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.
213 C<isl> is released under the MIT license.
217 Permission is hereby granted, free of charge, to any person obtaining a copy of
218 this software and associated documentation files (the "Software"), to deal in
219 the Software without restriction, including without limitation the rights to
220 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
221 of the Software, and to permit persons to whom the Software is furnished to do
222 so, subject to the following conditions:
224 The above copyright notice and this permission notice shall be included in all
225 copies or substantial portions of the Software.
227 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
228 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
229 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
230 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
231 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
232 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
237 Note that by default C<isl> requires C<GMP>, which is released
238 under the GNU Lesser General Public License (LGPL). This means
239 that code linked against C<isl> is also linked against LGPL code.
241 When configuring with C<--with-int=imath>, C<isl> will link against C<imath>, a
242 library for exact integer arithmetic released under the MIT license.
246 The source of C<isl> can be obtained either as a tarball
247 or from the git repository. Both are available from
248 L<http://freshmeat.net/projects/isl/>.
249 The installation process depends on how you obtained
252 =head2 Installation from the git repository
256 =item 1 Clone or update the repository
258 The first time the source is obtained, you need to clone
261 git clone git://repo.or.cz/isl.git
263 To obtain updates, you need to pull in the latest changes
267 =item 2 Optionally get C<imath> submodule
269 To build C<isl> with C<imath>, you need to obtain the C<imath>
270 submodule by running in the git source tree of C<isl>
275 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
277 =item 2 Generate C<configure>
283 After performing the above steps, continue
284 with the L<Common installation instructions>.
286 =head2 Common installation instructions
290 =item 1 Obtain C<GMP>
292 By default, building C<isl> requires C<GMP>, including its headers files.
293 Your distribution may not provide these header files by default
294 and you may need to install a package called C<gmp-devel> or something
295 similar. Alternatively, C<GMP> can be built from
296 source, available from L<http://gmplib.org/>.
297 C<GMP> is not needed if you build C<isl> with C<imath>.
301 C<isl> uses the standard C<autoconf> C<configure> script.
306 optionally followed by some configure options.
307 A complete list of options can be obtained by running
311 Below we discuss some of the more common options.
317 Installation prefix for C<isl>
319 =item C<--with-int=[gmp|imath]>
321 Select the integer library to be used by C<isl>, the default is C<gmp>.
322 Note that C<isl> may run significantly slower if you use C<imath>.
324 =item C<--with-gmp-prefix>
326 Installation prefix for C<GMP> (architecture-independent files).
328 =item C<--with-gmp-exec-prefix>
330 Installation prefix for C<GMP> (architecture-dependent files).
338 =item 4 Install (optional)
344 =head1 Integer Set Library
346 =head2 Initialization
348 All manipulations of integer sets and relations occur within
349 the context of an C<isl_ctx>.
350 A given C<isl_ctx> can only be used within a single thread.
351 All arguments of a function are required to have been allocated
352 within the same context.
353 There are currently no functions available for moving an object
354 from one C<isl_ctx> to another C<isl_ctx>. This means that
355 there is currently no way of safely moving an object from one
356 thread to another, unless the whole C<isl_ctx> is moved.
358 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
359 freed using C<isl_ctx_free>.
360 All objects allocated within an C<isl_ctx> should be freed
361 before the C<isl_ctx> itself is freed.
363 isl_ctx *isl_ctx_alloc();
364 void isl_ctx_free(isl_ctx *ctx);
366 The user can impose a bound on the number of low-level I<operations>
367 that can be performed by an C<isl_ctx>. This bound can be set and
368 retrieved using the following functions. A bound of zero means that
369 no bound is imposed. The number of operations performed can be
370 reset using C<isl_ctx_reset_operations>. Note that the number
371 of low-level operations needed to perform a high-level computation
372 may differ significantly across different versions
373 of C<isl>, but it should be the same across different platforms
374 for the same version of C<isl>.
376 Warning: This feature is experimental. C<isl> has good support to abort and
377 bail out during the computation, but this feature may exercise error code paths
378 that are normally not used that much. Consequently, it is not unlikely that
379 hidden bugs will be exposed.
381 void isl_ctx_set_max_operations(isl_ctx *ctx,
382 unsigned long max_operations);
383 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
384 void isl_ctx_reset_operations(isl_ctx *ctx);
386 =head2 Memory Management
388 Since a high-level operation on isl objects usually involves
389 several substeps and since the user is usually not interested in
390 the intermediate results, most functions that return a new object
391 will also release all the objects passed as arguments.
392 If the user still wants to use one or more of these arguments
393 after the function call, she should pass along a copy of the
394 object rather than the object itself.
395 The user is then responsible for making sure that the original
396 object gets used somewhere else or is explicitly freed.
398 The arguments and return values of all documented functions are
399 annotated to make clear which arguments are released and which
400 arguments are preserved. In particular, the following annotations
407 C<__isl_give> means that a new object is returned.
408 The user should make sure that the returned pointer is
409 used exactly once as a value for an C<__isl_take> argument.
410 In between, it can be used as a value for as many
411 C<__isl_keep> arguments as the user likes.
412 There is one exception, and that is the case where the
413 pointer returned is C<NULL>. Is this case, the user
414 is free to use it as an C<__isl_take> argument or not.
418 C<__isl_null> means that a C<NULL> value is returned.
422 C<__isl_take> means that the object the argument points to
423 is taken over by the function and may no longer be used
424 by the user as an argument to any other function.
425 The pointer value must be one returned by a function
426 returning an C<__isl_give> pointer.
427 If the user passes in a C<NULL> value, then this will
428 be treated as an error in the sense that the function will
429 not perform its usual operation. However, it will still
430 make sure that all the other C<__isl_take> arguments
435 C<__isl_keep> means that the function will only use the object
436 temporarily. After the function has finished, the user
437 can still use it as an argument to other functions.
438 A C<NULL> value will be treated in the same way as
439 a C<NULL> value for an C<__isl_take> argument.
445 An C<isl_val> represents an integer value, a rational value
446 or one of three special values, infinity, negative infinity and NaN.
447 Some predefined values can be created using the following functions.
450 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
451 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
452 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
453 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
454 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
455 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
457 Specific integer values can be created using the following functions.
460 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
462 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
464 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
465 size_t n, size_t size, const void *chunks);
467 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
468 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
469 The least significant digit is assumed to be stored first.
471 Value objects can be copied and freed using the following functions.
474 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
475 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
477 They can be inspected using the following functions.
480 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
481 long isl_val_get_num_si(__isl_keep isl_val *v);
482 long isl_val_get_den_si(__isl_keep isl_val *v);
483 double isl_val_get_d(__isl_keep isl_val *v);
484 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
486 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
487 size_t size, void *chunks);
489 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
490 of C<size> bytes needed to store the absolute value of the
492 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
493 which is assumed to have been preallocated by the caller.
494 The least significant digit is stored first.
495 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
496 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
497 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
499 An C<isl_val> can be modified using the following function.
502 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
505 The following unary properties are defined on C<isl_val>s.
508 int isl_val_sgn(__isl_keep isl_val *v);
509 int isl_val_is_zero(__isl_keep isl_val *v);
510 int isl_val_is_one(__isl_keep isl_val *v);
511 int isl_val_is_negone(__isl_keep isl_val *v);
512 int isl_val_is_nonneg(__isl_keep isl_val *v);
513 int isl_val_is_nonpos(__isl_keep isl_val *v);
514 int isl_val_is_pos(__isl_keep isl_val *v);
515 int isl_val_is_neg(__isl_keep isl_val *v);
516 int isl_val_is_int(__isl_keep isl_val *v);
517 int isl_val_is_rat(__isl_keep isl_val *v);
518 int isl_val_is_nan(__isl_keep isl_val *v);
519 int isl_val_is_infty(__isl_keep isl_val *v);
520 int isl_val_is_neginfty(__isl_keep isl_val *v);
522 Note that the sign of NaN is undefined.
524 The following binary properties are defined on pairs of C<isl_val>s.
527 int isl_val_lt(__isl_keep isl_val *v1,
528 __isl_keep isl_val *v2);
529 int isl_val_le(__isl_keep isl_val *v1,
530 __isl_keep isl_val *v2);
531 int isl_val_gt(__isl_keep isl_val *v1,
532 __isl_keep isl_val *v2);
533 int isl_val_ge(__isl_keep isl_val *v1,
534 __isl_keep isl_val *v2);
535 int isl_val_eq(__isl_keep isl_val *v1,
536 __isl_keep isl_val *v2);
537 int isl_val_ne(__isl_keep isl_val *v1,
538 __isl_keep isl_val *v2);
539 int isl_val_abs_eq(__isl_keep isl_val *v1,
540 __isl_keep isl_val *v2);
542 The function C<isl_val_abs_eq> checks whether its two arguments
543 are equal in absolute value.
545 For integer C<isl_val>s we additionally have the following binary property.
548 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
549 __isl_keep isl_val *v2);
551 An C<isl_val> can also be compared to an integer using the following
552 function. The result is undefined for NaN.
555 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
557 The following unary operations are available on C<isl_val>s.
560 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
561 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
562 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
563 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
564 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
565 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
567 The following binary operations are available on C<isl_val>s.
570 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
571 __isl_take isl_val *v2);
572 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
573 __isl_take isl_val *v2);
574 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
575 __isl_take isl_val *v2);
576 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
578 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
579 __isl_take isl_val *v2);
580 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
582 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
583 __isl_take isl_val *v2);
584 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
586 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
587 __isl_take isl_val *v2);
589 On integer values, we additionally have the following operations.
592 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
593 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
594 __isl_take isl_val *v2);
595 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
596 __isl_take isl_val *v2);
597 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
598 __isl_take isl_val *v2, __isl_give isl_val **x,
599 __isl_give isl_val **y);
601 The function C<isl_val_gcdext> returns the greatest common divisor g
602 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
603 that C<*x> * C<v1> + C<*y> * C<v2> = g.
605 A value can be read from input using
608 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
611 A value can be printed using
614 __isl_give isl_printer *isl_printer_print_val(
615 __isl_take isl_printer *p, __isl_keep isl_val *v);
617 =head3 GMP specific functions
619 These functions are only available if C<isl> has been compiled with C<GMP>
622 Specific integer and rational values can be created from C<GMP> values using
623 the following functions.
625 #include <isl/val_gmp.h>
626 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
628 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
629 const mpz_t n, const mpz_t d);
631 The numerator and denominator of a rational value can be extracted as
632 C<GMP> values using the following functions.
634 #include <isl/val_gmp.h>
635 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
636 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
638 =head2 Sets and Relations
640 C<isl> uses six types of objects for representing sets and relations,
641 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
642 C<isl_union_set> and C<isl_union_map>.
643 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
644 can be described as a conjunction of affine constraints, while
645 C<isl_set> and C<isl_map> represent unions of
646 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
647 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
648 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
649 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
650 where spaces are considered different if they have a different number
651 of dimensions and/or different names (see L<"Spaces">).
652 The difference between sets and relations (maps) is that sets have
653 one set of variables, while relations have two sets of variables,
654 input variables and output variables.
656 =head2 Error Handling
658 C<isl> supports different ways to react in case a runtime error is triggered.
659 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
660 with two maps that have incompatible spaces. There are three possible ways
661 to react on error: to warn, to continue or to abort.
663 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
664 the last error in the corresponding C<isl_ctx> and the function in which the
665 error was triggered returns C<NULL>. An error does not corrupt internal state,
666 such that isl can continue to be used. C<isl> also provides functions to
667 read the last error and to reset the memory that stores the last error. The
668 last error is only stored for information purposes. Its presence does not
669 change the behavior of C<isl>. Hence, resetting an error is not required to
670 continue to use isl, but only to observe new errors.
673 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
674 void isl_ctx_reset_error(isl_ctx *ctx);
676 Another option is to continue on error. This is similar to warn on error mode,
677 except that C<isl> does not print any warning. This allows a program to
678 implement its own error reporting.
680 The last option is to directly abort the execution of the program from within
681 the isl library. This makes it obviously impossible to recover from an error,
682 but it allows to directly spot the error location. By aborting on error,
683 debuggers break at the location the error occurred and can provide a stack
684 trace. Other tools that automatically provide stack traces on abort or that do
685 not want to continue execution after an error was triggered may also prefer to
688 The on error behavior of isl can be specified by calling
689 C<isl_options_set_on_error> or by setting the command line option
690 C<--isl-on-error>. Valid arguments for the function call are
691 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
692 choices for the command line option are C<warn>, C<continue> and C<abort>.
693 It is also possible to query the current error mode.
695 #include <isl/options.h>
696 int isl_options_set_on_error(isl_ctx *ctx, int val);
697 int isl_options_get_on_error(isl_ctx *ctx);
701 Identifiers are used to identify both individual dimensions
702 and tuples of dimensions. They consist of an optional name and an optional
703 user pointer. The name and the user pointer cannot both be C<NULL>, however.
704 Identifiers with the same name but different pointer values
705 are considered to be distinct.
706 Similarly, identifiers with different names but the same pointer value
707 are also considered to be distinct.
708 Equal identifiers are represented using the same object.
709 Pairs of identifiers can therefore be tested for equality using the
711 Identifiers can be constructed, copied, freed, inspected and printed
712 using the following functions.
715 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
716 __isl_keep const char *name, void *user);
717 __isl_give isl_id *isl_id_set_free_user(
718 __isl_take isl_id *id,
719 __isl_give void (*free_user)(void *user));
720 __isl_give isl_id *isl_id_copy(isl_id *id);
721 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
723 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
724 void *isl_id_get_user(__isl_keep isl_id *id);
725 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
727 __isl_give isl_printer *isl_printer_print_id(
728 __isl_take isl_printer *p, __isl_keep isl_id *id);
730 The callback set by C<isl_id_set_free_user> is called on the user
731 pointer when the last reference to the C<isl_id> is freed.
732 Note that C<isl_id_get_name> returns a pointer to some internal
733 data structure, so the result can only be used while the
734 corresponding C<isl_id> is alive.
738 Whenever a new set, relation or similar object is created from scratch,
739 the space in which it lives needs to be specified using an C<isl_space>.
740 Each space involves zero or more parameters and zero, one or two
741 tuples of set or input/output dimensions. The parameters and dimensions
742 are identified by an C<isl_dim_type> and a position.
743 The type C<isl_dim_param> refers to parameters,
744 the type C<isl_dim_set> refers to set dimensions (for spaces
745 with a single tuple of dimensions) and the types C<isl_dim_in>
746 and C<isl_dim_out> refer to input and output dimensions
747 (for spaces with two tuples of dimensions).
748 Local spaces (see L</"Local Spaces">) also contain dimensions
749 of type C<isl_dim_div>.
750 Note that parameters are only identified by their position within
751 a given object. Across different objects, parameters are (usually)
752 identified by their names or identifiers. Only unnamed parameters
753 are identified by their positions across objects. The use of unnamed
754 parameters is discouraged.
756 #include <isl/space.h>
757 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
758 unsigned nparam, unsigned n_in, unsigned n_out);
759 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
761 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
762 unsigned nparam, unsigned dim);
763 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
764 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
765 unsigned isl_space_dim(__isl_keep isl_space *space,
766 enum isl_dim_type type);
768 The space used for creating a parameter domain
769 needs to be created using C<isl_space_params_alloc>.
770 For other sets, the space
771 needs to be created using C<isl_space_set_alloc>, while
772 for a relation, the space
773 needs to be created using C<isl_space_alloc>.
774 C<isl_space_dim> can be used
775 to find out the number of dimensions of each type in
776 a space, where type may be
777 C<isl_dim_param>, C<isl_dim_in> (only for relations),
778 C<isl_dim_out> (only for relations), C<isl_dim_set>
779 (only for sets) or C<isl_dim_all>.
781 To check whether a given space is that of a set or a map
782 or whether it is a parameter space, use these functions:
784 #include <isl/space.h>
785 int isl_space_is_params(__isl_keep isl_space *space);
786 int isl_space_is_set(__isl_keep isl_space *space);
787 int isl_space_is_map(__isl_keep isl_space *space);
789 Spaces can be compared using the following functions:
791 #include <isl/space.h>
792 int isl_space_is_equal(__isl_keep isl_space *space1,
793 __isl_keep isl_space *space2);
794 int isl_space_is_domain(__isl_keep isl_space *space1,
795 __isl_keep isl_space *space2);
796 int isl_space_is_range(__isl_keep isl_space *space1,
797 __isl_keep isl_space *space2);
798 int isl_space_tuple_is_equal(
799 __isl_keep isl_space *space1,
800 enum isl_dim_type type1,
801 __isl_keep isl_space *space2,
802 enum isl_dim_type type2);
804 C<isl_space_is_domain> checks whether the first argument is equal
805 to the domain of the second argument. This requires in particular that
806 the first argument is a set space and that the second argument
807 is a map space. C<isl_space_tuple_is_equal> checks whether the given
808 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
809 spaces are the same. That is, it checks if they have the same
810 identifier (if any), the same dimension and the same internal structure
813 It is often useful to create objects that live in the
814 same space as some other object. This can be accomplished
815 by creating the new objects
816 (see L</"Creating New Sets and Relations"> or
817 L</"Creating New (Piecewise) Quasipolynomials">) based on the space
818 of the original object.
821 __isl_give isl_space *isl_basic_set_get_space(
822 __isl_keep isl_basic_set *bset);
823 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
825 #include <isl/union_set.h>
826 __isl_give isl_space *isl_union_set_get_space(
827 __isl_keep isl_union_set *uset);
830 __isl_give isl_space *isl_basic_map_get_space(
831 __isl_keep isl_basic_map *bmap);
832 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
834 #include <isl/union_map.h>
835 __isl_give isl_space *isl_union_map_get_space(
836 __isl_keep isl_union_map *umap);
838 #include <isl/constraint.h>
839 __isl_give isl_space *isl_constraint_get_space(
840 __isl_keep isl_constraint *constraint);
842 #include <isl/polynomial.h>
843 __isl_give isl_space *isl_qpolynomial_get_domain_space(
844 __isl_keep isl_qpolynomial *qp);
845 __isl_give isl_space *isl_qpolynomial_get_space(
846 __isl_keep isl_qpolynomial *qp);
847 __isl_give isl_space *isl_qpolynomial_fold_get_space(
848 __isl_keep isl_qpolynomial_fold *fold);
849 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
850 __isl_keep isl_pw_qpolynomial *pwqp);
851 __isl_give isl_space *isl_pw_qpolynomial_get_space(
852 __isl_keep isl_pw_qpolynomial *pwqp);
853 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
854 __isl_keep isl_pw_qpolynomial_fold *pwf);
855 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
856 __isl_keep isl_pw_qpolynomial_fold *pwf);
857 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
858 __isl_keep isl_union_pw_qpolynomial *upwqp);
859 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
860 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
863 __isl_give isl_space *isl_multi_val_get_space(
864 __isl_keep isl_multi_val *mv);
867 __isl_give isl_space *isl_aff_get_domain_space(
868 __isl_keep isl_aff *aff);
869 __isl_give isl_space *isl_aff_get_space(
870 __isl_keep isl_aff *aff);
871 __isl_give isl_space *isl_pw_aff_get_domain_space(
872 __isl_keep isl_pw_aff *pwaff);
873 __isl_give isl_space *isl_pw_aff_get_space(
874 __isl_keep isl_pw_aff *pwaff);
875 __isl_give isl_space *isl_multi_aff_get_domain_space(
876 __isl_keep isl_multi_aff *maff);
877 __isl_give isl_space *isl_multi_aff_get_space(
878 __isl_keep isl_multi_aff *maff);
879 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
880 __isl_keep isl_pw_multi_aff *pma);
881 __isl_give isl_space *isl_pw_multi_aff_get_space(
882 __isl_keep isl_pw_multi_aff *pma);
883 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
884 __isl_keep isl_union_pw_multi_aff *upma);
885 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
886 __isl_keep isl_multi_pw_aff *mpa);
887 __isl_give isl_space *isl_multi_pw_aff_get_space(
888 __isl_keep isl_multi_pw_aff *mpa);
890 #include <isl/point.h>
891 __isl_give isl_space *isl_point_get_space(
892 __isl_keep isl_point *pnt);
894 The identifiers or names of the individual dimensions may be set or read off
895 using the following functions.
897 #include <isl/space.h>
898 __isl_give isl_space *isl_space_set_dim_id(
899 __isl_take isl_space *space,
900 enum isl_dim_type type, unsigned pos,
901 __isl_take isl_id *id);
902 int isl_space_has_dim_id(__isl_keep isl_space *space,
903 enum isl_dim_type type, unsigned pos);
904 __isl_give isl_id *isl_space_get_dim_id(
905 __isl_keep isl_space *space,
906 enum isl_dim_type type, unsigned pos);
907 __isl_give isl_space *isl_space_set_dim_name(
908 __isl_take isl_space *space,
909 enum isl_dim_type type, unsigned pos,
910 __isl_keep const char *name);
911 int isl_space_has_dim_name(__isl_keep isl_space *space,
912 enum isl_dim_type type, unsigned pos);
913 __isl_keep const char *isl_space_get_dim_name(
914 __isl_keep isl_space *space,
915 enum isl_dim_type type, unsigned pos);
917 Note that C<isl_space_get_name> returns a pointer to some internal
918 data structure, so the result can only be used while the
919 corresponding C<isl_space> is alive.
920 Also note that every function that operates on two sets or relations
921 requires that both arguments have the same parameters. This also
922 means that if one of the arguments has named parameters, then the
923 other needs to have named parameters too and the names need to match.
924 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
925 arguments may have different parameters (as long as they are named),
926 in which case the result will have as parameters the union of the parameters of
929 Given the identifier or name of a dimension (typically a parameter),
930 its position can be obtained from the following function.
932 #include <isl/space.h>
933 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
934 enum isl_dim_type type, __isl_keep isl_id *id);
935 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
936 enum isl_dim_type type, const char *name);
938 The identifiers or names of entire spaces may be set or read off
939 using the following functions.
941 #include <isl/space.h>
942 __isl_give isl_space *isl_space_set_tuple_id(
943 __isl_take isl_space *space,
944 enum isl_dim_type type, __isl_take isl_id *id);
945 __isl_give isl_space *isl_space_reset_tuple_id(
946 __isl_take isl_space *space, enum isl_dim_type type);
947 int isl_space_has_tuple_id(__isl_keep isl_space *space,
948 enum isl_dim_type type);
949 __isl_give isl_id *isl_space_get_tuple_id(
950 __isl_keep isl_space *space, enum isl_dim_type type);
951 __isl_give isl_space *isl_space_set_tuple_name(
952 __isl_take isl_space *space,
953 enum isl_dim_type type, const char *s);
954 int isl_space_has_tuple_name(__isl_keep isl_space *space,
955 enum isl_dim_type type);
956 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
957 enum isl_dim_type type);
959 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
960 or C<isl_dim_set>. As with C<isl_space_get_name>,
961 the C<isl_space_get_tuple_name> function returns a pointer to some internal
963 Binary operations require the corresponding spaces of their arguments
964 to have the same name.
966 To keep the names of all parameters and tuples, but reset the user pointers
967 of all the corresponding identifiers, use the following function.
969 __isl_give isl_space *isl_space_reset_user(
970 __isl_take isl_space *space);
972 Spaces can be nested. In particular, the domain of a set or
973 the domain or range of a relation can be a nested relation.
974 This process is also called I<wrapping>.
975 The functions for detecting, constructing and deconstructing
976 such nested spaces can be found in the wrapping properties
977 of L</"Unary Properties">, the wrapping operations
978 of L</"Unary Operations"> and the Cartesian product operations
979 of L</"Basic Operations">.
981 Spaces can be created from other spaces
982 using the following functions.
984 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
985 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
986 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
987 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
988 __isl_give isl_space *isl_space_domain_map(
989 __isl_take isl_space *space);
990 __isl_give isl_space *isl_space_range_map(
991 __isl_take isl_space *space);
992 __isl_give isl_space *isl_space_params(
993 __isl_take isl_space *space);
994 __isl_give isl_space *isl_space_set_from_params(
995 __isl_take isl_space *space);
996 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
997 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
998 __isl_take isl_space *right);
999 __isl_give isl_space *isl_space_align_params(
1000 __isl_take isl_space *space1, __isl_take isl_space *space2)
1001 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
1002 enum isl_dim_type type, unsigned pos, unsigned n);
1003 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
1004 enum isl_dim_type type, unsigned n);
1005 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
1006 enum isl_dim_type type, unsigned first, unsigned n);
1007 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
1008 enum isl_dim_type dst_type, unsigned dst_pos,
1009 enum isl_dim_type src_type, unsigned src_pos,
1011 __isl_give isl_space *isl_space_map_from_set(
1012 __isl_take isl_space *space);
1013 __isl_give isl_space *isl_space_map_from_domain_and_range(
1014 __isl_take isl_space *domain,
1015 __isl_take isl_space *range);
1016 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
1017 __isl_give isl_space *isl_space_curry(
1018 __isl_take isl_space *space);
1019 __isl_give isl_space *isl_space_uncurry(
1020 __isl_take isl_space *space);
1022 Note that if dimensions are added or removed from a space, then
1023 the name and the internal structure are lost.
1027 A local space is essentially a space with
1028 zero or more existentially quantified variables.
1029 The local space of a (constraint of a) basic set or relation can be obtained
1030 using the following functions.
1032 #include <isl/constraint.h>
1033 __isl_give isl_local_space *isl_constraint_get_local_space(
1034 __isl_keep isl_constraint *constraint);
1036 #include <isl/set.h>
1037 __isl_give isl_local_space *isl_basic_set_get_local_space(
1038 __isl_keep isl_basic_set *bset);
1040 #include <isl/map.h>
1041 __isl_give isl_local_space *isl_basic_map_get_local_space(
1042 __isl_keep isl_basic_map *bmap);
1044 A new local space can be created from a space using
1046 #include <isl/local_space.h>
1047 __isl_give isl_local_space *isl_local_space_from_space(
1048 __isl_take isl_space *space);
1050 They can be inspected, modified, copied and freed using the following functions.
1052 #include <isl/local_space.h>
1053 isl_ctx *isl_local_space_get_ctx(
1054 __isl_keep isl_local_space *ls);
1055 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1056 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1057 enum isl_dim_type type);
1058 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1059 __isl_take isl_local_space *ls,
1060 enum isl_dim_type type, __isl_take isl_id *id);
1061 int isl_local_space_has_dim_id(
1062 __isl_keep isl_local_space *ls,
1063 enum isl_dim_type type, unsigned pos);
1064 __isl_give isl_id *isl_local_space_get_dim_id(
1065 __isl_keep isl_local_space *ls,
1066 enum isl_dim_type type, unsigned pos);
1067 int isl_local_space_has_dim_name(
1068 __isl_keep isl_local_space *ls,
1069 enum isl_dim_type type, unsigned pos)
1070 const char *isl_local_space_get_dim_name(
1071 __isl_keep isl_local_space *ls,
1072 enum isl_dim_type type, unsigned pos);
1073 __isl_give isl_local_space *isl_local_space_set_dim_name(
1074 __isl_take isl_local_space *ls,
1075 enum isl_dim_type type, unsigned pos, const char *s);
1076 __isl_give isl_local_space *isl_local_space_set_dim_id(
1077 __isl_take isl_local_space *ls,
1078 enum isl_dim_type type, unsigned pos,
1079 __isl_take isl_id *id);
1080 __isl_give isl_space *isl_local_space_get_space(
1081 __isl_keep isl_local_space *ls);
1082 __isl_give isl_aff *isl_local_space_get_div(
1083 __isl_keep isl_local_space *ls, int pos);
1084 __isl_give isl_local_space *isl_local_space_copy(
1085 __isl_keep isl_local_space *ls);
1086 __isl_null isl_local_space *isl_local_space_free(
1087 __isl_take isl_local_space *ls);
1089 Note that C<isl_local_space_get_div> can only be used on local spaces
1092 Two local spaces can be compared using
1094 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1095 __isl_keep isl_local_space *ls2);
1097 Local spaces can be created from other local spaces
1098 using the functions described in L</"Unary Operations">
1099 and L</"Binary Operations">.
1101 =head2 Input and Output
1103 C<isl> supports its own input/output format, which is similar
1104 to the C<Omega> format, but also supports the C<PolyLib> format
1107 =head3 C<isl> format
1109 The C<isl> format is similar to that of C<Omega>, but has a different
1110 syntax for describing the parameters and allows for the definition
1111 of an existentially quantified variable as the integer division
1112 of an affine expression.
1113 For example, the set of integers C<i> between C<0> and C<n>
1114 such that C<i % 10 <= 6> can be described as
1116 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1119 A set or relation can have several disjuncts, separated
1120 by the keyword C<or>. Each disjunct is either a conjunction
1121 of constraints or a projection (C<exists>) of a conjunction
1122 of constraints. The constraints are separated by the keyword
1125 =head3 C<PolyLib> format
1127 If the represented set is a union, then the first line
1128 contains a single number representing the number of disjuncts.
1129 Otherwise, a line containing the number C<1> is optional.
1131 Each disjunct is represented by a matrix of constraints.
1132 The first line contains two numbers representing
1133 the number of rows and columns,
1134 where the number of rows is equal to the number of constraints
1135 and the number of columns is equal to two plus the number of variables.
1136 The following lines contain the actual rows of the constraint matrix.
1137 In each row, the first column indicates whether the constraint
1138 is an equality (C<0>) or inequality (C<1>). The final column
1139 corresponds to the constant term.
1141 If the set is parametric, then the coefficients of the parameters
1142 appear in the last columns before the constant column.
1143 The coefficients of any existentially quantified variables appear
1144 between those of the set variables and those of the parameters.
1146 =head3 Extended C<PolyLib> format
1148 The extended C<PolyLib> format is nearly identical to the
1149 C<PolyLib> format. The only difference is that the line
1150 containing the number of rows and columns of a constraint matrix
1151 also contains four additional numbers:
1152 the number of output dimensions, the number of input dimensions,
1153 the number of local dimensions (i.e., the number of existentially
1154 quantified variables) and the number of parameters.
1155 For sets, the number of ``output'' dimensions is equal
1156 to the number of set dimensions, while the number of ``input''
1161 #include <isl/set.h>
1162 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1163 isl_ctx *ctx, FILE *input);
1164 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1165 isl_ctx *ctx, const char *str);
1166 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1168 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1171 #include <isl/map.h>
1172 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1173 isl_ctx *ctx, FILE *input);
1174 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1175 isl_ctx *ctx, const char *str);
1176 __isl_give isl_map *isl_map_read_from_file(
1177 isl_ctx *ctx, FILE *input);
1178 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1181 #include <isl/union_set.h>
1182 __isl_give isl_union_set *isl_union_set_read_from_file(
1183 isl_ctx *ctx, FILE *input);
1184 __isl_give isl_union_set *isl_union_set_read_from_str(
1185 isl_ctx *ctx, const char *str);
1187 #include <isl/union_map.h>
1188 __isl_give isl_union_map *isl_union_map_read_from_file(
1189 isl_ctx *ctx, FILE *input);
1190 __isl_give isl_union_map *isl_union_map_read_from_str(
1191 isl_ctx *ctx, const char *str);
1193 The input format is autodetected and may be either the C<PolyLib> format
1194 or the C<isl> format.
1198 Before anything can be printed, an C<isl_printer> needs to
1201 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1203 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1204 __isl_null isl_printer *isl_printer_free(
1205 __isl_take isl_printer *printer);
1206 __isl_give char *isl_printer_get_str(
1207 __isl_keep isl_printer *printer);
1209 The printer can be inspected using the following functions.
1211 FILE *isl_printer_get_file(
1212 __isl_keep isl_printer *printer);
1213 int isl_printer_get_output_format(
1214 __isl_keep isl_printer *p);
1216 The behavior of the printer can be modified in various ways
1218 __isl_give isl_printer *isl_printer_set_output_format(
1219 __isl_take isl_printer *p, int output_format);
1220 __isl_give isl_printer *isl_printer_set_indent(
1221 __isl_take isl_printer *p, int indent);
1222 __isl_give isl_printer *isl_printer_set_indent_prefix(
1223 __isl_take isl_printer *p, const char *prefix);
1224 __isl_give isl_printer *isl_printer_indent(
1225 __isl_take isl_printer *p, int indent);
1226 __isl_give isl_printer *isl_printer_set_prefix(
1227 __isl_take isl_printer *p, const char *prefix);
1228 __isl_give isl_printer *isl_printer_set_suffix(
1229 __isl_take isl_printer *p, const char *suffix);
1231 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1232 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1233 and defaults to C<ISL_FORMAT_ISL>.
1234 Each line in the output is prefixed by C<indent_prefix>,
1235 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
1236 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1237 In the C<PolyLib> format output,
1238 the coefficients of the existentially quantified variables
1239 appear between those of the set variables and those
1241 The function C<isl_printer_indent> increases the indentation
1242 by the specified amount (which may be negative).
1244 To actually print something, use
1246 #include <isl/printer.h>
1247 __isl_give isl_printer *isl_printer_print_double(
1248 __isl_take isl_printer *p, double d);
1250 #include <isl/set.h>
1251 __isl_give isl_printer *isl_printer_print_basic_set(
1252 __isl_take isl_printer *printer,
1253 __isl_keep isl_basic_set *bset);
1254 __isl_give isl_printer *isl_printer_print_set(
1255 __isl_take isl_printer *printer,
1256 __isl_keep isl_set *set);
1258 #include <isl/map.h>
1259 __isl_give isl_printer *isl_printer_print_basic_map(
1260 __isl_take isl_printer *printer,
1261 __isl_keep isl_basic_map *bmap);
1262 __isl_give isl_printer *isl_printer_print_map(
1263 __isl_take isl_printer *printer,
1264 __isl_keep isl_map *map);
1266 #include <isl/union_set.h>
1267 __isl_give isl_printer *isl_printer_print_union_set(
1268 __isl_take isl_printer *p,
1269 __isl_keep isl_union_set *uset);
1271 #include <isl/union_map.h>
1272 __isl_give isl_printer *isl_printer_print_union_map(
1273 __isl_take isl_printer *p,
1274 __isl_keep isl_union_map *umap);
1276 When called on a file printer, the following function flushes
1277 the file. When called on a string printer, the buffer is cleared.
1279 __isl_give isl_printer *isl_printer_flush(
1280 __isl_take isl_printer *p);
1282 =head2 Creating New Sets and Relations
1284 C<isl> has functions for creating some standard sets and relations.
1288 =item * Empty sets and relations
1290 __isl_give isl_basic_set *isl_basic_set_empty(
1291 __isl_take isl_space *space);
1292 __isl_give isl_basic_map *isl_basic_map_empty(
1293 __isl_take isl_space *space);
1294 __isl_give isl_set *isl_set_empty(
1295 __isl_take isl_space *space);
1296 __isl_give isl_map *isl_map_empty(
1297 __isl_take isl_space *space);
1298 __isl_give isl_union_set *isl_union_set_empty(
1299 __isl_take isl_space *space);
1300 __isl_give isl_union_map *isl_union_map_empty(
1301 __isl_take isl_space *space);
1303 For C<isl_union_set>s and C<isl_union_map>s, the space
1304 is only used to specify the parameters.
1306 =item * Universe sets and relations
1308 __isl_give isl_basic_set *isl_basic_set_universe(
1309 __isl_take isl_space *space);
1310 __isl_give isl_basic_map *isl_basic_map_universe(
1311 __isl_take isl_space *space);
1312 __isl_give isl_set *isl_set_universe(
1313 __isl_take isl_space *space);
1314 __isl_give isl_map *isl_map_universe(
1315 __isl_take isl_space *space);
1316 __isl_give isl_union_set *isl_union_set_universe(
1317 __isl_take isl_union_set *uset);
1318 __isl_give isl_union_map *isl_union_map_universe(
1319 __isl_take isl_union_map *umap);
1321 The sets and relations constructed by the functions above
1322 contain all integer values, while those constructed by the
1323 functions below only contain non-negative values.
1325 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1326 __isl_take isl_space *space);
1327 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1328 __isl_take isl_space *space);
1329 __isl_give isl_set *isl_set_nat_universe(
1330 __isl_take isl_space *space);
1331 __isl_give isl_map *isl_map_nat_universe(
1332 __isl_take isl_space *space);
1334 =item * Identity relations
1336 __isl_give isl_basic_map *isl_basic_map_identity(
1337 __isl_take isl_space *space);
1338 __isl_give isl_map *isl_map_identity(
1339 __isl_take isl_space *space);
1341 The number of input and output dimensions in C<space> needs
1344 =item * Lexicographic order
1346 __isl_give isl_map *isl_map_lex_lt(
1347 __isl_take isl_space *set_space);
1348 __isl_give isl_map *isl_map_lex_le(
1349 __isl_take isl_space *set_space);
1350 __isl_give isl_map *isl_map_lex_gt(
1351 __isl_take isl_space *set_space);
1352 __isl_give isl_map *isl_map_lex_ge(
1353 __isl_take isl_space *set_space);
1354 __isl_give isl_map *isl_map_lex_lt_first(
1355 __isl_take isl_space *space, unsigned n);
1356 __isl_give isl_map *isl_map_lex_le_first(
1357 __isl_take isl_space *space, unsigned n);
1358 __isl_give isl_map *isl_map_lex_gt_first(
1359 __isl_take isl_space *space, unsigned n);
1360 __isl_give isl_map *isl_map_lex_ge_first(
1361 __isl_take isl_space *space, unsigned n);
1363 The first four functions take a space for a B<set>
1364 and return relations that express that the elements in the domain
1365 are lexicographically less
1366 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1367 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1368 than the elements in the range.
1369 The last four functions take a space for a map
1370 and return relations that express that the first C<n> dimensions
1371 in the domain are lexicographically less
1372 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1373 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1374 than the first C<n> dimensions in the range.
1378 A basic set or relation can be converted to a set or relation
1379 using the following functions.
1381 __isl_give isl_set *isl_set_from_basic_set(
1382 __isl_take isl_basic_set *bset);
1383 __isl_give isl_map *isl_map_from_basic_map(
1384 __isl_take isl_basic_map *bmap);
1386 Sets and relations can be converted to union sets and relations
1387 using the following functions.
1389 __isl_give isl_union_set *isl_union_set_from_basic_set(
1390 __isl_take isl_basic_set *bset);
1391 __isl_give isl_union_map *isl_union_map_from_basic_map(
1392 __isl_take isl_basic_map *bmap);
1393 __isl_give isl_union_set *isl_union_set_from_set(
1394 __isl_take isl_set *set);
1395 __isl_give isl_union_map *isl_union_map_from_map(
1396 __isl_take isl_map *map);
1398 The inverse conversions below can only be used if the input
1399 union set or relation is known to contain elements in exactly one
1402 __isl_give isl_set *isl_set_from_union_set(
1403 __isl_take isl_union_set *uset);
1404 __isl_give isl_map *isl_map_from_union_map(
1405 __isl_take isl_union_map *umap);
1407 A zero-dimensional (basic) set can be constructed on a given parameter domain
1408 using the following function.
1410 __isl_give isl_basic_set *isl_basic_set_from_params(
1411 __isl_take isl_basic_set *bset);
1412 __isl_give isl_set *isl_set_from_params(
1413 __isl_take isl_set *set);
1415 Sets and relations can be copied and freed again using the following
1418 __isl_give isl_basic_set *isl_basic_set_copy(
1419 __isl_keep isl_basic_set *bset);
1420 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1421 __isl_give isl_union_set *isl_union_set_copy(
1422 __isl_keep isl_union_set *uset);
1423 __isl_give isl_basic_map *isl_basic_map_copy(
1424 __isl_keep isl_basic_map *bmap);
1425 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1426 __isl_give isl_union_map *isl_union_map_copy(
1427 __isl_keep isl_union_map *umap);
1428 __isl_null isl_basic_set *isl_basic_set_free(
1429 __isl_take isl_basic_set *bset);
1430 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1431 __isl_null isl_union_set *isl_union_set_free(
1432 __isl_take isl_union_set *uset);
1433 __isl_null isl_basic_map *isl_basic_map_free(
1434 __isl_take isl_basic_map *bmap);
1435 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1436 __isl_null isl_union_map *isl_union_map_free(
1437 __isl_take isl_union_map *umap);
1439 Other sets and relations can be constructed by starting
1440 from a universe set or relation, adding equality and/or
1441 inequality constraints and then projecting out the
1442 existentially quantified variables, if any.
1443 Constraints can be constructed, manipulated and
1444 added to (or removed from) (basic) sets and relations
1445 using the following functions.
1447 #include <isl/constraint.h>
1448 __isl_give isl_constraint *isl_equality_alloc(
1449 __isl_take isl_local_space *ls);
1450 __isl_give isl_constraint *isl_inequality_alloc(
1451 __isl_take isl_local_space *ls);
1452 __isl_give isl_constraint *isl_constraint_set_constant_si(
1453 __isl_take isl_constraint *constraint, int v);
1454 __isl_give isl_constraint *isl_constraint_set_constant_val(
1455 __isl_take isl_constraint *constraint,
1456 __isl_take isl_val *v);
1457 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1458 __isl_take isl_constraint *constraint,
1459 enum isl_dim_type type, int pos, int v);
1460 __isl_give isl_constraint *
1461 isl_constraint_set_coefficient_val(
1462 __isl_take isl_constraint *constraint,
1463 enum isl_dim_type type, int pos,
1464 __isl_take isl_val *v);
1465 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1466 __isl_take isl_basic_map *bmap,
1467 __isl_take isl_constraint *constraint);
1468 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1469 __isl_take isl_basic_set *bset,
1470 __isl_take isl_constraint *constraint);
1471 __isl_give isl_map *isl_map_add_constraint(
1472 __isl_take isl_map *map,
1473 __isl_take isl_constraint *constraint);
1474 __isl_give isl_set *isl_set_add_constraint(
1475 __isl_take isl_set *set,
1476 __isl_take isl_constraint *constraint);
1477 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1478 __isl_take isl_basic_set *bset,
1479 __isl_take isl_constraint *constraint);
1481 For example, to create a set containing the even integers
1482 between 10 and 42, you would use the following code.
1485 isl_local_space *ls;
1487 isl_basic_set *bset;
1489 space = isl_space_set_alloc(ctx, 0, 2);
1490 bset = isl_basic_set_universe(isl_space_copy(space));
1491 ls = isl_local_space_from_space(space);
1493 c = isl_equality_alloc(isl_local_space_copy(ls));
1494 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1495 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1496 bset = isl_basic_set_add_constraint(bset, c);
1498 c = isl_inequality_alloc(isl_local_space_copy(ls));
1499 c = isl_constraint_set_constant_si(c, -10);
1500 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1501 bset = isl_basic_set_add_constraint(bset, c);
1503 c = isl_inequality_alloc(ls);
1504 c = isl_constraint_set_constant_si(c, 42);
1505 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1506 bset = isl_basic_set_add_constraint(bset, c);
1508 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1512 isl_basic_set *bset;
1513 bset = isl_basic_set_read_from_str(ctx,
1514 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1516 A basic set or relation can also be constructed from two matrices
1517 describing the equalities and the inequalities.
1519 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1520 __isl_take isl_space *space,
1521 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1522 enum isl_dim_type c1,
1523 enum isl_dim_type c2, enum isl_dim_type c3,
1524 enum isl_dim_type c4);
1525 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1526 __isl_take isl_space *space,
1527 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1528 enum isl_dim_type c1,
1529 enum isl_dim_type c2, enum isl_dim_type c3,
1530 enum isl_dim_type c4, enum isl_dim_type c5);
1532 The C<isl_dim_type> arguments indicate the order in which
1533 different kinds of variables appear in the input matrices
1534 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1535 C<isl_dim_set> and C<isl_dim_div> for sets and
1536 of C<isl_dim_cst>, C<isl_dim_param>,
1537 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1539 A (basic or union) set or relation can also be constructed from a
1540 (union) (piecewise) (multiple) affine expression
1541 or a list of affine expressions
1542 (See L<"Piecewise Quasi Affine Expressions"> and
1543 L<"Piecewise Multiple Quasi Affine Expressions">).
1545 __isl_give isl_basic_map *isl_basic_map_from_aff(
1546 __isl_take isl_aff *aff);
1547 __isl_give isl_map *isl_map_from_aff(
1548 __isl_take isl_aff *aff);
1549 __isl_give isl_set *isl_set_from_pw_aff(
1550 __isl_take isl_pw_aff *pwaff);
1551 __isl_give isl_map *isl_map_from_pw_aff(
1552 __isl_take isl_pw_aff *pwaff);
1553 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1554 __isl_take isl_space *domain_space,
1555 __isl_take isl_aff_list *list);
1556 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1557 __isl_take isl_multi_aff *maff)
1558 __isl_give isl_map *isl_map_from_multi_aff(
1559 __isl_take isl_multi_aff *maff)
1560 __isl_give isl_set *isl_set_from_pw_multi_aff(
1561 __isl_take isl_pw_multi_aff *pma);
1562 __isl_give isl_map *isl_map_from_pw_multi_aff(
1563 __isl_take isl_pw_multi_aff *pma);
1564 __isl_give isl_set *isl_set_from_multi_pw_aff(
1565 __isl_take isl_multi_pw_aff *mpa);
1566 __isl_give isl_map *isl_map_from_multi_pw_aff(
1567 __isl_take isl_multi_pw_aff *mpa);
1568 __isl_give isl_union_map *
1569 isl_union_map_from_union_pw_multi_aff(
1570 __isl_take isl_union_pw_multi_aff *upma);
1572 The C<domain_space> argument describes the domain of the resulting
1573 basic relation. It is required because the C<list> may consist
1574 of zero affine expressions.
1576 =head2 Inspecting Sets and Relations
1578 Usually, the user should not have to care about the actual constraints
1579 of the sets and maps, but should instead apply the abstract operations
1580 explained in the following sections.
1581 Occasionally, however, it may be required to inspect the individual
1582 coefficients of the constraints. This section explains how to do so.
1583 In these cases, it may also be useful to have C<isl> compute
1584 an explicit representation of the existentially quantified variables.
1586 __isl_give isl_set *isl_set_compute_divs(
1587 __isl_take isl_set *set);
1588 __isl_give isl_map *isl_map_compute_divs(
1589 __isl_take isl_map *map);
1590 __isl_give isl_union_set *isl_union_set_compute_divs(
1591 __isl_take isl_union_set *uset);
1592 __isl_give isl_union_map *isl_union_map_compute_divs(
1593 __isl_take isl_union_map *umap);
1595 This explicit representation defines the existentially quantified
1596 variables as integer divisions of the other variables, possibly
1597 including earlier existentially quantified variables.
1598 An explicitly represented existentially quantified variable therefore
1599 has a unique value when the values of the other variables are known.
1600 If, furthermore, the same existentials, i.e., existentials
1601 with the same explicit representations, should appear in the
1602 same order in each of the disjuncts of a set or map, then the user should call
1603 either of the following functions.
1605 __isl_give isl_set *isl_set_align_divs(
1606 __isl_take isl_set *set);
1607 __isl_give isl_map *isl_map_align_divs(
1608 __isl_take isl_map *map);
1610 Alternatively, the existentially quantified variables can be removed
1611 using the following functions, which compute an overapproximation.
1613 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1614 __isl_take isl_basic_set *bset);
1615 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1616 __isl_take isl_basic_map *bmap);
1617 __isl_give isl_set *isl_set_remove_divs(
1618 __isl_take isl_set *set);
1619 __isl_give isl_map *isl_map_remove_divs(
1620 __isl_take isl_map *map);
1622 It is also possible to only remove those divs that are defined
1623 in terms of a given range of dimensions or only those for which
1624 no explicit representation is known.
1626 __isl_give isl_basic_set *
1627 isl_basic_set_remove_divs_involving_dims(
1628 __isl_take isl_basic_set *bset,
1629 enum isl_dim_type type,
1630 unsigned first, unsigned n);
1631 __isl_give isl_basic_map *
1632 isl_basic_map_remove_divs_involving_dims(
1633 __isl_take isl_basic_map *bmap,
1634 enum isl_dim_type type,
1635 unsigned first, unsigned n);
1636 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1637 __isl_take isl_set *set, enum isl_dim_type type,
1638 unsigned first, unsigned n);
1639 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1640 __isl_take isl_map *map, enum isl_dim_type type,
1641 unsigned first, unsigned n);
1643 __isl_give isl_basic_set *
1644 isl_basic_set_remove_unknown_divs(
1645 __isl_take isl_basic_set *bset);
1646 __isl_give isl_set *isl_set_remove_unknown_divs(
1647 __isl_take isl_set *set);
1648 __isl_give isl_map *isl_map_remove_unknown_divs(
1649 __isl_take isl_map *map);
1651 To iterate over all the sets or maps in a union set or map, use
1653 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1654 int (*fn)(__isl_take isl_set *set, void *user),
1656 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1657 int (*fn)(__isl_take isl_map *map, void *user),
1660 The number of sets or maps in a union set or map can be obtained
1663 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1664 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1666 To extract the set or map in a given space from a union, use
1668 __isl_give isl_set *isl_union_set_extract_set(
1669 __isl_keep isl_union_set *uset,
1670 __isl_take isl_space *space);
1671 __isl_give isl_map *isl_union_map_extract_map(
1672 __isl_keep isl_union_map *umap,
1673 __isl_take isl_space *space);
1675 To iterate over all the basic sets or maps in a set or map, use
1677 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1678 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1680 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1681 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1684 The callback function C<fn> should return 0 if successful and
1685 -1 if an error occurs. In the latter case, or if any other error
1686 occurs, the above functions will return -1.
1688 It should be noted that C<isl> does not guarantee that
1689 the basic sets or maps passed to C<fn> are disjoint.
1690 If this is required, then the user should call one of
1691 the following functions first.
1693 __isl_give isl_set *isl_set_make_disjoint(
1694 __isl_take isl_set *set);
1695 __isl_give isl_map *isl_map_make_disjoint(
1696 __isl_take isl_map *map);
1698 The number of basic sets in a set can be obtained
1699 or the number of basic maps in a map can be obtained
1702 #include <isl/set.h>
1703 int isl_set_n_basic_set(__isl_keep isl_set *set);
1705 #include <isl/map.h>
1706 int isl_map_n_basic_map(__isl_keep isl_map *map);
1708 To iterate over the constraints of a basic set or map, use
1710 #include <isl/constraint.h>
1712 int isl_basic_set_n_constraint(
1713 __isl_keep isl_basic_set *bset);
1714 int isl_basic_set_foreach_constraint(
1715 __isl_keep isl_basic_set *bset,
1716 int (*fn)(__isl_take isl_constraint *c, void *user),
1718 int isl_basic_map_n_constraint(
1719 __isl_keep isl_basic_map *bmap);
1720 int isl_basic_map_foreach_constraint(
1721 __isl_keep isl_basic_map *bmap,
1722 int (*fn)(__isl_take isl_constraint *c, void *user),
1724 __isl_null isl_constraint *isl_constraint_free(
1725 __isl_take isl_constraint *c);
1727 Again, the callback function C<fn> should return 0 if successful and
1728 -1 if an error occurs. In the latter case, or if any other error
1729 occurs, the above functions will return -1.
1730 The constraint C<c> represents either an equality or an inequality.
1731 Use the following function to find out whether a constraint
1732 represents an equality. If not, it represents an inequality.
1734 int isl_constraint_is_equality(
1735 __isl_keep isl_constraint *constraint);
1737 It is also possible to obtain a list of constraints from a basic
1740 #include <isl/constraint.h>
1741 __isl_give isl_constraint_list *
1742 isl_basic_map_get_constraint_list(
1743 __isl_keep isl_basic_map *bmap);
1744 __isl_give isl_constraint_list *
1745 isl_basic_set_get_constraint_list(
1746 __isl_keep isl_basic_set *bset);
1748 These functions require that all existentially quantified variables
1749 have an explicit representation.
1750 The returned list can be manipulated using the functions in L<"Lists">.
1752 The coefficients of the constraints can be inspected using
1753 the following functions.
1755 int isl_constraint_is_lower_bound(
1756 __isl_keep isl_constraint *constraint,
1757 enum isl_dim_type type, unsigned pos);
1758 int isl_constraint_is_upper_bound(
1759 __isl_keep isl_constraint *constraint,
1760 enum isl_dim_type type, unsigned pos);
1761 __isl_give isl_val *isl_constraint_get_constant_val(
1762 __isl_keep isl_constraint *constraint);
1763 __isl_give isl_val *isl_constraint_get_coefficient_val(
1764 __isl_keep isl_constraint *constraint,
1765 enum isl_dim_type type, int pos);
1766 int isl_constraint_involves_dims(
1767 __isl_keep isl_constraint *constraint,
1768 enum isl_dim_type type, unsigned first, unsigned n);
1770 The explicit representations of the existentially quantified
1771 variables can be inspected using the following function.
1772 Note that the user is only allowed to use this function
1773 if the inspected set or map is the result of a call
1774 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1775 The existentially quantified variable is equal to the floor
1776 of the returned affine expression. The affine expression
1777 itself can be inspected using the functions in
1778 L<"Piecewise Quasi Affine Expressions">.
1780 __isl_give isl_aff *isl_constraint_get_div(
1781 __isl_keep isl_constraint *constraint, int pos);
1783 To obtain the constraints of a basic set or map in matrix
1784 form, use the following functions.
1786 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1787 __isl_keep isl_basic_set *bset,
1788 enum isl_dim_type c1, enum isl_dim_type c2,
1789 enum isl_dim_type c3, enum isl_dim_type c4);
1790 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1791 __isl_keep isl_basic_set *bset,
1792 enum isl_dim_type c1, enum isl_dim_type c2,
1793 enum isl_dim_type c3, enum isl_dim_type c4);
1794 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1795 __isl_keep isl_basic_map *bmap,
1796 enum isl_dim_type c1,
1797 enum isl_dim_type c2, enum isl_dim_type c3,
1798 enum isl_dim_type c4, enum isl_dim_type c5);
1799 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1800 __isl_keep isl_basic_map *bmap,
1801 enum isl_dim_type c1,
1802 enum isl_dim_type c2, enum isl_dim_type c3,
1803 enum isl_dim_type c4, enum isl_dim_type c5);
1805 The C<isl_dim_type> arguments dictate the order in which
1806 different kinds of variables appear in the resulting matrix.
1807 For set inputs, they should be a permutation of
1808 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
1809 For map inputs, they should be a permutation of
1810 C<isl_dim_cst>, C<isl_dim_param>,
1811 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1813 The number of parameters, input, output or set dimensions can
1814 be obtained using the following functions.
1816 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1817 enum isl_dim_type type);
1818 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1819 enum isl_dim_type type);
1820 unsigned isl_set_dim(__isl_keep isl_set *set,
1821 enum isl_dim_type type);
1822 unsigned isl_map_dim(__isl_keep isl_map *map,
1823 enum isl_dim_type type);
1824 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1825 enum isl_dim_type type);
1827 Note that a C<isl_union_map> only has parameters.
1829 To check whether the description of a set or relation depends
1830 on one or more given dimensions, it is not necessary to iterate over all
1831 constraints. Instead the following functions can be used.
1833 int isl_basic_set_involves_dims(
1834 __isl_keep isl_basic_set *bset,
1835 enum isl_dim_type type, unsigned first, unsigned n);
1836 int isl_set_involves_dims(__isl_keep isl_set *set,
1837 enum isl_dim_type type, unsigned first, unsigned n);
1838 int isl_basic_map_involves_dims(
1839 __isl_keep isl_basic_map *bmap,
1840 enum isl_dim_type type, unsigned first, unsigned n);
1841 int isl_map_involves_dims(__isl_keep isl_map *map,
1842 enum isl_dim_type type, unsigned first, unsigned n);
1844 Similarly, the following functions can be used to check whether
1845 a given dimension is involved in any lower or upper bound.
1847 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1848 enum isl_dim_type type, unsigned pos);
1849 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1850 enum isl_dim_type type, unsigned pos);
1852 Note that these functions return true even if there is a bound on
1853 the dimension on only some of the basic sets of C<set>.
1854 To check if they have a bound for all of the basic sets in C<set>,
1855 use the following functions instead.
1857 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1858 enum isl_dim_type type, unsigned pos);
1859 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1860 enum isl_dim_type type, unsigned pos);
1862 The identifiers or names of the domain and range spaces of a set
1863 or relation can be read off or set using the following functions.
1865 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1866 __isl_take isl_basic_set *bset,
1867 __isl_take isl_id *id);
1868 __isl_give isl_set *isl_set_set_tuple_id(
1869 __isl_take isl_set *set, __isl_take isl_id *id);
1870 __isl_give isl_set *isl_set_reset_tuple_id(
1871 __isl_take isl_set *set);
1872 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1873 __isl_give isl_id *isl_set_get_tuple_id(
1874 __isl_keep isl_set *set);
1875 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1876 __isl_take isl_basic_map *bmap,
1877 enum isl_dim_type type, __isl_take isl_id *id);
1878 __isl_give isl_map *isl_map_set_tuple_id(
1879 __isl_take isl_map *map, enum isl_dim_type type,
1880 __isl_take isl_id *id);
1881 __isl_give isl_map *isl_map_reset_tuple_id(
1882 __isl_take isl_map *map, enum isl_dim_type type);
1883 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1884 enum isl_dim_type type);
1885 __isl_give isl_id *isl_map_get_tuple_id(
1886 __isl_keep isl_map *map, enum isl_dim_type type);
1888 const char *isl_basic_set_get_tuple_name(
1889 __isl_keep isl_basic_set *bset);
1890 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1891 __isl_take isl_basic_set *set, const char *s);
1892 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1893 const char *isl_set_get_tuple_name(
1894 __isl_keep isl_set *set);
1895 __isl_give isl_set *isl_set_set_tuple_name(
1896 __isl_take isl_set *set, const char *s);
1897 const char *isl_basic_map_get_tuple_name(
1898 __isl_keep isl_basic_map *bmap,
1899 enum isl_dim_type type);
1900 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1901 __isl_take isl_basic_map *bmap,
1902 enum isl_dim_type type, const char *s);
1903 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1904 enum isl_dim_type type);
1905 const char *isl_map_get_tuple_name(
1906 __isl_keep isl_map *map,
1907 enum isl_dim_type type);
1908 __isl_give isl_map *isl_map_set_tuple_name(
1909 __isl_take isl_map *map,
1910 enum isl_dim_type type, const char *s);
1912 As with C<isl_space_get_tuple_name>, the value returned points to
1913 an internal data structure.
1914 The identifiers, positions or names of individual dimensions can be
1915 read off using the following functions.
1917 __isl_give isl_id *isl_basic_set_get_dim_id(
1918 __isl_keep isl_basic_set *bset,
1919 enum isl_dim_type type, unsigned pos);
1920 __isl_give isl_set *isl_set_set_dim_id(
1921 __isl_take isl_set *set, enum isl_dim_type type,
1922 unsigned pos, __isl_take isl_id *id);
1923 int isl_set_has_dim_id(__isl_keep isl_set *set,
1924 enum isl_dim_type type, unsigned pos);
1925 __isl_give isl_id *isl_set_get_dim_id(
1926 __isl_keep isl_set *set, enum isl_dim_type type,
1928 int isl_basic_map_has_dim_id(
1929 __isl_keep isl_basic_map *bmap,
1930 enum isl_dim_type type, unsigned pos);
1931 __isl_give isl_map *isl_map_set_dim_id(
1932 __isl_take isl_map *map, enum isl_dim_type type,
1933 unsigned pos, __isl_take isl_id *id);
1934 int isl_map_has_dim_id(__isl_keep isl_map *map,
1935 enum isl_dim_type type, unsigned pos);
1936 __isl_give isl_id *isl_map_get_dim_id(
1937 __isl_keep isl_map *map, enum isl_dim_type type,
1939 __isl_give isl_id *isl_union_map_get_dim_id(
1940 __isl_keep isl_union_map *umap,
1941 enum isl_dim_type type, unsigned pos);
1943 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1944 enum isl_dim_type type, __isl_keep isl_id *id);
1945 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1946 enum isl_dim_type type, __isl_keep isl_id *id);
1947 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1948 enum isl_dim_type type, const char *name);
1949 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1950 enum isl_dim_type type, const char *name);
1952 const char *isl_constraint_get_dim_name(
1953 __isl_keep isl_constraint *constraint,
1954 enum isl_dim_type type, unsigned pos);
1955 const char *isl_basic_set_get_dim_name(
1956 __isl_keep isl_basic_set *bset,
1957 enum isl_dim_type type, unsigned pos);
1958 int isl_set_has_dim_name(__isl_keep isl_set *set,
1959 enum isl_dim_type type, unsigned pos);
1960 const char *isl_set_get_dim_name(
1961 __isl_keep isl_set *set,
1962 enum isl_dim_type type, unsigned pos);
1963 const char *isl_basic_map_get_dim_name(
1964 __isl_keep isl_basic_map *bmap,
1965 enum isl_dim_type type, unsigned pos);
1966 int isl_map_has_dim_name(__isl_keep isl_map *map,
1967 enum isl_dim_type type, unsigned pos);
1968 const char *isl_map_get_dim_name(
1969 __isl_keep isl_map *map,
1970 enum isl_dim_type type, unsigned pos);
1972 These functions are mostly useful to obtain the identifiers, positions
1973 or names of the parameters. Identifiers of individual dimensions are
1974 essentially only useful for printing. They are ignored by all other
1975 operations and may not be preserved across those operations.
1977 The user pointers on all parameters and tuples can be reset
1978 using the following functions.
1980 #include <isl/set.h>
1981 __isl_give isl_set *isl_set_reset_user(
1982 __isl_take isl_set *set);
1983 #include <isl/map.h>
1984 __isl_give isl_map *isl_map_reset_user(
1985 __isl_take isl_map *map);
1986 #include <isl/union_set.h>
1987 __isl_give isl_union_set *isl_union_set_reset_user(
1988 __isl_take isl_union_set *uset);
1989 #include <isl/union_map.h>
1990 __isl_give isl_union_map *isl_union_map_reset_user(
1991 __isl_take isl_union_map *umap);
1995 =head3 Unary Properties
2001 The following functions test whether the given set or relation
2002 contains any integer points. The ``plain'' variants do not perform
2003 any computations, but simply check if the given set or relation
2004 is already known to be empty.
2006 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
2007 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
2008 int isl_set_plain_is_empty(__isl_keep isl_set *set);
2009 int isl_set_is_empty(__isl_keep isl_set *set);
2010 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
2011 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
2012 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
2013 int isl_map_plain_is_empty(__isl_keep isl_map *map);
2014 int isl_map_is_empty(__isl_keep isl_map *map);
2015 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
2017 =item * Universality
2019 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
2020 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
2021 int isl_set_plain_is_universe(__isl_keep isl_set *set);
2023 =item * Single-valuedness
2025 #include <isl/set.h>
2026 int isl_set_is_singleton(__isl_keep isl_set *set);
2028 #include <isl/map.h>
2029 int isl_basic_map_is_single_valued(
2030 __isl_keep isl_basic_map *bmap);
2031 int isl_map_plain_is_single_valued(
2032 __isl_keep isl_map *map);
2033 int isl_map_is_single_valued(__isl_keep isl_map *map);
2035 #include <isl/union_map.h>
2036 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
2040 int isl_map_plain_is_injective(__isl_keep isl_map *map);
2041 int isl_map_is_injective(__isl_keep isl_map *map);
2042 int isl_union_map_plain_is_injective(
2043 __isl_keep isl_union_map *umap);
2044 int isl_union_map_is_injective(
2045 __isl_keep isl_union_map *umap);
2049 int isl_map_is_bijective(__isl_keep isl_map *map);
2050 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
2054 __isl_give isl_val *
2055 isl_basic_map_plain_get_val_if_fixed(
2056 __isl_keep isl_basic_map *bmap,
2057 enum isl_dim_type type, unsigned pos);
2058 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
2059 __isl_keep isl_set *set,
2060 enum isl_dim_type type, unsigned pos);
2061 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
2062 __isl_keep isl_map *map,
2063 enum isl_dim_type type, unsigned pos);
2065 If the set or relation obviously lies on a hyperplane where the given dimension
2066 has a fixed value, then return that value.
2067 Otherwise return NaN.
2071 int isl_set_dim_residue_class_val(
2072 __isl_keep isl_set *set,
2073 int pos, __isl_give isl_val **modulo,
2074 __isl_give isl_val **residue);
2076 Check if the values of the given set dimension are equal to a fixed
2077 value modulo some integer value. If so, assign the modulo to C<*modulo>
2078 and the fixed value to C<*residue>. If the given dimension attains only
2079 a single value, then assign C<0> to C<*modulo> and the fixed value to
2081 If the dimension does not attain only a single value and if no modulo
2082 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
2086 To check whether a set is a parameter domain, use this function:
2088 int isl_set_is_params(__isl_keep isl_set *set);
2089 int isl_union_set_is_params(
2090 __isl_keep isl_union_set *uset);
2094 The following functions check whether the space of the given
2095 (basic) set or relation range is a wrapped relation.
2097 #include <isl/space.h>
2098 int isl_space_is_wrapping(
2099 __isl_keep isl_space *space);
2100 int isl_space_domain_is_wrapping(
2101 __isl_keep isl_space *space);
2102 int isl_space_range_is_wrapping(
2103 __isl_keep isl_space *space);
2105 #include <isl/set.h>
2106 int isl_basic_set_is_wrapping(
2107 __isl_keep isl_basic_set *bset);
2108 int isl_set_is_wrapping(__isl_keep isl_set *set);
2110 #include <isl/map.h>
2111 int isl_map_domain_is_wrapping(
2112 __isl_keep isl_map *map);
2113 int isl_map_range_is_wrapping(
2114 __isl_keep isl_map *map);
2116 The input to C<isl_space_is_wrapping> should
2117 be the space of a set, while that of
2118 C<isl_space_domain_is_wrapping> and
2119 C<isl_space_range_is_wrapping> should be the space of a relation.
2121 =item * Internal Product
2123 int isl_basic_map_can_zip(
2124 __isl_keep isl_basic_map *bmap);
2125 int isl_map_can_zip(__isl_keep isl_map *map);
2127 Check whether the product of domain and range of the given relation
2129 i.e., whether both domain and range are nested relations.
2133 int isl_basic_map_can_curry(
2134 __isl_keep isl_basic_map *bmap);
2135 int isl_map_can_curry(__isl_keep isl_map *map);
2137 Check whether the domain of the (basic) relation is a wrapped relation.
2139 int isl_basic_map_can_uncurry(
2140 __isl_keep isl_basic_map *bmap);
2141 int isl_map_can_uncurry(__isl_keep isl_map *map);
2143 Check whether the range of the (basic) relation is a wrapped relation.
2147 =head3 Binary Properties
2153 int isl_basic_set_plain_is_equal(
2154 __isl_keep isl_basic_set *bset1,
2155 __isl_keep isl_basic_set *bset2);
2156 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2157 __isl_keep isl_set *set2);
2158 int isl_set_is_equal(__isl_keep isl_set *set1,
2159 __isl_keep isl_set *set2);
2160 int isl_union_set_is_equal(
2161 __isl_keep isl_union_set *uset1,
2162 __isl_keep isl_union_set *uset2);
2163 int isl_basic_map_is_equal(
2164 __isl_keep isl_basic_map *bmap1,
2165 __isl_keep isl_basic_map *bmap2);
2166 int isl_map_is_equal(__isl_keep isl_map *map1,
2167 __isl_keep isl_map *map2);
2168 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2169 __isl_keep isl_map *map2);
2170 int isl_union_map_is_equal(
2171 __isl_keep isl_union_map *umap1,
2172 __isl_keep isl_union_map *umap2);
2174 =item * Disjointness
2176 int isl_basic_set_is_disjoint(
2177 __isl_keep isl_basic_set *bset1,
2178 __isl_keep isl_basic_set *bset2);
2179 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2180 __isl_keep isl_set *set2);
2181 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2182 __isl_keep isl_set *set2);
2183 int isl_basic_map_is_disjoint(
2184 __isl_keep isl_basic_map *bmap1,
2185 __isl_keep isl_basic_map *bmap2);
2186 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2187 __isl_keep isl_map *map2);
2191 int isl_basic_set_is_subset(
2192 __isl_keep isl_basic_set *bset1,
2193 __isl_keep isl_basic_set *bset2);
2194 int isl_set_is_subset(__isl_keep isl_set *set1,
2195 __isl_keep isl_set *set2);
2196 int isl_set_is_strict_subset(
2197 __isl_keep isl_set *set1,
2198 __isl_keep isl_set *set2);
2199 int isl_union_set_is_subset(
2200 __isl_keep isl_union_set *uset1,
2201 __isl_keep isl_union_set *uset2);
2202 int isl_union_set_is_strict_subset(
2203 __isl_keep isl_union_set *uset1,
2204 __isl_keep isl_union_set *uset2);
2205 int isl_basic_map_is_subset(
2206 __isl_keep isl_basic_map *bmap1,
2207 __isl_keep isl_basic_map *bmap2);
2208 int isl_basic_map_is_strict_subset(
2209 __isl_keep isl_basic_map *bmap1,
2210 __isl_keep isl_basic_map *bmap2);
2211 int isl_map_is_subset(
2212 __isl_keep isl_map *map1,
2213 __isl_keep isl_map *map2);
2214 int isl_map_is_strict_subset(
2215 __isl_keep isl_map *map1,
2216 __isl_keep isl_map *map2);
2217 int isl_union_map_is_subset(
2218 __isl_keep isl_union_map *umap1,
2219 __isl_keep isl_union_map *umap2);
2220 int isl_union_map_is_strict_subset(
2221 __isl_keep isl_union_map *umap1,
2222 __isl_keep isl_union_map *umap2);
2224 Check whether the first argument is a (strict) subset of the
2229 Every comparison function returns a negative value if the first
2230 argument is considered smaller than the second, a positive value
2231 if the first argument is considered greater and zero if the two
2232 constraints are considered the same by the comparison criterion.
2234 #include <isl/constraint.h>
2235 int isl_constraint_plain_cmp(
2236 __isl_keep isl_constraint *c1,
2237 __isl_keep isl_constraint *c2);
2239 This function is useful for sorting C<isl_constraint>s.
2240 The order depends on the internal representation of the inputs.
2241 The order is fixed over different calls to the function (assuming
2242 the internal representation of the inputs has not changed), but may
2243 change over different versions of C<isl>.
2245 #include <isl/constraint.h>
2246 int isl_constraint_cmp_last_non_zero(
2247 __isl_keep isl_constraint *c1,
2248 __isl_keep isl_constraint *c2);
2250 This function can be used to sort constraints that live in the same
2251 local space. Constraints that involve ``earlier'' dimensions or
2252 that have a smaller coefficient for the shared latest dimension
2253 are considered smaller than other constraints.
2254 This function only defines a B<partial> order.
2256 #include <isl/set.h>
2257 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2258 __isl_keep isl_set *set2);
2260 This function is useful for sorting C<isl_set>s.
2261 The order depends on the internal representation of the inputs.
2262 The order is fixed over different calls to the function (assuming
2263 the internal representation of the inputs has not changed), but may
2264 change over different versions of C<isl>.
2268 =head2 Unary Operations
2274 __isl_give isl_set *isl_set_complement(
2275 __isl_take isl_set *set);
2276 __isl_give isl_map *isl_map_complement(
2277 __isl_take isl_map *map);
2281 __isl_give isl_basic_map *isl_basic_map_reverse(
2282 __isl_take isl_basic_map *bmap);
2283 __isl_give isl_map *isl_map_reverse(
2284 __isl_take isl_map *map);
2285 __isl_give isl_union_map *isl_union_map_reverse(
2286 __isl_take isl_union_map *umap);
2290 #include <isl/local_space.h>
2291 __isl_give isl_local_space *isl_local_space_domain(
2292 __isl_take isl_local_space *ls);
2293 __isl_give isl_local_space *isl_local_space_range(
2294 __isl_take isl_local_space *ls);
2296 #include <isl/set.h>
2297 __isl_give isl_basic_set *isl_basic_set_project_out(
2298 __isl_take isl_basic_set *bset,
2299 enum isl_dim_type type, unsigned first, unsigned n);
2300 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2301 enum isl_dim_type type, unsigned first, unsigned n);
2302 __isl_give isl_basic_set *isl_basic_set_params(
2303 __isl_take isl_basic_set *bset);
2304 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2306 #include <isl/map.h>
2307 __isl_give isl_basic_map *isl_basic_map_project_out(
2308 __isl_take isl_basic_map *bmap,
2309 enum isl_dim_type type, unsigned first, unsigned n);
2310 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2311 enum isl_dim_type type, unsigned first, unsigned n);
2312 __isl_give isl_basic_set *isl_basic_map_domain(
2313 __isl_take isl_basic_map *bmap);
2314 __isl_give isl_basic_set *isl_basic_map_range(
2315 __isl_take isl_basic_map *bmap);
2316 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2317 __isl_give isl_set *isl_map_domain(
2318 __isl_take isl_map *bmap);
2319 __isl_give isl_set *isl_map_range(
2320 __isl_take isl_map *map);
2322 #include <isl/union_set.h>
2323 __isl_give isl_set *isl_union_set_params(
2324 __isl_take isl_union_set *uset);
2326 #include <isl/union_map.h>
2327 __isl_give isl_union_map *isl_union_map_project_out(
2328 __isl_take isl_union_map *umap,
2329 enum isl_dim_type type, unsigned first, unsigned n);
2330 __isl_give isl_set *isl_union_map_params(
2331 __isl_take isl_union_map *umap);
2332 __isl_give isl_union_set *isl_union_map_domain(
2333 __isl_take isl_union_map *umap);
2334 __isl_give isl_union_set *isl_union_map_range(
2335 __isl_take isl_union_map *umap);
2337 The function C<isl_union_map_project_out> can only project out
2340 #include <isl/map.h>
2341 __isl_give isl_basic_map *isl_basic_map_domain_map(
2342 __isl_take isl_basic_map *bmap);
2343 __isl_give isl_basic_map *isl_basic_map_range_map(
2344 __isl_take isl_basic_map *bmap);
2345 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2346 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2348 #include <isl/union_map.h>
2349 __isl_give isl_union_map *isl_union_map_domain_map(
2350 __isl_take isl_union_map *umap);
2351 __isl_give isl_union_map *isl_union_map_range_map(
2352 __isl_take isl_union_map *umap);
2354 The functions above construct a (basic, regular or union) relation
2355 that maps (a wrapped version of) the input relation to its domain or range.
2359 __isl_give isl_basic_set *isl_basic_set_eliminate(
2360 __isl_take isl_basic_set *bset,
2361 enum isl_dim_type type,
2362 unsigned first, unsigned n);
2363 __isl_give isl_set *isl_set_eliminate(
2364 __isl_take isl_set *set, enum isl_dim_type type,
2365 unsigned first, unsigned n);
2366 __isl_give isl_basic_map *isl_basic_map_eliminate(
2367 __isl_take isl_basic_map *bmap,
2368 enum isl_dim_type type,
2369 unsigned first, unsigned n);
2370 __isl_give isl_map *isl_map_eliminate(
2371 __isl_take isl_map *map, enum isl_dim_type type,
2372 unsigned first, unsigned n);
2374 Eliminate the coefficients for the given dimensions from the constraints,
2375 without removing the dimensions.
2377 =item * Constructing a relation from a set
2379 #include <isl/local_space.h>
2380 __isl_give isl_local_space *isl_local_space_from_domain(
2381 __isl_take isl_local_space *ls);
2383 #include <isl/map.h>
2384 __isl_give isl_map *isl_map_from_domain(
2385 __isl_take isl_set *set);
2386 __isl_give isl_map *isl_map_from_range(
2387 __isl_take isl_set *set);
2389 Create a relation with the given set as domain or range.
2390 The range or domain of the created relation is a zero-dimensional
2391 flat anonymous space.
2395 __isl_give isl_basic_set *isl_basic_set_fix_si(
2396 __isl_take isl_basic_set *bset,
2397 enum isl_dim_type type, unsigned pos, int value);
2398 __isl_give isl_basic_set *isl_basic_set_fix_val(
2399 __isl_take isl_basic_set *bset,
2400 enum isl_dim_type type, unsigned pos,
2401 __isl_take isl_val *v);
2402 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2403 enum isl_dim_type type, unsigned pos, int value);
2404 __isl_give isl_set *isl_set_fix_val(
2405 __isl_take isl_set *set,
2406 enum isl_dim_type type, unsigned pos,
2407 __isl_take isl_val *v);
2408 __isl_give isl_basic_map *isl_basic_map_fix_si(
2409 __isl_take isl_basic_map *bmap,
2410 enum isl_dim_type type, unsigned pos, int value);
2411 __isl_give isl_basic_map *isl_basic_map_fix_val(
2412 __isl_take isl_basic_map *bmap,
2413 enum isl_dim_type type, unsigned pos,
2414 __isl_take isl_val *v);
2415 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2416 enum isl_dim_type type, unsigned pos, int value);
2417 __isl_give isl_map *isl_map_fix_val(
2418 __isl_take isl_map *map,
2419 enum isl_dim_type type, unsigned pos,
2420 __isl_take isl_val *v);
2422 Intersect the set or relation with the hyperplane where the given
2423 dimension has the fixed given value.
2425 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2426 __isl_take isl_basic_map *bmap,
2427 enum isl_dim_type type, unsigned pos, int value);
2428 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2429 __isl_take isl_basic_map *bmap,
2430 enum isl_dim_type type, unsigned pos, int value);
2431 __isl_give isl_set *isl_set_lower_bound_si(
2432 __isl_take isl_set *set,
2433 enum isl_dim_type type, unsigned pos, int value);
2434 __isl_give isl_set *isl_set_lower_bound_val(
2435 __isl_take isl_set *set,
2436 enum isl_dim_type type, unsigned pos,
2437 __isl_take isl_val *value);
2438 __isl_give isl_map *isl_map_lower_bound_si(
2439 __isl_take isl_map *map,
2440 enum isl_dim_type type, unsigned pos, int value);
2441 __isl_give isl_set *isl_set_upper_bound_si(
2442 __isl_take isl_set *set,
2443 enum isl_dim_type type, unsigned pos, int value);
2444 __isl_give isl_set *isl_set_upper_bound_val(
2445 __isl_take isl_set *set,
2446 enum isl_dim_type type, unsigned pos,
2447 __isl_take isl_val *value);
2448 __isl_give isl_map *isl_map_upper_bound_si(
2449 __isl_take isl_map *map,
2450 enum isl_dim_type type, unsigned pos, int value);
2452 Intersect the set or relation with the half-space where the given
2453 dimension has a value bounded by the fixed given integer value.
2455 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2456 enum isl_dim_type type1, int pos1,
2457 enum isl_dim_type type2, int pos2);
2458 __isl_give isl_basic_map *isl_basic_map_equate(
2459 __isl_take isl_basic_map *bmap,
2460 enum isl_dim_type type1, int pos1,
2461 enum isl_dim_type type2, int pos2);
2462 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2463 enum isl_dim_type type1, int pos1,
2464 enum isl_dim_type type2, int pos2);
2466 Intersect the set or relation with the hyperplane where the given
2467 dimensions are equal to each other.
2469 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2470 enum isl_dim_type type1, int pos1,
2471 enum isl_dim_type type2, int pos2);
2473 Intersect the relation with the hyperplane where the given
2474 dimensions have opposite values.
2476 __isl_give isl_map *isl_map_order_le(
2477 __isl_take isl_map *map,
2478 enum isl_dim_type type1, int pos1,
2479 enum isl_dim_type type2, int pos2);
2480 __isl_give isl_basic_map *isl_basic_map_order_ge(
2481 __isl_take isl_basic_map *bmap,
2482 enum isl_dim_type type1, int pos1,
2483 enum isl_dim_type type2, int pos2);
2484 __isl_give isl_map *isl_map_order_ge(
2485 __isl_take isl_map *map,
2486 enum isl_dim_type type1, int pos1,
2487 enum isl_dim_type type2, int pos2);
2488 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2489 enum isl_dim_type type1, int pos1,
2490 enum isl_dim_type type2, int pos2);
2491 __isl_give isl_basic_map *isl_basic_map_order_gt(
2492 __isl_take isl_basic_map *bmap,
2493 enum isl_dim_type type1, int pos1,
2494 enum isl_dim_type type2, int pos2);
2495 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2496 enum isl_dim_type type1, int pos1,
2497 enum isl_dim_type type2, int pos2);
2499 Intersect the relation with the half-space where the given
2500 dimensions satisfy the given ordering.
2504 __isl_give isl_map *isl_set_identity(
2505 __isl_take isl_set *set);
2506 __isl_give isl_union_map *isl_union_set_identity(
2507 __isl_take isl_union_set *uset);
2509 Construct an identity relation on the given (union) set.
2513 __isl_give isl_basic_set *isl_basic_map_deltas(
2514 __isl_take isl_basic_map *bmap);
2515 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2516 __isl_give isl_union_set *isl_union_map_deltas(
2517 __isl_take isl_union_map *umap);
2519 These functions return a (basic) set containing the differences
2520 between image elements and corresponding domain elements in the input.
2522 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2523 __isl_take isl_basic_map *bmap);
2524 __isl_give isl_map *isl_map_deltas_map(
2525 __isl_take isl_map *map);
2526 __isl_give isl_union_map *isl_union_map_deltas_map(
2527 __isl_take isl_union_map *umap);
2529 The functions above construct a (basic, regular or union) relation
2530 that maps (a wrapped version of) the input relation to its delta set.
2534 Simplify the representation of a set or relation by trying
2535 to combine pairs of basic sets or relations into a single
2536 basic set or relation.
2538 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2539 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2540 __isl_give isl_union_set *isl_union_set_coalesce(
2541 __isl_take isl_union_set *uset);
2542 __isl_give isl_union_map *isl_union_map_coalesce(
2543 __isl_take isl_union_map *umap);
2545 One of the methods for combining pairs of basic sets or relations
2546 can result in coefficients that are much larger than those that appear
2547 in the constraints of the input. By default, the coefficients are
2548 not allowed to grow larger, but this can be changed by unsetting
2549 the following option.
2551 int isl_options_set_coalesce_bounded_wrapping(
2552 isl_ctx *ctx, int val);
2553 int isl_options_get_coalesce_bounded_wrapping(
2556 =item * Detecting equalities
2558 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2559 __isl_take isl_basic_set *bset);
2560 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2561 __isl_take isl_basic_map *bmap);
2562 __isl_give isl_set *isl_set_detect_equalities(
2563 __isl_take isl_set *set);
2564 __isl_give isl_map *isl_map_detect_equalities(
2565 __isl_take isl_map *map);
2566 __isl_give isl_union_set *isl_union_set_detect_equalities(
2567 __isl_take isl_union_set *uset);
2568 __isl_give isl_union_map *isl_union_map_detect_equalities(
2569 __isl_take isl_union_map *umap);
2571 Simplify the representation of a set or relation by detecting implicit
2574 =item * Removing redundant constraints
2576 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2577 __isl_take isl_basic_set *bset);
2578 __isl_give isl_set *isl_set_remove_redundancies(
2579 __isl_take isl_set *set);
2580 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2581 __isl_take isl_basic_map *bmap);
2582 __isl_give isl_map *isl_map_remove_redundancies(
2583 __isl_take isl_map *map);
2587 __isl_give isl_basic_set *isl_set_convex_hull(
2588 __isl_take isl_set *set);
2589 __isl_give isl_basic_map *isl_map_convex_hull(
2590 __isl_take isl_map *map);
2592 If the input set or relation has any existentially quantified
2593 variables, then the result of these operations is currently undefined.
2597 #include <isl/set.h>
2598 __isl_give isl_basic_set *
2599 isl_set_unshifted_simple_hull(
2600 __isl_take isl_set *set);
2601 __isl_give isl_basic_set *isl_set_simple_hull(
2602 __isl_take isl_set *set);
2603 __isl_give isl_basic_set *
2604 isl_set_unshifted_simple_hull_from_set_list(
2605 __isl_take isl_set *set,
2606 __isl_take isl_set_list *list);
2608 #include <isl/map.h>
2609 __isl_give isl_basic_map *
2610 isl_map_unshifted_simple_hull(
2611 __isl_take isl_map *map);
2612 __isl_give isl_basic_map *isl_map_simple_hull(
2613 __isl_take isl_map *map);
2615 #include <isl/union_map.h>
2616 __isl_give isl_union_map *isl_union_map_simple_hull(
2617 __isl_take isl_union_map *umap);
2619 These functions compute a single basic set or relation
2620 that contains the whole input set or relation.
2621 In particular, the output is described by translates
2622 of the constraints describing the basic sets or relations in the input.
2623 In case of C<isl_set_unshifted_simple_hull>, only the original
2624 constraints are used, without any translation.
2625 In case of C<isl_set_unshifted_simple_hull_from_set_list>, the
2626 constraints are taken from the elements of the second argument.
2630 (See \autoref{s:simple hull}.)
2636 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2637 __isl_take isl_basic_set *bset);
2638 __isl_give isl_basic_set *isl_set_affine_hull(
2639 __isl_take isl_set *set);
2640 __isl_give isl_union_set *isl_union_set_affine_hull(
2641 __isl_take isl_union_set *uset);
2642 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2643 __isl_take isl_basic_map *bmap);
2644 __isl_give isl_basic_map *isl_map_affine_hull(
2645 __isl_take isl_map *map);
2646 __isl_give isl_union_map *isl_union_map_affine_hull(
2647 __isl_take isl_union_map *umap);
2649 In case of union sets and relations, the affine hull is computed
2652 =item * Polyhedral hull
2654 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2655 __isl_take isl_set *set);
2656 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2657 __isl_take isl_map *map);
2658 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2659 __isl_take isl_union_set *uset);
2660 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2661 __isl_take isl_union_map *umap);
2663 These functions compute a single basic set or relation
2664 not involving any existentially quantified variables
2665 that contains the whole input set or relation.
2666 In case of union sets and relations, the polyhedral hull is computed
2669 =item * Other approximations
2671 __isl_give isl_basic_set *
2672 isl_basic_set_drop_constraints_involving_dims(
2673 __isl_take isl_basic_set *bset,
2674 enum isl_dim_type type,
2675 unsigned first, unsigned n);
2676 __isl_give isl_basic_map *
2677 isl_basic_map_drop_constraints_involving_dims(
2678 __isl_take isl_basic_map *bmap,
2679 enum isl_dim_type type,
2680 unsigned first, unsigned n);
2681 __isl_give isl_basic_set *
2682 isl_basic_set_drop_constraints_not_involving_dims(
2683 __isl_take isl_basic_set *bset,
2684 enum isl_dim_type type,
2685 unsigned first, unsigned n);
2686 __isl_give isl_set *
2687 isl_set_drop_constraints_involving_dims(
2688 __isl_take isl_set *set,
2689 enum isl_dim_type type,
2690 unsigned first, unsigned n);
2691 __isl_give isl_map *
2692 isl_map_drop_constraints_involving_dims(
2693 __isl_take isl_map *map,
2694 enum isl_dim_type type,
2695 unsigned first, unsigned n);
2697 These functions drop any constraints (not) involving the specified dimensions.
2698 Note that the result depends on the representation of the input.
2702 __isl_give isl_basic_set *isl_basic_set_sample(
2703 __isl_take isl_basic_set *bset);
2704 __isl_give isl_basic_set *isl_set_sample(
2705 __isl_take isl_set *set);
2706 __isl_give isl_basic_map *isl_basic_map_sample(
2707 __isl_take isl_basic_map *bmap);
2708 __isl_give isl_basic_map *isl_map_sample(
2709 __isl_take isl_map *map);
2711 If the input (basic) set or relation is non-empty, then return
2712 a singleton subset of the input. Otherwise, return an empty set.
2714 =item * Optimization
2716 #include <isl/ilp.h>
2717 __isl_give isl_val *isl_basic_set_max_val(
2718 __isl_keep isl_basic_set *bset,
2719 __isl_keep isl_aff *obj);
2720 __isl_give isl_val *isl_set_min_val(
2721 __isl_keep isl_set *set,
2722 __isl_keep isl_aff *obj);
2723 __isl_give isl_val *isl_set_max_val(
2724 __isl_keep isl_set *set,
2725 __isl_keep isl_aff *obj);
2727 Compute the minimum or maximum of the integer affine expression C<obj>
2728 over the points in C<set>, returning the result in C<opt>.
2729 The result is C<NULL> in case of an error, the optimal value in case
2730 there is one, negative infinity or infinity if the problem is unbounded and
2731 NaN if the problem is empty.
2733 =item * Parametric optimization
2735 __isl_give isl_pw_aff *isl_set_dim_min(
2736 __isl_take isl_set *set, int pos);
2737 __isl_give isl_pw_aff *isl_set_dim_max(
2738 __isl_take isl_set *set, int pos);
2739 __isl_give isl_pw_aff *isl_map_dim_max(
2740 __isl_take isl_map *map, int pos);
2742 Compute the minimum or maximum of the given set or output dimension
2743 as a function of the parameters (and input dimensions), but independently
2744 of the other set or output dimensions.
2745 For lexicographic optimization, see L<"Lexicographic Optimization">.
2749 The following functions compute either the set of (rational) coefficient
2750 values of valid constraints for the given set or the set of (rational)
2751 values satisfying the constraints with coefficients from the given set.
2752 Internally, these two sets of functions perform essentially the
2753 same operations, except that the set of coefficients is assumed to
2754 be a cone, while the set of values may be any polyhedron.
2755 The current implementation is based on the Farkas lemma and
2756 Fourier-Motzkin elimination, but this may change or be made optional
2757 in future. In particular, future implementations may use different
2758 dualization algorithms or skip the elimination step.
2760 __isl_give isl_basic_set *isl_basic_set_coefficients(
2761 __isl_take isl_basic_set *bset);
2762 __isl_give isl_basic_set *isl_set_coefficients(
2763 __isl_take isl_set *set);
2764 __isl_give isl_union_set *isl_union_set_coefficients(
2765 __isl_take isl_union_set *bset);
2766 __isl_give isl_basic_set *isl_basic_set_solutions(
2767 __isl_take isl_basic_set *bset);
2768 __isl_give isl_basic_set *isl_set_solutions(
2769 __isl_take isl_set *set);
2770 __isl_give isl_union_set *isl_union_set_solutions(
2771 __isl_take isl_union_set *bset);
2775 __isl_give isl_map *isl_map_fixed_power_val(
2776 __isl_take isl_map *map,
2777 __isl_take isl_val *exp);
2778 __isl_give isl_union_map *
2779 isl_union_map_fixed_power_val(
2780 __isl_take isl_union_map *umap,
2781 __isl_take isl_val *exp);
2783 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2784 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2785 of C<map> is computed.
2787 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2789 __isl_give isl_union_map *isl_union_map_power(
2790 __isl_take isl_union_map *umap, int *exact);
2792 Compute a parametric representation for all positive powers I<k> of C<map>.
2793 The result maps I<k> to a nested relation corresponding to the
2794 I<k>th power of C<map>.
2795 The result may be an overapproximation. If the result is known to be exact,
2796 then C<*exact> is set to C<1>.
2798 =item * Transitive closure
2800 __isl_give isl_map *isl_map_transitive_closure(
2801 __isl_take isl_map *map, int *exact);
2802 __isl_give isl_union_map *isl_union_map_transitive_closure(
2803 __isl_take isl_union_map *umap, int *exact);
2805 Compute the transitive closure of C<map>.
2806 The result may be an overapproximation. If the result is known to be exact,
2807 then C<*exact> is set to C<1>.
2809 =item * Reaching path lengths
2811 __isl_give isl_map *isl_map_reaching_path_lengths(
2812 __isl_take isl_map *map, int *exact);
2814 Compute a relation that maps each element in the range of C<map>
2815 to the lengths of all paths composed of edges in C<map> that
2816 end up in the given element.
2817 The result may be an overapproximation. If the result is known to be exact,
2818 then C<*exact> is set to C<1>.
2819 To compute the I<maximal> path length, the resulting relation
2820 should be postprocessed by C<isl_map_lexmax>.
2821 In particular, if the input relation is a dependence relation
2822 (mapping sources to sinks), then the maximal path length corresponds
2823 to the free schedule.
2824 Note, however, that C<isl_map_lexmax> expects the maximum to be
2825 finite, so if the path lengths are unbounded (possibly due to
2826 the overapproximation), then you will get an error message.
2830 #include <isl/space.h>
2831 __isl_give isl_space *isl_space_wrap(
2832 __isl_take isl_space *space);
2833 __isl_give isl_space *isl_space_unwrap(
2834 __isl_take isl_space *space);
2836 #include <isl/set.h>
2837 __isl_give isl_basic_map *isl_basic_set_unwrap(
2838 __isl_take isl_basic_set *bset);
2839 __isl_give isl_map *isl_set_unwrap(
2840 __isl_take isl_set *set);
2842 #include <isl/map.h>
2843 __isl_give isl_basic_set *isl_basic_map_wrap(
2844 __isl_take isl_basic_map *bmap);
2845 __isl_give isl_set *isl_map_wrap(
2846 __isl_take isl_map *map);
2848 #include <isl/union_set.h>
2849 __isl_give isl_union_map *isl_union_set_unwrap(
2850 __isl_take isl_union_set *uset);
2852 #include <isl/union_map.h>
2853 __isl_give isl_union_set *isl_union_map_wrap(
2854 __isl_take isl_union_map *umap);
2856 The input to C<isl_space_unwrap> should
2857 be the space of a set, while that of
2858 C<isl_space_wrap> should be the space of a relation.
2859 Conversely, the output of C<isl_space_unwrap> is the space
2860 of a relation, while that of C<isl_space_wrap> is the space of a set.
2864 Remove any internal structure of domain (and range) of the given
2865 set or relation. If there is any such internal structure in the input,
2866 then the name of the space is also removed.
2868 #include <isl/local_space.h>
2869 __isl_give isl_local_space *
2870 isl_local_space_flatten_domain(
2871 __isl_take isl_local_space *ls);
2872 __isl_give isl_local_space *
2873 isl_local_space_flatten_range(
2874 __isl_take isl_local_space *ls);
2876 #include <isl/set.h>
2877 __isl_give isl_basic_set *isl_basic_set_flatten(
2878 __isl_take isl_basic_set *bset);
2879 __isl_give isl_set *isl_set_flatten(
2880 __isl_take isl_set *set);
2882 #include <isl/map.h>
2883 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2884 __isl_take isl_basic_map *bmap);
2885 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2886 __isl_take isl_basic_map *bmap);
2887 __isl_give isl_map *isl_map_flatten_range(
2888 __isl_take isl_map *map);
2889 __isl_give isl_map *isl_map_flatten_domain(
2890 __isl_take isl_map *map);
2891 __isl_give isl_basic_map *isl_basic_map_flatten(
2892 __isl_take isl_basic_map *bmap);
2893 __isl_give isl_map *isl_map_flatten(
2894 __isl_take isl_map *map);
2896 #include <isl/map.h>
2897 __isl_give isl_map *isl_set_flatten_map(
2898 __isl_take isl_set *set);
2900 The function above constructs a relation
2901 that maps the input set to a flattened version of the set.
2905 Lift the input set to a space with extra dimensions corresponding
2906 to the existentially quantified variables in the input.
2907 In particular, the result lives in a wrapped map where the domain
2908 is the original space and the range corresponds to the original
2909 existentially quantified variables.
2911 __isl_give isl_basic_set *isl_basic_set_lift(
2912 __isl_take isl_basic_set *bset);
2913 __isl_give isl_set *isl_set_lift(
2914 __isl_take isl_set *set);
2915 __isl_give isl_union_set *isl_union_set_lift(
2916 __isl_take isl_union_set *uset);
2918 Given a local space that contains the existentially quantified
2919 variables of a set, a basic relation that, when applied to
2920 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2921 can be constructed using the following function.
2923 #include <isl/local_space.h>
2924 __isl_give isl_basic_map *isl_local_space_lifting(
2925 __isl_take isl_local_space *ls);
2927 =item * Internal Product
2929 __isl_give isl_basic_map *isl_basic_map_zip(
2930 __isl_take isl_basic_map *bmap);
2931 __isl_give isl_map *isl_map_zip(
2932 __isl_take isl_map *map);
2933 __isl_give isl_union_map *isl_union_map_zip(
2934 __isl_take isl_union_map *umap);
2936 Given a relation with nested relations for domain and range,
2937 interchange the range of the domain with the domain of the range.
2941 __isl_give isl_basic_map *isl_basic_map_curry(
2942 __isl_take isl_basic_map *bmap);
2943 __isl_give isl_basic_map *isl_basic_map_uncurry(
2944 __isl_take isl_basic_map *bmap);
2945 __isl_give isl_map *isl_map_curry(
2946 __isl_take isl_map *map);
2947 __isl_give isl_map *isl_map_uncurry(
2948 __isl_take isl_map *map);
2949 __isl_give isl_union_map *isl_union_map_curry(
2950 __isl_take isl_union_map *umap);
2951 __isl_give isl_union_map *isl_union_map_uncurry(
2952 __isl_take isl_union_map *umap);
2954 Given a relation with a nested relation for domain,
2955 the C<curry> functions
2956 move the range of the nested relation out of the domain
2957 and use it as the domain of a nested relation in the range,
2958 with the original range as range of this nested relation.
2959 The C<uncurry> functions perform the inverse operation.
2961 =item * Aligning parameters
2963 __isl_give isl_basic_set *isl_basic_set_align_params(
2964 __isl_take isl_basic_set *bset,
2965 __isl_take isl_space *model);
2966 __isl_give isl_set *isl_set_align_params(
2967 __isl_take isl_set *set,
2968 __isl_take isl_space *model);
2969 __isl_give isl_basic_map *isl_basic_map_align_params(
2970 __isl_take isl_basic_map *bmap,
2971 __isl_take isl_space *model);
2972 __isl_give isl_map *isl_map_align_params(
2973 __isl_take isl_map *map,
2974 __isl_take isl_space *model);
2976 Change the order of the parameters of the given set or relation
2977 such that the first parameters match those of C<model>.
2978 This may involve the introduction of extra parameters.
2979 All parameters need to be named.
2981 =item * Dimension manipulation
2983 #include <isl/local_space.h>
2984 __isl_give isl_local_space *isl_local_space_add_dims(
2985 __isl_take isl_local_space *ls,
2986 enum isl_dim_type type, unsigned n);
2987 __isl_give isl_local_space *isl_local_space_insert_dims(
2988 __isl_take isl_local_space *ls,
2989 enum isl_dim_type type, unsigned first, unsigned n);
2990 __isl_give isl_local_space *isl_local_space_drop_dims(
2991 __isl_take isl_local_space *ls,
2992 enum isl_dim_type type, unsigned first, unsigned n);
2994 #include <isl/set.h>
2995 __isl_give isl_basic_set *isl_basic_set_add_dims(
2996 __isl_take isl_basic_set *bset,
2997 enum isl_dim_type type, unsigned n);
2998 __isl_give isl_set *isl_set_add_dims(
2999 __isl_take isl_set *set,
3000 enum isl_dim_type type, unsigned n);
3001 __isl_give isl_basic_set *isl_basic_set_insert_dims(
3002 __isl_take isl_basic_set *bset,
3003 enum isl_dim_type type, unsigned pos,
3005 __isl_give isl_set *isl_set_insert_dims(
3006 __isl_take isl_set *set,
3007 enum isl_dim_type type, unsigned pos, unsigned n);
3008 __isl_give isl_basic_set *isl_basic_set_move_dims(
3009 __isl_take isl_basic_set *bset,
3010 enum isl_dim_type dst_type, unsigned dst_pos,
3011 enum isl_dim_type src_type, unsigned src_pos,
3013 __isl_give isl_set *isl_set_move_dims(
3014 __isl_take isl_set *set,
3015 enum isl_dim_type dst_type, unsigned dst_pos,
3016 enum isl_dim_type src_type, unsigned src_pos,
3019 #include <isl/map.h>
3020 __isl_give isl_map *isl_map_add_dims(
3021 __isl_take isl_map *map,
3022 enum isl_dim_type type, unsigned n);
3023 __isl_give isl_basic_map *isl_basic_map_insert_dims(
3024 __isl_take isl_basic_map *bmap,
3025 enum isl_dim_type type, unsigned pos,
3027 __isl_give isl_map *isl_map_insert_dims(
3028 __isl_take isl_map *map,
3029 enum isl_dim_type type, unsigned pos, unsigned n);
3030 __isl_give isl_basic_map *isl_basic_map_move_dims(
3031 __isl_take isl_basic_map *bmap,
3032 enum isl_dim_type dst_type, unsigned dst_pos,
3033 enum isl_dim_type src_type, unsigned src_pos,
3035 __isl_give isl_map *isl_map_move_dims(
3036 __isl_take isl_map *map,
3037 enum isl_dim_type dst_type, unsigned dst_pos,
3038 enum isl_dim_type src_type, unsigned src_pos,
3041 It is usually not advisable to directly change the (input or output)
3042 space of a set or a relation as this removes the name and the internal
3043 structure of the space. However, the above functions can be useful
3044 to add new parameters, assuming
3045 C<isl_set_align_params> and C<isl_map_align_params>
3050 =head2 Binary Operations
3052 The two arguments of a binary operation not only need to live
3053 in the same C<isl_ctx>, they currently also need to have
3054 the same (number of) parameters.
3056 =head3 Basic Operations
3060 =item * Intersection
3062 #include <isl/local_space.h>
3063 __isl_give isl_local_space *isl_local_space_intersect(
3064 __isl_take isl_local_space *ls1,
3065 __isl_take isl_local_space *ls2);
3067 #include <isl/set.h>
3068 __isl_give isl_basic_set *isl_basic_set_intersect_params(
3069 __isl_take isl_basic_set *bset1,
3070 __isl_take isl_basic_set *bset2);
3071 __isl_give isl_basic_set *isl_basic_set_intersect(
3072 __isl_take isl_basic_set *bset1,
3073 __isl_take isl_basic_set *bset2);
3074 __isl_give isl_basic_set *isl_basic_set_list_intersect(
3075 __isl_take struct isl_basic_set_list *list);
3076 __isl_give isl_set *isl_set_intersect_params(
3077 __isl_take isl_set *set,
3078 __isl_take isl_set *params);
3079 __isl_give isl_set *isl_set_intersect(
3080 __isl_take isl_set *set1,
3081 __isl_take isl_set *set2);
3083 #include <isl/map.h>
3084 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
3085 __isl_take isl_basic_map *bmap,
3086 __isl_take isl_basic_set *bset);
3087 __isl_give isl_basic_map *isl_basic_map_intersect_range(
3088 __isl_take isl_basic_map *bmap,
3089 __isl_take isl_basic_set *bset);
3090 __isl_give isl_basic_map *isl_basic_map_intersect(
3091 __isl_take isl_basic_map *bmap1,
3092 __isl_take isl_basic_map *bmap2);
3093 __isl_give isl_map *isl_map_intersect_params(
3094 __isl_take isl_map *map,
3095 __isl_take isl_set *params);
3096 __isl_give isl_map *isl_map_intersect_domain(
3097 __isl_take isl_map *map,
3098 __isl_take isl_set *set);
3099 __isl_give isl_map *isl_map_intersect_range(
3100 __isl_take isl_map *map,
3101 __isl_take isl_set *set);
3102 __isl_give isl_map *isl_map_intersect(
3103 __isl_take isl_map *map1,
3104 __isl_take isl_map *map2);
3106 #include <isl/union_set.h>
3107 __isl_give isl_union_set *isl_union_set_intersect_params(
3108 __isl_take isl_union_set *uset,
3109 __isl_take isl_set *set);
3110 __isl_give isl_union_set *isl_union_set_intersect(
3111 __isl_take isl_union_set *uset1,
3112 __isl_take isl_union_set *uset2);
3114 #include <isl/union_map.h>
3115 __isl_give isl_union_map *isl_union_map_intersect_params(
3116 __isl_take isl_union_map *umap,
3117 __isl_take isl_set *set);
3118 __isl_give isl_union_map *isl_union_map_intersect_domain(
3119 __isl_take isl_union_map *umap,
3120 __isl_take isl_union_set *uset);
3121 __isl_give isl_union_map *isl_union_map_intersect_range(
3122 __isl_take isl_union_map *umap,
3123 __isl_take isl_union_set *uset);
3124 __isl_give isl_union_map *isl_union_map_intersect(
3125 __isl_take isl_union_map *umap1,
3126 __isl_take isl_union_map *umap2);
3128 The second argument to the C<_params> functions needs to be
3129 a parametric (basic) set. For the other functions, a parametric set
3130 for either argument is only allowed if the other argument is
3131 a parametric set as well.
3132 The list passed to C<isl_basic_set_list_intersect> needs to have
3133 at least one element and all elements need to live in the same space.
3137 __isl_give isl_set *isl_basic_set_union(
3138 __isl_take isl_basic_set *bset1,
3139 __isl_take isl_basic_set *bset2);
3140 __isl_give isl_map *isl_basic_map_union(
3141 __isl_take isl_basic_map *bmap1,
3142 __isl_take isl_basic_map *bmap2);
3143 __isl_give isl_set *isl_set_union(
3144 __isl_take isl_set *set1,
3145 __isl_take isl_set *set2);
3146 __isl_give isl_map *isl_map_union(
3147 __isl_take isl_map *map1,
3148 __isl_take isl_map *map2);
3149 __isl_give isl_union_set *isl_union_set_union(
3150 __isl_take isl_union_set *uset1,
3151 __isl_take isl_union_set *uset2);
3152 __isl_give isl_union_map *isl_union_map_union(
3153 __isl_take isl_union_map *umap1,
3154 __isl_take isl_union_map *umap2);
3156 =item * Set difference
3158 __isl_give isl_set *isl_set_subtract(
3159 __isl_take isl_set *set1,
3160 __isl_take isl_set *set2);
3161 __isl_give isl_map *isl_map_subtract(
3162 __isl_take isl_map *map1,
3163 __isl_take isl_map *map2);
3164 __isl_give isl_map *isl_map_subtract_domain(
3165 __isl_take isl_map *map,
3166 __isl_take isl_set *dom);
3167 __isl_give isl_map *isl_map_subtract_range(
3168 __isl_take isl_map *map,
3169 __isl_take isl_set *dom);
3170 __isl_give isl_union_set *isl_union_set_subtract(
3171 __isl_take isl_union_set *uset1,
3172 __isl_take isl_union_set *uset2);
3173 __isl_give isl_union_map *isl_union_map_subtract(
3174 __isl_take isl_union_map *umap1,
3175 __isl_take isl_union_map *umap2);
3176 __isl_give isl_union_map *isl_union_map_subtract_domain(
3177 __isl_take isl_union_map *umap,
3178 __isl_take isl_union_set *dom);
3179 __isl_give isl_union_map *isl_union_map_subtract_range(
3180 __isl_take isl_union_map *umap,
3181 __isl_take isl_union_set *dom);
3185 __isl_give isl_basic_set *isl_basic_set_apply(
3186 __isl_take isl_basic_set *bset,
3187 __isl_take isl_basic_map *bmap);
3188 __isl_give isl_set *isl_set_apply(
3189 __isl_take isl_set *set,
3190 __isl_take isl_map *map);
3191 __isl_give isl_union_set *isl_union_set_apply(
3192 __isl_take isl_union_set *uset,
3193 __isl_take isl_union_map *umap);
3194 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3195 __isl_take isl_basic_map *bmap1,
3196 __isl_take isl_basic_map *bmap2);
3197 __isl_give isl_basic_map *isl_basic_map_apply_range(
3198 __isl_take isl_basic_map *bmap1,
3199 __isl_take isl_basic_map *bmap2);
3200 __isl_give isl_map *isl_map_apply_domain(
3201 __isl_take isl_map *map1,
3202 __isl_take isl_map *map2);
3203 __isl_give isl_union_map *isl_union_map_apply_domain(
3204 __isl_take isl_union_map *umap1,
3205 __isl_take isl_union_map *umap2);
3206 __isl_give isl_map *isl_map_apply_range(
3207 __isl_take isl_map *map1,
3208 __isl_take isl_map *map2);
3209 __isl_give isl_union_map *isl_union_map_apply_range(
3210 __isl_take isl_union_map *umap1,
3211 __isl_take isl_union_map *umap2);
3215 #include <isl/set.h>
3216 __isl_give isl_basic_set *
3217 isl_basic_set_preimage_multi_aff(
3218 __isl_take isl_basic_set *bset,
3219 __isl_take isl_multi_aff *ma);
3220 __isl_give isl_set *isl_set_preimage_multi_aff(
3221 __isl_take isl_set *set,
3222 __isl_take isl_multi_aff *ma);
3223 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3224 __isl_take isl_set *set,
3225 __isl_take isl_pw_multi_aff *pma);
3226 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
3227 __isl_take isl_set *set,
3228 __isl_take isl_multi_pw_aff *mpa);
3230 #include <isl/union_set.h>
3231 __isl_give isl_union_set *
3232 isl_union_set_preimage_multi_aff(
3233 __isl_take isl_union_set *uset,
3234 __isl_take isl_multi_aff *ma);
3235 __isl_give isl_union_set *
3236 isl_union_set_preimage_pw_multi_aff(
3237 __isl_take isl_union_set *uset,
3238 __isl_take isl_pw_multi_aff *pma);
3239 __isl_give isl_union_set *
3240 isl_union_set_preimage_union_pw_multi_aff(
3241 __isl_take isl_union_set *uset,
3242 __isl_take isl_union_pw_multi_aff *upma);
3244 #include <isl/map.h>
3245 __isl_give isl_basic_map *
3246 isl_basic_map_preimage_domain_multi_aff(
3247 __isl_take isl_basic_map *bmap,
3248 __isl_take isl_multi_aff *ma);
3249 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3250 __isl_take isl_map *map,
3251 __isl_take isl_multi_aff *ma);
3252 __isl_give isl_map *isl_map_preimage_range_multi_aff(
3253 __isl_take isl_map *map,
3254 __isl_take isl_multi_aff *ma);
3255 __isl_give isl_map *
3256 isl_map_preimage_domain_pw_multi_aff(
3257 __isl_take isl_map *map,
3258 __isl_take isl_pw_multi_aff *pma);
3259 __isl_give isl_map *
3260 isl_map_preimage_range_pw_multi_aff(
3261 __isl_take isl_map *map,
3262 __isl_take isl_pw_multi_aff *pma);
3263 __isl_give isl_map *
3264 isl_map_preimage_domain_multi_pw_aff(
3265 __isl_take isl_map *map,
3266 __isl_take isl_multi_pw_aff *mpa);
3267 __isl_give isl_basic_map *
3268 isl_basic_map_preimage_range_multi_aff(
3269 __isl_take isl_basic_map *bmap,
3270 __isl_take isl_multi_aff *ma);
3272 #include <isl/union_map.h>
3273 __isl_give isl_union_map *
3274 isl_union_map_preimage_domain_multi_aff(
3275 __isl_take isl_union_map *umap,
3276 __isl_take isl_multi_aff *ma);
3277 __isl_give isl_union_map *
3278 isl_union_map_preimage_range_multi_aff(
3279 __isl_take isl_union_map *umap,
3280 __isl_take isl_multi_aff *ma);
3281 __isl_give isl_union_map *
3282 isl_union_map_preimage_domain_pw_multi_aff(
3283 __isl_take isl_union_map *umap,
3284 __isl_take isl_pw_multi_aff *pma);
3285 __isl_give isl_union_map *
3286 isl_union_map_preimage_range_pw_multi_aff(
3287 __isl_take isl_union_map *umap,
3288 __isl_take isl_pw_multi_aff *pma);
3289 __isl_give isl_union_map *
3290 isl_union_map_preimage_domain_union_pw_multi_aff(
3291 __isl_take isl_union_map *umap,
3292 __isl_take isl_union_pw_multi_aff *upma);
3293 __isl_give isl_union_map *
3294 isl_union_map_preimage_range_union_pw_multi_aff(
3295 __isl_take isl_union_map *umap,
3296 __isl_take isl_union_pw_multi_aff *upma);
3298 These functions compute the preimage of the given set or map domain/range under
3299 the given function. In other words, the expression is plugged
3300 into the set description or into the domain/range of the map.
3301 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3302 L</"Piecewise Multiple Quasi Affine Expressions">.
3304 =item * Cartesian Product
3306 #include <isl/space.h>
3307 __isl_give isl_space *isl_space_product(
3308 __isl_take isl_space *space1,
3309 __isl_take isl_space *space2);
3310 __isl_give isl_space *isl_space_domain_product(
3311 __isl_take isl_space *space1,
3312 __isl_take isl_space *space2);
3313 __isl_give isl_space *isl_space_range_product(
3314 __isl_take isl_space *space1,
3315 __isl_take isl_space *space2);
3318 C<isl_space_product>, C<isl_space_domain_product>
3319 and C<isl_space_range_product> take pairs or relation spaces and
3320 produce a single relations space, where either the domain, the range
3321 or both domain and range are wrapped spaces of relations between
3322 the domains and/or ranges of the input spaces.
3323 If the product is only constructed over the domain or the range
3324 then the ranges or the domains of the inputs should be the same.
3325 The function C<isl_space_product> also accepts a pair of set spaces,
3326 in which case it returns a wrapped space of a relation between the
3329 #include <isl/set.h>
3330 __isl_give isl_set *isl_set_product(
3331 __isl_take isl_set *set1,
3332 __isl_take isl_set *set2);
3334 #include <isl/map.h>
3335 __isl_give isl_basic_map *isl_basic_map_domain_product(
3336 __isl_take isl_basic_map *bmap1,
3337 __isl_take isl_basic_map *bmap2);
3338 __isl_give isl_basic_map *isl_basic_map_range_product(
3339 __isl_take isl_basic_map *bmap1,
3340 __isl_take isl_basic_map *bmap2);
3341 __isl_give isl_basic_map *isl_basic_map_product(
3342 __isl_take isl_basic_map *bmap1,
3343 __isl_take isl_basic_map *bmap2);
3344 __isl_give isl_map *isl_map_domain_product(
3345 __isl_take isl_map *map1,
3346 __isl_take isl_map *map2);
3347 __isl_give isl_map *isl_map_range_product(
3348 __isl_take isl_map *map1,
3349 __isl_take isl_map *map2);
3350 __isl_give isl_map *isl_map_product(
3351 __isl_take isl_map *map1,
3352 __isl_take isl_map *map2);
3354 #include <isl/union_set.h>
3355 __isl_give isl_union_set *isl_union_set_product(
3356 __isl_take isl_union_set *uset1,
3357 __isl_take isl_union_set *uset2);
3359 #include <isl/union_map.h>
3360 __isl_give isl_union_map *isl_union_map_domain_product(
3361 __isl_take isl_union_map *umap1,
3362 __isl_take isl_union_map *umap2);
3363 __isl_give isl_union_map *isl_union_map_range_product(
3364 __isl_take isl_union_map *umap1,
3365 __isl_take isl_union_map *umap2);
3366 __isl_give isl_union_map *isl_union_map_product(
3367 __isl_take isl_union_map *umap1,
3368 __isl_take isl_union_map *umap2);
3370 The above functions compute the cross product of the given
3371 sets or relations. The domains and ranges of the results
3372 are wrapped maps between domains and ranges of the inputs.
3373 To obtain a ``flat'' product, use the following functions
3376 __isl_give isl_basic_set *isl_basic_set_flat_product(
3377 __isl_take isl_basic_set *bset1,
3378 __isl_take isl_basic_set *bset2);
3379 __isl_give isl_set *isl_set_flat_product(
3380 __isl_take isl_set *set1,
3381 __isl_take isl_set *set2);
3382 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3383 __isl_take isl_basic_map *bmap1,
3384 __isl_take isl_basic_map *bmap2);
3385 __isl_give isl_map *isl_map_flat_domain_product(
3386 __isl_take isl_map *map1,
3387 __isl_take isl_map *map2);
3388 __isl_give isl_map *isl_map_flat_range_product(
3389 __isl_take isl_map *map1,
3390 __isl_take isl_map *map2);
3391 __isl_give isl_union_map *isl_union_map_flat_range_product(
3392 __isl_take isl_union_map *umap1,
3393 __isl_take isl_union_map *umap2);
3394 __isl_give isl_basic_map *isl_basic_map_flat_product(
3395 __isl_take isl_basic_map *bmap1,
3396 __isl_take isl_basic_map *bmap2);
3397 __isl_give isl_map *isl_map_flat_product(
3398 __isl_take isl_map *map1,
3399 __isl_take isl_map *map2);
3401 #include <isl/space.h>
3402 __isl_give isl_space *isl_space_domain_factor_domain(
3403 __isl_take isl_space *space);
3404 __isl_give isl_space *isl_space_range_factor_domain(
3405 __isl_take isl_space *space);
3406 __isl_give isl_space *isl_space_range_factor_range(
3407 __isl_take isl_space *space);
3409 The functions C<isl_space_range_factor_domain> and
3410 C<isl_space_range_factor_range> extract the two arguments from
3411 the result of a call to C<isl_space_range_product>.
3413 The arguments of a call to C<isl_map_range_product> can be extracted
3414 from the result using the following two functions.
3416 #include <isl/map.h>
3417 __isl_give isl_map *isl_map_range_factor_domain(
3418 __isl_take isl_map *map);
3419 __isl_give isl_map *isl_map_range_factor_range(
3420 __isl_take isl_map *map);
3422 =item * Simplification
3424 __isl_give isl_basic_set *isl_basic_set_gist(
3425 __isl_take isl_basic_set *bset,
3426 __isl_take isl_basic_set *context);
3427 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3428 __isl_take isl_set *context);
3429 __isl_give isl_set *isl_set_gist_params(
3430 __isl_take isl_set *set,
3431 __isl_take isl_set *context);
3432 __isl_give isl_union_set *isl_union_set_gist(
3433 __isl_take isl_union_set *uset,
3434 __isl_take isl_union_set *context);
3435 __isl_give isl_union_set *isl_union_set_gist_params(
3436 __isl_take isl_union_set *uset,
3437 __isl_take isl_set *set);
3438 __isl_give isl_basic_map *isl_basic_map_gist(
3439 __isl_take isl_basic_map *bmap,
3440 __isl_take isl_basic_map *context);
3441 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3442 __isl_take isl_map *context);
3443 __isl_give isl_map *isl_map_gist_params(
3444 __isl_take isl_map *map,
3445 __isl_take isl_set *context);
3446 __isl_give isl_map *isl_map_gist_domain(
3447 __isl_take isl_map *map,
3448 __isl_take isl_set *context);
3449 __isl_give isl_map *isl_map_gist_range(
3450 __isl_take isl_map *map,
3451 __isl_take isl_set *context);
3452 __isl_give isl_union_map *isl_union_map_gist(
3453 __isl_take isl_union_map *umap,
3454 __isl_take isl_union_map *context);
3455 __isl_give isl_union_map *isl_union_map_gist_params(
3456 __isl_take isl_union_map *umap,
3457 __isl_take isl_set *set);
3458 __isl_give isl_union_map *isl_union_map_gist_domain(
3459 __isl_take isl_union_map *umap,
3460 __isl_take isl_union_set *uset);
3461 __isl_give isl_union_map *isl_union_map_gist_range(
3462 __isl_take isl_union_map *umap,
3463 __isl_take isl_union_set *uset);
3465 The gist operation returns a set or relation that has the
3466 same intersection with the context as the input set or relation.
3467 Any implicit equality in the intersection is made explicit in the result,
3468 while all inequalities that are redundant with respect to the intersection
3470 In case of union sets and relations, the gist operation is performed
3475 =head3 Lexicographic Optimization
3477 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3478 the following functions
3479 compute a set that contains the lexicographic minimum or maximum
3480 of the elements in C<set> (or C<bset>) for those values of the parameters
3481 that satisfy C<dom>.
3482 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3483 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3485 In other words, the union of the parameter values
3486 for which the result is non-empty and of C<*empty>
3489 __isl_give isl_set *isl_basic_set_partial_lexmin(
3490 __isl_take isl_basic_set *bset,
3491 __isl_take isl_basic_set *dom,
3492 __isl_give isl_set **empty);
3493 __isl_give isl_set *isl_basic_set_partial_lexmax(
3494 __isl_take isl_basic_set *bset,
3495 __isl_take isl_basic_set *dom,
3496 __isl_give isl_set **empty);
3497 __isl_give isl_set *isl_set_partial_lexmin(
3498 __isl_take isl_set *set, __isl_take isl_set *dom,
3499 __isl_give isl_set **empty);
3500 __isl_give isl_set *isl_set_partial_lexmax(
3501 __isl_take isl_set *set, __isl_take isl_set *dom,
3502 __isl_give isl_set **empty);
3504 Given a (basic) set C<set> (or C<bset>), the following functions simply
3505 return a set containing the lexicographic minimum or maximum
3506 of the elements in C<set> (or C<bset>).
3507 In case of union sets, the optimum is computed per space.
3509 __isl_give isl_set *isl_basic_set_lexmin(
3510 __isl_take isl_basic_set *bset);
3511 __isl_give isl_set *isl_basic_set_lexmax(
3512 __isl_take isl_basic_set *bset);
3513 __isl_give isl_set *isl_set_lexmin(
3514 __isl_take isl_set *set);
3515 __isl_give isl_set *isl_set_lexmax(
3516 __isl_take isl_set *set);
3517 __isl_give isl_union_set *isl_union_set_lexmin(
3518 __isl_take isl_union_set *uset);
3519 __isl_give isl_union_set *isl_union_set_lexmax(
3520 __isl_take isl_union_set *uset);
3522 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3523 the following functions
3524 compute a relation that maps each element of C<dom>
3525 to the single lexicographic minimum or maximum
3526 of the elements that are associated to that same
3527 element in C<map> (or C<bmap>).
3528 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3529 that contains the elements in C<dom> that do not map
3530 to any elements in C<map> (or C<bmap>).
3531 In other words, the union of the domain of the result and of C<*empty>
3534 __isl_give isl_map *isl_basic_map_partial_lexmax(
3535 __isl_take isl_basic_map *bmap,
3536 __isl_take isl_basic_set *dom,
3537 __isl_give isl_set **empty);
3538 __isl_give isl_map *isl_basic_map_partial_lexmin(
3539 __isl_take isl_basic_map *bmap,
3540 __isl_take isl_basic_set *dom,
3541 __isl_give isl_set **empty);
3542 __isl_give isl_map *isl_map_partial_lexmax(
3543 __isl_take isl_map *map, __isl_take isl_set *dom,
3544 __isl_give isl_set **empty);
3545 __isl_give isl_map *isl_map_partial_lexmin(
3546 __isl_take isl_map *map, __isl_take isl_set *dom,
3547 __isl_give isl_set **empty);
3549 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3550 return a map mapping each element in the domain of
3551 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3552 of all elements associated to that element.
3553 In case of union relations, the optimum is computed per space.
3555 __isl_give isl_map *isl_basic_map_lexmin(
3556 __isl_take isl_basic_map *bmap);
3557 __isl_give isl_map *isl_basic_map_lexmax(
3558 __isl_take isl_basic_map *bmap);
3559 __isl_give isl_map *isl_map_lexmin(
3560 __isl_take isl_map *map);
3561 __isl_give isl_map *isl_map_lexmax(
3562 __isl_take isl_map *map);
3563 __isl_give isl_union_map *isl_union_map_lexmin(
3564 __isl_take isl_union_map *umap);
3565 __isl_give isl_union_map *isl_union_map_lexmax(
3566 __isl_take isl_union_map *umap);
3568 The following functions return their result in the form of
3569 a piecewise multi-affine expression
3570 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3571 but are otherwise equivalent to the corresponding functions
3572 returning a basic set or relation.
3574 __isl_give isl_pw_multi_aff *
3575 isl_basic_map_lexmin_pw_multi_aff(
3576 __isl_take isl_basic_map *bmap);
3577 __isl_give isl_pw_multi_aff *
3578 isl_basic_set_partial_lexmin_pw_multi_aff(
3579 __isl_take isl_basic_set *bset,
3580 __isl_take isl_basic_set *dom,
3581 __isl_give isl_set **empty);
3582 __isl_give isl_pw_multi_aff *
3583 isl_basic_set_partial_lexmax_pw_multi_aff(
3584 __isl_take isl_basic_set *bset,
3585 __isl_take isl_basic_set *dom,
3586 __isl_give isl_set **empty);
3587 __isl_give isl_pw_multi_aff *
3588 isl_basic_map_partial_lexmin_pw_multi_aff(
3589 __isl_take isl_basic_map *bmap,
3590 __isl_take isl_basic_set *dom,
3591 __isl_give isl_set **empty);
3592 __isl_give isl_pw_multi_aff *
3593 isl_basic_map_partial_lexmax_pw_multi_aff(
3594 __isl_take isl_basic_map *bmap,
3595 __isl_take isl_basic_set *dom,
3596 __isl_give isl_set **empty);
3597 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3598 __isl_take isl_set *set);
3599 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3600 __isl_take isl_set *set);
3601 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3602 __isl_take isl_map *map);
3603 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3604 __isl_take isl_map *map);
3608 Lists are defined over several element types, including
3609 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3610 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3611 Here we take lists of C<isl_set>s as an example.
3612 Lists can be created, copied, modified and freed using the following functions.
3614 #include <isl/set.h>
3615 __isl_give isl_set_list *isl_set_list_from_set(
3616 __isl_take isl_set *el);
3617 __isl_give isl_set_list *isl_set_list_alloc(
3618 isl_ctx *ctx, int n);
3619 __isl_give isl_set_list *isl_set_list_copy(
3620 __isl_keep isl_set_list *list);
3621 __isl_give isl_set_list *isl_set_list_insert(
3622 __isl_take isl_set_list *list, unsigned pos,
3623 __isl_take isl_set *el);
3624 __isl_give isl_set_list *isl_set_list_add(
3625 __isl_take isl_set_list *list,
3626 __isl_take isl_set *el);
3627 __isl_give isl_set_list *isl_set_list_drop(
3628 __isl_take isl_set_list *list,
3629 unsigned first, unsigned n);
3630 __isl_give isl_set_list *isl_set_list_set_set(
3631 __isl_take isl_set_list *list, int index,
3632 __isl_take isl_set *set);
3633 __isl_give isl_set_list *isl_set_list_concat(
3634 __isl_take isl_set_list *list1,
3635 __isl_take isl_set_list *list2);
3636 __isl_give isl_set_list *isl_set_list_sort(
3637 __isl_take isl_set_list *list,
3638 int (*cmp)(__isl_keep isl_set *a,
3639 __isl_keep isl_set *b, void *user),
3641 __isl_null isl_set_list *isl_set_list_free(
3642 __isl_take isl_set_list *list);
3644 C<isl_set_list_alloc> creates an empty list with a capacity for
3645 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3648 Lists can be inspected using the following functions.
3650 #include <isl/set.h>
3651 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3652 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3653 __isl_give isl_set *isl_set_list_get_set(
3654 __isl_keep isl_set_list *list, int index);
3655 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3656 int (*fn)(__isl_take isl_set *el, void *user),
3658 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3659 int (*follows)(__isl_keep isl_set *a,
3660 __isl_keep isl_set *b, void *user),
3662 int (*fn)(__isl_take isl_set *el, void *user),
3665 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3666 strongly connected components of the graph with as vertices the elements
3667 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3668 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3669 should return C<-1> on error.
3671 Lists can be printed using
3673 #include <isl/set.h>
3674 __isl_give isl_printer *isl_printer_print_set_list(
3675 __isl_take isl_printer *p,
3676 __isl_keep isl_set_list *list);
3678 =head2 Associative arrays
3680 Associative arrays map isl objects of a specific type to isl objects
3681 of some (other) specific type. They are defined for several pairs
3682 of types, including (C<isl_map>, C<isl_basic_set>),
3683 (C<isl_id>, C<isl_ast_expr>) and.
3684 (C<isl_id>, C<isl_pw_aff>).
3685 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3688 Associative arrays can be created, copied and freed using
3689 the following functions.
3691 #include <isl/id_to_ast_expr.h>
3692 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3693 isl_ctx *ctx, int min_size);
3694 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3695 __isl_keep id_to_ast_expr *id2expr);
3696 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
3697 __isl_take id_to_ast_expr *id2expr);
3699 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3700 to specify the expected size of the associative array.
3701 The associative array will be grown automatically as needed.
3703 Associative arrays can be inspected using the following functions.
3705 #include <isl/id_to_ast_expr.h>
3706 isl_ctx *isl_id_to_ast_expr_get_ctx(
3707 __isl_keep id_to_ast_expr *id2expr);
3708 int isl_id_to_ast_expr_has(
3709 __isl_keep id_to_ast_expr *id2expr,
3710 __isl_keep isl_id *key);
3711 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3712 __isl_keep id_to_ast_expr *id2expr,
3713 __isl_take isl_id *key);
3714 int isl_id_to_ast_expr_foreach(
3715 __isl_keep id_to_ast_expr *id2expr,
3716 int (*fn)(__isl_take isl_id *key,
3717 __isl_take isl_ast_expr *val, void *user),
3720 They can be modified using the following function.
3722 #include <isl/id_to_ast_expr.h>
3723 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3724 __isl_take id_to_ast_expr *id2expr,
3725 __isl_take isl_id *key,
3726 __isl_take isl_ast_expr *val);
3727 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
3728 __isl_take id_to_ast_expr *id2expr,
3729 __isl_take isl_id *key);
3731 Associative arrays can be printed using the following function.
3733 #include <isl/id_to_ast_expr.h>
3734 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3735 __isl_take isl_printer *p,
3736 __isl_keep id_to_ast_expr *id2expr);
3738 =head2 Multiple Values
3740 An C<isl_multi_val> object represents a sequence of zero or more values,
3741 living in a set space.
3743 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3744 using the following function
3746 #include <isl/val.h>
3747 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3748 __isl_take isl_space *space,
3749 __isl_take isl_val_list *list);
3751 The zero multiple value (with value zero for each set dimension)
3752 can be created using the following function.
3754 #include <isl/val.h>
3755 __isl_give isl_multi_val *isl_multi_val_zero(
3756 __isl_take isl_space *space);
3758 Multiple values can be copied and freed using
3760 #include <isl/val.h>
3761 __isl_give isl_multi_val *isl_multi_val_copy(
3762 __isl_keep isl_multi_val *mv);
3763 __isl_null isl_multi_val *isl_multi_val_free(
3764 __isl_take isl_multi_val *mv);
3766 They can be inspected using
3768 #include <isl/val.h>
3769 isl_ctx *isl_multi_val_get_ctx(
3770 __isl_keep isl_multi_val *mv);
3771 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3772 enum isl_dim_type type);
3773 __isl_give isl_val *isl_multi_val_get_val(
3774 __isl_keep isl_multi_val *mv, int pos);
3775 int isl_multi_val_find_dim_by_id(
3776 __isl_keep isl_multi_val *mv,
3777 enum isl_dim_type type, __isl_keep isl_id *id);
3778 __isl_give isl_id *isl_multi_val_get_dim_id(
3779 __isl_keep isl_multi_val *mv,
3780 enum isl_dim_type type, unsigned pos);
3781 const char *isl_multi_val_get_tuple_name(
3782 __isl_keep isl_multi_val *mv,
3783 enum isl_dim_type type);
3784 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3785 enum isl_dim_type type);
3786 __isl_give isl_id *isl_multi_val_get_tuple_id(
3787 __isl_keep isl_multi_val *mv,
3788 enum isl_dim_type type);
3789 int isl_multi_val_range_is_wrapping(
3790 __isl_keep isl_multi_val *mv);
3792 They can be modified using
3794 #include <isl/val.h>
3795 __isl_give isl_multi_val *isl_multi_val_set_val(
3796 __isl_take isl_multi_val *mv, int pos,
3797 __isl_take isl_val *val);
3798 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3799 __isl_take isl_multi_val *mv,
3800 enum isl_dim_type type, unsigned pos, const char *s);
3801 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3802 __isl_take isl_multi_val *mv,
3803 enum isl_dim_type type, unsigned pos,
3804 __isl_take isl_id *id);
3805 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3806 __isl_take isl_multi_val *mv,
3807 enum isl_dim_type type, const char *s);
3808 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3809 __isl_take isl_multi_val *mv,
3810 enum isl_dim_type type, __isl_take isl_id *id);
3811 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3812 __isl_take isl_multi_val *mv,
3813 enum isl_dim_type type);
3814 __isl_give isl_multi_val *isl_multi_val_reset_user(
3815 __isl_take isl_multi_val *mv);
3817 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3818 __isl_take isl_multi_val *mv,
3819 enum isl_dim_type type, unsigned first, unsigned n);
3820 __isl_give isl_multi_val *isl_multi_val_add_dims(
3821 __isl_take isl_multi_val *mv,
3822 enum isl_dim_type type, unsigned n);
3823 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3824 __isl_take isl_multi_val *mv,
3825 enum isl_dim_type type, unsigned first, unsigned n);
3829 #include <isl/val.h>
3830 __isl_give isl_multi_val *isl_multi_val_align_params(
3831 __isl_take isl_multi_val *mv,
3832 __isl_take isl_space *model);
3833 __isl_give isl_multi_val *isl_multi_val_from_range(
3834 __isl_take isl_multi_val *mv);
3835 __isl_give isl_multi_val *isl_multi_val_range_splice(
3836 __isl_take isl_multi_val *mv1, unsigned pos,
3837 __isl_take isl_multi_val *mv2);
3838 __isl_give isl_multi_val *isl_multi_val_range_product(
3839 __isl_take isl_multi_val *mv1,
3840 __isl_take isl_multi_val *mv2);
3841 __isl_give isl_multi_val *
3842 isl_multi_val_range_factor_domain(
3843 __isl_take isl_multi_val *mv);
3844 __isl_give isl_multi_val *
3845 isl_multi_val_range_factor_range(
3846 __isl_take isl_multi_val *mv);
3847 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3848 __isl_take isl_multi_val *mv1,
3849 __isl_take isl_multi_aff *mv2);
3850 __isl_give isl_multi_val *isl_multi_val_product(
3851 __isl_take isl_multi_val *mv1,
3852 __isl_take isl_multi_val *mv2);
3853 __isl_give isl_multi_val *isl_multi_val_add_val(
3854 __isl_take isl_multi_val *mv,
3855 __isl_take isl_val *v);
3856 __isl_give isl_multi_val *isl_multi_val_mod_val(
3857 __isl_take isl_multi_val *mv,
3858 __isl_take isl_val *v);
3859 __isl_give isl_multi_val *isl_multi_val_scale_val(
3860 __isl_take isl_multi_val *mv,
3861 __isl_take isl_val *v);
3862 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3863 __isl_take isl_multi_val *mv1,
3864 __isl_take isl_multi_val *mv2);
3865 __isl_give isl_multi_val *
3866 isl_multi_val_scale_down_multi_val(
3867 __isl_take isl_multi_val *mv1,
3868 __isl_take isl_multi_val *mv2);
3870 A multiple value can be printed using
3872 __isl_give isl_printer *isl_printer_print_multi_val(
3873 __isl_take isl_printer *p,
3874 __isl_keep isl_multi_val *mv);
3878 Vectors can be created, copied and freed using the following functions.
3880 #include <isl/vec.h>
3881 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3883 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3884 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
3886 Note that the elements of a newly created vector may have arbitrary values.
3887 The elements can be changed and inspected using the following functions.
3889 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3890 int isl_vec_size(__isl_keep isl_vec *vec);
3891 __isl_give isl_val *isl_vec_get_element_val(
3892 __isl_keep isl_vec *vec, int pos);
3893 __isl_give isl_vec *isl_vec_set_element_si(
3894 __isl_take isl_vec *vec, int pos, int v);
3895 __isl_give isl_vec *isl_vec_set_element_val(
3896 __isl_take isl_vec *vec, int pos,
3897 __isl_take isl_val *v);
3898 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3900 __isl_give isl_vec *isl_vec_set_val(
3901 __isl_take isl_vec *vec, __isl_take isl_val *v);
3902 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3903 __isl_keep isl_vec *vec2, int pos);
3905 C<isl_vec_get_element> will return a negative value if anything went wrong.
3906 In that case, the value of C<*v> is undefined.
3908 The following function can be used to concatenate two vectors.
3910 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3911 __isl_take isl_vec *vec2);
3915 Matrices can be created, copied and freed using the following functions.
3917 #include <isl/mat.h>
3918 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3919 unsigned n_row, unsigned n_col);
3920 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3921 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
3923 Note that the elements of a newly created matrix may have arbitrary values.
3924 The elements can be changed and inspected using the following functions.
3926 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3927 int isl_mat_rows(__isl_keep isl_mat *mat);
3928 int isl_mat_cols(__isl_keep isl_mat *mat);
3929 __isl_give isl_val *isl_mat_get_element_val(
3930 __isl_keep isl_mat *mat, int row, int col);
3931 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3932 int row, int col, int v);
3933 __isl_give isl_mat *isl_mat_set_element_val(
3934 __isl_take isl_mat *mat, int row, int col,
3935 __isl_take isl_val *v);
3937 C<isl_mat_get_element> will return a negative value if anything went wrong.
3938 In that case, the value of C<*v> is undefined.
3940 The following function can be used to compute the (right) inverse
3941 of a matrix, i.e., a matrix such that the product of the original
3942 and the inverse (in that order) is a multiple of the identity matrix.
3943 The input matrix is assumed to be of full row-rank.
3945 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3947 The following function can be used to compute the (right) kernel
3948 (or null space) of a matrix, i.e., a matrix such that the product of
3949 the original and the kernel (in that order) is the zero matrix.
3951 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3953 =head2 Piecewise Quasi Affine Expressions
3955 The zero quasi affine expression or the quasi affine expression
3956 that is equal to a given value or
3957 a specified dimension on a given domain can be created using
3959 __isl_give isl_aff *isl_aff_zero_on_domain(
3960 __isl_take isl_local_space *ls);
3961 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3962 __isl_take isl_local_space *ls);
3963 __isl_give isl_aff *isl_aff_val_on_domain(
3964 __isl_take isl_local_space *ls,
3965 __isl_take isl_val *val);
3966 __isl_give isl_aff *isl_aff_var_on_domain(
3967 __isl_take isl_local_space *ls,
3968 enum isl_dim_type type, unsigned pos);
3969 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3970 __isl_take isl_local_space *ls,
3971 enum isl_dim_type type, unsigned pos);
3972 __isl_give isl_aff *isl_aff_nan_on_domain(
3973 __isl_take isl_local_space *ls);
3974 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3975 __isl_take isl_local_space *ls);
3977 Note that the space in which the resulting objects live is a map space
3978 with the given space as domain and a one-dimensional range.
3980 An empty piecewise quasi affine expression (one with no cells)
3981 or a piecewise quasi affine expression with a single cell can
3982 be created using the following functions.
3984 #include <isl/aff.h>
3985 __isl_give isl_pw_aff *isl_pw_aff_empty(
3986 __isl_take isl_space *space);
3987 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3988 __isl_take isl_set *set, __isl_take isl_aff *aff);
3989 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3990 __isl_take isl_aff *aff);
3992 A piecewise quasi affine expression that is equal to 1 on a set
3993 and 0 outside the set can be created using the following function.
3995 #include <isl/aff.h>
3996 __isl_give isl_pw_aff *isl_set_indicator_function(
3997 __isl_take isl_set *set);
3999 Quasi affine expressions can be copied and freed using
4001 #include <isl/aff.h>
4002 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
4003 __isl_null isl_aff *isl_aff_free(__isl_take isl_aff *aff);
4005 __isl_give isl_pw_aff *isl_pw_aff_copy(
4006 __isl_keep isl_pw_aff *pwaff);
4007 __isl_null isl_pw_aff *isl_pw_aff_free(
4008 __isl_take isl_pw_aff *pwaff);
4010 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
4011 using the following function. The constraint is required to have
4012 a non-zero coefficient for the specified dimension.
4014 #include <isl/constraint.h>
4015 __isl_give isl_aff *isl_constraint_get_bound(
4016 __isl_keep isl_constraint *constraint,
4017 enum isl_dim_type type, int pos);
4019 The entire affine expression of the constraint can also be extracted
4020 using the following function.
4022 #include <isl/constraint.h>
4023 __isl_give isl_aff *isl_constraint_get_aff(
4024 __isl_keep isl_constraint *constraint);
4026 Conversely, an equality constraint equating
4027 the affine expression to zero or an inequality constraint enforcing
4028 the affine expression to be non-negative, can be constructed using
4030 __isl_give isl_constraint *isl_equality_from_aff(
4031 __isl_take isl_aff *aff);
4032 __isl_give isl_constraint *isl_inequality_from_aff(
4033 __isl_take isl_aff *aff);
4035 The expression can be inspected using
4037 #include <isl/aff.h>
4038 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
4039 int isl_aff_dim(__isl_keep isl_aff *aff,
4040 enum isl_dim_type type);
4041 __isl_give isl_local_space *isl_aff_get_domain_local_space(
4042 __isl_keep isl_aff *aff);
4043 __isl_give isl_local_space *isl_aff_get_local_space(
4044 __isl_keep isl_aff *aff);
4045 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
4046 enum isl_dim_type type, unsigned pos);
4047 const char *isl_pw_aff_get_dim_name(
4048 __isl_keep isl_pw_aff *pa,
4049 enum isl_dim_type type, unsigned pos);
4050 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
4051 enum isl_dim_type type, unsigned pos);
4052 __isl_give isl_id *isl_pw_aff_get_dim_id(
4053 __isl_keep isl_pw_aff *pa,
4054 enum isl_dim_type type, unsigned pos);
4055 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
4056 enum isl_dim_type type);
4057 __isl_give isl_id *isl_pw_aff_get_tuple_id(
4058 __isl_keep isl_pw_aff *pa,
4059 enum isl_dim_type type);
4060 __isl_give isl_val *isl_aff_get_constant_val(
4061 __isl_keep isl_aff *aff);
4062 __isl_give isl_val *isl_aff_get_coefficient_val(
4063 __isl_keep isl_aff *aff,
4064 enum isl_dim_type type, int pos);
4065 __isl_give isl_val *isl_aff_get_denominator_val(
4066 __isl_keep isl_aff *aff);
4067 __isl_give isl_aff *isl_aff_get_div(
4068 __isl_keep isl_aff *aff, int pos);
4070 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
4071 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
4072 int (*fn)(__isl_take isl_set *set,
4073 __isl_take isl_aff *aff,
4074 void *user), void *user);
4076 int isl_aff_is_cst(__isl_keep isl_aff *aff);
4077 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4079 int isl_aff_is_nan(__isl_keep isl_aff *aff);
4080 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
4082 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
4083 enum isl_dim_type type, unsigned first, unsigned n);
4084 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
4085 enum isl_dim_type type, unsigned first, unsigned n);
4087 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
4088 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
4089 enum isl_dim_type type);
4090 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
4092 It can be modified using
4094 #include <isl/aff.h>
4095 __isl_give isl_aff *isl_aff_set_tuple_id(
4096 __isl_take isl_aff *aff,
4097 enum isl_dim_type type, __isl_take isl_id *id);
4098 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
4099 __isl_take isl_pw_aff *pwaff,
4100 enum isl_dim_type type, __isl_take isl_id *id);
4101 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
4102 __isl_take isl_pw_aff *pa,
4103 enum isl_dim_type type);
4104 __isl_give isl_aff *isl_aff_set_dim_name(
4105 __isl_take isl_aff *aff, enum isl_dim_type type,
4106 unsigned pos, const char *s);
4107 __isl_give isl_aff *isl_aff_set_dim_id(
4108 __isl_take isl_aff *aff, enum isl_dim_type type,
4109 unsigned pos, __isl_take isl_id *id);
4110 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
4111 __isl_take isl_pw_aff *pma,
4112 enum isl_dim_type type, unsigned pos,
4113 __isl_take isl_id *id);
4114 __isl_give isl_aff *isl_aff_set_constant_si(
4115 __isl_take isl_aff *aff, int v);
4116 __isl_give isl_aff *isl_aff_set_constant_val(
4117 __isl_take isl_aff *aff, __isl_take isl_val *v);
4118 __isl_give isl_aff *isl_aff_set_coefficient_si(
4119 __isl_take isl_aff *aff,
4120 enum isl_dim_type type, int pos, int v);
4121 __isl_give isl_aff *isl_aff_set_coefficient_val(
4122 __isl_take isl_aff *aff,
4123 enum isl_dim_type type, int pos,
4124 __isl_take isl_val *v);
4126 __isl_give isl_aff *isl_aff_add_constant_si(
4127 __isl_take isl_aff *aff, int v);
4128 __isl_give isl_aff *isl_aff_add_constant_val(
4129 __isl_take isl_aff *aff, __isl_take isl_val *v);
4130 __isl_give isl_aff *isl_aff_add_constant_num_si(
4131 __isl_take isl_aff *aff, int v);
4132 __isl_give isl_aff *isl_aff_add_coefficient_si(
4133 __isl_take isl_aff *aff,
4134 enum isl_dim_type type, int pos, int v);
4135 __isl_give isl_aff *isl_aff_add_coefficient_val(
4136 __isl_take isl_aff *aff,
4137 enum isl_dim_type type, int pos,
4138 __isl_take isl_val *v);
4140 __isl_give isl_aff *isl_aff_insert_dims(
4141 __isl_take isl_aff *aff,
4142 enum isl_dim_type type, unsigned first, unsigned n);
4143 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
4144 __isl_take isl_pw_aff *pwaff,
4145 enum isl_dim_type type, unsigned first, unsigned n);
4146 __isl_give isl_aff *isl_aff_add_dims(
4147 __isl_take isl_aff *aff,
4148 enum isl_dim_type type, unsigned n);
4149 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
4150 __isl_take isl_pw_aff *pwaff,
4151 enum isl_dim_type type, unsigned n);
4152 __isl_give isl_aff *isl_aff_drop_dims(
4153 __isl_take isl_aff *aff,
4154 enum isl_dim_type type, unsigned first, unsigned n);
4155 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
4156 __isl_take isl_pw_aff *pwaff,
4157 enum isl_dim_type type, unsigned first, unsigned n);
4158 __isl_give isl_aff *isl_aff_move_dims(
4159 __isl_take isl_aff *aff,
4160 enum isl_dim_type dst_type, unsigned dst_pos,
4161 enum isl_dim_type src_type, unsigned src_pos,
4163 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
4164 __isl_take isl_pw_aff *pa,
4165 enum isl_dim_type dst_type, unsigned dst_pos,
4166 enum isl_dim_type src_type, unsigned src_pos,
4169 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
4170 set the I<numerator> of the constant or coefficient, while
4171 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
4172 the constant or coefficient as a whole.
4173 The C<add_constant> and C<add_coefficient> functions add an integer
4174 or rational value to
4175 the possibly rational constant or coefficient.
4176 The C<add_constant_num> functions add an integer value to
4179 To check whether an affine expressions is obviously zero
4180 or (obviously) equal to some other affine expression, use
4182 #include <isl/aff.h>
4183 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
4184 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
4185 __isl_keep isl_aff *aff2);
4186 int isl_pw_aff_plain_is_equal(
4187 __isl_keep isl_pw_aff *pwaff1,
4188 __isl_keep isl_pw_aff *pwaff2);
4189 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
4190 __isl_keep isl_pw_aff *pa2);
4191 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4192 __isl_keep isl_pw_aff *pa2);
4194 The function C<isl_pw_aff_plain_cmp> can be used to sort
4195 C<isl_pw_aff>s. The order is not strictly defined.
4196 The current order sorts expressions that only involve
4197 earlier dimensions before those that involve later dimensions.
4201 #include <isl/aff.h>
4202 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
4203 __isl_take isl_aff *aff2);
4204 __isl_give isl_pw_aff *isl_pw_aff_add(
4205 __isl_take isl_pw_aff *pwaff1,
4206 __isl_take isl_pw_aff *pwaff2);
4207 __isl_give isl_pw_aff *isl_pw_aff_min(
4208 __isl_take isl_pw_aff *pwaff1,
4209 __isl_take isl_pw_aff *pwaff2);
4210 __isl_give isl_pw_aff *isl_pw_aff_max(
4211 __isl_take isl_pw_aff *pwaff1,
4212 __isl_take isl_pw_aff *pwaff2);
4213 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
4214 __isl_take isl_aff *aff2);
4215 __isl_give isl_pw_aff *isl_pw_aff_sub(
4216 __isl_take isl_pw_aff *pwaff1,
4217 __isl_take isl_pw_aff *pwaff2);
4218 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
4219 __isl_give isl_pw_aff *isl_pw_aff_neg(
4220 __isl_take isl_pw_aff *pwaff);
4221 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
4222 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4223 __isl_take isl_pw_aff *pwaff);
4224 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
4225 __isl_give isl_pw_aff *isl_pw_aff_floor(
4226 __isl_take isl_pw_aff *pwaff);
4227 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
4228 __isl_take isl_val *mod);
4229 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
4230 __isl_take isl_pw_aff *pa,
4231 __isl_take isl_val *mod);
4232 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
4233 __isl_take isl_val *v);
4234 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
4235 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
4236 __isl_give isl_aff *isl_aff_scale_down_ui(
4237 __isl_take isl_aff *aff, unsigned f);
4238 __isl_give isl_aff *isl_aff_scale_down_val(
4239 __isl_take isl_aff *aff, __isl_take isl_val *v);
4240 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
4241 __isl_take isl_pw_aff *pa,
4242 __isl_take isl_val *f);
4244 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4245 __isl_take isl_pw_aff_list *list);
4246 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4247 __isl_take isl_pw_aff_list *list);
4249 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4250 __isl_take isl_pw_aff *pwqp);
4252 __isl_give isl_aff *isl_aff_align_params(
4253 __isl_take isl_aff *aff,
4254 __isl_take isl_space *model);
4255 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4256 __isl_take isl_pw_aff *pwaff,
4257 __isl_take isl_space *model);
4259 __isl_give isl_aff *isl_aff_project_domain_on_params(
4260 __isl_take isl_aff *aff);
4261 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4262 __isl_take isl_pw_aff *pwa);
4264 __isl_give isl_aff *isl_aff_gist_params(
4265 __isl_take isl_aff *aff,
4266 __isl_take isl_set *context);
4267 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
4268 __isl_take isl_set *context);
4269 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
4270 __isl_take isl_pw_aff *pwaff,
4271 __isl_take isl_set *context);
4272 __isl_give isl_pw_aff *isl_pw_aff_gist(
4273 __isl_take isl_pw_aff *pwaff,
4274 __isl_take isl_set *context);
4276 __isl_give isl_set *isl_pw_aff_domain(
4277 __isl_take isl_pw_aff *pwaff);
4278 __isl_give isl_set *isl_pw_aff_params(
4279 __isl_take isl_pw_aff *pwa);
4280 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4281 __isl_take isl_pw_aff *pa,
4282 __isl_take isl_set *set);
4283 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4284 __isl_take isl_pw_aff *pa,
4285 __isl_take isl_set *set);
4287 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
4288 __isl_take isl_aff *aff2);
4289 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
4290 __isl_take isl_aff *aff2);
4291 __isl_give isl_pw_aff *isl_pw_aff_mul(
4292 __isl_take isl_pw_aff *pwaff1,
4293 __isl_take isl_pw_aff *pwaff2);
4294 __isl_give isl_pw_aff *isl_pw_aff_div(
4295 __isl_take isl_pw_aff *pa1,
4296 __isl_take isl_pw_aff *pa2);
4297 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
4298 __isl_take isl_pw_aff *pa1,
4299 __isl_take isl_pw_aff *pa2);
4300 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
4301 __isl_take isl_pw_aff *pa1,
4302 __isl_take isl_pw_aff *pa2);
4304 When multiplying two affine expressions, at least one of the two needs
4305 to be a constant. Similarly, when dividing an affine expression by another,
4306 the second expression needs to be a constant.
4307 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
4308 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
4311 #include <isl/aff.h>
4312 __isl_give isl_aff *isl_aff_pullback_aff(
4313 __isl_take isl_aff *aff1,
4314 __isl_take isl_aff *aff2);
4315 __isl_give isl_aff *isl_aff_pullback_multi_aff(
4316 __isl_take isl_aff *aff,
4317 __isl_take isl_multi_aff *ma);
4318 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
4319 __isl_take isl_pw_aff *pa,
4320 __isl_take isl_multi_aff *ma);
4321 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
4322 __isl_take isl_pw_aff *pa,
4323 __isl_take isl_pw_multi_aff *pma);
4324 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
4325 __isl_take isl_pw_aff *pa,
4326 __isl_take isl_multi_pw_aff *mpa);
4328 These functions precompose the input expression by the given
4329 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
4330 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
4331 into the (piecewise) affine expression.
4332 Objects of type C<isl_multi_aff> are described in
4333 L</"Piecewise Multiple Quasi Affine Expressions">.
4335 #include <isl/aff.h>
4336 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4337 __isl_take isl_aff *aff);
4338 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4339 __isl_take isl_aff *aff);
4340 __isl_give isl_basic_set *isl_aff_le_basic_set(
4341 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4342 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4343 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4344 __isl_give isl_set *isl_pw_aff_eq_set(
4345 __isl_take isl_pw_aff *pwaff1,
4346 __isl_take isl_pw_aff *pwaff2);
4347 __isl_give isl_set *isl_pw_aff_ne_set(
4348 __isl_take isl_pw_aff *pwaff1,
4349 __isl_take isl_pw_aff *pwaff2);
4350 __isl_give isl_set *isl_pw_aff_le_set(
4351 __isl_take isl_pw_aff *pwaff1,
4352 __isl_take isl_pw_aff *pwaff2);
4353 __isl_give isl_set *isl_pw_aff_lt_set(
4354 __isl_take isl_pw_aff *pwaff1,
4355 __isl_take isl_pw_aff *pwaff2);
4356 __isl_give isl_set *isl_pw_aff_ge_set(
4357 __isl_take isl_pw_aff *pwaff1,
4358 __isl_take isl_pw_aff *pwaff2);
4359 __isl_give isl_set *isl_pw_aff_gt_set(
4360 __isl_take isl_pw_aff *pwaff1,
4361 __isl_take isl_pw_aff *pwaff2);
4363 __isl_give isl_set *isl_pw_aff_list_eq_set(
4364 __isl_take isl_pw_aff_list *list1,
4365 __isl_take isl_pw_aff_list *list2);
4366 __isl_give isl_set *isl_pw_aff_list_ne_set(
4367 __isl_take isl_pw_aff_list *list1,
4368 __isl_take isl_pw_aff_list *list2);
4369 __isl_give isl_set *isl_pw_aff_list_le_set(
4370 __isl_take isl_pw_aff_list *list1,
4371 __isl_take isl_pw_aff_list *list2);
4372 __isl_give isl_set *isl_pw_aff_list_lt_set(
4373 __isl_take isl_pw_aff_list *list1,
4374 __isl_take isl_pw_aff_list *list2);
4375 __isl_give isl_set *isl_pw_aff_list_ge_set(
4376 __isl_take isl_pw_aff_list *list1,
4377 __isl_take isl_pw_aff_list *list2);
4378 __isl_give isl_set *isl_pw_aff_list_gt_set(
4379 __isl_take isl_pw_aff_list *list1,
4380 __isl_take isl_pw_aff_list *list2);
4382 The function C<isl_aff_neg_basic_set> returns a basic set
4383 containing those elements in the domain space
4384 of C<aff> where C<aff> is negative.
4385 The function C<isl_aff_ge_basic_set> returns a basic set
4386 containing those elements in the shared space
4387 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4388 The function C<isl_pw_aff_ge_set> returns a set
4389 containing those elements in the shared domain
4390 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4391 The functions operating on C<isl_pw_aff_list> apply the corresponding
4392 C<isl_pw_aff> function to each pair of elements in the two lists.
4394 #include <isl/aff.h>
4395 __isl_give isl_set *isl_pw_aff_nonneg_set(
4396 __isl_take isl_pw_aff *pwaff);
4397 __isl_give isl_set *isl_pw_aff_zero_set(
4398 __isl_take isl_pw_aff *pwaff);
4399 __isl_give isl_set *isl_pw_aff_non_zero_set(
4400 __isl_take isl_pw_aff *pwaff);
4402 The function C<isl_pw_aff_nonneg_set> returns a set
4403 containing those elements in the domain
4404 of C<pwaff> where C<pwaff> is non-negative.
4406 #include <isl/aff.h>
4407 __isl_give isl_pw_aff *isl_pw_aff_cond(
4408 __isl_take isl_pw_aff *cond,
4409 __isl_take isl_pw_aff *pwaff_true,
4410 __isl_take isl_pw_aff *pwaff_false);
4412 The function C<isl_pw_aff_cond> performs a conditional operator
4413 and returns an expression that is equal to C<pwaff_true>
4414 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4415 where C<cond> is zero.
4417 #include <isl/aff.h>
4418 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4419 __isl_take isl_pw_aff *pwaff1,
4420 __isl_take isl_pw_aff *pwaff2);
4421 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4422 __isl_take isl_pw_aff *pwaff1,
4423 __isl_take isl_pw_aff *pwaff2);
4424 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4425 __isl_take isl_pw_aff *pwaff1,
4426 __isl_take isl_pw_aff *pwaff2);
4428 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4429 expression with a domain that is the union of those of C<pwaff1> and
4430 C<pwaff2> and such that on each cell, the quasi-affine expression is
4431 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4432 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4433 associated expression is the defined one.
4435 An expression can be read from input using
4437 #include <isl/aff.h>
4438 __isl_give isl_aff *isl_aff_read_from_str(
4439 isl_ctx *ctx, const char *str);
4440 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4441 isl_ctx *ctx, const char *str);
4443 An expression can be printed using
4445 #include <isl/aff.h>
4446 __isl_give isl_printer *isl_printer_print_aff(
4447 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4449 __isl_give isl_printer *isl_printer_print_pw_aff(
4450 __isl_take isl_printer *p,
4451 __isl_keep isl_pw_aff *pwaff);
4453 =head2 Piecewise Multiple Quasi Affine Expressions
4455 An C<isl_multi_aff> object represents a sequence of
4456 zero or more affine expressions, all defined on the same domain space.
4457 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4458 zero or more piecewise affine expressions.
4460 An C<isl_multi_aff> can be constructed from a single
4461 C<isl_aff> or an C<isl_aff_list> using the
4462 following functions. Similarly for C<isl_multi_pw_aff>
4463 and C<isl_pw_multi_aff>.
4465 #include <isl/aff.h>
4466 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4467 __isl_take isl_aff *aff);
4468 __isl_give isl_multi_pw_aff *
4469 isl_multi_pw_aff_from_multi_aff(
4470 __isl_take isl_multi_aff *ma);
4471 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4472 __isl_take isl_pw_aff *pa);
4473 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4474 __isl_take isl_pw_aff *pa);
4475 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4476 __isl_take isl_space *space,
4477 __isl_take isl_aff_list *list);
4479 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4480 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4481 Note however that the domain
4482 of the result is the intersection of the domains of the input.
4483 The reverse conversion is exact.
4485 #include <isl/aff.h>
4486 __isl_give isl_pw_multi_aff *
4487 isl_pw_multi_aff_from_multi_pw_aff(
4488 __isl_take isl_multi_pw_aff *mpa);
4489 __isl_give isl_multi_pw_aff *
4490 isl_multi_pw_aff_from_pw_multi_aff(
4491 __isl_take isl_pw_multi_aff *pma);
4493 An empty piecewise multiple quasi affine expression (one with no cells),
4494 the zero piecewise multiple quasi affine expression (with value zero
4495 for each output dimension),
4496 a piecewise multiple quasi affine expression with a single cell (with
4497 either a universe or a specified domain) or
4498 a zero-dimensional piecewise multiple quasi affine expression
4500 can be created using the following functions.
4502 #include <isl/aff.h>
4503 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4504 __isl_take isl_space *space);
4505 __isl_give isl_multi_aff *isl_multi_aff_zero(
4506 __isl_take isl_space *space);
4507 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4508 __isl_take isl_space *space);
4509 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4510 __isl_take isl_space *space);
4511 __isl_give isl_multi_aff *isl_multi_aff_identity(
4512 __isl_take isl_space *space);
4513 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4514 __isl_take isl_space *space);
4515 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4516 __isl_take isl_space *space);
4517 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4518 __isl_take isl_space *space);
4519 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4520 __isl_take isl_space *space);
4521 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4522 __isl_take isl_space *space,
4523 enum isl_dim_type type,
4524 unsigned first, unsigned n);
4525 __isl_give isl_pw_multi_aff *
4526 isl_pw_multi_aff_project_out_map(
4527 __isl_take isl_space *space,
4528 enum isl_dim_type type,
4529 unsigned first, unsigned n);
4530 __isl_give isl_pw_multi_aff *
4531 isl_pw_multi_aff_from_multi_aff(
4532 __isl_take isl_multi_aff *ma);
4533 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4534 __isl_take isl_set *set,
4535 __isl_take isl_multi_aff *maff);
4536 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4537 __isl_take isl_set *set);
4539 __isl_give isl_union_pw_multi_aff *
4540 isl_union_pw_multi_aff_empty(
4541 __isl_take isl_space *space);
4542 __isl_give isl_union_pw_multi_aff *
4543 isl_union_pw_multi_aff_add_pw_multi_aff(
4544 __isl_take isl_union_pw_multi_aff *upma,
4545 __isl_take isl_pw_multi_aff *pma);
4546 __isl_give isl_union_pw_multi_aff *
4547 isl_union_pw_multi_aff_from_domain(
4548 __isl_take isl_union_set *uset);
4550 A piecewise multiple quasi affine expression can also be initialized
4551 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4552 and the C<isl_map> is single-valued.
4553 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4554 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4556 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4557 __isl_take isl_set *set);
4558 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4559 __isl_take isl_map *map);
4561 __isl_give isl_union_pw_multi_aff *
4562 isl_union_pw_multi_aff_from_union_set(
4563 __isl_take isl_union_set *uset);
4564 __isl_give isl_union_pw_multi_aff *
4565 isl_union_pw_multi_aff_from_union_map(
4566 __isl_take isl_union_map *umap);
4568 Multiple quasi affine expressions can be copied and freed using
4570 #include <isl/aff.h>
4571 __isl_give isl_multi_aff *isl_multi_aff_copy(
4572 __isl_keep isl_multi_aff *maff);
4573 __isl_null isl_multi_aff *isl_multi_aff_free(
4574 __isl_take isl_multi_aff *maff);
4576 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4577 __isl_keep isl_pw_multi_aff *pma);
4578 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
4579 __isl_take isl_pw_multi_aff *pma);
4581 __isl_give isl_union_pw_multi_aff *
4582 isl_union_pw_multi_aff_copy(
4583 __isl_keep isl_union_pw_multi_aff *upma);
4584 __isl_null isl_union_pw_multi_aff *
4585 isl_union_pw_multi_aff_free(
4586 __isl_take isl_union_pw_multi_aff *upma);
4588 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4589 __isl_keep isl_multi_pw_aff *mpa);
4590 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
4591 __isl_take isl_multi_pw_aff *mpa);
4593 The expression can be inspected using
4595 #include <isl/aff.h>
4596 isl_ctx *isl_multi_aff_get_ctx(
4597 __isl_keep isl_multi_aff *maff);
4598 isl_ctx *isl_pw_multi_aff_get_ctx(
4599 __isl_keep isl_pw_multi_aff *pma);
4600 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4601 __isl_keep isl_union_pw_multi_aff *upma);
4602 isl_ctx *isl_multi_pw_aff_get_ctx(
4603 __isl_keep isl_multi_pw_aff *mpa);
4605 int isl_multi_aff_involves_dims(
4606 __isl_keep isl_multi_aff *ma,
4607 enum isl_dim_type type, unsigned first, unsigned n);
4608 int isl_multi_pw_aff_involves_dims(
4609 __isl_keep isl_multi_pw_aff *mpa,
4610 enum isl_dim_type type, unsigned first, unsigned n);
4612 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4613 enum isl_dim_type type);
4614 unsigned isl_pw_multi_aff_dim(
4615 __isl_keep isl_pw_multi_aff *pma,
4616 enum isl_dim_type type);
4617 unsigned isl_multi_pw_aff_dim(
4618 __isl_keep isl_multi_pw_aff *mpa,
4619 enum isl_dim_type type);
4620 __isl_give isl_aff *isl_multi_aff_get_aff(
4621 __isl_keep isl_multi_aff *multi, int pos);
4622 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4623 __isl_keep isl_pw_multi_aff *pma, int pos);
4624 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4625 __isl_keep isl_multi_pw_aff *mpa, int pos);
4626 int isl_multi_aff_find_dim_by_id(
4627 __isl_keep isl_multi_aff *ma,
4628 enum isl_dim_type type, __isl_keep isl_id *id);
4629 int isl_multi_pw_aff_find_dim_by_id(
4630 __isl_keep isl_multi_pw_aff *mpa,
4631 enum isl_dim_type type, __isl_keep isl_id *id);
4632 const char *isl_pw_multi_aff_get_dim_name(
4633 __isl_keep isl_pw_multi_aff *pma,
4634 enum isl_dim_type type, unsigned pos);
4635 __isl_give isl_id *isl_multi_aff_get_dim_id(
4636 __isl_keep isl_multi_aff *ma,
4637 enum isl_dim_type type, unsigned pos);
4638 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4639 __isl_keep isl_pw_multi_aff *pma,
4640 enum isl_dim_type type, unsigned pos);
4641 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4642 __isl_keep isl_multi_pw_aff *mpa,
4643 enum isl_dim_type type, unsigned pos);
4644 const char *isl_multi_aff_get_tuple_name(
4645 __isl_keep isl_multi_aff *multi,
4646 enum isl_dim_type type);
4647 int isl_pw_multi_aff_has_tuple_name(
4648 __isl_keep isl_pw_multi_aff *pma,
4649 enum isl_dim_type type);
4650 const char *isl_pw_multi_aff_get_tuple_name(
4651 __isl_keep isl_pw_multi_aff *pma,
4652 enum isl_dim_type type);
4653 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4654 enum isl_dim_type type);
4655 int isl_pw_multi_aff_has_tuple_id(
4656 __isl_keep isl_pw_multi_aff *pma,
4657 enum isl_dim_type type);
4658 int isl_multi_pw_aff_has_tuple_id(
4659 __isl_keep isl_multi_pw_aff *mpa,
4660 enum isl_dim_type type);
4661 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4662 __isl_keep isl_multi_aff *ma,
4663 enum isl_dim_type type);
4664 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4665 __isl_keep isl_pw_multi_aff *pma,
4666 enum isl_dim_type type);
4667 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4668 __isl_keep isl_multi_pw_aff *mpa,
4669 enum isl_dim_type type);
4670 int isl_multi_aff_range_is_wrapping(
4671 __isl_keep isl_multi_aff *ma);
4672 int isl_multi_pw_aff_range_is_wrapping(
4673 __isl_keep isl_multi_pw_aff *mpa);
4675 int isl_pw_multi_aff_foreach_piece(
4676 __isl_keep isl_pw_multi_aff *pma,
4677 int (*fn)(__isl_take isl_set *set,
4678 __isl_take isl_multi_aff *maff,
4679 void *user), void *user);
4681 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4682 __isl_keep isl_union_pw_multi_aff *upma,
4683 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4684 void *user), void *user);
4686 It can be modified using
4688 #include <isl/aff.h>
4689 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4690 __isl_take isl_multi_aff *multi, int pos,
4691 __isl_take isl_aff *aff);
4692 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4693 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4694 __isl_take isl_pw_aff *pa);
4695 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4696 __isl_take isl_multi_aff *maff,
4697 enum isl_dim_type type, unsigned pos, const char *s);
4698 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4699 __isl_take isl_multi_aff *maff,
4700 enum isl_dim_type type, unsigned pos,
4701 __isl_take isl_id *id);
4702 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4703 __isl_take isl_multi_aff *maff,
4704 enum isl_dim_type type, const char *s);
4705 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4706 __isl_take isl_multi_aff *maff,
4707 enum isl_dim_type type, __isl_take isl_id *id);
4708 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4709 __isl_take isl_pw_multi_aff *pma,
4710 enum isl_dim_type type, __isl_take isl_id *id);
4711 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4712 __isl_take isl_multi_aff *ma,
4713 enum isl_dim_type type);
4714 __isl_give isl_multi_pw_aff *
4715 isl_multi_pw_aff_reset_tuple_id(
4716 __isl_take isl_multi_pw_aff *mpa,
4717 enum isl_dim_type type);
4718 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4719 __isl_take isl_multi_aff *ma);
4720 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4721 __isl_take isl_multi_pw_aff *mpa);
4723 __isl_give isl_multi_pw_aff *
4724 isl_multi_pw_aff_set_dim_name(
4725 __isl_take isl_multi_pw_aff *mpa,
4726 enum isl_dim_type type, unsigned pos, const char *s);
4727 __isl_give isl_multi_pw_aff *
4728 isl_multi_pw_aff_set_dim_id(
4729 __isl_take isl_multi_pw_aff *mpa,
4730 enum isl_dim_type type, unsigned pos,
4731 __isl_take isl_id *id);
4732 __isl_give isl_multi_pw_aff *
4733 isl_multi_pw_aff_set_tuple_name(
4734 __isl_take isl_multi_pw_aff *mpa,
4735 enum isl_dim_type type, const char *s);
4737 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4738 __isl_take isl_multi_aff *ma);
4740 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4741 __isl_take isl_multi_aff *ma,
4742 enum isl_dim_type type, unsigned first, unsigned n);
4743 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4744 __isl_take isl_multi_aff *ma,
4745 enum isl_dim_type type, unsigned n);
4746 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4747 __isl_take isl_multi_aff *maff,
4748 enum isl_dim_type type, unsigned first, unsigned n);
4749 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4750 __isl_take isl_pw_multi_aff *pma,
4751 enum isl_dim_type type, unsigned first, unsigned n);
4753 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4754 __isl_take isl_multi_pw_aff *mpa,
4755 enum isl_dim_type type, unsigned first, unsigned n);
4756 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4757 __isl_take isl_multi_pw_aff *mpa,
4758 enum isl_dim_type type, unsigned n);
4759 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4760 __isl_take isl_multi_pw_aff *pma,
4761 enum isl_dim_type dst_type, unsigned dst_pos,
4762 enum isl_dim_type src_type, unsigned src_pos,
4765 To check whether two multiple affine expressions are
4766 (obviously) equal to each other, use
4768 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4769 __isl_keep isl_multi_aff *maff2);
4770 int isl_pw_multi_aff_plain_is_equal(
4771 __isl_keep isl_pw_multi_aff *pma1,
4772 __isl_keep isl_pw_multi_aff *pma2);
4773 int isl_multi_pw_aff_plain_is_equal(
4774 __isl_keep isl_multi_pw_aff *mpa1,
4775 __isl_keep isl_multi_pw_aff *mpa2);
4776 int isl_multi_pw_aff_is_equal(
4777 __isl_keep isl_multi_pw_aff *mpa1,
4778 __isl_keep isl_multi_pw_aff *mpa2);
4782 #include <isl/aff.h>
4783 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4784 __isl_take isl_pw_multi_aff *pma1,
4785 __isl_take isl_pw_multi_aff *pma2);
4786 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4787 __isl_take isl_pw_multi_aff *pma1,
4788 __isl_take isl_pw_multi_aff *pma2);
4789 __isl_give isl_multi_aff *isl_multi_aff_floor(
4790 __isl_take isl_multi_aff *ma);
4791 __isl_give isl_multi_aff *isl_multi_aff_add(
4792 __isl_take isl_multi_aff *maff1,
4793 __isl_take isl_multi_aff *maff2);
4794 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4795 __isl_take isl_pw_multi_aff *pma1,
4796 __isl_take isl_pw_multi_aff *pma2);
4797 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4798 __isl_take isl_union_pw_multi_aff *upma1,
4799 __isl_take isl_union_pw_multi_aff *upma2);
4800 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4801 __isl_take isl_pw_multi_aff *pma1,
4802 __isl_take isl_pw_multi_aff *pma2);
4803 __isl_give isl_multi_aff *isl_multi_aff_sub(
4804 __isl_take isl_multi_aff *ma1,
4805 __isl_take isl_multi_aff *ma2);
4806 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4807 __isl_take isl_pw_multi_aff *pma1,
4808 __isl_take isl_pw_multi_aff *pma2);
4809 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4810 __isl_take isl_union_pw_multi_aff *upma1,
4811 __isl_take isl_union_pw_multi_aff *upma2);
4813 C<isl_multi_aff_sub> subtracts the second argument from the first.
4815 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4816 __isl_take isl_multi_aff *ma,
4817 __isl_take isl_val *v);
4818 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4819 __isl_take isl_pw_multi_aff *pma,
4820 __isl_take isl_val *v);
4821 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4822 __isl_take isl_multi_pw_aff *mpa,
4823 __isl_take isl_val *v);
4824 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4825 __isl_take isl_multi_aff *ma,
4826 __isl_take isl_multi_val *mv);
4827 __isl_give isl_pw_multi_aff *
4828 isl_pw_multi_aff_scale_multi_val(
4829 __isl_take isl_pw_multi_aff *pma,
4830 __isl_take isl_multi_val *mv);
4831 __isl_give isl_multi_pw_aff *
4832 isl_multi_pw_aff_scale_multi_val(
4833 __isl_take isl_multi_pw_aff *mpa,
4834 __isl_take isl_multi_val *mv);
4835 __isl_give isl_union_pw_multi_aff *
4836 isl_union_pw_multi_aff_scale_multi_val(
4837 __isl_take isl_union_pw_multi_aff *upma,
4838 __isl_take isl_multi_val *mv);
4839 __isl_give isl_multi_aff *
4840 isl_multi_aff_scale_down_multi_val(
4841 __isl_take isl_multi_aff *ma,
4842 __isl_take isl_multi_val *mv);
4843 __isl_give isl_multi_pw_aff *
4844 isl_multi_pw_aff_scale_down_multi_val(
4845 __isl_take isl_multi_pw_aff *mpa,
4846 __isl_take isl_multi_val *mv);
4848 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4849 by the corresponding elements of C<mv>.
4851 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4852 __isl_take isl_pw_multi_aff *pma,
4853 enum isl_dim_type type, unsigned pos, int value);
4854 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4855 __isl_take isl_pw_multi_aff *pma,
4856 __isl_take isl_set *set);
4857 __isl_give isl_set *isl_multi_pw_aff_domain(
4858 __isl_take isl_multi_pw_aff *mpa);
4859 __isl_give isl_multi_pw_aff *
4860 isl_multi_pw_aff_intersect_params(
4861 __isl_take isl_multi_pw_aff *mpa,
4862 __isl_take isl_set *set);
4863 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4864 __isl_take isl_pw_multi_aff *pma,
4865 __isl_take isl_set *set);
4866 __isl_give isl_multi_pw_aff *
4867 isl_multi_pw_aff_intersect_domain(
4868 __isl_take isl_multi_pw_aff *mpa,
4869 __isl_take isl_set *domain);
4870 __isl_give isl_union_pw_multi_aff *
4871 isl_union_pw_multi_aff_intersect_domain(
4872 __isl_take isl_union_pw_multi_aff *upma,
4873 __isl_take isl_union_set *uset);
4874 __isl_give isl_multi_aff *isl_multi_aff_lift(
4875 __isl_take isl_multi_aff *maff,
4876 __isl_give isl_local_space **ls);
4877 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4878 __isl_take isl_pw_multi_aff *pma);
4879 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4880 __isl_take isl_multi_pw_aff *mpa);
4881 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4882 __isl_take isl_multi_aff *multi,
4883 __isl_take isl_space *model);
4884 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4885 __isl_take isl_pw_multi_aff *pma,
4886 __isl_take isl_space *model);
4887 __isl_give isl_union_pw_multi_aff *
4888 isl_union_pw_multi_aff_align_params(
4889 __isl_take isl_union_pw_multi_aff *upma,
4890 __isl_take isl_space *model);
4891 __isl_give isl_pw_multi_aff *
4892 isl_pw_multi_aff_project_domain_on_params(
4893 __isl_take isl_pw_multi_aff *pma);
4894 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4895 __isl_take isl_multi_aff *maff,
4896 __isl_take isl_set *context);
4897 __isl_give isl_multi_aff *isl_multi_aff_gist(
4898 __isl_take isl_multi_aff *maff,
4899 __isl_take isl_set *context);
4900 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4901 __isl_take isl_pw_multi_aff *pma,
4902 __isl_take isl_set *set);
4903 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4904 __isl_take isl_pw_multi_aff *pma,
4905 __isl_take isl_set *set);
4906 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4907 __isl_take isl_multi_pw_aff *mpa,
4908 __isl_take isl_set *set);
4909 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4910 __isl_take isl_multi_pw_aff *mpa,
4911 __isl_take isl_set *set);
4912 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4913 __isl_take isl_multi_aff *ma);
4914 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4915 __isl_take isl_multi_pw_aff *mpa);
4916 __isl_give isl_set *isl_pw_multi_aff_domain(
4917 __isl_take isl_pw_multi_aff *pma);
4918 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4919 __isl_take isl_union_pw_multi_aff *upma);
4920 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4921 __isl_take isl_multi_aff *ma1, unsigned pos,
4922 __isl_take isl_multi_aff *ma2);
4923 __isl_give isl_multi_aff *isl_multi_aff_splice(
4924 __isl_take isl_multi_aff *ma1,
4925 unsigned in_pos, unsigned out_pos,
4926 __isl_take isl_multi_aff *ma2);
4927 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4928 __isl_take isl_multi_aff *ma1,
4929 __isl_take isl_multi_aff *ma2);
4930 __isl_give isl_multi_aff *
4931 isl_multi_aff_range_factor_domain(
4932 __isl_take isl_multi_aff *ma);
4933 __isl_give isl_multi_aff *
4934 isl_multi_aff_range_factor_range(
4935 __isl_take isl_multi_aff *ma);
4936 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4937 __isl_take isl_multi_aff *ma1,
4938 __isl_take isl_multi_aff *ma2);
4939 __isl_give isl_multi_aff *isl_multi_aff_product(
4940 __isl_take isl_multi_aff *ma1,
4941 __isl_take isl_multi_aff *ma2);
4942 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4943 __isl_take isl_multi_pw_aff *mpa1,
4944 __isl_take isl_multi_pw_aff *mpa2);
4945 __isl_give isl_pw_multi_aff *
4946 isl_pw_multi_aff_range_product(
4947 __isl_take isl_pw_multi_aff *pma1,
4948 __isl_take isl_pw_multi_aff *pma2);
4949 __isl_give isl_multi_pw_aff *
4950 isl_multi_pw_aff_range_factor_domain(
4951 __isl_take isl_multi_pw_aff *mpa);
4952 __isl_give isl_multi_pw_aff *
4953 isl_multi_pw_aff_range_factor_range(
4954 __isl_take isl_multi_pw_aff *mpa);
4955 __isl_give isl_pw_multi_aff *
4956 isl_pw_multi_aff_flat_range_product(
4957 __isl_take isl_pw_multi_aff *pma1,
4958 __isl_take isl_pw_multi_aff *pma2);
4959 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4960 __isl_take isl_pw_multi_aff *pma1,
4961 __isl_take isl_pw_multi_aff *pma2);
4962 __isl_give isl_union_pw_multi_aff *
4963 isl_union_pw_multi_aff_flat_range_product(
4964 __isl_take isl_union_pw_multi_aff *upma1,
4965 __isl_take isl_union_pw_multi_aff *upma2);
4966 __isl_give isl_multi_pw_aff *
4967 isl_multi_pw_aff_range_splice(
4968 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4969 __isl_take isl_multi_pw_aff *mpa2);
4970 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4971 __isl_take isl_multi_pw_aff *mpa1,
4972 unsigned in_pos, unsigned out_pos,
4973 __isl_take isl_multi_pw_aff *mpa2);
4974 __isl_give isl_multi_pw_aff *
4975 isl_multi_pw_aff_range_product(
4976 __isl_take isl_multi_pw_aff *mpa1,
4977 __isl_take isl_multi_pw_aff *mpa2);
4978 __isl_give isl_multi_pw_aff *
4979 isl_multi_pw_aff_flat_range_product(
4980 __isl_take isl_multi_pw_aff *mpa1,
4981 __isl_take isl_multi_pw_aff *mpa2);
4983 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4984 then it is assigned the local space that lies at the basis of
4985 the lifting applied.
4987 #include <isl/aff.h>
4988 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4989 __isl_take isl_multi_aff *ma1,
4990 __isl_take isl_multi_aff *ma2);
4991 __isl_give isl_pw_multi_aff *
4992 isl_pw_multi_aff_pullback_multi_aff(
4993 __isl_take isl_pw_multi_aff *pma,
4994 __isl_take isl_multi_aff *ma);
4995 __isl_give isl_multi_pw_aff *
4996 isl_multi_pw_aff_pullback_multi_aff(
4997 __isl_take isl_multi_pw_aff *mpa,
4998 __isl_take isl_multi_aff *ma);
4999 __isl_give isl_pw_multi_aff *
5000 isl_pw_multi_aff_pullback_pw_multi_aff(
5001 __isl_take isl_pw_multi_aff *pma1,
5002 __isl_take isl_pw_multi_aff *pma2);
5003 __isl_give isl_multi_pw_aff *
5004 isl_multi_pw_aff_pullback_pw_multi_aff(
5005 __isl_take isl_multi_pw_aff *mpa,
5006 __isl_take isl_pw_multi_aff *pma);
5007 __isl_give isl_multi_pw_aff *
5008 isl_multi_pw_aff_pullback_multi_pw_aff(
5009 __isl_take isl_multi_pw_aff *mpa1,
5010 __isl_take isl_multi_pw_aff *mpa2);
5012 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
5013 In other words, C<ma2> is plugged
5016 __isl_give isl_set *isl_multi_aff_lex_le_set(
5017 __isl_take isl_multi_aff *ma1,
5018 __isl_take isl_multi_aff *ma2);
5019 __isl_give isl_set *isl_multi_aff_lex_ge_set(
5020 __isl_take isl_multi_aff *ma1,
5021 __isl_take isl_multi_aff *ma2);
5023 The function C<isl_multi_aff_lex_le_set> returns a set
5024 containing those elements in the shared domain space
5025 where C<ma1> is lexicographically smaller than or
5028 An expression can be read from input using
5030 #include <isl/aff.h>
5031 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
5032 isl_ctx *ctx, const char *str);
5033 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
5034 isl_ctx *ctx, const char *str);
5035 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
5036 isl_ctx *ctx, const char *str);
5037 __isl_give isl_union_pw_multi_aff *
5038 isl_union_pw_multi_aff_read_from_str(
5039 isl_ctx *ctx, const char *str);
5041 An expression can be printed using
5043 #include <isl/aff.h>
5044 __isl_give isl_printer *isl_printer_print_multi_aff(
5045 __isl_take isl_printer *p,
5046 __isl_keep isl_multi_aff *maff);
5047 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
5048 __isl_take isl_printer *p,
5049 __isl_keep isl_pw_multi_aff *pma);
5050 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
5051 __isl_take isl_printer *p,
5052 __isl_keep isl_union_pw_multi_aff *upma);
5053 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
5054 __isl_take isl_printer *p,
5055 __isl_keep isl_multi_pw_aff *mpa);
5059 Points are elements of a set. They can be used to construct
5060 simple sets (boxes) or they can be used to represent the
5061 individual elements of a set.
5062 The zero point (the origin) can be created using
5064 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
5066 The coordinates of a point can be inspected, set and changed
5069 __isl_give isl_val *isl_point_get_coordinate_val(
5070 __isl_keep isl_point *pnt,
5071 enum isl_dim_type type, int pos);
5072 __isl_give isl_point *isl_point_set_coordinate_val(
5073 __isl_take isl_point *pnt,
5074 enum isl_dim_type type, int pos,
5075 __isl_take isl_val *v);
5077 __isl_give isl_point *isl_point_add_ui(
5078 __isl_take isl_point *pnt,
5079 enum isl_dim_type type, int pos, unsigned val);
5080 __isl_give isl_point *isl_point_sub_ui(
5081 __isl_take isl_point *pnt,
5082 enum isl_dim_type type, int pos, unsigned val);
5084 Other properties can be obtained using
5086 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
5088 Points can be copied or freed using
5090 __isl_give isl_point *isl_point_copy(
5091 __isl_keep isl_point *pnt);
5092 void isl_point_free(__isl_take isl_point *pnt);
5094 A singleton set can be created from a point using
5096 __isl_give isl_basic_set *isl_basic_set_from_point(
5097 __isl_take isl_point *pnt);
5098 __isl_give isl_set *isl_set_from_point(
5099 __isl_take isl_point *pnt);
5101 and a box can be created from two opposite extremal points using
5103 __isl_give isl_basic_set *isl_basic_set_box_from_points(
5104 __isl_take isl_point *pnt1,
5105 __isl_take isl_point *pnt2);
5106 __isl_give isl_set *isl_set_box_from_points(
5107 __isl_take isl_point *pnt1,
5108 __isl_take isl_point *pnt2);
5110 All elements of a B<bounded> (union) set can be enumerated using
5111 the following functions.
5113 int isl_set_foreach_point(__isl_keep isl_set *set,
5114 int (*fn)(__isl_take isl_point *pnt, void *user),
5116 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
5117 int (*fn)(__isl_take isl_point *pnt, void *user),
5120 The function C<fn> is called for each integer point in
5121 C<set> with as second argument the last argument of
5122 the C<isl_set_foreach_point> call. The function C<fn>
5123 should return C<0> on success and C<-1> on failure.
5124 In the latter case, C<isl_set_foreach_point> will stop
5125 enumerating and return C<-1> as well.
5126 If the enumeration is performed successfully and to completion,
5127 then C<isl_set_foreach_point> returns C<0>.
5129 To obtain a single point of a (basic) set, use
5131 __isl_give isl_point *isl_basic_set_sample_point(
5132 __isl_take isl_basic_set *bset);
5133 __isl_give isl_point *isl_set_sample_point(
5134 __isl_take isl_set *set);
5136 If C<set> does not contain any (integer) points, then the
5137 resulting point will be ``void'', a property that can be
5140 int isl_point_is_void(__isl_keep isl_point *pnt);
5142 =head2 Piecewise Quasipolynomials
5144 A piecewise quasipolynomial is a particular kind of function that maps
5145 a parametric point to a rational value.
5146 More specifically, a quasipolynomial is a polynomial expression in greatest
5147 integer parts of affine expressions of parameters and variables.
5148 A piecewise quasipolynomial is a subdivision of a given parametric
5149 domain into disjoint cells with a quasipolynomial associated to
5150 each cell. The value of the piecewise quasipolynomial at a given
5151 point is the value of the quasipolynomial associated to the cell
5152 that contains the point. Outside of the union of cells,
5153 the value is assumed to be zero.
5154 For example, the piecewise quasipolynomial
5156 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
5158 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
5159 A given piecewise quasipolynomial has a fixed domain dimension.
5160 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
5161 defined over different domains.
5162 Piecewise quasipolynomials are mainly used by the C<barvinok>
5163 library for representing the number of elements in a parametric set or map.
5164 For example, the piecewise quasipolynomial above represents
5165 the number of points in the map
5167 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
5169 =head3 Input and Output
5171 Piecewise quasipolynomials can be read from input using
5173 __isl_give isl_union_pw_qpolynomial *
5174 isl_union_pw_qpolynomial_read_from_str(
5175 isl_ctx *ctx, const char *str);
5177 Quasipolynomials and piecewise quasipolynomials can be printed
5178 using the following functions.
5180 __isl_give isl_printer *isl_printer_print_qpolynomial(
5181 __isl_take isl_printer *p,
5182 __isl_keep isl_qpolynomial *qp);
5184 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
5185 __isl_take isl_printer *p,
5186 __isl_keep isl_pw_qpolynomial *pwqp);
5188 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
5189 __isl_take isl_printer *p,
5190 __isl_keep isl_union_pw_qpolynomial *upwqp);
5192 The output format of the printer
5193 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5194 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
5196 In case of printing in C<ISL_FORMAT_C>, the user may want
5197 to set the names of all dimensions
5199 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
5200 __isl_take isl_qpolynomial *qp,
5201 enum isl_dim_type type, unsigned pos,
5203 __isl_give isl_pw_qpolynomial *
5204 isl_pw_qpolynomial_set_dim_name(
5205 __isl_take isl_pw_qpolynomial *pwqp,
5206 enum isl_dim_type type, unsigned pos,
5209 =head3 Creating New (Piecewise) Quasipolynomials
5211 Some simple quasipolynomials can be created using the following functions.
5212 More complicated quasipolynomials can be created by applying
5213 operations such as addition and multiplication
5214 on the resulting quasipolynomials
5216 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
5217 __isl_take isl_space *domain);
5218 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
5219 __isl_take isl_space *domain);
5220 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
5221 __isl_take isl_space *domain);
5222 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
5223 __isl_take isl_space *domain);
5224 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
5225 __isl_take isl_space *domain);
5226 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
5227 __isl_take isl_space *domain,
5228 __isl_take isl_val *val);
5229 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
5230 __isl_take isl_space *domain,
5231 enum isl_dim_type type, unsigned pos);
5232 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
5233 __isl_take isl_aff *aff);
5235 Note that the space in which a quasipolynomial lives is a map space
5236 with a one-dimensional range. The C<domain> argument in some of
5237 the functions above corresponds to the domain of this map space.
5239 The zero piecewise quasipolynomial or a piecewise quasipolynomial
5240 with a single cell can be created using the following functions.
5241 Multiple of these single cell piecewise quasipolynomials can
5242 be combined to create more complicated piecewise quasipolynomials.
5244 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
5245 __isl_take isl_space *space);
5246 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
5247 __isl_take isl_set *set,
5248 __isl_take isl_qpolynomial *qp);
5249 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
5250 __isl_take isl_qpolynomial *qp);
5251 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
5252 __isl_take isl_pw_aff *pwaff);
5254 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
5255 __isl_take isl_space *space);
5256 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
5257 __isl_take isl_pw_qpolynomial *pwqp);
5258 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
5259 __isl_take isl_union_pw_qpolynomial *upwqp,
5260 __isl_take isl_pw_qpolynomial *pwqp);
5262 Quasipolynomials can be copied and freed again using the following
5265 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
5266 __isl_keep isl_qpolynomial *qp);
5267 __isl_null isl_qpolynomial *isl_qpolynomial_free(
5268 __isl_take isl_qpolynomial *qp);
5270 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
5271 __isl_keep isl_pw_qpolynomial *pwqp);
5272 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
5273 __isl_take isl_pw_qpolynomial *pwqp);
5275 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
5276 __isl_keep isl_union_pw_qpolynomial *upwqp);
5277 __isl_null isl_union_pw_qpolynomial *
5278 isl_union_pw_qpolynomial_free(
5279 __isl_take isl_union_pw_qpolynomial *upwqp);
5281 =head3 Inspecting (Piecewise) Quasipolynomials
5283 To iterate over all piecewise quasipolynomials in a union
5284 piecewise quasipolynomial, use the following function
5286 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
5287 __isl_keep isl_union_pw_qpolynomial *upwqp,
5288 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
5291 To extract the piecewise quasipolynomial in a given space from a union, use
5293 __isl_give isl_pw_qpolynomial *
5294 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
5295 __isl_keep isl_union_pw_qpolynomial *upwqp,
5296 __isl_take isl_space *space);
5298 To iterate over the cells in a piecewise quasipolynomial,
5299 use either of the following two functions
5301 int isl_pw_qpolynomial_foreach_piece(
5302 __isl_keep isl_pw_qpolynomial *pwqp,
5303 int (*fn)(__isl_take isl_set *set,
5304 __isl_take isl_qpolynomial *qp,
5305 void *user), void *user);
5306 int isl_pw_qpolynomial_foreach_lifted_piece(
5307 __isl_keep isl_pw_qpolynomial *pwqp,
5308 int (*fn)(__isl_take isl_set *set,
5309 __isl_take isl_qpolynomial *qp,
5310 void *user), void *user);
5312 As usual, the function C<fn> should return C<0> on success
5313 and C<-1> on failure. The difference between
5314 C<isl_pw_qpolynomial_foreach_piece> and
5315 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
5316 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
5317 compute unique representations for all existentially quantified
5318 variables and then turn these existentially quantified variables
5319 into extra set variables, adapting the associated quasipolynomial
5320 accordingly. This means that the C<set> passed to C<fn>
5321 will not have any existentially quantified variables, but that
5322 the dimensions of the sets may be different for different
5323 invocations of C<fn>.
5325 The constant term of a quasipolynomial can be extracted using
5327 __isl_give isl_val *isl_qpolynomial_get_constant_val(
5328 __isl_keep isl_qpolynomial *qp);
5330 To iterate over all terms in a quasipolynomial,
5333 int isl_qpolynomial_foreach_term(
5334 __isl_keep isl_qpolynomial *qp,
5335 int (*fn)(__isl_take isl_term *term,
5336 void *user), void *user);
5338 The terms themselves can be inspected and freed using
5341 unsigned isl_term_dim(__isl_keep isl_term *term,
5342 enum isl_dim_type type);
5343 __isl_give isl_val *isl_term_get_coefficient_val(
5344 __isl_keep isl_term *term);
5345 int isl_term_get_exp(__isl_keep isl_term *term,
5346 enum isl_dim_type type, unsigned pos);
5347 __isl_give isl_aff *isl_term_get_div(
5348 __isl_keep isl_term *term, unsigned pos);
5349 void isl_term_free(__isl_take isl_term *term);
5351 Each term is a product of parameters, set variables and
5352 integer divisions. The function C<isl_term_get_exp>
5353 returns the exponent of a given dimensions in the given term.
5355 =head3 Properties of (Piecewise) Quasipolynomials
5357 To check whether two union piecewise quasipolynomials are
5358 obviously equal, use
5360 int isl_union_pw_qpolynomial_plain_is_equal(
5361 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5362 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5364 =head3 Operations on (Piecewise) Quasipolynomials
5366 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5367 __isl_take isl_qpolynomial *qp,
5368 __isl_take isl_val *v);
5369 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5370 __isl_take isl_qpolynomial *qp);
5371 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5372 __isl_take isl_qpolynomial *qp1,
5373 __isl_take isl_qpolynomial *qp2);
5374 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5375 __isl_take isl_qpolynomial *qp1,
5376 __isl_take isl_qpolynomial *qp2);
5377 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5378 __isl_take isl_qpolynomial *qp1,
5379 __isl_take isl_qpolynomial *qp2);
5380 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5381 __isl_take isl_qpolynomial *qp, unsigned exponent);
5383 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5384 __isl_take isl_pw_qpolynomial *pwqp,
5385 enum isl_dim_type type, unsigned n,
5386 __isl_take isl_val *v);
5387 __isl_give isl_pw_qpolynomial *
5388 isl_pw_qpolynomial_scale_val(
5389 __isl_take isl_pw_qpolynomial *pwqp,
5390 __isl_take isl_val *v);
5391 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5392 __isl_take isl_pw_qpolynomial *pwqp1,
5393 __isl_take isl_pw_qpolynomial *pwqp2);
5394 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5395 __isl_take isl_pw_qpolynomial *pwqp1,
5396 __isl_take isl_pw_qpolynomial *pwqp2);
5397 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5398 __isl_take isl_pw_qpolynomial *pwqp1,
5399 __isl_take isl_pw_qpolynomial *pwqp2);
5400 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5401 __isl_take isl_pw_qpolynomial *pwqp);
5402 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5403 __isl_take isl_pw_qpolynomial *pwqp1,
5404 __isl_take isl_pw_qpolynomial *pwqp2);
5405 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5406 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5408 __isl_give isl_union_pw_qpolynomial *
5409 isl_union_pw_qpolynomial_scale_val(
5410 __isl_take isl_union_pw_qpolynomial *upwqp,
5411 __isl_take isl_val *v);
5412 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5413 __isl_take isl_union_pw_qpolynomial *upwqp1,
5414 __isl_take isl_union_pw_qpolynomial *upwqp2);
5415 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5416 __isl_take isl_union_pw_qpolynomial *upwqp1,
5417 __isl_take isl_union_pw_qpolynomial *upwqp2);
5418 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5419 __isl_take isl_union_pw_qpolynomial *upwqp1,
5420 __isl_take isl_union_pw_qpolynomial *upwqp2);
5422 __isl_give isl_val *isl_pw_qpolynomial_eval(
5423 __isl_take isl_pw_qpolynomial *pwqp,
5424 __isl_take isl_point *pnt);
5426 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5427 __isl_take isl_union_pw_qpolynomial *upwqp,
5428 __isl_take isl_point *pnt);
5430 __isl_give isl_set *isl_pw_qpolynomial_domain(
5431 __isl_take isl_pw_qpolynomial *pwqp);
5432 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5433 __isl_take isl_pw_qpolynomial *pwpq,
5434 __isl_take isl_set *set);
5435 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5436 __isl_take isl_pw_qpolynomial *pwpq,
5437 __isl_take isl_set *set);
5439 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5440 __isl_take isl_union_pw_qpolynomial *upwqp);
5441 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5442 __isl_take isl_union_pw_qpolynomial *upwpq,
5443 __isl_take isl_union_set *uset);
5444 __isl_give isl_union_pw_qpolynomial *
5445 isl_union_pw_qpolynomial_intersect_params(
5446 __isl_take isl_union_pw_qpolynomial *upwpq,
5447 __isl_take isl_set *set);
5449 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5450 __isl_take isl_qpolynomial *qp,
5451 __isl_take isl_space *model);
5453 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5454 __isl_take isl_qpolynomial *qp);
5455 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5456 __isl_take isl_pw_qpolynomial *pwqp);
5458 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5459 __isl_take isl_union_pw_qpolynomial *upwqp);
5461 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5462 __isl_take isl_qpolynomial *qp,
5463 __isl_take isl_set *context);
5464 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5465 __isl_take isl_qpolynomial *qp,
5466 __isl_take isl_set *context);
5468 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5469 __isl_take isl_pw_qpolynomial *pwqp,
5470 __isl_take isl_set *context);
5471 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5472 __isl_take isl_pw_qpolynomial *pwqp,
5473 __isl_take isl_set *context);
5475 __isl_give isl_union_pw_qpolynomial *
5476 isl_union_pw_qpolynomial_gist_params(
5477 __isl_take isl_union_pw_qpolynomial *upwqp,
5478 __isl_take isl_set *context);
5479 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5480 __isl_take isl_union_pw_qpolynomial *upwqp,
5481 __isl_take isl_union_set *context);
5483 The gist operation applies the gist operation to each of
5484 the cells in the domain of the input piecewise quasipolynomial.
5485 The context is also exploited
5486 to simplify the quasipolynomials associated to each cell.
5488 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5489 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5490 __isl_give isl_union_pw_qpolynomial *
5491 isl_union_pw_qpolynomial_to_polynomial(
5492 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5494 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5495 the polynomial will be an overapproximation. If C<sign> is negative,
5496 it will be an underapproximation. If C<sign> is zero, the approximation
5497 will lie somewhere in between.
5499 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5501 A piecewise quasipolynomial reduction is a piecewise
5502 reduction (or fold) of quasipolynomials.
5503 In particular, the reduction can be maximum or a minimum.
5504 The objects are mainly used to represent the result of
5505 an upper or lower bound on a quasipolynomial over its domain,
5506 i.e., as the result of the following function.
5508 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5509 __isl_take isl_pw_qpolynomial *pwqp,
5510 enum isl_fold type, int *tight);
5512 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5513 __isl_take isl_union_pw_qpolynomial *upwqp,
5514 enum isl_fold type, int *tight);
5516 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5517 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5518 is the returned bound is known be tight, i.e., for each value
5519 of the parameters there is at least
5520 one element in the domain that reaches the bound.
5521 If the domain of C<pwqp> is not wrapping, then the bound is computed
5522 over all elements in that domain and the result has a purely parametric
5523 domain. If the domain of C<pwqp> is wrapping, then the bound is
5524 computed over the range of the wrapped relation. The domain of the
5525 wrapped relation becomes the domain of the result.
5527 A (piecewise) quasipolynomial reduction can be copied or freed using the
5528 following functions.
5530 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5531 __isl_keep isl_qpolynomial_fold *fold);
5532 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5533 __isl_keep isl_pw_qpolynomial_fold *pwf);
5534 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5535 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5536 void isl_qpolynomial_fold_free(
5537 __isl_take isl_qpolynomial_fold *fold);
5538 __isl_null isl_pw_qpolynomial_fold *
5539 isl_pw_qpolynomial_fold_free(
5540 __isl_take isl_pw_qpolynomial_fold *pwf);
5541 __isl_null isl_union_pw_qpolynomial_fold *
5542 isl_union_pw_qpolynomial_fold_free(
5543 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5545 =head3 Printing Piecewise Quasipolynomial Reductions
5547 Piecewise quasipolynomial reductions can be printed
5548 using the following function.
5550 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5551 __isl_take isl_printer *p,
5552 __isl_keep isl_pw_qpolynomial_fold *pwf);
5553 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5554 __isl_take isl_printer *p,
5555 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5557 For C<isl_printer_print_pw_qpolynomial_fold>,
5558 output format of the printer
5559 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5560 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5561 output format of the printer
5562 needs to be set to C<ISL_FORMAT_ISL>.
5563 In case of printing in C<ISL_FORMAT_C>, the user may want
5564 to set the names of all dimensions
5566 __isl_give isl_pw_qpolynomial_fold *
5567 isl_pw_qpolynomial_fold_set_dim_name(
5568 __isl_take isl_pw_qpolynomial_fold *pwf,
5569 enum isl_dim_type type, unsigned pos,
5572 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5574 To iterate over all piecewise quasipolynomial reductions in a union
5575 piecewise quasipolynomial reduction, use the following function
5577 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5578 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5579 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5580 void *user), void *user);
5582 To iterate over the cells in a piecewise quasipolynomial reduction,
5583 use either of the following two functions
5585 int isl_pw_qpolynomial_fold_foreach_piece(
5586 __isl_keep isl_pw_qpolynomial_fold *pwf,
5587 int (*fn)(__isl_take isl_set *set,
5588 __isl_take isl_qpolynomial_fold *fold,
5589 void *user), void *user);
5590 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5591 __isl_keep isl_pw_qpolynomial_fold *pwf,
5592 int (*fn)(__isl_take isl_set *set,
5593 __isl_take isl_qpolynomial_fold *fold,
5594 void *user), void *user);
5596 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5597 of the difference between these two functions.
5599 To iterate over all quasipolynomials in a reduction, use
5601 int isl_qpolynomial_fold_foreach_qpolynomial(
5602 __isl_keep isl_qpolynomial_fold *fold,
5603 int (*fn)(__isl_take isl_qpolynomial *qp,
5604 void *user), void *user);
5606 =head3 Properties of Piecewise Quasipolynomial Reductions
5608 To check whether two union piecewise quasipolynomial reductions are
5609 obviously equal, use
5611 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5612 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5613 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5615 =head3 Operations on Piecewise Quasipolynomial Reductions
5617 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5618 __isl_take isl_qpolynomial_fold *fold,
5619 __isl_take isl_val *v);
5620 __isl_give isl_pw_qpolynomial_fold *
5621 isl_pw_qpolynomial_fold_scale_val(
5622 __isl_take isl_pw_qpolynomial_fold *pwf,
5623 __isl_take isl_val *v);
5624 __isl_give isl_union_pw_qpolynomial_fold *
5625 isl_union_pw_qpolynomial_fold_scale_val(
5626 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5627 __isl_take isl_val *v);
5629 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5630 __isl_take isl_pw_qpolynomial_fold *pwf1,
5631 __isl_take isl_pw_qpolynomial_fold *pwf2);
5633 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5634 __isl_take isl_pw_qpolynomial_fold *pwf1,
5635 __isl_take isl_pw_qpolynomial_fold *pwf2);
5637 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5638 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5639 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5641 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5642 __isl_take isl_pw_qpolynomial_fold *pwf,
5643 __isl_take isl_point *pnt);
5645 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5646 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5647 __isl_take isl_point *pnt);
5649 __isl_give isl_pw_qpolynomial_fold *
5650 isl_pw_qpolynomial_fold_intersect_params(
5651 __isl_take isl_pw_qpolynomial_fold *pwf,
5652 __isl_take isl_set *set);
5654 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5655 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5656 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5657 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5658 __isl_take isl_union_set *uset);
5659 __isl_give isl_union_pw_qpolynomial_fold *
5660 isl_union_pw_qpolynomial_fold_intersect_params(
5661 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5662 __isl_take isl_set *set);
5664 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5665 __isl_take isl_pw_qpolynomial_fold *pwf);
5667 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5668 __isl_take isl_pw_qpolynomial_fold *pwf);
5670 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5671 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5673 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5674 __isl_take isl_qpolynomial_fold *fold,
5675 __isl_take isl_set *context);
5676 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5677 __isl_take isl_qpolynomial_fold *fold,
5678 __isl_take isl_set *context);
5680 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5681 __isl_take isl_pw_qpolynomial_fold *pwf,
5682 __isl_take isl_set *context);
5683 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5684 __isl_take isl_pw_qpolynomial_fold *pwf,
5685 __isl_take isl_set *context);
5687 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5688 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5689 __isl_take isl_union_set *context);
5690 __isl_give isl_union_pw_qpolynomial_fold *
5691 isl_union_pw_qpolynomial_fold_gist_params(
5692 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5693 __isl_take isl_set *context);
5695 The gist operation applies the gist operation to each of
5696 the cells in the domain of the input piecewise quasipolynomial reduction.
5697 In future, the operation will also exploit the context
5698 to simplify the quasipolynomial reductions associated to each cell.
5700 __isl_give isl_pw_qpolynomial_fold *
5701 isl_set_apply_pw_qpolynomial_fold(
5702 __isl_take isl_set *set,
5703 __isl_take isl_pw_qpolynomial_fold *pwf,
5705 __isl_give isl_pw_qpolynomial_fold *
5706 isl_map_apply_pw_qpolynomial_fold(
5707 __isl_take isl_map *map,
5708 __isl_take isl_pw_qpolynomial_fold *pwf,
5710 __isl_give isl_union_pw_qpolynomial_fold *
5711 isl_union_set_apply_union_pw_qpolynomial_fold(
5712 __isl_take isl_union_set *uset,
5713 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5715 __isl_give isl_union_pw_qpolynomial_fold *
5716 isl_union_map_apply_union_pw_qpolynomial_fold(
5717 __isl_take isl_union_map *umap,
5718 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5721 The functions taking a map
5722 compose the given map with the given piecewise quasipolynomial reduction.
5723 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5724 over all elements in the intersection of the range of the map
5725 and the domain of the piecewise quasipolynomial reduction
5726 as a function of an element in the domain of the map.
5727 The functions taking a set compute a bound over all elements in the
5728 intersection of the set and the domain of the
5729 piecewise quasipolynomial reduction.
5731 =head2 Parametric Vertex Enumeration
5733 The parametric vertex enumeration described in this section
5734 is mainly intended to be used internally and by the C<barvinok>
5737 #include <isl/vertices.h>
5738 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5739 __isl_keep isl_basic_set *bset);
5741 The function C<isl_basic_set_compute_vertices> performs the
5742 actual computation of the parametric vertices and the chamber
5743 decomposition and store the result in an C<isl_vertices> object.
5744 This information can be queried by either iterating over all
5745 the vertices or iterating over all the chambers or cells
5746 and then iterating over all vertices that are active on the chamber.
5748 int isl_vertices_foreach_vertex(
5749 __isl_keep isl_vertices *vertices,
5750 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5753 int isl_vertices_foreach_cell(
5754 __isl_keep isl_vertices *vertices,
5755 int (*fn)(__isl_take isl_cell *cell, void *user),
5757 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5758 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5761 Other operations that can be performed on an C<isl_vertices> object are
5764 isl_ctx *isl_vertices_get_ctx(
5765 __isl_keep isl_vertices *vertices);
5766 int isl_vertices_get_n_vertices(
5767 __isl_keep isl_vertices *vertices);
5768 void isl_vertices_free(__isl_take isl_vertices *vertices);
5770 Vertices can be inspected and destroyed using the following functions.
5772 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5773 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5774 __isl_give isl_basic_set *isl_vertex_get_domain(
5775 __isl_keep isl_vertex *vertex);
5776 __isl_give isl_multi_aff *isl_vertex_get_expr(
5777 __isl_keep isl_vertex *vertex);
5778 void isl_vertex_free(__isl_take isl_vertex *vertex);
5780 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
5781 describing the vertex in terms of the parameters,
5782 while C<isl_vertex_get_domain> returns the activity domain
5785 Chambers can be inspected and destroyed using the following functions.
5787 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5788 __isl_give isl_basic_set *isl_cell_get_domain(
5789 __isl_keep isl_cell *cell);
5790 void isl_cell_free(__isl_take isl_cell *cell);
5792 =head1 Polyhedral Compilation Library
5794 This section collects functionality in C<isl> that has been specifically
5795 designed for use during polyhedral compilation.
5797 =head2 Dependence Analysis
5799 C<isl> contains specialized functionality for performing
5800 array dataflow analysis. That is, given a I<sink> access relation
5801 and a collection of possible I<source> access relations,
5802 C<isl> can compute relations that describe
5803 for each iteration of the sink access, which iteration
5804 of which of the source access relations was the last
5805 to access the same data element before the given iteration
5807 The resulting dependence relations map source iterations
5808 to the corresponding sink iterations.
5809 To compute standard flow dependences, the sink should be
5810 a read, while the sources should be writes.
5811 If any of the source accesses are marked as being I<may>
5812 accesses, then there will be a dependence from the last
5813 I<must> access B<and> from any I<may> access that follows
5814 this last I<must> access.
5815 In particular, if I<all> sources are I<may> accesses,
5816 then memory based dependence analysis is performed.
5817 If, on the other hand, all sources are I<must> accesses,
5818 then value based dependence analysis is performed.
5820 #include <isl/flow.h>
5822 typedef int (*isl_access_level_before)(void *first, void *second);
5824 __isl_give isl_access_info *isl_access_info_alloc(
5825 __isl_take isl_map *sink,
5826 void *sink_user, isl_access_level_before fn,
5828 __isl_give isl_access_info *isl_access_info_add_source(
5829 __isl_take isl_access_info *acc,
5830 __isl_take isl_map *source, int must,
5832 __isl_null isl_access_info *isl_access_info_free(
5833 __isl_take isl_access_info *acc);
5835 __isl_give isl_flow *isl_access_info_compute_flow(
5836 __isl_take isl_access_info *acc);
5838 int isl_flow_foreach(__isl_keep isl_flow *deps,
5839 int (*fn)(__isl_take isl_map *dep, int must,
5840 void *dep_user, void *user),
5842 __isl_give isl_map *isl_flow_get_no_source(
5843 __isl_keep isl_flow *deps, int must);
5844 void isl_flow_free(__isl_take isl_flow *deps);
5846 The function C<isl_access_info_compute_flow> performs the actual
5847 dependence analysis. The other functions are used to construct
5848 the input for this function or to read off the output.
5850 The input is collected in an C<isl_access_info>, which can
5851 be created through a call to C<isl_access_info_alloc>.
5852 The arguments to this functions are the sink access relation
5853 C<sink>, a token C<sink_user> used to identify the sink
5854 access to the user, a callback function for specifying the
5855 relative order of source and sink accesses, and the number
5856 of source access relations that will be added.
5857 The callback function has type C<int (*)(void *first, void *second)>.
5858 The function is called with two user supplied tokens identifying
5859 either a source or the sink and it should return the shared nesting
5860 level and the relative order of the two accesses.
5861 In particular, let I<n> be the number of loops shared by
5862 the two accesses. If C<first> precedes C<second> textually,
5863 then the function should return I<2 * n + 1>; otherwise,
5864 it should return I<2 * n>.
5865 The sources can be added to the C<isl_access_info> by performing
5866 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5867 C<must> indicates whether the source is a I<must> access
5868 or a I<may> access. Note that a multi-valued access relation
5869 should only be marked I<must> if every iteration in the domain
5870 of the relation accesses I<all> elements in its image.
5871 The C<source_user> token is again used to identify
5872 the source access. The range of the source access relation
5873 C<source> should have the same dimension as the range
5874 of the sink access relation.
5875 The C<isl_access_info_free> function should usually not be
5876 called explicitly, because it is called implicitly by
5877 C<isl_access_info_compute_flow>.
5879 The result of the dependence analysis is collected in an
5880 C<isl_flow>. There may be elements of
5881 the sink access for which no preceding source access could be
5882 found or for which all preceding sources are I<may> accesses.
5883 The relations containing these elements can be obtained through
5884 calls to C<isl_flow_get_no_source>, the first with C<must> set
5885 and the second with C<must> unset.
5886 In the case of standard flow dependence analysis,
5887 with the sink a read and the sources I<must> writes,
5888 the first relation corresponds to the reads from uninitialized
5889 array elements and the second relation is empty.
5890 The actual flow dependences can be extracted using
5891 C<isl_flow_foreach>. This function will call the user-specified
5892 callback function C<fn> for each B<non-empty> dependence between
5893 a source and the sink. The callback function is called
5894 with four arguments, the actual flow dependence relation
5895 mapping source iterations to sink iterations, a boolean that
5896 indicates whether it is a I<must> or I<may> dependence, a token
5897 identifying the source and an additional C<void *> with value
5898 equal to the third argument of the C<isl_flow_foreach> call.
5899 A dependence is marked I<must> if it originates from a I<must>
5900 source and if it is not followed by any I<may> sources.
5902 After finishing with an C<isl_flow>, the user should call
5903 C<isl_flow_free> to free all associated memory.
5905 A higher-level interface to dependence analysis is provided
5906 by the following function.
5908 #include <isl/flow.h>
5910 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5911 __isl_take isl_union_map *must_source,
5912 __isl_take isl_union_map *may_source,
5913 __isl_take isl_union_map *schedule,
5914 __isl_give isl_union_map **must_dep,
5915 __isl_give isl_union_map **may_dep,
5916 __isl_give isl_union_map **must_no_source,
5917 __isl_give isl_union_map **may_no_source);
5919 The arrays are identified by the tuple names of the ranges
5920 of the accesses. The iteration domains by the tuple names
5921 of the domains of the accesses and of the schedule.
5922 The relative order of the iteration domains is given by the
5923 schedule. The relations returned through C<must_no_source>
5924 and C<may_no_source> are subsets of C<sink>.
5925 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5926 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5927 any of the other arguments is treated as an error.
5929 =head3 Interaction with Dependence Analysis
5931 During the dependence analysis, we frequently need to perform
5932 the following operation. Given a relation between sink iterations
5933 and potential source iterations from a particular source domain,
5934 what is the last potential source iteration corresponding to each
5935 sink iteration. It can sometimes be convenient to adjust
5936 the set of potential source iterations before or after each such operation.
5937 The prototypical example is fuzzy array dataflow analysis,
5938 where we need to analyze if, based on data-dependent constraints,
5939 the sink iteration can ever be executed without one or more of
5940 the corresponding potential source iterations being executed.
5941 If so, we can introduce extra parameters and select an unknown
5942 but fixed source iteration from the potential source iterations.
5943 To be able to perform such manipulations, C<isl> provides the following
5946 #include <isl/flow.h>
5948 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5949 __isl_keep isl_map *source_map,
5950 __isl_keep isl_set *sink, void *source_user,
5952 __isl_give isl_access_info *isl_access_info_set_restrict(
5953 __isl_take isl_access_info *acc,
5954 isl_access_restrict fn, void *user);
5956 The function C<isl_access_info_set_restrict> should be called
5957 before calling C<isl_access_info_compute_flow> and registers a callback function
5958 that will be called any time C<isl> is about to compute the last
5959 potential source. The first argument is the (reverse) proto-dependence,
5960 mapping sink iterations to potential source iterations.
5961 The second argument represents the sink iterations for which
5962 we want to compute the last source iteration.
5963 The third argument is the token corresponding to the source
5964 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5965 The callback is expected to return a restriction on either the input or
5966 the output of the operation computing the last potential source.
5967 If the input needs to be restricted then restrictions are needed
5968 for both the source and the sink iterations. The sink iterations
5969 and the potential source iterations will be intersected with these sets.
5970 If the output needs to be restricted then only a restriction on the source
5971 iterations is required.
5972 If any error occurs, the callback should return C<NULL>.
5973 An C<isl_restriction> object can be created, freed and inspected
5974 using the following functions.
5976 #include <isl/flow.h>
5978 __isl_give isl_restriction *isl_restriction_input(
5979 __isl_take isl_set *source_restr,
5980 __isl_take isl_set *sink_restr);
5981 __isl_give isl_restriction *isl_restriction_output(
5982 __isl_take isl_set *source_restr);
5983 __isl_give isl_restriction *isl_restriction_none(
5984 __isl_take isl_map *source_map);
5985 __isl_give isl_restriction *isl_restriction_empty(
5986 __isl_take isl_map *source_map);
5987 __isl_null isl_restriction *isl_restriction_free(
5988 __isl_take isl_restriction *restr);
5989 isl_ctx *isl_restriction_get_ctx(
5990 __isl_keep isl_restriction *restr);
5992 C<isl_restriction_none> and C<isl_restriction_empty> are special
5993 cases of C<isl_restriction_input>. C<isl_restriction_none>
5994 is essentially equivalent to
5996 isl_restriction_input(isl_set_universe(
5997 isl_space_range(isl_map_get_space(source_map))),
5999 isl_space_domain(isl_map_get_space(source_map))));
6001 whereas C<isl_restriction_empty> is essentially equivalent to
6003 isl_restriction_input(isl_set_empty(
6004 isl_space_range(isl_map_get_space(source_map))),
6006 isl_space_domain(isl_map_get_space(source_map))));
6010 B<The functionality described in this section is fairly new
6011 and may be subject to change.>
6013 #include <isl/schedule.h>
6014 __isl_give isl_schedule *
6015 isl_schedule_constraints_compute_schedule(
6016 __isl_take isl_schedule_constraints *sc);
6017 __isl_null isl_schedule *isl_schedule_free(
6018 __isl_take isl_schedule *sched);
6020 The function C<isl_schedule_constraints_compute_schedule> can be
6021 used to compute a schedule that satisfies the given schedule constraints.
6022 These schedule constraints include the iteration domain for which
6023 a schedule should be computed and dependences between pairs of
6024 iterations. In particular, these dependences include
6025 I<validity> dependences and I<proximity> dependences.
6026 By default, the algorithm used to construct the schedule is similar
6027 to that of C<Pluto>.
6028 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
6030 The generated schedule respects all validity dependences.
6031 That is, all dependence distances over these dependences in the
6032 scheduled space are lexicographically positive.
6033 The default algorithm tries to ensure that the dependence distances
6034 over coincidence constraints are zero and to minimize the
6035 dependence distances over proximity dependences.
6036 Moreover, it tries to obtain sequences (bands) of schedule dimensions
6037 for groups of domains where the dependence distances over validity
6038 dependences have only non-negative values.
6039 When using Feautrier's algorithm, the coincidence and proximity constraints
6040 are only taken into account during the extension to a
6041 full-dimensional schedule.
6043 An C<isl_schedule_constraints> object can be constructed
6044 and manipulated using the following functions.
6046 #include <isl/schedule.h>
6047 __isl_give isl_schedule_constraints *
6048 isl_schedule_constraints_copy(
6049 __isl_keep isl_schedule_constraints *sc);
6050 __isl_give isl_schedule_constraints *
6051 isl_schedule_constraints_on_domain(
6052 __isl_take isl_union_set *domain);
6053 isl_ctx *isl_schedule_constraints_get_ctx(
6054 __isl_keep isl_schedule_constraints *sc);
6055 __isl_give isl_schedule_constraints *
6056 isl_schedule_constraints_set_validity(
6057 __isl_take isl_schedule_constraints *sc,
6058 __isl_take isl_union_map *validity);
6059 __isl_give isl_schedule_constraints *
6060 isl_schedule_constraints_set_coincidence(
6061 __isl_take isl_schedule_constraints *sc,
6062 __isl_take isl_union_map *coincidence);
6063 __isl_give isl_schedule_constraints *
6064 isl_schedule_constraints_set_proximity(
6065 __isl_take isl_schedule_constraints *sc,
6066 __isl_take isl_union_map *proximity);
6067 __isl_give isl_schedule_constraints *
6068 isl_schedule_constraints_set_conditional_validity(
6069 __isl_take isl_schedule_constraints *sc,
6070 __isl_take isl_union_map *condition,
6071 __isl_take isl_union_map *validity);
6072 __isl_null isl_schedule_constraints *
6073 isl_schedule_constraints_free(
6074 __isl_take isl_schedule_constraints *sc);
6076 The initial C<isl_schedule_constraints> object created by
6077 C<isl_schedule_constraints_on_domain> does not impose any constraints.
6078 That is, it has an empty set of dependences.
6079 The function C<isl_schedule_constraints_set_validity> replaces the
6080 validity dependences, mapping domain elements I<i> to domain
6081 elements that should be scheduled after I<i>.
6082 The function C<isl_schedule_constraints_set_coincidence> replaces the
6083 coincidence dependences, mapping domain elements I<i> to domain
6084 elements that should be scheduled together with I<I>, if possible.
6085 The function C<isl_schedule_constraints_set_proximity> replaces the
6086 proximity dependences, mapping domain elements I<i> to domain
6087 elements that should be scheduled either before I<I>
6088 or as early as possible after I<i>.
6090 The function C<isl_schedule_constraints_set_conditional_validity>
6091 replaces the conditional validity constraints.
6092 A conditional validity constraint is only imposed when any of the corresponding
6093 conditions is satisfied, i.e., when any of them is non-zero.
6094 That is, the scheduler ensures that within each band if the dependence
6095 distances over the condition constraints are not all zero
6096 then all corresponding conditional validity constraints are respected.
6097 A conditional validity constraint corresponds to a condition
6098 if the two are adjacent, i.e., if the domain of one relation intersect
6099 the range of the other relation.
6100 The typical use case of conditional validity constraints is
6101 to allow order constraints between live ranges to be violated
6102 as long as the live ranges themselves are local to the band.
6103 To allow more fine-grained control over which conditions correspond
6104 to which conditional validity constraints, the domains and ranges
6105 of these relations may include I<tags>. That is, the domains and
6106 ranges of those relation may themselves be wrapped relations
6107 where the iteration domain appears in the domain of those wrapped relations
6108 and the range of the wrapped relations can be arbitrarily chosen
6109 by the user. Conditions and conditional validity constraints are only
6110 considered adjacent to each other if the entire wrapped relation matches.
6111 In particular, a relation with a tag will never be considered adjacent
6112 to a relation without a tag.
6114 The following function computes a schedule directly from
6115 an iteration domain and validity and proximity dependences
6116 and is implemented in terms of the functions described above.
6117 The use of C<isl_union_set_compute_schedule> is discouraged.
6119 #include <isl/schedule.h>
6120 __isl_give isl_schedule *isl_union_set_compute_schedule(
6121 __isl_take isl_union_set *domain,
6122 __isl_take isl_union_map *validity,
6123 __isl_take isl_union_map *proximity);
6125 A mapping from the domains to the scheduled space can be obtained
6126 from an C<isl_schedule> using the following function.
6128 __isl_give isl_union_map *isl_schedule_get_map(
6129 __isl_keep isl_schedule *sched);
6131 A representation of the schedule can be printed using
6133 __isl_give isl_printer *isl_printer_print_schedule(
6134 __isl_take isl_printer *p,
6135 __isl_keep isl_schedule *schedule);
6137 A representation of the schedule as a forest of bands can be obtained
6138 using the following function.
6140 __isl_give isl_band_list *isl_schedule_get_band_forest(
6141 __isl_keep isl_schedule *schedule);
6143 The individual bands can be visited in depth-first post-order
6144 using the following function.
6146 #include <isl/schedule.h>
6147 int isl_schedule_foreach_band(
6148 __isl_keep isl_schedule *sched,
6149 int (*fn)(__isl_keep isl_band *band, void *user),
6152 The list can be manipulated as explained in L<"Lists">.
6153 The bands inside the list can be copied and freed using the following
6156 #include <isl/band.h>
6157 __isl_give isl_band *isl_band_copy(
6158 __isl_keep isl_band *band);
6159 __isl_null isl_band *isl_band_free(
6160 __isl_take isl_band *band);
6162 Each band contains zero or more scheduling dimensions.
6163 These are referred to as the members of the band.
6164 The section of the schedule that corresponds to the band is
6165 referred to as the partial schedule of the band.
6166 For those nodes that participate in a band, the outer scheduling
6167 dimensions form the prefix schedule, while the inner scheduling
6168 dimensions form the suffix schedule.
6169 That is, if we take a cut of the band forest, then the union of
6170 the concatenations of the prefix, partial and suffix schedules of
6171 each band in the cut is equal to the entire schedule (modulo
6172 some possible padding at the end with zero scheduling dimensions).
6173 The properties of a band can be inspected using the following functions.
6175 #include <isl/band.h>
6176 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
6178 int isl_band_has_children(__isl_keep isl_band *band);
6179 __isl_give isl_band_list *isl_band_get_children(
6180 __isl_keep isl_band *band);
6182 __isl_give isl_union_map *isl_band_get_prefix_schedule(
6183 __isl_keep isl_band *band);
6184 __isl_give isl_union_map *isl_band_get_partial_schedule(
6185 __isl_keep isl_band *band);
6186 __isl_give isl_union_map *isl_band_get_suffix_schedule(
6187 __isl_keep isl_band *band);
6189 int isl_band_n_member(__isl_keep isl_band *band);
6190 int isl_band_member_is_coincident(
6191 __isl_keep isl_band *band, int pos);
6193 int isl_band_list_foreach_band(
6194 __isl_keep isl_band_list *list,
6195 int (*fn)(__isl_keep isl_band *band, void *user),
6198 Note that a scheduling dimension is considered to be ``coincident''
6199 if it satisfies the coincidence constraints within its band.
6200 That is, if the dependence distances of the coincidence
6201 constraints are all zero in that direction (for fixed
6202 iterations of outer bands).
6203 Like C<isl_schedule_foreach_band>,
6204 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
6205 in depth-first post-order.
6207 A band can be tiled using the following function.
6209 #include <isl/band.h>
6210 int isl_band_tile(__isl_keep isl_band *band,
6211 __isl_take isl_vec *sizes);
6213 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
6215 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
6216 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
6218 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
6220 The C<isl_band_tile> function tiles the band using the given tile sizes
6221 inside its schedule.
6222 A new child band is created to represent the point loops and it is
6223 inserted between the modified band and its children.
6224 The C<tile_scale_tile_loops> option specifies whether the tile
6225 loops iterators should be scaled by the tile sizes.
6226 If the C<tile_shift_point_loops> option is set, then the point loops
6227 are shifted to start at zero.
6229 A band can be split into two nested bands using the following function.
6231 int isl_band_split(__isl_keep isl_band *band, int pos);
6233 The resulting outer band contains the first C<pos> dimensions of C<band>
6234 while the inner band contains the remaining dimensions.
6236 A representation of the band can be printed using
6238 #include <isl/band.h>
6239 __isl_give isl_printer *isl_printer_print_band(
6240 __isl_take isl_printer *p,
6241 __isl_keep isl_band *band);
6245 #include <isl/schedule.h>
6246 int isl_options_set_schedule_max_coefficient(
6247 isl_ctx *ctx, int val);
6248 int isl_options_get_schedule_max_coefficient(
6250 int isl_options_set_schedule_max_constant_term(
6251 isl_ctx *ctx, int val);
6252 int isl_options_get_schedule_max_constant_term(
6254 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
6255 int isl_options_get_schedule_fuse(isl_ctx *ctx);
6256 int isl_options_set_schedule_maximize_band_depth(
6257 isl_ctx *ctx, int val);
6258 int isl_options_get_schedule_maximize_band_depth(
6260 int isl_options_set_schedule_outer_coincidence(
6261 isl_ctx *ctx, int val);
6262 int isl_options_get_schedule_outer_coincidence(
6264 int isl_options_set_schedule_split_scaled(
6265 isl_ctx *ctx, int val);
6266 int isl_options_get_schedule_split_scaled(
6268 int isl_options_set_schedule_algorithm(
6269 isl_ctx *ctx, int val);
6270 int isl_options_get_schedule_algorithm(
6272 int isl_options_set_schedule_separate_components(
6273 isl_ctx *ctx, int val);
6274 int isl_options_get_schedule_separate_components(
6279 =item * schedule_max_coefficient
6281 This option enforces that the coefficients for variable and parameter
6282 dimensions in the calculated schedule are not larger than the specified value.
6283 This option can significantly increase the speed of the scheduling calculation
6284 and may also prevent fusing of unrelated dimensions. A value of -1 means that
6285 this option does not introduce bounds on the variable or parameter
6288 =item * schedule_max_constant_term
6290 This option enforces that the constant coefficients in the calculated schedule
6291 are not larger than the maximal constant term. This option can significantly
6292 increase the speed of the scheduling calculation and may also prevent fusing of
6293 unrelated dimensions. A value of -1 means that this option does not introduce
6294 bounds on the constant coefficients.
6296 =item * schedule_fuse
6298 This option controls the level of fusion.
6299 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6300 resulting schedule will be distributed as much as possible.
6301 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6302 try to fuse loops in the resulting schedule.
6304 =item * schedule_maximize_band_depth
6306 If this option is set, we do not split bands at the point
6307 where we detect splitting is necessary. Instead, we
6308 backtrack and split bands as early as possible. This
6309 reduces the number of splits and maximizes the width of
6310 the bands. Wider bands give more possibilities for tiling.
6311 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6312 then bands will be split as early as possible, even if there is no need.
6313 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6315 =item * schedule_outer_coincidence
6317 If this option is set, then we try to construct schedules
6318 where the outermost scheduling dimension in each band
6319 satisfies the coincidence constraints.
6321 =item * schedule_split_scaled
6323 If this option is set, then we try to construct schedules in which the
6324 constant term is split off from the linear part if the linear parts of
6325 the scheduling rows for all nodes in the graphs have a common non-trivial
6327 The constant term is then placed in a separate band and the linear
6330 =item * schedule_algorithm
6332 Selects the scheduling algorithm to be used.
6333 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6334 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6336 =item * schedule_separate_components
6338 If at any point the dependence graph contains any (weakly connected) components,
6339 then these components are scheduled separately.
6340 If this option is not set, then some iterations of the domains
6341 in these components may be scheduled together.
6342 If this option is set, then the components are given consecutive
6347 =head2 AST Generation
6349 This section describes the C<isl> functionality for generating
6350 ASTs that visit all the elements
6351 in a domain in an order specified by a schedule.
6352 In particular, given a C<isl_union_map>, an AST is generated
6353 that visits all the elements in the domain of the C<isl_union_map>
6354 according to the lexicographic order of the corresponding image
6355 element(s). If the range of the C<isl_union_map> consists of
6356 elements in more than one space, then each of these spaces is handled
6357 separately in an arbitrary order.
6358 It should be noted that the image elements only specify the I<order>
6359 in which the corresponding domain elements should be visited.
6360 No direct relation between the image elements and the loop iterators
6361 in the generated AST should be assumed.
6363 Each AST is generated within a build. The initial build
6364 simply specifies the constraints on the parameters (if any)
6365 and can be created, inspected, copied and freed using the following functions.
6367 #include <isl/ast_build.h>
6368 __isl_give isl_ast_build *isl_ast_build_from_context(
6369 __isl_take isl_set *set);
6370 isl_ctx *isl_ast_build_get_ctx(
6371 __isl_keep isl_ast_build *build);
6372 __isl_give isl_ast_build *isl_ast_build_copy(
6373 __isl_keep isl_ast_build *build);
6374 __isl_null isl_ast_build *isl_ast_build_free(
6375 __isl_take isl_ast_build *build);
6377 The C<set> argument is usually a parameter set with zero or more parameters.
6378 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6379 and L</"Fine-grained Control over AST Generation">.
6380 Finally, the AST itself can be constructed using the following
6383 #include <isl/ast_build.h>
6384 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6385 __isl_keep isl_ast_build *build,
6386 __isl_take isl_union_map *schedule);
6388 =head3 Inspecting the AST
6390 The basic properties of an AST node can be obtained as follows.
6392 #include <isl/ast.h>
6393 isl_ctx *isl_ast_node_get_ctx(
6394 __isl_keep isl_ast_node *node);
6395 enum isl_ast_node_type isl_ast_node_get_type(
6396 __isl_keep isl_ast_node *node);
6398 The type of an AST node is one of
6399 C<isl_ast_node_for>,
6401 C<isl_ast_node_block> or
6402 C<isl_ast_node_user>.
6403 An C<isl_ast_node_for> represents a for node.
6404 An C<isl_ast_node_if> represents an if node.
6405 An C<isl_ast_node_block> represents a compound node.
6406 An C<isl_ast_node_user> represents an expression statement.
6407 An expression statement typically corresponds to a domain element, i.e.,
6408 one of the elements that is visited by the AST.
6410 Each type of node has its own additional properties.
6412 #include <isl/ast.h>
6413 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6414 __isl_keep isl_ast_node *node);
6415 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6416 __isl_keep isl_ast_node *node);
6417 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6418 __isl_keep isl_ast_node *node);
6419 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6420 __isl_keep isl_ast_node *node);
6421 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6422 __isl_keep isl_ast_node *node);
6423 int isl_ast_node_for_is_degenerate(
6424 __isl_keep isl_ast_node *node);
6426 An C<isl_ast_for> is considered degenerate if it is known to execute
6429 #include <isl/ast.h>
6430 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6431 __isl_keep isl_ast_node *node);
6432 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6433 __isl_keep isl_ast_node *node);
6434 int isl_ast_node_if_has_else(
6435 __isl_keep isl_ast_node *node);
6436 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6437 __isl_keep isl_ast_node *node);
6439 __isl_give isl_ast_node_list *
6440 isl_ast_node_block_get_children(
6441 __isl_keep isl_ast_node *node);
6443 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6444 __isl_keep isl_ast_node *node);
6446 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6447 the following functions.
6449 #include <isl/ast.h>
6450 isl_ctx *isl_ast_expr_get_ctx(
6451 __isl_keep isl_ast_expr *expr);
6452 enum isl_ast_expr_type isl_ast_expr_get_type(
6453 __isl_keep isl_ast_expr *expr);
6455 The type of an AST expression is one of
6457 C<isl_ast_expr_id> or
6458 C<isl_ast_expr_int>.
6459 An C<isl_ast_expr_op> represents the result of an operation.
6460 An C<isl_ast_expr_id> represents an identifier.
6461 An C<isl_ast_expr_int> represents an integer value.
6463 Each type of expression has its own additional properties.
6465 #include <isl/ast.h>
6466 enum isl_ast_op_type isl_ast_expr_get_op_type(
6467 __isl_keep isl_ast_expr *expr);
6468 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6469 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6470 __isl_keep isl_ast_expr *expr, int pos);
6471 int isl_ast_node_foreach_ast_op_type(
6472 __isl_keep isl_ast_node *node,
6473 int (*fn)(enum isl_ast_op_type type, void *user),
6476 C<isl_ast_expr_get_op_type> returns the type of the operation
6477 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6478 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6480 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6481 C<isl_ast_op_type> that appears in C<node>.
6482 The operation type is one of the following.
6486 =item C<isl_ast_op_and>
6488 Logical I<and> of two arguments.
6489 Both arguments can be evaluated.
6491 =item C<isl_ast_op_and_then>
6493 Logical I<and> of two arguments.
6494 The second argument can only be evaluated if the first evaluates to true.
6496 =item C<isl_ast_op_or>
6498 Logical I<or> of two arguments.
6499 Both arguments can be evaluated.
6501 =item C<isl_ast_op_or_else>
6503 Logical I<or> of two arguments.
6504 The second argument can only be evaluated if the first evaluates to false.
6506 =item C<isl_ast_op_max>
6508 Maximum of two or more arguments.
6510 =item C<isl_ast_op_min>
6512 Minimum of two or more arguments.
6514 =item C<isl_ast_op_minus>
6518 =item C<isl_ast_op_add>
6520 Sum of two arguments.
6522 =item C<isl_ast_op_sub>
6524 Difference of two arguments.
6526 =item C<isl_ast_op_mul>
6528 Product of two arguments.
6530 =item C<isl_ast_op_div>
6532 Exact division. That is, the result is known to be an integer.
6534 =item C<isl_ast_op_fdiv_q>
6536 Result of integer division, rounded towards negative
6539 =item C<isl_ast_op_pdiv_q>
6541 Result of integer division, where dividend is known to be non-negative.
6543 =item C<isl_ast_op_pdiv_r>
6545 Remainder of integer division, where dividend is known to be non-negative.
6547 =item C<isl_ast_op_cond>
6549 Conditional operator defined on three arguments.
6550 If the first argument evaluates to true, then the result
6551 is equal to the second argument. Otherwise, the result
6552 is equal to the third argument.
6553 The second and third argument may only be evaluated if
6554 the first argument evaluates to true and false, respectively.
6555 Corresponds to C<a ? b : c> in C.
6557 =item C<isl_ast_op_select>
6559 Conditional operator defined on three arguments.
6560 If the first argument evaluates to true, then the result
6561 is equal to the second argument. Otherwise, the result
6562 is equal to the third argument.
6563 The second and third argument may be evaluated independently
6564 of the value of the first argument.
6565 Corresponds to C<a * b + (1 - a) * c> in C.
6567 =item C<isl_ast_op_eq>
6571 =item C<isl_ast_op_le>
6573 Less than or equal relation.
6575 =item C<isl_ast_op_lt>
6579 =item C<isl_ast_op_ge>
6581 Greater than or equal relation.
6583 =item C<isl_ast_op_gt>
6585 Greater than relation.
6587 =item C<isl_ast_op_call>
6590 The number of arguments of the C<isl_ast_expr> is one more than
6591 the number of arguments in the function call, the first argument
6592 representing the function being called.
6594 =item C<isl_ast_op_access>
6597 The number of arguments of the C<isl_ast_expr> is one more than
6598 the number of index expressions in the array access, the first argument
6599 representing the array being accessed.
6601 =item C<isl_ast_op_member>
6604 This operation has two arguments, a structure and the name of
6605 the member of the structure being accessed.
6609 #include <isl/ast.h>
6610 __isl_give isl_id *isl_ast_expr_get_id(
6611 __isl_keep isl_ast_expr *expr);
6613 Return the identifier represented by the AST expression.
6615 #include <isl/ast.h>
6616 __isl_give isl_val *isl_ast_expr_get_val(
6617 __isl_keep isl_ast_expr *expr);
6619 Return the integer represented by the AST expression.
6621 =head3 Properties of ASTs
6623 #include <isl/ast.h>
6624 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6625 __isl_keep isl_ast_expr *expr2);
6627 Check if two C<isl_ast_expr>s are equal to each other.
6629 =head3 Manipulating and printing the AST
6631 AST nodes can be copied and freed using the following functions.
6633 #include <isl/ast.h>
6634 __isl_give isl_ast_node *isl_ast_node_copy(
6635 __isl_keep isl_ast_node *node);
6636 __isl_null isl_ast_node *isl_ast_node_free(
6637 __isl_take isl_ast_node *node);
6639 AST expressions can be copied and freed using the following functions.
6641 #include <isl/ast.h>
6642 __isl_give isl_ast_expr *isl_ast_expr_copy(
6643 __isl_keep isl_ast_expr *expr);
6644 __isl_null isl_ast_expr *isl_ast_expr_free(
6645 __isl_take isl_ast_expr *expr);
6647 New AST expressions can be created either directly or within
6648 the context of an C<isl_ast_build>.
6650 #include <isl/ast.h>
6651 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6652 __isl_take isl_val *v);
6653 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6654 __isl_take isl_id *id);
6655 __isl_give isl_ast_expr *isl_ast_expr_neg(
6656 __isl_take isl_ast_expr *expr);
6657 __isl_give isl_ast_expr *isl_ast_expr_address_of(
6658 __isl_take isl_ast_expr *expr);
6659 __isl_give isl_ast_expr *isl_ast_expr_add(
6660 __isl_take isl_ast_expr *expr1,
6661 __isl_take isl_ast_expr *expr2);
6662 __isl_give isl_ast_expr *isl_ast_expr_sub(
6663 __isl_take isl_ast_expr *expr1,
6664 __isl_take isl_ast_expr *expr2);
6665 __isl_give isl_ast_expr *isl_ast_expr_mul(
6666 __isl_take isl_ast_expr *expr1,
6667 __isl_take isl_ast_expr *expr2);
6668 __isl_give isl_ast_expr *isl_ast_expr_div(
6669 __isl_take isl_ast_expr *expr1,
6670 __isl_take isl_ast_expr *expr2);
6671 __isl_give isl_ast_expr *isl_ast_expr_and(
6672 __isl_take isl_ast_expr *expr1,
6673 __isl_take isl_ast_expr *expr2)
6674 __isl_give isl_ast_expr *isl_ast_expr_or(
6675 __isl_take isl_ast_expr *expr1,
6676 __isl_take isl_ast_expr *expr2)
6677 __isl_give isl_ast_expr *isl_ast_expr_eq(
6678 __isl_take isl_ast_expr *expr1,
6679 __isl_take isl_ast_expr *expr2);
6680 __isl_give isl_ast_expr *isl_ast_expr_le(
6681 __isl_take isl_ast_expr *expr1,
6682 __isl_take isl_ast_expr *expr2);
6683 __isl_give isl_ast_expr *isl_ast_expr_lt(
6684 __isl_take isl_ast_expr *expr1,
6685 __isl_take isl_ast_expr *expr2);
6686 __isl_give isl_ast_expr *isl_ast_expr_ge(
6687 __isl_take isl_ast_expr *expr1,
6688 __isl_take isl_ast_expr *expr2);
6689 __isl_give isl_ast_expr *isl_ast_expr_gt(
6690 __isl_take isl_ast_expr *expr1,
6691 __isl_take isl_ast_expr *expr2);
6692 __isl_give isl_ast_expr *isl_ast_expr_access(
6693 __isl_take isl_ast_expr *array,
6694 __isl_take isl_ast_expr_list *indices);
6696 The function C<isl_ast_expr_address_of> can be applied to an
6697 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
6698 to represent the address of the C<isl_ast_expr_access>.
6700 #include <isl/ast_build.h>
6701 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6702 __isl_keep isl_ast_build *build,
6703 __isl_take isl_pw_aff *pa);
6704 __isl_give isl_ast_expr *
6705 isl_ast_build_access_from_pw_multi_aff(
6706 __isl_keep isl_ast_build *build,
6707 __isl_take isl_pw_multi_aff *pma);
6708 __isl_give isl_ast_expr *
6709 isl_ast_build_access_from_multi_pw_aff(
6710 __isl_keep isl_ast_build *build,
6711 __isl_take isl_multi_pw_aff *mpa);
6712 __isl_give isl_ast_expr *
6713 isl_ast_build_call_from_pw_multi_aff(
6714 __isl_keep isl_ast_build *build,
6715 __isl_take isl_pw_multi_aff *pma);
6716 __isl_give isl_ast_expr *
6717 isl_ast_build_call_from_multi_pw_aff(
6718 __isl_keep isl_ast_build *build,
6719 __isl_take isl_multi_pw_aff *mpa);
6721 The domains of C<pa>, C<mpa> and C<pma> should correspond
6722 to the schedule space of C<build>.
6723 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6724 the function being called.
6725 If the accessed space is a nested relation, then it is taken
6726 to represent an access of the member specified by the range
6727 of this nested relation of the structure specified by the domain
6728 of the nested relation.
6730 The following functions can be used to modify an C<isl_ast_expr>.
6732 #include <isl/ast.h>
6733 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6734 __isl_take isl_ast_expr *expr, int pos,
6735 __isl_take isl_ast_expr *arg);
6737 Replace the argument of C<expr> at position C<pos> by C<arg>.
6739 #include <isl/ast.h>
6740 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6741 __isl_take isl_ast_expr *expr,
6742 __isl_take isl_id_to_ast_expr *id2expr);
6744 The function C<isl_ast_expr_substitute_ids> replaces the
6745 subexpressions of C<expr> of type C<isl_ast_expr_id>
6746 by the corresponding expression in C<id2expr>, if there is any.
6749 User specified data can be attached to an C<isl_ast_node> and obtained
6750 from the same C<isl_ast_node> using the following functions.
6752 #include <isl/ast.h>
6753 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6754 __isl_take isl_ast_node *node,
6755 __isl_take isl_id *annotation);
6756 __isl_give isl_id *isl_ast_node_get_annotation(
6757 __isl_keep isl_ast_node *node);
6759 Basic printing can be performed using the following functions.
6761 #include <isl/ast.h>
6762 __isl_give isl_printer *isl_printer_print_ast_expr(
6763 __isl_take isl_printer *p,
6764 __isl_keep isl_ast_expr *expr);
6765 __isl_give isl_printer *isl_printer_print_ast_node(
6766 __isl_take isl_printer *p,
6767 __isl_keep isl_ast_node *node);
6769 More advanced printing can be performed using the following functions.
6771 #include <isl/ast.h>
6772 __isl_give isl_printer *isl_ast_op_type_print_macro(
6773 enum isl_ast_op_type type,
6774 __isl_take isl_printer *p);
6775 __isl_give isl_printer *isl_ast_node_print_macros(
6776 __isl_keep isl_ast_node *node,
6777 __isl_take isl_printer *p);
6778 __isl_give isl_printer *isl_ast_node_print(
6779 __isl_keep isl_ast_node *node,
6780 __isl_take isl_printer *p,
6781 __isl_take isl_ast_print_options *options);
6782 __isl_give isl_printer *isl_ast_node_for_print(
6783 __isl_keep isl_ast_node *node,
6784 __isl_take isl_printer *p,
6785 __isl_take isl_ast_print_options *options);
6786 __isl_give isl_printer *isl_ast_node_if_print(
6787 __isl_keep isl_ast_node *node,
6788 __isl_take isl_printer *p,
6789 __isl_take isl_ast_print_options *options);
6791 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6792 C<isl> may print out an AST that makes use of macros such
6793 as C<floord>, C<min> and C<max>.
6794 C<isl_ast_op_type_print_macro> prints out the macro
6795 corresponding to a specific C<isl_ast_op_type>.
6796 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6797 for expressions where these macros would be used and prints
6798 out the required macro definitions.
6799 Essentially, C<isl_ast_node_print_macros> calls
6800 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6801 as function argument.
6802 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6803 C<isl_ast_node_if_print> print an C<isl_ast_node>
6804 in C<ISL_FORMAT_C>, but allow for some extra control
6805 through an C<isl_ast_print_options> object.
6806 This object can be created using the following functions.
6808 #include <isl/ast.h>
6809 __isl_give isl_ast_print_options *
6810 isl_ast_print_options_alloc(isl_ctx *ctx);
6811 __isl_give isl_ast_print_options *
6812 isl_ast_print_options_copy(
6813 __isl_keep isl_ast_print_options *options);
6814 __isl_null isl_ast_print_options *
6815 isl_ast_print_options_free(
6816 __isl_take isl_ast_print_options *options);
6818 __isl_give isl_ast_print_options *
6819 isl_ast_print_options_set_print_user(
6820 __isl_take isl_ast_print_options *options,
6821 __isl_give isl_printer *(*print_user)(
6822 __isl_take isl_printer *p,
6823 __isl_take isl_ast_print_options *options,
6824 __isl_keep isl_ast_node *node, void *user),
6826 __isl_give isl_ast_print_options *
6827 isl_ast_print_options_set_print_for(
6828 __isl_take isl_ast_print_options *options,
6829 __isl_give isl_printer *(*print_for)(
6830 __isl_take isl_printer *p,
6831 __isl_take isl_ast_print_options *options,
6832 __isl_keep isl_ast_node *node, void *user),
6835 The callback set by C<isl_ast_print_options_set_print_user>
6836 is called whenever a node of type C<isl_ast_node_user> needs to
6838 The callback set by C<isl_ast_print_options_set_print_for>
6839 is called whenever a node of type C<isl_ast_node_for> needs to
6841 Note that C<isl_ast_node_for_print> will I<not> call the
6842 callback set by C<isl_ast_print_options_set_print_for> on the node
6843 on which C<isl_ast_node_for_print> is called, but only on nested
6844 nodes of type C<isl_ast_node_for>. It is therefore safe to
6845 call C<isl_ast_node_for_print> from within the callback set by
6846 C<isl_ast_print_options_set_print_for>.
6848 The following option determines the type to be used for iterators
6849 while printing the AST.
6851 int isl_options_set_ast_iterator_type(
6852 isl_ctx *ctx, const char *val);
6853 const char *isl_options_get_ast_iterator_type(
6856 The AST printer only prints body nodes as blocks if these
6857 blocks cannot be safely omitted.
6858 For example, a C<for> node with one body node will not be
6859 surrounded with braces in C<ISL_FORMAT_C>.
6860 A block will always be printed by setting the following option.
6862 int isl_options_set_ast_always_print_block(isl_ctx *ctx,
6864 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
6868 #include <isl/ast_build.h>
6869 int isl_options_set_ast_build_atomic_upper_bound(
6870 isl_ctx *ctx, int val);
6871 int isl_options_get_ast_build_atomic_upper_bound(
6873 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6875 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6876 int isl_options_set_ast_build_exploit_nested_bounds(
6877 isl_ctx *ctx, int val);
6878 int isl_options_get_ast_build_exploit_nested_bounds(
6880 int isl_options_set_ast_build_group_coscheduled(
6881 isl_ctx *ctx, int val);
6882 int isl_options_get_ast_build_group_coscheduled(
6884 int isl_options_set_ast_build_scale_strides(
6885 isl_ctx *ctx, int val);
6886 int isl_options_get_ast_build_scale_strides(
6888 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6890 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6891 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6893 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6897 =item * ast_build_atomic_upper_bound
6899 Generate loop upper bounds that consist of the current loop iterator,
6900 an operator and an expression not involving the iterator.
6901 If this option is not set, then the current loop iterator may appear
6902 several times in the upper bound.
6903 For example, when this option is turned off, AST generation
6906 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6910 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6913 When the option is turned on, the following AST is generated
6915 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6918 =item * ast_build_prefer_pdiv
6920 If this option is turned off, then the AST generation will
6921 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6922 operators, but no C<isl_ast_op_pdiv_q> or
6923 C<isl_ast_op_pdiv_r> operators.
6924 If this options is turned on, then C<isl> will try to convert
6925 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6926 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6928 =item * ast_build_exploit_nested_bounds
6930 Simplify conditions based on bounds of nested for loops.
6931 In particular, remove conditions that are implied by the fact
6932 that one or more nested loops have at least one iteration,
6933 meaning that the upper bound is at least as large as the lower bound.
6934 For example, when this option is turned off, AST generation
6937 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6943 for (int c0 = 0; c0 <= N; c0 += 1)
6944 for (int c1 = 0; c1 <= M; c1 += 1)
6947 When the option is turned on, the following AST is generated
6949 for (int c0 = 0; c0 <= N; c0 += 1)
6950 for (int c1 = 0; c1 <= M; c1 += 1)
6953 =item * ast_build_group_coscheduled
6955 If two domain elements are assigned the same schedule point, then
6956 they may be executed in any order and they may even appear in different
6957 loops. If this options is set, then the AST generator will make
6958 sure that coscheduled domain elements do not appear in separate parts
6959 of the AST. This is useful in case of nested AST generation
6960 if the outer AST generation is given only part of a schedule
6961 and the inner AST generation should handle the domains that are
6962 coscheduled by this initial part of the schedule together.
6963 For example if an AST is generated for a schedule
6965 { A[i] -> [0]; B[i] -> [0] }
6967 then the C<isl_ast_build_set_create_leaf> callback described
6968 below may get called twice, once for each domain.
6969 Setting this option ensures that the callback is only called once
6970 on both domains together.
6972 =item * ast_build_separation_bounds
6974 This option specifies which bounds to use during separation.
6975 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6976 then all (possibly implicit) bounds on the current dimension will
6977 be used during separation.
6978 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6979 then only those bounds that are explicitly available will
6980 be used during separation.
6982 =item * ast_build_scale_strides
6984 This option specifies whether the AST generator is allowed
6985 to scale down iterators of strided loops.
6987 =item * ast_build_allow_else
6989 This option specifies whether the AST generator is allowed
6990 to construct if statements with else branches.
6992 =item * ast_build_allow_or
6994 This option specifies whether the AST generator is allowed
6995 to construct if conditions with disjunctions.
6999 =head3 Fine-grained Control over AST Generation
7001 Besides specifying the constraints on the parameters,
7002 an C<isl_ast_build> object can be used to control
7003 various aspects of the AST generation process.
7004 The most prominent way of control is through ``options'',
7005 which can be set using the following function.
7007 #include <isl/ast_build.h>
7008 __isl_give isl_ast_build *
7009 isl_ast_build_set_options(
7010 __isl_take isl_ast_build *control,
7011 __isl_take isl_union_map *options);
7013 The options are encoded in an C<isl_union_map>.
7014 The domain of this union relation refers to the schedule domain,
7015 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
7016 In the case of nested AST generation (see L</"Nested AST Generation">),
7017 the domain of C<options> should refer to the extra piece of the schedule.
7018 That is, it should be equal to the range of the wrapped relation in the
7019 range of the schedule.
7020 The range of the options can consist of elements in one or more spaces,
7021 the names of which determine the effect of the option.
7022 The values of the range typically also refer to the schedule dimension
7023 to which the option applies. In case of nested AST generation
7024 (see L</"Nested AST Generation">), these values refer to the position
7025 of the schedule dimension within the innermost AST generation.
7026 The constraints on the domain elements of
7027 the option should only refer to this dimension and earlier dimensions.
7028 We consider the following spaces.
7032 =item C<separation_class>
7034 This space is a wrapped relation between two one dimensional spaces.
7035 The input space represents the schedule dimension to which the option
7036 applies and the output space represents the separation class.
7037 While constructing a loop corresponding to the specified schedule
7038 dimension(s), the AST generator will try to generate separate loops
7039 for domain elements that are assigned different classes.
7040 If only some of the elements are assigned a class, then those elements
7041 that are not assigned any class will be treated as belonging to a class
7042 that is separate from the explicitly assigned classes.
7043 The typical use case for this option is to separate full tiles from
7045 The other options, described below, are applied after the separation
7048 As an example, consider the separation into full and partial tiles
7049 of a tiling of a triangular domain.
7050 Take, for example, the domain
7052 { A[i,j] : 0 <= i,j and i + j <= 100 }
7054 and a tiling into tiles of 10 by 10. The input to the AST generator
7055 is then the schedule
7057 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
7060 Without any options, the following AST is generated
7062 for (int c0 = 0; c0 <= 10; c0 += 1)
7063 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
7064 for (int c2 = 10 * c0;
7065 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7067 for (int c3 = 10 * c1;
7068 c3 <= min(10 * c1 + 9, -c2 + 100);
7072 Separation into full and partial tiles can be obtained by assigning
7073 a class, say C<0>, to the full tiles. The full tiles are represented by those
7074 values of the first and second schedule dimensions for which there are
7075 values of the third and fourth dimensions to cover an entire tile.
7076 That is, we need to specify the following option
7078 { [a,b,c,d] -> separation_class[[0]->[0]] :
7079 exists b': 0 <= 10a,10b' and
7080 10a+9+10b'+9 <= 100;
7081 [a,b,c,d] -> separation_class[[1]->[0]] :
7082 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
7086 { [a, b, c, d] -> separation_class[[1] -> [0]] :
7087 a >= 0 and b >= 0 and b <= 8 - a;
7088 [a, b, c, d] -> separation_class[[0] -> [0]] :
7091 With this option, the generated AST is as follows
7094 for (int c0 = 0; c0 <= 8; c0 += 1) {
7095 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
7096 for (int c2 = 10 * c0;
7097 c2 <= 10 * c0 + 9; c2 += 1)
7098 for (int c3 = 10 * c1;
7099 c3 <= 10 * c1 + 9; c3 += 1)
7101 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
7102 for (int c2 = 10 * c0;
7103 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7105 for (int c3 = 10 * c1;
7106 c3 <= min(-c2 + 100, 10 * c1 + 9);
7110 for (int c0 = 9; c0 <= 10; c0 += 1)
7111 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
7112 for (int c2 = 10 * c0;
7113 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7115 for (int c3 = 10 * c1;
7116 c3 <= min(10 * c1 + 9, -c2 + 100);
7123 This is a single-dimensional space representing the schedule dimension(s)
7124 to which ``separation'' should be applied. Separation tries to split
7125 a loop into several pieces if this can avoid the generation of guards
7127 See also the C<atomic> option.
7131 This is a single-dimensional space representing the schedule dimension(s)
7132 for which the domains should be considered ``atomic''. That is, the
7133 AST generator will make sure that any given domain space will only appear
7134 in a single loop at the specified level.
7136 Consider the following schedule
7138 { a[i] -> [i] : 0 <= i < 10;
7139 b[i] -> [i+1] : 0 <= i < 10 }
7141 If the following option is specified
7143 { [i] -> separate[x] }
7145 then the following AST will be generated
7149 for (int c0 = 1; c0 <= 9; c0 += 1) {
7156 If, on the other hand, the following option is specified
7158 { [i] -> atomic[x] }
7160 then the following AST will be generated
7162 for (int c0 = 0; c0 <= 10; c0 += 1) {
7169 If neither C<atomic> nor C<separate> is specified, then the AST generator
7170 may produce either of these two results or some intermediate form.
7174 This is a single-dimensional space representing the schedule dimension(s)
7175 that should be I<completely> unrolled.
7176 To obtain a partial unrolling, the user should apply an additional
7177 strip-mining to the schedule and fully unroll the inner loop.
7181 Additional control is available through the following functions.
7183 #include <isl/ast_build.h>
7184 __isl_give isl_ast_build *
7185 isl_ast_build_set_iterators(
7186 __isl_take isl_ast_build *control,
7187 __isl_take isl_id_list *iterators);
7189 The function C<isl_ast_build_set_iterators> allows the user to
7190 specify a list of iterator C<isl_id>s to be used as iterators.
7191 If the input schedule is injective, then
7192 the number of elements in this list should be as large as the dimension
7193 of the schedule space, but no direct correspondence should be assumed
7194 between dimensions and elements.
7195 If the input schedule is not injective, then an additional number
7196 of C<isl_id>s equal to the largest dimension of the input domains
7198 If the number of provided C<isl_id>s is insufficient, then additional
7199 names are automatically generated.
7201 #include <isl/ast_build.h>
7202 __isl_give isl_ast_build *
7203 isl_ast_build_set_create_leaf(
7204 __isl_take isl_ast_build *control,
7205 __isl_give isl_ast_node *(*fn)(
7206 __isl_take isl_ast_build *build,
7207 void *user), void *user);
7210 C<isl_ast_build_set_create_leaf> function allows for the
7211 specification of a callback that should be called whenever the AST
7212 generator arrives at an element of the schedule domain.
7213 The callback should return an AST node that should be inserted
7214 at the corresponding position of the AST. The default action (when
7215 the callback is not set) is to continue generating parts of the AST to scan
7216 all the domain elements associated to the schedule domain element
7217 and to insert user nodes, ``calling'' the domain element, for each of them.
7218 The C<build> argument contains the current state of the C<isl_ast_build>.
7219 To ease nested AST generation (see L</"Nested AST Generation">),
7220 all control information that is
7221 specific to the current AST generation such as the options and
7222 the callbacks has been removed from this C<isl_ast_build>.
7223 The callback would typically return the result of a nested
7225 user defined node created using the following function.
7227 #include <isl/ast.h>
7228 __isl_give isl_ast_node *isl_ast_node_alloc_user(
7229 __isl_take isl_ast_expr *expr);
7231 #include <isl/ast_build.h>
7232 __isl_give isl_ast_build *
7233 isl_ast_build_set_at_each_domain(
7234 __isl_take isl_ast_build *build,
7235 __isl_give isl_ast_node *(*fn)(
7236 __isl_take isl_ast_node *node,
7237 __isl_keep isl_ast_build *build,
7238 void *user), void *user);
7239 __isl_give isl_ast_build *
7240 isl_ast_build_set_before_each_for(
7241 __isl_take isl_ast_build *build,
7242 __isl_give isl_id *(*fn)(
7243 __isl_keep isl_ast_build *build,
7244 void *user), void *user);
7245 __isl_give isl_ast_build *
7246 isl_ast_build_set_after_each_for(
7247 __isl_take isl_ast_build *build,
7248 __isl_give isl_ast_node *(*fn)(
7249 __isl_take isl_ast_node *node,
7250 __isl_keep isl_ast_build *build,
7251 void *user), void *user);
7253 The callback set by C<isl_ast_build_set_at_each_domain> will
7254 be called for each domain AST node.
7255 The callbacks set by C<isl_ast_build_set_before_each_for>
7256 and C<isl_ast_build_set_after_each_for> will be called
7257 for each for AST node. The first will be called in depth-first
7258 pre-order, while the second will be called in depth-first post-order.
7259 Since C<isl_ast_build_set_before_each_for> is called before the for
7260 node is actually constructed, it is only passed an C<isl_ast_build>.
7261 The returned C<isl_id> will be added as an annotation (using
7262 C<isl_ast_node_set_annotation>) to the constructed for node.
7263 In particular, if the user has also specified an C<after_each_for>
7264 callback, then the annotation can be retrieved from the node passed to
7265 that callback using C<isl_ast_node_get_annotation>.
7266 All callbacks should C<NULL> on failure.
7267 The given C<isl_ast_build> can be used to create new
7268 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
7269 or C<isl_ast_build_call_from_pw_multi_aff>.
7271 =head3 Nested AST Generation
7273 C<isl> allows the user to create an AST within the context
7274 of another AST. These nested ASTs are created using the
7275 same C<isl_ast_build_ast_from_schedule> function that is used to create the
7276 outer AST. The C<build> argument should be an C<isl_ast_build>
7277 passed to a callback set by
7278 C<isl_ast_build_set_create_leaf>.
7279 The space of the range of the C<schedule> argument should refer
7280 to this build. In particular, the space should be a wrapped
7281 relation and the domain of this wrapped relation should be the
7282 same as that of the range of the schedule returned by
7283 C<isl_ast_build_get_schedule> below.
7284 In practice, the new schedule is typically
7285 created by calling C<isl_union_map_range_product> on the old schedule
7286 and some extra piece of the schedule.
7287 The space of the schedule domain is also available from
7288 the C<isl_ast_build>.
7290 #include <isl/ast_build.h>
7291 __isl_give isl_union_map *isl_ast_build_get_schedule(
7292 __isl_keep isl_ast_build *build);
7293 __isl_give isl_space *isl_ast_build_get_schedule_space(
7294 __isl_keep isl_ast_build *build);
7295 __isl_give isl_ast_build *isl_ast_build_restrict(
7296 __isl_take isl_ast_build *build,
7297 __isl_take isl_set *set);
7299 The C<isl_ast_build_get_schedule> function returns a (partial)
7300 schedule for the domains elements for which part of the AST still needs to
7301 be generated in the current build.
7302 In particular, the domain elements are mapped to those iterations of the loops
7303 enclosing the current point of the AST generation inside which
7304 the domain elements are executed.
7305 No direct correspondence between
7306 the input schedule and this schedule should be assumed.
7307 The space obtained from C<isl_ast_build_get_schedule_space> can be used
7308 to create a set for C<isl_ast_build_restrict> to intersect
7309 with the current build. In particular, the set passed to
7310 C<isl_ast_build_restrict> can have additional parameters.
7311 The ids of the set dimensions in the space returned by
7312 C<isl_ast_build_get_schedule_space> correspond to the
7313 iterators of the already generated loops.
7314 The user should not rely on the ids of the output dimensions
7315 of the relations in the union relation returned by
7316 C<isl_ast_build_get_schedule> having any particular value.
7320 Although C<isl> is mainly meant to be used as a library,
7321 it also contains some basic applications that use some
7322 of the functionality of C<isl>.
7323 The input may be specified in either the L<isl format>
7324 or the L<PolyLib format>.
7326 =head2 C<isl_polyhedron_sample>
7328 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7329 an integer element of the polyhedron, if there is any.
7330 The first column in the output is the denominator and is always
7331 equal to 1. If the polyhedron contains no integer points,
7332 then a vector of length zero is printed.
7336 C<isl_pip> takes the same input as the C<example> program
7337 from the C<piplib> distribution, i.e., a set of constraints
7338 on the parameters, a line containing only -1 and finally a set
7339 of constraints on a parametric polyhedron.
7340 The coefficients of the parameters appear in the last columns
7341 (but before the final constant column).
7342 The output is the lexicographic minimum of the parametric polyhedron.
7343 As C<isl> currently does not have its own output format, the output
7344 is just a dump of the internal state.
7346 =head2 C<isl_polyhedron_minimize>
7348 C<isl_polyhedron_minimize> computes the minimum of some linear
7349 or affine objective function over the integer points in a polyhedron.
7350 If an affine objective function
7351 is given, then the constant should appear in the last column.
7353 =head2 C<isl_polytope_scan>
7355 Given a polytope, C<isl_polytope_scan> prints
7356 all integer points in the polytope.
7358 =head2 C<isl_codegen>
7360 Given a schedule, a context set and an options relation,
7361 C<isl_codegen> prints out an AST that scans the domain elements
7362 of the schedule in the order of their image(s) taking into account
7363 the constraints in the context set.