast_build *build);
5231 __isl_give isl_ast_build *isl_ast_build_copy(
5232 __isl_keep isl_ast_build *build);
5233 void *isl_ast_build_free(
5234 __isl_take isl_ast_build *build);
5236 The C<set> argument is usually a parameter set with zero or more parameters.
5237 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5238 and L</"Fine-grained Control over AST Generation">.
5239 Finally, the AST itself can be constructed using the following
5242 #include <isl/ast_build.h>
5243 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5244 __isl_keep isl_ast_build *build,
5245 __isl_take isl_union_map *schedule);
5247 =head3 Inspecting the AST
5249 The basic properties of an AST node can be obtained as follows.
5251 #include <isl/ast.h>
5252 isl_ctx *isl_ast_node_get_ctx(
5253 __isl_keep isl_ast_node *node);
5254 enum isl_ast_node_type isl_ast_node_get_type(
5255 __isl_keep isl_ast_node *node);
5257 The type of an AST node is one of
5258 C<isl_ast_node_for>,
5260 C<isl_ast_node_block> or
5261 C<isl_ast_node_user>.
5262 An C<isl_ast_node_for> represents a for node.
5263 An C<isl_ast_node_if> represents an if node.
5264 An C<isl_ast_node_block> represents a compound node.
5265 An C<isl_ast_node_user> represents an expression statement.
5266 An expression statement typically corresponds to a domain element, i.e.,
5267 one of the elements that is visited by the AST.
5269 Each type of node has its own additional properties.
5271 #include <isl/ast.h>
5272 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5273 __isl_keep isl_ast_node *node);
5274 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5275 __isl_keep isl_ast_node *node);
5276 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5277 __isl_keep isl_ast_node *node);
5278 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5279 __isl_keep isl_ast_node *node);
5280 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5281 __isl_keep isl_ast_node *node);
5282 int isl_ast_node_for_is_degenerate(
5283 __isl_keep isl_ast_node *node);
5285 An C<isl_ast_for> is considered degenerate if it is known to execute
5288 #include <isl/ast.h>
5289 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5290 __isl_keep isl_ast_node *node);
5291 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5292 __isl_keep isl_ast_node *node);
5293 int isl_ast_node_if_has_else(
5294 __isl_keep isl_ast_node *node);
5295 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5296 __isl_keep isl_ast_node *node);
5298 __isl_give isl_ast_node_list *
5299 isl_ast_node_block_get_children(
5300 __isl_keep isl_ast_node *node);
5302 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5303 __isl_keep isl_ast_node *node);
5305 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5306 the following functions.
5308 #include <isl/ast.h>
5309 isl_ctx *isl_ast_expr_get_ctx(
5310 __isl_keep isl_ast_expr *expr);
5311 enum isl_ast_expr_type isl_ast_expr_get_type(
5312 __isl_keep isl_ast_expr *expr);
5314 The type of an AST expression is one of
5316 C<isl_ast_expr_id> or
5317 C<isl_ast_expr_int>.
5318 An C<isl_ast_expr_op> represents the result of an operation.
5319 An C<isl_ast_expr_id> represents an identifier.
5320 An C<isl_ast_expr_int> represents an integer value.
5322 Each type of expression has its own additional properties.
5324 #include <isl/ast.h>
5325 enum isl_ast_op_type isl_ast_expr_get_op_type(
5326 __isl_keep isl_ast_expr *expr);
5327 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5328 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5329 __isl_keep isl_ast_expr *expr, int pos);
5330 int isl_ast_node_foreach_ast_op_type(
5331 __isl_keep isl_ast_node *node,
5332 int (*fn)(enum isl_ast_op_type type, void *user),
5335 C<isl_ast_expr_get_op_type> returns the type of the operation
5336 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5337 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5339 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5340 C<isl_ast_op_type> that appears in C<node>.
5341 The operation type is one of the following.
5345 =item C<isl_ast_op_and>
5347 Logical I<and> of two arguments.
5348 Both arguments can be evaluated.
5350 =item C<isl_ast_op_and_then>
5352 Logical I<and> of two arguments.
5353 The second argument can only be evaluated if the first evaluates to true.
5355 =item C<isl_ast_op_or>
5357 Logical I<or> of two arguments.
5358 Both arguments can be evaluated.
5360 =item C<isl_ast_op_or_else>
5362 Logical I<or> of two arguments.
5363 The second argument can only be evaluated if the first evaluates to false.
5365 =item C<isl_ast_op_max>
5367 Maximum of two or more arguments.
5369 =item C<isl_ast_op_min>
5371 Minimum of two or more arguments.
5373 =item C<isl_ast_op_minus>
5377 =item C<isl_ast_op_add>
5379 Sum of two arguments.
5381 =item C<isl_ast_op_sub>
5383 Difference of two arguments.
5385 =item C<isl_ast_op_mul>
5387 Product of two arguments.
5389 =item C<isl_ast_op_div>
5391 Exact division. That is, the result is known to be an integer.
5393 =item C<isl_ast_op_fdiv_q>
5395 Result of integer division, rounded towards negative
5398 =item C<isl_ast_op_pdiv_q>
5400 Result of integer division, where dividend is known to be non-negative.
5402 =item C<isl_ast_op_pdiv_r>
5404 Remainder of integer division, where dividend is known to be non-negative.
5406 =item C<isl_ast_op_cond>
5408 Conditional operator defined on three arguments.
5409 If the first argument evaluates to true, then the result
5410 is equal to the second argument. Otherwise, the result
5411 is equal to the third argument.
5412 The second and third argument may only be evaluated if
5413 the first argument evaluates to true and false, respectively.
5414 Corresponds to C<a ? b : c> in C.
5416 =item C<isl_ast_op_select>
5418 Conditional operator defined on three arguments.
5419 If the first argument evaluates to true, then the result
5420 is equal to the second argument. Otherwise, the result
5421 is equal to the third argument.
5422 The second and third argument may be evaluated independently
5423 of the value of the first argument.
5424 Corresponds to C<a * b + (1 - a) * c> in C.
5426 =item C<isl_ast_op_eq>
5430 =item C<isl_ast_op_le>
5432 Less than or equal relation.
5434 =item C<isl_ast_op_lt>
5438 =item C<isl_ast_op_ge>
5440 Greater than or equal relation.
5442 =item C<isl_ast_op_gt>
5444 Greater than relation.
5446 =item C<isl_ast_op_call>
5449 The number of arguments of the C<isl_ast_expr> is one more than
5450 the number of arguments in the function call, the first argument
5451 representing the function being called.
5455 #include <isl/ast.h>
5456 __isl_give isl_id *isl_ast_expr_get_id(
5457 __isl_keep isl_ast_expr *expr);
5459 Return the identifier represented by the AST expression.
5461 #include <isl/ast.h>
5462 int isl_ast_expr_get_int(__isl_keep isl_ast_expr *expr,
5465 Return the integer represented by the AST expression.
5466 Note that the integer is returned through the C<v> argument.
5467 The return value of the function itself indicates whether the
5468 operation was performed successfully.
5470 =head3 Manipulating and printing the AST
5472 AST nodes can be copied and freed using the following functions.
5474 #include <isl/ast.h>
5475 __isl_give isl_ast_node *isl_ast_node_copy(
5476 __isl_keep isl_ast_node *node);
5477 void *isl_ast_node_free(__isl_take isl_ast_node *node);
5479 AST expressions can be copied and freed using the following functions.
5481 #include <isl/ast.h>
5482 __isl_give isl_ast_expr *isl_ast_expr_copy(
5483 __isl_keep isl_ast_expr *expr);
5484 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
5486 New AST expressions can be created either directly or within
5487 the context of an C<isl_ast_build>.
5489 #include <isl/ast.h>
5490 __isl_give isl_ast_expr *isl_ast_expr_from_id(
5491 __isl_take isl_id *id);
5492 __isl_give isl_ast_expr *isl_ast_expr_neg(
5493 __isl_take isl_ast_expr *expr);
5494 __isl_give isl_ast_expr *isl_ast_expr_add(
5495 __isl_take isl_ast_expr *expr1,
5496 __isl_take isl_ast_expr *expr2);
5497 __isl_give isl_ast_expr *isl_ast_expr_sub(
5498 __isl_take isl_ast_expr *expr1,
5499 __isl_take isl_ast_expr *expr2);
5500 __isl_give isl_ast_expr *isl_ast_expr_mul(
5501 __isl_take isl_ast_expr *expr1,
5502 __isl_take isl_ast_expr *expr2);
5503 __isl_give isl_ast_expr *isl_ast_expr_div(
5504 __isl_take isl_ast_expr *expr1,
5505 __isl_take isl_ast_expr *expr2);
5506 __isl_give isl_ast_expr *isl_ast_expr_and(
5507 __isl_take isl_ast_expr *expr1,
5508 __isl_take isl_ast_expr *expr2)
5509 __isl_give isl_ast_expr *isl_ast_expr_or(
5510 __isl_take isl_ast_expr *expr1,
5511 __isl_take isl_ast_expr *expr2)
5513 #include <isl/ast_build.h>
5514 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
5515 __isl_keep isl_ast_build *build,
5516 __isl_take isl_pw_aff *pa);
5517 __isl_give isl_ast_expr *
5518 isl_ast_build_call_from_pw_multi_aff(
5519 __isl_keep isl_ast_build *build,
5520 __isl_take isl_pw_multi_aff *pma);
5522 The domains of C<pa> and C<pma> should correspond
5523 to the schedule space of C<build>.
5524 The tuple id of C<pma> is used as the function being called.
5526 User specified data can be attached to an C<isl_ast_node> and obtained
5527 from the same C<isl_ast_node> using the following functions.
5529 #include <isl/ast.h>
5530 __isl_give isl_ast_node *isl_ast_node_set_annotation(
5531 __isl_take isl_ast_node *node,
5532 __isl_take isl_id *annotation);
5533 __isl_give isl_id *isl_ast_node_get_annotation(
5534 __isl_keep isl_ast_node *node);
5536 Basic printing can be performed using the following functions.
5538 #include <isl/ast.h>
5539 __isl_give isl_printer *isl_printer_print_ast_expr(
5540 __isl_take isl_printer *p,
5541 __isl_keep isl_ast_expr *expr);
5542 __isl_give isl_printer *isl_printer_print_ast_node(
5543 __isl_take isl_printer *p,
5544 __isl_keep isl_ast_node *node);
5546 More advanced printing can be performed using the following functions.
5548 #include <isl/ast.h>
5549 __isl_give isl_printer *isl_ast_op_type_print_macro(
5550 enum isl_ast_op_type type,
5551 __isl_take isl_printer *p);
5552 __isl_give isl_printer *isl_ast_node_print_macros(
5553 __isl_keep isl_ast_node *node,
5554 __isl_take isl_printer *p);
5555 __isl_give isl_printer *isl_ast_node_print(
5556 __isl_keep isl_ast_node *node,
5557 __isl_take isl_printer *p,
5558 __isl_take isl_ast_print_options *options);
5559 __isl_give isl_printer *isl_ast_node_for_print(
5560 __isl_keep isl_ast_node *node,
5561 __isl_take isl_printer *p,
5562 __isl_take isl_ast_print_options *options);
5563 __isl_give isl_printer *isl_ast_node_if_print(
5564 __isl_keep isl_ast_node *node,
5565 __isl_take isl_printer *p,
5566 __isl_take isl_ast_print_options *options);
5568 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
5569 C<isl> may print out an AST that makes use of macros such
5570 as C<floord>, C<min> and C<max>.
5571 C<isl_ast_op_type_print_macro> prints out the macro
5572 corresponding to a specific C<isl_ast_op_type>.
5573 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
5574 for expressions where these macros would be used and prints
5575 out the required macro definitions.
5576 Essentially, C<isl_ast_node_print_macros> calls
5577 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
5578 as function argument.
5579 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
5580 C<isl_ast_node_if_print> print an C<isl_ast_node>
5581 in C<ISL_FORMAT_C>, but allow for some extra control
5582 through an C<isl_ast_print_options> object.
5583 This object can be created using the following functions.
5585 #include <isl/ast.h>
5586 __isl_give isl_ast_print_options *
5587 isl_ast_print_options_alloc(isl_ctx *ctx);
5588 __isl_give isl_ast_print_options *
5589 isl_ast_print_options_copy(
5590 __isl_keep isl_ast_print_options *options);
5591 void *isl_ast_print_options_free(
5592 __isl_take isl_ast_print_options *options);
5594 __isl_give isl_ast_print_options *
5595 isl_ast_print_options_set_print_user(
5596 __isl_take isl_ast_print_options *options,
5597 __isl_give isl_printer *(*print_user)(
5598 __isl_take isl_printer *p,
5599 __isl_take isl_ast_print_options *options,
5600 __isl_keep isl_ast_node *node, void *user),
5602 __isl_give isl_ast_print_options *
5603 isl_ast_print_options_set_print_for(
5604 __isl_take isl_ast_print_options *options,
5605 __isl_give isl_printer *(*print_for)(
5606 __isl_take isl_printer *p,
5607 __isl_take isl_ast_print_options *options,
5608 __isl_keep isl_ast_node *node, void *user),
5611 The callback set by C<isl_ast_print_options_set_print_user>
5612 is called whenever a node of type C<isl_ast_node_user> needs to
5614 The callback set by C<isl_ast_print_options_set_print_for>
5615 is called whenever a node of type C<isl_ast_node_for> needs to
5617 Note that C<isl_ast_node_for_print> will I<not> call the
5618 callback set by C<isl_ast_print_options_set_print_for> on the node
5619 on which C<isl_ast_node_for_print> is called, but only on nested
5620 nodes of type C<isl_ast_node_for>. It is therefore safe to
5621 call C<isl_ast_node_for_print> from within the callback set by
5622 C<isl_ast_print_options_set_print_for>.
5624 The following option determines the type to be used for iterators
5625 while printing the AST.
5627 int isl_options_set_ast_iterator_type(
5628 isl_ctx *ctx, const char *val);
5629 const char *isl_options_get_ast_iterator_type(
5634 #include <isl/ast_build.h>
5635 int isl_options_set_ast_build_atomic_upper_bound(
5636 isl_ctx *ctx, int val);
5637 int isl_options_get_ast_build_atomic_upper_bound(
5639 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
5641 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
5642 int isl_options_set_ast_build_exploit_nested_bounds(
5643 isl_ctx *ctx, int val);
5644 int isl_options_get_ast_build_exploit_nested_bounds(
5646 int isl_options_set_ast_build_group_coscheduled(
5647 isl_ctx *ctx, int val);
5648 int isl_options_get_ast_build_group_coscheduled(
5650 int isl_options_set_ast_build_scale_strides(
5651 isl_ctx *ctx, int val);
5652 int isl_options_get_ast_build_scale_strides(
5654 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
5656 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
5660 =item * ast_build_atomic_upper_bound
5662 Generate loop upper bounds that consist of the current loop iterator,
5663 an operator and an expression not involving the iterator.
5664 If this option is not set, then the current loop iterator may appear
5665 several times in the upper bound.
5666 For example, when this option is turned off, AST generation
5669 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
5673 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
5676 When the option is turned on, the following AST is generated
5678 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
5681 =item * ast_build_prefer_pdiv
5683 If this option is turned off, then the AST generation will
5684 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
5685 operators, but no C<isl_ast_op_pdiv_q> or
5686 C<isl_ast_op_pdiv_r> operators.
5687 If this options is turned on, then C<isl> will try to convert
5688 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
5689 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
5691 =item * ast_build_exploit_nested_bounds
5693 Simplify conditions based on bounds of nested for loops.
5694 In particular, remove conditions that are implied by the fact
5695 that one or more nested loops have at least one iteration,
5696 meaning that the upper bound is at least as large as the lower bound.
5697 For example, when this option is turned off, AST generation
5700 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
5706 for (int c0 = 0; c0 <= N; c0 += 1)
5707 for (int c1 = 0; c1 <= M; c1 += 1)
5710 When the option is turned on, the following AST is generated
5712 for (int c0 = 0; c0 <= N; c0 += 1)
5713 for (int c1 = 0; c1 <= M; c1 += 1)
5716 =item * ast_build_group_coscheduled
5718 If two domain elements are assigned the same schedule point, then
5719 they may be executed in any order and they may even appear in different
5720 loops. If this options is set, then the AST generator will make
5721 sure that coscheduled domain elements do not appear in separate parts
5722 of the AST. This is useful in case of nested AST generation
5723 if the outer AST generation is given only part of a schedule
5724 and the inner AST generation should handle the domains that are
5725 coscheduled by this initial part of the schedule together.
5726 For example if an AST is generated for a schedule
5728 { A[i] -> [0]; B[i] -> [0] }
5730 then the C<isl_ast_build_set_create_leaf> callback described
5731 below may get called twice, once for each domain.
5732 Setting this option ensures that the callback is only called once
5733 on both domains together.
5735 =item * ast_build_separation_bounds
5737 This option specifies which bounds to use during separation.
5738 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
5739 then all (possibly implicit) bounds on the current dimension will
5740 be used during separation.
5741 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
5742 then only those bounds that are explicitly available will
5743 be used during separation.
5745 =item * ast_build_scale_strides
5747 This option specifies whether the AST generator is allowed
5748 to scale down iterators of strided loops.
5750 =item * ast_build_allow_else
5752 This option specifies whether the AST generator is allowed
5753 to construct if statements with else branches.
5757 =head3 Fine-grained Control over AST Generation
5759 Besides specifying the constraints on the parameters,
5760 an C<isl_ast_build> object can be used to control
5761 various aspects of the AST generation process.
5762 The most prominent way of control is through ``options'',
5763 which can be set using the following function.
5765 #include <isl/ast_build.h>
5766 __isl_give isl_ast_build *
5767 isl_ast_build_set_options(
5768 __isl_take isl_ast_build *control,
5769 __isl_take isl_union_map *options);
5771 The options are encoded in an <isl_union_map>.
5772 The domain of this union relation refers to the schedule domain,
5773 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
5774 In the case of nested AST generation (see L</"Nested AST Generation">),
5775 the domain of C<options> should refer to the extra piece of the schedule.
5776 That is, it should be equal to the range of the wrapped relation in the
5777 range of the schedule.
5778 The range of the options can consist of elements in one or more spaces,
5779 the names of which determine the effect of the option.
5780 The values of the range typically also refer to the schedule dimension
5781 to which the option applies. In case of nested AST generation
5782 (see L</"Nested AST Generation">), these values refer to the position
5783 of the schedule dimension within the innermost AST generation.
5784 The constraints on the domain elements of
5785 the option should only refer to this dimension and earlier dimensions.
5786 We consider the following spaces.
5790 =item C<separation_class>
5792 This space is a wrapped relation between two one dimensional spaces.
5793 The input space represents the schedule dimension to which the option
5794 applies and the output space represents the separation class.
5795 While constructing a loop corresponding to the specified schedule
5796 dimension(s), the AST generator will try to generate separate loops
5797 for domain elements that are assigned different classes.
5798 If only some of the elements are assigned a class, then those elements
5799 that are not assigned any class will be treated as belonging to a class
5800 that is separate from the explicitly assigned classes.
5801 The typical use case for this option is to separate full tiles from
5803 The other options, described below, are applied after the separation
5806 As an example, consider the separation into full and partial tiles
5807 of a tiling of a triangular domain.
5808 Take, for example, the domain
5810 { A[i,j] : 0 <= i,j and i + j <= 100 }
5812 and a tiling into tiles of 10 by 10. The input to the AST generator
5813 is then the schedule
5815 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
5818 Without any options, the following AST is generated
5820 for (int c0 = 0; c0 <= 10; c0 += 1)
5821 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
5822 for (int c2 = 10 * c0;
5823 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
5825 for (int c3 = 10 * c1;
5826 c3 <= min(10 * c1 + 9, -c2 + 100);
5830 Separation into full and partial tiles can be obtained by assigning
5831 a class, say C<0>, to the full tiles. The full tiles are represented by those
5832 values of the first and second schedule dimensions for which there are
5833 values of the third and fourth dimensions to cover an entire tile.
5834 That is, we need to specify the following option
5836 { [a,b,c,d] -> separation_class[[0]->[0]] :
5837 exists b': 0 <= 10a,10b' and
5838 10a+9+10b'+9 <= 100;
5839 [a,b,c,d] -> separation_class[[1]->[0]] :
5840 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
5844 { [a, b, c, d] -> separation_class[[1] -> [0]] :
5845 a >= 0 and b >= 0 and b <= 8 - a;
5846 [a, b, c, d] -> separation_class[[0] -> [0]] :
5849 With this option, the generated AST is as follows
5852 for (int c0 = 0; c0 <= 8; c0 += 1) {
5853 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
5854 for (int c2 = 10 * c0;
5855 c2 <= 10 * c0 + 9; c2 += 1)
5856 for (int c3 = 10 * c1;
5857 c3 <= 10 * c1 + 9; c3 += 1)
5859 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
5860 for (int c2 = 10 * c0;
5861 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
5863 for (int c3 = 10 * c1;
5864 c3 <= min(-c2 + 100, 10 * c1 + 9);
5868 for (int c0 = 9; c0 <= 10; c0 += 1)
5869 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
5870 for (int c2 = 10 * c0;
5871 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
5873 for (int c3 = 10 * c1;
5874 c3 <= min(10 * c1 + 9, -c2 + 100);
5881 This is a single-dimensional space representing the schedule dimension(s)
5882 to which ``separation'' should be applied. Separation tries to split
5883 a loop into several pieces if this can avoid the generation of guards
5885 See also the C<atomic> option.
5889 This is a single-dimensional space representing the schedule dimension(s)
5890 for which the domains should be considered ``atomic''. That is, the
5891 AST generator will make sure that any given domain space will only appear
5892 in a single loop at the specified level.
5894 Consider the following schedule
5896 { a[i] -> [i] : 0 <= i < 10;
5897 b[i] -> [i+1] : 0 <= i < 10 }
5899 If the following option is specified
5901 { [i] -> separate[x] }
5903 then the following AST will be generated
5907 for (int c0 = 1; c0 <= 9; c0 += 1) {
5914 If, on the other hand, the following option is specified
5916 { [i] -> atomic[x] }
5918 then the following AST will be generated
5920 for (int c0 = 0; c0 <= 10; c0 += 1) {
5927 If neither C<atomic> nor C<separate> is specified, then the AST generator
5928 may produce either of these two results or some intermediate form.
5932 This is a single-dimensional space representing the schedule dimension(s)
5933 that should be I<completely> unrolled.
5934 To obtain a partial unrolling, the user should apply an additional
5935 strip-mining to the schedule and fully unroll the inner loop.
5939 Additional control is available through the following functions.
5941 #include <isl/ast_build.h>
5942 __isl_give isl_ast_build *
5943 isl_ast_build_set_iterators(
5944 __isl_take isl_ast_build *control,
5945 __isl_take isl_id_list *iterators);
5947 The function C<isl_ast_build_set_iterators> allows the user to
5948 specify a list of iterator C<isl_id>s to be used as iterators.
5949 If the input schedule is injective, then
5950 the number of elements in this list should be as large as the dimension
5951 of the schedule space, but no direct correspondence should be assumed
5952 between dimensions and elements.
5953 If the input schedule is not injective, then an additional number
5954 of C<isl_id>s equal to the largest dimension of the input domains
5956 If the number of provided C<isl_id>s is insufficient, then additional
5957 names are automatically generated.
5959 #include <isl/ast_build.h>
5960 __isl_give isl_ast_build *
5961 isl_ast_build_set_create_leaf(
5962 __isl_take isl_ast_build *control,
5963 __isl_give isl_ast_node *(*fn)(
5964 __isl_take isl_ast_build *build,
5965 void *user), void *user);
5968 C<isl_ast_build_set_create_leaf> function allows for the
5969 specification of a callback that should be called whenever the AST
5970 generator arrives at an element of the schedule domain.
5971 The callback should return an AST node that should be inserted
5972 at the corresponding position of the AST. The default action (when
5973 the callback is not set) is to continue generating parts of the AST to scan
5974 all the domain elements associated to the schedule domain element
5975 and to insert user nodes, ``calling'' the domain element, for each of them.
5976 The C<build> argument contains the current state of the C<isl_ast_build>.
5977 To ease nested AST generation (see L</"Nested AST Generation">),
5978 all control information that is
5979 specific to the current AST generation such as the options and
5980 the callbacks has been removed from this C<isl_ast_build>.
5981 The callback would typically return the result of a nested
5983 user defined node created using the following function.
5985 #include <isl/ast.h>
5986 __isl_give isl_ast_node *isl_ast_node_alloc_user(
5987 __isl_take isl_ast_expr *expr);
5989 #include <isl/ast_build.h>
5990 __isl_give isl_ast_build *
5991 isl_ast_build_set_at_each_domain(
5992 __isl_take isl_ast_build *build,
5993 __isl_give isl_ast_node *(*fn)(
5994 __isl_take isl_ast_node *node,
5995 __isl_keep isl_ast_build *build,
5996 void *user), void *user);
5997 __isl_give isl_ast_build *
5998 isl_ast_build_set_before_each_for(
5999 __isl_take isl_ast_build *build,
6000 __isl_give isl_id *(*fn)(
6001 __isl_keep isl_ast_build *build,
6002 void *user), void *user);
6003 __isl_give isl_ast_build *
6004 isl_ast_build_set_after_each_for(
6005 __isl_take isl_ast_build *build,
6006 __isl_give isl_ast_node *(*fn)(
6007 __isl_take isl_ast_node *node,
6008 __isl_keep isl_ast_build *build,
6009 void *user), void *user);
6011 The callback set by C<isl_ast_build_set_at_each_domain> will
6012 be called for each domain AST node.
6013 The callbacks set by C<isl_ast_build_set_before_each_for>
6014 and C<isl_ast_build_set_after_each_for> will be called
6015 for each for AST node. The first will be called in depth-first
6016 pre-order, while the second will be called in depth-first post-order.
6017 Since C<isl_ast_build_set_before_each_for> is called before the for
6018 node is actually constructed, it is only passed an C<isl_ast_build>.
6019 The returned C<isl_id> will be added as an annotation (using
6020 C<isl_ast_node_set_annotation>) to the constructed for node.
6021 In particular, if the user has also specified an C<after_each_for>
6022 callback, then the annotation can be retrieved from the node passed to
6023 that callback using C<isl_ast_node_get_annotation>.
6024 All callbacks should C<NULL> on failure.
6025 The given C<isl_ast_build> can be used to create new
6026 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6027 or C<isl_ast_build_call_from_pw_multi_aff>.
6029 =head3 Nested AST Generation
6031 C<isl> allows the user to create an AST within the context
6032 of another AST. These nested ASTs are created using the
6033 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6034 outer AST. The C<build> argument should be an C<isl_ast_build>
6035 passed to a callback set by
6036 C<isl_ast_build_set_create_leaf>.
6037 The space of the range of the C<schedule> argument should refer
6038 to this build. In particular, the space should be a wrapped
6039 relation and the domain of this wrapped relation should be the
6040 same as that of the range of the schedule returned by
6041 C<isl_ast_build_get_schedule> below.
6042 In practice, the new schedule is typically
6043 created by calling C<isl_union_map_range_product> on the old schedule
6044 and some extra piece of the schedule.
6045 The space of the schedule domain is also available from
6046 the C<isl_ast_build>.
6048 #include <isl/ast_build.h>
6049 __isl_give isl_union_map *isl_ast_build_get_schedule(
6050 __isl_keep isl_ast_build *build);
6051 __isl_give isl_space *isl_ast_build_get_schedule_space(
6052 __isl_keep isl_ast_build *build);
6053 __isl_give isl_ast_build *isl_ast_build_restrict(
6054 __isl_take isl_ast_build *build,
6055 __isl_take isl_set *set);
6057 The C<isl_ast_build_get_schedule> function returns a (partial)
6058 schedule for the domains elements for which part of the AST still needs to
6059 be generated in the current build.
6060 In particular, the domain elements are mapped to those iterations of the loops
6061 enclosing the current point of the AST generation inside which
6062 the domain elements are executed.
6063 No direct correspondence between
6064 the input schedule and this schedule should be assumed.
6065 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6066 to create a set for C<isl_ast_build_restrict> to intersect
6067 with the current build. In particular, the set passed to
6068 C<isl_ast_build_restrict> can have additional parameters.
6069 The ids of the set dimensions in the space returned by
6070 C<isl_ast_build_get_schedule_space> correspond to the
6071 iterators of the already generated loops.
6072 The user should not rely on the ids of the output dimensions
6073 of the relations in the union relation returned by
6074 C<isl_ast_build_get_schedule> having any particular value.
6078 Although C<isl> is mainly meant to be used as a library,
6079 it also contains some basic applications that use some
6080 of the functionality of C<isl>.
6081 The input may be specified in either the L<isl format>
6082 or the L<PolyLib format>.
6084 =head2 C<isl_polyhedron_sample>
6086 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6087 an integer element of the polyhedron, if there is any.
6088 The first column in the output is the denominator and is always
6089 equal to 1. If the polyhedron contains no integer points,
6090 then a vector of length zero is printed.
6094 C<isl_pip> takes the same input as the C<example> program
6095 from the C<piplib> distribution, i.e., a set of constraints
6096 on the parameters, a line containing only -1 and finally a set
6097 of constraints on a parametric polyhedron.
6098 The coefficients of the parameters appear in the last columns
6099 (but before the final constant column).
6100 The output is the lexicographic minimum of the parametric polyhedron.
6101 As C<isl> currently does not have its own output format, the output
6102 is just a dump of the internal state.
6104 =head2 C<isl_polyhedron_minimize>
6106 C<isl_polyhedron_minimize> computes the minimum of some linear
6107 or affine objective function over the integer points in a polyhedron.
6108 If an affine objective function
6109 is given, then the constant should appear in the last column.
6111 =head2 C<isl_polytope_scan>
6113 Given a polytope, C<isl_polytope_scan> prints
6114 all integer points in the polytope.
6116 =head2 C<isl_codegen>
6118 Given a schedule, a context set and an options relation,
6119 C<isl_codegen> prints out an AST that scans the domain elements
6120 of the schedule in the order of their image(s) taking into account
6121 the constraints in the context set.