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
8 using C<GMP> or C<imath>.
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 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.
184 =head3 Changes since isl-0.12
188 =item * C<isl_int> has been replaced by C<isl_val>.
189 Some of the old functions are still available in C<isl/deprecated/*.h>
190 but they will be removed in the future.
192 =item * The functions C<isl_pw_qpolynomial_eval>,
193 C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval>
194 and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return
195 an C<isl_val> instead of an C<isl_qpolynomial>.
197 =item * The function C<isl_band_member_is_zero_distance>
198 has been removed. Essentially the same functionality is available
199 through C<isl_band_member_is_coincident>, except that is requires
200 setting up coincidence constraints.
201 The option C<schedule_outer_zero_distance> has accordingly been
202 replaced by the option C<schedule_outer_coincidence>.
204 =item * The function C<isl_vertex_get_expr> has been changed
205 to return an C<isl_multi_aff> instead of a rational C<isl_basic_set>.
206 The function C<isl_vertex_get_domain> has been changed to return
207 a regular basic set, rather than a rational basic set.
211 =head3 Changes since isl-0.14
215 =item * Objects of type C<isl_union_pw_multi_aff> can no longer contain
216 two or more C<isl_pw_multi_aff> objects with the same domain space.
222 C<isl> is released under the MIT license.
226 Permission is hereby granted, free of charge, to any person obtaining a copy of
227 this software and associated documentation files (the "Software"), to deal in
228 the Software without restriction, including without limitation the rights to
229 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
230 of the Software, and to permit persons to whom the Software is furnished to do
231 so, subject to the following conditions:
233 The above copyright notice and this permission notice shall be included in all
234 copies or substantial portions of the Software.
236 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
237 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
238 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
239 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
240 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
241 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
246 Note that by default C<isl> requires C<GMP>, which is released
247 under the GNU Lesser General Public License (LGPL). This means
248 that code linked against C<isl> is also linked against LGPL code.
250 When configuring with C<--with-int=imath>, C<isl> will link against C<imath>, a
251 library for exact integer arithmetic released under the MIT license.
255 The source of C<isl> can be obtained either as a tarball
256 or from the git repository. Both are available from
257 L<http://freshmeat.net/projects/isl/>.
258 The installation process depends on how you obtained
261 =head2 Installation from the git repository
265 =item 1 Clone or update the repository
267 The first time the source is obtained, you need to clone
270 git clone git://repo.or.cz/isl.git
272 To obtain updates, you need to pull in the latest changes
276 =item 2 Optionally get C<imath> submodule
278 To build C<isl> with C<imath>, you need to obtain the C<imath>
279 submodule by running in the git source tree of C<isl>
284 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
286 =item 2 Generate C<configure>
292 After performing the above steps, continue
293 with the L<Common installation instructions>.
295 =head2 Common installation instructions
299 =item 1 Obtain C<GMP>
301 By default, building C<isl> requires C<GMP>, including its headers files.
302 Your distribution may not provide these header files by default
303 and you may need to install a package called C<gmp-devel> or something
304 similar. Alternatively, C<GMP> can be built from
305 source, available from L<http://gmplib.org/>.
306 C<GMP> is not needed if you build C<isl> with C<imath>.
310 C<isl> uses the standard C<autoconf> C<configure> script.
315 optionally followed by some configure options.
316 A complete list of options can be obtained by running
320 Below we discuss some of the more common options.
326 Installation prefix for C<isl>
328 =item C<--with-int=[gmp|imath]>
330 Select the integer library to be used by C<isl>, the default is C<gmp>.
331 Note that C<isl> may run significantly slower if you use C<imath>.
333 =item C<--with-gmp-prefix>
335 Installation prefix for C<GMP> (architecture-independent files).
337 =item C<--with-gmp-exec-prefix>
339 Installation prefix for C<GMP> (architecture-dependent files).
347 =item 4 Install (optional)
353 =head1 Integer Set Library
355 =head2 Initialization
357 All manipulations of integer sets and relations occur within
358 the context of an C<isl_ctx>.
359 A given C<isl_ctx> can only be used within a single thread.
360 All arguments of a function are required to have been allocated
361 within the same context.
362 There are currently no functions available for moving an object
363 from one C<isl_ctx> to another C<isl_ctx>. This means that
364 there is currently no way of safely moving an object from one
365 thread to another, unless the whole C<isl_ctx> is moved.
367 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
368 freed using C<isl_ctx_free>.
369 All objects allocated within an C<isl_ctx> should be freed
370 before the C<isl_ctx> itself is freed.
372 isl_ctx *isl_ctx_alloc();
373 void isl_ctx_free(isl_ctx *ctx);
375 The user can impose a bound on the number of low-level I<operations>
376 that can be performed by an C<isl_ctx>. This bound can be set and
377 retrieved using the following functions. A bound of zero means that
378 no bound is imposed. The number of operations performed can be
379 reset using C<isl_ctx_reset_operations>. Note that the number
380 of low-level operations needed to perform a high-level computation
381 may differ significantly across different versions
382 of C<isl>, but it should be the same across different platforms
383 for the same version of C<isl>.
385 Warning: This feature is experimental. C<isl> has good support to abort and
386 bail out during the computation, but this feature may exercise error code paths
387 that are normally not used that much. Consequently, it is not unlikely that
388 hidden bugs will be exposed.
390 void isl_ctx_set_max_operations(isl_ctx *ctx,
391 unsigned long max_operations);
392 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
393 void isl_ctx_reset_operations(isl_ctx *ctx);
395 =head2 Memory Management
397 Since a high-level operation on isl objects usually involves
398 several substeps and since the user is usually not interested in
399 the intermediate results, most functions that return a new object
400 will also release all the objects passed as arguments.
401 If the user still wants to use one or more of these arguments
402 after the function call, she should pass along a copy of the
403 object rather than the object itself.
404 The user is then responsible for making sure that the original
405 object gets used somewhere else or is explicitly freed.
407 The arguments and return values of all documented functions are
408 annotated to make clear which arguments are released and which
409 arguments are preserved. In particular, the following annotations
416 C<__isl_give> means that a new object is returned.
417 The user should make sure that the returned pointer is
418 used exactly once as a value for an C<__isl_take> argument.
419 In between, it can be used as a value for as many
420 C<__isl_keep> arguments as the user likes.
421 There is one exception, and that is the case where the
422 pointer returned is C<NULL>. Is this case, the user
423 is free to use it as an C<__isl_take> argument or not.
427 C<__isl_null> means that a C<NULL> value is returned.
431 C<__isl_take> means that the object the argument points to
432 is taken over by the function and may no longer be used
433 by the user as an argument to any other function.
434 The pointer value must be one returned by a function
435 returning an C<__isl_give> pointer.
436 If the user passes in a C<NULL> value, then this will
437 be treated as an error in the sense that the function will
438 not perform its usual operation. However, it will still
439 make sure that all the other C<__isl_take> arguments
444 C<__isl_keep> means that the function will only use the object
445 temporarily. After the function has finished, the user
446 can still use it as an argument to other functions.
447 A C<NULL> value will be treated in the same way as
448 a C<NULL> value for an C<__isl_take> argument.
454 An C<isl_val> represents an integer value, a rational value
455 or one of three special values, infinity, negative infinity and NaN.
456 Some predefined values can be created using the following functions.
459 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
460 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
461 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
462 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
463 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
464 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
466 Specific integer values can be created using the following functions.
469 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
471 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
473 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
474 size_t n, size_t size, const void *chunks);
476 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
477 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
478 The least significant digit is assumed to be stored first.
480 Value objects can be copied and freed using the following functions.
483 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
484 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
486 They can be inspected using the following functions.
489 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
490 long isl_val_get_num_si(__isl_keep isl_val *v);
491 long isl_val_get_den_si(__isl_keep isl_val *v);
492 double isl_val_get_d(__isl_keep isl_val *v);
493 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
495 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
496 size_t size, void *chunks);
498 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
499 of C<size> bytes needed to store the absolute value of the
501 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
502 which is assumed to have been preallocated by the caller.
503 The least significant digit is stored first.
504 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
505 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
506 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
508 An C<isl_val> can be modified using the following function.
511 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
514 The following unary properties are defined on C<isl_val>s.
517 int isl_val_sgn(__isl_keep isl_val *v);
518 int isl_val_is_zero(__isl_keep isl_val *v);
519 int isl_val_is_one(__isl_keep isl_val *v);
520 int isl_val_is_negone(__isl_keep isl_val *v);
521 int isl_val_is_nonneg(__isl_keep isl_val *v);
522 int isl_val_is_nonpos(__isl_keep isl_val *v);
523 int isl_val_is_pos(__isl_keep isl_val *v);
524 int isl_val_is_neg(__isl_keep isl_val *v);
525 int isl_val_is_int(__isl_keep isl_val *v);
526 int isl_val_is_rat(__isl_keep isl_val *v);
527 int isl_val_is_nan(__isl_keep isl_val *v);
528 int isl_val_is_infty(__isl_keep isl_val *v);
529 int isl_val_is_neginfty(__isl_keep isl_val *v);
531 Note that the sign of NaN is undefined.
533 The following binary properties are defined on pairs of C<isl_val>s.
536 int isl_val_lt(__isl_keep isl_val *v1,
537 __isl_keep isl_val *v2);
538 int isl_val_le(__isl_keep isl_val *v1,
539 __isl_keep isl_val *v2);
540 int isl_val_gt(__isl_keep isl_val *v1,
541 __isl_keep isl_val *v2);
542 int isl_val_ge(__isl_keep isl_val *v1,
543 __isl_keep isl_val *v2);
544 int isl_val_eq(__isl_keep isl_val *v1,
545 __isl_keep isl_val *v2);
546 int isl_val_ne(__isl_keep isl_val *v1,
547 __isl_keep isl_val *v2);
548 int isl_val_abs_eq(__isl_keep isl_val *v1,
549 __isl_keep isl_val *v2);
551 The function C<isl_val_abs_eq> checks whether its two arguments
552 are equal in absolute value.
554 For integer C<isl_val>s we additionally have the following binary property.
557 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
558 __isl_keep isl_val *v2);
560 An C<isl_val> can also be compared to an integer using the following
561 function. The result is undefined for NaN.
564 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
566 The following unary operations are available on C<isl_val>s.
569 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
570 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
571 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
572 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
573 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
574 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
576 The following binary operations are available on C<isl_val>s.
579 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
580 __isl_take isl_val *v2);
581 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
582 __isl_take isl_val *v2);
583 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
584 __isl_take isl_val *v2);
585 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
587 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
588 __isl_take isl_val *v2);
589 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
591 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
592 __isl_take isl_val *v2);
593 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
595 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
596 __isl_take isl_val *v2);
598 On integer values, we additionally have the following operations.
601 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
602 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
603 __isl_take isl_val *v2);
604 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
605 __isl_take isl_val *v2);
606 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
607 __isl_take isl_val *v2, __isl_give isl_val **x,
608 __isl_give isl_val **y);
610 The function C<isl_val_gcdext> returns the greatest common divisor g
611 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
612 that C<*x> * C<v1> + C<*y> * C<v2> = g.
614 A value can be read from input using
617 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
620 A value can be printed using
623 __isl_give isl_printer *isl_printer_print_val(
624 __isl_take isl_printer *p, __isl_keep isl_val *v);
626 =head3 GMP specific functions
628 These functions are only available if C<isl> has been compiled with C<GMP>
631 Specific integer and rational values can be created from C<GMP> values using
632 the following functions.
634 #include <isl/val_gmp.h>
635 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
637 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
638 const mpz_t n, const mpz_t d);
640 The numerator and denominator of a rational value can be extracted as
641 C<GMP> values using the following functions.
643 #include <isl/val_gmp.h>
644 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
645 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
647 =head2 Sets and Relations
649 C<isl> uses six types of objects for representing sets and relations,
650 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
651 C<isl_union_set> and C<isl_union_map>.
652 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
653 can be described as a conjunction of affine constraints, while
654 C<isl_set> and C<isl_map> represent unions of
655 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
656 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
657 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
658 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
659 where spaces are considered different if they have a different number
660 of dimensions and/or different names (see L<"Spaces">).
661 The difference between sets and relations (maps) is that sets have
662 one set of variables, while relations have two sets of variables,
663 input variables and output variables.
665 =head2 Error Handling
667 C<isl> supports different ways to react in case a runtime error is triggered.
668 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
669 with two maps that have incompatible spaces. There are three possible ways
670 to react on error: to warn, to continue or to abort.
672 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
673 the last error in the corresponding C<isl_ctx> and the function in which the
674 error was triggered returns C<NULL>. An error does not corrupt internal state,
675 such that isl can continue to be used. C<isl> also provides functions to
676 read the last error and to reset the memory that stores the last error. The
677 last error is only stored for information purposes. Its presence does not
678 change the behavior of C<isl>. Hence, resetting an error is not required to
679 continue to use isl, but only to observe new errors.
682 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
683 void isl_ctx_reset_error(isl_ctx *ctx);
685 Another option is to continue on error. This is similar to warn on error mode,
686 except that C<isl> does not print any warning. This allows a program to
687 implement its own error reporting.
689 The last option is to directly abort the execution of the program from within
690 the isl library. This makes it obviously impossible to recover from an error,
691 but it allows to directly spot the error location. By aborting on error,
692 debuggers break at the location the error occurred and can provide a stack
693 trace. Other tools that automatically provide stack traces on abort or that do
694 not want to continue execution after an error was triggered may also prefer to
697 The on error behavior of isl can be specified by calling
698 C<isl_options_set_on_error> or by setting the command line option
699 C<--isl-on-error>. Valid arguments for the function call are
700 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
701 choices for the command line option are C<warn>, C<continue> and C<abort>.
702 It is also possible to query the current error mode.
704 #include <isl/options.h>
705 int isl_options_set_on_error(isl_ctx *ctx, int val);
706 int isl_options_get_on_error(isl_ctx *ctx);
710 Identifiers are used to identify both individual dimensions
711 and tuples of dimensions. They consist of an optional name and an optional
712 user pointer. The name and the user pointer cannot both be C<NULL>, however.
713 Identifiers with the same name but different pointer values
714 are considered to be distinct.
715 Similarly, identifiers with different names but the same pointer value
716 are also considered to be distinct.
717 Equal identifiers are represented using the same object.
718 Pairs of identifiers can therefore be tested for equality using the
720 Identifiers can be constructed, copied, freed, inspected and printed
721 using the following functions.
724 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
725 __isl_keep const char *name, void *user);
726 __isl_give isl_id *isl_id_set_free_user(
727 __isl_take isl_id *id,
728 __isl_give void (*free_user)(void *user));
729 __isl_give isl_id *isl_id_copy(isl_id *id);
730 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
732 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
733 void *isl_id_get_user(__isl_keep isl_id *id);
734 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
736 __isl_give isl_printer *isl_printer_print_id(
737 __isl_take isl_printer *p, __isl_keep isl_id *id);
739 The callback set by C<isl_id_set_free_user> is called on the user
740 pointer when the last reference to the C<isl_id> is freed.
741 Note that C<isl_id_get_name> returns a pointer to some internal
742 data structure, so the result can only be used while the
743 corresponding C<isl_id> is alive.
747 Whenever a new set, relation or similar object is created from scratch,
748 the space in which it lives needs to be specified using an C<isl_space>.
749 Each space involves zero or more parameters and zero, one or two
750 tuples of set or input/output dimensions. The parameters and dimensions
751 are identified by an C<isl_dim_type> and a position.
752 The type C<isl_dim_param> refers to parameters,
753 the type C<isl_dim_set> refers to set dimensions (for spaces
754 with a single tuple of dimensions) and the types C<isl_dim_in>
755 and C<isl_dim_out> refer to input and output dimensions
756 (for spaces with two tuples of dimensions).
757 Local spaces (see L</"Local Spaces">) also contain dimensions
758 of type C<isl_dim_div>.
759 Note that parameters are only identified by their position within
760 a given object. Across different objects, parameters are (usually)
761 identified by their names or identifiers. Only unnamed parameters
762 are identified by their positions across objects. The use of unnamed
763 parameters is discouraged.
765 #include <isl/space.h>
766 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
767 unsigned nparam, unsigned n_in, unsigned n_out);
768 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
770 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
771 unsigned nparam, unsigned dim);
772 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
773 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
774 unsigned isl_space_dim(__isl_keep isl_space *space,
775 enum isl_dim_type type);
777 The space used for creating a parameter domain
778 needs to be created using C<isl_space_params_alloc>.
779 For other sets, the space
780 needs to be created using C<isl_space_set_alloc>, while
781 for a relation, the space
782 needs to be created using C<isl_space_alloc>.
783 C<isl_space_dim> can be used
784 to find out the number of dimensions of each type in
785 a space, where type may be
786 C<isl_dim_param>, C<isl_dim_in> (only for relations),
787 C<isl_dim_out> (only for relations), C<isl_dim_set>
788 (only for sets) or C<isl_dim_all>.
790 To check whether a given space is that of a set or a map
791 or whether it is a parameter space, use these functions:
793 #include <isl/space.h>
794 int isl_space_is_params(__isl_keep isl_space *space);
795 int isl_space_is_set(__isl_keep isl_space *space);
796 int isl_space_is_map(__isl_keep isl_space *space);
798 Spaces can be compared using the following functions:
800 #include <isl/space.h>
801 int isl_space_is_equal(__isl_keep isl_space *space1,
802 __isl_keep isl_space *space2);
803 int isl_space_is_domain(__isl_keep isl_space *space1,
804 __isl_keep isl_space *space2);
805 int isl_space_is_range(__isl_keep isl_space *space1,
806 __isl_keep isl_space *space2);
807 int isl_space_tuple_is_equal(
808 __isl_keep isl_space *space1,
809 enum isl_dim_type type1,
810 __isl_keep isl_space *space2,
811 enum isl_dim_type type2);
813 C<isl_space_is_domain> checks whether the first argument is equal
814 to the domain of the second argument. This requires in particular that
815 the first argument is a set space and that the second argument
816 is a map space. C<isl_space_tuple_is_equal> checks whether the given
817 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
818 spaces are the same. That is, it checks if they have the same
819 identifier (if any), the same dimension and the same internal structure
822 It is often useful to create objects that live in the
823 same space as some other object. This can be accomplished
824 by creating the new objects
825 (see L</"Creating New Sets and Relations"> or
826 L</"Creating New (Piecewise) Quasipolynomials">) based on the space
827 of the original object.
830 __isl_give isl_space *isl_basic_set_get_space(
831 __isl_keep isl_basic_set *bset);
832 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
834 #include <isl/union_set.h>
835 __isl_give isl_space *isl_union_set_get_space(
836 __isl_keep isl_union_set *uset);
839 __isl_give isl_space *isl_basic_map_get_space(
840 __isl_keep isl_basic_map *bmap);
841 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
843 #include <isl/union_map.h>
844 __isl_give isl_space *isl_union_map_get_space(
845 __isl_keep isl_union_map *umap);
847 #include <isl/constraint.h>
848 __isl_give isl_space *isl_constraint_get_space(
849 __isl_keep isl_constraint *constraint);
851 #include <isl/polynomial.h>
852 __isl_give isl_space *isl_qpolynomial_get_domain_space(
853 __isl_keep isl_qpolynomial *qp);
854 __isl_give isl_space *isl_qpolynomial_get_space(
855 __isl_keep isl_qpolynomial *qp);
856 __isl_give isl_space *isl_qpolynomial_fold_get_space(
857 __isl_keep isl_qpolynomial_fold *fold);
858 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
859 __isl_keep isl_pw_qpolynomial *pwqp);
860 __isl_give isl_space *isl_pw_qpolynomial_get_space(
861 __isl_keep isl_pw_qpolynomial *pwqp);
862 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
863 __isl_keep isl_pw_qpolynomial_fold *pwf);
864 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
865 __isl_keep isl_pw_qpolynomial_fold *pwf);
866 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
867 __isl_keep isl_union_pw_qpolynomial *upwqp);
868 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
869 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
872 __isl_give isl_space *isl_multi_val_get_space(
873 __isl_keep isl_multi_val *mv);
876 __isl_give isl_space *isl_aff_get_domain_space(
877 __isl_keep isl_aff *aff);
878 __isl_give isl_space *isl_aff_get_space(
879 __isl_keep isl_aff *aff);
880 __isl_give isl_space *isl_pw_aff_get_domain_space(
881 __isl_keep isl_pw_aff *pwaff);
882 __isl_give isl_space *isl_pw_aff_get_space(
883 __isl_keep isl_pw_aff *pwaff);
884 __isl_give isl_space *isl_multi_aff_get_domain_space(
885 __isl_keep isl_multi_aff *maff);
886 __isl_give isl_space *isl_multi_aff_get_space(
887 __isl_keep isl_multi_aff *maff);
888 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
889 __isl_keep isl_pw_multi_aff *pma);
890 __isl_give isl_space *isl_pw_multi_aff_get_space(
891 __isl_keep isl_pw_multi_aff *pma);
892 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
893 __isl_keep isl_union_pw_multi_aff *upma);
894 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
895 __isl_keep isl_multi_pw_aff *mpa);
896 __isl_give isl_space *isl_multi_pw_aff_get_space(
897 __isl_keep isl_multi_pw_aff *mpa);
899 #include <isl/point.h>
900 __isl_give isl_space *isl_point_get_space(
901 __isl_keep isl_point *pnt);
903 The identifiers or names of the individual dimensions may be set or read off
904 using the following functions.
906 #include <isl/space.h>
907 __isl_give isl_space *isl_space_set_dim_id(
908 __isl_take isl_space *space,
909 enum isl_dim_type type, unsigned pos,
910 __isl_take isl_id *id);
911 int isl_space_has_dim_id(__isl_keep isl_space *space,
912 enum isl_dim_type type, unsigned pos);
913 __isl_give isl_id *isl_space_get_dim_id(
914 __isl_keep isl_space *space,
915 enum isl_dim_type type, unsigned pos);
916 __isl_give isl_space *isl_space_set_dim_name(
917 __isl_take isl_space *space,
918 enum isl_dim_type type, unsigned pos,
919 __isl_keep const char *name);
920 int isl_space_has_dim_name(__isl_keep isl_space *space,
921 enum isl_dim_type type, unsigned pos);
922 __isl_keep const char *isl_space_get_dim_name(
923 __isl_keep isl_space *space,
924 enum isl_dim_type type, unsigned pos);
926 Note that C<isl_space_get_name> returns a pointer to some internal
927 data structure, so the result can only be used while the
928 corresponding C<isl_space> is alive.
929 Also note that every function that operates on two sets or relations
930 requires that both arguments have the same parameters. This also
931 means that if one of the arguments has named parameters, then the
932 other needs to have named parameters too and the names need to match.
933 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
934 arguments may have different parameters (as long as they are named),
935 in which case the result will have as parameters the union of the parameters of
938 Given the identifier or name of a dimension (typically a parameter),
939 its position can be obtained from the following function.
941 #include <isl/space.h>
942 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
943 enum isl_dim_type type, __isl_keep isl_id *id);
944 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
945 enum isl_dim_type type, const char *name);
947 The identifiers or names of entire spaces may be set or read off
948 using the following functions.
950 #include <isl/space.h>
951 __isl_give isl_space *isl_space_set_tuple_id(
952 __isl_take isl_space *space,
953 enum isl_dim_type type, __isl_take isl_id *id);
954 __isl_give isl_space *isl_space_reset_tuple_id(
955 __isl_take isl_space *space, enum isl_dim_type type);
956 int isl_space_has_tuple_id(__isl_keep isl_space *space,
957 enum isl_dim_type type);
958 __isl_give isl_id *isl_space_get_tuple_id(
959 __isl_keep isl_space *space, enum isl_dim_type type);
960 __isl_give isl_space *isl_space_set_tuple_name(
961 __isl_take isl_space *space,
962 enum isl_dim_type type, const char *s);
963 int isl_space_has_tuple_name(__isl_keep isl_space *space,
964 enum isl_dim_type type);
965 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
966 enum isl_dim_type type);
968 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
969 or C<isl_dim_set>. As with C<isl_space_get_name>,
970 the C<isl_space_get_tuple_name> function returns a pointer to some internal
972 Binary operations require the corresponding spaces of their arguments
973 to have the same name.
975 To keep the names of all parameters and tuples, but reset the user pointers
976 of all the corresponding identifiers, use the following function.
978 __isl_give isl_space *isl_space_reset_user(
979 __isl_take isl_space *space);
981 Spaces can be nested. In particular, the domain of a set or
982 the domain or range of a relation can be a nested relation.
983 This process is also called I<wrapping>.
984 The functions for detecting, constructing and deconstructing
985 such nested spaces can be found in the wrapping properties
986 of L</"Unary Properties">, the wrapping operations
987 of L</"Unary Operations"> and the Cartesian product operations
988 of L</"Basic Operations">.
990 Spaces can be created from other spaces
991 using the functions described in L</"Unary Operations">
992 and L</"Binary Operations">.
996 A local space is essentially a space with
997 zero or more existentially quantified variables.
998 The local space of a (constraint of a) basic set or relation can be obtained
999 using the following functions.
1001 #include <isl/constraint.h>
1002 __isl_give isl_local_space *isl_constraint_get_local_space(
1003 __isl_keep isl_constraint *constraint);
1005 #include <isl/set.h>
1006 __isl_give isl_local_space *isl_basic_set_get_local_space(
1007 __isl_keep isl_basic_set *bset);
1009 #include <isl/map.h>
1010 __isl_give isl_local_space *isl_basic_map_get_local_space(
1011 __isl_keep isl_basic_map *bmap);
1013 A new local space can be created from a space using
1015 #include <isl/local_space.h>
1016 __isl_give isl_local_space *isl_local_space_from_space(
1017 __isl_take isl_space *space);
1019 They can be inspected, modified, copied and freed using the following functions.
1021 #include <isl/local_space.h>
1022 isl_ctx *isl_local_space_get_ctx(
1023 __isl_keep isl_local_space *ls);
1024 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1025 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1026 enum isl_dim_type type);
1027 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1028 __isl_take isl_local_space *ls,
1029 enum isl_dim_type type, __isl_take isl_id *id);
1030 int isl_local_space_has_dim_id(
1031 __isl_keep isl_local_space *ls,
1032 enum isl_dim_type type, unsigned pos);
1033 __isl_give isl_id *isl_local_space_get_dim_id(
1034 __isl_keep isl_local_space *ls,
1035 enum isl_dim_type type, unsigned pos);
1036 int isl_local_space_has_dim_name(
1037 __isl_keep isl_local_space *ls,
1038 enum isl_dim_type type, unsigned pos)
1039 const char *isl_local_space_get_dim_name(
1040 __isl_keep isl_local_space *ls,
1041 enum isl_dim_type type, unsigned pos);
1042 __isl_give isl_local_space *isl_local_space_set_dim_name(
1043 __isl_take isl_local_space *ls,
1044 enum isl_dim_type type, unsigned pos, const char *s);
1045 __isl_give isl_local_space *isl_local_space_set_dim_id(
1046 __isl_take isl_local_space *ls,
1047 enum isl_dim_type type, unsigned pos,
1048 __isl_take isl_id *id);
1049 __isl_give isl_space *isl_local_space_get_space(
1050 __isl_keep isl_local_space *ls);
1051 __isl_give isl_aff *isl_local_space_get_div(
1052 __isl_keep isl_local_space *ls, int pos);
1053 __isl_give isl_local_space *isl_local_space_copy(
1054 __isl_keep isl_local_space *ls);
1055 __isl_null isl_local_space *isl_local_space_free(
1056 __isl_take isl_local_space *ls);
1058 Note that C<isl_local_space_get_div> can only be used on local spaces
1061 Two local spaces can be compared using
1063 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1064 __isl_keep isl_local_space *ls2);
1066 Local spaces can be created from other local spaces
1067 using the functions described in L</"Unary Operations">
1068 and L</"Binary Operations">.
1070 =head2 Input and Output
1072 C<isl> supports its own input/output format, which is similar
1073 to the C<Omega> format, but also supports the C<PolyLib> format
1076 =head3 C<isl> format
1078 The C<isl> format is similar to that of C<Omega>, but has a different
1079 syntax for describing the parameters and allows for the definition
1080 of an existentially quantified variable as the integer division
1081 of an affine expression.
1082 For example, the set of integers C<i> between C<0> and C<n>
1083 such that C<i % 10 <= 6> can be described as
1085 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1088 A set or relation can have several disjuncts, separated
1089 by the keyword C<or>. Each disjunct is either a conjunction
1090 of constraints or a projection (C<exists>) of a conjunction
1091 of constraints. The constraints are separated by the keyword
1094 =head3 C<PolyLib> format
1096 If the represented set is a union, then the first line
1097 contains a single number representing the number of disjuncts.
1098 Otherwise, a line containing the number C<1> is optional.
1100 Each disjunct is represented by a matrix of constraints.
1101 The first line contains two numbers representing
1102 the number of rows and columns,
1103 where the number of rows is equal to the number of constraints
1104 and the number of columns is equal to two plus the number of variables.
1105 The following lines contain the actual rows of the constraint matrix.
1106 In each row, the first column indicates whether the constraint
1107 is an equality (C<0>) or inequality (C<1>). The final column
1108 corresponds to the constant term.
1110 If the set is parametric, then the coefficients of the parameters
1111 appear in the last columns before the constant column.
1112 The coefficients of any existentially quantified variables appear
1113 between those of the set variables and those of the parameters.
1115 =head3 Extended C<PolyLib> format
1117 The extended C<PolyLib> format is nearly identical to the
1118 C<PolyLib> format. The only difference is that the line
1119 containing the number of rows and columns of a constraint matrix
1120 also contains four additional numbers:
1121 the number of output dimensions, the number of input dimensions,
1122 the number of local dimensions (i.e., the number of existentially
1123 quantified variables) and the number of parameters.
1124 For sets, the number of ``output'' dimensions is equal
1125 to the number of set dimensions, while the number of ``input''
1130 #include <isl/set.h>
1131 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1132 isl_ctx *ctx, FILE *input);
1133 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1134 isl_ctx *ctx, const char *str);
1135 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1137 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1140 #include <isl/map.h>
1141 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1142 isl_ctx *ctx, FILE *input);
1143 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1144 isl_ctx *ctx, const char *str);
1145 __isl_give isl_map *isl_map_read_from_file(
1146 isl_ctx *ctx, FILE *input);
1147 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1150 #include <isl/union_set.h>
1151 __isl_give isl_union_set *isl_union_set_read_from_file(
1152 isl_ctx *ctx, FILE *input);
1153 __isl_give isl_union_set *isl_union_set_read_from_str(
1154 isl_ctx *ctx, const char *str);
1156 #include <isl/union_map.h>
1157 __isl_give isl_union_map *isl_union_map_read_from_file(
1158 isl_ctx *ctx, FILE *input);
1159 __isl_give isl_union_map *isl_union_map_read_from_str(
1160 isl_ctx *ctx, const char *str);
1162 The input format is autodetected and may be either the C<PolyLib> format
1163 or the C<isl> format.
1167 Before anything can be printed, an C<isl_printer> needs to
1170 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1172 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1173 __isl_null isl_printer *isl_printer_free(
1174 __isl_take isl_printer *printer);
1175 __isl_give char *isl_printer_get_str(
1176 __isl_keep isl_printer *printer);
1178 The printer can be inspected using the following functions.
1180 FILE *isl_printer_get_file(
1181 __isl_keep isl_printer *printer);
1182 int isl_printer_get_output_format(
1183 __isl_keep isl_printer *p);
1185 The behavior of the printer can be modified in various ways
1187 __isl_give isl_printer *isl_printer_set_output_format(
1188 __isl_take isl_printer *p, int output_format);
1189 __isl_give isl_printer *isl_printer_set_indent(
1190 __isl_take isl_printer *p, int indent);
1191 __isl_give isl_printer *isl_printer_set_indent_prefix(
1192 __isl_take isl_printer *p, const char *prefix);
1193 __isl_give isl_printer *isl_printer_indent(
1194 __isl_take isl_printer *p, int indent);
1195 __isl_give isl_printer *isl_printer_set_prefix(
1196 __isl_take isl_printer *p, const char *prefix);
1197 __isl_give isl_printer *isl_printer_set_suffix(
1198 __isl_take isl_printer *p, const char *suffix);
1200 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1201 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1202 and defaults to C<ISL_FORMAT_ISL>.
1203 Each line in the output is prefixed by C<indent_prefix>,
1204 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
1205 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1206 In the C<PolyLib> format output,
1207 the coefficients of the existentially quantified variables
1208 appear between those of the set variables and those
1210 The function C<isl_printer_indent> increases the indentation
1211 by the specified amount (which may be negative).
1213 To actually print something, use
1215 #include <isl/printer.h>
1216 __isl_give isl_printer *isl_printer_print_double(
1217 __isl_take isl_printer *p, double d);
1219 #include <isl/set.h>
1220 __isl_give isl_printer *isl_printer_print_basic_set(
1221 __isl_take isl_printer *printer,
1222 __isl_keep isl_basic_set *bset);
1223 __isl_give isl_printer *isl_printer_print_set(
1224 __isl_take isl_printer *printer,
1225 __isl_keep isl_set *set);
1227 #include <isl/map.h>
1228 __isl_give isl_printer *isl_printer_print_basic_map(
1229 __isl_take isl_printer *printer,
1230 __isl_keep isl_basic_map *bmap);
1231 __isl_give isl_printer *isl_printer_print_map(
1232 __isl_take isl_printer *printer,
1233 __isl_keep isl_map *map);
1235 #include <isl/union_set.h>
1236 __isl_give isl_printer *isl_printer_print_union_set(
1237 __isl_take isl_printer *p,
1238 __isl_keep isl_union_set *uset);
1240 #include <isl/union_map.h>
1241 __isl_give isl_printer *isl_printer_print_union_map(
1242 __isl_take isl_printer *p,
1243 __isl_keep isl_union_map *umap);
1245 When called on a file printer, the following function flushes
1246 the file. When called on a string printer, the buffer is cleared.
1248 __isl_give isl_printer *isl_printer_flush(
1249 __isl_take isl_printer *p);
1251 =head2 Creating New Sets and Relations
1253 C<isl> has functions for creating some standard sets and relations.
1257 =item * Empty sets and relations
1259 __isl_give isl_basic_set *isl_basic_set_empty(
1260 __isl_take isl_space *space);
1261 __isl_give isl_basic_map *isl_basic_map_empty(
1262 __isl_take isl_space *space);
1263 __isl_give isl_set *isl_set_empty(
1264 __isl_take isl_space *space);
1265 __isl_give isl_map *isl_map_empty(
1266 __isl_take isl_space *space);
1267 __isl_give isl_union_set *isl_union_set_empty(
1268 __isl_take isl_space *space);
1269 __isl_give isl_union_map *isl_union_map_empty(
1270 __isl_take isl_space *space);
1272 For C<isl_union_set>s and C<isl_union_map>s, the space
1273 is only used to specify the parameters.
1275 =item * Universe sets and relations
1277 __isl_give isl_basic_set *isl_basic_set_universe(
1278 __isl_take isl_space *space);
1279 __isl_give isl_basic_map *isl_basic_map_universe(
1280 __isl_take isl_space *space);
1281 __isl_give isl_set *isl_set_universe(
1282 __isl_take isl_space *space);
1283 __isl_give isl_map *isl_map_universe(
1284 __isl_take isl_space *space);
1285 __isl_give isl_union_set *isl_union_set_universe(
1286 __isl_take isl_union_set *uset);
1287 __isl_give isl_union_map *isl_union_map_universe(
1288 __isl_take isl_union_map *umap);
1290 The sets and relations constructed by the functions above
1291 contain all integer values, while those constructed by the
1292 functions below only contain non-negative values.
1294 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1295 __isl_take isl_space *space);
1296 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1297 __isl_take isl_space *space);
1298 __isl_give isl_set *isl_set_nat_universe(
1299 __isl_take isl_space *space);
1300 __isl_give isl_map *isl_map_nat_universe(
1301 __isl_take isl_space *space);
1303 =item * Identity relations
1305 __isl_give isl_basic_map *isl_basic_map_identity(
1306 __isl_take isl_space *space);
1307 __isl_give isl_map *isl_map_identity(
1308 __isl_take isl_space *space);
1310 The number of input and output dimensions in C<space> needs
1313 =item * Lexicographic order
1315 __isl_give isl_map *isl_map_lex_lt(
1316 __isl_take isl_space *set_space);
1317 __isl_give isl_map *isl_map_lex_le(
1318 __isl_take isl_space *set_space);
1319 __isl_give isl_map *isl_map_lex_gt(
1320 __isl_take isl_space *set_space);
1321 __isl_give isl_map *isl_map_lex_ge(
1322 __isl_take isl_space *set_space);
1323 __isl_give isl_map *isl_map_lex_lt_first(
1324 __isl_take isl_space *space, unsigned n);
1325 __isl_give isl_map *isl_map_lex_le_first(
1326 __isl_take isl_space *space, unsigned n);
1327 __isl_give isl_map *isl_map_lex_gt_first(
1328 __isl_take isl_space *space, unsigned n);
1329 __isl_give isl_map *isl_map_lex_ge_first(
1330 __isl_take isl_space *space, unsigned n);
1332 The first four functions take a space for a B<set>
1333 and return relations that express that the elements in the domain
1334 are lexicographically less
1335 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1336 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1337 than the elements in the range.
1338 The last four functions take a space for a map
1339 and return relations that express that the first C<n> dimensions
1340 in the domain are lexicographically less
1341 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1342 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1343 than the first C<n> dimensions in the range.
1347 A basic set or relation can be converted to a set or relation
1348 using the following functions.
1350 __isl_give isl_set *isl_set_from_basic_set(
1351 __isl_take isl_basic_set *bset);
1352 __isl_give isl_map *isl_map_from_basic_map(
1353 __isl_take isl_basic_map *bmap);
1355 Sets and relations can be converted to union sets and relations
1356 using the following functions.
1358 __isl_give isl_union_set *isl_union_set_from_basic_set(
1359 __isl_take isl_basic_set *bset);
1360 __isl_give isl_union_map *isl_union_map_from_basic_map(
1361 __isl_take isl_basic_map *bmap);
1362 __isl_give isl_union_set *isl_union_set_from_set(
1363 __isl_take isl_set *set);
1364 __isl_give isl_union_map *isl_union_map_from_map(
1365 __isl_take isl_map *map);
1367 The inverse conversions below can only be used if the input
1368 union set or relation is known to contain elements in exactly one
1371 __isl_give isl_set *isl_set_from_union_set(
1372 __isl_take isl_union_set *uset);
1373 __isl_give isl_map *isl_map_from_union_map(
1374 __isl_take isl_union_map *umap);
1376 Sets and relations can be copied and freed again using the following
1379 __isl_give isl_basic_set *isl_basic_set_copy(
1380 __isl_keep isl_basic_set *bset);
1381 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1382 __isl_give isl_union_set *isl_union_set_copy(
1383 __isl_keep isl_union_set *uset);
1384 __isl_give isl_basic_map *isl_basic_map_copy(
1385 __isl_keep isl_basic_map *bmap);
1386 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1387 __isl_give isl_union_map *isl_union_map_copy(
1388 __isl_keep isl_union_map *umap);
1389 __isl_null isl_basic_set *isl_basic_set_free(
1390 __isl_take isl_basic_set *bset);
1391 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1392 __isl_null isl_union_set *isl_union_set_free(
1393 __isl_take isl_union_set *uset);
1394 __isl_null isl_basic_map *isl_basic_map_free(
1395 __isl_take isl_basic_map *bmap);
1396 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1397 __isl_null isl_union_map *isl_union_map_free(
1398 __isl_take isl_union_map *umap);
1400 Other sets and relations can be constructed by starting
1401 from a universe set or relation, adding equality and/or
1402 inequality constraints and then projecting out the
1403 existentially quantified variables, if any.
1404 Constraints can be constructed, manipulated and
1405 added to (or removed from) (basic) sets and relations
1406 using the following functions.
1408 #include <isl/constraint.h>
1409 __isl_give isl_constraint *isl_equality_alloc(
1410 __isl_take isl_local_space *ls);
1411 __isl_give isl_constraint *isl_inequality_alloc(
1412 __isl_take isl_local_space *ls);
1413 __isl_give isl_constraint *isl_constraint_set_constant_si(
1414 __isl_take isl_constraint *constraint, int v);
1415 __isl_give isl_constraint *isl_constraint_set_constant_val(
1416 __isl_take isl_constraint *constraint,
1417 __isl_take isl_val *v);
1418 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1419 __isl_take isl_constraint *constraint,
1420 enum isl_dim_type type, int pos, int v);
1421 __isl_give isl_constraint *
1422 isl_constraint_set_coefficient_val(
1423 __isl_take isl_constraint *constraint,
1424 enum isl_dim_type type, int pos,
1425 __isl_take isl_val *v);
1426 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1427 __isl_take isl_basic_map *bmap,
1428 __isl_take isl_constraint *constraint);
1429 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1430 __isl_take isl_basic_set *bset,
1431 __isl_take isl_constraint *constraint);
1432 __isl_give isl_map *isl_map_add_constraint(
1433 __isl_take isl_map *map,
1434 __isl_take isl_constraint *constraint);
1435 __isl_give isl_set *isl_set_add_constraint(
1436 __isl_take isl_set *set,
1437 __isl_take isl_constraint *constraint);
1438 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1439 __isl_take isl_basic_set *bset,
1440 __isl_take isl_constraint *constraint);
1442 For example, to create a set containing the even integers
1443 between 10 and 42, you would use the following code.
1446 isl_local_space *ls;
1448 isl_basic_set *bset;
1450 space = isl_space_set_alloc(ctx, 0, 2);
1451 bset = isl_basic_set_universe(isl_space_copy(space));
1452 ls = isl_local_space_from_space(space);
1454 c = isl_equality_alloc(isl_local_space_copy(ls));
1455 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1456 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1457 bset = isl_basic_set_add_constraint(bset, c);
1459 c = isl_inequality_alloc(isl_local_space_copy(ls));
1460 c = isl_constraint_set_constant_si(c, -10);
1461 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1462 bset = isl_basic_set_add_constraint(bset, c);
1464 c = isl_inequality_alloc(ls);
1465 c = isl_constraint_set_constant_si(c, 42);
1466 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1467 bset = isl_basic_set_add_constraint(bset, c);
1469 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1473 isl_basic_set *bset;
1474 bset = isl_basic_set_read_from_str(ctx,
1475 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1477 A basic set or relation can also be constructed from two matrices
1478 describing the equalities and the inequalities.
1480 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1481 __isl_take isl_space *space,
1482 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1483 enum isl_dim_type c1,
1484 enum isl_dim_type c2, enum isl_dim_type c3,
1485 enum isl_dim_type c4);
1486 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1487 __isl_take isl_space *space,
1488 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1489 enum isl_dim_type c1,
1490 enum isl_dim_type c2, enum isl_dim_type c3,
1491 enum isl_dim_type c4, enum isl_dim_type c5);
1493 The C<isl_dim_type> arguments indicate the order in which
1494 different kinds of variables appear in the input matrices
1495 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1496 C<isl_dim_set> and C<isl_dim_div> for sets and
1497 of C<isl_dim_cst>, C<isl_dim_param>,
1498 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1500 A (basic or union) set or relation can also be constructed from a
1501 (union) (piecewise) (multiple) affine expression
1502 or a list of affine expressions
1503 (See L<"Piecewise Quasi Affine Expressions"> and
1504 L<"Piecewise Multiple Quasi Affine Expressions">).
1506 __isl_give isl_basic_map *isl_basic_map_from_aff(
1507 __isl_take isl_aff *aff);
1508 __isl_give isl_map *isl_map_from_aff(
1509 __isl_take isl_aff *aff);
1510 __isl_give isl_set *isl_set_from_pw_aff(
1511 __isl_take isl_pw_aff *pwaff);
1512 __isl_give isl_map *isl_map_from_pw_aff(
1513 __isl_take isl_pw_aff *pwaff);
1514 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1515 __isl_take isl_space *domain_space,
1516 __isl_take isl_aff_list *list);
1517 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1518 __isl_take isl_multi_aff *maff)
1519 __isl_give isl_map *isl_map_from_multi_aff(
1520 __isl_take isl_multi_aff *maff)
1521 __isl_give isl_set *isl_set_from_pw_multi_aff(
1522 __isl_take isl_pw_multi_aff *pma);
1523 __isl_give isl_map *isl_map_from_pw_multi_aff(
1524 __isl_take isl_pw_multi_aff *pma);
1525 __isl_give isl_set *isl_set_from_multi_pw_aff(
1526 __isl_take isl_multi_pw_aff *mpa);
1527 __isl_give isl_map *isl_map_from_multi_pw_aff(
1528 __isl_take isl_multi_pw_aff *mpa);
1529 __isl_give isl_union_map *
1530 isl_union_map_from_union_pw_multi_aff(
1531 __isl_take isl_union_pw_multi_aff *upma);
1533 The C<domain_space> argument describes the domain of the resulting
1534 basic relation. It is required because the C<list> may consist
1535 of zero affine expressions.
1537 =head2 Inspecting Sets and Relations
1539 Usually, the user should not have to care about the actual constraints
1540 of the sets and maps, but should instead apply the abstract operations
1541 explained in the following sections.
1542 Occasionally, however, it may be required to inspect the individual
1543 coefficients of the constraints. This section explains how to do so.
1544 In these cases, it may also be useful to have C<isl> compute
1545 an explicit representation of the existentially quantified variables.
1547 __isl_give isl_set *isl_set_compute_divs(
1548 __isl_take isl_set *set);
1549 __isl_give isl_map *isl_map_compute_divs(
1550 __isl_take isl_map *map);
1551 __isl_give isl_union_set *isl_union_set_compute_divs(
1552 __isl_take isl_union_set *uset);
1553 __isl_give isl_union_map *isl_union_map_compute_divs(
1554 __isl_take isl_union_map *umap);
1556 This explicit representation defines the existentially quantified
1557 variables as integer divisions of the other variables, possibly
1558 including earlier existentially quantified variables.
1559 An explicitly represented existentially quantified variable therefore
1560 has a unique value when the values of the other variables are known.
1561 If, furthermore, the same existentials, i.e., existentials
1562 with the same explicit representations, should appear in the
1563 same order in each of the disjuncts of a set or map, then the user should call
1564 either of the following functions.
1566 __isl_give isl_set *isl_set_align_divs(
1567 __isl_take isl_set *set);
1568 __isl_give isl_map *isl_map_align_divs(
1569 __isl_take isl_map *map);
1571 Alternatively, the existentially quantified variables can be removed
1572 using the following functions, which compute an overapproximation.
1574 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1575 __isl_take isl_basic_set *bset);
1576 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1577 __isl_take isl_basic_map *bmap);
1578 __isl_give isl_set *isl_set_remove_divs(
1579 __isl_take isl_set *set);
1580 __isl_give isl_map *isl_map_remove_divs(
1581 __isl_take isl_map *map);
1583 It is also possible to only remove those divs that are defined
1584 in terms of a given range of dimensions or only those for which
1585 no explicit representation is known.
1587 __isl_give isl_basic_set *
1588 isl_basic_set_remove_divs_involving_dims(
1589 __isl_take isl_basic_set *bset,
1590 enum isl_dim_type type,
1591 unsigned first, unsigned n);
1592 __isl_give isl_basic_map *
1593 isl_basic_map_remove_divs_involving_dims(
1594 __isl_take isl_basic_map *bmap,
1595 enum isl_dim_type type,
1596 unsigned first, unsigned n);
1597 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1598 __isl_take isl_set *set, enum isl_dim_type type,
1599 unsigned first, unsigned n);
1600 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1601 __isl_take isl_map *map, enum isl_dim_type type,
1602 unsigned first, unsigned n);
1604 __isl_give isl_basic_set *
1605 isl_basic_set_remove_unknown_divs(
1606 __isl_take isl_basic_set *bset);
1607 __isl_give isl_set *isl_set_remove_unknown_divs(
1608 __isl_take isl_set *set);
1609 __isl_give isl_map *isl_map_remove_unknown_divs(
1610 __isl_take isl_map *map);
1612 To iterate over all the sets or maps in a union set or map, use
1614 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1615 int (*fn)(__isl_take isl_set *set, void *user),
1617 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1618 int (*fn)(__isl_take isl_map *map, void *user),
1621 The number of sets or maps in a union set or map can be obtained
1624 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1625 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1627 To extract the set or map in a given space from a union, use
1629 __isl_give isl_set *isl_union_set_extract_set(
1630 __isl_keep isl_union_set *uset,
1631 __isl_take isl_space *space);
1632 __isl_give isl_map *isl_union_map_extract_map(
1633 __isl_keep isl_union_map *umap,
1634 __isl_take isl_space *space);
1636 To iterate over all the basic sets or maps in a set or map, use
1638 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1639 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1641 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1642 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1645 The callback function C<fn> should return 0 if successful and
1646 -1 if an error occurs. In the latter case, or if any other error
1647 occurs, the above functions will return -1.
1649 It should be noted that C<isl> does not guarantee that
1650 the basic sets or maps passed to C<fn> are disjoint.
1651 If this is required, then the user should call one of
1652 the following functions first.
1654 __isl_give isl_set *isl_set_make_disjoint(
1655 __isl_take isl_set *set);
1656 __isl_give isl_map *isl_map_make_disjoint(
1657 __isl_take isl_map *map);
1659 The number of basic sets in a set can be obtained
1660 or the number of basic maps in a map can be obtained
1663 #include <isl/set.h>
1664 int isl_set_n_basic_set(__isl_keep isl_set *set);
1666 #include <isl/map.h>
1667 int isl_map_n_basic_map(__isl_keep isl_map *map);
1669 To iterate over the constraints of a basic set or map, use
1671 #include <isl/constraint.h>
1673 int isl_basic_set_n_constraint(
1674 __isl_keep isl_basic_set *bset);
1675 int isl_basic_set_foreach_constraint(
1676 __isl_keep isl_basic_set *bset,
1677 int (*fn)(__isl_take isl_constraint *c, void *user),
1679 int isl_basic_map_n_constraint(
1680 __isl_keep isl_basic_map *bmap);
1681 int isl_basic_map_foreach_constraint(
1682 __isl_keep isl_basic_map *bmap,
1683 int (*fn)(__isl_take isl_constraint *c, void *user),
1685 __isl_null isl_constraint *isl_constraint_free(
1686 __isl_take isl_constraint *c);
1688 Again, the callback function C<fn> should return 0 if successful and
1689 -1 if an error occurs. In the latter case, or if any other error
1690 occurs, the above functions will return -1.
1691 The constraint C<c> represents either an equality or an inequality.
1692 Use the following function to find out whether a constraint
1693 represents an equality. If not, it represents an inequality.
1695 int isl_constraint_is_equality(
1696 __isl_keep isl_constraint *constraint);
1698 It is also possible to obtain a list of constraints from a basic
1701 #include <isl/constraint.h>
1702 __isl_give isl_constraint_list *
1703 isl_basic_map_get_constraint_list(
1704 __isl_keep isl_basic_map *bmap);
1705 __isl_give isl_constraint_list *
1706 isl_basic_set_get_constraint_list(
1707 __isl_keep isl_basic_set *bset);
1709 These functions require that all existentially quantified variables
1710 have an explicit representation.
1711 The returned list can be manipulated using the functions in L<"Lists">.
1713 The coefficients of the constraints can be inspected using
1714 the following functions.
1716 int isl_constraint_is_lower_bound(
1717 __isl_keep isl_constraint *constraint,
1718 enum isl_dim_type type, unsigned pos);
1719 int isl_constraint_is_upper_bound(
1720 __isl_keep isl_constraint *constraint,
1721 enum isl_dim_type type, unsigned pos);
1722 __isl_give isl_val *isl_constraint_get_constant_val(
1723 __isl_keep isl_constraint *constraint);
1724 __isl_give isl_val *isl_constraint_get_coefficient_val(
1725 __isl_keep isl_constraint *constraint,
1726 enum isl_dim_type type, int pos);
1727 int isl_constraint_involves_dims(
1728 __isl_keep isl_constraint *constraint,
1729 enum isl_dim_type type, unsigned first, unsigned n);
1731 The explicit representations of the existentially quantified
1732 variables can be inspected using the following function.
1733 Note that the user is only allowed to use this function
1734 if the inspected set or map is the result of a call
1735 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1736 The existentially quantified variable is equal to the floor
1737 of the returned affine expression. The affine expression
1738 itself can be inspected using the functions in
1739 L<"Piecewise Quasi Affine Expressions">.
1741 __isl_give isl_aff *isl_constraint_get_div(
1742 __isl_keep isl_constraint *constraint, int pos);
1744 To obtain the constraints of a basic set or map in matrix
1745 form, use the following functions.
1747 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1748 __isl_keep isl_basic_set *bset,
1749 enum isl_dim_type c1, enum isl_dim_type c2,
1750 enum isl_dim_type c3, enum isl_dim_type c4);
1751 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1752 __isl_keep isl_basic_set *bset,
1753 enum isl_dim_type c1, enum isl_dim_type c2,
1754 enum isl_dim_type c3, enum isl_dim_type c4);
1755 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1756 __isl_keep isl_basic_map *bmap,
1757 enum isl_dim_type c1,
1758 enum isl_dim_type c2, enum isl_dim_type c3,
1759 enum isl_dim_type c4, enum isl_dim_type c5);
1760 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1761 __isl_keep isl_basic_map *bmap,
1762 enum isl_dim_type c1,
1763 enum isl_dim_type c2, enum isl_dim_type c3,
1764 enum isl_dim_type c4, enum isl_dim_type c5);
1766 The C<isl_dim_type> arguments dictate the order in which
1767 different kinds of variables appear in the resulting matrix.
1768 For set inputs, they should be a permutation of
1769 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
1770 For map inputs, they should be a permutation of
1771 C<isl_dim_cst>, C<isl_dim_param>,
1772 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1774 The number of parameters, input, output or set dimensions can
1775 be obtained using the following functions.
1777 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1778 enum isl_dim_type type);
1779 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1780 enum isl_dim_type type);
1781 unsigned isl_set_dim(__isl_keep isl_set *set,
1782 enum isl_dim_type type);
1783 unsigned isl_map_dim(__isl_keep isl_map *map,
1784 enum isl_dim_type type);
1785 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1786 enum isl_dim_type type);
1788 Note that a C<isl_union_map> only has parameters.
1790 To check whether the description of a set or relation depends
1791 on one or more given dimensions, it is not necessary to iterate over all
1792 constraints. Instead the following functions can be used.
1794 int isl_basic_set_involves_dims(
1795 __isl_keep isl_basic_set *bset,
1796 enum isl_dim_type type, unsigned first, unsigned n);
1797 int isl_set_involves_dims(__isl_keep isl_set *set,
1798 enum isl_dim_type type, unsigned first, unsigned n);
1799 int isl_basic_map_involves_dims(
1800 __isl_keep isl_basic_map *bmap,
1801 enum isl_dim_type type, unsigned first, unsigned n);
1802 int isl_map_involves_dims(__isl_keep isl_map *map,
1803 enum isl_dim_type type, unsigned first, unsigned n);
1805 Similarly, the following functions can be used to check whether
1806 a given dimension is involved in any lower or upper bound.
1808 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1809 enum isl_dim_type type, unsigned pos);
1810 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1811 enum isl_dim_type type, unsigned pos);
1813 Note that these functions return true even if there is a bound on
1814 the dimension on only some of the basic sets of C<set>.
1815 To check if they have a bound for all of the basic sets in C<set>,
1816 use the following functions instead.
1818 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1819 enum isl_dim_type type, unsigned pos);
1820 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1821 enum isl_dim_type type, unsigned pos);
1823 The identifiers or names of the domain and range spaces of a set
1824 or relation can be read off or set using the following functions.
1826 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1827 __isl_take isl_basic_set *bset,
1828 __isl_take isl_id *id);
1829 __isl_give isl_set *isl_set_set_tuple_id(
1830 __isl_take isl_set *set, __isl_take isl_id *id);
1831 __isl_give isl_set *isl_set_reset_tuple_id(
1832 __isl_take isl_set *set);
1833 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1834 __isl_give isl_id *isl_set_get_tuple_id(
1835 __isl_keep isl_set *set);
1836 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1837 __isl_take isl_basic_map *bmap,
1838 enum isl_dim_type type, __isl_take isl_id *id);
1839 __isl_give isl_map *isl_map_set_tuple_id(
1840 __isl_take isl_map *map, enum isl_dim_type type,
1841 __isl_take isl_id *id);
1842 __isl_give isl_map *isl_map_reset_tuple_id(
1843 __isl_take isl_map *map, enum isl_dim_type type);
1844 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1845 enum isl_dim_type type);
1846 __isl_give isl_id *isl_map_get_tuple_id(
1847 __isl_keep isl_map *map, enum isl_dim_type type);
1849 const char *isl_basic_set_get_tuple_name(
1850 __isl_keep isl_basic_set *bset);
1851 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1852 __isl_take isl_basic_set *set, const char *s);
1853 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1854 const char *isl_set_get_tuple_name(
1855 __isl_keep isl_set *set);
1856 __isl_give isl_set *isl_set_set_tuple_name(
1857 __isl_take isl_set *set, const char *s);
1858 const char *isl_basic_map_get_tuple_name(
1859 __isl_keep isl_basic_map *bmap,
1860 enum isl_dim_type type);
1861 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1862 __isl_take isl_basic_map *bmap,
1863 enum isl_dim_type type, const char *s);
1864 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1865 enum isl_dim_type type);
1866 const char *isl_map_get_tuple_name(
1867 __isl_keep isl_map *map,
1868 enum isl_dim_type type);
1869 __isl_give isl_map *isl_map_set_tuple_name(
1870 __isl_take isl_map *map,
1871 enum isl_dim_type type, const char *s);
1873 As with C<isl_space_get_tuple_name>, the value returned points to
1874 an internal data structure.
1875 The identifiers, positions or names of individual dimensions can be
1876 read off using the following functions.
1878 __isl_give isl_id *isl_basic_set_get_dim_id(
1879 __isl_keep isl_basic_set *bset,
1880 enum isl_dim_type type, unsigned pos);
1881 __isl_give isl_set *isl_set_set_dim_id(
1882 __isl_take isl_set *set, enum isl_dim_type type,
1883 unsigned pos, __isl_take isl_id *id);
1884 int isl_set_has_dim_id(__isl_keep isl_set *set,
1885 enum isl_dim_type type, unsigned pos);
1886 __isl_give isl_id *isl_set_get_dim_id(
1887 __isl_keep isl_set *set, enum isl_dim_type type,
1889 int isl_basic_map_has_dim_id(
1890 __isl_keep isl_basic_map *bmap,
1891 enum isl_dim_type type, unsigned pos);
1892 __isl_give isl_map *isl_map_set_dim_id(
1893 __isl_take isl_map *map, enum isl_dim_type type,
1894 unsigned pos, __isl_take isl_id *id);
1895 int isl_map_has_dim_id(__isl_keep isl_map *map,
1896 enum isl_dim_type type, unsigned pos);
1897 __isl_give isl_id *isl_map_get_dim_id(
1898 __isl_keep isl_map *map, enum isl_dim_type type,
1900 __isl_give isl_id *isl_union_map_get_dim_id(
1901 __isl_keep isl_union_map *umap,
1902 enum isl_dim_type type, unsigned pos);
1904 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1905 enum isl_dim_type type, __isl_keep isl_id *id);
1906 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1907 enum isl_dim_type type, __isl_keep isl_id *id);
1908 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1909 enum isl_dim_type type, const char *name);
1910 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1911 enum isl_dim_type type, const char *name);
1913 const char *isl_constraint_get_dim_name(
1914 __isl_keep isl_constraint *constraint,
1915 enum isl_dim_type type, unsigned pos);
1916 const char *isl_basic_set_get_dim_name(
1917 __isl_keep isl_basic_set *bset,
1918 enum isl_dim_type type, unsigned pos);
1919 int isl_set_has_dim_name(__isl_keep isl_set *set,
1920 enum isl_dim_type type, unsigned pos);
1921 const char *isl_set_get_dim_name(
1922 __isl_keep isl_set *set,
1923 enum isl_dim_type type, unsigned pos);
1924 const char *isl_basic_map_get_dim_name(
1925 __isl_keep isl_basic_map *bmap,
1926 enum isl_dim_type type, unsigned pos);
1927 int isl_map_has_dim_name(__isl_keep isl_map *map,
1928 enum isl_dim_type type, unsigned pos);
1929 const char *isl_map_get_dim_name(
1930 __isl_keep isl_map *map,
1931 enum isl_dim_type type, unsigned pos);
1933 These functions are mostly useful to obtain the identifiers, positions
1934 or names of the parameters. Identifiers of individual dimensions are
1935 essentially only useful for printing. They are ignored by all other
1936 operations and may not be preserved across those operations.
1938 The user pointers on all parameters and tuples can be reset
1939 using the following functions.
1941 #include <isl/set.h>
1942 __isl_give isl_set *isl_set_reset_user(
1943 __isl_take isl_set *set);
1944 #include <isl/map.h>
1945 __isl_give isl_map *isl_map_reset_user(
1946 __isl_take isl_map *map);
1947 #include <isl/union_set.h>
1948 __isl_give isl_union_set *isl_union_set_reset_user(
1949 __isl_take isl_union_set *uset);
1950 #include <isl/union_map.h>
1951 __isl_give isl_union_map *isl_union_map_reset_user(
1952 __isl_take isl_union_map *umap);
1956 =head3 Unary Properties
1962 The following functions test whether the given set or relation
1963 contains any integer points. The ``plain'' variants do not perform
1964 any computations, but simply check if the given set or relation
1965 is already known to be empty.
1967 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1968 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1969 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1970 int isl_set_is_empty(__isl_keep isl_set *set);
1971 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1972 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1973 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1974 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1975 int isl_map_is_empty(__isl_keep isl_map *map);
1976 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1978 =item * Universality
1980 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1981 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1982 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1984 =item * Single-valuedness
1986 #include <isl/set.h>
1987 int isl_set_is_singleton(__isl_keep isl_set *set);
1989 #include <isl/map.h>
1990 int isl_basic_map_is_single_valued(
1991 __isl_keep isl_basic_map *bmap);
1992 int isl_map_plain_is_single_valued(
1993 __isl_keep isl_map *map);
1994 int isl_map_is_single_valued(__isl_keep isl_map *map);
1996 #include <isl/union_map.h>
1997 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
2001 int isl_map_plain_is_injective(__isl_keep isl_map *map);
2002 int isl_map_is_injective(__isl_keep isl_map *map);
2003 int isl_union_map_plain_is_injective(
2004 __isl_keep isl_union_map *umap);
2005 int isl_union_map_is_injective(
2006 __isl_keep isl_union_map *umap);
2010 int isl_map_is_bijective(__isl_keep isl_map *map);
2011 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
2015 __isl_give isl_val *
2016 isl_basic_map_plain_get_val_if_fixed(
2017 __isl_keep isl_basic_map *bmap,
2018 enum isl_dim_type type, unsigned pos);
2019 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
2020 __isl_keep isl_set *set,
2021 enum isl_dim_type type, unsigned pos);
2022 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
2023 __isl_keep isl_map *map,
2024 enum isl_dim_type type, unsigned pos);
2026 If the set or relation obviously lies on a hyperplane where the given dimension
2027 has a fixed value, then return that value.
2028 Otherwise return NaN.
2032 int isl_set_dim_residue_class_val(
2033 __isl_keep isl_set *set,
2034 int pos, __isl_give isl_val **modulo,
2035 __isl_give isl_val **residue);
2037 Check if the values of the given set dimension are equal to a fixed
2038 value modulo some integer value. If so, assign the modulo to C<*modulo>
2039 and the fixed value to C<*residue>. If the given dimension attains only
2040 a single value, then assign C<0> to C<*modulo> and the fixed value to
2042 If the dimension does not attain only a single value and if no modulo
2043 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
2047 To check whether a set is a parameter domain, use this function:
2049 int isl_set_is_params(__isl_keep isl_set *set);
2050 int isl_union_set_is_params(
2051 __isl_keep isl_union_set *uset);
2055 The following functions check whether the space of the given
2056 (basic) set or relation range is a wrapped relation.
2058 #include <isl/space.h>
2059 int isl_space_is_wrapping(
2060 __isl_keep isl_space *space);
2061 int isl_space_domain_is_wrapping(
2062 __isl_keep isl_space *space);
2063 int isl_space_range_is_wrapping(
2064 __isl_keep isl_space *space);
2066 #include <isl/set.h>
2067 int isl_basic_set_is_wrapping(
2068 __isl_keep isl_basic_set *bset);
2069 int isl_set_is_wrapping(__isl_keep isl_set *set);
2071 #include <isl/map.h>
2072 int isl_map_domain_is_wrapping(
2073 __isl_keep isl_map *map);
2074 int isl_map_range_is_wrapping(
2075 __isl_keep isl_map *map);
2077 The input to C<isl_space_is_wrapping> should
2078 be the space of a set, while that of
2079 C<isl_space_domain_is_wrapping> and
2080 C<isl_space_range_is_wrapping> should be the space of a relation.
2082 =item * Internal Product
2084 int isl_basic_map_can_zip(
2085 __isl_keep isl_basic_map *bmap);
2086 int isl_map_can_zip(__isl_keep isl_map *map);
2088 Check whether the product of domain and range of the given relation
2090 i.e., whether both domain and range are nested relations.
2094 int isl_basic_map_can_curry(
2095 __isl_keep isl_basic_map *bmap);
2096 int isl_map_can_curry(__isl_keep isl_map *map);
2098 Check whether the domain of the (basic) relation is a wrapped relation.
2100 int isl_basic_map_can_uncurry(
2101 __isl_keep isl_basic_map *bmap);
2102 int isl_map_can_uncurry(__isl_keep isl_map *map);
2104 Check whether the range of the (basic) relation is a wrapped relation.
2108 =head3 Binary Properties
2114 int isl_basic_set_plain_is_equal(
2115 __isl_keep isl_basic_set *bset1,
2116 __isl_keep isl_basic_set *bset2);
2117 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2118 __isl_keep isl_set *set2);
2119 int isl_set_is_equal(__isl_keep isl_set *set1,
2120 __isl_keep isl_set *set2);
2121 int isl_union_set_is_equal(
2122 __isl_keep isl_union_set *uset1,
2123 __isl_keep isl_union_set *uset2);
2124 int isl_basic_map_is_equal(
2125 __isl_keep isl_basic_map *bmap1,
2126 __isl_keep isl_basic_map *bmap2);
2127 int isl_map_is_equal(__isl_keep isl_map *map1,
2128 __isl_keep isl_map *map2);
2129 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2130 __isl_keep isl_map *map2);
2131 int isl_union_map_is_equal(
2132 __isl_keep isl_union_map *umap1,
2133 __isl_keep isl_union_map *umap2);
2135 =item * Disjointness
2137 int isl_basic_set_is_disjoint(
2138 __isl_keep isl_basic_set *bset1,
2139 __isl_keep isl_basic_set *bset2);
2140 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2141 __isl_keep isl_set *set2);
2142 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2143 __isl_keep isl_set *set2);
2144 int isl_basic_map_is_disjoint(
2145 __isl_keep isl_basic_map *bmap1,
2146 __isl_keep isl_basic_map *bmap2);
2147 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2148 __isl_keep isl_map *map2);
2152 int isl_basic_set_is_subset(
2153 __isl_keep isl_basic_set *bset1,
2154 __isl_keep isl_basic_set *bset2);
2155 int isl_set_is_subset(__isl_keep isl_set *set1,
2156 __isl_keep isl_set *set2);
2157 int isl_set_is_strict_subset(
2158 __isl_keep isl_set *set1,
2159 __isl_keep isl_set *set2);
2160 int isl_union_set_is_subset(
2161 __isl_keep isl_union_set *uset1,
2162 __isl_keep isl_union_set *uset2);
2163 int isl_union_set_is_strict_subset(
2164 __isl_keep isl_union_set *uset1,
2165 __isl_keep isl_union_set *uset2);
2166 int isl_basic_map_is_subset(
2167 __isl_keep isl_basic_map *bmap1,
2168 __isl_keep isl_basic_map *bmap2);
2169 int isl_basic_map_is_strict_subset(
2170 __isl_keep isl_basic_map *bmap1,
2171 __isl_keep isl_basic_map *bmap2);
2172 int isl_map_is_subset(
2173 __isl_keep isl_map *map1,
2174 __isl_keep isl_map *map2);
2175 int isl_map_is_strict_subset(
2176 __isl_keep isl_map *map1,
2177 __isl_keep isl_map *map2);
2178 int isl_union_map_is_subset(
2179 __isl_keep isl_union_map *umap1,
2180 __isl_keep isl_union_map *umap2);
2181 int isl_union_map_is_strict_subset(
2182 __isl_keep isl_union_map *umap1,
2183 __isl_keep isl_union_map *umap2);
2185 Check whether the first argument is a (strict) subset of the
2190 Every comparison function returns a negative value if the first
2191 argument is considered smaller than the second, a positive value
2192 if the first argument is considered greater and zero if the two
2193 constraints are considered the same by the comparison criterion.
2195 #include <isl/constraint.h>
2196 int isl_constraint_plain_cmp(
2197 __isl_keep isl_constraint *c1,
2198 __isl_keep isl_constraint *c2);
2200 This function is useful for sorting C<isl_constraint>s.
2201 The order depends on the internal representation of the inputs.
2202 The order is fixed over different calls to the function (assuming
2203 the internal representation of the inputs has not changed), but may
2204 change over different versions of C<isl>.
2206 #include <isl/constraint.h>
2207 int isl_constraint_cmp_last_non_zero(
2208 __isl_keep isl_constraint *c1,
2209 __isl_keep isl_constraint *c2);
2211 This function can be used to sort constraints that live in the same
2212 local space. Constraints that involve ``earlier'' dimensions or
2213 that have a smaller coefficient for the shared latest dimension
2214 are considered smaller than other constraints.
2215 This function only defines a B<partial> order.
2217 #include <isl/set.h>
2218 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2219 __isl_keep isl_set *set2);
2221 This function is useful for sorting C<isl_set>s.
2222 The order depends on the internal representation of the inputs.
2223 The order is fixed over different calls to the function (assuming
2224 the internal representation of the inputs has not changed), but may
2225 change over different versions of C<isl>.
2229 =head2 Unary Operations
2235 __isl_give isl_set *isl_set_complement(
2236 __isl_take isl_set *set);
2237 __isl_give isl_map *isl_map_complement(
2238 __isl_take isl_map *map);
2242 #include <isl/space.h>
2243 __isl_give isl_space *isl_space_reverse(
2244 __isl_take isl_space *space);
2246 #include <isl/map.h>
2247 __isl_give isl_basic_map *isl_basic_map_reverse(
2248 __isl_take isl_basic_map *bmap);
2249 __isl_give isl_map *isl_map_reverse(
2250 __isl_take isl_map *map);
2251 __isl_give isl_union_map *isl_union_map_reverse(
2252 __isl_take isl_union_map *umap);
2256 #include <isl/space.h>
2257 __isl_give isl_space *isl_space_domain(
2258 __isl_take isl_space *space);
2259 __isl_give isl_space *isl_space_range(
2260 __isl_take isl_space *space);
2261 __isl_give isl_space *isl_space_params(
2262 __isl_take isl_space *space);
2264 #include <isl/local_space.h>
2265 __isl_give isl_local_space *isl_local_space_domain(
2266 __isl_take isl_local_space *ls);
2267 __isl_give isl_local_space *isl_local_space_range(
2268 __isl_take isl_local_space *ls);
2270 #include <isl/set.h>
2271 __isl_give isl_basic_set *isl_basic_set_project_out(
2272 __isl_take isl_basic_set *bset,
2273 enum isl_dim_type type, unsigned first, unsigned n);
2274 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2275 enum isl_dim_type type, unsigned first, unsigned n);
2276 __isl_give isl_basic_set *isl_basic_set_params(
2277 __isl_take isl_basic_set *bset);
2278 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2280 #include <isl/map.h>
2281 __isl_give isl_basic_map *isl_basic_map_project_out(
2282 __isl_take isl_basic_map *bmap,
2283 enum isl_dim_type type, unsigned first, unsigned n);
2284 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2285 enum isl_dim_type type, unsigned first, unsigned n);
2286 __isl_give isl_basic_set *isl_basic_map_domain(
2287 __isl_take isl_basic_map *bmap);
2288 __isl_give isl_basic_set *isl_basic_map_range(
2289 __isl_take isl_basic_map *bmap);
2290 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2291 __isl_give isl_set *isl_map_domain(
2292 __isl_take isl_map *bmap);
2293 __isl_give isl_set *isl_map_range(
2294 __isl_take isl_map *map);
2296 #include <isl/union_set.h>
2297 __isl_give isl_set *isl_union_set_params(
2298 __isl_take isl_union_set *uset);
2300 #include <isl/union_map.h>
2301 __isl_give isl_union_map *isl_union_map_project_out(
2302 __isl_take isl_union_map *umap,
2303 enum isl_dim_type type, unsigned first, unsigned n);
2304 __isl_give isl_set *isl_union_map_params(
2305 __isl_take isl_union_map *umap);
2306 __isl_give isl_union_set *isl_union_map_domain(
2307 __isl_take isl_union_map *umap);
2308 __isl_give isl_union_set *isl_union_map_range(
2309 __isl_take isl_union_map *umap);
2311 The function C<isl_union_map_project_out> can only project out
2314 #include <isl/space.h>
2315 __isl_give isl_space *isl_space_domain_map(
2316 __isl_take isl_space *space);
2317 __isl_give isl_space *isl_space_range_map(
2318 __isl_take isl_space *space);
2320 #include <isl/map.h>
2321 __isl_give isl_basic_map *isl_basic_map_domain_map(
2322 __isl_take isl_basic_map *bmap);
2323 __isl_give isl_basic_map *isl_basic_map_range_map(
2324 __isl_take isl_basic_map *bmap);
2325 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2326 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2328 #include <isl/union_map.h>
2329 __isl_give isl_union_map *isl_union_map_domain_map(
2330 __isl_take isl_union_map *umap);
2331 __isl_give isl_union_map *isl_union_map_range_map(
2332 __isl_take isl_union_map *umap);
2334 The functions above construct a (basic, regular or union) relation
2335 that maps (a wrapped version of) the input relation to its domain or range.
2339 __isl_give isl_basic_set *isl_basic_set_eliminate(
2340 __isl_take isl_basic_set *bset,
2341 enum isl_dim_type type,
2342 unsigned first, unsigned n);
2343 __isl_give isl_set *isl_set_eliminate(
2344 __isl_take isl_set *set, enum isl_dim_type type,
2345 unsigned first, unsigned n);
2346 __isl_give isl_basic_map *isl_basic_map_eliminate(
2347 __isl_take isl_basic_map *bmap,
2348 enum isl_dim_type type,
2349 unsigned first, unsigned n);
2350 __isl_give isl_map *isl_map_eliminate(
2351 __isl_take isl_map *map, enum isl_dim_type type,
2352 unsigned first, unsigned n);
2354 Eliminate the coefficients for the given dimensions from the constraints,
2355 without removing the dimensions.
2357 =item * Constructing a set from a parameter domain
2359 A zero-dimensional space or (basic) set can be constructed
2360 on a given parameter domain using the following functions.
2362 #include <isl/space.h>
2363 __isl_give isl_space *isl_space_set_from_params(
2364 __isl_take isl_space *space);
2366 #include <isl/set.h>
2367 __isl_give isl_basic_set *isl_basic_set_from_params(
2368 __isl_take isl_basic_set *bset);
2369 __isl_give isl_set *isl_set_from_params(
2370 __isl_take isl_set *set);
2372 =item * Constructing a relation from a set
2374 #include <isl/space.h>
2375 __isl_give isl_space *isl_space_from_domain(
2376 __isl_take isl_space *space);
2377 __isl_give isl_space *isl_space_from_range(
2378 __isl_take isl_space *space);
2379 __isl_give isl_space *isl_space_map_from_set(
2380 __isl_take isl_space *space);
2381 __isl_give isl_space *isl_space_map_from_domain_and_range(
2382 __isl_take isl_space *domain,
2383 __isl_take isl_space *range);
2385 #include <isl/local_space.h>
2386 __isl_give isl_local_space *isl_local_space_from_domain(
2387 __isl_take isl_local_space *ls);
2389 #include <isl/map.h>
2390 __isl_give isl_map *isl_map_from_domain(
2391 __isl_take isl_set *set);
2392 __isl_give isl_map *isl_map_from_range(
2393 __isl_take isl_set *set);
2395 Create a relation with the given set as domain or range.
2396 The range or domain of the created relation is a zero-dimensional
2397 flat anonymous space.
2401 __isl_give isl_basic_set *isl_basic_set_fix_si(
2402 __isl_take isl_basic_set *bset,
2403 enum isl_dim_type type, unsigned pos, int value);
2404 __isl_give isl_basic_set *isl_basic_set_fix_val(
2405 __isl_take isl_basic_set *bset,
2406 enum isl_dim_type type, unsigned pos,
2407 __isl_take isl_val *v);
2408 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2409 enum isl_dim_type type, unsigned pos, int value);
2410 __isl_give isl_set *isl_set_fix_val(
2411 __isl_take isl_set *set,
2412 enum isl_dim_type type, unsigned pos,
2413 __isl_take isl_val *v);
2414 __isl_give isl_basic_map *isl_basic_map_fix_si(
2415 __isl_take isl_basic_map *bmap,
2416 enum isl_dim_type type, unsigned pos, int value);
2417 __isl_give isl_basic_map *isl_basic_map_fix_val(
2418 __isl_take isl_basic_map *bmap,
2419 enum isl_dim_type type, unsigned pos,
2420 __isl_take isl_val *v);
2421 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2422 enum isl_dim_type type, unsigned pos, int value);
2423 __isl_give isl_map *isl_map_fix_val(
2424 __isl_take isl_map *map,
2425 enum isl_dim_type type, unsigned pos,
2426 __isl_take isl_val *v);
2428 Intersect the set or relation with the hyperplane where the given
2429 dimension has the fixed given value.
2431 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2432 __isl_take isl_basic_map *bmap,
2433 enum isl_dim_type type, unsigned pos, int value);
2434 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2435 __isl_take isl_basic_map *bmap,
2436 enum isl_dim_type type, unsigned pos, int value);
2437 __isl_give isl_set *isl_set_lower_bound_si(
2438 __isl_take isl_set *set,
2439 enum isl_dim_type type, unsigned pos, int value);
2440 __isl_give isl_set *isl_set_lower_bound_val(
2441 __isl_take isl_set *set,
2442 enum isl_dim_type type, unsigned pos,
2443 __isl_take isl_val *value);
2444 __isl_give isl_map *isl_map_lower_bound_si(
2445 __isl_take isl_map *map,
2446 enum isl_dim_type type, unsigned pos, int value);
2447 __isl_give isl_set *isl_set_upper_bound_si(
2448 __isl_take isl_set *set,
2449 enum isl_dim_type type, unsigned pos, int value);
2450 __isl_give isl_set *isl_set_upper_bound_val(
2451 __isl_take isl_set *set,
2452 enum isl_dim_type type, unsigned pos,
2453 __isl_take isl_val *value);
2454 __isl_give isl_map *isl_map_upper_bound_si(
2455 __isl_take isl_map *map,
2456 enum isl_dim_type type, unsigned pos, int value);
2458 Intersect the set or relation with the half-space where the given
2459 dimension has a value bounded by the fixed given integer value.
2461 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2462 enum isl_dim_type type1, int pos1,
2463 enum isl_dim_type type2, int pos2);
2464 __isl_give isl_basic_map *isl_basic_map_equate(
2465 __isl_take isl_basic_map *bmap,
2466 enum isl_dim_type type1, int pos1,
2467 enum isl_dim_type type2, int pos2);
2468 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2469 enum isl_dim_type type1, int pos1,
2470 enum isl_dim_type type2, int pos2);
2472 Intersect the set or relation with the hyperplane where the given
2473 dimensions are equal to each other.
2475 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2476 enum isl_dim_type type1, int pos1,
2477 enum isl_dim_type type2, int pos2);
2479 Intersect the relation with the hyperplane where the given
2480 dimensions have opposite values.
2482 __isl_give isl_map *isl_map_order_le(
2483 __isl_take isl_map *map,
2484 enum isl_dim_type type1, int pos1,
2485 enum isl_dim_type type2, int pos2);
2486 __isl_give isl_basic_map *isl_basic_map_order_ge(
2487 __isl_take isl_basic_map *bmap,
2488 enum isl_dim_type type1, int pos1,
2489 enum isl_dim_type type2, int pos2);
2490 __isl_give isl_map *isl_map_order_ge(
2491 __isl_take isl_map *map,
2492 enum isl_dim_type type1, int pos1,
2493 enum isl_dim_type type2, int pos2);
2494 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2495 enum isl_dim_type type1, int pos1,
2496 enum isl_dim_type type2, int pos2);
2497 __isl_give isl_basic_map *isl_basic_map_order_gt(
2498 __isl_take isl_basic_map *bmap,
2499 enum isl_dim_type type1, int pos1,
2500 enum isl_dim_type type2, int pos2);
2501 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2502 enum isl_dim_type type1, int pos1,
2503 enum isl_dim_type type2, int pos2);
2505 Intersect the relation with the half-space where the given
2506 dimensions satisfy the given ordering.
2510 __isl_give isl_map *isl_set_identity(
2511 __isl_take isl_set *set);
2512 __isl_give isl_union_map *isl_union_set_identity(
2513 __isl_take isl_union_set *uset);
2515 Construct an identity relation on the given (union) set.
2519 __isl_give isl_basic_set *isl_basic_map_deltas(
2520 __isl_take isl_basic_map *bmap);
2521 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2522 __isl_give isl_union_set *isl_union_map_deltas(
2523 __isl_take isl_union_map *umap);
2525 These functions return a (basic) set containing the differences
2526 between image elements and corresponding domain elements in the input.
2528 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2529 __isl_take isl_basic_map *bmap);
2530 __isl_give isl_map *isl_map_deltas_map(
2531 __isl_take isl_map *map);
2532 __isl_give isl_union_map *isl_union_map_deltas_map(
2533 __isl_take isl_union_map *umap);
2535 The functions above construct a (basic, regular or union) relation
2536 that maps (a wrapped version of) the input relation to its delta set.
2540 Simplify the representation of a set or relation by trying
2541 to combine pairs of basic sets or relations into a single
2542 basic set or relation.
2544 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2545 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2546 __isl_give isl_union_set *isl_union_set_coalesce(
2547 __isl_take isl_union_set *uset);
2548 __isl_give isl_union_map *isl_union_map_coalesce(
2549 __isl_take isl_union_map *umap);
2551 One of the methods for combining pairs of basic sets or relations
2552 can result in coefficients that are much larger than those that appear
2553 in the constraints of the input. By default, the coefficients are
2554 not allowed to grow larger, but this can be changed by unsetting
2555 the following option.
2557 int isl_options_set_coalesce_bounded_wrapping(
2558 isl_ctx *ctx, int val);
2559 int isl_options_get_coalesce_bounded_wrapping(
2562 =item * Detecting equalities
2564 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2565 __isl_take isl_basic_set *bset);
2566 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2567 __isl_take isl_basic_map *bmap);
2568 __isl_give isl_set *isl_set_detect_equalities(
2569 __isl_take isl_set *set);
2570 __isl_give isl_map *isl_map_detect_equalities(
2571 __isl_take isl_map *map);
2572 __isl_give isl_union_set *isl_union_set_detect_equalities(
2573 __isl_take isl_union_set *uset);
2574 __isl_give isl_union_map *isl_union_map_detect_equalities(
2575 __isl_take isl_union_map *umap);
2577 Simplify the representation of a set or relation by detecting implicit
2580 =item * Removing redundant constraints
2582 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2583 __isl_take isl_basic_set *bset);
2584 __isl_give isl_set *isl_set_remove_redundancies(
2585 __isl_take isl_set *set);
2586 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2587 __isl_take isl_basic_map *bmap);
2588 __isl_give isl_map *isl_map_remove_redundancies(
2589 __isl_take isl_map *map);
2593 __isl_give isl_basic_set *isl_set_convex_hull(
2594 __isl_take isl_set *set);
2595 __isl_give isl_basic_map *isl_map_convex_hull(
2596 __isl_take isl_map *map);
2598 If the input set or relation has any existentially quantified
2599 variables, then the result of these operations is currently undefined.
2603 #include <isl/set.h>
2604 __isl_give isl_basic_set *
2605 isl_set_unshifted_simple_hull(
2606 __isl_take isl_set *set);
2607 __isl_give isl_basic_set *isl_set_simple_hull(
2608 __isl_take isl_set *set);
2609 __isl_give isl_basic_set *
2610 isl_set_unshifted_simple_hull_from_set_list(
2611 __isl_take isl_set *set,
2612 __isl_take isl_set_list *list);
2614 #include <isl/map.h>
2615 __isl_give isl_basic_map *
2616 isl_map_unshifted_simple_hull(
2617 __isl_take isl_map *map);
2618 __isl_give isl_basic_map *isl_map_simple_hull(
2619 __isl_take isl_map *map);
2621 #include <isl/union_map.h>
2622 __isl_give isl_union_map *isl_union_map_simple_hull(
2623 __isl_take isl_union_map *umap);
2625 These functions compute a single basic set or relation
2626 that contains the whole input set or relation.
2627 In particular, the output is described by translates
2628 of the constraints describing the basic sets or relations in the input.
2629 In case of C<isl_set_unshifted_simple_hull>, only the original
2630 constraints are used, without any translation.
2631 In case of C<isl_set_unshifted_simple_hull_from_set_list>, the
2632 constraints are taken from the elements of the second argument.
2636 (See \autoref{s:simple hull}.)
2642 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2643 __isl_take isl_basic_set *bset);
2644 __isl_give isl_basic_set *isl_set_affine_hull(
2645 __isl_take isl_set *set);
2646 __isl_give isl_union_set *isl_union_set_affine_hull(
2647 __isl_take isl_union_set *uset);
2648 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2649 __isl_take isl_basic_map *bmap);
2650 __isl_give isl_basic_map *isl_map_affine_hull(
2651 __isl_take isl_map *map);
2652 __isl_give isl_union_map *isl_union_map_affine_hull(
2653 __isl_take isl_union_map *umap);
2655 In case of union sets and relations, the affine hull is computed
2658 =item * Polyhedral hull
2660 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2661 __isl_take isl_set *set);
2662 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2663 __isl_take isl_map *map);
2664 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2665 __isl_take isl_union_set *uset);
2666 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2667 __isl_take isl_union_map *umap);
2669 These functions compute a single basic set or relation
2670 not involving any existentially quantified variables
2671 that contains the whole input set or relation.
2672 In case of union sets and relations, the polyhedral hull is computed
2675 =item * Other approximations
2677 __isl_give isl_basic_set *
2678 isl_basic_set_drop_constraints_involving_dims(
2679 __isl_take isl_basic_set *bset,
2680 enum isl_dim_type type,
2681 unsigned first, unsigned n);
2682 __isl_give isl_basic_map *
2683 isl_basic_map_drop_constraints_involving_dims(
2684 __isl_take isl_basic_map *bmap,
2685 enum isl_dim_type type,
2686 unsigned first, unsigned n);
2687 __isl_give isl_basic_set *
2688 isl_basic_set_drop_constraints_not_involving_dims(
2689 __isl_take isl_basic_set *bset,
2690 enum isl_dim_type type,
2691 unsigned first, unsigned n);
2692 __isl_give isl_set *
2693 isl_set_drop_constraints_involving_dims(
2694 __isl_take isl_set *set,
2695 enum isl_dim_type type,
2696 unsigned first, unsigned n);
2697 __isl_give isl_map *
2698 isl_map_drop_constraints_involving_dims(
2699 __isl_take isl_map *map,
2700 enum isl_dim_type type,
2701 unsigned first, unsigned n);
2703 These functions drop any constraints (not) involving the specified dimensions.
2704 Note that the result depends on the representation of the input.
2708 __isl_give isl_basic_set *isl_basic_set_sample(
2709 __isl_take isl_basic_set *bset);
2710 __isl_give isl_basic_set *isl_set_sample(
2711 __isl_take isl_set *set);
2712 __isl_give isl_basic_map *isl_basic_map_sample(
2713 __isl_take isl_basic_map *bmap);
2714 __isl_give isl_basic_map *isl_map_sample(
2715 __isl_take isl_map *map);
2717 If the input (basic) set or relation is non-empty, then return
2718 a singleton subset of the input. Otherwise, return an empty set.
2720 =item * Optimization
2722 #include <isl/ilp.h>
2723 __isl_give isl_val *isl_basic_set_max_val(
2724 __isl_keep isl_basic_set *bset,
2725 __isl_keep isl_aff *obj);
2726 __isl_give isl_val *isl_set_min_val(
2727 __isl_keep isl_set *set,
2728 __isl_keep isl_aff *obj);
2729 __isl_give isl_val *isl_set_max_val(
2730 __isl_keep isl_set *set,
2731 __isl_keep isl_aff *obj);
2733 Compute the minimum or maximum of the integer affine expression C<obj>
2734 over the points in C<set>, returning the result in C<opt>.
2735 The result is C<NULL> in case of an error, the optimal value in case
2736 there is one, negative infinity or infinity if the problem is unbounded and
2737 NaN if the problem is empty.
2739 =item * Parametric optimization
2741 __isl_give isl_pw_aff *isl_set_dim_min(
2742 __isl_take isl_set *set, int pos);
2743 __isl_give isl_pw_aff *isl_set_dim_max(
2744 __isl_take isl_set *set, int pos);
2745 __isl_give isl_pw_aff *isl_map_dim_max(
2746 __isl_take isl_map *map, int pos);
2748 Compute the minimum or maximum of the given set or output dimension
2749 as a function of the parameters (and input dimensions), but independently
2750 of the other set or output dimensions.
2751 For lexicographic optimization, see L<"Lexicographic Optimization">.
2755 The following functions compute either the set of (rational) coefficient
2756 values of valid constraints for the given set or the set of (rational)
2757 values satisfying the constraints with coefficients from the given set.
2758 Internally, these two sets of functions perform essentially the
2759 same operations, except that the set of coefficients is assumed to
2760 be a cone, while the set of values may be any polyhedron.
2761 The current implementation is based on the Farkas lemma and
2762 Fourier-Motzkin elimination, but this may change or be made optional
2763 in future. In particular, future implementations may use different
2764 dualization algorithms or skip the elimination step.
2766 __isl_give isl_basic_set *isl_basic_set_coefficients(
2767 __isl_take isl_basic_set *bset);
2768 __isl_give isl_basic_set *isl_set_coefficients(
2769 __isl_take isl_set *set);
2770 __isl_give isl_union_set *isl_union_set_coefficients(
2771 __isl_take isl_union_set *bset);
2772 __isl_give isl_basic_set *isl_basic_set_solutions(
2773 __isl_take isl_basic_set *bset);
2774 __isl_give isl_basic_set *isl_set_solutions(
2775 __isl_take isl_set *set);
2776 __isl_give isl_union_set *isl_union_set_solutions(
2777 __isl_take isl_union_set *bset);
2781 __isl_give isl_map *isl_map_fixed_power_val(
2782 __isl_take isl_map *map,
2783 __isl_take isl_val *exp);
2784 __isl_give isl_union_map *
2785 isl_union_map_fixed_power_val(
2786 __isl_take isl_union_map *umap,
2787 __isl_take isl_val *exp);
2789 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2790 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2791 of C<map> is computed.
2793 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2795 __isl_give isl_union_map *isl_union_map_power(
2796 __isl_take isl_union_map *umap, int *exact);
2798 Compute a parametric representation for all positive powers I<k> of C<map>.
2799 The result maps I<k> to a nested relation corresponding to the
2800 I<k>th power of C<map>.
2801 The result may be an overapproximation. If the result is known to be exact,
2802 then C<*exact> is set to C<1>.
2804 =item * Transitive closure
2806 __isl_give isl_map *isl_map_transitive_closure(
2807 __isl_take isl_map *map, int *exact);
2808 __isl_give isl_union_map *isl_union_map_transitive_closure(
2809 __isl_take isl_union_map *umap, int *exact);
2811 Compute the transitive closure of C<map>.
2812 The result may be an overapproximation. If the result is known to be exact,
2813 then C<*exact> is set to C<1>.
2815 =item * Reaching path lengths
2817 __isl_give isl_map *isl_map_reaching_path_lengths(
2818 __isl_take isl_map *map, int *exact);
2820 Compute a relation that maps each element in the range of C<map>
2821 to the lengths of all paths composed of edges in C<map> that
2822 end up in the given element.
2823 The result may be an overapproximation. If the result is known to be exact,
2824 then C<*exact> is set to C<1>.
2825 To compute the I<maximal> path length, the resulting relation
2826 should be postprocessed by C<isl_map_lexmax>.
2827 In particular, if the input relation is a dependence relation
2828 (mapping sources to sinks), then the maximal path length corresponds
2829 to the free schedule.
2830 Note, however, that C<isl_map_lexmax> expects the maximum to be
2831 finite, so if the path lengths are unbounded (possibly due to
2832 the overapproximation), then you will get an error message.
2836 #include <isl/space.h>
2837 __isl_give isl_space *isl_space_wrap(
2838 __isl_take isl_space *space);
2839 __isl_give isl_space *isl_space_unwrap(
2840 __isl_take isl_space *space);
2842 #include <isl/set.h>
2843 __isl_give isl_basic_map *isl_basic_set_unwrap(
2844 __isl_take isl_basic_set *bset);
2845 __isl_give isl_map *isl_set_unwrap(
2846 __isl_take isl_set *set);
2848 #include <isl/map.h>
2849 __isl_give isl_basic_set *isl_basic_map_wrap(
2850 __isl_take isl_basic_map *bmap);
2851 __isl_give isl_set *isl_map_wrap(
2852 __isl_take isl_map *map);
2854 #include <isl/union_set.h>
2855 __isl_give isl_union_map *isl_union_set_unwrap(
2856 __isl_take isl_union_set *uset);
2858 #include <isl/union_map.h>
2859 __isl_give isl_union_set *isl_union_map_wrap(
2860 __isl_take isl_union_map *umap);
2862 The input to C<isl_space_unwrap> should
2863 be the space of a set, while that of
2864 C<isl_space_wrap> should be the space of a relation.
2865 Conversely, the output of C<isl_space_unwrap> is the space
2866 of a relation, while that of C<isl_space_wrap> is the space of a set.
2870 Remove any internal structure of domain (and range) of the given
2871 set or relation. If there is any such internal structure in the input,
2872 then the name of the space is also removed.
2874 #include <isl/local_space.h>
2875 __isl_give isl_local_space *
2876 isl_local_space_flatten_domain(
2877 __isl_take isl_local_space *ls);
2878 __isl_give isl_local_space *
2879 isl_local_space_flatten_range(
2880 __isl_take isl_local_space *ls);
2882 #include <isl/set.h>
2883 __isl_give isl_basic_set *isl_basic_set_flatten(
2884 __isl_take isl_basic_set *bset);
2885 __isl_give isl_set *isl_set_flatten(
2886 __isl_take isl_set *set);
2888 #include <isl/map.h>
2889 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2890 __isl_take isl_basic_map *bmap);
2891 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2892 __isl_take isl_basic_map *bmap);
2893 __isl_give isl_map *isl_map_flatten_range(
2894 __isl_take isl_map *map);
2895 __isl_give isl_map *isl_map_flatten_domain(
2896 __isl_take isl_map *map);
2897 __isl_give isl_basic_map *isl_basic_map_flatten(
2898 __isl_take isl_basic_map *bmap);
2899 __isl_give isl_map *isl_map_flatten(
2900 __isl_take isl_map *map);
2902 #include <isl/map.h>
2903 __isl_give isl_map *isl_set_flatten_map(
2904 __isl_take isl_set *set);
2906 The function above constructs a relation
2907 that maps the input set to a flattened version of the set.
2911 Lift the input set to a space with extra dimensions corresponding
2912 to the existentially quantified variables in the input.
2913 In particular, the result lives in a wrapped map where the domain
2914 is the original space and the range corresponds to the original
2915 existentially quantified variables.
2917 __isl_give isl_basic_set *isl_basic_set_lift(
2918 __isl_take isl_basic_set *bset);
2919 __isl_give isl_set *isl_set_lift(
2920 __isl_take isl_set *set);
2921 __isl_give isl_union_set *isl_union_set_lift(
2922 __isl_take isl_union_set *uset);
2924 Given a local space that contains the existentially quantified
2925 variables of a set, a basic relation that, when applied to
2926 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2927 can be constructed using the following function.
2929 #include <isl/local_space.h>
2930 __isl_give isl_basic_map *isl_local_space_lifting(
2931 __isl_take isl_local_space *ls);
2933 =item * Internal Product
2935 #include <isl/space.h>
2936 __isl_give isl_space *isl_space_zip(
2937 __isl_take isl_space *space);
2939 #include <isl/map.h>
2940 __isl_give isl_basic_map *isl_basic_map_zip(
2941 __isl_take isl_basic_map *bmap);
2942 __isl_give isl_map *isl_map_zip(
2943 __isl_take isl_map *map);
2944 __isl_give isl_union_map *isl_union_map_zip(
2945 __isl_take isl_union_map *umap);
2947 Given a relation with nested relations for domain and range,
2948 interchange the range of the domain with the domain of the range.
2952 #include <isl/space.h>
2953 __isl_give isl_space *isl_space_curry(
2954 __isl_take isl_space *space);
2955 __isl_give isl_space *isl_space_uncurry(
2956 __isl_take isl_space *space);
2958 #include <isl/map.h>
2959 __isl_give isl_basic_map *isl_basic_map_curry(
2960 __isl_take isl_basic_map *bmap);
2961 __isl_give isl_basic_map *isl_basic_map_uncurry(
2962 __isl_take isl_basic_map *bmap);
2963 __isl_give isl_map *isl_map_curry(
2964 __isl_take isl_map *map);
2965 __isl_give isl_map *isl_map_uncurry(
2966 __isl_take isl_map *map);
2968 #include <isl/union_map.h>
2969 __isl_give isl_union_map *isl_union_map_curry(
2970 __isl_take isl_union_map *umap);
2971 __isl_give isl_union_map *isl_union_map_uncurry(
2972 __isl_take isl_union_map *umap);
2974 Given a relation with a nested relation for domain,
2975 the C<curry> functions
2976 move the range of the nested relation out of the domain
2977 and use it as the domain of a nested relation in the range,
2978 with the original range as range of this nested relation.
2979 The C<uncurry> functions perform the inverse operation.
2981 =item * Aligning parameters
2983 #include <isl/space.h>
2984 __isl_give isl_space *isl_space_align_params(
2985 __isl_take isl_space *space1,
2986 __isl_take isl_space *space2)
2988 #include <isl/set.h>
2989 __isl_give isl_basic_set *isl_basic_set_align_params(
2990 __isl_take isl_basic_set *bset,
2991 __isl_take isl_space *model);
2992 __isl_give isl_set *isl_set_align_params(
2993 __isl_take isl_set *set,
2994 __isl_take isl_space *model);
2996 #include <isl/map.h>
2997 __isl_give isl_basic_map *isl_basic_map_align_params(
2998 __isl_take isl_basic_map *bmap,
2999 __isl_take isl_space *model);
3000 __isl_give isl_map *isl_map_align_params(
3001 __isl_take isl_map *map,
3002 __isl_take isl_space *model);
3004 Change the order of the parameters of the given set or relation
3005 such that the first parameters match those of C<model>.
3006 This may involve the introduction of extra parameters.
3007 All parameters need to be named.
3009 =item * Dimension manipulation
3011 #include <isl/space.h>
3012 __isl_give isl_space *isl_space_add_dims(
3013 __isl_take isl_space *space,
3014 enum isl_dim_type type, unsigned n);
3015 __isl_give isl_space *isl_space_insert_dims(
3016 __isl_take isl_space *space,
3017 enum isl_dim_type type, unsigned pos, unsigned n);
3018 __isl_give isl_space *isl_space_drop_dims(
3019 __isl_take isl_space *space,
3020 enum isl_dim_type type, unsigned first, unsigned n);
3021 __isl_give isl_space *isl_space_move_dims(
3022 __isl_take isl_space *space,
3023 enum isl_dim_type dst_type, unsigned dst_pos,
3024 enum isl_dim_type src_type, unsigned src_pos,
3027 #include <isl/local_space.h>
3028 __isl_give isl_local_space *isl_local_space_add_dims(
3029 __isl_take isl_local_space *ls,
3030 enum isl_dim_type type, unsigned n);
3031 __isl_give isl_local_space *isl_local_space_insert_dims(
3032 __isl_take isl_local_space *ls,
3033 enum isl_dim_type type, unsigned first, unsigned n);
3034 __isl_give isl_local_space *isl_local_space_drop_dims(
3035 __isl_take isl_local_space *ls,
3036 enum isl_dim_type type, unsigned first, unsigned n);
3038 #include <isl/set.h>
3039 __isl_give isl_basic_set *isl_basic_set_add_dims(
3040 __isl_take isl_basic_set *bset,
3041 enum isl_dim_type type, unsigned n);
3042 __isl_give isl_set *isl_set_add_dims(
3043 __isl_take isl_set *set,
3044 enum isl_dim_type type, unsigned n);
3045 __isl_give isl_basic_set *isl_basic_set_insert_dims(
3046 __isl_take isl_basic_set *bset,
3047 enum isl_dim_type type, unsigned pos,
3049 __isl_give isl_set *isl_set_insert_dims(
3050 __isl_take isl_set *set,
3051 enum isl_dim_type type, unsigned pos, unsigned n);
3052 __isl_give isl_basic_set *isl_basic_set_move_dims(
3053 __isl_take isl_basic_set *bset,
3054 enum isl_dim_type dst_type, unsigned dst_pos,
3055 enum isl_dim_type src_type, unsigned src_pos,
3057 __isl_give isl_set *isl_set_move_dims(
3058 __isl_take isl_set *set,
3059 enum isl_dim_type dst_type, unsigned dst_pos,
3060 enum isl_dim_type src_type, unsigned src_pos,
3063 #include <isl/map.h>
3064 __isl_give isl_map *isl_map_add_dims(
3065 __isl_take isl_map *map,
3066 enum isl_dim_type type, unsigned n);
3067 __isl_give isl_basic_map *isl_basic_map_insert_dims(
3068 __isl_take isl_basic_map *bmap,
3069 enum isl_dim_type type, unsigned pos,
3071 __isl_give isl_map *isl_map_insert_dims(
3072 __isl_take isl_map *map,
3073 enum isl_dim_type type, unsigned pos, unsigned n);
3074 __isl_give isl_basic_map *isl_basic_map_move_dims(
3075 __isl_take isl_basic_map *bmap,
3076 enum isl_dim_type dst_type, unsigned dst_pos,
3077 enum isl_dim_type src_type, unsigned src_pos,
3079 __isl_give isl_map *isl_map_move_dims(
3080 __isl_take isl_map *map,
3081 enum isl_dim_type dst_type, unsigned dst_pos,
3082 enum isl_dim_type src_type, unsigned src_pos,
3085 It is usually not advisable to directly change the (input or output)
3086 space of a set or a relation as this removes the name and the internal
3087 structure of the space. However, the above functions can be useful
3088 to add new parameters, assuming
3089 C<isl_set_align_params> and C<isl_map_align_params>
3094 =head2 Binary Operations
3096 The two arguments of a binary operation not only need to live
3097 in the same C<isl_ctx>, they currently also need to have
3098 the same (number of) parameters.
3100 =head3 Basic Operations
3104 =item * Intersection
3106 #include <isl/local_space.h>
3107 __isl_give isl_local_space *isl_local_space_intersect(
3108 __isl_take isl_local_space *ls1,
3109 __isl_take isl_local_space *ls2);
3111 #include <isl/set.h>
3112 __isl_give isl_basic_set *isl_basic_set_intersect_params(
3113 __isl_take isl_basic_set *bset1,
3114 __isl_take isl_basic_set *bset2);
3115 __isl_give isl_basic_set *isl_basic_set_intersect(
3116 __isl_take isl_basic_set *bset1,
3117 __isl_take isl_basic_set *bset2);
3118 __isl_give isl_basic_set *isl_basic_set_list_intersect(
3119 __isl_take struct isl_basic_set_list *list);
3120 __isl_give isl_set *isl_set_intersect_params(
3121 __isl_take isl_set *set,
3122 __isl_take isl_set *params);
3123 __isl_give isl_set *isl_set_intersect(
3124 __isl_take isl_set *set1,
3125 __isl_take isl_set *set2);
3127 #include <isl/map.h>
3128 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
3129 __isl_take isl_basic_map *bmap,
3130 __isl_take isl_basic_set *bset);
3131 __isl_give isl_basic_map *isl_basic_map_intersect_range(
3132 __isl_take isl_basic_map *bmap,
3133 __isl_take isl_basic_set *bset);
3134 __isl_give isl_basic_map *isl_basic_map_intersect(
3135 __isl_take isl_basic_map *bmap1,
3136 __isl_take isl_basic_map *bmap2);
3137 __isl_give isl_map *isl_map_intersect_params(
3138 __isl_take isl_map *map,
3139 __isl_take isl_set *params);
3140 __isl_give isl_map *isl_map_intersect_domain(
3141 __isl_take isl_map *map,
3142 __isl_take isl_set *set);
3143 __isl_give isl_map *isl_map_intersect_range(
3144 __isl_take isl_map *map,
3145 __isl_take isl_set *set);
3146 __isl_give isl_map *isl_map_intersect(
3147 __isl_take isl_map *map1,
3148 __isl_take isl_map *map2);
3150 #include <isl/union_set.h>
3151 __isl_give isl_union_set *isl_union_set_intersect_params(
3152 __isl_take isl_union_set *uset,
3153 __isl_take isl_set *set);
3154 __isl_give isl_union_set *isl_union_set_intersect(
3155 __isl_take isl_union_set *uset1,
3156 __isl_take isl_union_set *uset2);
3158 #include <isl/union_map.h>
3159 __isl_give isl_union_map *isl_union_map_intersect_params(
3160 __isl_take isl_union_map *umap,
3161 __isl_take isl_set *set);
3162 __isl_give isl_union_map *isl_union_map_intersect_domain(
3163 __isl_take isl_union_map *umap,
3164 __isl_take isl_union_set *uset);
3165 __isl_give isl_union_map *isl_union_map_intersect_range(
3166 __isl_take isl_union_map *umap,
3167 __isl_take isl_union_set *uset);
3168 __isl_give isl_union_map *isl_union_map_intersect(
3169 __isl_take isl_union_map *umap1,
3170 __isl_take isl_union_map *umap2);
3172 The second argument to the C<_params> functions needs to be
3173 a parametric (basic) set. For the other functions, a parametric set
3174 for either argument is only allowed if the other argument is
3175 a parametric set as well.
3176 The list passed to C<isl_basic_set_list_intersect> needs to have
3177 at least one element and all elements need to live in the same space.
3181 __isl_give isl_set *isl_basic_set_union(
3182 __isl_take isl_basic_set *bset1,
3183 __isl_take isl_basic_set *bset2);
3184 __isl_give isl_map *isl_basic_map_union(
3185 __isl_take isl_basic_map *bmap1,
3186 __isl_take isl_basic_map *bmap2);
3187 __isl_give isl_set *isl_set_union(
3188 __isl_take isl_set *set1,
3189 __isl_take isl_set *set2);
3190 __isl_give isl_map *isl_map_union(
3191 __isl_take isl_map *map1,
3192 __isl_take isl_map *map2);
3193 __isl_give isl_union_set *isl_union_set_union(
3194 __isl_take isl_union_set *uset1,
3195 __isl_take isl_union_set *uset2);
3196 __isl_give isl_union_map *isl_union_map_union(
3197 __isl_take isl_union_map *umap1,
3198 __isl_take isl_union_map *umap2);
3200 =item * Set difference
3202 __isl_give isl_set *isl_set_subtract(
3203 __isl_take isl_set *set1,
3204 __isl_take isl_set *set2);
3205 __isl_give isl_map *isl_map_subtract(
3206 __isl_take isl_map *map1,
3207 __isl_take isl_map *map2);
3208 __isl_give isl_map *isl_map_subtract_domain(
3209 __isl_take isl_map *map,
3210 __isl_take isl_set *dom);
3211 __isl_give isl_map *isl_map_subtract_range(
3212 __isl_take isl_map *map,
3213 __isl_take isl_set *dom);
3214 __isl_give isl_union_set *isl_union_set_subtract(
3215 __isl_take isl_union_set *uset1,
3216 __isl_take isl_union_set *uset2);
3217 __isl_give isl_union_map *isl_union_map_subtract(
3218 __isl_take isl_union_map *umap1,
3219 __isl_take isl_union_map *umap2);
3220 __isl_give isl_union_map *isl_union_map_subtract_domain(
3221 __isl_take isl_union_map *umap,
3222 __isl_take isl_union_set *dom);
3223 __isl_give isl_union_map *isl_union_map_subtract_range(
3224 __isl_take isl_union_map *umap,
3225 __isl_take isl_union_set *dom);
3229 #include <isl/space.h>
3230 __isl_give isl_space *isl_space_join(
3231 __isl_take isl_space *left,
3232 __isl_take isl_space *right);
3234 #include <isl/set.h>
3235 __isl_give isl_basic_set *isl_basic_set_apply(
3236 __isl_take isl_basic_set *bset,
3237 __isl_take isl_basic_map *bmap);
3238 __isl_give isl_set *isl_set_apply(
3239 __isl_take isl_set *set,
3240 __isl_take isl_map *map);
3242 #include <isl/union_set.h>
3243 __isl_give isl_union_set *isl_union_set_apply(
3244 __isl_take isl_union_set *uset,
3245 __isl_take isl_union_map *umap);
3247 #include <isl/map.h>
3248 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3249 __isl_take isl_basic_map *bmap1,
3250 __isl_take isl_basic_map *bmap2);
3251 __isl_give isl_basic_map *isl_basic_map_apply_range(
3252 __isl_take isl_basic_map *bmap1,
3253 __isl_take isl_basic_map *bmap2);
3254 __isl_give isl_map *isl_map_apply_domain(
3255 __isl_take isl_map *map1,
3256 __isl_take isl_map *map2);
3257 __isl_give isl_map *isl_map_apply_range(
3258 __isl_take isl_map *map1,
3259 __isl_take isl_map *map2);
3261 #include <isl/union_map.h>
3262 __isl_give isl_union_map *isl_union_map_apply_domain(
3263 __isl_take isl_union_map *umap1,
3264 __isl_take isl_union_map *umap2);
3265 __isl_give isl_union_map *isl_union_map_apply_range(
3266 __isl_take isl_union_map *umap1,
3267 __isl_take isl_union_map *umap2);
3271 #include <isl/set.h>
3272 __isl_give isl_basic_set *
3273 isl_basic_set_preimage_multi_aff(
3274 __isl_take isl_basic_set *bset,
3275 __isl_take isl_multi_aff *ma);
3276 __isl_give isl_set *isl_set_preimage_multi_aff(
3277 __isl_take isl_set *set,
3278 __isl_take isl_multi_aff *ma);
3279 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3280 __isl_take isl_set *set,
3281 __isl_take isl_pw_multi_aff *pma);
3282 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
3283 __isl_take isl_set *set,
3284 __isl_take isl_multi_pw_aff *mpa);
3286 #include <isl/union_set.h>
3287 __isl_give isl_union_set *
3288 isl_union_set_preimage_multi_aff(
3289 __isl_take isl_union_set *uset,
3290 __isl_take isl_multi_aff *ma);
3291 __isl_give isl_union_set *
3292 isl_union_set_preimage_pw_multi_aff(
3293 __isl_take isl_union_set *uset,
3294 __isl_take isl_pw_multi_aff *pma);
3295 __isl_give isl_union_set *
3296 isl_union_set_preimage_union_pw_multi_aff(
3297 __isl_take isl_union_set *uset,
3298 __isl_take isl_union_pw_multi_aff *upma);
3300 #include <isl/map.h>
3301 __isl_give isl_basic_map *
3302 isl_basic_map_preimage_domain_multi_aff(
3303 __isl_take isl_basic_map *bmap,
3304 __isl_take isl_multi_aff *ma);
3305 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3306 __isl_take isl_map *map,
3307 __isl_take isl_multi_aff *ma);
3308 __isl_give isl_map *isl_map_preimage_range_multi_aff(
3309 __isl_take isl_map *map,
3310 __isl_take isl_multi_aff *ma);
3311 __isl_give isl_map *
3312 isl_map_preimage_domain_pw_multi_aff(
3313 __isl_take isl_map *map,
3314 __isl_take isl_pw_multi_aff *pma);
3315 __isl_give isl_map *
3316 isl_map_preimage_range_pw_multi_aff(
3317 __isl_take isl_map *map,
3318 __isl_take isl_pw_multi_aff *pma);
3319 __isl_give isl_map *
3320 isl_map_preimage_domain_multi_pw_aff(
3321 __isl_take isl_map *map,
3322 __isl_take isl_multi_pw_aff *mpa);
3323 __isl_give isl_basic_map *
3324 isl_basic_map_preimage_range_multi_aff(
3325 __isl_take isl_basic_map *bmap,
3326 __isl_take isl_multi_aff *ma);
3328 #include <isl/union_map.h>
3329 __isl_give isl_union_map *
3330 isl_union_map_preimage_domain_multi_aff(
3331 __isl_take isl_union_map *umap,
3332 __isl_take isl_multi_aff *ma);
3333 __isl_give isl_union_map *
3334 isl_union_map_preimage_range_multi_aff(
3335 __isl_take isl_union_map *umap,
3336 __isl_take isl_multi_aff *ma);
3337 __isl_give isl_union_map *
3338 isl_union_map_preimage_domain_pw_multi_aff(
3339 __isl_take isl_union_map *umap,
3340 __isl_take isl_pw_multi_aff *pma);
3341 __isl_give isl_union_map *
3342 isl_union_map_preimage_range_pw_multi_aff(
3343 __isl_take isl_union_map *umap,
3344 __isl_take isl_pw_multi_aff *pma);
3345 __isl_give isl_union_map *
3346 isl_union_map_preimage_domain_union_pw_multi_aff(
3347 __isl_take isl_union_map *umap,
3348 __isl_take isl_union_pw_multi_aff *upma);
3349 __isl_give isl_union_map *
3350 isl_union_map_preimage_range_union_pw_multi_aff(
3351 __isl_take isl_union_map *umap,
3352 __isl_take isl_union_pw_multi_aff *upma);
3354 These functions compute the preimage of the given set or map domain/range under
3355 the given function. In other words, the expression is plugged
3356 into the set description or into the domain/range of the map.
3357 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3358 L</"Piecewise Multiple Quasi Affine Expressions">.
3360 =item * Cartesian Product
3362 #include <isl/space.h>
3363 __isl_give isl_space *isl_space_product(
3364 __isl_take isl_space *space1,
3365 __isl_take isl_space *space2);
3366 __isl_give isl_space *isl_space_domain_product(
3367 __isl_take isl_space *space1,
3368 __isl_take isl_space *space2);
3369 __isl_give isl_space *isl_space_range_product(
3370 __isl_take isl_space *space1,
3371 __isl_take isl_space *space2);
3374 C<isl_space_product>, C<isl_space_domain_product>
3375 and C<isl_space_range_product> take pairs or relation spaces and
3376 produce a single relations space, where either the domain, the range
3377 or both domain and range are wrapped spaces of relations between
3378 the domains and/or ranges of the input spaces.
3379 If the product is only constructed over the domain or the range
3380 then the ranges or the domains of the inputs should be the same.
3381 The function C<isl_space_product> also accepts a pair of set spaces,
3382 in which case it returns a wrapped space of a relation between the
3385 #include <isl/set.h>
3386 __isl_give isl_set *isl_set_product(
3387 __isl_take isl_set *set1,
3388 __isl_take isl_set *set2);
3390 #include <isl/map.h>
3391 __isl_give isl_basic_map *isl_basic_map_domain_product(
3392 __isl_take isl_basic_map *bmap1,
3393 __isl_take isl_basic_map *bmap2);
3394 __isl_give isl_basic_map *isl_basic_map_range_product(
3395 __isl_take isl_basic_map *bmap1,
3396 __isl_take isl_basic_map *bmap2);
3397 __isl_give isl_basic_map *isl_basic_map_product(
3398 __isl_take isl_basic_map *bmap1,
3399 __isl_take isl_basic_map *bmap2);
3400 __isl_give isl_map *isl_map_domain_product(
3401 __isl_take isl_map *map1,
3402 __isl_take isl_map *map2);
3403 __isl_give isl_map *isl_map_range_product(
3404 __isl_take isl_map *map1,
3405 __isl_take isl_map *map2);
3406 __isl_give isl_map *isl_map_product(
3407 __isl_take isl_map *map1,
3408 __isl_take isl_map *map2);
3410 #include <isl/union_set.h>
3411 __isl_give isl_union_set *isl_union_set_product(
3412 __isl_take isl_union_set *uset1,
3413 __isl_take isl_union_set *uset2);
3415 #include <isl/union_map.h>
3416 __isl_give isl_union_map *isl_union_map_domain_product(
3417 __isl_take isl_union_map *umap1,
3418 __isl_take isl_union_map *umap2);
3419 __isl_give isl_union_map *isl_union_map_range_product(
3420 __isl_take isl_union_map *umap1,
3421 __isl_take isl_union_map *umap2);
3422 __isl_give isl_union_map *isl_union_map_product(
3423 __isl_take isl_union_map *umap1,
3424 __isl_take isl_union_map *umap2);
3426 The above functions compute the cross product of the given
3427 sets or relations. The domains and ranges of the results
3428 are wrapped maps between domains and ranges of the inputs.
3429 To obtain a ``flat'' product, use the following functions
3432 __isl_give isl_basic_set *isl_basic_set_flat_product(
3433 __isl_take isl_basic_set *bset1,
3434 __isl_take isl_basic_set *bset2);
3435 __isl_give isl_set *isl_set_flat_product(
3436 __isl_take isl_set *set1,
3437 __isl_take isl_set *set2);
3438 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3439 __isl_take isl_basic_map *bmap1,
3440 __isl_take isl_basic_map *bmap2);
3441 __isl_give isl_map *isl_map_flat_domain_product(
3442 __isl_take isl_map *map1,
3443 __isl_take isl_map *map2);
3444 __isl_give isl_map *isl_map_flat_range_product(
3445 __isl_take isl_map *map1,
3446 __isl_take isl_map *map2);
3447 __isl_give isl_union_map *isl_union_map_flat_range_product(
3448 __isl_take isl_union_map *umap1,
3449 __isl_take isl_union_map *umap2);
3450 __isl_give isl_basic_map *isl_basic_map_flat_product(
3451 __isl_take isl_basic_map *bmap1,
3452 __isl_take isl_basic_map *bmap2);
3453 __isl_give isl_map *isl_map_flat_product(
3454 __isl_take isl_map *map1,
3455 __isl_take isl_map *map2);
3457 #include <isl/space.h>
3458 __isl_give isl_space *isl_space_domain_factor_domain(
3459 __isl_take isl_space *space);
3460 __isl_give isl_space *isl_space_range_factor_domain(
3461 __isl_take isl_space *space);
3462 __isl_give isl_space *isl_space_range_factor_range(
3463 __isl_take isl_space *space);
3465 The functions C<isl_space_range_factor_domain> and
3466 C<isl_space_range_factor_range> extract the two arguments from
3467 the result of a call to C<isl_space_range_product>.
3469 The arguments of a call to C<isl_map_range_product> can be extracted
3470 from the result using the following two functions.
3472 #include <isl/map.h>
3473 __isl_give isl_map *isl_map_range_factor_domain(
3474 __isl_take isl_map *map);
3475 __isl_give isl_map *isl_map_range_factor_range(
3476 __isl_take isl_map *map);
3478 =item * Simplification
3480 __isl_give isl_basic_set *isl_basic_set_gist(
3481 __isl_take isl_basic_set *bset,
3482 __isl_take isl_basic_set *context);
3483 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3484 __isl_take isl_set *context);
3485 __isl_give isl_set *isl_set_gist_params(
3486 __isl_take isl_set *set,
3487 __isl_take isl_set *context);
3488 __isl_give isl_union_set *isl_union_set_gist(
3489 __isl_take isl_union_set *uset,
3490 __isl_take isl_union_set *context);
3491 __isl_give isl_union_set *isl_union_set_gist_params(
3492 __isl_take isl_union_set *uset,
3493 __isl_take isl_set *set);
3494 __isl_give isl_basic_map *isl_basic_map_gist(
3495 __isl_take isl_basic_map *bmap,
3496 __isl_take isl_basic_map *context);
3497 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3498 __isl_take isl_map *context);
3499 __isl_give isl_map *isl_map_gist_params(
3500 __isl_take isl_map *map,
3501 __isl_take isl_set *context);
3502 __isl_give isl_map *isl_map_gist_domain(
3503 __isl_take isl_map *map,
3504 __isl_take isl_set *context);
3505 __isl_give isl_map *isl_map_gist_range(
3506 __isl_take isl_map *map,
3507 __isl_take isl_set *context);
3508 __isl_give isl_union_map *isl_union_map_gist(
3509 __isl_take isl_union_map *umap,
3510 __isl_take isl_union_map *context);
3511 __isl_give isl_union_map *isl_union_map_gist_params(
3512 __isl_take isl_union_map *umap,
3513 __isl_take isl_set *set);
3514 __isl_give isl_union_map *isl_union_map_gist_domain(
3515 __isl_take isl_union_map *umap,
3516 __isl_take isl_union_set *uset);
3517 __isl_give isl_union_map *isl_union_map_gist_range(
3518 __isl_take isl_union_map *umap,
3519 __isl_take isl_union_set *uset);
3521 The gist operation returns a set or relation that has the
3522 same intersection with the context as the input set or relation.
3523 Any implicit equality in the intersection is made explicit in the result,
3524 while all inequalities that are redundant with respect to the intersection
3526 In case of union sets and relations, the gist operation is performed
3531 =head3 Lexicographic Optimization
3533 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3534 the following functions
3535 compute a set that contains the lexicographic minimum or maximum
3536 of the elements in C<set> (or C<bset>) for those values of the parameters
3537 that satisfy C<dom>.
3538 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3539 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3541 In other words, the union of the parameter values
3542 for which the result is non-empty and of C<*empty>
3545 __isl_give isl_set *isl_basic_set_partial_lexmin(
3546 __isl_take isl_basic_set *bset,
3547 __isl_take isl_basic_set *dom,
3548 __isl_give isl_set **empty);
3549 __isl_give isl_set *isl_basic_set_partial_lexmax(
3550 __isl_take isl_basic_set *bset,
3551 __isl_take isl_basic_set *dom,
3552 __isl_give isl_set **empty);
3553 __isl_give isl_set *isl_set_partial_lexmin(
3554 __isl_take isl_set *set, __isl_take isl_set *dom,
3555 __isl_give isl_set **empty);
3556 __isl_give isl_set *isl_set_partial_lexmax(
3557 __isl_take isl_set *set, __isl_take isl_set *dom,
3558 __isl_give isl_set **empty);
3560 Given a (basic) set C<set> (or C<bset>), the following functions simply
3561 return a set containing the lexicographic minimum or maximum
3562 of the elements in C<set> (or C<bset>).
3563 In case of union sets, the optimum is computed per space.
3565 __isl_give isl_set *isl_basic_set_lexmin(
3566 __isl_take isl_basic_set *bset);
3567 __isl_give isl_set *isl_basic_set_lexmax(
3568 __isl_take isl_basic_set *bset);
3569 __isl_give isl_set *isl_set_lexmin(
3570 __isl_take isl_set *set);
3571 __isl_give isl_set *isl_set_lexmax(
3572 __isl_take isl_set *set);
3573 __isl_give isl_union_set *isl_union_set_lexmin(
3574 __isl_take isl_union_set *uset);
3575 __isl_give isl_union_set *isl_union_set_lexmax(
3576 __isl_take isl_union_set *uset);
3578 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3579 the following functions
3580 compute a relation that maps each element of C<dom>
3581 to the single lexicographic minimum or maximum
3582 of the elements that are associated to that same
3583 element in C<map> (or C<bmap>).
3584 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3585 that contains the elements in C<dom> that do not map
3586 to any elements in C<map> (or C<bmap>).
3587 In other words, the union of the domain of the result and of C<*empty>
3590 __isl_give isl_map *isl_basic_map_partial_lexmax(
3591 __isl_take isl_basic_map *bmap,
3592 __isl_take isl_basic_set *dom,
3593 __isl_give isl_set **empty);
3594 __isl_give isl_map *isl_basic_map_partial_lexmin(
3595 __isl_take isl_basic_map *bmap,
3596 __isl_take isl_basic_set *dom,
3597 __isl_give isl_set **empty);
3598 __isl_give isl_map *isl_map_partial_lexmax(
3599 __isl_take isl_map *map, __isl_take isl_set *dom,
3600 __isl_give isl_set **empty);
3601 __isl_give isl_map *isl_map_partial_lexmin(
3602 __isl_take isl_map *map, __isl_take isl_set *dom,
3603 __isl_give isl_set **empty);
3605 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3606 return a map mapping each element in the domain of
3607 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3608 of all elements associated to that element.
3609 In case of union relations, the optimum is computed per space.
3611 __isl_give isl_map *isl_basic_map_lexmin(
3612 __isl_take isl_basic_map *bmap);
3613 __isl_give isl_map *isl_basic_map_lexmax(
3614 __isl_take isl_basic_map *bmap);
3615 __isl_give isl_map *isl_map_lexmin(
3616 __isl_take isl_map *map);
3617 __isl_give isl_map *isl_map_lexmax(
3618 __isl_take isl_map *map);
3619 __isl_give isl_union_map *isl_union_map_lexmin(
3620 __isl_take isl_union_map *umap);
3621 __isl_give isl_union_map *isl_union_map_lexmax(
3622 __isl_take isl_union_map *umap);
3624 The following functions return their result in the form of
3625 a piecewise multi-affine expression
3626 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3627 but are otherwise equivalent to the corresponding functions
3628 returning a basic set or relation.
3630 __isl_give isl_pw_multi_aff *
3631 isl_basic_map_lexmin_pw_multi_aff(
3632 __isl_take isl_basic_map *bmap);
3633 __isl_give isl_pw_multi_aff *
3634 isl_basic_set_partial_lexmin_pw_multi_aff(
3635 __isl_take isl_basic_set *bset,
3636 __isl_take isl_basic_set *dom,
3637 __isl_give isl_set **empty);
3638 __isl_give isl_pw_multi_aff *
3639 isl_basic_set_partial_lexmax_pw_multi_aff(
3640 __isl_take isl_basic_set *bset,
3641 __isl_take isl_basic_set *dom,
3642 __isl_give isl_set **empty);
3643 __isl_give isl_pw_multi_aff *
3644 isl_basic_map_partial_lexmin_pw_multi_aff(
3645 __isl_take isl_basic_map *bmap,
3646 __isl_take isl_basic_set *dom,
3647 __isl_give isl_set **empty);
3648 __isl_give isl_pw_multi_aff *
3649 isl_basic_map_partial_lexmax_pw_multi_aff(
3650 __isl_take isl_basic_map *bmap,
3651 __isl_take isl_basic_set *dom,
3652 __isl_give isl_set **empty);
3653 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3654 __isl_take isl_set *set);
3655 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3656 __isl_take isl_set *set);
3657 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3658 __isl_take isl_map *map);
3659 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3660 __isl_take isl_map *map);
3664 Lists are defined over several element types, including
3665 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3666 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3667 Here we take lists of C<isl_set>s as an example.
3668 Lists can be created, copied, modified and freed using the following functions.
3670 #include <isl/set.h>
3671 __isl_give isl_set_list *isl_set_list_from_set(
3672 __isl_take isl_set *el);
3673 __isl_give isl_set_list *isl_set_list_alloc(
3674 isl_ctx *ctx, int n);
3675 __isl_give isl_set_list *isl_set_list_copy(
3676 __isl_keep isl_set_list *list);
3677 __isl_give isl_set_list *isl_set_list_insert(
3678 __isl_take isl_set_list *list, unsigned pos,
3679 __isl_take isl_set *el);
3680 __isl_give isl_set_list *isl_set_list_add(
3681 __isl_take isl_set_list *list,
3682 __isl_take isl_set *el);
3683 __isl_give isl_set_list *isl_set_list_drop(
3684 __isl_take isl_set_list *list,
3685 unsigned first, unsigned n);
3686 __isl_give isl_set_list *isl_set_list_set_set(
3687 __isl_take isl_set_list *list, int index,
3688 __isl_take isl_set *set);
3689 __isl_give isl_set_list *isl_set_list_concat(
3690 __isl_take isl_set_list *list1,
3691 __isl_take isl_set_list *list2);
3692 __isl_give isl_set_list *isl_set_list_sort(
3693 __isl_take isl_set_list *list,
3694 int (*cmp)(__isl_keep isl_set *a,
3695 __isl_keep isl_set *b, void *user),
3697 __isl_null isl_set_list *isl_set_list_free(
3698 __isl_take isl_set_list *list);
3700 C<isl_set_list_alloc> creates an empty list with a capacity for
3701 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3704 Lists can be inspected using the following functions.
3706 #include <isl/set.h>
3707 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3708 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3709 __isl_give isl_set *isl_set_list_get_set(
3710 __isl_keep isl_set_list *list, int index);
3711 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3712 int (*fn)(__isl_take isl_set *el, void *user),
3714 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3715 int (*follows)(__isl_keep isl_set *a,
3716 __isl_keep isl_set *b, void *user),
3718 int (*fn)(__isl_take isl_set *el, void *user),
3721 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3722 strongly connected components of the graph with as vertices the elements
3723 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3724 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3725 should return C<-1> on error.
3727 Lists can be printed using
3729 #include <isl/set.h>
3730 __isl_give isl_printer *isl_printer_print_set_list(
3731 __isl_take isl_printer *p,
3732 __isl_keep isl_set_list *list);
3734 =head2 Associative arrays
3736 Associative arrays map isl objects of a specific type to isl objects
3737 of some (other) specific type. They are defined for several pairs
3738 of types, including (C<isl_map>, C<isl_basic_set>),
3739 (C<isl_id>, C<isl_ast_expr>) and.
3740 (C<isl_id>, C<isl_pw_aff>).
3741 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3744 Associative arrays can be created, copied and freed using
3745 the following functions.
3747 #include <isl/id_to_ast_expr.h>
3748 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3749 isl_ctx *ctx, int min_size);
3750 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3751 __isl_keep id_to_ast_expr *id2expr);
3752 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
3753 __isl_take id_to_ast_expr *id2expr);
3755 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3756 to specify the expected size of the associative array.
3757 The associative array will be grown automatically as needed.
3759 Associative arrays can be inspected using the following functions.
3761 #include <isl/id_to_ast_expr.h>
3762 isl_ctx *isl_id_to_ast_expr_get_ctx(
3763 __isl_keep id_to_ast_expr *id2expr);
3764 int isl_id_to_ast_expr_has(
3765 __isl_keep id_to_ast_expr *id2expr,
3766 __isl_keep isl_id *key);
3767 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3768 __isl_keep id_to_ast_expr *id2expr,
3769 __isl_take isl_id *key);
3770 int isl_id_to_ast_expr_foreach(
3771 __isl_keep id_to_ast_expr *id2expr,
3772 int (*fn)(__isl_take isl_id *key,
3773 __isl_take isl_ast_expr *val, void *user),
3776 They can be modified using the following function.
3778 #include <isl/id_to_ast_expr.h>
3779 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3780 __isl_take id_to_ast_expr *id2expr,
3781 __isl_take isl_id *key,
3782 __isl_take isl_ast_expr *val);
3783 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
3784 __isl_take id_to_ast_expr *id2expr,
3785 __isl_take isl_id *key);
3787 Associative arrays can be printed using the following function.
3789 #include <isl/id_to_ast_expr.h>
3790 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3791 __isl_take isl_printer *p,
3792 __isl_keep id_to_ast_expr *id2expr);
3794 =head2 Multiple Values
3796 An C<isl_multi_val> object represents a sequence of zero or more values,
3797 living in a set space.
3799 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3800 using the following function
3802 #include <isl/val.h>
3803 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3804 __isl_take isl_space *space,
3805 __isl_take isl_val_list *list);
3807 The zero multiple value (with value zero for each set dimension)
3808 can be created using the following function.
3810 #include <isl/val.h>
3811 __isl_give isl_multi_val *isl_multi_val_zero(
3812 __isl_take isl_space *space);
3814 Multiple values can be copied and freed using
3816 #include <isl/val.h>
3817 __isl_give isl_multi_val *isl_multi_val_copy(
3818 __isl_keep isl_multi_val *mv);
3819 __isl_null isl_multi_val *isl_multi_val_free(
3820 __isl_take isl_multi_val *mv);
3822 They can be inspected using
3824 #include <isl/val.h>
3825 isl_ctx *isl_multi_val_get_ctx(
3826 __isl_keep isl_multi_val *mv);
3827 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3828 enum isl_dim_type type);
3829 __isl_give isl_val *isl_multi_val_get_val(
3830 __isl_keep isl_multi_val *mv, int pos);
3831 int isl_multi_val_find_dim_by_id(
3832 __isl_keep isl_multi_val *mv,
3833 enum isl_dim_type type, __isl_keep isl_id *id);
3834 __isl_give isl_id *isl_multi_val_get_dim_id(
3835 __isl_keep isl_multi_val *mv,
3836 enum isl_dim_type type, unsigned pos);
3837 const char *isl_multi_val_get_tuple_name(
3838 __isl_keep isl_multi_val *mv,
3839 enum isl_dim_type type);
3840 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3841 enum isl_dim_type type);
3842 __isl_give isl_id *isl_multi_val_get_tuple_id(
3843 __isl_keep isl_multi_val *mv,
3844 enum isl_dim_type type);
3845 int isl_multi_val_range_is_wrapping(
3846 __isl_keep isl_multi_val *mv);
3848 They can be modified using
3850 #include <isl/val.h>
3851 __isl_give isl_multi_val *isl_multi_val_set_val(
3852 __isl_take isl_multi_val *mv, int pos,
3853 __isl_take isl_val *val);
3854 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3855 __isl_take isl_multi_val *mv,
3856 enum isl_dim_type type, unsigned pos, const char *s);
3857 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3858 __isl_take isl_multi_val *mv,
3859 enum isl_dim_type type, unsigned pos,
3860 __isl_take isl_id *id);
3861 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3862 __isl_take isl_multi_val *mv,
3863 enum isl_dim_type type, const char *s);
3864 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3865 __isl_take isl_multi_val *mv,
3866 enum isl_dim_type type, __isl_take isl_id *id);
3867 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3868 __isl_take isl_multi_val *mv,
3869 enum isl_dim_type type);
3870 __isl_give isl_multi_val *isl_multi_val_reset_user(
3871 __isl_take isl_multi_val *mv);
3873 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3874 __isl_take isl_multi_val *mv,
3875 enum isl_dim_type type, unsigned first, unsigned n);
3876 __isl_give isl_multi_val *isl_multi_val_add_dims(
3877 __isl_take isl_multi_val *mv,
3878 enum isl_dim_type type, unsigned n);
3879 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3880 __isl_take isl_multi_val *mv,
3881 enum isl_dim_type type, unsigned first, unsigned n);
3885 #include <isl/val.h>
3886 __isl_give isl_multi_val *isl_multi_val_align_params(
3887 __isl_take isl_multi_val *mv,
3888 __isl_take isl_space *model);
3889 __isl_give isl_multi_val *isl_multi_val_from_range(
3890 __isl_take isl_multi_val *mv);
3891 __isl_give isl_multi_val *isl_multi_val_range_splice(
3892 __isl_take isl_multi_val *mv1, unsigned pos,
3893 __isl_take isl_multi_val *mv2);
3894 __isl_give isl_multi_val *isl_multi_val_range_product(
3895 __isl_take isl_multi_val *mv1,
3896 __isl_take isl_multi_val *mv2);
3897 __isl_give isl_multi_val *
3898 isl_multi_val_range_factor_domain(
3899 __isl_take isl_multi_val *mv);
3900 __isl_give isl_multi_val *
3901 isl_multi_val_range_factor_range(
3902 __isl_take isl_multi_val *mv);
3903 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3904 __isl_take isl_multi_val *mv1,
3905 __isl_take isl_multi_aff *mv2);
3906 __isl_give isl_multi_val *isl_multi_val_product(
3907 __isl_take isl_multi_val *mv1,
3908 __isl_take isl_multi_val *mv2);
3909 __isl_give isl_multi_val *isl_multi_val_add_val(
3910 __isl_take isl_multi_val *mv,
3911 __isl_take isl_val *v);
3912 __isl_give isl_multi_val *isl_multi_val_mod_val(
3913 __isl_take isl_multi_val *mv,
3914 __isl_take isl_val *v);
3915 __isl_give isl_multi_val *isl_multi_val_scale_val(
3916 __isl_take isl_multi_val *mv,
3917 __isl_take isl_val *v);
3918 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3919 __isl_take isl_multi_val *mv1,
3920 __isl_take isl_multi_val *mv2);
3921 __isl_give isl_multi_val *
3922 isl_multi_val_scale_down_multi_val(
3923 __isl_take isl_multi_val *mv1,
3924 __isl_take isl_multi_val *mv2);
3926 A multiple value can be printed using
3928 __isl_give isl_printer *isl_printer_print_multi_val(
3929 __isl_take isl_printer *p,
3930 __isl_keep isl_multi_val *mv);
3934 Vectors can be created, copied and freed using the following functions.
3936 #include <isl/vec.h>
3937 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3939 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3940 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
3942 Note that the elements of a newly created vector may have arbitrary values.
3943 The elements can be changed and inspected using the following functions.
3945 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3946 int isl_vec_size(__isl_keep isl_vec *vec);
3947 __isl_give isl_val *isl_vec_get_element_val(
3948 __isl_keep isl_vec *vec, int pos);
3949 __isl_give isl_vec *isl_vec_set_element_si(
3950 __isl_take isl_vec *vec, int pos, int v);
3951 __isl_give isl_vec *isl_vec_set_element_val(
3952 __isl_take isl_vec *vec, int pos,
3953 __isl_take isl_val *v);
3954 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3956 __isl_give isl_vec *isl_vec_set_val(
3957 __isl_take isl_vec *vec, __isl_take isl_val *v);
3958 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3959 __isl_keep isl_vec *vec2, int pos);
3961 C<isl_vec_get_element> will return a negative value if anything went wrong.
3962 In that case, the value of C<*v> is undefined.
3964 The following function can be used to concatenate two vectors.
3966 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3967 __isl_take isl_vec *vec2);
3971 Matrices can be created, copied and freed using the following functions.
3973 #include <isl/mat.h>
3974 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3975 unsigned n_row, unsigned n_col);
3976 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3977 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
3979 Note that the elements of a newly created matrix may have arbitrary values.
3980 The elements can be changed and inspected using the following functions.
3982 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3983 int isl_mat_rows(__isl_keep isl_mat *mat);
3984 int isl_mat_cols(__isl_keep isl_mat *mat);
3985 __isl_give isl_val *isl_mat_get_element_val(
3986 __isl_keep isl_mat *mat, int row, int col);
3987 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3988 int row, int col, int v);
3989 __isl_give isl_mat *isl_mat_set_element_val(
3990 __isl_take isl_mat *mat, int row, int col,
3991 __isl_take isl_val *v);
3993 C<isl_mat_get_element> will return a negative value if anything went wrong.
3994 In that case, the value of C<*v> is undefined.
3996 The following function can be used to compute the (right) inverse
3997 of a matrix, i.e., a matrix such that the product of the original
3998 and the inverse (in that order) is a multiple of the identity matrix.
3999 The input matrix is assumed to be of full row-rank.
4001 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
4003 The following function can be used to compute the (right) kernel
4004 (or null space) of a matrix, i.e., a matrix such that the product of
4005 the original and the kernel (in that order) is the zero matrix.
4007 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
4009 =head2 Piecewise Quasi Affine Expressions
4011 The zero quasi affine expression or the quasi affine expression
4012 that is equal to a given value or
4013 a specified dimension on a given domain can be created using
4015 __isl_give isl_aff *isl_aff_zero_on_domain(
4016 __isl_take isl_local_space *ls);
4017 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
4018 __isl_take isl_local_space *ls);
4019 __isl_give isl_aff *isl_aff_val_on_domain(
4020 __isl_take isl_local_space *ls,
4021 __isl_take isl_val *val);
4022 __isl_give isl_aff *isl_aff_var_on_domain(
4023 __isl_take isl_local_space *ls,
4024 enum isl_dim_type type, unsigned pos);
4025 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
4026 __isl_take isl_local_space *ls,
4027 enum isl_dim_type type, unsigned pos);
4028 __isl_give isl_aff *isl_aff_nan_on_domain(
4029 __isl_take isl_local_space *ls);
4030 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
4031 __isl_take isl_local_space *ls);
4033 Note that the space in which the resulting objects live is a map space
4034 with the given space as domain and a one-dimensional range.
4036 An empty piecewise quasi affine expression (one with no cells)
4037 or a piecewise quasi affine expression with a single cell can
4038 be created using the following functions.
4040 #include <isl/aff.h>
4041 __isl_give isl_pw_aff *isl_pw_aff_empty(
4042 __isl_take isl_space *space);
4043 __isl_give isl_pw_aff *isl_pw_aff_alloc(
4044 __isl_take isl_set *set, __isl_take isl_aff *aff);
4045 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
4046 __isl_take isl_aff *aff);
4048 A piecewise quasi affine expression that is equal to 1 on a set
4049 and 0 outside the set can be created using the following function.
4051 #include <isl/aff.h>
4052 __isl_give isl_pw_aff *isl_set_indicator_function(
4053 __isl_take isl_set *set);
4055 Quasi affine expressions can be copied and freed using
4057 #include <isl/aff.h>
4058 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
4059 __isl_null isl_aff *isl_aff_free(__isl_take isl_aff *aff);
4061 __isl_give isl_pw_aff *isl_pw_aff_copy(
4062 __isl_keep isl_pw_aff *pwaff);
4063 __isl_null isl_pw_aff *isl_pw_aff_free(
4064 __isl_take isl_pw_aff *pwaff);
4066 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
4067 using the following function. The constraint is required to have
4068 a non-zero coefficient for the specified dimension.
4070 #include <isl/constraint.h>
4071 __isl_give isl_aff *isl_constraint_get_bound(
4072 __isl_keep isl_constraint *constraint,
4073 enum isl_dim_type type, int pos);
4075 The entire affine expression of the constraint can also be extracted
4076 using the following function.
4078 #include <isl/constraint.h>
4079 __isl_give isl_aff *isl_constraint_get_aff(
4080 __isl_keep isl_constraint *constraint);
4082 Conversely, an equality constraint equating
4083 the affine expression to zero or an inequality constraint enforcing
4084 the affine expression to be non-negative, can be constructed using
4086 __isl_give isl_constraint *isl_equality_from_aff(
4087 __isl_take isl_aff *aff);
4088 __isl_give isl_constraint *isl_inequality_from_aff(
4089 __isl_take isl_aff *aff);
4091 The expression can be inspected using
4093 #include <isl/aff.h>
4094 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
4095 int isl_aff_dim(__isl_keep isl_aff *aff,
4096 enum isl_dim_type type);
4097 __isl_give isl_local_space *isl_aff_get_domain_local_space(
4098 __isl_keep isl_aff *aff);
4099 __isl_give isl_local_space *isl_aff_get_local_space(
4100 __isl_keep isl_aff *aff);
4101 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
4102 enum isl_dim_type type, unsigned pos);
4103 const char *isl_pw_aff_get_dim_name(
4104 __isl_keep isl_pw_aff *pa,
4105 enum isl_dim_type type, unsigned pos);
4106 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
4107 enum isl_dim_type type, unsigned pos);
4108 __isl_give isl_id *isl_pw_aff_get_dim_id(
4109 __isl_keep isl_pw_aff *pa,
4110 enum isl_dim_type type, unsigned pos);
4111 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
4112 enum isl_dim_type type);
4113 __isl_give isl_id *isl_pw_aff_get_tuple_id(
4114 __isl_keep isl_pw_aff *pa,
4115 enum isl_dim_type type);
4116 __isl_give isl_val *isl_aff_get_constant_val(
4117 __isl_keep isl_aff *aff);
4118 __isl_give isl_val *isl_aff_get_coefficient_val(
4119 __isl_keep isl_aff *aff,
4120 enum isl_dim_type type, int pos);
4121 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
4122 enum isl_dim_type type, int pos);
4123 __isl_give isl_val *isl_aff_get_denominator_val(
4124 __isl_keep isl_aff *aff);
4125 __isl_give isl_aff *isl_aff_get_div(
4126 __isl_keep isl_aff *aff, int pos);
4128 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
4129 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
4130 int (*fn)(__isl_take isl_set *set,
4131 __isl_take isl_aff *aff,
4132 void *user), void *user);
4134 int isl_aff_is_cst(__isl_keep isl_aff *aff);
4135 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4137 int isl_aff_is_nan(__isl_keep isl_aff *aff);
4138 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
4140 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
4141 enum isl_dim_type type, unsigned first, unsigned n);
4142 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
4143 enum isl_dim_type type, unsigned first, unsigned n);
4145 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
4146 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
4147 enum isl_dim_type type);
4148 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
4150 It can be modified using
4152 #include <isl/aff.h>
4153 __isl_give isl_aff *isl_aff_set_tuple_id(
4154 __isl_take isl_aff *aff,
4155 enum isl_dim_type type, __isl_take isl_id *id);
4156 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
4157 __isl_take isl_pw_aff *pwaff,
4158 enum isl_dim_type type, __isl_take isl_id *id);
4159 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
4160 __isl_take isl_pw_aff *pa,
4161 enum isl_dim_type type);
4162 __isl_give isl_aff *isl_aff_set_dim_name(
4163 __isl_take isl_aff *aff, enum isl_dim_type type,
4164 unsigned pos, const char *s);
4165 __isl_give isl_aff *isl_aff_set_dim_id(
4166 __isl_take isl_aff *aff, enum isl_dim_type type,
4167 unsigned pos, __isl_take isl_id *id);
4168 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
4169 __isl_take isl_pw_aff *pma,
4170 enum isl_dim_type type, unsigned pos,
4171 __isl_take isl_id *id);
4172 __isl_give isl_aff *isl_aff_set_constant_si(
4173 __isl_take isl_aff *aff, int v);
4174 __isl_give isl_aff *isl_aff_set_constant_val(
4175 __isl_take isl_aff *aff, __isl_take isl_val *v);
4176 __isl_give isl_aff *isl_aff_set_coefficient_si(
4177 __isl_take isl_aff *aff,
4178 enum isl_dim_type type, int pos, int v);
4179 __isl_give isl_aff *isl_aff_set_coefficient_val(
4180 __isl_take isl_aff *aff,
4181 enum isl_dim_type type, int pos,
4182 __isl_take isl_val *v);
4184 __isl_give isl_aff *isl_aff_add_constant_si(
4185 __isl_take isl_aff *aff, int v);
4186 __isl_give isl_aff *isl_aff_add_constant_val(
4187 __isl_take isl_aff *aff, __isl_take isl_val *v);
4188 __isl_give isl_aff *isl_aff_add_constant_num_si(
4189 __isl_take isl_aff *aff, int v);
4190 __isl_give isl_aff *isl_aff_add_coefficient_si(
4191 __isl_take isl_aff *aff,
4192 enum isl_dim_type type, int pos, int v);
4193 __isl_give isl_aff *isl_aff_add_coefficient_val(
4194 __isl_take isl_aff *aff,
4195 enum isl_dim_type type, int pos,
4196 __isl_take isl_val *v);
4198 __isl_give isl_aff *isl_aff_insert_dims(
4199 __isl_take isl_aff *aff,
4200 enum isl_dim_type type, unsigned first, unsigned n);
4201 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
4202 __isl_take isl_pw_aff *pwaff,
4203 enum isl_dim_type type, unsigned first, unsigned n);
4204 __isl_give isl_aff *isl_aff_add_dims(
4205 __isl_take isl_aff *aff,
4206 enum isl_dim_type type, unsigned n);
4207 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
4208 __isl_take isl_pw_aff *pwaff,
4209 enum isl_dim_type type, unsigned n);
4210 __isl_give isl_aff *isl_aff_drop_dims(
4211 __isl_take isl_aff *aff,
4212 enum isl_dim_type type, unsigned first, unsigned n);
4213 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
4214 __isl_take isl_pw_aff *pwaff,
4215 enum isl_dim_type type, unsigned first, unsigned n);
4216 __isl_give isl_aff *isl_aff_move_dims(
4217 __isl_take isl_aff *aff,
4218 enum isl_dim_type dst_type, unsigned dst_pos,
4219 enum isl_dim_type src_type, unsigned src_pos,
4221 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
4222 __isl_take isl_pw_aff *pa,
4223 enum isl_dim_type dst_type, unsigned dst_pos,
4224 enum isl_dim_type src_type, unsigned src_pos,
4227 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
4228 set the I<numerator> of the constant or coefficient, while
4229 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
4230 the constant or coefficient as a whole.
4231 The C<add_constant> and C<add_coefficient> functions add an integer
4232 or rational value to
4233 the possibly rational constant or coefficient.
4234 The C<add_constant_num> functions add an integer value to
4237 To check whether an affine expressions is obviously zero
4238 or (obviously) equal to some other affine expression, use
4240 #include <isl/aff.h>
4241 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
4242 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
4243 __isl_keep isl_aff *aff2);
4244 int isl_pw_aff_plain_is_equal(
4245 __isl_keep isl_pw_aff *pwaff1,
4246 __isl_keep isl_pw_aff *pwaff2);
4247 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
4248 __isl_keep isl_pw_aff *pa2);
4249 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4250 __isl_keep isl_pw_aff *pa2);
4252 The function C<isl_pw_aff_plain_cmp> can be used to sort
4253 C<isl_pw_aff>s. The order is not strictly defined.
4254 The current order sorts expressions that only involve
4255 earlier dimensions before those that involve later dimensions.
4259 #include <isl/aff.h>
4260 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
4261 __isl_take isl_aff *aff2);
4262 __isl_give isl_pw_aff *isl_pw_aff_add(
4263 __isl_take isl_pw_aff *pwaff1,
4264 __isl_take isl_pw_aff *pwaff2);
4265 __isl_give isl_pw_aff *isl_pw_aff_min(
4266 __isl_take isl_pw_aff *pwaff1,
4267 __isl_take isl_pw_aff *pwaff2);
4268 __isl_give isl_pw_aff *isl_pw_aff_max(
4269 __isl_take isl_pw_aff *pwaff1,
4270 __isl_take isl_pw_aff *pwaff2);
4271 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
4272 __isl_take isl_aff *aff2);
4273 __isl_give isl_pw_aff *isl_pw_aff_sub(
4274 __isl_take isl_pw_aff *pwaff1,
4275 __isl_take isl_pw_aff *pwaff2);
4276 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
4277 __isl_give isl_pw_aff *isl_pw_aff_neg(
4278 __isl_take isl_pw_aff *pwaff);
4279 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
4280 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4281 __isl_take isl_pw_aff *pwaff);
4282 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
4283 __isl_give isl_pw_aff *isl_pw_aff_floor(
4284 __isl_take isl_pw_aff *pwaff);
4285 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
4286 __isl_take isl_val *mod);
4287 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
4288 __isl_take isl_pw_aff *pa,
4289 __isl_take isl_val *mod);
4290 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
4291 __isl_take isl_val *v);
4292 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
4293 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
4294 __isl_give isl_aff *isl_aff_scale_down_ui(
4295 __isl_take isl_aff *aff, unsigned f);
4296 __isl_give isl_aff *isl_aff_scale_down_val(
4297 __isl_take isl_aff *aff, __isl_take isl_val *v);
4298 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
4299 __isl_take isl_pw_aff *pa,
4300 __isl_take isl_val *f);
4302 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4303 __isl_take isl_pw_aff_list *list);
4304 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4305 __isl_take isl_pw_aff_list *list);
4307 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4308 __isl_take isl_pw_aff *pwqp);
4310 __isl_give isl_aff *isl_aff_align_params(
4311 __isl_take isl_aff *aff,
4312 __isl_take isl_space *model);
4313 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4314 __isl_take isl_pw_aff *pwaff,
4315 __isl_take isl_space *model);
4317 __isl_give isl_aff *isl_aff_project_domain_on_params(
4318 __isl_take isl_aff *aff);
4319 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4320 __isl_take isl_pw_aff *pwa);
4322 __isl_give isl_aff *isl_aff_gist_params(
4323 __isl_take isl_aff *aff,
4324 __isl_take isl_set *context);
4325 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
4326 __isl_take isl_set *context);
4327 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
4328 __isl_take isl_pw_aff *pwaff,
4329 __isl_take isl_set *context);
4330 __isl_give isl_pw_aff *isl_pw_aff_gist(
4331 __isl_take isl_pw_aff *pwaff,
4332 __isl_take isl_set *context);
4334 __isl_give isl_set *isl_pw_aff_domain(
4335 __isl_take isl_pw_aff *pwaff);
4336 __isl_give isl_set *isl_pw_aff_params(
4337 __isl_take isl_pw_aff *pwa);
4338 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4339 __isl_take isl_pw_aff *pa,
4340 __isl_take isl_set *set);
4341 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4342 __isl_take isl_pw_aff *pa,
4343 __isl_take isl_set *set);
4345 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
4346 __isl_take isl_aff *aff2);
4347 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
4348 __isl_take isl_aff *aff2);
4349 __isl_give isl_pw_aff *isl_pw_aff_mul(
4350 __isl_take isl_pw_aff *pwaff1,
4351 __isl_take isl_pw_aff *pwaff2);
4352 __isl_give isl_pw_aff *isl_pw_aff_div(
4353 __isl_take isl_pw_aff *pa1,
4354 __isl_take isl_pw_aff *pa2);
4355 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
4356 __isl_take isl_pw_aff *pa1,
4357 __isl_take isl_pw_aff *pa2);
4358 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
4359 __isl_take isl_pw_aff *pa1,
4360 __isl_take isl_pw_aff *pa2);
4362 When multiplying two affine expressions, at least one of the two needs
4363 to be a constant. Similarly, when dividing an affine expression by another,
4364 the second expression needs to be a constant.
4365 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
4366 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
4369 #include <isl/aff.h>
4370 __isl_give isl_aff *isl_aff_pullback_aff(
4371 __isl_take isl_aff *aff1,
4372 __isl_take isl_aff *aff2);
4373 __isl_give isl_aff *isl_aff_pullback_multi_aff(
4374 __isl_take isl_aff *aff,
4375 __isl_take isl_multi_aff *ma);
4376 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
4377 __isl_take isl_pw_aff *pa,
4378 __isl_take isl_multi_aff *ma);
4379 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
4380 __isl_take isl_pw_aff *pa,
4381 __isl_take isl_pw_multi_aff *pma);
4382 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
4383 __isl_take isl_pw_aff *pa,
4384 __isl_take isl_multi_pw_aff *mpa);
4386 These functions precompose the input expression by the given
4387 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
4388 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
4389 into the (piecewise) affine expression.
4390 Objects of type C<isl_multi_aff> are described in
4391 L</"Piecewise Multiple Quasi Affine Expressions">.
4393 #include <isl/aff.h>
4394 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4395 __isl_take isl_aff *aff);
4396 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4397 __isl_take isl_aff *aff);
4398 __isl_give isl_basic_set *isl_aff_le_basic_set(
4399 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4400 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4401 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4402 __isl_give isl_set *isl_pw_aff_eq_set(
4403 __isl_take isl_pw_aff *pwaff1,
4404 __isl_take isl_pw_aff *pwaff2);
4405 __isl_give isl_set *isl_pw_aff_ne_set(
4406 __isl_take isl_pw_aff *pwaff1,
4407 __isl_take isl_pw_aff *pwaff2);
4408 __isl_give isl_set *isl_pw_aff_le_set(
4409 __isl_take isl_pw_aff *pwaff1,
4410 __isl_take isl_pw_aff *pwaff2);
4411 __isl_give isl_set *isl_pw_aff_lt_set(
4412 __isl_take isl_pw_aff *pwaff1,
4413 __isl_take isl_pw_aff *pwaff2);
4414 __isl_give isl_set *isl_pw_aff_ge_set(
4415 __isl_take isl_pw_aff *pwaff1,
4416 __isl_take isl_pw_aff *pwaff2);
4417 __isl_give isl_set *isl_pw_aff_gt_set(
4418 __isl_take isl_pw_aff *pwaff1,
4419 __isl_take isl_pw_aff *pwaff2);
4421 __isl_give isl_set *isl_pw_aff_list_eq_set(
4422 __isl_take isl_pw_aff_list *list1,
4423 __isl_take isl_pw_aff_list *list2);
4424 __isl_give isl_set *isl_pw_aff_list_ne_set(
4425 __isl_take isl_pw_aff_list *list1,
4426 __isl_take isl_pw_aff_list *list2);
4427 __isl_give isl_set *isl_pw_aff_list_le_set(
4428 __isl_take isl_pw_aff_list *list1,
4429 __isl_take isl_pw_aff_list *list2);
4430 __isl_give isl_set *isl_pw_aff_list_lt_set(
4431 __isl_take isl_pw_aff_list *list1,
4432 __isl_take isl_pw_aff_list *list2);
4433 __isl_give isl_set *isl_pw_aff_list_ge_set(
4434 __isl_take isl_pw_aff_list *list1,
4435 __isl_take isl_pw_aff_list *list2);
4436 __isl_give isl_set *isl_pw_aff_list_gt_set(
4437 __isl_take isl_pw_aff_list *list1,
4438 __isl_take isl_pw_aff_list *list2);
4440 The function C<isl_aff_neg_basic_set> returns a basic set
4441 containing those elements in the domain space
4442 of C<aff> where C<aff> is negative.
4443 The function C<isl_aff_ge_basic_set> returns a basic set
4444 containing those elements in the shared space
4445 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4446 The function C<isl_pw_aff_ge_set> returns a set
4447 containing those elements in the shared domain
4448 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4449 The functions operating on C<isl_pw_aff_list> apply the corresponding
4450 C<isl_pw_aff> function to each pair of elements in the two lists.
4452 #include <isl/aff.h>
4453 __isl_give isl_set *isl_pw_aff_nonneg_set(
4454 __isl_take isl_pw_aff *pwaff);
4455 __isl_give isl_set *isl_pw_aff_zero_set(
4456 __isl_take isl_pw_aff *pwaff);
4457 __isl_give isl_set *isl_pw_aff_non_zero_set(
4458 __isl_take isl_pw_aff *pwaff);
4460 The function C<isl_pw_aff_nonneg_set> returns a set
4461 containing those elements in the domain
4462 of C<pwaff> where C<pwaff> is non-negative.
4464 #include <isl/aff.h>
4465 __isl_give isl_pw_aff *isl_pw_aff_cond(
4466 __isl_take isl_pw_aff *cond,
4467 __isl_take isl_pw_aff *pwaff_true,
4468 __isl_take isl_pw_aff *pwaff_false);
4470 The function C<isl_pw_aff_cond> performs a conditional operator
4471 and returns an expression that is equal to C<pwaff_true>
4472 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4473 where C<cond> is zero.
4475 #include <isl/aff.h>
4476 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4477 __isl_take isl_pw_aff *pwaff1,
4478 __isl_take isl_pw_aff *pwaff2);
4479 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4480 __isl_take isl_pw_aff *pwaff1,
4481 __isl_take isl_pw_aff *pwaff2);
4482 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4483 __isl_take isl_pw_aff *pwaff1,
4484 __isl_take isl_pw_aff *pwaff2);
4486 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4487 expression with a domain that is the union of those of C<pwaff1> and
4488 C<pwaff2> and such that on each cell, the quasi-affine expression is
4489 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4490 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4491 associated expression is the defined one.
4493 An expression can be read from input using
4495 #include <isl/aff.h>
4496 __isl_give isl_aff *isl_aff_read_from_str(
4497 isl_ctx *ctx, const char *str);
4498 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4499 isl_ctx *ctx, const char *str);
4501 An expression can be printed using
4503 #include <isl/aff.h>
4504 __isl_give isl_printer *isl_printer_print_aff(
4505 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4507 __isl_give isl_printer *isl_printer_print_pw_aff(
4508 __isl_take isl_printer *p,
4509 __isl_keep isl_pw_aff *pwaff);
4511 =head2 Piecewise Multiple Quasi Affine Expressions
4513 An C<isl_multi_aff> object represents a sequence of
4514 zero or more affine expressions, all defined on the same domain space.
4515 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4516 zero or more piecewise affine expressions.
4518 An C<isl_multi_aff> can be constructed from a single
4519 C<isl_aff> or an C<isl_aff_list> using the
4520 following functions. Similarly for C<isl_multi_pw_aff>
4521 and C<isl_pw_multi_aff>.
4523 #include <isl/aff.h>
4524 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4525 __isl_take isl_aff *aff);
4526 __isl_give isl_multi_pw_aff *
4527 isl_multi_pw_aff_from_multi_aff(
4528 __isl_take isl_multi_aff *ma);
4529 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4530 __isl_take isl_pw_aff *pa);
4531 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4532 __isl_take isl_pw_aff *pa);
4533 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4534 __isl_take isl_space *space,
4535 __isl_take isl_aff_list *list);
4537 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4538 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4539 Note however that the domain
4540 of the result is the intersection of the domains of the input.
4541 The reverse conversion is exact.
4543 #include <isl/aff.h>
4544 __isl_give isl_pw_multi_aff *
4545 isl_pw_multi_aff_from_multi_pw_aff(
4546 __isl_take isl_multi_pw_aff *mpa);
4547 __isl_give isl_multi_pw_aff *
4548 isl_multi_pw_aff_from_pw_multi_aff(
4549 __isl_take isl_pw_multi_aff *pma);
4551 An empty piecewise multiple quasi affine expression (one with no cells),
4552 the zero piecewise multiple quasi affine expression (with value zero
4553 for each output dimension),
4554 a piecewise multiple quasi affine expression with a single cell (with
4555 either a universe or a specified domain) or
4556 a zero-dimensional piecewise multiple quasi affine expression
4558 can be created using the following functions.
4560 #include <isl/aff.h>
4561 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4562 __isl_take isl_space *space);
4563 __isl_give isl_multi_aff *isl_multi_aff_zero(
4564 __isl_take isl_space *space);
4565 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4566 __isl_take isl_space *space);
4567 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4568 __isl_take isl_space *space);
4569 __isl_give isl_multi_aff *isl_multi_aff_identity(
4570 __isl_take isl_space *space);
4571 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4572 __isl_take isl_space *space);
4573 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4574 __isl_take isl_space *space);
4575 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4576 __isl_take isl_space *space);
4577 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4578 __isl_take isl_space *space);
4579 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4580 __isl_take isl_space *space,
4581 enum isl_dim_type type,
4582 unsigned first, unsigned n);
4583 __isl_give isl_pw_multi_aff *
4584 isl_pw_multi_aff_project_out_map(
4585 __isl_take isl_space *space,
4586 enum isl_dim_type type,
4587 unsigned first, unsigned n);
4588 __isl_give isl_pw_multi_aff *
4589 isl_pw_multi_aff_from_multi_aff(
4590 __isl_take isl_multi_aff *ma);
4591 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4592 __isl_take isl_set *set,
4593 __isl_take isl_multi_aff *maff);
4594 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4595 __isl_take isl_set *set);
4597 __isl_give isl_union_pw_multi_aff *
4598 isl_union_pw_multi_aff_empty(
4599 __isl_take isl_space *space);
4600 __isl_give isl_union_pw_multi_aff *
4601 isl_union_pw_multi_aff_add_pw_multi_aff(
4602 __isl_take isl_union_pw_multi_aff *upma,
4603 __isl_take isl_pw_multi_aff *pma);
4604 __isl_give isl_union_pw_multi_aff *
4605 isl_union_pw_multi_aff_from_domain(
4606 __isl_take isl_union_set *uset);
4608 A piecewise multiple quasi affine expression can also be initialized
4609 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4610 and the C<isl_map> is single-valued.
4611 In case of a conversion from an C<isl_union_map>
4612 to an C<isl_union_pw_multi_aff>, these properties need to hold
4613 in each domain space.
4615 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4616 __isl_take isl_set *set);
4617 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4618 __isl_take isl_map *map);
4620 __isl_give isl_union_pw_multi_aff *
4621 isl_union_pw_multi_aff_from_union_set(
4622 __isl_take isl_union_set *uset);
4623 __isl_give isl_union_pw_multi_aff *
4624 isl_union_pw_multi_aff_from_union_map(
4625 __isl_take isl_union_map *umap);
4627 Multiple quasi affine expressions can be copied and freed using
4629 #include <isl/aff.h>
4630 __isl_give isl_multi_aff *isl_multi_aff_copy(
4631 __isl_keep isl_multi_aff *maff);
4632 __isl_null isl_multi_aff *isl_multi_aff_free(
4633 __isl_take isl_multi_aff *maff);
4635 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4636 __isl_keep isl_pw_multi_aff *pma);
4637 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
4638 __isl_take isl_pw_multi_aff *pma);
4640 __isl_give isl_union_pw_multi_aff *
4641 isl_union_pw_multi_aff_copy(
4642 __isl_keep isl_union_pw_multi_aff *upma);
4643 __isl_null isl_union_pw_multi_aff *
4644 isl_union_pw_multi_aff_free(
4645 __isl_take isl_union_pw_multi_aff *upma);
4647 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4648 __isl_keep isl_multi_pw_aff *mpa);
4649 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
4650 __isl_take isl_multi_pw_aff *mpa);
4652 The expression can be inspected using
4654 #include <isl/aff.h>
4655 isl_ctx *isl_multi_aff_get_ctx(
4656 __isl_keep isl_multi_aff *maff);
4657 isl_ctx *isl_pw_multi_aff_get_ctx(
4658 __isl_keep isl_pw_multi_aff *pma);
4659 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4660 __isl_keep isl_union_pw_multi_aff *upma);
4661 isl_ctx *isl_multi_pw_aff_get_ctx(
4662 __isl_keep isl_multi_pw_aff *mpa);
4664 int isl_multi_aff_involves_dims(
4665 __isl_keep isl_multi_aff *ma,
4666 enum isl_dim_type type, unsigned first, unsigned n);
4667 int isl_multi_pw_aff_involves_dims(
4668 __isl_keep isl_multi_pw_aff *mpa,
4669 enum isl_dim_type type, unsigned first, unsigned n);
4671 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4672 enum isl_dim_type type);
4673 unsigned isl_pw_multi_aff_dim(
4674 __isl_keep isl_pw_multi_aff *pma,
4675 enum isl_dim_type type);
4676 unsigned isl_multi_pw_aff_dim(
4677 __isl_keep isl_multi_pw_aff *mpa,
4678 enum isl_dim_type type);
4679 __isl_give isl_aff *isl_multi_aff_get_aff(
4680 __isl_keep isl_multi_aff *multi, int pos);
4681 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4682 __isl_keep isl_pw_multi_aff *pma, int pos);
4683 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4684 __isl_keep isl_multi_pw_aff *mpa, int pos);
4685 int isl_multi_aff_find_dim_by_id(
4686 __isl_keep isl_multi_aff *ma,
4687 enum isl_dim_type type, __isl_keep isl_id *id);
4688 int isl_multi_pw_aff_find_dim_by_id(
4689 __isl_keep isl_multi_pw_aff *mpa,
4690 enum isl_dim_type type, __isl_keep isl_id *id);
4691 const char *isl_pw_multi_aff_get_dim_name(
4692 __isl_keep isl_pw_multi_aff *pma,
4693 enum isl_dim_type type, unsigned pos);
4694 __isl_give isl_id *isl_multi_aff_get_dim_id(
4695 __isl_keep isl_multi_aff *ma,
4696 enum isl_dim_type type, unsigned pos);
4697 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4698 __isl_keep isl_pw_multi_aff *pma,
4699 enum isl_dim_type type, unsigned pos);
4700 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4701 __isl_keep isl_multi_pw_aff *mpa,
4702 enum isl_dim_type type, unsigned pos);
4703 const char *isl_multi_aff_get_tuple_name(
4704 __isl_keep isl_multi_aff *multi,
4705 enum isl_dim_type type);
4706 int isl_pw_multi_aff_has_tuple_name(
4707 __isl_keep isl_pw_multi_aff *pma,
4708 enum isl_dim_type type);
4709 const char *isl_pw_multi_aff_get_tuple_name(
4710 __isl_keep isl_pw_multi_aff *pma,
4711 enum isl_dim_type type);
4712 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4713 enum isl_dim_type type);
4714 int isl_pw_multi_aff_has_tuple_id(
4715 __isl_keep isl_pw_multi_aff *pma,
4716 enum isl_dim_type type);
4717 int isl_multi_pw_aff_has_tuple_id(
4718 __isl_keep isl_multi_pw_aff *mpa,
4719 enum isl_dim_type type);
4720 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4721 __isl_keep isl_multi_aff *ma,
4722 enum isl_dim_type type);
4723 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4724 __isl_keep isl_pw_multi_aff *pma,
4725 enum isl_dim_type type);
4726 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4727 __isl_keep isl_multi_pw_aff *mpa,
4728 enum isl_dim_type type);
4729 int isl_multi_aff_range_is_wrapping(
4730 __isl_keep isl_multi_aff *ma);
4731 int isl_multi_pw_aff_range_is_wrapping(
4732 __isl_keep isl_multi_pw_aff *mpa);
4734 int isl_pw_multi_aff_foreach_piece(
4735 __isl_keep isl_pw_multi_aff *pma,
4736 int (*fn)(__isl_take isl_set *set,
4737 __isl_take isl_multi_aff *maff,
4738 void *user), void *user);
4740 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4741 __isl_keep isl_union_pw_multi_aff *upma,
4742 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4743 void *user), void *user);
4745 It can be modified using
4747 #include <isl/aff.h>
4748 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4749 __isl_take isl_multi_aff *multi, int pos,
4750 __isl_take isl_aff *aff);
4751 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4752 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4753 __isl_take isl_pw_aff *pa);
4754 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4755 __isl_take isl_multi_aff *maff,
4756 enum isl_dim_type type, unsigned pos, const char *s);
4757 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4758 __isl_take isl_multi_aff *maff,
4759 enum isl_dim_type type, unsigned pos,
4760 __isl_take isl_id *id);
4761 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4762 __isl_take isl_multi_aff *maff,
4763 enum isl_dim_type type, const char *s);
4764 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4765 __isl_take isl_multi_aff *maff,
4766 enum isl_dim_type type, __isl_take isl_id *id);
4767 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4768 __isl_take isl_pw_multi_aff *pma,
4769 enum isl_dim_type type, __isl_take isl_id *id);
4770 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4771 __isl_take isl_multi_aff *ma,
4772 enum isl_dim_type type);
4773 __isl_give isl_multi_pw_aff *
4774 isl_multi_pw_aff_reset_tuple_id(
4775 __isl_take isl_multi_pw_aff *mpa,
4776 enum isl_dim_type type);
4777 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4778 __isl_take isl_multi_aff *ma);
4779 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4780 __isl_take isl_multi_pw_aff *mpa);
4782 __isl_give isl_multi_pw_aff *
4783 isl_multi_pw_aff_set_dim_name(
4784 __isl_take isl_multi_pw_aff *mpa,
4785 enum isl_dim_type type, unsigned pos, const char *s);
4786 __isl_give isl_multi_pw_aff *
4787 isl_multi_pw_aff_set_dim_id(
4788 __isl_take isl_multi_pw_aff *mpa,
4789 enum isl_dim_type type, unsigned pos,
4790 __isl_take isl_id *id);
4791 __isl_give isl_multi_pw_aff *
4792 isl_multi_pw_aff_set_tuple_name(
4793 __isl_take isl_multi_pw_aff *mpa,
4794 enum isl_dim_type type, const char *s);
4796 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4797 __isl_take isl_multi_aff *ma);
4799 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4800 __isl_take isl_multi_aff *ma,
4801 enum isl_dim_type type, unsigned first, unsigned n);
4802 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4803 __isl_take isl_multi_aff *ma,
4804 enum isl_dim_type type, unsigned n);
4805 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4806 __isl_take isl_multi_aff *maff,
4807 enum isl_dim_type type, unsigned first, unsigned n);
4808 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4809 __isl_take isl_pw_multi_aff *pma,
4810 enum isl_dim_type type, unsigned first, unsigned n);
4812 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4813 __isl_take isl_multi_pw_aff *mpa,
4814 enum isl_dim_type type, unsigned first, unsigned n);
4815 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4816 __isl_take isl_multi_pw_aff *mpa,
4817 enum isl_dim_type type, unsigned n);
4818 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4819 __isl_take isl_multi_pw_aff *pma,
4820 enum isl_dim_type dst_type, unsigned dst_pos,
4821 enum isl_dim_type src_type, unsigned src_pos,
4824 To check whether two multiple affine expressions are
4825 (obviously) equal to each other, use
4827 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4828 __isl_keep isl_multi_aff *maff2);
4829 int isl_pw_multi_aff_plain_is_equal(
4830 __isl_keep isl_pw_multi_aff *pma1,
4831 __isl_keep isl_pw_multi_aff *pma2);
4832 int isl_multi_pw_aff_plain_is_equal(
4833 __isl_keep isl_multi_pw_aff *mpa1,
4834 __isl_keep isl_multi_pw_aff *mpa2);
4835 int isl_multi_pw_aff_is_equal(
4836 __isl_keep isl_multi_pw_aff *mpa1,
4837 __isl_keep isl_multi_pw_aff *mpa2);
4841 #include <isl/aff.h>
4842 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4843 __isl_take isl_pw_multi_aff *pma1,
4844 __isl_take isl_pw_multi_aff *pma2);
4845 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4846 __isl_take isl_pw_multi_aff *pma1,
4847 __isl_take isl_pw_multi_aff *pma2);
4848 __isl_give isl_multi_aff *isl_multi_aff_floor(
4849 __isl_take isl_multi_aff *ma);
4850 __isl_give isl_multi_aff *isl_multi_aff_add(
4851 __isl_take isl_multi_aff *maff1,
4852 __isl_take isl_multi_aff *maff2);
4853 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4854 __isl_take isl_pw_multi_aff *pma1,
4855 __isl_take isl_pw_multi_aff *pma2);
4856 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4857 __isl_take isl_union_pw_multi_aff *upma1,
4858 __isl_take isl_union_pw_multi_aff *upma2);
4859 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4860 __isl_take isl_pw_multi_aff *pma1,
4861 __isl_take isl_pw_multi_aff *pma2);
4862 __isl_give isl_multi_aff *isl_multi_aff_sub(
4863 __isl_take isl_multi_aff *ma1,
4864 __isl_take isl_multi_aff *ma2);
4865 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4866 __isl_take isl_pw_multi_aff *pma1,
4867 __isl_take isl_pw_multi_aff *pma2);
4868 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4869 __isl_take isl_union_pw_multi_aff *upma1,
4870 __isl_take isl_union_pw_multi_aff *upma2);
4872 C<isl_multi_aff_sub> subtracts the second argument from the first.
4874 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4875 __isl_take isl_multi_aff *ma,
4876 __isl_take isl_val *v);
4877 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4878 __isl_take isl_pw_multi_aff *pma,
4879 __isl_take isl_val *v);
4880 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4881 __isl_take isl_multi_pw_aff *mpa,
4882 __isl_take isl_val *v);
4883 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4884 __isl_take isl_multi_aff *ma,
4885 __isl_take isl_multi_val *mv);
4886 __isl_give isl_pw_multi_aff *
4887 isl_pw_multi_aff_scale_multi_val(
4888 __isl_take isl_pw_multi_aff *pma,
4889 __isl_take isl_multi_val *mv);
4890 __isl_give isl_multi_pw_aff *
4891 isl_multi_pw_aff_scale_multi_val(
4892 __isl_take isl_multi_pw_aff *mpa,
4893 __isl_take isl_multi_val *mv);
4894 __isl_give isl_union_pw_multi_aff *
4895 isl_union_pw_multi_aff_scale_multi_val(
4896 __isl_take isl_union_pw_multi_aff *upma,
4897 __isl_take isl_multi_val *mv);
4898 __isl_give isl_multi_aff *
4899 isl_multi_aff_scale_down_multi_val(
4900 __isl_take isl_multi_aff *ma,
4901 __isl_take isl_multi_val *mv);
4902 __isl_give isl_multi_pw_aff *
4903 isl_multi_pw_aff_scale_down_multi_val(
4904 __isl_take isl_multi_pw_aff *mpa,
4905 __isl_take isl_multi_val *mv);
4907 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4908 by the corresponding elements of C<mv>.
4910 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4911 __isl_take isl_pw_multi_aff *pma,
4912 enum isl_dim_type type, unsigned pos, int value);
4913 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4914 __isl_take isl_pw_multi_aff *pma,
4915 __isl_take isl_set *set);
4916 __isl_give isl_set *isl_multi_pw_aff_domain(
4917 __isl_take isl_multi_pw_aff *mpa);
4918 __isl_give isl_multi_pw_aff *
4919 isl_multi_pw_aff_intersect_params(
4920 __isl_take isl_multi_pw_aff *mpa,
4921 __isl_take isl_set *set);
4922 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4923 __isl_take isl_pw_multi_aff *pma,
4924 __isl_take isl_set *set);
4925 __isl_give isl_multi_pw_aff *
4926 isl_multi_pw_aff_intersect_domain(
4927 __isl_take isl_multi_pw_aff *mpa,
4928 __isl_take isl_set *domain);
4929 __isl_give isl_union_pw_multi_aff *
4930 isl_union_pw_multi_aff_intersect_domain(
4931 __isl_take isl_union_pw_multi_aff *upma,
4932 __isl_take isl_union_set *uset);
4933 __isl_give isl_multi_aff *isl_multi_aff_lift(
4934 __isl_take isl_multi_aff *maff,
4935 __isl_give isl_local_space **ls);
4936 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4937 __isl_take isl_pw_multi_aff *pma);
4938 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4939 __isl_take isl_multi_pw_aff *mpa);
4940 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4941 __isl_take isl_multi_aff *multi,
4942 __isl_take isl_space *model);
4943 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4944 __isl_take isl_pw_multi_aff *pma,
4945 __isl_take isl_space *model);
4946 __isl_give isl_union_pw_multi_aff *
4947 isl_union_pw_multi_aff_align_params(
4948 __isl_take isl_union_pw_multi_aff *upma,
4949 __isl_take isl_space *model);
4950 __isl_give isl_pw_multi_aff *
4951 isl_pw_multi_aff_project_domain_on_params(
4952 __isl_take isl_pw_multi_aff *pma);
4953 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4954 __isl_take isl_multi_aff *maff,
4955 __isl_take isl_set *context);
4956 __isl_give isl_multi_aff *isl_multi_aff_gist(
4957 __isl_take isl_multi_aff *maff,
4958 __isl_take isl_set *context);
4959 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4960 __isl_take isl_pw_multi_aff *pma,
4961 __isl_take isl_set *set);
4962 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4963 __isl_take isl_pw_multi_aff *pma,
4964 __isl_take isl_set *set);
4965 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4966 __isl_take isl_multi_pw_aff *mpa,
4967 __isl_take isl_set *set);
4968 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4969 __isl_take isl_multi_pw_aff *mpa,
4970 __isl_take isl_set *set);
4971 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4972 __isl_take isl_multi_aff *ma);
4973 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4974 __isl_take isl_multi_pw_aff *mpa);
4975 __isl_give isl_set *isl_pw_multi_aff_domain(
4976 __isl_take isl_pw_multi_aff *pma);
4977 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4978 __isl_take isl_union_pw_multi_aff *upma);
4979 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4980 __isl_take isl_multi_aff *ma1, unsigned pos,
4981 __isl_take isl_multi_aff *ma2);
4982 __isl_give isl_multi_aff *isl_multi_aff_splice(
4983 __isl_take isl_multi_aff *ma1,
4984 unsigned in_pos, unsigned out_pos,
4985 __isl_take isl_multi_aff *ma2);
4986 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4987 __isl_take isl_multi_aff *ma1,
4988 __isl_take isl_multi_aff *ma2);
4989 __isl_give isl_multi_aff *
4990 isl_multi_aff_range_factor_domain(
4991 __isl_take isl_multi_aff *ma);
4992 __isl_give isl_multi_aff *
4993 isl_multi_aff_range_factor_range(
4994 __isl_take isl_multi_aff *ma);
4995 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4996 __isl_take isl_multi_aff *ma1,
4997 __isl_take isl_multi_aff *ma2);
4998 __isl_give isl_multi_aff *isl_multi_aff_product(
4999 __isl_take isl_multi_aff *ma1,
5000 __isl_take isl_multi_aff *ma2);
5001 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
5002 __isl_take isl_multi_pw_aff *mpa1,
5003 __isl_take isl_multi_pw_aff *mpa2);
5004 __isl_give isl_pw_multi_aff *
5005 isl_pw_multi_aff_range_product(
5006 __isl_take isl_pw_multi_aff *pma1,
5007 __isl_take isl_pw_multi_aff *pma2);
5008 __isl_give isl_multi_pw_aff *
5009 isl_multi_pw_aff_range_factor_domain(
5010 __isl_take isl_multi_pw_aff *mpa);
5011 __isl_give isl_multi_pw_aff *
5012 isl_multi_pw_aff_range_factor_range(
5013 __isl_take isl_multi_pw_aff *mpa);
5014 __isl_give isl_pw_multi_aff *
5015 isl_pw_multi_aff_flat_range_product(
5016 __isl_take isl_pw_multi_aff *pma1,
5017 __isl_take isl_pw_multi_aff *pma2);
5018 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
5019 __isl_take isl_pw_multi_aff *pma1,
5020 __isl_take isl_pw_multi_aff *pma2);
5021 __isl_give isl_union_pw_multi_aff *
5022 isl_union_pw_multi_aff_flat_range_product(
5023 __isl_take isl_union_pw_multi_aff *upma1,
5024 __isl_take isl_union_pw_multi_aff *upma2);
5025 __isl_give isl_multi_pw_aff *
5026 isl_multi_pw_aff_range_splice(
5027 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
5028 __isl_take isl_multi_pw_aff *mpa2);
5029 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
5030 __isl_take isl_multi_pw_aff *mpa1,
5031 unsigned in_pos, unsigned out_pos,
5032 __isl_take isl_multi_pw_aff *mpa2);
5033 __isl_give isl_multi_pw_aff *
5034 isl_multi_pw_aff_range_product(
5035 __isl_take isl_multi_pw_aff *mpa1,
5036 __isl_take isl_multi_pw_aff *mpa2);
5037 __isl_give isl_multi_pw_aff *
5038 isl_multi_pw_aff_flat_range_product(
5039 __isl_take isl_multi_pw_aff *mpa1,
5040 __isl_take isl_multi_pw_aff *mpa2);
5042 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5043 then it is assigned the local space that lies at the basis of
5044 the lifting applied.
5046 #include <isl/aff.h>
5047 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
5048 __isl_take isl_multi_aff *ma1,
5049 __isl_take isl_multi_aff *ma2);
5050 __isl_give isl_pw_multi_aff *
5051 isl_pw_multi_aff_pullback_multi_aff(
5052 __isl_take isl_pw_multi_aff *pma,
5053 __isl_take isl_multi_aff *ma);
5054 __isl_give isl_multi_pw_aff *
5055 isl_multi_pw_aff_pullback_multi_aff(
5056 __isl_take isl_multi_pw_aff *mpa,
5057 __isl_take isl_multi_aff *ma);
5058 __isl_give isl_pw_multi_aff *
5059 isl_pw_multi_aff_pullback_pw_multi_aff(
5060 __isl_take isl_pw_multi_aff *pma1,
5061 __isl_take isl_pw_multi_aff *pma2);
5062 __isl_give isl_multi_pw_aff *
5063 isl_multi_pw_aff_pullback_pw_multi_aff(
5064 __isl_take isl_multi_pw_aff *mpa,
5065 __isl_take isl_pw_multi_aff *pma);
5066 __isl_give isl_multi_pw_aff *
5067 isl_multi_pw_aff_pullback_multi_pw_aff(
5068 __isl_take isl_multi_pw_aff *mpa1,
5069 __isl_take isl_multi_pw_aff *mpa2);
5071 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
5072 In other words, C<ma2> is plugged
5075 __isl_give isl_set *isl_multi_aff_lex_le_set(
5076 __isl_take isl_multi_aff *ma1,
5077 __isl_take isl_multi_aff *ma2);
5078 __isl_give isl_set *isl_multi_aff_lex_ge_set(
5079 __isl_take isl_multi_aff *ma1,
5080 __isl_take isl_multi_aff *ma2);
5082 The function C<isl_multi_aff_lex_le_set> returns a set
5083 containing those elements in the shared domain space
5084 where C<ma1> is lexicographically smaller than or
5087 An expression can be read from input using
5089 #include <isl/aff.h>
5090 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
5091 isl_ctx *ctx, const char *str);
5092 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
5093 isl_ctx *ctx, const char *str);
5094 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
5095 isl_ctx *ctx, const char *str);
5096 __isl_give isl_union_pw_multi_aff *
5097 isl_union_pw_multi_aff_read_from_str(
5098 isl_ctx *ctx, const char *str);
5100 An expression can be printed using
5102 #include <isl/aff.h>
5103 __isl_give isl_printer *isl_printer_print_multi_aff(
5104 __isl_take isl_printer *p,
5105 __isl_keep isl_multi_aff *maff);
5106 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
5107 __isl_take isl_printer *p,
5108 __isl_keep isl_pw_multi_aff *pma);
5109 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
5110 __isl_take isl_printer *p,
5111 __isl_keep isl_union_pw_multi_aff *upma);
5112 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
5113 __isl_take isl_printer *p,
5114 __isl_keep isl_multi_pw_aff *mpa);
5118 Points are elements of a set. They can be used to construct
5119 simple sets (boxes) or they can be used to represent the
5120 individual elements of a set.
5121 The zero point (the origin) can be created using
5123 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
5125 The coordinates of a point can be inspected, set and changed
5128 __isl_give isl_val *isl_point_get_coordinate_val(
5129 __isl_keep isl_point *pnt,
5130 enum isl_dim_type type, int pos);
5131 __isl_give isl_point *isl_point_set_coordinate_val(
5132 __isl_take isl_point *pnt,
5133 enum isl_dim_type type, int pos,
5134 __isl_take isl_val *v);
5136 __isl_give isl_point *isl_point_add_ui(
5137 __isl_take isl_point *pnt,
5138 enum isl_dim_type type, int pos, unsigned val);
5139 __isl_give isl_point *isl_point_sub_ui(
5140 __isl_take isl_point *pnt,
5141 enum isl_dim_type type, int pos, unsigned val);
5143 Other properties can be obtained using
5145 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
5147 Points can be copied or freed using
5149 __isl_give isl_point *isl_point_copy(
5150 __isl_keep isl_point *pnt);
5151 void isl_point_free(__isl_take isl_point *pnt);
5153 A singleton set can be created from a point using
5155 __isl_give isl_basic_set *isl_basic_set_from_point(
5156 __isl_take isl_point *pnt);
5157 __isl_give isl_set *isl_set_from_point(
5158 __isl_take isl_point *pnt);
5160 and a box can be created from two opposite extremal points using
5162 __isl_give isl_basic_set *isl_basic_set_box_from_points(
5163 __isl_take isl_point *pnt1,
5164 __isl_take isl_point *pnt2);
5165 __isl_give isl_set *isl_set_box_from_points(
5166 __isl_take isl_point *pnt1,
5167 __isl_take isl_point *pnt2);
5169 All elements of a B<bounded> (union) set can be enumerated using
5170 the following functions.
5172 int isl_set_foreach_point(__isl_keep isl_set *set,
5173 int (*fn)(__isl_take isl_point *pnt, void *user),
5175 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
5176 int (*fn)(__isl_take isl_point *pnt, void *user),
5179 The function C<fn> is called for each integer point in
5180 C<set> with as second argument the last argument of
5181 the C<isl_set_foreach_point> call. The function C<fn>
5182 should return C<0> on success and C<-1> on failure.
5183 In the latter case, C<isl_set_foreach_point> will stop
5184 enumerating and return C<-1> as well.
5185 If the enumeration is performed successfully and to completion,
5186 then C<isl_set_foreach_point> returns C<0>.
5188 To obtain a single point of a (basic) set, use
5190 __isl_give isl_point *isl_basic_set_sample_point(
5191 __isl_take isl_basic_set *bset);
5192 __isl_give isl_point *isl_set_sample_point(
5193 __isl_take isl_set *set);
5195 If C<set> does not contain any (integer) points, then the
5196 resulting point will be ``void'', a property that can be
5199 int isl_point_is_void(__isl_keep isl_point *pnt);
5201 =head2 Piecewise Quasipolynomials
5203 A piecewise quasipolynomial is a particular kind of function that maps
5204 a parametric point to a rational value.
5205 More specifically, a quasipolynomial is a polynomial expression in greatest
5206 integer parts of affine expressions of parameters and variables.
5207 A piecewise quasipolynomial is a subdivision of a given parametric
5208 domain into disjoint cells with a quasipolynomial associated to
5209 each cell. The value of the piecewise quasipolynomial at a given
5210 point is the value of the quasipolynomial associated to the cell
5211 that contains the point. Outside of the union of cells,
5212 the value is assumed to be zero.
5213 For example, the piecewise quasipolynomial
5215 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
5217 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
5218 A given piecewise quasipolynomial has a fixed domain dimension.
5219 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
5220 defined over different domains.
5221 Piecewise quasipolynomials are mainly used by the C<barvinok>
5222 library for representing the number of elements in a parametric set or map.
5223 For example, the piecewise quasipolynomial above represents
5224 the number of points in the map
5226 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
5228 =head3 Input and Output
5230 Piecewise quasipolynomials can be read from input using
5232 __isl_give isl_union_pw_qpolynomial *
5233 isl_union_pw_qpolynomial_read_from_str(
5234 isl_ctx *ctx, const char *str);
5236 Quasipolynomials and piecewise quasipolynomials can be printed
5237 using the following functions.
5239 __isl_give isl_printer *isl_printer_print_qpolynomial(
5240 __isl_take isl_printer *p,
5241 __isl_keep isl_qpolynomial *qp);
5243 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
5244 __isl_take isl_printer *p,
5245 __isl_keep isl_pw_qpolynomial *pwqp);
5247 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
5248 __isl_take isl_printer *p,
5249 __isl_keep isl_union_pw_qpolynomial *upwqp);
5251 The output format of the printer
5252 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5253 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
5255 In case of printing in C<ISL_FORMAT_C>, the user may want
5256 to set the names of all dimensions
5258 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
5259 __isl_take isl_qpolynomial *qp,
5260 enum isl_dim_type type, unsigned pos,
5262 __isl_give isl_pw_qpolynomial *
5263 isl_pw_qpolynomial_set_dim_name(
5264 __isl_take isl_pw_qpolynomial *pwqp,
5265 enum isl_dim_type type, unsigned pos,
5268 =head3 Creating New (Piecewise) Quasipolynomials
5270 Some simple quasipolynomials can be created using the following functions.
5271 More complicated quasipolynomials can be created by applying
5272 operations such as addition and multiplication
5273 on the resulting quasipolynomials
5275 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
5276 __isl_take isl_space *domain);
5277 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
5278 __isl_take isl_space *domain);
5279 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
5280 __isl_take isl_space *domain);
5281 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
5282 __isl_take isl_space *domain);
5283 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
5284 __isl_take isl_space *domain);
5285 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
5286 __isl_take isl_space *domain,
5287 __isl_take isl_val *val);
5288 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
5289 __isl_take isl_space *domain,
5290 enum isl_dim_type type, unsigned pos);
5291 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
5292 __isl_take isl_aff *aff);
5294 Note that the space in which a quasipolynomial lives is a map space
5295 with a one-dimensional range. The C<domain> argument in some of
5296 the functions above corresponds to the domain of this map space.
5298 The zero piecewise quasipolynomial or a piecewise quasipolynomial
5299 with a single cell can be created using the following functions.
5300 Multiple of these single cell piecewise quasipolynomials can
5301 be combined to create more complicated piecewise quasipolynomials.
5303 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
5304 __isl_take isl_space *space);
5305 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
5306 __isl_take isl_set *set,
5307 __isl_take isl_qpolynomial *qp);
5308 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
5309 __isl_take isl_qpolynomial *qp);
5310 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
5311 __isl_take isl_pw_aff *pwaff);
5313 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
5314 __isl_take isl_space *space);
5315 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
5316 __isl_take isl_pw_qpolynomial *pwqp);
5317 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
5318 __isl_take isl_union_pw_qpolynomial *upwqp,
5319 __isl_take isl_pw_qpolynomial *pwqp);
5321 Quasipolynomials can be copied and freed again using the following
5324 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
5325 __isl_keep isl_qpolynomial *qp);
5326 __isl_null isl_qpolynomial *isl_qpolynomial_free(
5327 __isl_take isl_qpolynomial *qp);
5329 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
5330 __isl_keep isl_pw_qpolynomial *pwqp);
5331 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
5332 __isl_take isl_pw_qpolynomial *pwqp);
5334 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
5335 __isl_keep isl_union_pw_qpolynomial *upwqp);
5336 __isl_null isl_union_pw_qpolynomial *
5337 isl_union_pw_qpolynomial_free(
5338 __isl_take isl_union_pw_qpolynomial *upwqp);
5340 =head3 Inspecting (Piecewise) Quasipolynomials
5342 To iterate over all piecewise quasipolynomials in a union
5343 piecewise quasipolynomial, use the following function
5345 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
5346 __isl_keep isl_union_pw_qpolynomial *upwqp,
5347 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
5350 To extract the piecewise quasipolynomial in a given space from a union, use
5352 __isl_give isl_pw_qpolynomial *
5353 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
5354 __isl_keep isl_union_pw_qpolynomial *upwqp,
5355 __isl_take isl_space *space);
5357 To iterate over the cells in a piecewise quasipolynomial,
5358 use either of the following two functions
5360 int isl_pw_qpolynomial_foreach_piece(
5361 __isl_keep isl_pw_qpolynomial *pwqp,
5362 int (*fn)(__isl_take isl_set *set,
5363 __isl_take isl_qpolynomial *qp,
5364 void *user), void *user);
5365 int isl_pw_qpolynomial_foreach_lifted_piece(
5366 __isl_keep isl_pw_qpolynomial *pwqp,
5367 int (*fn)(__isl_take isl_set *set,
5368 __isl_take isl_qpolynomial *qp,
5369 void *user), void *user);
5371 As usual, the function C<fn> should return C<0> on success
5372 and C<-1> on failure. The difference between
5373 C<isl_pw_qpolynomial_foreach_piece> and
5374 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
5375 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
5376 compute unique representations for all existentially quantified
5377 variables and then turn these existentially quantified variables
5378 into extra set variables, adapting the associated quasipolynomial
5379 accordingly. This means that the C<set> passed to C<fn>
5380 will not have any existentially quantified variables, but that
5381 the dimensions of the sets may be different for different
5382 invocations of C<fn>.
5384 The constant term of a quasipolynomial can be extracted using
5386 __isl_give isl_val *isl_qpolynomial_get_constant_val(
5387 __isl_keep isl_qpolynomial *qp);
5389 To iterate over all terms in a quasipolynomial,
5392 int isl_qpolynomial_foreach_term(
5393 __isl_keep isl_qpolynomial *qp,
5394 int (*fn)(__isl_take isl_term *term,
5395 void *user), void *user);
5397 The terms themselves can be inspected and freed using
5400 unsigned isl_term_dim(__isl_keep isl_term *term,
5401 enum isl_dim_type type);
5402 __isl_give isl_val *isl_term_get_coefficient_val(
5403 __isl_keep isl_term *term);
5404 int isl_term_get_exp(__isl_keep isl_term *term,
5405 enum isl_dim_type type, unsigned pos);
5406 __isl_give isl_aff *isl_term_get_div(
5407 __isl_keep isl_term *term, unsigned pos);
5408 void isl_term_free(__isl_take isl_term *term);
5410 Each term is a product of parameters, set variables and
5411 integer divisions. The function C<isl_term_get_exp>
5412 returns the exponent of a given dimensions in the given term.
5414 =head3 Properties of (Piecewise) Quasipolynomials
5416 To check whether two union piecewise quasipolynomials are
5417 obviously equal, use
5419 int isl_union_pw_qpolynomial_plain_is_equal(
5420 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5421 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5423 =head3 Operations on (Piecewise) Quasipolynomials
5425 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5426 __isl_take isl_qpolynomial *qp,
5427 __isl_take isl_val *v);
5428 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5429 __isl_take isl_qpolynomial *qp);
5430 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5431 __isl_take isl_qpolynomial *qp1,
5432 __isl_take isl_qpolynomial *qp2);
5433 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5434 __isl_take isl_qpolynomial *qp1,
5435 __isl_take isl_qpolynomial *qp2);
5436 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5437 __isl_take isl_qpolynomial *qp1,
5438 __isl_take isl_qpolynomial *qp2);
5439 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5440 __isl_take isl_qpolynomial *qp, unsigned exponent);
5442 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5443 __isl_take isl_pw_qpolynomial *pwqp,
5444 enum isl_dim_type type, unsigned n,
5445 __isl_take isl_val *v);
5446 __isl_give isl_pw_qpolynomial *
5447 isl_pw_qpolynomial_scale_val(
5448 __isl_take isl_pw_qpolynomial *pwqp,
5449 __isl_take isl_val *v);
5450 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5451 __isl_take isl_pw_qpolynomial *pwqp1,
5452 __isl_take isl_pw_qpolynomial *pwqp2);
5453 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5454 __isl_take isl_pw_qpolynomial *pwqp1,
5455 __isl_take isl_pw_qpolynomial *pwqp2);
5456 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5457 __isl_take isl_pw_qpolynomial *pwqp1,
5458 __isl_take isl_pw_qpolynomial *pwqp2);
5459 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5460 __isl_take isl_pw_qpolynomial *pwqp);
5461 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5462 __isl_take isl_pw_qpolynomial *pwqp1,
5463 __isl_take isl_pw_qpolynomial *pwqp2);
5464 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5465 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5467 __isl_give isl_union_pw_qpolynomial *
5468 isl_union_pw_qpolynomial_scale_val(
5469 __isl_take isl_union_pw_qpolynomial *upwqp,
5470 __isl_take isl_val *v);
5471 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5472 __isl_take isl_union_pw_qpolynomial *upwqp1,
5473 __isl_take isl_union_pw_qpolynomial *upwqp2);
5474 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5475 __isl_take isl_union_pw_qpolynomial *upwqp1,
5476 __isl_take isl_union_pw_qpolynomial *upwqp2);
5477 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5478 __isl_take isl_union_pw_qpolynomial *upwqp1,
5479 __isl_take isl_union_pw_qpolynomial *upwqp2);
5481 __isl_give isl_val *isl_pw_qpolynomial_eval(
5482 __isl_take isl_pw_qpolynomial *pwqp,
5483 __isl_take isl_point *pnt);
5485 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5486 __isl_take isl_union_pw_qpolynomial *upwqp,
5487 __isl_take isl_point *pnt);
5489 __isl_give isl_set *isl_pw_qpolynomial_domain(
5490 __isl_take isl_pw_qpolynomial *pwqp);
5491 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5492 __isl_take isl_pw_qpolynomial *pwpq,
5493 __isl_take isl_set *set);
5494 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5495 __isl_take isl_pw_qpolynomial *pwpq,
5496 __isl_take isl_set *set);
5498 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5499 __isl_take isl_union_pw_qpolynomial *upwqp);
5500 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5501 __isl_take isl_union_pw_qpolynomial *upwpq,
5502 __isl_take isl_union_set *uset);
5503 __isl_give isl_union_pw_qpolynomial *
5504 isl_union_pw_qpolynomial_intersect_params(
5505 __isl_take isl_union_pw_qpolynomial *upwpq,
5506 __isl_take isl_set *set);
5508 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5509 __isl_take isl_qpolynomial *qp,
5510 __isl_take isl_space *model);
5512 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5513 __isl_take isl_qpolynomial *qp);
5514 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5515 __isl_take isl_pw_qpolynomial *pwqp);
5517 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5518 __isl_take isl_union_pw_qpolynomial *upwqp);
5520 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5521 __isl_take isl_qpolynomial *qp,
5522 __isl_take isl_set *context);
5523 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5524 __isl_take isl_qpolynomial *qp,
5525 __isl_take isl_set *context);
5527 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5528 __isl_take isl_pw_qpolynomial *pwqp,
5529 __isl_take isl_set *context);
5530 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5531 __isl_take isl_pw_qpolynomial *pwqp,
5532 __isl_take isl_set *context);
5534 __isl_give isl_union_pw_qpolynomial *
5535 isl_union_pw_qpolynomial_gist_params(
5536 __isl_take isl_union_pw_qpolynomial *upwqp,
5537 __isl_take isl_set *context);
5538 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5539 __isl_take isl_union_pw_qpolynomial *upwqp,
5540 __isl_take isl_union_set *context);
5542 The gist operation applies the gist operation to each of
5543 the cells in the domain of the input piecewise quasipolynomial.
5544 The context is also exploited
5545 to simplify the quasipolynomials associated to each cell.
5547 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5548 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5549 __isl_give isl_union_pw_qpolynomial *
5550 isl_union_pw_qpolynomial_to_polynomial(
5551 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5553 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5554 the polynomial will be an overapproximation. If C<sign> is negative,
5555 it will be an underapproximation. If C<sign> is zero, the approximation
5556 will lie somewhere in between.
5558 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5560 A piecewise quasipolynomial reduction is a piecewise
5561 reduction (or fold) of quasipolynomials.
5562 In particular, the reduction can be maximum or a minimum.
5563 The objects are mainly used to represent the result of
5564 an upper or lower bound on a quasipolynomial over its domain,
5565 i.e., as the result of the following function.
5567 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5568 __isl_take isl_pw_qpolynomial *pwqp,
5569 enum isl_fold type, int *tight);
5571 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5572 __isl_take isl_union_pw_qpolynomial *upwqp,
5573 enum isl_fold type, int *tight);
5575 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5576 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5577 is the returned bound is known be tight, i.e., for each value
5578 of the parameters there is at least
5579 one element in the domain that reaches the bound.
5580 If the domain of C<pwqp> is not wrapping, then the bound is computed
5581 over all elements in that domain and the result has a purely parametric
5582 domain. If the domain of C<pwqp> is wrapping, then the bound is
5583 computed over the range of the wrapped relation. The domain of the
5584 wrapped relation becomes the domain of the result.
5586 A (piecewise) quasipolynomial reduction can be copied or freed using the
5587 following functions.
5589 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5590 __isl_keep isl_qpolynomial_fold *fold);
5591 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5592 __isl_keep isl_pw_qpolynomial_fold *pwf);
5593 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5594 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5595 void isl_qpolynomial_fold_free(
5596 __isl_take isl_qpolynomial_fold *fold);
5597 __isl_null isl_pw_qpolynomial_fold *
5598 isl_pw_qpolynomial_fold_free(
5599 __isl_take isl_pw_qpolynomial_fold *pwf);
5600 __isl_null isl_union_pw_qpolynomial_fold *
5601 isl_union_pw_qpolynomial_fold_free(
5602 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5604 =head3 Printing Piecewise Quasipolynomial Reductions
5606 Piecewise quasipolynomial reductions can be printed
5607 using the following function.
5609 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5610 __isl_take isl_printer *p,
5611 __isl_keep isl_pw_qpolynomial_fold *pwf);
5612 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5613 __isl_take isl_printer *p,
5614 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5616 For C<isl_printer_print_pw_qpolynomial_fold>,
5617 output format of the printer
5618 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5619 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5620 output format of the printer
5621 needs to be set to C<ISL_FORMAT_ISL>.
5622 In case of printing in C<ISL_FORMAT_C>, the user may want
5623 to set the names of all dimensions
5625 __isl_give isl_pw_qpolynomial_fold *
5626 isl_pw_qpolynomial_fold_set_dim_name(
5627 __isl_take isl_pw_qpolynomial_fold *pwf,
5628 enum isl_dim_type type, unsigned pos,
5631 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5633 To iterate over all piecewise quasipolynomial reductions in a union
5634 piecewise quasipolynomial reduction, use the following function
5636 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5637 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5638 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5639 void *user), void *user);
5641 To iterate over the cells in a piecewise quasipolynomial reduction,
5642 use either of the following two functions
5644 int isl_pw_qpolynomial_fold_foreach_piece(
5645 __isl_keep isl_pw_qpolynomial_fold *pwf,
5646 int (*fn)(__isl_take isl_set *set,
5647 __isl_take isl_qpolynomial_fold *fold,
5648 void *user), void *user);
5649 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5650 __isl_keep isl_pw_qpolynomial_fold *pwf,
5651 int (*fn)(__isl_take isl_set *set,
5652 __isl_take isl_qpolynomial_fold *fold,
5653 void *user), void *user);
5655 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5656 of the difference between these two functions.
5658 To iterate over all quasipolynomials in a reduction, use
5660 int isl_qpolynomial_fold_foreach_qpolynomial(
5661 __isl_keep isl_qpolynomial_fold *fold,
5662 int (*fn)(__isl_take isl_qpolynomial *qp,
5663 void *user), void *user);
5665 =head3 Properties of Piecewise Quasipolynomial Reductions
5667 To check whether two union piecewise quasipolynomial reductions are
5668 obviously equal, use
5670 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5671 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5672 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5674 =head3 Operations on Piecewise Quasipolynomial Reductions
5676 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5677 __isl_take isl_qpolynomial_fold *fold,
5678 __isl_take isl_val *v);
5679 __isl_give isl_pw_qpolynomial_fold *
5680 isl_pw_qpolynomial_fold_scale_val(
5681 __isl_take isl_pw_qpolynomial_fold *pwf,
5682 __isl_take isl_val *v);
5683 __isl_give isl_union_pw_qpolynomial_fold *
5684 isl_union_pw_qpolynomial_fold_scale_val(
5685 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5686 __isl_take isl_val *v);
5688 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5689 __isl_take isl_pw_qpolynomial_fold *pwf1,
5690 __isl_take isl_pw_qpolynomial_fold *pwf2);
5692 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5693 __isl_take isl_pw_qpolynomial_fold *pwf1,
5694 __isl_take isl_pw_qpolynomial_fold *pwf2);
5696 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5697 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5698 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5700 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5701 __isl_take isl_pw_qpolynomial_fold *pwf,
5702 __isl_take isl_point *pnt);
5704 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5705 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5706 __isl_take isl_point *pnt);
5708 __isl_give isl_pw_qpolynomial_fold *
5709 isl_pw_qpolynomial_fold_intersect_params(
5710 __isl_take isl_pw_qpolynomial_fold *pwf,
5711 __isl_take isl_set *set);
5713 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5714 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5715 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5716 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5717 __isl_take isl_union_set *uset);
5718 __isl_give isl_union_pw_qpolynomial_fold *
5719 isl_union_pw_qpolynomial_fold_intersect_params(
5720 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5721 __isl_take isl_set *set);
5723 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5724 __isl_take isl_pw_qpolynomial_fold *pwf);
5726 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5727 __isl_take isl_pw_qpolynomial_fold *pwf);
5729 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5730 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5732 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5733 __isl_take isl_qpolynomial_fold *fold,
5734 __isl_take isl_set *context);
5735 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5736 __isl_take isl_qpolynomial_fold *fold,
5737 __isl_take isl_set *context);
5739 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5740 __isl_take isl_pw_qpolynomial_fold *pwf,
5741 __isl_take isl_set *context);
5742 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5743 __isl_take isl_pw_qpolynomial_fold *pwf,
5744 __isl_take isl_set *context);
5746 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5747 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5748 __isl_take isl_union_set *context);
5749 __isl_give isl_union_pw_qpolynomial_fold *
5750 isl_union_pw_qpolynomial_fold_gist_params(
5751 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5752 __isl_take isl_set *context);
5754 The gist operation applies the gist operation to each of
5755 the cells in the domain of the input piecewise quasipolynomial reduction.
5756 In future, the operation will also exploit the context
5757 to simplify the quasipolynomial reductions associated to each cell.
5759 __isl_give isl_pw_qpolynomial_fold *
5760 isl_set_apply_pw_qpolynomial_fold(
5761 __isl_take isl_set *set,
5762 __isl_take isl_pw_qpolynomial_fold *pwf,
5764 __isl_give isl_pw_qpolynomial_fold *
5765 isl_map_apply_pw_qpolynomial_fold(
5766 __isl_take isl_map *map,
5767 __isl_take isl_pw_qpolynomial_fold *pwf,
5769 __isl_give isl_union_pw_qpolynomial_fold *
5770 isl_union_set_apply_union_pw_qpolynomial_fold(
5771 __isl_take isl_union_set *uset,
5772 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5774 __isl_give isl_union_pw_qpolynomial_fold *
5775 isl_union_map_apply_union_pw_qpolynomial_fold(
5776 __isl_take isl_union_map *umap,
5777 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5780 The functions taking a map
5781 compose the given map with the given piecewise quasipolynomial reduction.
5782 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5783 over all elements in the intersection of the range of the map
5784 and the domain of the piecewise quasipolynomial reduction
5785 as a function of an element in the domain of the map.
5786 The functions taking a set compute a bound over all elements in the
5787 intersection of the set and the domain of the
5788 piecewise quasipolynomial reduction.
5790 =head2 Parametric Vertex Enumeration
5792 The parametric vertex enumeration described in this section
5793 is mainly intended to be used internally and by the C<barvinok>
5796 #include <isl/vertices.h>
5797 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5798 __isl_keep isl_basic_set *bset);
5800 The function C<isl_basic_set_compute_vertices> performs the
5801 actual computation of the parametric vertices and the chamber
5802 decomposition and store the result in an C<isl_vertices> object.
5803 This information can be queried by either iterating over all
5804 the vertices or iterating over all the chambers or cells
5805 and then iterating over all vertices that are active on the chamber.
5807 int isl_vertices_foreach_vertex(
5808 __isl_keep isl_vertices *vertices,
5809 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5812 int isl_vertices_foreach_cell(
5813 __isl_keep isl_vertices *vertices,
5814 int (*fn)(__isl_take isl_cell *cell, void *user),
5816 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5817 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5820 Other operations that can be performed on an C<isl_vertices> object are
5823 isl_ctx *isl_vertices_get_ctx(
5824 __isl_keep isl_vertices *vertices);
5825 int isl_vertices_get_n_vertices(
5826 __isl_keep isl_vertices *vertices);
5827 void isl_vertices_free(__isl_take isl_vertices *vertices);
5829 Vertices can be inspected and destroyed using the following functions.
5831 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5832 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5833 __isl_give isl_basic_set *isl_vertex_get_domain(
5834 __isl_keep isl_vertex *vertex);
5835 __isl_give isl_multi_aff *isl_vertex_get_expr(
5836 __isl_keep isl_vertex *vertex);
5837 void isl_vertex_free(__isl_take isl_vertex *vertex);
5839 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
5840 describing the vertex in terms of the parameters,
5841 while C<isl_vertex_get_domain> returns the activity domain
5844 Chambers can be inspected and destroyed using the following functions.
5846 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5847 __isl_give isl_basic_set *isl_cell_get_domain(
5848 __isl_keep isl_cell *cell);
5849 void isl_cell_free(__isl_take isl_cell *cell);
5851 =head1 Polyhedral Compilation Library
5853 This section collects functionality in C<isl> that has been specifically
5854 designed for use during polyhedral compilation.
5856 =head2 Dependence Analysis
5858 C<isl> contains specialized functionality for performing
5859 array dataflow analysis. That is, given a I<sink> access relation
5860 and a collection of possible I<source> access relations,
5861 C<isl> can compute relations that describe
5862 for each iteration of the sink access, which iteration
5863 of which of the source access relations was the last
5864 to access the same data element before the given iteration
5866 The resulting dependence relations map source iterations
5867 to the corresponding sink iterations.
5868 To compute standard flow dependences, the sink should be
5869 a read, while the sources should be writes.
5870 If any of the source accesses are marked as being I<may>
5871 accesses, then there will be a dependence from the last
5872 I<must> access B<and> from any I<may> access that follows
5873 this last I<must> access.
5874 In particular, if I<all> sources are I<may> accesses,
5875 then memory based dependence analysis is performed.
5876 If, on the other hand, all sources are I<must> accesses,
5877 then value based dependence analysis is performed.
5879 #include <isl/flow.h>
5881 typedef int (*isl_access_level_before)(void *first, void *second);
5883 __isl_give isl_access_info *isl_access_info_alloc(
5884 __isl_take isl_map *sink,
5885 void *sink_user, isl_access_level_before fn,
5887 __isl_give isl_access_info *isl_access_info_add_source(
5888 __isl_take isl_access_info *acc,
5889 __isl_take isl_map *source, int must,
5891 __isl_null isl_access_info *isl_access_info_free(
5892 __isl_take isl_access_info *acc);
5894 __isl_give isl_flow *isl_access_info_compute_flow(
5895 __isl_take isl_access_info *acc);
5897 int isl_flow_foreach(__isl_keep isl_flow *deps,
5898 int (*fn)(__isl_take isl_map *dep, int must,
5899 void *dep_user, void *user),
5901 __isl_give isl_map *isl_flow_get_no_source(
5902 __isl_keep isl_flow *deps, int must);
5903 void isl_flow_free(__isl_take isl_flow *deps);
5905 The function C<isl_access_info_compute_flow> performs the actual
5906 dependence analysis. The other functions are used to construct
5907 the input for this function or to read off the output.
5909 The input is collected in an C<isl_access_info>, which can
5910 be created through a call to C<isl_access_info_alloc>.
5911 The arguments to this functions are the sink access relation
5912 C<sink>, a token C<sink_user> used to identify the sink
5913 access to the user, a callback function for specifying the
5914 relative order of source and sink accesses, and the number
5915 of source access relations that will be added.
5916 The callback function has type C<int (*)(void *first, void *second)>.
5917 The function is called with two user supplied tokens identifying
5918 either a source or the sink and it should return the shared nesting
5919 level and the relative order of the two accesses.
5920 In particular, let I<n> be the number of loops shared by
5921 the two accesses. If C<first> precedes C<second> textually,
5922 then the function should return I<2 * n + 1>; otherwise,
5923 it should return I<2 * n>.
5924 The sources can be added to the C<isl_access_info> by performing
5925 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5926 C<must> indicates whether the source is a I<must> access
5927 or a I<may> access. Note that a multi-valued access relation
5928 should only be marked I<must> if every iteration in the domain
5929 of the relation accesses I<all> elements in its image.
5930 The C<source_user> token is again used to identify
5931 the source access. The range of the source access relation
5932 C<source> should have the same dimension as the range
5933 of the sink access relation.
5934 The C<isl_access_info_free> function should usually not be
5935 called explicitly, because it is called implicitly by
5936 C<isl_access_info_compute_flow>.
5938 The result of the dependence analysis is collected in an
5939 C<isl_flow>. There may be elements of
5940 the sink access for which no preceding source access could be
5941 found or for which all preceding sources are I<may> accesses.
5942 The relations containing these elements can be obtained through
5943 calls to C<isl_flow_get_no_source>, the first with C<must> set
5944 and the second with C<must> unset.
5945 In the case of standard flow dependence analysis,
5946 with the sink a read and the sources I<must> writes,
5947 the first relation corresponds to the reads from uninitialized
5948 array elements and the second relation is empty.
5949 The actual flow dependences can be extracted using
5950 C<isl_flow_foreach>. This function will call the user-specified
5951 callback function C<fn> for each B<non-empty> dependence between
5952 a source and the sink. The callback function is called
5953 with four arguments, the actual flow dependence relation
5954 mapping source iterations to sink iterations, a boolean that
5955 indicates whether it is a I<must> or I<may> dependence, a token
5956 identifying the source and an additional C<void *> with value
5957 equal to the third argument of the C<isl_flow_foreach> call.
5958 A dependence is marked I<must> if it originates from a I<must>
5959 source and if it is not followed by any I<may> sources.
5961 After finishing with an C<isl_flow>, the user should call
5962 C<isl_flow_free> to free all associated memory.
5964 A higher-level interface to dependence analysis is provided
5965 by the following function.
5967 #include <isl/flow.h>
5969 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5970 __isl_take isl_union_map *must_source,
5971 __isl_take isl_union_map *may_source,
5972 __isl_take isl_union_map *schedule,
5973 __isl_give isl_union_map **must_dep,
5974 __isl_give isl_union_map **may_dep,
5975 __isl_give isl_union_map **must_no_source,
5976 __isl_give isl_union_map **may_no_source);
5978 The arrays are identified by the tuple names of the ranges
5979 of the accesses. The iteration domains by the tuple names
5980 of the domains of the accesses and of the schedule.
5981 The relative order of the iteration domains is given by the
5982 schedule. The relations returned through C<must_no_source>
5983 and C<may_no_source> are subsets of C<sink>.
5984 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5985 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5986 any of the other arguments is treated as an error.
5988 =head3 Interaction with Dependence Analysis
5990 During the dependence analysis, we frequently need to perform
5991 the following operation. Given a relation between sink iterations
5992 and potential source iterations from a particular source domain,
5993 what is the last potential source iteration corresponding to each
5994 sink iteration. It can sometimes be convenient to adjust
5995 the set of potential source iterations before or after each such operation.
5996 The prototypical example is fuzzy array dataflow analysis,
5997 where we need to analyze if, based on data-dependent constraints,
5998 the sink iteration can ever be executed without one or more of
5999 the corresponding potential source iterations being executed.
6000 If so, we can introduce extra parameters and select an unknown
6001 but fixed source iteration from the potential source iterations.
6002 To be able to perform such manipulations, C<isl> provides the following
6005 #include <isl/flow.h>
6007 typedef __isl_give isl_restriction *(*isl_access_restrict)(
6008 __isl_keep isl_map *source_map,
6009 __isl_keep isl_set *sink, void *source_user,
6011 __isl_give isl_access_info *isl_access_info_set_restrict(
6012 __isl_take isl_access_info *acc,
6013 isl_access_restrict fn, void *user);
6015 The function C<isl_access_info_set_restrict> should be called
6016 before calling C<isl_access_info_compute_flow> and registers a callback function
6017 that will be called any time C<isl> is about to compute the last
6018 potential source. The first argument is the (reverse) proto-dependence,
6019 mapping sink iterations to potential source iterations.
6020 The second argument represents the sink iterations for which
6021 we want to compute the last source iteration.
6022 The third argument is the token corresponding to the source
6023 and the final argument is the token passed to C<isl_access_info_set_restrict>.
6024 The callback is expected to return a restriction on either the input or
6025 the output of the operation computing the last potential source.
6026 If the input needs to be restricted then restrictions are needed
6027 for both the source and the sink iterations. The sink iterations
6028 and the potential source iterations will be intersected with these sets.
6029 If the output needs to be restricted then only a restriction on the source
6030 iterations is required.
6031 If any error occurs, the callback should return C<NULL>.
6032 An C<isl_restriction> object can be created, freed and inspected
6033 using the following functions.
6035 #include <isl/flow.h>
6037 __isl_give isl_restriction *isl_restriction_input(
6038 __isl_take isl_set *source_restr,
6039 __isl_take isl_set *sink_restr);
6040 __isl_give isl_restriction *isl_restriction_output(
6041 __isl_take isl_set *source_restr);
6042 __isl_give isl_restriction *isl_restriction_none(
6043 __isl_take isl_map *source_map);
6044 __isl_give isl_restriction *isl_restriction_empty(
6045 __isl_take isl_map *source_map);
6046 __isl_null isl_restriction *isl_restriction_free(
6047 __isl_take isl_restriction *restr);
6048 isl_ctx *isl_restriction_get_ctx(
6049 __isl_keep isl_restriction *restr);
6051 C<isl_restriction_none> and C<isl_restriction_empty> are special
6052 cases of C<isl_restriction_input>. C<isl_restriction_none>
6053 is essentially equivalent to
6055 isl_restriction_input(isl_set_universe(
6056 isl_space_range(isl_map_get_space(source_map))),
6058 isl_space_domain(isl_map_get_space(source_map))));
6060 whereas C<isl_restriction_empty> is essentially equivalent to
6062 isl_restriction_input(isl_set_empty(
6063 isl_space_range(isl_map_get_space(source_map))),
6065 isl_space_domain(isl_map_get_space(source_map))));
6069 B<The functionality described in this section is fairly new
6070 and may be subject to change.>
6072 #include <isl/schedule.h>
6073 __isl_give isl_schedule *
6074 isl_schedule_constraints_compute_schedule(
6075 __isl_take isl_schedule_constraints *sc);
6076 __isl_null isl_schedule *isl_schedule_free(
6077 __isl_take isl_schedule *sched);
6079 The function C<isl_schedule_constraints_compute_schedule> can be
6080 used to compute a schedule that satisfies the given schedule constraints.
6081 These schedule constraints include the iteration domain for which
6082 a schedule should be computed and dependences between pairs of
6083 iterations. In particular, these dependences include
6084 I<validity> dependences and I<proximity> dependences.
6085 By default, the algorithm used to construct the schedule is similar
6086 to that of C<Pluto>.
6087 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
6089 The generated schedule respects all validity dependences.
6090 That is, all dependence distances over these dependences in the
6091 scheduled space are lexicographically positive.
6092 The default algorithm tries to ensure that the dependence distances
6093 over coincidence constraints are zero and to minimize the
6094 dependence distances over proximity dependences.
6095 Moreover, it tries to obtain sequences (bands) of schedule dimensions
6096 for groups of domains where the dependence distances over validity
6097 dependences have only non-negative values.
6098 When using Feautrier's algorithm, the coincidence and proximity constraints
6099 are only taken into account during the extension to a
6100 full-dimensional schedule.
6102 An C<isl_schedule_constraints> object can be constructed
6103 and manipulated using the following functions.
6105 #include <isl/schedule.h>
6106 __isl_give isl_schedule_constraints *
6107 isl_schedule_constraints_copy(
6108 __isl_keep isl_schedule_constraints *sc);
6109 __isl_give isl_schedule_constraints *
6110 isl_schedule_constraints_on_domain(
6111 __isl_take isl_union_set *domain);
6112 isl_ctx *isl_schedule_constraints_get_ctx(
6113 __isl_keep isl_schedule_constraints *sc);
6114 __isl_give isl_schedule_constraints *
6115 isl_schedule_constraints_set_validity(
6116 __isl_take isl_schedule_constraints *sc,
6117 __isl_take isl_union_map *validity);
6118 __isl_give isl_schedule_constraints *
6119 isl_schedule_constraints_set_coincidence(
6120 __isl_take isl_schedule_constraints *sc,
6121 __isl_take isl_union_map *coincidence);
6122 __isl_give isl_schedule_constraints *
6123 isl_schedule_constraints_set_proximity(
6124 __isl_take isl_schedule_constraints *sc,
6125 __isl_take isl_union_map *proximity);
6126 __isl_give isl_schedule_constraints *
6127 isl_schedule_constraints_set_conditional_validity(
6128 __isl_take isl_schedule_constraints *sc,
6129 __isl_take isl_union_map *condition,
6130 __isl_take isl_union_map *validity);
6131 __isl_null isl_schedule_constraints *
6132 isl_schedule_constraints_free(
6133 __isl_take isl_schedule_constraints *sc);
6135 The initial C<isl_schedule_constraints> object created by
6136 C<isl_schedule_constraints_on_domain> does not impose any constraints.
6137 That is, it has an empty set of dependences.
6138 The function C<isl_schedule_constraints_set_validity> replaces the
6139 validity dependences, mapping domain elements I<i> to domain
6140 elements that should be scheduled after I<i>.
6141 The function C<isl_schedule_constraints_set_coincidence> replaces the
6142 coincidence dependences, mapping domain elements I<i> to domain
6143 elements that should be scheduled together with I<I>, if possible.
6144 The function C<isl_schedule_constraints_set_proximity> replaces the
6145 proximity dependences, mapping domain elements I<i> to domain
6146 elements that should be scheduled either before I<I>
6147 or as early as possible after I<i>.
6149 The function C<isl_schedule_constraints_set_conditional_validity>
6150 replaces the conditional validity constraints.
6151 A conditional validity constraint is only imposed when any of the corresponding
6152 conditions is satisfied, i.e., when any of them is non-zero.
6153 That is, the scheduler ensures that within each band if the dependence
6154 distances over the condition constraints are not all zero
6155 then all corresponding conditional validity constraints are respected.
6156 A conditional validity constraint corresponds to a condition
6157 if the two are adjacent, i.e., if the domain of one relation intersect
6158 the range of the other relation.
6159 The typical use case of conditional validity constraints is
6160 to allow order constraints between live ranges to be violated
6161 as long as the live ranges themselves are local to the band.
6162 To allow more fine-grained control over which conditions correspond
6163 to which conditional validity constraints, the domains and ranges
6164 of these relations may include I<tags>. That is, the domains and
6165 ranges of those relation may themselves be wrapped relations
6166 where the iteration domain appears in the domain of those wrapped relations
6167 and the range of the wrapped relations can be arbitrarily chosen
6168 by the user. Conditions and conditional validity constraints are only
6169 considered adjacent to each other if the entire wrapped relation matches.
6170 In particular, a relation with a tag will never be considered adjacent
6171 to a relation without a tag.
6173 The following function computes a schedule directly from
6174 an iteration domain and validity and proximity dependences
6175 and is implemented in terms of the functions described above.
6176 The use of C<isl_union_set_compute_schedule> is discouraged.
6178 #include <isl/schedule.h>
6179 __isl_give isl_schedule *isl_union_set_compute_schedule(
6180 __isl_take isl_union_set *domain,
6181 __isl_take isl_union_map *validity,
6182 __isl_take isl_union_map *proximity);
6184 A mapping from the domains to the scheduled space can be obtained
6185 from an C<isl_schedule> using the following function.
6187 __isl_give isl_union_map *isl_schedule_get_map(
6188 __isl_keep isl_schedule *sched);
6190 A representation of the schedule can be printed using
6192 __isl_give isl_printer *isl_printer_print_schedule(
6193 __isl_take isl_printer *p,
6194 __isl_keep isl_schedule *schedule);
6196 A representation of the schedule as a forest of bands can be obtained
6197 using the following function.
6199 __isl_give isl_band_list *isl_schedule_get_band_forest(
6200 __isl_keep isl_schedule *schedule);
6202 The individual bands can be visited in depth-first post-order
6203 using the following function.
6205 #include <isl/schedule.h>
6206 int isl_schedule_foreach_band(
6207 __isl_keep isl_schedule *sched,
6208 int (*fn)(__isl_keep isl_band *band, void *user),
6211 The list can be manipulated as explained in L<"Lists">.
6212 The bands inside the list can be copied and freed using the following
6215 #include <isl/band.h>
6216 __isl_give isl_band *isl_band_copy(
6217 __isl_keep isl_band *band);
6218 __isl_null isl_band *isl_band_free(
6219 __isl_take isl_band *band);
6221 Each band contains zero or more scheduling dimensions.
6222 These are referred to as the members of the band.
6223 The section of the schedule that corresponds to the band is
6224 referred to as the partial schedule of the band.
6225 For those nodes that participate in a band, the outer scheduling
6226 dimensions form the prefix schedule, while the inner scheduling
6227 dimensions form the suffix schedule.
6228 That is, if we take a cut of the band forest, then the union of
6229 the concatenations of the prefix, partial and suffix schedules of
6230 each band in the cut is equal to the entire schedule (modulo
6231 some possible padding at the end with zero scheduling dimensions).
6232 The properties of a band can be inspected using the following functions.
6234 #include <isl/band.h>
6235 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
6237 int isl_band_has_children(__isl_keep isl_band *band);
6238 __isl_give isl_band_list *isl_band_get_children(
6239 __isl_keep isl_band *band);
6241 __isl_give isl_union_map *isl_band_get_prefix_schedule(
6242 __isl_keep isl_band *band);
6243 __isl_give isl_union_map *isl_band_get_partial_schedule(
6244 __isl_keep isl_band *band);
6245 __isl_give isl_union_map *isl_band_get_suffix_schedule(
6246 __isl_keep isl_band *band);
6248 int isl_band_n_member(__isl_keep isl_band *band);
6249 int isl_band_member_is_coincident(
6250 __isl_keep isl_band *band, int pos);
6252 int isl_band_list_foreach_band(
6253 __isl_keep isl_band_list *list,
6254 int (*fn)(__isl_keep isl_band *band, void *user),
6257 Note that a scheduling dimension is considered to be ``coincident''
6258 if it satisfies the coincidence constraints within its band.
6259 That is, if the dependence distances of the coincidence
6260 constraints are all zero in that direction (for fixed
6261 iterations of outer bands).
6262 Like C<isl_schedule_foreach_band>,
6263 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
6264 in depth-first post-order.
6266 A band can be tiled using the following function.
6268 #include <isl/band.h>
6269 int isl_band_tile(__isl_keep isl_band *band,
6270 __isl_take isl_vec *sizes);
6272 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
6274 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
6275 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
6277 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
6279 The C<isl_band_tile> function tiles the band using the given tile sizes
6280 inside its schedule.
6281 A new child band is created to represent the point loops and it is
6282 inserted between the modified band and its children.
6283 The C<tile_scale_tile_loops> option specifies whether the tile
6284 loops iterators should be scaled by the tile sizes.
6285 If the C<tile_shift_point_loops> option is set, then the point loops
6286 are shifted to start at zero.
6288 A band can be split into two nested bands using the following function.
6290 int isl_band_split(__isl_keep isl_band *band, int pos);
6292 The resulting outer band contains the first C<pos> dimensions of C<band>
6293 while the inner band contains the remaining dimensions.
6295 A representation of the band can be printed using
6297 #include <isl/band.h>
6298 __isl_give isl_printer *isl_printer_print_band(
6299 __isl_take isl_printer *p,
6300 __isl_keep isl_band *band);
6304 #include <isl/schedule.h>
6305 int isl_options_set_schedule_max_coefficient(
6306 isl_ctx *ctx, int val);
6307 int isl_options_get_schedule_max_coefficient(
6309 int isl_options_set_schedule_max_constant_term(
6310 isl_ctx *ctx, int val);
6311 int isl_options_get_schedule_max_constant_term(
6313 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
6314 int isl_options_get_schedule_fuse(isl_ctx *ctx);
6315 int isl_options_set_schedule_maximize_band_depth(
6316 isl_ctx *ctx, int val);
6317 int isl_options_get_schedule_maximize_band_depth(
6319 int isl_options_set_schedule_outer_coincidence(
6320 isl_ctx *ctx, int val);
6321 int isl_options_get_schedule_outer_coincidence(
6323 int isl_options_set_schedule_split_scaled(
6324 isl_ctx *ctx, int val);
6325 int isl_options_get_schedule_split_scaled(
6327 int isl_options_set_schedule_algorithm(
6328 isl_ctx *ctx, int val);
6329 int isl_options_get_schedule_algorithm(
6331 int isl_options_set_schedule_separate_components(
6332 isl_ctx *ctx, int val);
6333 int isl_options_get_schedule_separate_components(
6338 =item * schedule_max_coefficient
6340 This option enforces that the coefficients for variable and parameter
6341 dimensions in the calculated schedule are not larger than the specified value.
6342 This option can significantly increase the speed of the scheduling calculation
6343 and may also prevent fusing of unrelated dimensions. A value of -1 means that
6344 this option does not introduce bounds on the variable or parameter
6347 =item * schedule_max_constant_term
6349 This option enforces that the constant coefficients in the calculated schedule
6350 are not larger than the maximal constant term. This option can significantly
6351 increase the speed of the scheduling calculation and may also prevent fusing of
6352 unrelated dimensions. A value of -1 means that this option does not introduce
6353 bounds on the constant coefficients.
6355 =item * schedule_fuse
6357 This option controls the level of fusion.
6358 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6359 resulting schedule will be distributed as much as possible.
6360 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6361 try to fuse loops in the resulting schedule.
6363 =item * schedule_maximize_band_depth
6365 If this option is set, we do not split bands at the point
6366 where we detect splitting is necessary. Instead, we
6367 backtrack and split bands as early as possible. This
6368 reduces the number of splits and maximizes the width of
6369 the bands. Wider bands give more possibilities for tiling.
6370 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6371 then bands will be split as early as possible, even if there is no need.
6372 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6374 =item * schedule_outer_coincidence
6376 If this option is set, then we try to construct schedules
6377 where the outermost scheduling dimension in each band
6378 satisfies the coincidence constraints.
6380 =item * schedule_split_scaled
6382 If this option is set, then we try to construct schedules in which the
6383 constant term is split off from the linear part if the linear parts of
6384 the scheduling rows for all nodes in the graphs have a common non-trivial
6386 The constant term is then placed in a separate band and the linear
6389 =item * schedule_algorithm
6391 Selects the scheduling algorithm to be used.
6392 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6393 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6395 =item * schedule_separate_components
6397 If at any point the dependence graph contains any (weakly connected) components,
6398 then these components are scheduled separately.
6399 If this option is not set, then some iterations of the domains
6400 in these components may be scheduled together.
6401 If this option is set, then the components are given consecutive
6406 =head2 AST Generation
6408 This section describes the C<isl> functionality for generating
6409 ASTs that visit all the elements
6410 in a domain in an order specified by a schedule.
6411 In particular, given a C<isl_union_map>, an AST is generated
6412 that visits all the elements in the domain of the C<isl_union_map>
6413 according to the lexicographic order of the corresponding image
6414 element(s). If the range of the C<isl_union_map> consists of
6415 elements in more than one space, then each of these spaces is handled
6416 separately in an arbitrary order.
6417 It should be noted that the image elements only specify the I<order>
6418 in which the corresponding domain elements should be visited.
6419 No direct relation between the image elements and the loop iterators
6420 in the generated AST should be assumed.
6422 Each AST is generated within a build. The initial build
6423 simply specifies the constraints on the parameters (if any)
6424 and can be created, inspected, copied and freed using the following functions.
6426 #include <isl/ast_build.h>
6427 __isl_give isl_ast_build *isl_ast_build_from_context(
6428 __isl_take isl_set *set);
6429 isl_ctx *isl_ast_build_get_ctx(
6430 __isl_keep isl_ast_build *build);
6431 __isl_give isl_ast_build *isl_ast_build_copy(
6432 __isl_keep isl_ast_build *build);
6433 __isl_null isl_ast_build *isl_ast_build_free(
6434 __isl_take isl_ast_build *build);
6436 The C<set> argument is usually a parameter set with zero or more parameters.
6437 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6438 and L</"Fine-grained Control over AST Generation">.
6439 Finally, the AST itself can be constructed using the following
6442 #include <isl/ast_build.h>
6443 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6444 __isl_keep isl_ast_build *build,
6445 __isl_take isl_union_map *schedule);
6447 =head3 Inspecting the AST
6449 The basic properties of an AST node can be obtained as follows.
6451 #include <isl/ast.h>
6452 isl_ctx *isl_ast_node_get_ctx(
6453 __isl_keep isl_ast_node *node);
6454 enum isl_ast_node_type isl_ast_node_get_type(
6455 __isl_keep isl_ast_node *node);
6457 The type of an AST node is one of
6458 C<isl_ast_node_for>,
6460 C<isl_ast_node_block> or
6461 C<isl_ast_node_user>.
6462 An C<isl_ast_node_for> represents a for node.
6463 An C<isl_ast_node_if> represents an if node.
6464 An C<isl_ast_node_block> represents a compound node.
6465 An C<isl_ast_node_user> represents an expression statement.
6466 An expression statement typically corresponds to a domain element, i.e.,
6467 one of the elements that is visited by the AST.
6469 Each type of node has its own additional properties.
6471 #include <isl/ast.h>
6472 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6473 __isl_keep isl_ast_node *node);
6474 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6475 __isl_keep isl_ast_node *node);
6476 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6477 __isl_keep isl_ast_node *node);
6478 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6479 __isl_keep isl_ast_node *node);
6480 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6481 __isl_keep isl_ast_node *node);
6482 int isl_ast_node_for_is_degenerate(
6483 __isl_keep isl_ast_node *node);
6485 An C<isl_ast_for> is considered degenerate if it is known to execute
6488 #include <isl/ast.h>
6489 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6490 __isl_keep isl_ast_node *node);
6491 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6492 __isl_keep isl_ast_node *node);
6493 int isl_ast_node_if_has_else(
6494 __isl_keep isl_ast_node *node);
6495 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6496 __isl_keep isl_ast_node *node);
6498 __isl_give isl_ast_node_list *
6499 isl_ast_node_block_get_children(
6500 __isl_keep isl_ast_node *node);
6502 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6503 __isl_keep isl_ast_node *node);
6505 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6506 the following functions.
6508 #include <isl/ast.h>
6509 isl_ctx *isl_ast_expr_get_ctx(
6510 __isl_keep isl_ast_expr *expr);
6511 enum isl_ast_expr_type isl_ast_expr_get_type(
6512 __isl_keep isl_ast_expr *expr);
6514 The type of an AST expression is one of
6516 C<isl_ast_expr_id> or
6517 C<isl_ast_expr_int>.
6518 An C<isl_ast_expr_op> represents the result of an operation.
6519 An C<isl_ast_expr_id> represents an identifier.
6520 An C<isl_ast_expr_int> represents an integer value.
6522 Each type of expression has its own additional properties.
6524 #include <isl/ast.h>
6525 enum isl_ast_op_type isl_ast_expr_get_op_type(
6526 __isl_keep isl_ast_expr *expr);
6527 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6528 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6529 __isl_keep isl_ast_expr *expr, int pos);
6530 int isl_ast_node_foreach_ast_op_type(
6531 __isl_keep isl_ast_node *node,
6532 int (*fn)(enum isl_ast_op_type type, void *user),
6535 C<isl_ast_expr_get_op_type> returns the type of the operation
6536 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6537 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6539 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6540 C<isl_ast_op_type> that appears in C<node>.
6541 The operation type is one of the following.
6545 =item C<isl_ast_op_and>
6547 Logical I<and> of two arguments.
6548 Both arguments can be evaluated.
6550 =item C<isl_ast_op_and_then>
6552 Logical I<and> of two arguments.
6553 The second argument can only be evaluated if the first evaluates to true.
6555 =item C<isl_ast_op_or>
6557 Logical I<or> of two arguments.
6558 Both arguments can be evaluated.
6560 =item C<isl_ast_op_or_else>
6562 Logical I<or> of two arguments.
6563 The second argument can only be evaluated if the first evaluates to false.
6565 =item C<isl_ast_op_max>
6567 Maximum of two or more arguments.
6569 =item C<isl_ast_op_min>
6571 Minimum of two or more arguments.
6573 =item C<isl_ast_op_minus>
6577 =item C<isl_ast_op_add>
6579 Sum of two arguments.
6581 =item C<isl_ast_op_sub>
6583 Difference of two arguments.
6585 =item C<isl_ast_op_mul>
6587 Product of two arguments.
6589 =item C<isl_ast_op_div>
6591 Exact division. That is, the result is known to be an integer.
6593 =item C<isl_ast_op_fdiv_q>
6595 Result of integer division, rounded towards negative
6598 =item C<isl_ast_op_pdiv_q>
6600 Result of integer division, where dividend is known to be non-negative.
6602 =item C<isl_ast_op_pdiv_r>
6604 Remainder of integer division, where dividend is known to be non-negative.
6606 =item C<isl_ast_op_zdiv_r>
6608 Equal to zero iff the remainder on integer division is zero.
6610 =item C<isl_ast_op_cond>
6612 Conditional operator defined on three arguments.
6613 If the first argument evaluates to true, then the result
6614 is equal to the second argument. Otherwise, the result
6615 is equal to the third argument.
6616 The second and third argument may only be evaluated if
6617 the first argument evaluates to true and false, respectively.
6618 Corresponds to C<a ? b : c> in C.
6620 =item C<isl_ast_op_select>
6622 Conditional operator defined on three arguments.
6623 If the first argument evaluates to true, then the result
6624 is equal to the second argument. Otherwise, the result
6625 is equal to the third argument.
6626 The second and third argument may be evaluated independently
6627 of the value of the first argument.
6628 Corresponds to C<a * b + (1 - a) * c> in C.
6630 =item C<isl_ast_op_eq>
6634 =item C<isl_ast_op_le>
6636 Less than or equal relation.
6638 =item C<isl_ast_op_lt>
6642 =item C<isl_ast_op_ge>
6644 Greater than or equal relation.
6646 =item C<isl_ast_op_gt>
6648 Greater than relation.
6650 =item C<isl_ast_op_call>
6653 The number of arguments of the C<isl_ast_expr> is one more than
6654 the number of arguments in the function call, the first argument
6655 representing the function being called.
6657 =item C<isl_ast_op_access>
6660 The number of arguments of the C<isl_ast_expr> is one more than
6661 the number of index expressions in the array access, the first argument
6662 representing the array being accessed.
6664 =item C<isl_ast_op_member>
6667 This operation has two arguments, a structure and the name of
6668 the member of the structure being accessed.
6672 #include <isl/ast.h>
6673 __isl_give isl_id *isl_ast_expr_get_id(
6674 __isl_keep isl_ast_expr *expr);
6676 Return the identifier represented by the AST expression.
6678 #include <isl/ast.h>
6679 __isl_give isl_val *isl_ast_expr_get_val(
6680 __isl_keep isl_ast_expr *expr);
6682 Return the integer represented by the AST expression.
6684 =head3 Properties of ASTs
6686 #include <isl/ast.h>
6687 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6688 __isl_keep isl_ast_expr *expr2);
6690 Check if two C<isl_ast_expr>s are equal to each other.
6692 =head3 Manipulating and printing the AST
6694 AST nodes can be copied and freed using the following functions.
6696 #include <isl/ast.h>
6697 __isl_give isl_ast_node *isl_ast_node_copy(
6698 __isl_keep isl_ast_node *node);
6699 __isl_null isl_ast_node *isl_ast_node_free(
6700 __isl_take isl_ast_node *node);
6702 AST expressions can be copied and freed using the following functions.
6704 #include <isl/ast.h>
6705 __isl_give isl_ast_expr *isl_ast_expr_copy(
6706 __isl_keep isl_ast_expr *expr);
6707 __isl_null isl_ast_expr *isl_ast_expr_free(
6708 __isl_take isl_ast_expr *expr);
6710 New AST expressions can be created either directly or within
6711 the context of an C<isl_ast_build>.
6713 #include <isl/ast.h>
6714 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6715 __isl_take isl_val *v);
6716 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6717 __isl_take isl_id *id);
6718 __isl_give isl_ast_expr *isl_ast_expr_neg(
6719 __isl_take isl_ast_expr *expr);
6720 __isl_give isl_ast_expr *isl_ast_expr_address_of(
6721 __isl_take isl_ast_expr *expr);
6722 __isl_give isl_ast_expr *isl_ast_expr_add(
6723 __isl_take isl_ast_expr *expr1,
6724 __isl_take isl_ast_expr *expr2);
6725 __isl_give isl_ast_expr *isl_ast_expr_sub(
6726 __isl_take isl_ast_expr *expr1,
6727 __isl_take isl_ast_expr *expr2);
6728 __isl_give isl_ast_expr *isl_ast_expr_mul(
6729 __isl_take isl_ast_expr *expr1,
6730 __isl_take isl_ast_expr *expr2);
6731 __isl_give isl_ast_expr *isl_ast_expr_div(
6732 __isl_take isl_ast_expr *expr1,
6733 __isl_take isl_ast_expr *expr2);
6734 __isl_give isl_ast_expr *isl_ast_expr_and(
6735 __isl_take isl_ast_expr *expr1,
6736 __isl_take isl_ast_expr *expr2)
6737 __isl_give isl_ast_expr *isl_ast_expr_or(
6738 __isl_take isl_ast_expr *expr1,
6739 __isl_take isl_ast_expr *expr2)
6740 __isl_give isl_ast_expr *isl_ast_expr_eq(
6741 __isl_take isl_ast_expr *expr1,
6742 __isl_take isl_ast_expr *expr2);
6743 __isl_give isl_ast_expr *isl_ast_expr_le(
6744 __isl_take isl_ast_expr *expr1,
6745 __isl_take isl_ast_expr *expr2);
6746 __isl_give isl_ast_expr *isl_ast_expr_lt(
6747 __isl_take isl_ast_expr *expr1,
6748 __isl_take isl_ast_expr *expr2);
6749 __isl_give isl_ast_expr *isl_ast_expr_ge(
6750 __isl_take isl_ast_expr *expr1,
6751 __isl_take isl_ast_expr *expr2);
6752 __isl_give isl_ast_expr *isl_ast_expr_gt(
6753 __isl_take isl_ast_expr *expr1,
6754 __isl_take isl_ast_expr *expr2);
6755 __isl_give isl_ast_expr *isl_ast_expr_access(
6756 __isl_take isl_ast_expr *array,
6757 __isl_take isl_ast_expr_list *indices);
6759 The function C<isl_ast_expr_address_of> can be applied to an
6760 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
6761 to represent the address of the C<isl_ast_expr_access>.
6763 #include <isl/ast_build.h>
6764 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6765 __isl_keep isl_ast_build *build,
6766 __isl_take isl_pw_aff *pa);
6767 __isl_give isl_ast_expr *
6768 isl_ast_build_access_from_pw_multi_aff(
6769 __isl_keep isl_ast_build *build,
6770 __isl_take isl_pw_multi_aff *pma);
6771 __isl_give isl_ast_expr *
6772 isl_ast_build_access_from_multi_pw_aff(
6773 __isl_keep isl_ast_build *build,
6774 __isl_take isl_multi_pw_aff *mpa);
6775 __isl_give isl_ast_expr *
6776 isl_ast_build_call_from_pw_multi_aff(
6777 __isl_keep isl_ast_build *build,
6778 __isl_take isl_pw_multi_aff *pma);
6779 __isl_give isl_ast_expr *
6780 isl_ast_build_call_from_multi_pw_aff(
6781 __isl_keep isl_ast_build *build,
6782 __isl_take isl_multi_pw_aff *mpa);
6784 The domains of C<pa>, C<mpa> and C<pma> should correspond
6785 to the schedule space of C<build>.
6786 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6787 the function being called.
6788 If the accessed space is a nested relation, then it is taken
6789 to represent an access of the member specified by the range
6790 of this nested relation of the structure specified by the domain
6791 of the nested relation.
6793 The following functions can be used to modify an C<isl_ast_expr>.
6795 #include <isl/ast.h>
6796 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6797 __isl_take isl_ast_expr *expr, int pos,
6798 __isl_take isl_ast_expr *arg);
6800 Replace the argument of C<expr> at position C<pos> by C<arg>.
6802 #include <isl/ast.h>
6803 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6804 __isl_take isl_ast_expr *expr,
6805 __isl_take isl_id_to_ast_expr *id2expr);
6807 The function C<isl_ast_expr_substitute_ids> replaces the
6808 subexpressions of C<expr> of type C<isl_ast_expr_id>
6809 by the corresponding expression in C<id2expr>, if there is any.
6812 User specified data can be attached to an C<isl_ast_node> and obtained
6813 from the same C<isl_ast_node> using the following functions.
6815 #include <isl/ast.h>
6816 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6817 __isl_take isl_ast_node *node,
6818 __isl_take isl_id *annotation);
6819 __isl_give isl_id *isl_ast_node_get_annotation(
6820 __isl_keep isl_ast_node *node);
6822 Basic printing can be performed using the following functions.
6824 #include <isl/ast.h>
6825 __isl_give isl_printer *isl_printer_print_ast_expr(
6826 __isl_take isl_printer *p,
6827 __isl_keep isl_ast_expr *expr);
6828 __isl_give isl_printer *isl_printer_print_ast_node(
6829 __isl_take isl_printer *p,
6830 __isl_keep isl_ast_node *node);
6832 More advanced printing can be performed using the following functions.
6834 #include <isl/ast.h>
6835 __isl_give isl_printer *isl_ast_op_type_print_macro(
6836 enum isl_ast_op_type type,
6837 __isl_take isl_printer *p);
6838 __isl_give isl_printer *isl_ast_node_print_macros(
6839 __isl_keep isl_ast_node *node,
6840 __isl_take isl_printer *p);
6841 __isl_give isl_printer *isl_ast_node_print(
6842 __isl_keep isl_ast_node *node,
6843 __isl_take isl_printer *p,
6844 __isl_take isl_ast_print_options *options);
6845 __isl_give isl_printer *isl_ast_node_for_print(
6846 __isl_keep isl_ast_node *node,
6847 __isl_take isl_printer *p,
6848 __isl_take isl_ast_print_options *options);
6849 __isl_give isl_printer *isl_ast_node_if_print(
6850 __isl_keep isl_ast_node *node,
6851 __isl_take isl_printer *p,
6852 __isl_take isl_ast_print_options *options);
6854 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6855 C<isl> may print out an AST that makes use of macros such
6856 as C<floord>, C<min> and C<max>.
6857 C<isl_ast_op_type_print_macro> prints out the macro
6858 corresponding to a specific C<isl_ast_op_type>.
6859 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6860 for expressions where these macros would be used and prints
6861 out the required macro definitions.
6862 Essentially, C<isl_ast_node_print_macros> calls
6863 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6864 as function argument.
6865 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6866 C<isl_ast_node_if_print> print an C<isl_ast_node>
6867 in C<ISL_FORMAT_C>, but allow for some extra control
6868 through an C<isl_ast_print_options> object.
6869 This object can be created using the following functions.
6871 #include <isl/ast.h>
6872 __isl_give isl_ast_print_options *
6873 isl_ast_print_options_alloc(isl_ctx *ctx);
6874 __isl_give isl_ast_print_options *
6875 isl_ast_print_options_copy(
6876 __isl_keep isl_ast_print_options *options);
6877 __isl_null isl_ast_print_options *
6878 isl_ast_print_options_free(
6879 __isl_take isl_ast_print_options *options);
6881 __isl_give isl_ast_print_options *
6882 isl_ast_print_options_set_print_user(
6883 __isl_take isl_ast_print_options *options,
6884 __isl_give isl_printer *(*print_user)(
6885 __isl_take isl_printer *p,
6886 __isl_take isl_ast_print_options *options,
6887 __isl_keep isl_ast_node *node, void *user),
6889 __isl_give isl_ast_print_options *
6890 isl_ast_print_options_set_print_for(
6891 __isl_take isl_ast_print_options *options,
6892 __isl_give isl_printer *(*print_for)(
6893 __isl_take isl_printer *p,
6894 __isl_take isl_ast_print_options *options,
6895 __isl_keep isl_ast_node *node, void *user),
6898 The callback set by C<isl_ast_print_options_set_print_user>
6899 is called whenever a node of type C<isl_ast_node_user> needs to
6901 The callback set by C<isl_ast_print_options_set_print_for>
6902 is called whenever a node of type C<isl_ast_node_for> needs to
6904 Note that C<isl_ast_node_for_print> will I<not> call the
6905 callback set by C<isl_ast_print_options_set_print_for> on the node
6906 on which C<isl_ast_node_for_print> is called, but only on nested
6907 nodes of type C<isl_ast_node_for>. It is therefore safe to
6908 call C<isl_ast_node_for_print> from within the callback set by
6909 C<isl_ast_print_options_set_print_for>.
6911 The following option determines the type to be used for iterators
6912 while printing the AST.
6914 int isl_options_set_ast_iterator_type(
6915 isl_ctx *ctx, const char *val);
6916 const char *isl_options_get_ast_iterator_type(
6919 The AST printer only prints body nodes as blocks if these
6920 blocks cannot be safely omitted.
6921 For example, a C<for> node with one body node will not be
6922 surrounded with braces in C<ISL_FORMAT_C>.
6923 A block will always be printed by setting the following option.
6925 int isl_options_set_ast_always_print_block(isl_ctx *ctx,
6927 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
6931 #include <isl/ast_build.h>
6932 int isl_options_set_ast_build_atomic_upper_bound(
6933 isl_ctx *ctx, int val);
6934 int isl_options_get_ast_build_atomic_upper_bound(
6936 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6938 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6939 int isl_options_set_ast_build_exploit_nested_bounds(
6940 isl_ctx *ctx, int val);
6941 int isl_options_get_ast_build_exploit_nested_bounds(
6943 int isl_options_set_ast_build_group_coscheduled(
6944 isl_ctx *ctx, int val);
6945 int isl_options_get_ast_build_group_coscheduled(
6947 int isl_options_set_ast_build_scale_strides(
6948 isl_ctx *ctx, int val);
6949 int isl_options_get_ast_build_scale_strides(
6951 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6953 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6954 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6956 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6960 =item * ast_build_atomic_upper_bound
6962 Generate loop upper bounds that consist of the current loop iterator,
6963 an operator and an expression not involving the iterator.
6964 If this option is not set, then the current loop iterator may appear
6965 several times in the upper bound.
6966 For example, when this option is turned off, AST generation
6969 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6973 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6976 When the option is turned on, the following AST is generated
6978 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6981 =item * ast_build_prefer_pdiv
6983 If this option is turned off, then the AST generation will
6984 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6985 operators, but no C<isl_ast_op_pdiv_q> or
6986 C<isl_ast_op_pdiv_r> operators.
6987 If this options is turned on, then C<isl> will try to convert
6988 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6989 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6991 =item * ast_build_exploit_nested_bounds
6993 Simplify conditions based on bounds of nested for loops.
6994 In particular, remove conditions that are implied by the fact
6995 that one or more nested loops have at least one iteration,
6996 meaning that the upper bound is at least as large as the lower bound.
6997 For example, when this option is turned off, AST generation
7000 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
7006 for (int c0 = 0; c0 <= N; c0 += 1)
7007 for (int c1 = 0; c1 <= M; c1 += 1)
7010 When the option is turned on, the following AST is generated
7012 for (int c0 = 0; c0 <= N; c0 += 1)
7013 for (int c1 = 0; c1 <= M; c1 += 1)
7016 =item * ast_build_group_coscheduled
7018 If two domain elements are assigned the same schedule point, then
7019 they may be executed in any order and they may even appear in different
7020 loops. If this options is set, then the AST generator will make
7021 sure that coscheduled domain elements do not appear in separate parts
7022 of the AST. This is useful in case of nested AST generation
7023 if the outer AST generation is given only part of a schedule
7024 and the inner AST generation should handle the domains that are
7025 coscheduled by this initial part of the schedule together.
7026 For example if an AST is generated for a schedule
7028 { A[i] -> [0]; B[i] -> [0] }
7030 then the C<isl_ast_build_set_create_leaf> callback described
7031 below may get called twice, once for each domain.
7032 Setting this option ensures that the callback is only called once
7033 on both domains together.
7035 =item * ast_build_separation_bounds
7037 This option specifies which bounds to use during separation.
7038 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
7039 then all (possibly implicit) bounds on the current dimension will
7040 be used during separation.
7041 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
7042 then only those bounds that are explicitly available will
7043 be used during separation.
7045 =item * ast_build_scale_strides
7047 This option specifies whether the AST generator is allowed
7048 to scale down iterators of strided loops.
7050 =item * ast_build_allow_else
7052 This option specifies whether the AST generator is allowed
7053 to construct if statements with else branches.
7055 =item * ast_build_allow_or
7057 This option specifies whether the AST generator is allowed
7058 to construct if conditions with disjunctions.
7062 =head3 Fine-grained Control over AST Generation
7064 Besides specifying the constraints on the parameters,
7065 an C<isl_ast_build> object can be used to control
7066 various aspects of the AST generation process.
7067 The most prominent way of control is through ``options'',
7068 which can be set using the following function.
7070 #include <isl/ast_build.h>
7071 __isl_give isl_ast_build *
7072 isl_ast_build_set_options(
7073 __isl_take isl_ast_build *control,
7074 __isl_take isl_union_map *options);
7076 The options are encoded in an C<isl_union_map>.
7077 The domain of this union relation refers to the schedule domain,
7078 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
7079 In the case of nested AST generation (see L</"Nested AST Generation">),
7080 the domain of C<options> should refer to the extra piece of the schedule.
7081 That is, it should be equal to the range of the wrapped relation in the
7082 range of the schedule.
7083 The range of the options can consist of elements in one or more spaces,
7084 the names of which determine the effect of the option.
7085 The values of the range typically also refer to the schedule dimension
7086 to which the option applies. In case of nested AST generation
7087 (see L</"Nested AST Generation">), these values refer to the position
7088 of the schedule dimension within the innermost AST generation.
7089 The constraints on the domain elements of
7090 the option should only refer to this dimension and earlier dimensions.
7091 We consider the following spaces.
7095 =item C<separation_class>
7097 This space is a wrapped relation between two one dimensional spaces.
7098 The input space represents the schedule dimension to which the option
7099 applies and the output space represents the separation class.
7100 While constructing a loop corresponding to the specified schedule
7101 dimension(s), the AST generator will try to generate separate loops
7102 for domain elements that are assigned different classes.
7103 If only some of the elements are assigned a class, then those elements
7104 that are not assigned any class will be treated as belonging to a class
7105 that is separate from the explicitly assigned classes.
7106 The typical use case for this option is to separate full tiles from
7108 The other options, described below, are applied after the separation
7111 As an example, consider the separation into full and partial tiles
7112 of a tiling of a triangular domain.
7113 Take, for example, the domain
7115 { A[i,j] : 0 <= i,j and i + j <= 100 }
7117 and a tiling into tiles of 10 by 10. The input to the AST generator
7118 is then the schedule
7120 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
7123 Without any options, the following AST is generated
7125 for (int c0 = 0; c0 <= 10; c0 += 1)
7126 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
7127 for (int c2 = 10 * c0;
7128 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7130 for (int c3 = 10 * c1;
7131 c3 <= min(10 * c1 + 9, -c2 + 100);
7135 Separation into full and partial tiles can be obtained by assigning
7136 a class, say C<0>, to the full tiles. The full tiles are represented by those
7137 values of the first and second schedule dimensions for which there are
7138 values of the third and fourth dimensions to cover an entire tile.
7139 That is, we need to specify the following option
7141 { [a,b,c,d] -> separation_class[[0]->[0]] :
7142 exists b': 0 <= 10a,10b' and
7143 10a+9+10b'+9 <= 100;
7144 [a,b,c,d] -> separation_class[[1]->[0]] :
7145 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
7149 { [a, b, c, d] -> separation_class[[1] -> [0]] :
7150 a >= 0 and b >= 0 and b <= 8 - a;
7151 [a, b, c, d] -> separation_class[[0] -> [0]] :
7154 With this option, the generated AST is as follows
7157 for (int c0 = 0; c0 <= 8; c0 += 1) {
7158 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
7159 for (int c2 = 10 * c0;
7160 c2 <= 10 * c0 + 9; c2 += 1)
7161 for (int c3 = 10 * c1;
7162 c3 <= 10 * c1 + 9; c3 += 1)
7164 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
7165 for (int c2 = 10 * c0;
7166 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7168 for (int c3 = 10 * c1;
7169 c3 <= min(-c2 + 100, 10 * c1 + 9);
7173 for (int c0 = 9; c0 <= 10; c0 += 1)
7174 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
7175 for (int c2 = 10 * c0;
7176 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7178 for (int c3 = 10 * c1;
7179 c3 <= min(10 * c1 + 9, -c2 + 100);
7186 This is a single-dimensional space representing the schedule dimension(s)
7187 to which ``separation'' should be applied. Separation tries to split
7188 a loop into several pieces if this can avoid the generation of guards
7190 See also the C<atomic> option.
7194 This is a single-dimensional space representing the schedule dimension(s)
7195 for which the domains should be considered ``atomic''. That is, the
7196 AST generator will make sure that any given domain space will only appear
7197 in a single loop at the specified level.
7199 Consider the following schedule
7201 { a[i] -> [i] : 0 <= i < 10;
7202 b[i] -> [i+1] : 0 <= i < 10 }
7204 If the following option is specified
7206 { [i] -> separate[x] }
7208 then the following AST will be generated
7212 for (int c0 = 1; c0 <= 9; c0 += 1) {
7219 If, on the other hand, the following option is specified
7221 { [i] -> atomic[x] }
7223 then the following AST will be generated
7225 for (int c0 = 0; c0 <= 10; c0 += 1) {
7232 If neither C<atomic> nor C<separate> is specified, then the AST generator
7233 may produce either of these two results or some intermediate form.
7237 This is a single-dimensional space representing the schedule dimension(s)
7238 that should be I<completely> unrolled.
7239 To obtain a partial unrolling, the user should apply an additional
7240 strip-mining to the schedule and fully unroll the inner loop.
7244 Additional control is available through the following functions.
7246 #include <isl/ast_build.h>
7247 __isl_give isl_ast_build *
7248 isl_ast_build_set_iterators(
7249 __isl_take isl_ast_build *control,
7250 __isl_take isl_id_list *iterators);
7252 The function C<isl_ast_build_set_iterators> allows the user to
7253 specify a list of iterator C<isl_id>s to be used as iterators.
7254 If the input schedule is injective, then
7255 the number of elements in this list should be as large as the dimension
7256 of the schedule space, but no direct correspondence should be assumed
7257 between dimensions and elements.
7258 If the input schedule is not injective, then an additional number
7259 of C<isl_id>s equal to the largest dimension of the input domains
7261 If the number of provided C<isl_id>s is insufficient, then additional
7262 names are automatically generated.
7264 #include <isl/ast_build.h>
7265 __isl_give isl_ast_build *
7266 isl_ast_build_set_create_leaf(
7267 __isl_take isl_ast_build *control,
7268 __isl_give isl_ast_node *(*fn)(
7269 __isl_take isl_ast_build *build,
7270 void *user), void *user);
7273 C<isl_ast_build_set_create_leaf> function allows for the
7274 specification of a callback that should be called whenever the AST
7275 generator arrives at an element of the schedule domain.
7276 The callback should return an AST node that should be inserted
7277 at the corresponding position of the AST. The default action (when
7278 the callback is not set) is to continue generating parts of the AST to scan
7279 all the domain elements associated to the schedule domain element
7280 and to insert user nodes, ``calling'' the domain element, for each of them.
7281 The C<build> argument contains the current state of the C<isl_ast_build>.
7282 To ease nested AST generation (see L</"Nested AST Generation">),
7283 all control information that is
7284 specific to the current AST generation such as the options and
7285 the callbacks has been removed from this C<isl_ast_build>.
7286 The callback would typically return the result of a nested
7288 user defined node created using the following function.
7290 #include <isl/ast.h>
7291 __isl_give isl_ast_node *isl_ast_node_alloc_user(
7292 __isl_take isl_ast_expr *expr);
7294 #include <isl/ast_build.h>
7295 __isl_give isl_ast_build *
7296 isl_ast_build_set_at_each_domain(
7297 __isl_take isl_ast_build *build,
7298 __isl_give isl_ast_node *(*fn)(
7299 __isl_take isl_ast_node *node,
7300 __isl_keep isl_ast_build *build,
7301 void *user), void *user);
7302 __isl_give isl_ast_build *
7303 isl_ast_build_set_before_each_for(
7304 __isl_take isl_ast_build *build,
7305 __isl_give isl_id *(*fn)(
7306 __isl_keep isl_ast_build *build,
7307 void *user), void *user);
7308 __isl_give isl_ast_build *
7309 isl_ast_build_set_after_each_for(
7310 __isl_take isl_ast_build *build,
7311 __isl_give isl_ast_node *(*fn)(
7312 __isl_take isl_ast_node *node,
7313 __isl_keep isl_ast_build *build,
7314 void *user), void *user);
7316 The callback set by C<isl_ast_build_set_at_each_domain> will
7317 be called for each domain AST node.
7318 The callbacks set by C<isl_ast_build_set_before_each_for>
7319 and C<isl_ast_build_set_after_each_for> will be called
7320 for each for AST node. The first will be called in depth-first
7321 pre-order, while the second will be called in depth-first post-order.
7322 Since C<isl_ast_build_set_before_each_for> is called before the for
7323 node is actually constructed, it is only passed an C<isl_ast_build>.
7324 The returned C<isl_id> will be added as an annotation (using
7325 C<isl_ast_node_set_annotation>) to the constructed for node.
7326 In particular, if the user has also specified an C<after_each_for>
7327 callback, then the annotation can be retrieved from the node passed to
7328 that callback using C<isl_ast_node_get_annotation>.
7329 All callbacks should C<NULL> on failure.
7330 The given C<isl_ast_build> can be used to create new
7331 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
7332 or C<isl_ast_build_call_from_pw_multi_aff>.
7334 =head3 Nested AST Generation
7336 C<isl> allows the user to create an AST within the context
7337 of another AST. These nested ASTs are created using the
7338 same C<isl_ast_build_ast_from_schedule> function that is used to create the
7339 outer AST. The C<build> argument should be an C<isl_ast_build>
7340 passed to a callback set by
7341 C<isl_ast_build_set_create_leaf>.
7342 The space of the range of the C<schedule> argument should refer
7343 to this build. In particular, the space should be a wrapped
7344 relation and the domain of this wrapped relation should be the
7345 same as that of the range of the schedule returned by
7346 C<isl_ast_build_get_schedule> below.
7347 In practice, the new schedule is typically
7348 created by calling C<isl_union_map_range_product> on the old schedule
7349 and some extra piece of the schedule.
7350 The space of the schedule domain is also available from
7351 the C<isl_ast_build>.
7353 #include <isl/ast_build.h>
7354 __isl_give isl_union_map *isl_ast_build_get_schedule(
7355 __isl_keep isl_ast_build *build);
7356 __isl_give isl_space *isl_ast_build_get_schedule_space(
7357 __isl_keep isl_ast_build *build);
7358 __isl_give isl_ast_build *isl_ast_build_restrict(
7359 __isl_take isl_ast_build *build,
7360 __isl_take isl_set *set);
7362 The C<isl_ast_build_get_schedule> function returns a (partial)
7363 schedule for the domains elements for which part of the AST still needs to
7364 be generated in the current build.
7365 In particular, the domain elements are mapped to those iterations of the loops
7366 enclosing the current point of the AST generation inside which
7367 the domain elements are executed.
7368 No direct correspondence between
7369 the input schedule and this schedule should be assumed.
7370 The space obtained from C<isl_ast_build_get_schedule_space> can be used
7371 to create a set for C<isl_ast_build_restrict> to intersect
7372 with the current build. In particular, the set passed to
7373 C<isl_ast_build_restrict> can have additional parameters.
7374 The ids of the set dimensions in the space returned by
7375 C<isl_ast_build_get_schedule_space> correspond to the
7376 iterators of the already generated loops.
7377 The user should not rely on the ids of the output dimensions
7378 of the relations in the union relation returned by
7379 C<isl_ast_build_get_schedule> having any particular value.
7383 Although C<isl> is mainly meant to be used as a library,
7384 it also contains some basic applications that use some
7385 of the functionality of C<isl>.
7386 The input may be specified in either the L<isl format>
7387 or the L<PolyLib format>.
7389 =head2 C<isl_polyhedron_sample>
7391 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7392 an integer element of the polyhedron, if there is any.
7393 The first column in the output is the denominator and is always
7394 equal to 1. If the polyhedron contains no integer points,
7395 then a vector of length zero is printed.
7399 C<isl_pip> takes the same input as the C<example> program
7400 from the C<piplib> distribution, i.e., a set of constraints
7401 on the parameters, a line containing only -1 and finally a set
7402 of constraints on a parametric polyhedron.
7403 The coefficients of the parameters appear in the last columns
7404 (but before the final constant column).
7405 The output is the lexicographic minimum of the parametric polyhedron.
7406 As C<isl> currently does not have its own output format, the output
7407 is just a dump of the internal state.
7409 =head2 C<isl_polyhedron_minimize>
7411 C<isl_polyhedron_minimize> computes the minimum of some linear
7412 or affine objective function over the integer points in a polyhedron.
7413 If an affine objective function
7414 is given, then the constant should appear in the last column.
7416 =head2 C<isl_polytope_scan>
7418 Given a polytope, C<isl_polytope_scan> prints
7419 all integer points in the polytope.
7421 =head2 C<isl_codegen>
7423 Given a schedule, a context set and an options relation,
7424 C<isl_codegen> prints out an AST that scans the domain elements
7425 of the schedule in the order of their image(s) taking into account
7426 the constraints in the context set.