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 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);
540 For integer C<isl_val>s we additionally have the following binary property.
543 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
544 __isl_keep isl_val *v2);
546 An C<isl_val> can also be compared to an integer using the following
547 function. The result is undefined for NaN.
550 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
552 The following unary operations are available on C<isl_val>s.
555 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
556 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
557 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
558 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
559 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
561 The following binary operations are available on C<isl_val>s.
564 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
565 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
566 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
567 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
568 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
569 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
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 similiar 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);
799 C<isl_space_is_domain> checks whether the first argument is equal
800 to the domain of the second argument. This requires in particular that
801 the first argument is a set space and that the second argument
804 It is often useful to create objects that live in the
805 same space as some other object. This can be accomplished
806 by creating the new objects
807 (see L</"Creating New Sets and Relations"> or
808 L</"Creating New (Piecewise) Quasipolynomials">) based on the space
809 of the original object.
812 __isl_give isl_space *isl_basic_set_get_space(
813 __isl_keep isl_basic_set *bset);
814 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
816 #include <isl/union_set.h>
817 __isl_give isl_space *isl_union_set_get_space(
818 __isl_keep isl_union_set *uset);
821 __isl_give isl_space *isl_basic_map_get_space(
822 __isl_keep isl_basic_map *bmap);
823 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
825 #include <isl/union_map.h>
826 __isl_give isl_space *isl_union_map_get_space(
827 __isl_keep isl_union_map *umap);
829 #include <isl/constraint.h>
830 __isl_give isl_space *isl_constraint_get_space(
831 __isl_keep isl_constraint *constraint);
833 #include <isl/polynomial.h>
834 __isl_give isl_space *isl_qpolynomial_get_domain_space(
835 __isl_keep isl_qpolynomial *qp);
836 __isl_give isl_space *isl_qpolynomial_get_space(
837 __isl_keep isl_qpolynomial *qp);
838 __isl_give isl_space *isl_qpolynomial_fold_get_space(
839 __isl_keep isl_qpolynomial_fold *fold);
840 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
841 __isl_keep isl_pw_qpolynomial *pwqp);
842 __isl_give isl_space *isl_pw_qpolynomial_get_space(
843 __isl_keep isl_pw_qpolynomial *pwqp);
844 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
845 __isl_keep isl_pw_qpolynomial_fold *pwf);
846 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
847 __isl_keep isl_pw_qpolynomial_fold *pwf);
848 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
849 __isl_keep isl_union_pw_qpolynomial *upwqp);
850 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
851 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
854 __isl_give isl_space *isl_multi_val_get_space(
855 __isl_keep isl_multi_val *mv);
858 __isl_give isl_space *isl_aff_get_domain_space(
859 __isl_keep isl_aff *aff);
860 __isl_give isl_space *isl_aff_get_space(
861 __isl_keep isl_aff *aff);
862 __isl_give isl_space *isl_pw_aff_get_domain_space(
863 __isl_keep isl_pw_aff *pwaff);
864 __isl_give isl_space *isl_pw_aff_get_space(
865 __isl_keep isl_pw_aff *pwaff);
866 __isl_give isl_space *isl_multi_aff_get_domain_space(
867 __isl_keep isl_multi_aff *maff);
868 __isl_give isl_space *isl_multi_aff_get_space(
869 __isl_keep isl_multi_aff *maff);
870 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
871 __isl_keep isl_pw_multi_aff *pma);
872 __isl_give isl_space *isl_pw_multi_aff_get_space(
873 __isl_keep isl_pw_multi_aff *pma);
874 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
875 __isl_keep isl_union_pw_multi_aff *upma);
876 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
877 __isl_keep isl_multi_pw_aff *mpa);
878 __isl_give isl_space *isl_multi_pw_aff_get_space(
879 __isl_keep isl_multi_pw_aff *mpa);
881 #include <isl/point.h>
882 __isl_give isl_space *isl_point_get_space(
883 __isl_keep isl_point *pnt);
885 The identifiers or names of the individual dimensions may be set or read off
886 using the following functions.
888 #include <isl/space.h>
889 __isl_give isl_space *isl_space_set_dim_id(
890 __isl_take isl_space *space,
891 enum isl_dim_type type, unsigned pos,
892 __isl_take isl_id *id);
893 int isl_space_has_dim_id(__isl_keep isl_space *space,
894 enum isl_dim_type type, unsigned pos);
895 __isl_give isl_id *isl_space_get_dim_id(
896 __isl_keep isl_space *space,
897 enum isl_dim_type type, unsigned pos);
898 __isl_give isl_space *isl_space_set_dim_name(
899 __isl_take isl_space *space,
900 enum isl_dim_type type, unsigned pos,
901 __isl_keep const char *name);
902 int isl_space_has_dim_name(__isl_keep isl_space *space,
903 enum isl_dim_type type, unsigned pos);
904 __isl_keep const char *isl_space_get_dim_name(
905 __isl_keep isl_space *space,
906 enum isl_dim_type type, unsigned pos);
908 Note that C<isl_space_get_name> returns a pointer to some internal
909 data structure, so the result can only be used while the
910 corresponding C<isl_space> is alive.
911 Also note that every function that operates on two sets or relations
912 requires that both arguments have the same parameters. This also
913 means that if one of the arguments has named parameters, then the
914 other needs to have named parameters too and the names need to match.
915 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
916 arguments may have different parameters (as long as they are named),
917 in which case the result will have as parameters the union of the parameters of
920 Given the identifier or name of a dimension (typically a parameter),
921 its position can be obtained from the following function.
923 #include <isl/space.h>
924 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
925 enum isl_dim_type type, __isl_keep isl_id *id);
926 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
927 enum isl_dim_type type, const char *name);
929 The identifiers or names of entire spaces may be set or read off
930 using the following functions.
932 #include <isl/space.h>
933 __isl_give isl_space *isl_space_set_tuple_id(
934 __isl_take isl_space *space,
935 enum isl_dim_type type, __isl_take isl_id *id);
936 __isl_give isl_space *isl_space_reset_tuple_id(
937 __isl_take isl_space *space, enum isl_dim_type type);
938 int isl_space_has_tuple_id(__isl_keep isl_space *space,
939 enum isl_dim_type type);
940 __isl_give isl_id *isl_space_get_tuple_id(
941 __isl_keep isl_space *space, enum isl_dim_type type);
942 __isl_give isl_space *isl_space_set_tuple_name(
943 __isl_take isl_space *space,
944 enum isl_dim_type type, const char *s);
945 int isl_space_has_tuple_name(__isl_keep isl_space *space,
946 enum isl_dim_type type);
947 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
948 enum isl_dim_type type);
950 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
951 or C<isl_dim_set>. As with C<isl_space_get_name>,
952 the C<isl_space_get_tuple_name> function returns a pointer to some internal
954 Binary operations require the corresponding spaces of their arguments
955 to have the same name.
957 To keep the names of all parameters and tuples, but reset the user pointers
958 of all the corresponding identifiers, use the following function.
960 __isl_give isl_space *isl_space_reset_user(
961 __isl_take isl_space *space);
963 Spaces can be nested. In particular, the domain of a set or
964 the domain or range of a relation can be a nested relation.
965 This process is also called I<wrapping>.
966 The functions for detecting, constructing and deconstructing
967 such nested spaces can be found in the wrapping properties
968 of L</"Unary Properties">, the wrapping operations
969 of L</"Unary Operations"> and the Cartesian product operations
970 of L</"Basic Operations">.
972 Spaces can be created from other spaces
973 using the following functions.
975 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
976 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
977 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
978 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
979 __isl_give isl_space *isl_space_domain_map(
980 __isl_take isl_space *space);
981 __isl_give isl_space *isl_space_range_map(
982 __isl_take isl_space *space);
983 __isl_give isl_space *isl_space_params(
984 __isl_take isl_space *space);
985 __isl_give isl_space *isl_space_set_from_params(
986 __isl_take isl_space *space);
987 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
988 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
989 __isl_take isl_space *right);
990 __isl_give isl_space *isl_space_align_params(
991 __isl_take isl_space *space1, __isl_take isl_space *space2)
992 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
993 enum isl_dim_type type, unsigned pos, unsigned n);
994 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
995 enum isl_dim_type type, unsigned n);
996 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
997 enum isl_dim_type type, unsigned first, unsigned n);
998 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
999 enum isl_dim_type dst_type, unsigned dst_pos,
1000 enum isl_dim_type src_type, unsigned src_pos,
1002 __isl_give isl_space *isl_space_map_from_set(
1003 __isl_take isl_space *space);
1004 __isl_give isl_space *isl_space_map_from_domain_and_range(
1005 __isl_take isl_space *domain,
1006 __isl_take isl_space *range);
1007 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
1008 __isl_give isl_space *isl_space_curry(
1009 __isl_take isl_space *space);
1010 __isl_give isl_space *isl_space_uncurry(
1011 __isl_take isl_space *space);
1013 Note that if dimensions are added or removed from a space, then
1014 the name and the internal structure are lost.
1018 A local space is essentially a space with
1019 zero or more existentially quantified variables.
1020 The local space of a (constraint of a) basic set or relation can be obtained
1021 using the following functions.
1023 #include <isl/constraint.h>
1024 __isl_give isl_local_space *isl_constraint_get_local_space(
1025 __isl_keep isl_constraint *constraint);
1027 #include <isl/set.h>
1028 __isl_give isl_local_space *isl_basic_set_get_local_space(
1029 __isl_keep isl_basic_set *bset);
1031 #include <isl/map.h>
1032 __isl_give isl_local_space *isl_basic_map_get_local_space(
1033 __isl_keep isl_basic_map *bmap);
1035 A new local space can be created from a space using
1037 #include <isl/local_space.h>
1038 __isl_give isl_local_space *isl_local_space_from_space(
1039 __isl_take isl_space *space);
1041 They can be inspected, modified, copied and freed using the following functions.
1043 #include <isl/local_space.h>
1044 isl_ctx *isl_local_space_get_ctx(
1045 __isl_keep isl_local_space *ls);
1046 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1047 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1048 enum isl_dim_type type);
1049 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1050 __isl_take isl_local_space *ls,
1051 enum isl_dim_type type, __isl_take isl_id *id);
1052 int isl_local_space_has_dim_id(
1053 __isl_keep isl_local_space *ls,
1054 enum isl_dim_type type, unsigned pos);
1055 __isl_give isl_id *isl_local_space_get_dim_id(
1056 __isl_keep isl_local_space *ls,
1057 enum isl_dim_type type, unsigned pos);
1058 int isl_local_space_has_dim_name(
1059 __isl_keep isl_local_space *ls,
1060 enum isl_dim_type type, unsigned pos)
1061 const char *isl_local_space_get_dim_name(
1062 __isl_keep isl_local_space *ls,
1063 enum isl_dim_type type, unsigned pos);
1064 __isl_give isl_local_space *isl_local_space_set_dim_name(
1065 __isl_take isl_local_space *ls,
1066 enum isl_dim_type type, unsigned pos, const char *s);
1067 __isl_give isl_local_space *isl_local_space_set_dim_id(
1068 __isl_take isl_local_space *ls,
1069 enum isl_dim_type type, unsigned pos,
1070 __isl_take isl_id *id);
1071 __isl_give isl_space *isl_local_space_get_space(
1072 __isl_keep isl_local_space *ls);
1073 __isl_give isl_aff *isl_local_space_get_div(
1074 __isl_keep isl_local_space *ls, int pos);
1075 __isl_give isl_local_space *isl_local_space_copy(
1076 __isl_keep isl_local_space *ls);
1077 __isl_null isl_local_space *isl_local_space_free(
1078 __isl_take isl_local_space *ls);
1080 Note that C<isl_local_space_get_div> can only be used on local spaces
1083 Two local spaces can be compared using
1085 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1086 __isl_keep isl_local_space *ls2);
1088 Local spaces can be created from other local spaces
1089 using the functions described in L</"Unary Operations">
1090 and L</"Binary Operations">.
1092 =head2 Input and Output
1094 C<isl> supports its own input/output format, which is similar
1095 to the C<Omega> format, but also supports the C<PolyLib> format
1098 =head3 C<isl> format
1100 The C<isl> format is similar to that of C<Omega>, but has a different
1101 syntax for describing the parameters and allows for the definition
1102 of an existentially quantified variable as the integer division
1103 of an affine expression.
1104 For example, the set of integers C<i> between C<0> and C<n>
1105 such that C<i % 10 <= 6> can be described as
1107 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1110 A set or relation can have several disjuncts, separated
1111 by the keyword C<or>. Each disjunct is either a conjunction
1112 of constraints or a projection (C<exists>) of a conjunction
1113 of constraints. The constraints are separated by the keyword
1116 =head3 C<PolyLib> format
1118 If the represented set is a union, then the first line
1119 contains a single number representing the number of disjuncts.
1120 Otherwise, a line containing the number C<1> is optional.
1122 Each disjunct is represented by a matrix of constraints.
1123 The first line contains two numbers representing
1124 the number of rows and columns,
1125 where the number of rows is equal to the number of constraints
1126 and the number of columns is equal to two plus the number of variables.
1127 The following lines contain the actual rows of the constraint matrix.
1128 In each row, the first column indicates whether the constraint
1129 is an equality (C<0>) or inequality (C<1>). The final column
1130 corresponds to the constant term.
1132 If the set is parametric, then the coefficients of the parameters
1133 appear in the last columns before the constant column.
1134 The coefficients of any existentially quantified variables appear
1135 between those of the set variables and those of the parameters.
1137 =head3 Extended C<PolyLib> format
1139 The extended C<PolyLib> format is nearly identical to the
1140 C<PolyLib> format. The only difference is that the line
1141 containing the number of rows and columns of a constraint matrix
1142 also contains four additional numbers:
1143 the number of output dimensions, the number of input dimensions,
1144 the number of local dimensions (i.e., the number of existentially
1145 quantified variables) and the number of parameters.
1146 For sets, the number of ``output'' dimensions is equal
1147 to the number of set dimensions, while the number of ``input''
1152 #include <isl/set.h>
1153 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1154 isl_ctx *ctx, FILE *input);
1155 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1156 isl_ctx *ctx, const char *str);
1157 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1159 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1162 #include <isl/map.h>
1163 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1164 isl_ctx *ctx, FILE *input);
1165 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1166 isl_ctx *ctx, const char *str);
1167 __isl_give isl_map *isl_map_read_from_file(
1168 isl_ctx *ctx, FILE *input);
1169 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1172 #include <isl/union_set.h>
1173 __isl_give isl_union_set *isl_union_set_read_from_file(
1174 isl_ctx *ctx, FILE *input);
1175 __isl_give isl_union_set *isl_union_set_read_from_str(
1176 isl_ctx *ctx, const char *str);
1178 #include <isl/union_map.h>
1179 __isl_give isl_union_map *isl_union_map_read_from_file(
1180 isl_ctx *ctx, FILE *input);
1181 __isl_give isl_union_map *isl_union_map_read_from_str(
1182 isl_ctx *ctx, const char *str);
1184 The input format is autodetected and may be either the C<PolyLib> format
1185 or the C<isl> format.
1189 Before anything can be printed, an C<isl_printer> needs to
1192 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1194 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1195 __isl_null isl_printer *isl_printer_free(
1196 __isl_take isl_printer *printer);
1197 __isl_give char *isl_printer_get_str(
1198 __isl_keep isl_printer *printer);
1200 The printer can be inspected using the following functions.
1202 FILE *isl_printer_get_file(
1203 __isl_keep isl_printer *printer);
1204 int isl_printer_get_output_format(
1205 __isl_keep isl_printer *p);
1207 The behavior of the printer can be modified in various ways
1209 __isl_give isl_printer *isl_printer_set_output_format(
1210 __isl_take isl_printer *p, int output_format);
1211 __isl_give isl_printer *isl_printer_set_indent(
1212 __isl_take isl_printer *p, int indent);
1213 __isl_give isl_printer *isl_printer_set_indent_prefix(
1214 __isl_take isl_printer *p, const char *prefix);
1215 __isl_give isl_printer *isl_printer_indent(
1216 __isl_take isl_printer *p, int indent);
1217 __isl_give isl_printer *isl_printer_set_prefix(
1218 __isl_take isl_printer *p, const char *prefix);
1219 __isl_give isl_printer *isl_printer_set_suffix(
1220 __isl_take isl_printer *p, const char *suffix);
1222 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1223 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1224 and defaults to C<ISL_FORMAT_ISL>.
1225 Each line in the output is prefixed by C<indent_prefix>,
1226 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
1227 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1228 In the C<PolyLib> format output,
1229 the coefficients of the existentially quantified variables
1230 appear between those of the set variables and those
1232 The function C<isl_printer_indent> increases the indentation
1233 by the specified amount (which may be negative).
1235 To actually print something, use
1237 #include <isl/printer.h>
1238 __isl_give isl_printer *isl_printer_print_double(
1239 __isl_take isl_printer *p, double d);
1241 #include <isl/set.h>
1242 __isl_give isl_printer *isl_printer_print_basic_set(
1243 __isl_take isl_printer *printer,
1244 __isl_keep isl_basic_set *bset);
1245 __isl_give isl_printer *isl_printer_print_set(
1246 __isl_take isl_printer *printer,
1247 __isl_keep isl_set *set);
1249 #include <isl/map.h>
1250 __isl_give isl_printer *isl_printer_print_basic_map(
1251 __isl_take isl_printer *printer,
1252 __isl_keep isl_basic_map *bmap);
1253 __isl_give isl_printer *isl_printer_print_map(
1254 __isl_take isl_printer *printer,
1255 __isl_keep isl_map *map);
1257 #include <isl/union_set.h>
1258 __isl_give isl_printer *isl_printer_print_union_set(
1259 __isl_take isl_printer *p,
1260 __isl_keep isl_union_set *uset);
1262 #include <isl/union_map.h>
1263 __isl_give isl_printer *isl_printer_print_union_map(
1264 __isl_take isl_printer *p,
1265 __isl_keep isl_union_map *umap);
1267 When called on a file printer, the following function flushes
1268 the file. When called on a string printer, the buffer is cleared.
1270 __isl_give isl_printer *isl_printer_flush(
1271 __isl_take isl_printer *p);
1273 =head2 Creating New Sets and Relations
1275 C<isl> has functions for creating some standard sets and relations.
1279 =item * Empty sets and relations
1281 __isl_give isl_basic_set *isl_basic_set_empty(
1282 __isl_take isl_space *space);
1283 __isl_give isl_basic_map *isl_basic_map_empty(
1284 __isl_take isl_space *space);
1285 __isl_give isl_set *isl_set_empty(
1286 __isl_take isl_space *space);
1287 __isl_give isl_map *isl_map_empty(
1288 __isl_take isl_space *space);
1289 __isl_give isl_union_set *isl_union_set_empty(
1290 __isl_take isl_space *space);
1291 __isl_give isl_union_map *isl_union_map_empty(
1292 __isl_take isl_space *space);
1294 For C<isl_union_set>s and C<isl_union_map>s, the space
1295 is only used to specify the parameters.
1297 =item * Universe sets and relations
1299 __isl_give isl_basic_set *isl_basic_set_universe(
1300 __isl_take isl_space *space);
1301 __isl_give isl_basic_map *isl_basic_map_universe(
1302 __isl_take isl_space *space);
1303 __isl_give isl_set *isl_set_universe(
1304 __isl_take isl_space *space);
1305 __isl_give isl_map *isl_map_universe(
1306 __isl_take isl_space *space);
1307 __isl_give isl_union_set *isl_union_set_universe(
1308 __isl_take isl_union_set *uset);
1309 __isl_give isl_union_map *isl_union_map_universe(
1310 __isl_take isl_union_map *umap);
1312 The sets and relations constructed by the functions above
1313 contain all integer values, while those constructed by the
1314 functions below only contain non-negative values.
1316 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1317 __isl_take isl_space *space);
1318 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1319 __isl_take isl_space *space);
1320 __isl_give isl_set *isl_set_nat_universe(
1321 __isl_take isl_space *space);
1322 __isl_give isl_map *isl_map_nat_universe(
1323 __isl_take isl_space *space);
1325 =item * Identity relations
1327 __isl_give isl_basic_map *isl_basic_map_identity(
1328 __isl_take isl_space *space);
1329 __isl_give isl_map *isl_map_identity(
1330 __isl_take isl_space *space);
1332 The number of input and output dimensions in C<space> needs
1335 =item * Lexicographic order
1337 __isl_give isl_map *isl_map_lex_lt(
1338 __isl_take isl_space *set_space);
1339 __isl_give isl_map *isl_map_lex_le(
1340 __isl_take isl_space *set_space);
1341 __isl_give isl_map *isl_map_lex_gt(
1342 __isl_take isl_space *set_space);
1343 __isl_give isl_map *isl_map_lex_ge(
1344 __isl_take isl_space *set_space);
1345 __isl_give isl_map *isl_map_lex_lt_first(
1346 __isl_take isl_space *space, unsigned n);
1347 __isl_give isl_map *isl_map_lex_le_first(
1348 __isl_take isl_space *space, unsigned n);
1349 __isl_give isl_map *isl_map_lex_gt_first(
1350 __isl_take isl_space *space, unsigned n);
1351 __isl_give isl_map *isl_map_lex_ge_first(
1352 __isl_take isl_space *space, unsigned n);
1354 The first four functions take a space for a B<set>
1355 and return relations that express that the elements in the domain
1356 are lexicographically less
1357 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1358 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1359 than the elements in the range.
1360 The last four functions take a space for a map
1361 and return relations that express that the first C<n> dimensions
1362 in the domain are lexicographically less
1363 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1364 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1365 than the first C<n> dimensions in the range.
1369 A basic set or relation can be converted to a set or relation
1370 using the following functions.
1372 __isl_give isl_set *isl_set_from_basic_set(
1373 __isl_take isl_basic_set *bset);
1374 __isl_give isl_map *isl_map_from_basic_map(
1375 __isl_take isl_basic_map *bmap);
1377 Sets and relations can be converted to union sets and relations
1378 using the following functions.
1380 __isl_give isl_union_set *isl_union_set_from_basic_set(
1381 __isl_take isl_basic_set *bset);
1382 __isl_give isl_union_map *isl_union_map_from_basic_map(
1383 __isl_take isl_basic_map *bmap);
1384 __isl_give isl_union_set *isl_union_set_from_set(
1385 __isl_take isl_set *set);
1386 __isl_give isl_union_map *isl_union_map_from_map(
1387 __isl_take isl_map *map);
1389 The inverse conversions below can only be used if the input
1390 union set or relation is known to contain elements in exactly one
1393 __isl_give isl_set *isl_set_from_union_set(
1394 __isl_take isl_union_set *uset);
1395 __isl_give isl_map *isl_map_from_union_map(
1396 __isl_take isl_union_map *umap);
1398 A zero-dimensional (basic) set can be constructed on a given parameter domain
1399 using the following function.
1401 __isl_give isl_basic_set *isl_basic_set_from_params(
1402 __isl_take isl_basic_set *bset);
1403 __isl_give isl_set *isl_set_from_params(
1404 __isl_take isl_set *set);
1406 Sets and relations can be copied and freed again using the following
1409 __isl_give isl_basic_set *isl_basic_set_copy(
1410 __isl_keep isl_basic_set *bset);
1411 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1412 __isl_give isl_union_set *isl_union_set_copy(
1413 __isl_keep isl_union_set *uset);
1414 __isl_give isl_basic_map *isl_basic_map_copy(
1415 __isl_keep isl_basic_map *bmap);
1416 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1417 __isl_give isl_union_map *isl_union_map_copy(
1418 __isl_keep isl_union_map *umap);
1419 __isl_null isl_basic_set *isl_basic_set_free(
1420 __isl_take isl_basic_set *bset);
1421 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1422 __isl_null isl_union_set *isl_union_set_free(
1423 __isl_take isl_union_set *uset);
1424 __isl_null isl_basic_map *isl_basic_map_free(
1425 __isl_take isl_basic_map *bmap);
1426 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1427 __isl_null isl_union_map *isl_union_map_free(
1428 __isl_take isl_union_map *umap);
1430 Other sets and relations can be constructed by starting
1431 from a universe set or relation, adding equality and/or
1432 inequality constraints and then projecting out the
1433 existentially quantified variables, if any.
1434 Constraints can be constructed, manipulated and
1435 added to (or removed from) (basic) sets and relations
1436 using the following functions.
1438 #include <isl/constraint.h>
1439 __isl_give isl_constraint *isl_equality_alloc(
1440 __isl_take isl_local_space *ls);
1441 __isl_give isl_constraint *isl_inequality_alloc(
1442 __isl_take isl_local_space *ls);
1443 __isl_give isl_constraint *isl_constraint_set_constant_si(
1444 __isl_take isl_constraint *constraint, int v);
1445 __isl_give isl_constraint *isl_constraint_set_constant_val(
1446 __isl_take isl_constraint *constraint,
1447 __isl_take isl_val *v);
1448 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1449 __isl_take isl_constraint *constraint,
1450 enum isl_dim_type type, int pos, int v);
1451 __isl_give isl_constraint *
1452 isl_constraint_set_coefficient_val(
1453 __isl_take isl_constraint *constraint,
1454 enum isl_dim_type type, int pos,
1455 __isl_take isl_val *v);
1456 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1457 __isl_take isl_basic_map *bmap,
1458 __isl_take isl_constraint *constraint);
1459 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1460 __isl_take isl_basic_set *bset,
1461 __isl_take isl_constraint *constraint);
1462 __isl_give isl_map *isl_map_add_constraint(
1463 __isl_take isl_map *map,
1464 __isl_take isl_constraint *constraint);
1465 __isl_give isl_set *isl_set_add_constraint(
1466 __isl_take isl_set *set,
1467 __isl_take isl_constraint *constraint);
1468 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1469 __isl_take isl_basic_set *bset,
1470 __isl_take isl_constraint *constraint);
1472 For example, to create a set containing the even integers
1473 between 10 and 42, you would use the following code.
1476 isl_local_space *ls;
1478 isl_basic_set *bset;
1480 space = isl_space_set_alloc(ctx, 0, 2);
1481 bset = isl_basic_set_universe(isl_space_copy(space));
1482 ls = isl_local_space_from_space(space);
1484 c = isl_equality_alloc(isl_local_space_copy(ls));
1485 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1486 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1487 bset = isl_basic_set_add_constraint(bset, c);
1489 c = isl_inequality_alloc(isl_local_space_copy(ls));
1490 c = isl_constraint_set_constant_si(c, -10);
1491 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1492 bset = isl_basic_set_add_constraint(bset, c);
1494 c = isl_inequality_alloc(ls);
1495 c = isl_constraint_set_constant_si(c, 42);
1496 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1497 bset = isl_basic_set_add_constraint(bset, c);
1499 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1503 isl_basic_set *bset;
1504 bset = isl_basic_set_read_from_str(ctx,
1505 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1507 A basic set or relation can also be constructed from two matrices
1508 describing the equalities and the inequalities.
1510 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1511 __isl_take isl_space *space,
1512 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1513 enum isl_dim_type c1,
1514 enum isl_dim_type c2, enum isl_dim_type c3,
1515 enum isl_dim_type c4);
1516 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1517 __isl_take isl_space *space,
1518 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1519 enum isl_dim_type c1,
1520 enum isl_dim_type c2, enum isl_dim_type c3,
1521 enum isl_dim_type c4, enum isl_dim_type c5);
1523 The C<isl_dim_type> arguments indicate the order in which
1524 different kinds of variables appear in the input matrices
1525 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1526 C<isl_dim_set> and C<isl_dim_div> for sets and
1527 of C<isl_dim_cst>, C<isl_dim_param>,
1528 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1530 A (basic or union) set or relation can also be constructed from a
1531 (union) (piecewise) (multiple) affine expression
1532 or a list of affine expressions
1533 (See L<"Piecewise Quasi Affine Expressions"> and
1534 L<"Piecewise Multiple Quasi Affine Expressions">).
1536 __isl_give isl_basic_map *isl_basic_map_from_aff(
1537 __isl_take isl_aff *aff);
1538 __isl_give isl_map *isl_map_from_aff(
1539 __isl_take isl_aff *aff);
1540 __isl_give isl_set *isl_set_from_pw_aff(
1541 __isl_take isl_pw_aff *pwaff);
1542 __isl_give isl_map *isl_map_from_pw_aff(
1543 __isl_take isl_pw_aff *pwaff);
1544 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1545 __isl_take isl_space *domain_space,
1546 __isl_take isl_aff_list *list);
1547 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1548 __isl_take isl_multi_aff *maff)
1549 __isl_give isl_map *isl_map_from_multi_aff(
1550 __isl_take isl_multi_aff *maff)
1551 __isl_give isl_set *isl_set_from_pw_multi_aff(
1552 __isl_take isl_pw_multi_aff *pma);
1553 __isl_give isl_map *isl_map_from_pw_multi_aff(
1554 __isl_take isl_pw_multi_aff *pma);
1555 __isl_give isl_set *isl_set_from_multi_pw_aff(
1556 __isl_take isl_multi_pw_aff *mpa);
1557 __isl_give isl_map *isl_map_from_multi_pw_aff(
1558 __isl_take isl_multi_pw_aff *mpa);
1559 __isl_give isl_union_map *
1560 isl_union_map_from_union_pw_multi_aff(
1561 __isl_take isl_union_pw_multi_aff *upma);
1563 The C<domain_space> argument describes the domain of the resulting
1564 basic relation. It is required because the C<list> may consist
1565 of zero affine expressions.
1567 =head2 Inspecting Sets and Relations
1569 Usually, the user should not have to care about the actual constraints
1570 of the sets and maps, but should instead apply the abstract operations
1571 explained in the following sections.
1572 Occasionally, however, it may be required to inspect the individual
1573 coefficients of the constraints. This section explains how to do so.
1574 In these cases, it may also be useful to have C<isl> compute
1575 an explicit representation of the existentially quantified variables.
1577 __isl_give isl_set *isl_set_compute_divs(
1578 __isl_take isl_set *set);
1579 __isl_give isl_map *isl_map_compute_divs(
1580 __isl_take isl_map *map);
1581 __isl_give isl_union_set *isl_union_set_compute_divs(
1582 __isl_take isl_union_set *uset);
1583 __isl_give isl_union_map *isl_union_map_compute_divs(
1584 __isl_take isl_union_map *umap);
1586 This explicit representation defines the existentially quantified
1587 variables as integer divisions of the other variables, possibly
1588 including earlier existentially quantified variables.
1589 An explicitly represented existentially quantified variable therefore
1590 has a unique value when the values of the other variables are known.
1591 If, furthermore, the same existentials, i.e., existentials
1592 with the same explicit representations, should appear in the
1593 same order in each of the disjuncts of a set or map, then the user should call
1594 either of the following functions.
1596 __isl_give isl_set *isl_set_align_divs(
1597 __isl_take isl_set *set);
1598 __isl_give isl_map *isl_map_align_divs(
1599 __isl_take isl_map *map);
1601 Alternatively, the existentially quantified variables can be removed
1602 using the following functions, which compute an overapproximation.
1604 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1605 __isl_take isl_basic_set *bset);
1606 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1607 __isl_take isl_basic_map *bmap);
1608 __isl_give isl_set *isl_set_remove_divs(
1609 __isl_take isl_set *set);
1610 __isl_give isl_map *isl_map_remove_divs(
1611 __isl_take isl_map *map);
1613 It is also possible to only remove those divs that are defined
1614 in terms of a given range of dimensions or only those for which
1615 no explicit representation is known.
1617 __isl_give isl_basic_set *
1618 isl_basic_set_remove_divs_involving_dims(
1619 __isl_take isl_basic_set *bset,
1620 enum isl_dim_type type,
1621 unsigned first, unsigned n);
1622 __isl_give isl_basic_map *
1623 isl_basic_map_remove_divs_involving_dims(
1624 __isl_take isl_basic_map *bmap,
1625 enum isl_dim_type type,
1626 unsigned first, unsigned n);
1627 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1628 __isl_take isl_set *set, enum isl_dim_type type,
1629 unsigned first, unsigned n);
1630 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1631 __isl_take isl_map *map, enum isl_dim_type type,
1632 unsigned first, unsigned n);
1634 __isl_give isl_basic_set *
1635 isl_basic_set_remove_unknown_divs(
1636 __isl_take isl_basic_set *bset);
1637 __isl_give isl_set *isl_set_remove_unknown_divs(
1638 __isl_take isl_set *set);
1639 __isl_give isl_map *isl_map_remove_unknown_divs(
1640 __isl_take isl_map *map);
1642 To iterate over all the sets or maps in a union set or map, use
1644 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1645 int (*fn)(__isl_take isl_set *set, void *user),
1647 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1648 int (*fn)(__isl_take isl_map *map, void *user),
1651 The number of sets or maps in a union set or map can be obtained
1654 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1655 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1657 To extract the set or map in a given space from a union, use
1659 __isl_give isl_set *isl_union_set_extract_set(
1660 __isl_keep isl_union_set *uset,
1661 __isl_take isl_space *space);
1662 __isl_give isl_map *isl_union_map_extract_map(
1663 __isl_keep isl_union_map *umap,
1664 __isl_take isl_space *space);
1666 To iterate over all the basic sets or maps in a set or map, use
1668 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1669 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1671 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1672 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1675 The callback function C<fn> should return 0 if successful and
1676 -1 if an error occurs. In the latter case, or if any other error
1677 occurs, the above functions will return -1.
1679 It should be noted that C<isl> does not guarantee that
1680 the basic sets or maps passed to C<fn> are disjoint.
1681 If this is required, then the user should call one of
1682 the following functions first.
1684 __isl_give isl_set *isl_set_make_disjoint(
1685 __isl_take isl_set *set);
1686 __isl_give isl_map *isl_map_make_disjoint(
1687 __isl_take isl_map *map);
1689 The number of basic sets in a set can be obtained
1692 int isl_set_n_basic_set(__isl_keep isl_set *set);
1694 To iterate over the constraints of a basic set or map, use
1696 #include <isl/constraint.h>
1698 int isl_basic_set_n_constraint(
1699 __isl_keep isl_basic_set *bset);
1700 int isl_basic_set_foreach_constraint(
1701 __isl_keep isl_basic_set *bset,
1702 int (*fn)(__isl_take isl_constraint *c, void *user),
1704 int isl_basic_map_n_constraint(
1705 __isl_keep isl_basic_map *bmap);
1706 int isl_basic_map_foreach_constraint(
1707 __isl_keep isl_basic_map *bmap,
1708 int (*fn)(__isl_take isl_constraint *c, void *user),
1710 __isl_null isl_constraint *isl_constraint_free(
1711 __isl_take isl_constraint *c);
1713 Again, the callback function C<fn> should return 0 if successful and
1714 -1 if an error occurs. In the latter case, or if any other error
1715 occurs, the above functions will return -1.
1716 The constraint C<c> represents either an equality or an inequality.
1717 Use the following function to find out whether a constraint
1718 represents an equality. If not, it represents an inequality.
1720 int isl_constraint_is_equality(
1721 __isl_keep isl_constraint *constraint);
1723 It is also possible to obtain a list of constraints from a basic
1726 #include <isl/constraint.h>
1727 __isl_give isl_constraint_list *
1728 isl_basic_map_get_constraint_list(
1729 __isl_keep isl_basic_map *bmap);
1730 __isl_give isl_constraint_list *
1731 isl_basic_set_get_constraint_list(
1732 __isl_keep isl_basic_set *bset);
1734 These functions require that all existentially quantified variables
1735 have an explicit representation.
1736 The returned list can be manipulated using the functions in L<"Lists">.
1738 The coefficients of the constraints can be inspected using
1739 the following functions.
1741 int isl_constraint_is_lower_bound(
1742 __isl_keep isl_constraint *constraint,
1743 enum isl_dim_type type, unsigned pos);
1744 int isl_constraint_is_upper_bound(
1745 __isl_keep isl_constraint *constraint,
1746 enum isl_dim_type type, unsigned pos);
1747 __isl_give isl_val *isl_constraint_get_constant_val(
1748 __isl_keep isl_constraint *constraint);
1749 __isl_give isl_val *isl_constraint_get_coefficient_val(
1750 __isl_keep isl_constraint *constraint,
1751 enum isl_dim_type type, int pos);
1752 int isl_constraint_involves_dims(
1753 __isl_keep isl_constraint *constraint,
1754 enum isl_dim_type type, unsigned first, unsigned n);
1756 The explicit representations of the existentially quantified
1757 variables can be inspected using the following function.
1758 Note that the user is only allowed to use this function
1759 if the inspected set or map is the result of a call
1760 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1761 The existentially quantified variable is equal to the floor
1762 of the returned affine expression. The affine expression
1763 itself can be inspected using the functions in
1764 L<"Piecewise Quasi Affine Expressions">.
1766 __isl_give isl_aff *isl_constraint_get_div(
1767 __isl_keep isl_constraint *constraint, int pos);
1769 To obtain the constraints of a basic set or map in matrix
1770 form, use the following functions.
1772 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1773 __isl_keep isl_basic_set *bset,
1774 enum isl_dim_type c1, enum isl_dim_type c2,
1775 enum isl_dim_type c3, enum isl_dim_type c4);
1776 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1777 __isl_keep isl_basic_set *bset,
1778 enum isl_dim_type c1, enum isl_dim_type c2,
1779 enum isl_dim_type c3, enum isl_dim_type c4);
1780 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1781 __isl_keep isl_basic_map *bmap,
1782 enum isl_dim_type c1,
1783 enum isl_dim_type c2, enum isl_dim_type c3,
1784 enum isl_dim_type c4, enum isl_dim_type c5);
1785 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1786 __isl_keep isl_basic_map *bmap,
1787 enum isl_dim_type c1,
1788 enum isl_dim_type c2, enum isl_dim_type c3,
1789 enum isl_dim_type c4, enum isl_dim_type c5);
1791 The C<isl_dim_type> arguments dictate the order in which
1792 different kinds of variables appear in the resulting matrix
1793 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1794 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1796 The number of parameters, input, output or set dimensions can
1797 be obtained using the following functions.
1799 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1800 enum isl_dim_type type);
1801 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1802 enum isl_dim_type type);
1803 unsigned isl_set_dim(__isl_keep isl_set *set,
1804 enum isl_dim_type type);
1805 unsigned isl_map_dim(__isl_keep isl_map *map,
1806 enum isl_dim_type type);
1807 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1808 enum isl_dim_type type);
1810 Note that a C<isl_union_map> only has parameters.
1812 To check whether the description of a set or relation depends
1813 on one or more given dimensions, it is not necessary to iterate over all
1814 constraints. Instead the following functions can be used.
1816 int isl_basic_set_involves_dims(
1817 __isl_keep isl_basic_set *bset,
1818 enum isl_dim_type type, unsigned first, unsigned n);
1819 int isl_set_involves_dims(__isl_keep isl_set *set,
1820 enum isl_dim_type type, unsigned first, unsigned n);
1821 int isl_basic_map_involves_dims(
1822 __isl_keep isl_basic_map *bmap,
1823 enum isl_dim_type type, unsigned first, unsigned n);
1824 int isl_map_involves_dims(__isl_keep isl_map *map,
1825 enum isl_dim_type type, unsigned first, unsigned n);
1827 Similarly, the following functions can be used to check whether
1828 a given dimension is involved in any lower or upper bound.
1830 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1831 enum isl_dim_type type, unsigned pos);
1832 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1833 enum isl_dim_type type, unsigned pos);
1835 Note that these functions return true even if there is a bound on
1836 the dimension on only some of the basic sets of C<set>.
1837 To check if they have a bound for all of the basic sets in C<set>,
1838 use the following functions instead.
1840 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1841 enum isl_dim_type type, unsigned pos);
1842 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1843 enum isl_dim_type type, unsigned pos);
1845 The identifiers or names of the domain and range spaces of a set
1846 or relation can be read off or set using the following functions.
1848 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1849 __isl_take isl_basic_set *bset,
1850 __isl_take isl_id *id);
1851 __isl_give isl_set *isl_set_set_tuple_id(
1852 __isl_take isl_set *set, __isl_take isl_id *id);
1853 __isl_give isl_set *isl_set_reset_tuple_id(
1854 __isl_take isl_set *set);
1855 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1856 __isl_give isl_id *isl_set_get_tuple_id(
1857 __isl_keep isl_set *set);
1858 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1859 __isl_take isl_basic_map *bmap,
1860 enum isl_dim_type type, __isl_take isl_id *id);
1861 __isl_give isl_map *isl_map_set_tuple_id(
1862 __isl_take isl_map *map, enum isl_dim_type type,
1863 __isl_take isl_id *id);
1864 __isl_give isl_map *isl_map_reset_tuple_id(
1865 __isl_take isl_map *map, enum isl_dim_type type);
1866 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1867 enum isl_dim_type type);
1868 __isl_give isl_id *isl_map_get_tuple_id(
1869 __isl_keep isl_map *map, enum isl_dim_type type);
1871 const char *isl_basic_set_get_tuple_name(
1872 __isl_keep isl_basic_set *bset);
1873 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1874 __isl_take isl_basic_set *set, const char *s);
1875 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1876 const char *isl_set_get_tuple_name(
1877 __isl_keep isl_set *set);
1878 __isl_give isl_set *isl_set_set_tuple_name(
1879 __isl_take isl_set *set, const char *s);
1880 const char *isl_basic_map_get_tuple_name(
1881 __isl_keep isl_basic_map *bmap,
1882 enum isl_dim_type type);
1883 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1884 __isl_take isl_basic_map *bmap,
1885 enum isl_dim_type type, const char *s);
1886 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1887 enum isl_dim_type type);
1888 const char *isl_map_get_tuple_name(
1889 __isl_keep isl_map *map,
1890 enum isl_dim_type type);
1891 __isl_give isl_map *isl_map_set_tuple_name(
1892 __isl_take isl_map *map,
1893 enum isl_dim_type type, const char *s);
1895 As with C<isl_space_get_tuple_name>, the value returned points to
1896 an internal data structure.
1897 The identifiers, positions or names of individual dimensions can be
1898 read off using the following functions.
1900 __isl_give isl_id *isl_basic_set_get_dim_id(
1901 __isl_keep isl_basic_set *bset,
1902 enum isl_dim_type type, unsigned pos);
1903 __isl_give isl_set *isl_set_set_dim_id(
1904 __isl_take isl_set *set, enum isl_dim_type type,
1905 unsigned pos, __isl_take isl_id *id);
1906 int isl_set_has_dim_id(__isl_keep isl_set *set,
1907 enum isl_dim_type type, unsigned pos);
1908 __isl_give isl_id *isl_set_get_dim_id(
1909 __isl_keep isl_set *set, enum isl_dim_type type,
1911 int isl_basic_map_has_dim_id(
1912 __isl_keep isl_basic_map *bmap,
1913 enum isl_dim_type type, unsigned pos);
1914 __isl_give isl_map *isl_map_set_dim_id(
1915 __isl_take isl_map *map, enum isl_dim_type type,
1916 unsigned pos, __isl_take isl_id *id);
1917 int isl_map_has_dim_id(__isl_keep isl_map *map,
1918 enum isl_dim_type type, unsigned pos);
1919 __isl_give isl_id *isl_map_get_dim_id(
1920 __isl_keep isl_map *map, enum isl_dim_type type,
1922 __isl_give isl_id *isl_union_map_get_dim_id(
1923 __isl_keep isl_union_map *umap,
1924 enum isl_dim_type type, unsigned pos);
1926 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1927 enum isl_dim_type type, __isl_keep isl_id *id);
1928 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1929 enum isl_dim_type type, __isl_keep isl_id *id);
1930 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1931 enum isl_dim_type type, const char *name);
1932 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1933 enum isl_dim_type type, const char *name);
1935 const char *isl_constraint_get_dim_name(
1936 __isl_keep isl_constraint *constraint,
1937 enum isl_dim_type type, unsigned pos);
1938 const char *isl_basic_set_get_dim_name(
1939 __isl_keep isl_basic_set *bset,
1940 enum isl_dim_type type, unsigned pos);
1941 int isl_set_has_dim_name(__isl_keep isl_set *set,
1942 enum isl_dim_type type, unsigned pos);
1943 const char *isl_set_get_dim_name(
1944 __isl_keep isl_set *set,
1945 enum isl_dim_type type, unsigned pos);
1946 const char *isl_basic_map_get_dim_name(
1947 __isl_keep isl_basic_map *bmap,
1948 enum isl_dim_type type, unsigned pos);
1949 int isl_map_has_dim_name(__isl_keep isl_map *map,
1950 enum isl_dim_type type, unsigned pos);
1951 const char *isl_map_get_dim_name(
1952 __isl_keep isl_map *map,
1953 enum isl_dim_type type, unsigned pos);
1955 These functions are mostly useful to obtain the identifiers, positions
1956 or names of the parameters. Identifiers of individual dimensions are
1957 essentially only useful for printing. They are ignored by all other
1958 operations and may not be preserved across those operations.
1960 The user pointers on all parameters and tuples can be reset
1961 using the following functions.
1963 #include <isl/set.h>
1964 __isl_give isl_set *isl_set_reset_user(
1965 __isl_take isl_set *set);
1966 #include <isl/map.h>
1967 __isl_give isl_map *isl_map_reset_user(
1968 __isl_take isl_map *map);
1969 #include <isl/union_set.h>
1970 __isl_give isl_union_set *isl_union_set_reset_user(
1971 __isl_take isl_union_set *uset);
1972 #include <isl/union_map.h>
1973 __isl_give isl_union_map *isl_union_map_reset_user(
1974 __isl_take isl_union_map *umap);
1978 =head3 Unary Properties
1984 The following functions test whether the given set or relation
1985 contains any integer points. The ``plain'' variants do not perform
1986 any computations, but simply check if the given set or relation
1987 is already known to be empty.
1989 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1990 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1991 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1992 int isl_set_is_empty(__isl_keep isl_set *set);
1993 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1994 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1995 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1996 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1997 int isl_map_is_empty(__isl_keep isl_map *map);
1998 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
2000 =item * Universality
2002 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
2003 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
2004 int isl_set_plain_is_universe(__isl_keep isl_set *set);
2006 =item * Single-valuedness
2008 int isl_basic_map_is_single_valued(
2009 __isl_keep isl_basic_map *bmap);
2010 int isl_map_plain_is_single_valued(
2011 __isl_keep isl_map *map);
2012 int isl_map_is_single_valued(__isl_keep isl_map *map);
2013 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
2017 int isl_map_plain_is_injective(__isl_keep isl_map *map);
2018 int isl_map_is_injective(__isl_keep isl_map *map);
2019 int isl_union_map_plain_is_injective(
2020 __isl_keep isl_union_map *umap);
2021 int isl_union_map_is_injective(
2022 __isl_keep isl_union_map *umap);
2026 int isl_map_is_bijective(__isl_keep isl_map *map);
2027 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
2031 __isl_give isl_val *
2032 isl_basic_map_plain_get_val_if_fixed(
2033 __isl_keep isl_basic_map *bmap,
2034 enum isl_dim_type type, unsigned pos);
2035 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
2036 __isl_keep isl_set *set,
2037 enum isl_dim_type type, unsigned pos);
2038 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
2039 __isl_keep isl_map *map,
2040 enum isl_dim_type type, unsigned pos);
2042 If the set or relation obviously lies on a hyperplane where the given dimension
2043 has a fixed value, then return that value.
2044 Otherwise return NaN.
2048 int isl_set_dim_residue_class_val(
2049 __isl_keep isl_set *set,
2050 int pos, __isl_give isl_val **modulo,
2051 __isl_give isl_val **residue);
2053 Check if the values of the given set dimension are equal to a fixed
2054 value modulo some integer value. If so, assign the modulo to C<*modulo>
2055 and the fixed value to C<*residue>. If the given dimension attains only
2056 a single value, then assign C<0> to C<*modulo> and the fixed value to
2058 If the dimension does not attain only a single value and if no modulo
2059 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
2063 To check whether a set is a parameter domain, use this function:
2065 int isl_set_is_params(__isl_keep isl_set *set);
2066 int isl_union_set_is_params(
2067 __isl_keep isl_union_set *uset);
2071 The following functions check whether the space of the given
2072 (basic) set or relation range is a wrapped relation.
2074 #include <isl/space.h>
2075 int isl_space_is_wrapping(
2076 __isl_keep isl_space *space);
2077 int isl_space_domain_is_wrapping(
2078 __isl_keep isl_space *space);
2079 int isl_space_range_is_wrapping(
2080 __isl_keep isl_space *space);
2082 #include <isl/set.h>
2083 int isl_basic_set_is_wrapping(
2084 __isl_keep isl_basic_set *bset);
2085 int isl_set_is_wrapping(__isl_keep isl_set *set);
2087 #include <isl/map.h>
2088 int isl_map_domain_is_wrapping(
2089 __isl_keep isl_map *map);
2090 int isl_map_range_is_wrapping(
2091 __isl_keep isl_map *map);
2093 The input to C<isl_space_is_wrapping> should
2094 be the space of a set, while that of
2095 C<isl_space_domain_is_wrapping> and
2096 C<isl_space_range_is_wrapping> should be the space of a relation.
2098 =item * Internal Product
2100 int isl_basic_map_can_zip(
2101 __isl_keep isl_basic_map *bmap);
2102 int isl_map_can_zip(__isl_keep isl_map *map);
2104 Check whether the product of domain and range of the given relation
2106 i.e., whether both domain and range are nested relations.
2110 int isl_basic_map_can_curry(
2111 __isl_keep isl_basic_map *bmap);
2112 int isl_map_can_curry(__isl_keep isl_map *map);
2114 Check whether the domain of the (basic) relation is a wrapped relation.
2116 int isl_basic_map_can_uncurry(
2117 __isl_keep isl_basic_map *bmap);
2118 int isl_map_can_uncurry(__isl_keep isl_map *map);
2120 Check whether the range of the (basic) relation is a wrapped relation.
2124 =head3 Binary Properties
2130 int isl_basic_set_plain_is_equal(
2131 __isl_keep isl_basic_set *bset1,
2132 __isl_keep isl_basic_set *bset2);
2133 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2134 __isl_keep isl_set *set2);
2135 int isl_set_is_equal(__isl_keep isl_set *set1,
2136 __isl_keep isl_set *set2);
2137 int isl_union_set_is_equal(
2138 __isl_keep isl_union_set *uset1,
2139 __isl_keep isl_union_set *uset2);
2140 int isl_basic_map_is_equal(
2141 __isl_keep isl_basic_map *bmap1,
2142 __isl_keep isl_basic_map *bmap2);
2143 int isl_map_is_equal(__isl_keep isl_map *map1,
2144 __isl_keep isl_map *map2);
2145 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2146 __isl_keep isl_map *map2);
2147 int isl_union_map_is_equal(
2148 __isl_keep isl_union_map *umap1,
2149 __isl_keep isl_union_map *umap2);
2151 =item * Disjointness
2153 int isl_basic_set_is_disjoint(
2154 __isl_keep isl_basic_set *bset1,
2155 __isl_keep isl_basic_set *bset2);
2156 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2157 __isl_keep isl_set *set2);
2158 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2159 __isl_keep isl_set *set2);
2160 int isl_basic_map_is_disjoint(
2161 __isl_keep isl_basic_map *bmap1,
2162 __isl_keep isl_basic_map *bmap2);
2163 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2164 __isl_keep isl_map *map2);
2168 int isl_basic_set_is_subset(
2169 __isl_keep isl_basic_set *bset1,
2170 __isl_keep isl_basic_set *bset2);
2171 int isl_set_is_subset(__isl_keep isl_set *set1,
2172 __isl_keep isl_set *set2);
2173 int isl_set_is_strict_subset(
2174 __isl_keep isl_set *set1,
2175 __isl_keep isl_set *set2);
2176 int isl_union_set_is_subset(
2177 __isl_keep isl_union_set *uset1,
2178 __isl_keep isl_union_set *uset2);
2179 int isl_union_set_is_strict_subset(
2180 __isl_keep isl_union_set *uset1,
2181 __isl_keep isl_union_set *uset2);
2182 int isl_basic_map_is_subset(
2183 __isl_keep isl_basic_map *bmap1,
2184 __isl_keep isl_basic_map *bmap2);
2185 int isl_basic_map_is_strict_subset(
2186 __isl_keep isl_basic_map *bmap1,
2187 __isl_keep isl_basic_map *bmap2);
2188 int isl_map_is_subset(
2189 __isl_keep isl_map *map1,
2190 __isl_keep isl_map *map2);
2191 int isl_map_is_strict_subset(
2192 __isl_keep isl_map *map1,
2193 __isl_keep isl_map *map2);
2194 int isl_union_map_is_subset(
2195 __isl_keep isl_union_map *umap1,
2196 __isl_keep isl_union_map *umap2);
2197 int isl_union_map_is_strict_subset(
2198 __isl_keep isl_union_map *umap1,
2199 __isl_keep isl_union_map *umap2);
2201 Check whether the first argument is a (strict) subset of the
2206 Every comparison function returns a negative value if the first
2207 argument is considered smaller than the second, a positive value
2208 if the first argument is considered greater and zero if the two
2209 constraints are considered the same by the comparison criterion.
2211 #include <isl/constraint.h>
2212 int isl_constraint_plain_cmp(
2213 __isl_keep isl_constraint *c1,
2214 __isl_keep isl_constraint *c2);
2216 This function is useful for sorting C<isl_constraint>s.
2217 The order depends on the internal representation of the inputs.
2218 The order is fixed over different calls to the function (assuming
2219 the internal representation of the inputs has not changed), but may
2220 change over different versions of C<isl>.
2222 #include <isl/constraint.h>
2223 int isl_constraint_cmp_last_non_zero(
2224 __isl_keep isl_constraint *c1,
2225 __isl_keep isl_constraint *c2);
2227 This function can be used to sort constraints that live in the same
2228 local space. Constraints that involve ``earlier'' dimensions or
2229 that have a smaller coefficient for the shared latest dimension
2230 are considered smaller than other constraints.
2231 This function only defines a B<partial> order.
2233 #include <isl/set.h>
2234 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2235 __isl_keep isl_set *set2);
2237 This function is useful for sorting C<isl_set>s.
2238 The order depends on the internal representation of the inputs.
2239 The order is fixed over different calls to the function (assuming
2240 the internal representation of the inputs has not changed), but may
2241 change over different versions of C<isl>.
2245 =head2 Unary Operations
2251 __isl_give isl_set *isl_set_complement(
2252 __isl_take isl_set *set);
2253 __isl_give isl_map *isl_map_complement(
2254 __isl_take isl_map *map);
2258 __isl_give isl_basic_map *isl_basic_map_reverse(
2259 __isl_take isl_basic_map *bmap);
2260 __isl_give isl_map *isl_map_reverse(
2261 __isl_take isl_map *map);
2262 __isl_give isl_union_map *isl_union_map_reverse(
2263 __isl_take isl_union_map *umap);
2267 #include <isl/local_space.h>
2268 __isl_give isl_local_space *isl_local_space_domain(
2269 __isl_take isl_local_space *ls);
2270 __isl_give isl_local_space *isl_local_space_range(
2271 __isl_take isl_local_space *ls);
2273 #include <isl/set.h>
2274 __isl_give isl_basic_set *isl_basic_set_project_out(
2275 __isl_take isl_basic_set *bset,
2276 enum isl_dim_type type, unsigned first, unsigned n);
2277 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2278 enum isl_dim_type type, unsigned first, unsigned n);
2279 __isl_give isl_basic_set *isl_basic_set_params(
2280 __isl_take isl_basic_set *bset);
2281 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2283 #include <isl/map.h>
2284 __isl_give isl_basic_map *isl_basic_map_project_out(
2285 __isl_take isl_basic_map *bmap,
2286 enum isl_dim_type type, unsigned first, unsigned n);
2287 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2288 enum isl_dim_type type, unsigned first, unsigned n);
2289 __isl_give isl_basic_set *isl_basic_map_domain(
2290 __isl_take isl_basic_map *bmap);
2291 __isl_give isl_basic_set *isl_basic_map_range(
2292 __isl_take isl_basic_map *bmap);
2293 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2294 __isl_give isl_set *isl_map_domain(
2295 __isl_take isl_map *bmap);
2296 __isl_give isl_set *isl_map_range(
2297 __isl_take isl_map *map);
2299 #include <isl/union_set.h>
2300 __isl_give isl_set *isl_union_set_params(
2301 __isl_take isl_union_set *uset);
2303 #include <isl/union_map.h>
2304 __isl_give isl_union_map *isl_union_map_project_out(
2305 __isl_take isl_union_map *umap,
2306 enum isl_dim_type type, unsigned first, unsigned n);
2307 __isl_give isl_set *isl_union_map_params(
2308 __isl_take isl_union_map *umap);
2309 __isl_give isl_union_set *isl_union_map_domain(
2310 __isl_take isl_union_map *umap);
2311 __isl_give isl_union_set *isl_union_map_range(
2312 __isl_take isl_union_map *umap);
2314 The function C<isl_union_map_project_out> can only project out
2317 #include <isl/map.h>
2318 __isl_give isl_basic_map *isl_basic_map_domain_map(
2319 __isl_take isl_basic_map *bmap);
2320 __isl_give isl_basic_map *isl_basic_map_range_map(
2321 __isl_take isl_basic_map *bmap);
2322 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2323 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2325 #include <isl/union_map.h>
2326 __isl_give isl_union_map *isl_union_map_domain_map(
2327 __isl_take isl_union_map *umap);
2328 __isl_give isl_union_map *isl_union_map_range_map(
2329 __isl_take isl_union_map *umap);
2331 The functions above construct a (basic, regular or union) relation
2332 that maps (a wrapped version of) the input relation to its domain or range.
2336 __isl_give isl_basic_set *isl_basic_set_eliminate(
2337 __isl_take isl_basic_set *bset,
2338 enum isl_dim_type type,
2339 unsigned first, unsigned n);
2340 __isl_give isl_set *isl_set_eliminate(
2341 __isl_take isl_set *set, enum isl_dim_type type,
2342 unsigned first, unsigned n);
2343 __isl_give isl_basic_map *isl_basic_map_eliminate(
2344 __isl_take isl_basic_map *bmap,
2345 enum isl_dim_type type,
2346 unsigned first, unsigned n);
2347 __isl_give isl_map *isl_map_eliminate(
2348 __isl_take isl_map *map, enum isl_dim_type type,
2349 unsigned first, unsigned n);
2351 Eliminate the coefficients for the given dimensions from the constraints,
2352 without removing the dimensions.
2354 =item * Constructing a relation from a set
2356 #include <isl/local_space.h>
2357 __isl_give isl_local_space *isl_local_space_from_domain(
2358 __isl_take isl_local_space *ls);
2360 #include <isl/map.h>
2361 __isl_give isl_map *isl_map_from_domain(
2362 __isl_take isl_set *set);
2363 __isl_give isl_map *isl_map_from_range(
2364 __isl_take isl_set *set);
2366 Create a relation with the given set as domain or range.
2367 The range or domain of the created relation is a zero-dimensional
2368 flat anonymous space.
2372 __isl_give isl_basic_set *isl_basic_set_fix_si(
2373 __isl_take isl_basic_set *bset,
2374 enum isl_dim_type type, unsigned pos, int value);
2375 __isl_give isl_basic_set *isl_basic_set_fix_val(
2376 __isl_take isl_basic_set *bset,
2377 enum isl_dim_type type, unsigned pos,
2378 __isl_take isl_val *v);
2379 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2380 enum isl_dim_type type, unsigned pos, int value);
2381 __isl_give isl_set *isl_set_fix_val(
2382 __isl_take isl_set *set,
2383 enum isl_dim_type type, unsigned pos,
2384 __isl_take isl_val *v);
2385 __isl_give isl_basic_map *isl_basic_map_fix_si(
2386 __isl_take isl_basic_map *bmap,
2387 enum isl_dim_type type, unsigned pos, int value);
2388 __isl_give isl_basic_map *isl_basic_map_fix_val(
2389 __isl_take isl_basic_map *bmap,
2390 enum isl_dim_type type, unsigned pos,
2391 __isl_take isl_val *v);
2392 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2393 enum isl_dim_type type, unsigned pos, int value);
2394 __isl_give isl_map *isl_map_fix_val(
2395 __isl_take isl_map *map,
2396 enum isl_dim_type type, unsigned pos,
2397 __isl_take isl_val *v);
2399 Intersect the set or relation with the hyperplane where the given
2400 dimension has the fixed given value.
2402 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2403 __isl_take isl_basic_map *bmap,
2404 enum isl_dim_type type, unsigned pos, int value);
2405 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2406 __isl_take isl_basic_map *bmap,
2407 enum isl_dim_type type, unsigned pos, int value);
2408 __isl_give isl_set *isl_set_lower_bound_si(
2409 __isl_take isl_set *set,
2410 enum isl_dim_type type, unsigned pos, int value);
2411 __isl_give isl_set *isl_set_lower_bound_val(
2412 __isl_take isl_set *set,
2413 enum isl_dim_type type, unsigned pos,
2414 __isl_take isl_val *value);
2415 __isl_give isl_map *isl_map_lower_bound_si(
2416 __isl_take isl_map *map,
2417 enum isl_dim_type type, unsigned pos, int value);
2418 __isl_give isl_set *isl_set_upper_bound_si(
2419 __isl_take isl_set *set,
2420 enum isl_dim_type type, unsigned pos, int value);
2421 __isl_give isl_set *isl_set_upper_bound_val(
2422 __isl_take isl_set *set,
2423 enum isl_dim_type type, unsigned pos,
2424 __isl_take isl_val *value);
2425 __isl_give isl_map *isl_map_upper_bound_si(
2426 __isl_take isl_map *map,
2427 enum isl_dim_type type, unsigned pos, int value);
2429 Intersect the set or relation with the half-space where the given
2430 dimension has a value bounded by the fixed given integer value.
2432 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2433 enum isl_dim_type type1, int pos1,
2434 enum isl_dim_type type2, int pos2);
2435 __isl_give isl_basic_map *isl_basic_map_equate(
2436 __isl_take isl_basic_map *bmap,
2437 enum isl_dim_type type1, int pos1,
2438 enum isl_dim_type type2, int pos2);
2439 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2440 enum isl_dim_type type1, int pos1,
2441 enum isl_dim_type type2, int pos2);
2443 Intersect the set or relation with the hyperplane where the given
2444 dimensions are equal to each other.
2446 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2447 enum isl_dim_type type1, int pos1,
2448 enum isl_dim_type type2, int pos2);
2450 Intersect the relation with the hyperplane where the given
2451 dimensions have opposite values.
2453 __isl_give isl_map *isl_map_order_le(
2454 __isl_take isl_map *map,
2455 enum isl_dim_type type1, int pos1,
2456 enum isl_dim_type type2, int pos2);
2457 __isl_give isl_basic_map *isl_basic_map_order_ge(
2458 __isl_take isl_basic_map *bmap,
2459 enum isl_dim_type type1, int pos1,
2460 enum isl_dim_type type2, int pos2);
2461 __isl_give isl_map *isl_map_order_ge(
2462 __isl_take isl_map *map,
2463 enum isl_dim_type type1, int pos1,
2464 enum isl_dim_type type2, int pos2);
2465 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2466 enum isl_dim_type type1, int pos1,
2467 enum isl_dim_type type2, int pos2);
2468 __isl_give isl_basic_map *isl_basic_map_order_gt(
2469 __isl_take isl_basic_map *bmap,
2470 enum isl_dim_type type1, int pos1,
2471 enum isl_dim_type type2, int pos2);
2472 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2473 enum isl_dim_type type1, int pos1,
2474 enum isl_dim_type type2, int pos2);
2476 Intersect the relation with the half-space where the given
2477 dimensions satisfy the given ordering.
2481 __isl_give isl_map *isl_set_identity(
2482 __isl_take isl_set *set);
2483 __isl_give isl_union_map *isl_union_set_identity(
2484 __isl_take isl_union_set *uset);
2486 Construct an identity relation on the given (union) set.
2490 __isl_give isl_basic_set *isl_basic_map_deltas(
2491 __isl_take isl_basic_map *bmap);
2492 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2493 __isl_give isl_union_set *isl_union_map_deltas(
2494 __isl_take isl_union_map *umap);
2496 These functions return a (basic) set containing the differences
2497 between image elements and corresponding domain elements in the input.
2499 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2500 __isl_take isl_basic_map *bmap);
2501 __isl_give isl_map *isl_map_deltas_map(
2502 __isl_take isl_map *map);
2503 __isl_give isl_union_map *isl_union_map_deltas_map(
2504 __isl_take isl_union_map *umap);
2506 The functions above construct a (basic, regular or union) relation
2507 that maps (a wrapped version of) the input relation to its delta set.
2511 Simplify the representation of a set or relation by trying
2512 to combine pairs of basic sets or relations into a single
2513 basic set or relation.
2515 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2516 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2517 __isl_give isl_union_set *isl_union_set_coalesce(
2518 __isl_take isl_union_set *uset);
2519 __isl_give isl_union_map *isl_union_map_coalesce(
2520 __isl_take isl_union_map *umap);
2522 One of the methods for combining pairs of basic sets or relations
2523 can result in coefficients that are much larger than those that appear
2524 in the constraints of the input. By default, the coefficients are
2525 not allowed to grow larger, but this can be changed by unsetting
2526 the following option.
2528 int isl_options_set_coalesce_bounded_wrapping(
2529 isl_ctx *ctx, int val);
2530 int isl_options_get_coalesce_bounded_wrapping(
2533 =item * Detecting equalities
2535 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2536 __isl_take isl_basic_set *bset);
2537 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2538 __isl_take isl_basic_map *bmap);
2539 __isl_give isl_set *isl_set_detect_equalities(
2540 __isl_take isl_set *set);
2541 __isl_give isl_map *isl_map_detect_equalities(
2542 __isl_take isl_map *map);
2543 __isl_give isl_union_set *isl_union_set_detect_equalities(
2544 __isl_take isl_union_set *uset);
2545 __isl_give isl_union_map *isl_union_map_detect_equalities(
2546 __isl_take isl_union_map *umap);
2548 Simplify the representation of a set or relation by detecting implicit
2551 =item * Removing redundant constraints
2553 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2554 __isl_take isl_basic_set *bset);
2555 __isl_give isl_set *isl_set_remove_redundancies(
2556 __isl_take isl_set *set);
2557 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2558 __isl_take isl_basic_map *bmap);
2559 __isl_give isl_map *isl_map_remove_redundancies(
2560 __isl_take isl_map *map);
2564 __isl_give isl_basic_set *isl_set_convex_hull(
2565 __isl_take isl_set *set);
2566 __isl_give isl_basic_map *isl_map_convex_hull(
2567 __isl_take isl_map *map);
2569 If the input set or relation has any existentially quantified
2570 variables, then the result of these operations is currently undefined.
2574 #include <isl/set.h>
2575 __isl_give isl_basic_set *
2576 isl_set_unshifted_simple_hull(
2577 __isl_take isl_set *set);
2578 __isl_give isl_basic_set *isl_set_simple_hull(
2579 __isl_take isl_set *set);
2580 __isl_give isl_basic_set *
2581 isl_set_unshifted_simple_hull_from_set_list(
2582 __isl_take isl_set *set,
2583 __isl_take isl_set_list *list);
2585 #include <isl/map.h>
2586 __isl_give isl_basic_map *
2587 isl_map_unshifted_simple_hull(
2588 __isl_take isl_map *map);
2589 __isl_give isl_basic_map *isl_map_simple_hull(
2590 __isl_take isl_map *map);
2592 #include <isl/union_map.h>
2593 __isl_give isl_union_map *isl_union_map_simple_hull(
2594 __isl_take isl_union_map *umap);
2596 These functions compute a single basic set or relation
2597 that contains the whole input set or relation.
2598 In particular, the output is described by translates
2599 of the constraints describing the basic sets or relations in the input.
2600 In case of C<isl_set_unshifted_simple_hull>, only the original
2601 constraints are used, without any translation.
2602 In case of C<isl_set_unshifted_simple_hull_from_set_list>, the
2603 constraints are taken from the elements of the second argument.
2607 (See \autoref{s:simple hull}.)
2613 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2614 __isl_take isl_basic_set *bset);
2615 __isl_give isl_basic_set *isl_set_affine_hull(
2616 __isl_take isl_set *set);
2617 __isl_give isl_union_set *isl_union_set_affine_hull(
2618 __isl_take isl_union_set *uset);
2619 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2620 __isl_take isl_basic_map *bmap);
2621 __isl_give isl_basic_map *isl_map_affine_hull(
2622 __isl_take isl_map *map);
2623 __isl_give isl_union_map *isl_union_map_affine_hull(
2624 __isl_take isl_union_map *umap);
2626 In case of union sets and relations, the affine hull is computed
2629 =item * Polyhedral hull
2631 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2632 __isl_take isl_set *set);
2633 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2634 __isl_take isl_map *map);
2635 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2636 __isl_take isl_union_set *uset);
2637 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2638 __isl_take isl_union_map *umap);
2640 These functions compute a single basic set or relation
2641 not involving any existentially quantified variables
2642 that contains the whole input set or relation.
2643 In case of union sets and relations, the polyhedral hull is computed
2646 =item * Other approximations
2648 __isl_give isl_basic_set *
2649 isl_basic_set_drop_constraints_involving_dims(
2650 __isl_take isl_basic_set *bset,
2651 enum isl_dim_type type,
2652 unsigned first, unsigned n);
2653 __isl_give isl_basic_map *
2654 isl_basic_map_drop_constraints_involving_dims(
2655 __isl_take isl_basic_map *bmap,
2656 enum isl_dim_type type,
2657 unsigned first, unsigned n);
2658 __isl_give isl_basic_set *
2659 isl_basic_set_drop_constraints_not_involving_dims(
2660 __isl_take isl_basic_set *bset,
2661 enum isl_dim_type type,
2662 unsigned first, unsigned n);
2663 __isl_give isl_set *
2664 isl_set_drop_constraints_involving_dims(
2665 __isl_take isl_set *set,
2666 enum isl_dim_type type,
2667 unsigned first, unsigned n);
2668 __isl_give isl_map *
2669 isl_map_drop_constraints_involving_dims(
2670 __isl_take isl_map *map,
2671 enum isl_dim_type type,
2672 unsigned first, unsigned n);
2674 These functions drop any constraints (not) involving the specified dimensions.
2675 Note that the result depends on the representation of the input.
2679 __isl_give isl_basic_set *isl_basic_set_sample(
2680 __isl_take isl_basic_set *bset);
2681 __isl_give isl_basic_set *isl_set_sample(
2682 __isl_take isl_set *set);
2683 __isl_give isl_basic_map *isl_basic_map_sample(
2684 __isl_take isl_basic_map *bmap);
2685 __isl_give isl_basic_map *isl_map_sample(
2686 __isl_take isl_map *map);
2688 If the input (basic) set or relation is non-empty, then return
2689 a singleton subset of the input. Otherwise, return an empty set.
2691 =item * Optimization
2693 #include <isl/ilp.h>
2694 __isl_give isl_val *isl_basic_set_max_val(
2695 __isl_keep isl_basic_set *bset,
2696 __isl_keep isl_aff *obj);
2697 __isl_give isl_val *isl_set_min_val(
2698 __isl_keep isl_set *set,
2699 __isl_keep isl_aff *obj);
2700 __isl_give isl_val *isl_set_max_val(
2701 __isl_keep isl_set *set,
2702 __isl_keep isl_aff *obj);
2704 Compute the minimum or maximum of the integer affine expression C<obj>
2705 over the points in C<set>, returning the result in C<opt>.
2706 The result is C<NULL> in case of an error, the optimal value in case
2707 there is one, negative infinity or infinity if the problem is unbounded and
2708 NaN if the problem is empty.
2710 =item * Parametric optimization
2712 __isl_give isl_pw_aff *isl_set_dim_min(
2713 __isl_take isl_set *set, int pos);
2714 __isl_give isl_pw_aff *isl_set_dim_max(
2715 __isl_take isl_set *set, int pos);
2716 __isl_give isl_pw_aff *isl_map_dim_max(
2717 __isl_take isl_map *map, int pos);
2719 Compute the minimum or maximum of the given set or output dimension
2720 as a function of the parameters (and input dimensions), but independently
2721 of the other set or output dimensions.
2722 For lexicographic optimization, see L<"Lexicographic Optimization">.
2726 The following functions compute either the set of (rational) coefficient
2727 values of valid constraints for the given set or the set of (rational)
2728 values satisfying the constraints with coefficients from the given set.
2729 Internally, these two sets of functions perform essentially the
2730 same operations, except that the set of coefficients is assumed to
2731 be a cone, while the set of values may be any polyhedron.
2732 The current implementation is based on the Farkas lemma and
2733 Fourier-Motzkin elimination, but this may change or be made optional
2734 in future. In particular, future implementations may use different
2735 dualization algorithms or skip the elimination step.
2737 __isl_give isl_basic_set *isl_basic_set_coefficients(
2738 __isl_take isl_basic_set *bset);
2739 __isl_give isl_basic_set *isl_set_coefficients(
2740 __isl_take isl_set *set);
2741 __isl_give isl_union_set *isl_union_set_coefficients(
2742 __isl_take isl_union_set *bset);
2743 __isl_give isl_basic_set *isl_basic_set_solutions(
2744 __isl_take isl_basic_set *bset);
2745 __isl_give isl_basic_set *isl_set_solutions(
2746 __isl_take isl_set *set);
2747 __isl_give isl_union_set *isl_union_set_solutions(
2748 __isl_take isl_union_set *bset);
2752 __isl_give isl_map *isl_map_fixed_power_val(
2753 __isl_take isl_map *map,
2754 __isl_take isl_val *exp);
2755 __isl_give isl_union_map *
2756 isl_union_map_fixed_power_val(
2757 __isl_take isl_union_map *umap,
2758 __isl_take isl_val *exp);
2760 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2761 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2762 of C<map> is computed.
2764 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2766 __isl_give isl_union_map *isl_union_map_power(
2767 __isl_take isl_union_map *umap, int *exact);
2769 Compute a parametric representation for all positive powers I<k> of C<map>.
2770 The result maps I<k> to a nested relation corresponding to the
2771 I<k>th power of C<map>.
2772 The result may be an overapproximation. If the result is known to be exact,
2773 then C<*exact> is set to C<1>.
2775 =item * Transitive closure
2777 __isl_give isl_map *isl_map_transitive_closure(
2778 __isl_take isl_map *map, int *exact);
2779 __isl_give isl_union_map *isl_union_map_transitive_closure(
2780 __isl_take isl_union_map *umap, int *exact);
2782 Compute the transitive closure of C<map>.
2783 The result may be an overapproximation. If the result is known to be exact,
2784 then C<*exact> is set to C<1>.
2786 =item * Reaching path lengths
2788 __isl_give isl_map *isl_map_reaching_path_lengths(
2789 __isl_take isl_map *map, int *exact);
2791 Compute a relation that maps each element in the range of C<map>
2792 to the lengths of all paths composed of edges in C<map> that
2793 end up in the given element.
2794 The result may be an overapproximation. If the result is known to be exact,
2795 then C<*exact> is set to C<1>.
2796 To compute the I<maximal> path length, the resulting relation
2797 should be postprocessed by C<isl_map_lexmax>.
2798 In particular, if the input relation is a dependence relation
2799 (mapping sources to sinks), then the maximal path length corresponds
2800 to the free schedule.
2801 Note, however, that C<isl_map_lexmax> expects the maximum to be
2802 finite, so if the path lengths are unbounded (possibly due to
2803 the overapproximation), then you will get an error message.
2807 #include <isl/space.h>
2808 __isl_give isl_space *isl_space_wrap(
2809 __isl_take isl_space *space);
2810 __isl_give isl_space *isl_space_unwrap(
2811 __isl_take isl_space *space);
2813 #include <isl/set.h>
2814 __isl_give isl_basic_map *isl_basic_set_unwrap(
2815 __isl_take isl_basic_set *bset);
2816 __isl_give isl_map *isl_set_unwrap(
2817 __isl_take isl_set *set);
2819 #include <isl/map.h>
2820 __isl_give isl_basic_set *isl_basic_map_wrap(
2821 __isl_take isl_basic_map *bmap);
2822 __isl_give isl_set *isl_map_wrap(
2823 __isl_take isl_map *map);
2825 #include <isl/union_set.h>
2826 __isl_give isl_union_map *isl_union_set_unwrap(
2827 __isl_take isl_union_set *uset);
2829 #include <isl/union_map.h>
2830 __isl_give isl_union_set *isl_union_map_wrap(
2831 __isl_take isl_union_map *umap);
2833 The input to C<isl_space_unwrap> should
2834 be the space of a set, while that of
2835 C<isl_space_wrap> should be the space of a relation.
2836 Conversely, the output of C<isl_space_unwrap> is the space
2837 of a relation, while that of C<isl_space_wrap> is the space of a set.
2841 Remove any internal structure of domain (and range) of the given
2842 set or relation. If there is any such internal structure in the input,
2843 then the name of the space is also removed.
2845 #include <isl/local_space.h>
2846 __isl_give isl_local_space *
2847 isl_local_space_flatten_domain(
2848 __isl_take isl_local_space *ls);
2849 __isl_give isl_local_space *
2850 isl_local_space_flatten_range(
2851 __isl_take isl_local_space *ls);
2853 #include <isl/set.h>
2854 __isl_give isl_basic_set *isl_basic_set_flatten(
2855 __isl_take isl_basic_set *bset);
2856 __isl_give isl_set *isl_set_flatten(
2857 __isl_take isl_set *set);
2859 #include <isl/map.h>
2860 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2861 __isl_take isl_basic_map *bmap);
2862 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2863 __isl_take isl_basic_map *bmap);
2864 __isl_give isl_map *isl_map_flatten_range(
2865 __isl_take isl_map *map);
2866 __isl_give isl_map *isl_map_flatten_domain(
2867 __isl_take isl_map *map);
2868 __isl_give isl_basic_map *isl_basic_map_flatten(
2869 __isl_take isl_basic_map *bmap);
2870 __isl_give isl_map *isl_map_flatten(
2871 __isl_take isl_map *map);
2873 #include <isl/map.h>
2874 __isl_give isl_map *isl_set_flatten_map(
2875 __isl_take isl_set *set);
2877 The function above constructs a relation
2878 that maps the input set to a flattened version of the set.
2882 Lift the input set to a space with extra dimensions corresponding
2883 to the existentially quantified variables in the input.
2884 In particular, the result lives in a wrapped map where the domain
2885 is the original space and the range corresponds to the original
2886 existentially quantified variables.
2888 __isl_give isl_basic_set *isl_basic_set_lift(
2889 __isl_take isl_basic_set *bset);
2890 __isl_give isl_set *isl_set_lift(
2891 __isl_take isl_set *set);
2892 __isl_give isl_union_set *isl_union_set_lift(
2893 __isl_take isl_union_set *uset);
2895 Given a local space that contains the existentially quantified
2896 variables of a set, a basic relation that, when applied to
2897 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2898 can be constructed using the following function.
2900 #include <isl/local_space.h>
2901 __isl_give isl_basic_map *isl_local_space_lifting(
2902 __isl_take isl_local_space *ls);
2904 =item * Internal Product
2906 __isl_give isl_basic_map *isl_basic_map_zip(
2907 __isl_take isl_basic_map *bmap);
2908 __isl_give isl_map *isl_map_zip(
2909 __isl_take isl_map *map);
2910 __isl_give isl_union_map *isl_union_map_zip(
2911 __isl_take isl_union_map *umap);
2913 Given a relation with nested relations for domain and range,
2914 interchange the range of the domain with the domain of the range.
2918 __isl_give isl_basic_map *isl_basic_map_curry(
2919 __isl_take isl_basic_map *bmap);
2920 __isl_give isl_basic_map *isl_basic_map_uncurry(
2921 __isl_take isl_basic_map *bmap);
2922 __isl_give isl_map *isl_map_curry(
2923 __isl_take isl_map *map);
2924 __isl_give isl_map *isl_map_uncurry(
2925 __isl_take isl_map *map);
2926 __isl_give isl_union_map *isl_union_map_curry(
2927 __isl_take isl_union_map *umap);
2928 __isl_give isl_union_map *isl_union_map_uncurry(
2929 __isl_take isl_union_map *umap);
2931 Given a relation with a nested relation for domain,
2932 the C<curry> functions
2933 move the range of the nested relation out of the domain
2934 and use it as the domain of a nested relation in the range,
2935 with the original range as range of this nested relation.
2936 The C<uncurry> functions perform the inverse operation.
2938 =item * Aligning parameters
2940 __isl_give isl_basic_set *isl_basic_set_align_params(
2941 __isl_take isl_basic_set *bset,
2942 __isl_take isl_space *model);
2943 __isl_give isl_set *isl_set_align_params(
2944 __isl_take isl_set *set,
2945 __isl_take isl_space *model);
2946 __isl_give isl_basic_map *isl_basic_map_align_params(
2947 __isl_take isl_basic_map *bmap,
2948 __isl_take isl_space *model);
2949 __isl_give isl_map *isl_map_align_params(
2950 __isl_take isl_map *map,
2951 __isl_take isl_space *model);
2953 Change the order of the parameters of the given set or relation
2954 such that the first parameters match those of C<model>.
2955 This may involve the introduction of extra parameters.
2956 All parameters need to be named.
2958 =item * Dimension manipulation
2960 #include <isl/local_space.h>
2961 __isl_give isl_local_space *isl_local_space_add_dims(
2962 __isl_take isl_local_space *ls,
2963 enum isl_dim_type type, unsigned n);
2964 __isl_give isl_local_space *isl_local_space_insert_dims(
2965 __isl_take isl_local_space *ls,
2966 enum isl_dim_type type, unsigned first, unsigned n);
2967 __isl_give isl_local_space *isl_local_space_drop_dims(
2968 __isl_take isl_local_space *ls,
2969 enum isl_dim_type type, unsigned first, unsigned n);
2971 #include <isl/set.h>
2972 __isl_give isl_basic_set *isl_basic_set_add_dims(
2973 __isl_take isl_basic_set *bset,
2974 enum isl_dim_type type, unsigned n);
2975 __isl_give isl_set *isl_set_add_dims(
2976 __isl_take isl_set *set,
2977 enum isl_dim_type type, unsigned n);
2978 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2979 __isl_take isl_basic_set *bset,
2980 enum isl_dim_type type, unsigned pos,
2982 __isl_give isl_set *isl_set_insert_dims(
2983 __isl_take isl_set *set,
2984 enum isl_dim_type type, unsigned pos, unsigned n);
2985 __isl_give isl_basic_set *isl_basic_set_move_dims(
2986 __isl_take isl_basic_set *bset,
2987 enum isl_dim_type dst_type, unsigned dst_pos,
2988 enum isl_dim_type src_type, unsigned src_pos,
2990 __isl_give isl_set *isl_set_move_dims(
2991 __isl_take isl_set *set,
2992 enum isl_dim_type dst_type, unsigned dst_pos,
2993 enum isl_dim_type src_type, unsigned src_pos,
2996 #include <isl/map.h>
2997 __isl_give isl_map *isl_map_add_dims(
2998 __isl_take isl_map *map,
2999 enum isl_dim_type type, unsigned n);
3000 __isl_give isl_basic_map *isl_basic_map_insert_dims(
3001 __isl_take isl_basic_map *bmap,
3002 enum isl_dim_type type, unsigned pos,
3004 __isl_give isl_map *isl_map_insert_dims(
3005 __isl_take isl_map *map,
3006 enum isl_dim_type type, unsigned pos, unsigned n);
3007 __isl_give isl_basic_map *isl_basic_map_move_dims(
3008 __isl_take isl_basic_map *bmap,
3009 enum isl_dim_type dst_type, unsigned dst_pos,
3010 enum isl_dim_type src_type, unsigned src_pos,
3012 __isl_give isl_map *isl_map_move_dims(
3013 __isl_take isl_map *map,
3014 enum isl_dim_type dst_type, unsigned dst_pos,
3015 enum isl_dim_type src_type, unsigned src_pos,
3018 It is usually not advisable to directly change the (input or output)
3019 space of a set or a relation as this removes the name and the internal
3020 structure of the space. However, the above functions can be useful
3021 to add new parameters, assuming
3022 C<isl_set_align_params> and C<isl_map_align_params>
3027 =head2 Binary Operations
3029 The two arguments of a binary operation not only need to live
3030 in the same C<isl_ctx>, they currently also need to have
3031 the same (number of) parameters.
3033 =head3 Basic Operations
3037 =item * Intersection
3039 #include <isl/local_space.h>
3040 __isl_give isl_local_space *isl_local_space_intersect(
3041 __isl_take isl_local_space *ls1,
3042 __isl_take isl_local_space *ls2);
3044 #include <isl/set.h>
3045 __isl_give isl_basic_set *isl_basic_set_intersect_params(
3046 __isl_take isl_basic_set *bset1,
3047 __isl_take isl_basic_set *bset2);
3048 __isl_give isl_basic_set *isl_basic_set_intersect(
3049 __isl_take isl_basic_set *bset1,
3050 __isl_take isl_basic_set *bset2);
3051 __isl_give isl_basic_set *isl_basic_set_list_intersect(
3052 __isl_take struct isl_basic_set_list *list);
3053 __isl_give isl_set *isl_set_intersect_params(
3054 __isl_take isl_set *set,
3055 __isl_take isl_set *params);
3056 __isl_give isl_set *isl_set_intersect(
3057 __isl_take isl_set *set1,
3058 __isl_take isl_set *set2);
3060 #include <isl/map.h>
3061 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
3062 __isl_take isl_basic_map *bmap,
3063 __isl_take isl_basic_set *bset);
3064 __isl_give isl_basic_map *isl_basic_map_intersect_range(
3065 __isl_take isl_basic_map *bmap,
3066 __isl_take isl_basic_set *bset);
3067 __isl_give isl_basic_map *isl_basic_map_intersect(
3068 __isl_take isl_basic_map *bmap1,
3069 __isl_take isl_basic_map *bmap2);
3070 __isl_give isl_map *isl_map_intersect_params(
3071 __isl_take isl_map *map,
3072 __isl_take isl_set *params);
3073 __isl_give isl_map *isl_map_intersect_domain(
3074 __isl_take isl_map *map,
3075 __isl_take isl_set *set);
3076 __isl_give isl_map *isl_map_intersect_range(
3077 __isl_take isl_map *map,
3078 __isl_take isl_set *set);
3079 __isl_give isl_map *isl_map_intersect(
3080 __isl_take isl_map *map1,
3081 __isl_take isl_map *map2);
3083 #include <isl/union_set.h>
3084 __isl_give isl_union_set *isl_union_set_intersect_params(
3085 __isl_take isl_union_set *uset,
3086 __isl_take isl_set *set);
3087 __isl_give isl_union_set *isl_union_set_intersect(
3088 __isl_take isl_union_set *uset1,
3089 __isl_take isl_union_set *uset2);
3091 #include <isl/union_map.h>
3092 __isl_give isl_union_map *isl_union_map_intersect_params(
3093 __isl_take isl_union_map *umap,
3094 __isl_take isl_set *set);
3095 __isl_give isl_union_map *isl_union_map_intersect_domain(
3096 __isl_take isl_union_map *umap,
3097 __isl_take isl_union_set *uset);
3098 __isl_give isl_union_map *isl_union_map_intersect_range(
3099 __isl_take isl_union_map *umap,
3100 __isl_take isl_union_set *uset);
3101 __isl_give isl_union_map *isl_union_map_intersect(
3102 __isl_take isl_union_map *umap1,
3103 __isl_take isl_union_map *umap2);
3105 The second argument to the C<_params> functions needs to be
3106 a parametric (basic) set. For the other functions, a parametric set
3107 for either argument is only allowed if the other argument is
3108 a parametric set as well.
3109 The list passed to C<isl_basic_set_list_intersect> needs to have
3110 at least one element and all elements need to live in the same space.
3114 __isl_give isl_set *isl_basic_set_union(
3115 __isl_take isl_basic_set *bset1,
3116 __isl_take isl_basic_set *bset2);
3117 __isl_give isl_map *isl_basic_map_union(
3118 __isl_take isl_basic_map *bmap1,
3119 __isl_take isl_basic_map *bmap2);
3120 __isl_give isl_set *isl_set_union(
3121 __isl_take isl_set *set1,
3122 __isl_take isl_set *set2);
3123 __isl_give isl_map *isl_map_union(
3124 __isl_take isl_map *map1,
3125 __isl_take isl_map *map2);
3126 __isl_give isl_union_set *isl_union_set_union(
3127 __isl_take isl_union_set *uset1,
3128 __isl_take isl_union_set *uset2);
3129 __isl_give isl_union_map *isl_union_map_union(
3130 __isl_take isl_union_map *umap1,
3131 __isl_take isl_union_map *umap2);
3133 =item * Set difference
3135 __isl_give isl_set *isl_set_subtract(
3136 __isl_take isl_set *set1,
3137 __isl_take isl_set *set2);
3138 __isl_give isl_map *isl_map_subtract(
3139 __isl_take isl_map *map1,
3140 __isl_take isl_map *map2);
3141 __isl_give isl_map *isl_map_subtract_domain(
3142 __isl_take isl_map *map,
3143 __isl_take isl_set *dom);
3144 __isl_give isl_map *isl_map_subtract_range(
3145 __isl_take isl_map *map,
3146 __isl_take isl_set *dom);
3147 __isl_give isl_union_set *isl_union_set_subtract(
3148 __isl_take isl_union_set *uset1,
3149 __isl_take isl_union_set *uset2);
3150 __isl_give isl_union_map *isl_union_map_subtract(
3151 __isl_take isl_union_map *umap1,
3152 __isl_take isl_union_map *umap2);
3153 __isl_give isl_union_map *isl_union_map_subtract_domain(
3154 __isl_take isl_union_map *umap,
3155 __isl_take isl_union_set *dom);
3156 __isl_give isl_union_map *isl_union_map_subtract_range(
3157 __isl_take isl_union_map *umap,
3158 __isl_take isl_union_set *dom);
3162 __isl_give isl_basic_set *isl_basic_set_apply(
3163 __isl_take isl_basic_set *bset,
3164 __isl_take isl_basic_map *bmap);
3165 __isl_give isl_set *isl_set_apply(
3166 __isl_take isl_set *set,
3167 __isl_take isl_map *map);
3168 __isl_give isl_union_set *isl_union_set_apply(
3169 __isl_take isl_union_set *uset,
3170 __isl_take isl_union_map *umap);
3171 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3172 __isl_take isl_basic_map *bmap1,
3173 __isl_take isl_basic_map *bmap2);
3174 __isl_give isl_basic_map *isl_basic_map_apply_range(
3175 __isl_take isl_basic_map *bmap1,
3176 __isl_take isl_basic_map *bmap2);
3177 __isl_give isl_map *isl_map_apply_domain(
3178 __isl_take isl_map *map1,
3179 __isl_take isl_map *map2);
3180 __isl_give isl_union_map *isl_union_map_apply_domain(
3181 __isl_take isl_union_map *umap1,
3182 __isl_take isl_union_map *umap2);
3183 __isl_give isl_map *isl_map_apply_range(
3184 __isl_take isl_map *map1,
3185 __isl_take isl_map *map2);
3186 __isl_give isl_union_map *isl_union_map_apply_range(
3187 __isl_take isl_union_map *umap1,
3188 __isl_take isl_union_map *umap2);
3192 #include <isl/set.h>
3193 __isl_give isl_basic_set *
3194 isl_basic_set_preimage_multi_aff(
3195 __isl_take isl_basic_set *bset,
3196 __isl_take isl_multi_aff *ma);
3197 __isl_give isl_set *isl_set_preimage_multi_aff(
3198 __isl_take isl_set *set,
3199 __isl_take isl_multi_aff *ma);
3200 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3201 __isl_take isl_set *set,
3202 __isl_take isl_pw_multi_aff *pma);
3203 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
3204 __isl_take isl_set *set,
3205 __isl_take isl_multi_pw_aff *mpa);
3207 #include <isl/union_set.h>
3208 __isl_give isl_union_set *
3209 isl_union_set_preimage_multi_aff(
3210 __isl_take isl_union_set *uset,
3211 __isl_take isl_multi_aff *ma);
3212 __isl_give isl_union_set *
3213 isl_union_set_preimage_pw_multi_aff(
3214 __isl_take isl_union_set *uset,
3215 __isl_take isl_pw_multi_aff *pma);
3216 __isl_give isl_union_set *
3217 isl_union_set_preimage_union_pw_multi_aff(
3218 __isl_take isl_union_set *uset,
3219 __isl_take isl_union_pw_multi_aff *upma);
3221 #include <isl/map.h>
3222 __isl_give isl_basic_map *
3223 isl_basic_map_preimage_domain_multi_aff(
3224 __isl_take isl_basic_map *bmap,
3225 __isl_take isl_multi_aff *ma);
3226 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3227 __isl_take isl_map *map,
3228 __isl_take isl_multi_aff *ma);
3229 __isl_give isl_map *isl_map_preimage_range_multi_aff(
3230 __isl_take isl_map *map,
3231 __isl_take isl_multi_aff *ma);
3232 __isl_give isl_map *
3233 isl_map_preimage_domain_pw_multi_aff(
3234 __isl_take isl_map *map,
3235 __isl_take isl_pw_multi_aff *pma);
3236 __isl_give isl_map *
3237 isl_map_preimage_range_pw_multi_aff(
3238 __isl_take isl_map *map,
3239 __isl_take isl_pw_multi_aff *pma);
3240 __isl_give isl_map *
3241 isl_map_preimage_domain_multi_pw_aff(
3242 __isl_take isl_map *map,
3243 __isl_take isl_multi_pw_aff *mpa);
3244 __isl_give isl_basic_map *
3245 isl_basic_map_preimage_range_multi_aff(
3246 __isl_take isl_basic_map *bmap,
3247 __isl_take isl_multi_aff *ma);
3249 #include <isl/union_map.h>
3250 __isl_give isl_union_map *
3251 isl_union_map_preimage_domain_multi_aff(
3252 __isl_take isl_union_map *umap,
3253 __isl_take isl_multi_aff *ma);
3254 __isl_give isl_union_map *
3255 isl_union_map_preimage_range_multi_aff(
3256 __isl_take isl_union_map *umap,
3257 __isl_take isl_multi_aff *ma);
3258 __isl_give isl_union_map *
3259 isl_union_map_preimage_domain_pw_multi_aff(
3260 __isl_take isl_union_map *umap,
3261 __isl_take isl_pw_multi_aff *pma);
3262 __isl_give isl_union_map *
3263 isl_union_map_preimage_range_pw_multi_aff(
3264 __isl_take isl_union_map *umap,
3265 __isl_take isl_pw_multi_aff *pma);
3266 __isl_give isl_union_map *
3267 isl_union_map_preimage_domain_union_pw_multi_aff(
3268 __isl_take isl_union_map *umap,
3269 __isl_take isl_union_pw_multi_aff *upma);
3270 __isl_give isl_union_map *
3271 isl_union_map_preimage_range_union_pw_multi_aff(
3272 __isl_take isl_union_map *umap,
3273 __isl_take isl_union_pw_multi_aff *upma);
3275 These functions compute the preimage of the given set or map domain/range under
3276 the given function. In other words, the expression is plugged
3277 into the set description or into the domain/range of the map.
3278 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3279 L</"Piecewise Multiple Quasi Affine Expressions">.
3281 =item * Cartesian Product
3283 #include <isl/space.h>
3284 __isl_give isl_space *isl_space_product(
3285 __isl_take isl_space *space1,
3286 __isl_take isl_space *space2);
3287 __isl_give isl_space *isl_space_domain_product(
3288 __isl_take isl_space *space1,
3289 __isl_take isl_space *space2);
3290 __isl_give isl_space *isl_space_range_product(
3291 __isl_take isl_space *space1,
3292 __isl_take isl_space *space2);
3295 C<isl_space_product>, C<isl_space_domain_product>
3296 and C<isl_space_range_product> take pairs or relation spaces and
3297 produce a single relations space, where either the domain, the range
3298 or both domain and range are wrapped spaces of relations between
3299 the domains and/or ranges of the input spaces.
3300 If the product is only constructed over the domain or the range
3301 then the ranges or the domains of the inputs should be the same.
3302 The function C<isl_space_product> also accepts a pair of set spaces,
3303 in which case it returns a wrapped space of a relation between the
3306 #include <isl/set.h>
3307 __isl_give isl_set *isl_set_product(
3308 __isl_take isl_set *set1,
3309 __isl_take isl_set *set2);
3311 #include <isl/map.h>
3312 __isl_give isl_basic_map *isl_basic_map_domain_product(
3313 __isl_take isl_basic_map *bmap1,
3314 __isl_take isl_basic_map *bmap2);
3315 __isl_give isl_basic_map *isl_basic_map_range_product(
3316 __isl_take isl_basic_map *bmap1,
3317 __isl_take isl_basic_map *bmap2);
3318 __isl_give isl_basic_map *isl_basic_map_product(
3319 __isl_take isl_basic_map *bmap1,
3320 __isl_take isl_basic_map *bmap2);
3321 __isl_give isl_map *isl_map_domain_product(
3322 __isl_take isl_map *map1,
3323 __isl_take isl_map *map2);
3324 __isl_give isl_map *isl_map_range_product(
3325 __isl_take isl_map *map1,
3326 __isl_take isl_map *map2);
3327 __isl_give isl_map *isl_map_product(
3328 __isl_take isl_map *map1,
3329 __isl_take isl_map *map2);
3331 #include <isl/union_set.h>
3332 __isl_give isl_union_set *isl_union_set_product(
3333 __isl_take isl_union_set *uset1,
3334 __isl_take isl_union_set *uset2);
3336 #include <isl/union_map.h>
3337 __isl_give isl_union_map *isl_union_map_domain_product(
3338 __isl_take isl_union_map *umap1,
3339 __isl_take isl_union_map *umap2);
3340 __isl_give isl_union_map *isl_union_map_range_product(
3341 __isl_take isl_union_map *umap1,
3342 __isl_take isl_union_map *umap2);
3343 __isl_give isl_union_map *isl_union_map_product(
3344 __isl_take isl_union_map *umap1,
3345 __isl_take isl_union_map *umap2);
3347 The above functions compute the cross product of the given
3348 sets or relations. The domains and ranges of the results
3349 are wrapped maps between domains and ranges of the inputs.
3350 To obtain a ``flat'' product, use the following functions
3353 __isl_give isl_basic_set *isl_basic_set_flat_product(
3354 __isl_take isl_basic_set *bset1,
3355 __isl_take isl_basic_set *bset2);
3356 __isl_give isl_set *isl_set_flat_product(
3357 __isl_take isl_set *set1,
3358 __isl_take isl_set *set2);
3359 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3360 __isl_take isl_basic_map *bmap1,
3361 __isl_take isl_basic_map *bmap2);
3362 __isl_give isl_map *isl_map_flat_domain_product(
3363 __isl_take isl_map *map1,
3364 __isl_take isl_map *map2);
3365 __isl_give isl_map *isl_map_flat_range_product(
3366 __isl_take isl_map *map1,
3367 __isl_take isl_map *map2);
3368 __isl_give isl_union_map *isl_union_map_flat_range_product(
3369 __isl_take isl_union_map *umap1,
3370 __isl_take isl_union_map *umap2);
3371 __isl_give isl_basic_map *isl_basic_map_flat_product(
3372 __isl_take isl_basic_map *bmap1,
3373 __isl_take isl_basic_map *bmap2);
3374 __isl_give isl_map *isl_map_flat_product(
3375 __isl_take isl_map *map1,
3376 __isl_take isl_map *map2);
3378 #include <isl/space.h>
3379 __isl_give isl_space *isl_space_domain_factor_domain(
3380 __isl_take isl_space *space);
3381 __isl_give isl_space *isl_space_range_factor_domain(
3382 __isl_take isl_space *space);
3383 __isl_give isl_space *isl_space_range_factor_range(
3384 __isl_take isl_space *space);
3386 The functions C<isl_space_range_factor_domain> and
3387 C<isl_space_range_factor_range> extract the two arguments from
3388 the result of a call to C<isl_space_range_product>.
3390 The arguments of a call to C<isl_map_range_product> can be extracted
3391 from the result using the following two functions.
3393 #include <isl/map.h>
3394 __isl_give isl_map *isl_map_range_factor_domain(
3395 __isl_take isl_map *map);
3396 __isl_give isl_map *isl_map_range_factor_range(
3397 __isl_take isl_map *map);
3399 =item * Simplification
3401 __isl_give isl_basic_set *isl_basic_set_gist(
3402 __isl_take isl_basic_set *bset,
3403 __isl_take isl_basic_set *context);
3404 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3405 __isl_take isl_set *context);
3406 __isl_give isl_set *isl_set_gist_params(
3407 __isl_take isl_set *set,
3408 __isl_take isl_set *context);
3409 __isl_give isl_union_set *isl_union_set_gist(
3410 __isl_take isl_union_set *uset,
3411 __isl_take isl_union_set *context);
3412 __isl_give isl_union_set *isl_union_set_gist_params(
3413 __isl_take isl_union_set *uset,
3414 __isl_take isl_set *set);
3415 __isl_give isl_basic_map *isl_basic_map_gist(
3416 __isl_take isl_basic_map *bmap,
3417 __isl_take isl_basic_map *context);
3418 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3419 __isl_take isl_map *context);
3420 __isl_give isl_map *isl_map_gist_params(
3421 __isl_take isl_map *map,
3422 __isl_take isl_set *context);
3423 __isl_give isl_map *isl_map_gist_domain(
3424 __isl_take isl_map *map,
3425 __isl_take isl_set *context);
3426 __isl_give isl_map *isl_map_gist_range(
3427 __isl_take isl_map *map,
3428 __isl_take isl_set *context);
3429 __isl_give isl_union_map *isl_union_map_gist(
3430 __isl_take isl_union_map *umap,
3431 __isl_take isl_union_map *context);
3432 __isl_give isl_union_map *isl_union_map_gist_params(
3433 __isl_take isl_union_map *umap,
3434 __isl_take isl_set *set);
3435 __isl_give isl_union_map *isl_union_map_gist_domain(
3436 __isl_take isl_union_map *umap,
3437 __isl_take isl_union_set *uset);
3438 __isl_give isl_union_map *isl_union_map_gist_range(
3439 __isl_take isl_union_map *umap,
3440 __isl_take isl_union_set *uset);
3442 The gist operation returns a set or relation that has the
3443 same intersection with the context as the input set or relation.
3444 Any implicit equality in the intersection is made explicit in the result,
3445 while all inequalities that are redundant with respect to the intersection
3447 In case of union sets and relations, the gist operation is performed
3452 =head3 Lexicographic Optimization
3454 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3455 the following functions
3456 compute a set that contains the lexicographic minimum or maximum
3457 of the elements in C<set> (or C<bset>) for those values of the parameters
3458 that satisfy C<dom>.
3459 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3460 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3462 In other words, the union of the parameter values
3463 for which the result is non-empty and of C<*empty>
3466 __isl_give isl_set *isl_basic_set_partial_lexmin(
3467 __isl_take isl_basic_set *bset,
3468 __isl_take isl_basic_set *dom,
3469 __isl_give isl_set **empty);
3470 __isl_give isl_set *isl_basic_set_partial_lexmax(
3471 __isl_take isl_basic_set *bset,
3472 __isl_take isl_basic_set *dom,
3473 __isl_give isl_set **empty);
3474 __isl_give isl_set *isl_set_partial_lexmin(
3475 __isl_take isl_set *set, __isl_take isl_set *dom,
3476 __isl_give isl_set **empty);
3477 __isl_give isl_set *isl_set_partial_lexmax(
3478 __isl_take isl_set *set, __isl_take isl_set *dom,
3479 __isl_give isl_set **empty);
3481 Given a (basic) set C<set> (or C<bset>), the following functions simply
3482 return a set containing the lexicographic minimum or maximum
3483 of the elements in C<set> (or C<bset>).
3484 In case of union sets, the optimum is computed per space.
3486 __isl_give isl_set *isl_basic_set_lexmin(
3487 __isl_take isl_basic_set *bset);
3488 __isl_give isl_set *isl_basic_set_lexmax(
3489 __isl_take isl_basic_set *bset);
3490 __isl_give isl_set *isl_set_lexmin(
3491 __isl_take isl_set *set);
3492 __isl_give isl_set *isl_set_lexmax(
3493 __isl_take isl_set *set);
3494 __isl_give isl_union_set *isl_union_set_lexmin(
3495 __isl_take isl_union_set *uset);
3496 __isl_give isl_union_set *isl_union_set_lexmax(
3497 __isl_take isl_union_set *uset);
3499 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3500 the following functions
3501 compute a relation that maps each element of C<dom>
3502 to the single lexicographic minimum or maximum
3503 of the elements that are associated to that same
3504 element in C<map> (or C<bmap>).
3505 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3506 that contains the elements in C<dom> that do not map
3507 to any elements in C<map> (or C<bmap>).
3508 In other words, the union of the domain of the result and of C<*empty>
3511 __isl_give isl_map *isl_basic_map_partial_lexmax(
3512 __isl_take isl_basic_map *bmap,
3513 __isl_take isl_basic_set *dom,
3514 __isl_give isl_set **empty);
3515 __isl_give isl_map *isl_basic_map_partial_lexmin(
3516 __isl_take isl_basic_map *bmap,
3517 __isl_take isl_basic_set *dom,
3518 __isl_give isl_set **empty);
3519 __isl_give isl_map *isl_map_partial_lexmax(
3520 __isl_take isl_map *map, __isl_take isl_set *dom,
3521 __isl_give isl_set **empty);
3522 __isl_give isl_map *isl_map_partial_lexmin(
3523 __isl_take isl_map *map, __isl_take isl_set *dom,
3524 __isl_give isl_set **empty);
3526 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3527 return a map mapping each element in the domain of
3528 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3529 of all elements associated to that element.
3530 In case of union relations, the optimum is computed per space.
3532 __isl_give isl_map *isl_basic_map_lexmin(
3533 __isl_take isl_basic_map *bmap);
3534 __isl_give isl_map *isl_basic_map_lexmax(
3535 __isl_take isl_basic_map *bmap);
3536 __isl_give isl_map *isl_map_lexmin(
3537 __isl_take isl_map *map);
3538 __isl_give isl_map *isl_map_lexmax(
3539 __isl_take isl_map *map);
3540 __isl_give isl_union_map *isl_union_map_lexmin(
3541 __isl_take isl_union_map *umap);
3542 __isl_give isl_union_map *isl_union_map_lexmax(
3543 __isl_take isl_union_map *umap);
3545 The following functions return their result in the form of
3546 a piecewise multi-affine expression
3547 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3548 but are otherwise equivalent to the corresponding functions
3549 returning a basic set or relation.
3551 __isl_give isl_pw_multi_aff *
3552 isl_basic_map_lexmin_pw_multi_aff(
3553 __isl_take isl_basic_map *bmap);
3554 __isl_give isl_pw_multi_aff *
3555 isl_basic_set_partial_lexmin_pw_multi_aff(
3556 __isl_take isl_basic_set *bset,
3557 __isl_take isl_basic_set *dom,
3558 __isl_give isl_set **empty);
3559 __isl_give isl_pw_multi_aff *
3560 isl_basic_set_partial_lexmax_pw_multi_aff(
3561 __isl_take isl_basic_set *bset,
3562 __isl_take isl_basic_set *dom,
3563 __isl_give isl_set **empty);
3564 __isl_give isl_pw_multi_aff *
3565 isl_basic_map_partial_lexmin_pw_multi_aff(
3566 __isl_take isl_basic_map *bmap,
3567 __isl_take isl_basic_set *dom,
3568 __isl_give isl_set **empty);
3569 __isl_give isl_pw_multi_aff *
3570 isl_basic_map_partial_lexmax_pw_multi_aff(
3571 __isl_take isl_basic_map *bmap,
3572 __isl_take isl_basic_set *dom,
3573 __isl_give isl_set **empty);
3574 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3575 __isl_take isl_set *set);
3576 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3577 __isl_take isl_set *set);
3578 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3579 __isl_take isl_map *map);
3580 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3581 __isl_take isl_map *map);
3585 Lists are defined over several element types, including
3586 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3587 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3588 Here we take lists of C<isl_set>s as an example.
3589 Lists can be created, copied, modified and freed using the following functions.
3591 #include <isl/list.h>
3592 __isl_give isl_set_list *isl_set_list_from_set(
3593 __isl_take isl_set *el);
3594 __isl_give isl_set_list *isl_set_list_alloc(
3595 isl_ctx *ctx, int n);
3596 __isl_give isl_set_list *isl_set_list_copy(
3597 __isl_keep isl_set_list *list);
3598 __isl_give isl_set_list *isl_set_list_insert(
3599 __isl_take isl_set_list *list, unsigned pos,
3600 __isl_take isl_set *el);
3601 __isl_give isl_set_list *isl_set_list_add(
3602 __isl_take isl_set_list *list,
3603 __isl_take isl_set *el);
3604 __isl_give isl_set_list *isl_set_list_drop(
3605 __isl_take isl_set_list *list,
3606 unsigned first, unsigned n);
3607 __isl_give isl_set_list *isl_set_list_set_set(
3608 __isl_take isl_set_list *list, int index,
3609 __isl_take isl_set *set);
3610 __isl_give isl_set_list *isl_set_list_concat(
3611 __isl_take isl_set_list *list1,
3612 __isl_take isl_set_list *list2);
3613 __isl_give isl_set_list *isl_set_list_sort(
3614 __isl_take isl_set_list *list,
3615 int (*cmp)(__isl_keep isl_set *a,
3616 __isl_keep isl_set *b, void *user),
3618 __isl_null isl_set_list *isl_set_list_free(
3619 __isl_take isl_set_list *list);
3621 C<isl_set_list_alloc> creates an empty list with a capacity for
3622 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3625 Lists can be inspected using the following functions.
3627 #include <isl/list.h>
3628 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3629 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3630 __isl_give isl_set *isl_set_list_get_set(
3631 __isl_keep isl_set_list *list, int index);
3632 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3633 int (*fn)(__isl_take isl_set *el, void *user),
3635 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3636 int (*follows)(__isl_keep isl_set *a,
3637 __isl_keep isl_set *b, void *user),
3639 int (*fn)(__isl_take isl_set *el, void *user),
3642 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3643 strongly connected components of the graph with as vertices the elements
3644 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3645 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3646 should return C<-1> on error.
3648 Lists can be printed using
3650 #include <isl/list.h>
3651 __isl_give isl_printer *isl_printer_print_set_list(
3652 __isl_take isl_printer *p,
3653 __isl_keep isl_set_list *list);
3655 =head2 Associative arrays
3657 Associative arrays map isl objects of a specific type to isl objects
3658 of some (other) specific type. They are defined for several pairs
3659 of types, including (C<isl_map>, C<isl_basic_set>),
3660 (C<isl_id>, C<isl_ast_expr>) and.
3661 (C<isl_id>, C<isl_pw_aff>).
3662 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3665 Associative arrays can be created, copied and freed using
3666 the following functions.
3668 #include <isl/id_to_ast_expr.h>
3669 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3670 isl_ctx *ctx, int min_size);
3671 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3672 __isl_keep id_to_ast_expr *id2expr);
3673 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
3674 __isl_take id_to_ast_expr *id2expr);
3676 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3677 to specify the expected size of the associative array.
3678 The associative array will be grown automatically as needed.
3680 Associative arrays can be inspected using the following functions.
3682 #include <isl/id_to_ast_expr.h>
3683 isl_ctx *isl_id_to_ast_expr_get_ctx(
3684 __isl_keep id_to_ast_expr *id2expr);
3685 int isl_id_to_ast_expr_has(
3686 __isl_keep id_to_ast_expr *id2expr,
3687 __isl_keep isl_id *key);
3688 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3689 __isl_keep id_to_ast_expr *id2expr,
3690 __isl_take isl_id *key);
3691 int isl_id_to_ast_expr_foreach(
3692 __isl_keep id_to_ast_expr *id2expr,
3693 int (*fn)(__isl_take isl_id *key,
3694 __isl_take isl_ast_expr *val, void *user),
3697 They can be modified using the following function.
3699 #include <isl/id_to_ast_expr.h>
3700 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3701 __isl_take id_to_ast_expr *id2expr,
3702 __isl_take isl_id *key,
3703 __isl_take isl_ast_expr *val);
3704 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
3705 __isl_take id_to_ast_expr *id2expr,
3706 __isl_take isl_id *key);
3708 Associative arrays can be printed using the following function.
3710 #include <isl/id_to_ast_expr.h>
3711 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3712 __isl_take isl_printer *p,
3713 __isl_keep id_to_ast_expr *id2expr);
3715 =head2 Multiple Values
3717 An C<isl_multi_val> object represents a sequence of zero or more values,
3718 living in a set space.
3720 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3721 using the following function
3723 #include <isl/val.h>
3724 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3725 __isl_take isl_space *space,
3726 __isl_take isl_val_list *list);
3728 The zero multiple value (with value zero for each set dimension)
3729 can be created using the following function.
3731 #include <isl/val.h>
3732 __isl_give isl_multi_val *isl_multi_val_zero(
3733 __isl_take isl_space *space);
3735 Multiple values can be copied and freed using
3737 #include <isl/val.h>
3738 __isl_give isl_multi_val *isl_multi_val_copy(
3739 __isl_keep isl_multi_val *mv);
3740 __isl_null isl_multi_val *isl_multi_val_free(
3741 __isl_take isl_multi_val *mv);
3743 They can be inspected using
3745 #include <isl/val.h>
3746 isl_ctx *isl_multi_val_get_ctx(
3747 __isl_keep isl_multi_val *mv);
3748 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3749 enum isl_dim_type type);
3750 __isl_give isl_val *isl_multi_val_get_val(
3751 __isl_keep isl_multi_val *mv, int pos);
3752 int isl_multi_val_find_dim_by_id(
3753 __isl_keep isl_multi_val *mv,
3754 enum isl_dim_type type, __isl_keep isl_id *id);
3755 __isl_give isl_id *isl_multi_val_get_dim_id(
3756 __isl_keep isl_multi_val *mv,
3757 enum isl_dim_type type, unsigned pos);
3758 const char *isl_multi_val_get_tuple_name(
3759 __isl_keep isl_multi_val *mv,
3760 enum isl_dim_type type);
3761 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3762 enum isl_dim_type type);
3763 __isl_give isl_id *isl_multi_val_get_tuple_id(
3764 __isl_keep isl_multi_val *mv,
3765 enum isl_dim_type type);
3766 int isl_multi_val_range_is_wrapping(
3767 __isl_keep isl_multi_val *mv);
3769 They can be modified using
3771 #include <isl/val.h>
3772 __isl_give isl_multi_val *isl_multi_val_set_val(
3773 __isl_take isl_multi_val *mv, int pos,
3774 __isl_take isl_val *val);
3775 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3776 __isl_take isl_multi_val *mv,
3777 enum isl_dim_type type, unsigned pos, const char *s);
3778 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3779 __isl_take isl_multi_val *mv,
3780 enum isl_dim_type type, unsigned pos,
3781 __isl_take isl_id *id);
3782 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3783 __isl_take isl_multi_val *mv,
3784 enum isl_dim_type type, const char *s);
3785 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3786 __isl_take isl_multi_val *mv,
3787 enum isl_dim_type type, __isl_take isl_id *id);
3788 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3789 __isl_take isl_multi_val *mv,
3790 enum isl_dim_type type);
3791 __isl_give isl_multi_val *isl_multi_val_reset_user(
3792 __isl_take isl_multi_val *mv);
3794 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3795 __isl_take isl_multi_val *mv,
3796 enum isl_dim_type type, unsigned first, unsigned n);
3797 __isl_give isl_multi_val *isl_multi_val_add_dims(
3798 __isl_take isl_multi_val *mv,
3799 enum isl_dim_type type, unsigned n);
3800 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3801 __isl_take isl_multi_val *mv,
3802 enum isl_dim_type type, unsigned first, unsigned n);
3806 #include <isl/val.h>
3807 __isl_give isl_multi_val *isl_multi_val_align_params(
3808 __isl_take isl_multi_val *mv,
3809 __isl_take isl_space *model);
3810 __isl_give isl_multi_val *isl_multi_val_from_range(
3811 __isl_take isl_multi_val *mv);
3812 __isl_give isl_multi_val *isl_multi_val_range_splice(
3813 __isl_take isl_multi_val *mv1, unsigned pos,
3814 __isl_take isl_multi_val *mv2);
3815 __isl_give isl_multi_val *isl_multi_val_range_product(
3816 __isl_take isl_multi_val *mv1,
3817 __isl_take isl_multi_val *mv2);
3818 __isl_give isl_multi_val *
3819 isl_multi_val_range_factor_domain(
3820 __isl_take isl_multi_val *mv);
3821 __isl_give isl_multi_val *
3822 isl_multi_val_range_factor_range(
3823 __isl_take isl_multi_val *mv);
3824 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3825 __isl_take isl_multi_val *mv1,
3826 __isl_take isl_multi_aff *mv2);
3827 __isl_give isl_multi_val *isl_multi_val_product(
3828 __isl_take isl_multi_val *mv1,
3829 __isl_take isl_multi_val *mv2);
3830 __isl_give isl_multi_val *isl_multi_val_add_val(
3831 __isl_take isl_multi_val *mv,
3832 __isl_take isl_val *v);
3833 __isl_give isl_multi_val *isl_multi_val_mod_val(
3834 __isl_take isl_multi_val *mv,
3835 __isl_take isl_val *v);
3836 __isl_give isl_multi_val *isl_multi_val_scale_val(
3837 __isl_take isl_multi_val *mv,
3838 __isl_take isl_val *v);
3839 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3840 __isl_take isl_multi_val *mv1,
3841 __isl_take isl_multi_val *mv2);
3842 __isl_give isl_multi_val *
3843 isl_multi_val_scale_down_multi_val(
3844 __isl_take isl_multi_val *mv1,
3845 __isl_take isl_multi_val *mv2);
3847 A multiple value can be printed using
3849 __isl_give isl_printer *isl_printer_print_multi_val(
3850 __isl_take isl_printer *p,
3851 __isl_keep isl_multi_val *mv);
3855 Vectors can be created, copied and freed using the following functions.
3857 #include <isl/vec.h>
3858 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3860 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3861 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
3863 Note that the elements of a newly created vector may have arbitrary values.
3864 The elements can be changed and inspected using the following functions.
3866 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3867 int isl_vec_size(__isl_keep isl_vec *vec);
3868 __isl_give isl_val *isl_vec_get_element_val(
3869 __isl_keep isl_vec *vec, int pos);
3870 __isl_give isl_vec *isl_vec_set_element_si(
3871 __isl_take isl_vec *vec, int pos, int v);
3872 __isl_give isl_vec *isl_vec_set_element_val(
3873 __isl_take isl_vec *vec, int pos,
3874 __isl_take isl_val *v);
3875 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3877 __isl_give isl_vec *isl_vec_set_val(
3878 __isl_take isl_vec *vec, __isl_take isl_val *v);
3879 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3880 __isl_keep isl_vec *vec2, int pos);
3882 C<isl_vec_get_element> will return a negative value if anything went wrong.
3883 In that case, the value of C<*v> is undefined.
3885 The following function can be used to concatenate two vectors.
3887 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3888 __isl_take isl_vec *vec2);
3892 Matrices can be created, copied and freed using the following functions.
3894 #include <isl/mat.h>
3895 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3896 unsigned n_row, unsigned n_col);
3897 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3898 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
3900 Note that the elements of a newly created matrix may have arbitrary values.
3901 The elements can be changed and inspected using the following functions.
3903 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3904 int isl_mat_rows(__isl_keep isl_mat *mat);
3905 int isl_mat_cols(__isl_keep isl_mat *mat);
3906 __isl_give isl_val *isl_mat_get_element_val(
3907 __isl_keep isl_mat *mat, int row, int col);
3908 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3909 int row, int col, int v);
3910 __isl_give isl_mat *isl_mat_set_element_val(
3911 __isl_take isl_mat *mat, int row, int col,
3912 __isl_take isl_val *v);
3914 C<isl_mat_get_element> will return a negative value if anything went wrong.
3915 In that case, the value of C<*v> is undefined.
3917 The following function can be used to compute the (right) inverse
3918 of a matrix, i.e., a matrix such that the product of the original
3919 and the inverse (in that order) is a multiple of the identity matrix.
3920 The input matrix is assumed to be of full row-rank.
3922 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3924 The following function can be used to compute the (right) kernel
3925 (or null space) of a matrix, i.e., a matrix such that the product of
3926 the original and the kernel (in that order) is the zero matrix.
3928 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3930 =head2 Piecewise Quasi Affine Expressions
3932 The zero quasi affine expression or the quasi affine expression
3933 that is equal to a given value or
3934 a specified dimension on a given domain can be created using
3936 __isl_give isl_aff *isl_aff_zero_on_domain(
3937 __isl_take isl_local_space *ls);
3938 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3939 __isl_take isl_local_space *ls);
3940 __isl_give isl_aff *isl_aff_val_on_domain(
3941 __isl_take isl_local_space *ls,
3942 __isl_take isl_val *val);
3943 __isl_give isl_aff *isl_aff_var_on_domain(
3944 __isl_take isl_local_space *ls,
3945 enum isl_dim_type type, unsigned pos);
3946 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3947 __isl_take isl_local_space *ls,
3948 enum isl_dim_type type, unsigned pos);
3949 __isl_give isl_aff *isl_aff_nan_on_domain(
3950 __isl_take isl_local_space *ls);
3951 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3952 __isl_take isl_local_space *ls);
3954 Note that the space in which the resulting objects live is a map space
3955 with the given space as domain and a one-dimensional range.
3957 An empty piecewise quasi affine expression (one with no cells)
3958 or a piecewise quasi affine expression with a single cell can
3959 be created using the following functions.
3961 #include <isl/aff.h>
3962 __isl_give isl_pw_aff *isl_pw_aff_empty(
3963 __isl_take isl_space *space);
3964 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3965 __isl_take isl_set *set, __isl_take isl_aff *aff);
3966 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3967 __isl_take isl_aff *aff);
3969 A piecewise quasi affine expression that is equal to 1 on a set
3970 and 0 outside the set can be created using the following function.
3972 #include <isl/aff.h>
3973 __isl_give isl_pw_aff *isl_set_indicator_function(
3974 __isl_take isl_set *set);
3976 Quasi affine expressions can be copied and freed using
3978 #include <isl/aff.h>
3979 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3980 __isl_null isl_aff *isl_aff_free(__isl_take isl_aff *aff);
3982 __isl_give isl_pw_aff *isl_pw_aff_copy(
3983 __isl_keep isl_pw_aff *pwaff);
3984 __isl_null isl_pw_aff *isl_pw_aff_free(
3985 __isl_take isl_pw_aff *pwaff);
3987 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3988 using the following function. The constraint is required to have
3989 a non-zero coefficient for the specified dimension.
3991 #include <isl/constraint.h>
3992 __isl_give isl_aff *isl_constraint_get_bound(
3993 __isl_keep isl_constraint *constraint,
3994 enum isl_dim_type type, int pos);
3996 The entire affine expression of the constraint can also be extracted
3997 using the following function.
3999 #include <isl/constraint.h>
4000 __isl_give isl_aff *isl_constraint_get_aff(
4001 __isl_keep isl_constraint *constraint);
4003 Conversely, an equality constraint equating
4004 the affine expression to zero or an inequality constraint enforcing
4005 the affine expression to be non-negative, can be constructed using
4007 __isl_give isl_constraint *isl_equality_from_aff(
4008 __isl_take isl_aff *aff);
4009 __isl_give isl_constraint *isl_inequality_from_aff(
4010 __isl_take isl_aff *aff);
4012 The expression can be inspected using
4014 #include <isl/aff.h>
4015 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
4016 int isl_aff_dim(__isl_keep isl_aff *aff,
4017 enum isl_dim_type type);
4018 __isl_give isl_local_space *isl_aff_get_domain_local_space(
4019 __isl_keep isl_aff *aff);
4020 __isl_give isl_local_space *isl_aff_get_local_space(
4021 __isl_keep isl_aff *aff);
4022 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
4023 enum isl_dim_type type, unsigned pos);
4024 const char *isl_pw_aff_get_dim_name(
4025 __isl_keep isl_pw_aff *pa,
4026 enum isl_dim_type type, unsigned pos);
4027 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
4028 enum isl_dim_type type, unsigned pos);
4029 __isl_give isl_id *isl_pw_aff_get_dim_id(
4030 __isl_keep isl_pw_aff *pa,
4031 enum isl_dim_type type, unsigned pos);
4032 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
4033 enum isl_dim_type type);
4034 __isl_give isl_id *isl_pw_aff_get_tuple_id(
4035 __isl_keep isl_pw_aff *pa,
4036 enum isl_dim_type type);
4037 __isl_give isl_val *isl_aff_get_constant_val(
4038 __isl_keep isl_aff *aff);
4039 __isl_give isl_val *isl_aff_get_coefficient_val(
4040 __isl_keep isl_aff *aff,
4041 enum isl_dim_type type, int pos);
4042 __isl_give isl_val *isl_aff_get_denominator_val(
4043 __isl_keep isl_aff *aff);
4044 __isl_give isl_aff *isl_aff_get_div(
4045 __isl_keep isl_aff *aff, int pos);
4047 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
4048 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
4049 int (*fn)(__isl_take isl_set *set,
4050 __isl_take isl_aff *aff,
4051 void *user), void *user);
4053 int isl_aff_is_cst(__isl_keep isl_aff *aff);
4054 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4056 int isl_aff_is_nan(__isl_keep isl_aff *aff);
4057 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
4059 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
4060 enum isl_dim_type type, unsigned first, unsigned n);
4061 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
4062 enum isl_dim_type type, unsigned first, unsigned n);
4064 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
4065 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
4066 enum isl_dim_type type);
4067 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
4069 It can be modified using
4071 #include <isl/aff.h>
4072 __isl_give isl_aff *isl_aff_set_tuple_id(
4073 __isl_take isl_aff *aff,
4074 enum isl_dim_type type, __isl_take isl_id *id);
4075 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
4076 __isl_take isl_pw_aff *pwaff,
4077 enum isl_dim_type type, __isl_take isl_id *id);
4078 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
4079 __isl_take isl_pw_aff *pa,
4080 enum isl_dim_type type);
4081 __isl_give isl_aff *isl_aff_set_dim_name(
4082 __isl_take isl_aff *aff, enum isl_dim_type type,
4083 unsigned pos, const char *s);
4084 __isl_give isl_aff *isl_aff_set_dim_id(
4085 __isl_take isl_aff *aff, enum isl_dim_type type,
4086 unsigned pos, __isl_take isl_id *id);
4087 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
4088 __isl_take isl_pw_aff *pma,
4089 enum isl_dim_type type, unsigned pos,
4090 __isl_take isl_id *id);
4091 __isl_give isl_aff *isl_aff_set_constant_si(
4092 __isl_take isl_aff *aff, int v);
4093 __isl_give isl_aff *isl_aff_set_constant_val(
4094 __isl_take isl_aff *aff, __isl_take isl_val *v);
4095 __isl_give isl_aff *isl_aff_set_coefficient_si(
4096 __isl_take isl_aff *aff,
4097 enum isl_dim_type type, int pos, int v);
4098 __isl_give isl_aff *isl_aff_set_coefficient_val(
4099 __isl_take isl_aff *aff,
4100 enum isl_dim_type type, int pos,
4101 __isl_take isl_val *v);
4103 __isl_give isl_aff *isl_aff_add_constant_si(
4104 __isl_take isl_aff *aff, int v);
4105 __isl_give isl_aff *isl_aff_add_constant_val(
4106 __isl_take isl_aff *aff, __isl_take isl_val *v);
4107 __isl_give isl_aff *isl_aff_add_constant_num_si(
4108 __isl_take isl_aff *aff, int v);
4109 __isl_give isl_aff *isl_aff_add_coefficient_si(
4110 __isl_take isl_aff *aff,
4111 enum isl_dim_type type, int pos, int v);
4112 __isl_give isl_aff *isl_aff_add_coefficient_val(
4113 __isl_take isl_aff *aff,
4114 enum isl_dim_type type, int pos,
4115 __isl_take isl_val *v);
4117 __isl_give isl_aff *isl_aff_insert_dims(
4118 __isl_take isl_aff *aff,
4119 enum isl_dim_type type, unsigned first, unsigned n);
4120 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
4121 __isl_take isl_pw_aff *pwaff,
4122 enum isl_dim_type type, unsigned first, unsigned n);
4123 __isl_give isl_aff *isl_aff_add_dims(
4124 __isl_take isl_aff *aff,
4125 enum isl_dim_type type, unsigned n);
4126 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
4127 __isl_take isl_pw_aff *pwaff,
4128 enum isl_dim_type type, unsigned n);
4129 __isl_give isl_aff *isl_aff_drop_dims(
4130 __isl_take isl_aff *aff,
4131 enum isl_dim_type type, unsigned first, unsigned n);
4132 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
4133 __isl_take isl_pw_aff *pwaff,
4134 enum isl_dim_type type, unsigned first, unsigned n);
4135 __isl_give isl_aff *isl_aff_move_dims(
4136 __isl_take isl_aff *aff,
4137 enum isl_dim_type dst_type, unsigned dst_pos,
4138 enum isl_dim_type src_type, unsigned src_pos,
4140 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
4141 __isl_take isl_pw_aff *pa,
4142 enum isl_dim_type dst_type, unsigned dst_pos,
4143 enum isl_dim_type src_type, unsigned src_pos,
4146 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
4147 set the I<numerator> of the constant or coefficient, while
4148 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
4149 the constant or coefficient as a whole.
4150 The C<add_constant> and C<add_coefficient> functions add an integer
4151 or rational value to
4152 the possibly rational constant or coefficient.
4153 The C<add_constant_num> functions add an integer value to
4156 To check whether an affine expressions is obviously zero
4157 or (obviously) equal to some other affine expression, use
4159 #include <isl/aff.h>
4160 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
4161 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
4162 __isl_keep isl_aff *aff2);
4163 int isl_pw_aff_plain_is_equal(
4164 __isl_keep isl_pw_aff *pwaff1,
4165 __isl_keep isl_pw_aff *pwaff2);
4166 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
4167 __isl_keep isl_pw_aff *pa2);
4168 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4169 __isl_keep isl_pw_aff *pa2);
4171 The function C<isl_pw_aff_plain_cmp> can be used to sort
4172 C<isl_pw_aff>s. The order is not strictly defined.
4173 The current order sorts expressions that only involve
4174 earlier dimensions before those that involve later dimensions.
4178 #include <isl/aff.h>
4179 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
4180 __isl_take isl_aff *aff2);
4181 __isl_give isl_pw_aff *isl_pw_aff_add(
4182 __isl_take isl_pw_aff *pwaff1,
4183 __isl_take isl_pw_aff *pwaff2);
4184 __isl_give isl_pw_aff *isl_pw_aff_min(
4185 __isl_take isl_pw_aff *pwaff1,
4186 __isl_take isl_pw_aff *pwaff2);
4187 __isl_give isl_pw_aff *isl_pw_aff_max(
4188 __isl_take isl_pw_aff *pwaff1,
4189 __isl_take isl_pw_aff *pwaff2);
4190 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
4191 __isl_take isl_aff *aff2);
4192 __isl_give isl_pw_aff *isl_pw_aff_sub(
4193 __isl_take isl_pw_aff *pwaff1,
4194 __isl_take isl_pw_aff *pwaff2);
4195 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
4196 __isl_give isl_pw_aff *isl_pw_aff_neg(
4197 __isl_take isl_pw_aff *pwaff);
4198 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
4199 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4200 __isl_take isl_pw_aff *pwaff);
4201 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
4202 __isl_give isl_pw_aff *isl_pw_aff_floor(
4203 __isl_take isl_pw_aff *pwaff);
4204 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
4205 __isl_take isl_val *mod);
4206 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
4207 __isl_take isl_pw_aff *pa,
4208 __isl_take isl_val *mod);
4209 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
4210 __isl_take isl_val *v);
4211 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
4212 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
4213 __isl_give isl_aff *isl_aff_scale_down_ui(
4214 __isl_take isl_aff *aff, unsigned f);
4215 __isl_give isl_aff *isl_aff_scale_down_val(
4216 __isl_take isl_aff *aff, __isl_take isl_val *v);
4217 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
4218 __isl_take isl_pw_aff *pa,
4219 __isl_take isl_val *f);
4221 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4222 __isl_take isl_pw_aff_list *list);
4223 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4224 __isl_take isl_pw_aff_list *list);
4226 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4227 __isl_take isl_pw_aff *pwqp);
4229 __isl_give isl_aff *isl_aff_align_params(
4230 __isl_take isl_aff *aff,
4231 __isl_take isl_space *model);
4232 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4233 __isl_take isl_pw_aff *pwaff,
4234 __isl_take isl_space *model);
4236 __isl_give isl_aff *isl_aff_project_domain_on_params(
4237 __isl_take isl_aff *aff);
4238 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4239 __isl_take isl_pw_aff *pwa);
4241 __isl_give isl_aff *isl_aff_gist_params(
4242 __isl_take isl_aff *aff,
4243 __isl_take isl_set *context);
4244 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
4245 __isl_take isl_set *context);
4246 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
4247 __isl_take isl_pw_aff *pwaff,
4248 __isl_take isl_set *context);
4249 __isl_give isl_pw_aff *isl_pw_aff_gist(
4250 __isl_take isl_pw_aff *pwaff,
4251 __isl_take isl_set *context);
4253 __isl_give isl_set *isl_pw_aff_domain(
4254 __isl_take isl_pw_aff *pwaff);
4255 __isl_give isl_set *isl_pw_aff_params(
4256 __isl_take isl_pw_aff *pwa);
4257 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4258 __isl_take isl_pw_aff *pa,
4259 __isl_take isl_set *set);
4260 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4261 __isl_take isl_pw_aff *pa,
4262 __isl_take isl_set *set);
4264 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
4265 __isl_take isl_aff *aff2);
4266 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
4267 __isl_take isl_aff *aff2);
4268 __isl_give isl_pw_aff *isl_pw_aff_mul(
4269 __isl_take isl_pw_aff *pwaff1,
4270 __isl_take isl_pw_aff *pwaff2);
4271 __isl_give isl_pw_aff *isl_pw_aff_div(
4272 __isl_take isl_pw_aff *pa1,
4273 __isl_take isl_pw_aff *pa2);
4274 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
4275 __isl_take isl_pw_aff *pa1,
4276 __isl_take isl_pw_aff *pa2);
4277 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
4278 __isl_take isl_pw_aff *pa1,
4279 __isl_take isl_pw_aff *pa2);
4281 When multiplying two affine expressions, at least one of the two needs
4282 to be a constant. Similarly, when dividing an affine expression by another,
4283 the second expression needs to be a constant.
4284 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
4285 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
4288 #include <isl/aff.h>
4289 __isl_give isl_aff *isl_aff_pullback_aff(
4290 __isl_take isl_aff *aff1,
4291 __isl_take isl_aff *aff2);
4292 __isl_give isl_aff *isl_aff_pullback_multi_aff(
4293 __isl_take isl_aff *aff,
4294 __isl_take isl_multi_aff *ma);
4295 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
4296 __isl_take isl_pw_aff *pa,
4297 __isl_take isl_multi_aff *ma);
4298 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
4299 __isl_take isl_pw_aff *pa,
4300 __isl_take isl_pw_multi_aff *pma);
4301 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
4302 __isl_take isl_pw_aff *pa,
4303 __isl_take isl_multi_pw_aff *mpa);
4305 These functions precompose the input expression by the given
4306 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
4307 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
4308 into the (piecewise) affine expression.
4309 Objects of type C<isl_multi_aff> are described in
4310 L</"Piecewise Multiple Quasi Affine Expressions">.
4312 #include <isl/aff.h>
4313 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4314 __isl_take isl_aff *aff);
4315 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4316 __isl_take isl_aff *aff);
4317 __isl_give isl_basic_set *isl_aff_le_basic_set(
4318 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4319 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4320 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4321 __isl_give isl_set *isl_pw_aff_eq_set(
4322 __isl_take isl_pw_aff *pwaff1,
4323 __isl_take isl_pw_aff *pwaff2);
4324 __isl_give isl_set *isl_pw_aff_ne_set(
4325 __isl_take isl_pw_aff *pwaff1,
4326 __isl_take isl_pw_aff *pwaff2);
4327 __isl_give isl_set *isl_pw_aff_le_set(
4328 __isl_take isl_pw_aff *pwaff1,
4329 __isl_take isl_pw_aff *pwaff2);
4330 __isl_give isl_set *isl_pw_aff_lt_set(
4331 __isl_take isl_pw_aff *pwaff1,
4332 __isl_take isl_pw_aff *pwaff2);
4333 __isl_give isl_set *isl_pw_aff_ge_set(
4334 __isl_take isl_pw_aff *pwaff1,
4335 __isl_take isl_pw_aff *pwaff2);
4336 __isl_give isl_set *isl_pw_aff_gt_set(
4337 __isl_take isl_pw_aff *pwaff1,
4338 __isl_take isl_pw_aff *pwaff2);
4340 __isl_give isl_set *isl_pw_aff_list_eq_set(
4341 __isl_take isl_pw_aff_list *list1,
4342 __isl_take isl_pw_aff_list *list2);
4343 __isl_give isl_set *isl_pw_aff_list_ne_set(
4344 __isl_take isl_pw_aff_list *list1,
4345 __isl_take isl_pw_aff_list *list2);
4346 __isl_give isl_set *isl_pw_aff_list_le_set(
4347 __isl_take isl_pw_aff_list *list1,
4348 __isl_take isl_pw_aff_list *list2);
4349 __isl_give isl_set *isl_pw_aff_list_lt_set(
4350 __isl_take isl_pw_aff_list *list1,
4351 __isl_take isl_pw_aff_list *list2);
4352 __isl_give isl_set *isl_pw_aff_list_ge_set(
4353 __isl_take isl_pw_aff_list *list1,
4354 __isl_take isl_pw_aff_list *list2);
4355 __isl_give isl_set *isl_pw_aff_list_gt_set(
4356 __isl_take isl_pw_aff_list *list1,
4357 __isl_take isl_pw_aff_list *list2);
4359 The function C<isl_aff_neg_basic_set> returns a basic set
4360 containing those elements in the domain space
4361 of C<aff> where C<aff> is negative.
4362 The function C<isl_aff_ge_basic_set> returns a basic set
4363 containing those elements in the shared space
4364 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4365 The function C<isl_pw_aff_ge_set> returns a set
4366 containing those elements in the shared domain
4367 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4368 The functions operating on C<isl_pw_aff_list> apply the corresponding
4369 C<isl_pw_aff> function to each pair of elements in the two lists.
4371 #include <isl/aff.h>
4372 __isl_give isl_set *isl_pw_aff_nonneg_set(
4373 __isl_take isl_pw_aff *pwaff);
4374 __isl_give isl_set *isl_pw_aff_zero_set(
4375 __isl_take isl_pw_aff *pwaff);
4376 __isl_give isl_set *isl_pw_aff_non_zero_set(
4377 __isl_take isl_pw_aff *pwaff);
4379 The function C<isl_pw_aff_nonneg_set> returns a set
4380 containing those elements in the domain
4381 of C<pwaff> where C<pwaff> is non-negative.
4383 #include <isl/aff.h>
4384 __isl_give isl_pw_aff *isl_pw_aff_cond(
4385 __isl_take isl_pw_aff *cond,
4386 __isl_take isl_pw_aff *pwaff_true,
4387 __isl_take isl_pw_aff *pwaff_false);
4389 The function C<isl_pw_aff_cond> performs a conditional operator
4390 and returns an expression that is equal to C<pwaff_true>
4391 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4392 where C<cond> is zero.
4394 #include <isl/aff.h>
4395 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4396 __isl_take isl_pw_aff *pwaff1,
4397 __isl_take isl_pw_aff *pwaff2);
4398 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4399 __isl_take isl_pw_aff *pwaff1,
4400 __isl_take isl_pw_aff *pwaff2);
4401 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4402 __isl_take isl_pw_aff *pwaff1,
4403 __isl_take isl_pw_aff *pwaff2);
4405 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4406 expression with a domain that is the union of those of C<pwaff1> and
4407 C<pwaff2> and such that on each cell, the quasi-affine expression is
4408 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4409 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4410 associated expression is the defined one.
4412 An expression can be read from input using
4414 #include <isl/aff.h>
4415 __isl_give isl_aff *isl_aff_read_from_str(
4416 isl_ctx *ctx, const char *str);
4417 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4418 isl_ctx *ctx, const char *str);
4420 An expression can be printed using
4422 #include <isl/aff.h>
4423 __isl_give isl_printer *isl_printer_print_aff(
4424 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4426 __isl_give isl_printer *isl_printer_print_pw_aff(
4427 __isl_take isl_printer *p,
4428 __isl_keep isl_pw_aff *pwaff);
4430 =head2 Piecewise Multiple Quasi Affine Expressions
4432 An C<isl_multi_aff> object represents a sequence of
4433 zero or more affine expressions, all defined on the same domain space.
4434 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4435 zero or more piecewise affine expressions.
4437 An C<isl_multi_aff> can be constructed from a single
4438 C<isl_aff> or an C<isl_aff_list> using the
4439 following functions. Similarly for C<isl_multi_pw_aff>
4440 and C<isl_pw_multi_aff>.
4442 #include <isl/aff.h>
4443 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4444 __isl_take isl_aff *aff);
4445 __isl_give isl_multi_pw_aff *
4446 isl_multi_pw_aff_from_multi_aff(
4447 __isl_take isl_multi_aff *ma);
4448 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4449 __isl_take isl_pw_aff *pa);
4450 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4451 __isl_take isl_pw_aff *pa);
4452 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4453 __isl_take isl_space *space,
4454 __isl_take isl_aff_list *list);
4456 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4457 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4458 Note however that the domain
4459 of the result is the intersection of the domains of the input.
4460 The reverse conversion is exact.
4462 #include <isl/aff.h>
4463 __isl_give isl_pw_multi_aff *
4464 isl_pw_multi_aff_from_multi_pw_aff(
4465 __isl_take isl_multi_pw_aff *mpa);
4466 __isl_give isl_multi_pw_aff *
4467 isl_multi_pw_aff_from_pw_multi_aff(
4468 __isl_take isl_pw_multi_aff *pma);
4470 An empty piecewise multiple quasi affine expression (one with no cells),
4471 the zero piecewise multiple quasi affine expression (with value zero
4472 for each output dimension),
4473 a piecewise multiple quasi affine expression with a single cell (with
4474 either a universe or a specified domain) or
4475 a zero-dimensional piecewise multiple quasi affine expression
4477 can be created using the following functions.
4479 #include <isl/aff.h>
4480 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4481 __isl_take isl_space *space);
4482 __isl_give isl_multi_aff *isl_multi_aff_zero(
4483 __isl_take isl_space *space);
4484 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4485 __isl_take isl_space *space);
4486 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4487 __isl_take isl_space *space);
4488 __isl_give isl_multi_aff *isl_multi_aff_identity(
4489 __isl_take isl_space *space);
4490 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4491 __isl_take isl_space *space);
4492 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4493 __isl_take isl_space *space);
4494 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4495 __isl_take isl_space *space);
4496 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4497 __isl_take isl_space *space);
4498 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4499 __isl_take isl_space *space,
4500 enum isl_dim_type type,
4501 unsigned first, unsigned n);
4502 __isl_give isl_pw_multi_aff *
4503 isl_pw_multi_aff_project_out_map(
4504 __isl_take isl_space *space,
4505 enum isl_dim_type type,
4506 unsigned first, unsigned n);
4507 __isl_give isl_pw_multi_aff *
4508 isl_pw_multi_aff_from_multi_aff(
4509 __isl_take isl_multi_aff *ma);
4510 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4511 __isl_take isl_set *set,
4512 __isl_take isl_multi_aff *maff);
4513 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4514 __isl_take isl_set *set);
4516 __isl_give isl_union_pw_multi_aff *
4517 isl_union_pw_multi_aff_empty(
4518 __isl_take isl_space *space);
4519 __isl_give isl_union_pw_multi_aff *
4520 isl_union_pw_multi_aff_add_pw_multi_aff(
4521 __isl_take isl_union_pw_multi_aff *upma,
4522 __isl_take isl_pw_multi_aff *pma);
4523 __isl_give isl_union_pw_multi_aff *
4524 isl_union_pw_multi_aff_from_domain(
4525 __isl_take isl_union_set *uset);
4527 A piecewise multiple quasi affine expression can also be initialized
4528 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4529 and the C<isl_map> is single-valued.
4530 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4531 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4533 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4534 __isl_take isl_set *set);
4535 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4536 __isl_take isl_map *map);
4538 __isl_give isl_union_pw_multi_aff *
4539 isl_union_pw_multi_aff_from_union_set(
4540 __isl_take isl_union_set *uset);
4541 __isl_give isl_union_pw_multi_aff *
4542 isl_union_pw_multi_aff_from_union_map(
4543 __isl_take isl_union_map *umap);
4545 Multiple quasi affine expressions can be copied and freed using
4547 #include <isl/aff.h>
4548 __isl_give isl_multi_aff *isl_multi_aff_copy(
4549 __isl_keep isl_multi_aff *maff);
4550 __isl_null isl_multi_aff *isl_multi_aff_free(
4551 __isl_take isl_multi_aff *maff);
4553 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4554 __isl_keep isl_pw_multi_aff *pma);
4555 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
4556 __isl_take isl_pw_multi_aff *pma);
4558 __isl_give isl_union_pw_multi_aff *
4559 isl_union_pw_multi_aff_copy(
4560 __isl_keep isl_union_pw_multi_aff *upma);
4561 __isl_null isl_union_pw_multi_aff *
4562 isl_union_pw_multi_aff_free(
4563 __isl_take isl_union_pw_multi_aff *upma);
4565 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4566 __isl_keep isl_multi_pw_aff *mpa);
4567 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
4568 __isl_take isl_multi_pw_aff *mpa);
4570 The expression can be inspected using
4572 #include <isl/aff.h>
4573 isl_ctx *isl_multi_aff_get_ctx(
4574 __isl_keep isl_multi_aff *maff);
4575 isl_ctx *isl_pw_multi_aff_get_ctx(
4576 __isl_keep isl_pw_multi_aff *pma);
4577 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4578 __isl_keep isl_union_pw_multi_aff *upma);
4579 isl_ctx *isl_multi_pw_aff_get_ctx(
4580 __isl_keep isl_multi_pw_aff *mpa);
4582 int isl_multi_aff_involves_dims(
4583 __isl_keep isl_multi_aff *ma,
4584 enum isl_dim_type type, unsigned first, unsigned n);
4585 int isl_multi_pw_aff_involves_dims(
4586 __isl_keep isl_multi_pw_aff *mpa,
4587 enum isl_dim_type type, unsigned first, unsigned n);
4589 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4590 enum isl_dim_type type);
4591 unsigned isl_pw_multi_aff_dim(
4592 __isl_keep isl_pw_multi_aff *pma,
4593 enum isl_dim_type type);
4594 unsigned isl_multi_pw_aff_dim(
4595 __isl_keep isl_multi_pw_aff *mpa,
4596 enum isl_dim_type type);
4597 __isl_give isl_aff *isl_multi_aff_get_aff(
4598 __isl_keep isl_multi_aff *multi, int pos);
4599 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4600 __isl_keep isl_pw_multi_aff *pma, int pos);
4601 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4602 __isl_keep isl_multi_pw_aff *mpa, int pos);
4603 int isl_multi_aff_find_dim_by_id(
4604 __isl_keep isl_multi_aff *ma,
4605 enum isl_dim_type type, __isl_keep isl_id *id);
4606 int isl_multi_pw_aff_find_dim_by_id(
4607 __isl_keep isl_multi_pw_aff *mpa,
4608 enum isl_dim_type type, __isl_keep isl_id *id);
4609 const char *isl_pw_multi_aff_get_dim_name(
4610 __isl_keep isl_pw_multi_aff *pma,
4611 enum isl_dim_type type, unsigned pos);
4612 __isl_give isl_id *isl_multi_aff_get_dim_id(
4613 __isl_keep isl_multi_aff *ma,
4614 enum isl_dim_type type, unsigned pos);
4615 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4616 __isl_keep isl_pw_multi_aff *pma,
4617 enum isl_dim_type type, unsigned pos);
4618 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4619 __isl_keep isl_multi_pw_aff *mpa,
4620 enum isl_dim_type type, unsigned pos);
4621 const char *isl_multi_aff_get_tuple_name(
4622 __isl_keep isl_multi_aff *multi,
4623 enum isl_dim_type type);
4624 int isl_pw_multi_aff_has_tuple_name(
4625 __isl_keep isl_pw_multi_aff *pma,
4626 enum isl_dim_type type);
4627 const char *isl_pw_multi_aff_get_tuple_name(
4628 __isl_keep isl_pw_multi_aff *pma,
4629 enum isl_dim_type type);
4630 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4631 enum isl_dim_type type);
4632 int isl_pw_multi_aff_has_tuple_id(
4633 __isl_keep isl_pw_multi_aff *pma,
4634 enum isl_dim_type type);
4635 int isl_multi_pw_aff_has_tuple_id(
4636 __isl_keep isl_multi_pw_aff *mpa,
4637 enum isl_dim_type type);
4638 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4639 __isl_keep isl_multi_aff *ma,
4640 enum isl_dim_type type);
4641 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4642 __isl_keep isl_pw_multi_aff *pma,
4643 enum isl_dim_type type);
4644 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4645 __isl_keep isl_multi_pw_aff *mpa,
4646 enum isl_dim_type type);
4647 int isl_multi_aff_range_is_wrapping(
4648 __isl_keep isl_multi_aff *ma);
4649 int isl_multi_pw_aff_range_is_wrapping(
4650 __isl_keep isl_multi_pw_aff *mpa);
4652 int isl_pw_multi_aff_foreach_piece(
4653 __isl_keep isl_pw_multi_aff *pma,
4654 int (*fn)(__isl_take isl_set *set,
4655 __isl_take isl_multi_aff *maff,
4656 void *user), void *user);
4658 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4659 __isl_keep isl_union_pw_multi_aff *upma,
4660 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4661 void *user), void *user);
4663 It can be modified using
4665 #include <isl/aff.h>
4666 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4667 __isl_take isl_multi_aff *multi, int pos,
4668 __isl_take isl_aff *aff);
4669 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4670 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4671 __isl_take isl_pw_aff *pa);
4672 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4673 __isl_take isl_multi_aff *maff,
4674 enum isl_dim_type type, unsigned pos, const char *s);
4675 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4676 __isl_take isl_multi_aff *maff,
4677 enum isl_dim_type type, unsigned pos,
4678 __isl_take isl_id *id);
4679 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4680 __isl_take isl_multi_aff *maff,
4681 enum isl_dim_type type, const char *s);
4682 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4683 __isl_take isl_multi_aff *maff,
4684 enum isl_dim_type type, __isl_take isl_id *id);
4685 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4686 __isl_take isl_pw_multi_aff *pma,
4687 enum isl_dim_type type, __isl_take isl_id *id);
4688 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4689 __isl_take isl_multi_aff *ma,
4690 enum isl_dim_type type);
4691 __isl_give isl_multi_pw_aff *
4692 isl_multi_pw_aff_reset_tuple_id(
4693 __isl_take isl_multi_pw_aff *mpa,
4694 enum isl_dim_type type);
4695 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4696 __isl_take isl_multi_aff *ma);
4697 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4698 __isl_take isl_multi_pw_aff *mpa);
4700 __isl_give isl_multi_pw_aff *
4701 isl_multi_pw_aff_set_dim_name(
4702 __isl_take isl_multi_pw_aff *mpa,
4703 enum isl_dim_type type, unsigned pos, const char *s);
4704 __isl_give isl_multi_pw_aff *
4705 isl_multi_pw_aff_set_dim_id(
4706 __isl_take isl_multi_pw_aff *mpa,
4707 enum isl_dim_type type, unsigned pos,
4708 __isl_take isl_id *id);
4709 __isl_give isl_multi_pw_aff *
4710 isl_multi_pw_aff_set_tuple_name(
4711 __isl_take isl_multi_pw_aff *mpa,
4712 enum isl_dim_type type, const char *s);
4714 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4715 __isl_take isl_multi_aff *ma);
4717 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4718 __isl_take isl_multi_aff *ma,
4719 enum isl_dim_type type, unsigned first, unsigned n);
4720 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4721 __isl_take isl_multi_aff *ma,
4722 enum isl_dim_type type, unsigned n);
4723 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4724 __isl_take isl_multi_aff *maff,
4725 enum isl_dim_type type, unsigned first, unsigned n);
4726 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4727 __isl_take isl_pw_multi_aff *pma,
4728 enum isl_dim_type type, unsigned first, unsigned n);
4730 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4731 __isl_take isl_multi_pw_aff *mpa,
4732 enum isl_dim_type type, unsigned first, unsigned n);
4733 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4734 __isl_take isl_multi_pw_aff *mpa,
4735 enum isl_dim_type type, unsigned n);
4736 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4737 __isl_take isl_multi_pw_aff *pma,
4738 enum isl_dim_type dst_type, unsigned dst_pos,
4739 enum isl_dim_type src_type, unsigned src_pos,
4742 To check whether two multiple affine expressions are
4743 (obviously) equal to each other, use
4745 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4746 __isl_keep isl_multi_aff *maff2);
4747 int isl_pw_multi_aff_plain_is_equal(
4748 __isl_keep isl_pw_multi_aff *pma1,
4749 __isl_keep isl_pw_multi_aff *pma2);
4750 int isl_multi_pw_aff_plain_is_equal(
4751 __isl_keep isl_multi_pw_aff *mpa1,
4752 __isl_keep isl_multi_pw_aff *mpa2);
4753 int isl_multi_pw_aff_is_equal(
4754 __isl_keep isl_multi_pw_aff *mpa1,
4755 __isl_keep isl_multi_pw_aff *mpa2);
4759 #include <isl/aff.h>
4760 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4761 __isl_take isl_pw_multi_aff *pma1,
4762 __isl_take isl_pw_multi_aff *pma2);
4763 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4764 __isl_take isl_pw_multi_aff *pma1,
4765 __isl_take isl_pw_multi_aff *pma2);
4766 __isl_give isl_multi_aff *isl_multi_aff_floor(
4767 __isl_take isl_multi_aff *ma);
4768 __isl_give isl_multi_aff *isl_multi_aff_add(
4769 __isl_take isl_multi_aff *maff1,
4770 __isl_take isl_multi_aff *maff2);
4771 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4772 __isl_take isl_pw_multi_aff *pma1,
4773 __isl_take isl_pw_multi_aff *pma2);
4774 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4775 __isl_take isl_union_pw_multi_aff *upma1,
4776 __isl_take isl_union_pw_multi_aff *upma2);
4777 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4778 __isl_take isl_pw_multi_aff *pma1,
4779 __isl_take isl_pw_multi_aff *pma2);
4780 __isl_give isl_multi_aff *isl_multi_aff_sub(
4781 __isl_take isl_multi_aff *ma1,
4782 __isl_take isl_multi_aff *ma2);
4783 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4784 __isl_take isl_pw_multi_aff *pma1,
4785 __isl_take isl_pw_multi_aff *pma2);
4786 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4787 __isl_take isl_union_pw_multi_aff *upma1,
4788 __isl_take isl_union_pw_multi_aff *upma2);
4790 C<isl_multi_aff_sub> subtracts the second argument from the first.
4792 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4793 __isl_take isl_multi_aff *ma,
4794 __isl_take isl_val *v);
4795 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4796 __isl_take isl_pw_multi_aff *pma,
4797 __isl_take isl_val *v);
4798 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4799 __isl_take isl_multi_pw_aff *mpa,
4800 __isl_take isl_val *v);
4801 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4802 __isl_take isl_multi_aff *ma,
4803 __isl_take isl_multi_val *mv);
4804 __isl_give isl_pw_multi_aff *
4805 isl_pw_multi_aff_scale_multi_val(
4806 __isl_take isl_pw_multi_aff *pma,
4807 __isl_take isl_multi_val *mv);
4808 __isl_give isl_multi_pw_aff *
4809 isl_multi_pw_aff_scale_multi_val(
4810 __isl_take isl_multi_pw_aff *mpa,
4811 __isl_take isl_multi_val *mv);
4812 __isl_give isl_union_pw_multi_aff *
4813 isl_union_pw_multi_aff_scale_multi_val(
4814 __isl_take isl_union_pw_multi_aff *upma,
4815 __isl_take isl_multi_val *mv);
4816 __isl_give isl_multi_aff *
4817 isl_multi_aff_scale_down_multi_val(
4818 __isl_take isl_multi_aff *ma,
4819 __isl_take isl_multi_val *mv);
4820 __isl_give isl_multi_pw_aff *
4821 isl_multi_pw_aff_scale_down_multi_val(
4822 __isl_take isl_multi_pw_aff *mpa,
4823 __isl_take isl_multi_val *mv);
4825 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4826 by the corresponding elements of C<mv>.
4828 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4829 __isl_take isl_pw_multi_aff *pma,
4830 enum isl_dim_type type, unsigned pos, int value);
4831 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4832 __isl_take isl_pw_multi_aff *pma,
4833 __isl_take isl_set *set);
4834 __isl_give isl_set *isl_multi_pw_aff_domain(
4835 __isl_take isl_multi_pw_aff *mpa);
4836 __isl_give isl_multi_pw_aff *
4837 isl_multi_pw_aff_intersect_params(
4838 __isl_take isl_multi_pw_aff *mpa,
4839 __isl_take isl_set *set);
4840 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4841 __isl_take isl_pw_multi_aff *pma,
4842 __isl_take isl_set *set);
4843 __isl_give isl_multi_pw_aff *
4844 isl_multi_pw_aff_intersect_domain(
4845 __isl_take isl_multi_pw_aff *mpa,
4846 __isl_take isl_set *domain);
4847 __isl_give isl_union_pw_multi_aff *
4848 isl_union_pw_multi_aff_intersect_domain(
4849 __isl_take isl_union_pw_multi_aff *upma,
4850 __isl_take isl_union_set *uset);
4851 __isl_give isl_multi_aff *isl_multi_aff_lift(
4852 __isl_take isl_multi_aff *maff,
4853 __isl_give isl_local_space **ls);
4854 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4855 __isl_take isl_pw_multi_aff *pma);
4856 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4857 __isl_take isl_multi_pw_aff *mpa);
4858 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4859 __isl_take isl_multi_aff *multi,
4860 __isl_take isl_space *model);
4861 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4862 __isl_take isl_pw_multi_aff *pma,
4863 __isl_take isl_space *model);
4864 __isl_give isl_union_pw_multi_aff *
4865 isl_union_pw_multi_aff_align_params(
4866 __isl_take isl_union_pw_multi_aff *upma,
4867 __isl_take isl_space *model);
4868 __isl_give isl_pw_multi_aff *
4869 isl_pw_multi_aff_project_domain_on_params(
4870 __isl_take isl_pw_multi_aff *pma);
4871 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4872 __isl_take isl_multi_aff *maff,
4873 __isl_take isl_set *context);
4874 __isl_give isl_multi_aff *isl_multi_aff_gist(
4875 __isl_take isl_multi_aff *maff,
4876 __isl_take isl_set *context);
4877 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4878 __isl_take isl_pw_multi_aff *pma,
4879 __isl_take isl_set *set);
4880 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4881 __isl_take isl_pw_multi_aff *pma,
4882 __isl_take isl_set *set);
4883 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4884 __isl_take isl_multi_pw_aff *mpa,
4885 __isl_take isl_set *set);
4886 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4887 __isl_take isl_multi_pw_aff *mpa,
4888 __isl_take isl_set *set);
4889 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4890 __isl_take isl_multi_aff *ma);
4891 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4892 __isl_take isl_multi_pw_aff *mpa);
4893 __isl_give isl_set *isl_pw_multi_aff_domain(
4894 __isl_take isl_pw_multi_aff *pma);
4895 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4896 __isl_take isl_union_pw_multi_aff *upma);
4897 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4898 __isl_take isl_multi_aff *ma1, unsigned pos,
4899 __isl_take isl_multi_aff *ma2);
4900 __isl_give isl_multi_aff *isl_multi_aff_splice(
4901 __isl_take isl_multi_aff *ma1,
4902 unsigned in_pos, unsigned out_pos,
4903 __isl_take isl_multi_aff *ma2);
4904 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4905 __isl_take isl_multi_aff *ma1,
4906 __isl_take isl_multi_aff *ma2);
4907 __isl_give isl_multi_aff *
4908 isl_multi_aff_range_factor_domain(
4909 __isl_take isl_multi_aff *ma);
4910 __isl_give isl_multi_aff *
4911 isl_multi_aff_range_factor_range(
4912 __isl_take isl_multi_aff *ma);
4913 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4914 __isl_take isl_multi_aff *ma1,
4915 __isl_take isl_multi_aff *ma2);
4916 __isl_give isl_multi_aff *isl_multi_aff_product(
4917 __isl_take isl_multi_aff *ma1,
4918 __isl_take isl_multi_aff *ma2);
4919 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4920 __isl_take isl_multi_pw_aff *mpa1,
4921 __isl_take isl_multi_pw_aff *mpa2);
4922 __isl_give isl_pw_multi_aff *
4923 isl_pw_multi_aff_range_product(
4924 __isl_take isl_pw_multi_aff *pma1,
4925 __isl_take isl_pw_multi_aff *pma2);
4926 __isl_give isl_multi_pw_aff *
4927 isl_multi_pw_aff_range_factor_domain(
4928 __isl_take isl_multi_pw_aff *mpa);
4929 __isl_give isl_multi_pw_aff *
4930 isl_multi_pw_aff_range_factor_range(
4931 __isl_take isl_multi_pw_aff *mpa);
4932 __isl_give isl_pw_multi_aff *
4933 isl_pw_multi_aff_flat_range_product(
4934 __isl_take isl_pw_multi_aff *pma1,
4935 __isl_take isl_pw_multi_aff *pma2);
4936 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4937 __isl_take isl_pw_multi_aff *pma1,
4938 __isl_take isl_pw_multi_aff *pma2);
4939 __isl_give isl_union_pw_multi_aff *
4940 isl_union_pw_multi_aff_flat_range_product(
4941 __isl_take isl_union_pw_multi_aff *upma1,
4942 __isl_take isl_union_pw_multi_aff *upma2);
4943 __isl_give isl_multi_pw_aff *
4944 isl_multi_pw_aff_range_splice(
4945 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4946 __isl_take isl_multi_pw_aff *mpa2);
4947 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4948 __isl_take isl_multi_pw_aff *mpa1,
4949 unsigned in_pos, unsigned out_pos,
4950 __isl_take isl_multi_pw_aff *mpa2);
4951 __isl_give isl_multi_pw_aff *
4952 isl_multi_pw_aff_range_product(
4953 __isl_take isl_multi_pw_aff *mpa1,
4954 __isl_take isl_multi_pw_aff *mpa2);
4955 __isl_give isl_multi_pw_aff *
4956 isl_multi_pw_aff_flat_range_product(
4957 __isl_take isl_multi_pw_aff *mpa1,
4958 __isl_take isl_multi_pw_aff *mpa2);
4960 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4961 then it is assigned the local space that lies at the basis of
4962 the lifting applied.
4964 #include <isl/aff.h>
4965 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4966 __isl_take isl_multi_aff *ma1,
4967 __isl_take isl_multi_aff *ma2);
4968 __isl_give isl_pw_multi_aff *
4969 isl_pw_multi_aff_pullback_multi_aff(
4970 __isl_take isl_pw_multi_aff *pma,
4971 __isl_take isl_multi_aff *ma);
4972 __isl_give isl_multi_pw_aff *
4973 isl_multi_pw_aff_pullback_multi_aff(
4974 __isl_take isl_multi_pw_aff *mpa,
4975 __isl_take isl_multi_aff *ma);
4976 __isl_give isl_pw_multi_aff *
4977 isl_pw_multi_aff_pullback_pw_multi_aff(
4978 __isl_take isl_pw_multi_aff *pma1,
4979 __isl_take isl_pw_multi_aff *pma2);
4980 __isl_give isl_multi_pw_aff *
4981 isl_multi_pw_aff_pullback_pw_multi_aff(
4982 __isl_take isl_multi_pw_aff *mpa,
4983 __isl_take isl_pw_multi_aff *pma);
4984 __isl_give isl_multi_pw_aff *
4985 isl_multi_pw_aff_pullback_multi_pw_aff(
4986 __isl_take isl_multi_pw_aff *mpa1,
4987 __isl_take isl_multi_pw_aff *mpa2);
4989 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4990 In other words, C<ma2> is plugged
4993 __isl_give isl_set *isl_multi_aff_lex_le_set(
4994 __isl_take isl_multi_aff *ma1,
4995 __isl_take isl_multi_aff *ma2);
4996 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4997 __isl_take isl_multi_aff *ma1,
4998 __isl_take isl_multi_aff *ma2);
5000 The function C<isl_multi_aff_lex_le_set> returns a set
5001 containing those elements in the shared domain space
5002 where C<ma1> is lexicographically smaller than or
5005 An expression can be read from input using
5007 #include <isl/aff.h>
5008 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
5009 isl_ctx *ctx, const char *str);
5010 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
5011 isl_ctx *ctx, const char *str);
5012 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
5013 isl_ctx *ctx, const char *str);
5014 __isl_give isl_union_pw_multi_aff *
5015 isl_union_pw_multi_aff_read_from_str(
5016 isl_ctx *ctx, const char *str);
5018 An expression can be printed using
5020 #include <isl/aff.h>
5021 __isl_give isl_printer *isl_printer_print_multi_aff(
5022 __isl_take isl_printer *p,
5023 __isl_keep isl_multi_aff *maff);
5024 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
5025 __isl_take isl_printer *p,
5026 __isl_keep isl_pw_multi_aff *pma);
5027 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
5028 __isl_take isl_printer *p,
5029 __isl_keep isl_union_pw_multi_aff *upma);
5030 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
5031 __isl_take isl_printer *p,
5032 __isl_keep isl_multi_pw_aff *mpa);
5036 Points are elements of a set. They can be used to construct
5037 simple sets (boxes) or they can be used to represent the
5038 individual elements of a set.
5039 The zero point (the origin) can be created using
5041 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
5043 The coordinates of a point can be inspected, set and changed
5046 __isl_give isl_val *isl_point_get_coordinate_val(
5047 __isl_keep isl_point *pnt,
5048 enum isl_dim_type type, int pos);
5049 __isl_give isl_point *isl_point_set_coordinate_val(
5050 __isl_take isl_point *pnt,
5051 enum isl_dim_type type, int pos,
5052 __isl_take isl_val *v);
5054 __isl_give isl_point *isl_point_add_ui(
5055 __isl_take isl_point *pnt,
5056 enum isl_dim_type type, int pos, unsigned val);
5057 __isl_give isl_point *isl_point_sub_ui(
5058 __isl_take isl_point *pnt,
5059 enum isl_dim_type type, int pos, unsigned val);
5061 Other properties can be obtained using
5063 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
5065 Points can be copied or freed using
5067 __isl_give isl_point *isl_point_copy(
5068 __isl_keep isl_point *pnt);
5069 void isl_point_free(__isl_take isl_point *pnt);
5071 A singleton set can be created from a point using
5073 __isl_give isl_basic_set *isl_basic_set_from_point(
5074 __isl_take isl_point *pnt);
5075 __isl_give isl_set *isl_set_from_point(
5076 __isl_take isl_point *pnt);
5078 and a box can be created from two opposite extremal points using
5080 __isl_give isl_basic_set *isl_basic_set_box_from_points(
5081 __isl_take isl_point *pnt1,
5082 __isl_take isl_point *pnt2);
5083 __isl_give isl_set *isl_set_box_from_points(
5084 __isl_take isl_point *pnt1,
5085 __isl_take isl_point *pnt2);
5087 All elements of a B<bounded> (union) set can be enumerated using
5088 the following functions.
5090 int isl_set_foreach_point(__isl_keep isl_set *set,
5091 int (*fn)(__isl_take isl_point *pnt, void *user),
5093 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
5094 int (*fn)(__isl_take isl_point *pnt, void *user),
5097 The function C<fn> is called for each integer point in
5098 C<set> with as second argument the last argument of
5099 the C<isl_set_foreach_point> call. The function C<fn>
5100 should return C<0> on success and C<-1> on failure.
5101 In the latter case, C<isl_set_foreach_point> will stop
5102 enumerating and return C<-1> as well.
5103 If the enumeration is performed successfully and to completion,
5104 then C<isl_set_foreach_point> returns C<0>.
5106 To obtain a single point of a (basic) set, use
5108 __isl_give isl_point *isl_basic_set_sample_point(
5109 __isl_take isl_basic_set *bset);
5110 __isl_give isl_point *isl_set_sample_point(
5111 __isl_take isl_set *set);
5113 If C<set> does not contain any (integer) points, then the
5114 resulting point will be ``void'', a property that can be
5117 int isl_point_is_void(__isl_keep isl_point *pnt);
5119 =head2 Piecewise Quasipolynomials
5121 A piecewise quasipolynomial is a particular kind of function that maps
5122 a parametric point to a rational value.
5123 More specifically, a quasipolynomial is a polynomial expression in greatest
5124 integer parts of affine expressions of parameters and variables.
5125 A piecewise quasipolynomial is a subdivision of a given parametric
5126 domain into disjoint cells with a quasipolynomial associated to
5127 each cell. The value of the piecewise quasipolynomial at a given
5128 point is the value of the quasipolynomial associated to the cell
5129 that contains the point. Outside of the union of cells,
5130 the value is assumed to be zero.
5131 For example, the piecewise quasipolynomial
5133 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
5135 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
5136 A given piecewise quasipolynomial has a fixed domain dimension.
5137 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
5138 defined over different domains.
5139 Piecewise quasipolynomials are mainly used by the C<barvinok>
5140 library for representing the number of elements in a parametric set or map.
5141 For example, the piecewise quasipolynomial above represents
5142 the number of points in the map
5144 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
5146 =head3 Input and Output
5148 Piecewise quasipolynomials can be read from input using
5150 __isl_give isl_union_pw_qpolynomial *
5151 isl_union_pw_qpolynomial_read_from_str(
5152 isl_ctx *ctx, const char *str);
5154 Quasipolynomials and piecewise quasipolynomials can be printed
5155 using the following functions.
5157 __isl_give isl_printer *isl_printer_print_qpolynomial(
5158 __isl_take isl_printer *p,
5159 __isl_keep isl_qpolynomial *qp);
5161 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
5162 __isl_take isl_printer *p,
5163 __isl_keep isl_pw_qpolynomial *pwqp);
5165 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
5166 __isl_take isl_printer *p,
5167 __isl_keep isl_union_pw_qpolynomial *upwqp);
5169 The output format of the printer
5170 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5171 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
5173 In case of printing in C<ISL_FORMAT_C>, the user may want
5174 to set the names of all dimensions
5176 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
5177 __isl_take isl_qpolynomial *qp,
5178 enum isl_dim_type type, unsigned pos,
5180 __isl_give isl_pw_qpolynomial *
5181 isl_pw_qpolynomial_set_dim_name(
5182 __isl_take isl_pw_qpolynomial *pwqp,
5183 enum isl_dim_type type, unsigned pos,
5186 =head3 Creating New (Piecewise) Quasipolynomials
5188 Some simple quasipolynomials can be created using the following functions.
5189 More complicated quasipolynomials can be created by applying
5190 operations such as addition and multiplication
5191 on the resulting quasipolynomials
5193 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
5194 __isl_take isl_space *domain);
5195 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
5196 __isl_take isl_space *domain);
5197 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
5198 __isl_take isl_space *domain);
5199 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
5200 __isl_take isl_space *domain);
5201 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
5202 __isl_take isl_space *domain);
5203 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
5204 __isl_take isl_space *domain,
5205 __isl_take isl_val *val);
5206 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
5207 __isl_take isl_space *domain,
5208 enum isl_dim_type type, unsigned pos);
5209 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
5210 __isl_take isl_aff *aff);
5212 Note that the space in which a quasipolynomial lives is a map space
5213 with a one-dimensional range. The C<domain> argument in some of
5214 the functions above corresponds to the domain of this map space.
5216 The zero piecewise quasipolynomial or a piecewise quasipolynomial
5217 with a single cell can be created using the following functions.
5218 Multiple of these single cell piecewise quasipolynomials can
5219 be combined to create more complicated piecewise quasipolynomials.
5221 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
5222 __isl_take isl_space *space);
5223 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
5224 __isl_take isl_set *set,
5225 __isl_take isl_qpolynomial *qp);
5226 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
5227 __isl_take isl_qpolynomial *qp);
5228 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
5229 __isl_take isl_pw_aff *pwaff);
5231 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
5232 __isl_take isl_space *space);
5233 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
5234 __isl_take isl_pw_qpolynomial *pwqp);
5235 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
5236 __isl_take isl_union_pw_qpolynomial *upwqp,
5237 __isl_take isl_pw_qpolynomial *pwqp);
5239 Quasipolynomials can be copied and freed again using the following
5242 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
5243 __isl_keep isl_qpolynomial *qp);
5244 __isl_null isl_qpolynomial *isl_qpolynomial_free(
5245 __isl_take isl_qpolynomial *qp);
5247 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
5248 __isl_keep isl_pw_qpolynomial *pwqp);
5249 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
5250 __isl_take isl_pw_qpolynomial *pwqp);
5252 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
5253 __isl_keep isl_union_pw_qpolynomial *upwqp);
5254 __isl_null isl_union_pw_qpolynomial *
5255 isl_union_pw_qpolynomial_free(
5256 __isl_take isl_union_pw_qpolynomial *upwqp);
5258 =head3 Inspecting (Piecewise) Quasipolynomials
5260 To iterate over all piecewise quasipolynomials in a union
5261 piecewise quasipolynomial, use the following function
5263 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
5264 __isl_keep isl_union_pw_qpolynomial *upwqp,
5265 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
5268 To extract the piecewise quasipolynomial in a given space from a union, use
5270 __isl_give isl_pw_qpolynomial *
5271 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
5272 __isl_keep isl_union_pw_qpolynomial *upwqp,
5273 __isl_take isl_space *space);
5275 To iterate over the cells in a piecewise quasipolynomial,
5276 use either of the following two functions
5278 int isl_pw_qpolynomial_foreach_piece(
5279 __isl_keep isl_pw_qpolynomial *pwqp,
5280 int (*fn)(__isl_take isl_set *set,
5281 __isl_take isl_qpolynomial *qp,
5282 void *user), void *user);
5283 int isl_pw_qpolynomial_foreach_lifted_piece(
5284 __isl_keep isl_pw_qpolynomial *pwqp,
5285 int (*fn)(__isl_take isl_set *set,
5286 __isl_take isl_qpolynomial *qp,
5287 void *user), void *user);
5289 As usual, the function C<fn> should return C<0> on success
5290 and C<-1> on failure. The difference between
5291 C<isl_pw_qpolynomial_foreach_piece> and
5292 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
5293 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
5294 compute unique representations for all existentially quantified
5295 variables and then turn these existentially quantified variables
5296 into extra set variables, adapting the associated quasipolynomial
5297 accordingly. This means that the C<set> passed to C<fn>
5298 will not have any existentially quantified variables, but that
5299 the dimensions of the sets may be different for different
5300 invocations of C<fn>.
5302 The constant term of a quasipolynomial can be extracted using
5304 __isl_give isl_val *isl_qpolynomial_get_constant_val(
5305 __isl_keep isl_qpolynomial *qp);
5307 To iterate over all terms in a quasipolynomial,
5310 int isl_qpolynomial_foreach_term(
5311 __isl_keep isl_qpolynomial *qp,
5312 int (*fn)(__isl_take isl_term *term,
5313 void *user), void *user);
5315 The terms themselves can be inspected and freed using
5318 unsigned isl_term_dim(__isl_keep isl_term *term,
5319 enum isl_dim_type type);
5320 __isl_give isl_val *isl_term_get_coefficient_val(
5321 __isl_keep isl_term *term);
5322 int isl_term_get_exp(__isl_keep isl_term *term,
5323 enum isl_dim_type type, unsigned pos);
5324 __isl_give isl_aff *isl_term_get_div(
5325 __isl_keep isl_term *term, unsigned pos);
5326 void isl_term_free(__isl_take isl_term *term);
5328 Each term is a product of parameters, set variables and
5329 integer divisions. The function C<isl_term_get_exp>
5330 returns the exponent of a given dimensions in the given term.
5332 =head3 Properties of (Piecewise) Quasipolynomials
5334 To check whether two union piecewise quasipolynomials are
5335 obviously equal, use
5337 int isl_union_pw_qpolynomial_plain_is_equal(
5338 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5339 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5341 =head3 Operations on (Piecewise) Quasipolynomials
5343 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5344 __isl_take isl_qpolynomial *qp,
5345 __isl_take isl_val *v);
5346 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5347 __isl_take isl_qpolynomial *qp);
5348 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5349 __isl_take isl_qpolynomial *qp1,
5350 __isl_take isl_qpolynomial *qp2);
5351 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5352 __isl_take isl_qpolynomial *qp1,
5353 __isl_take isl_qpolynomial *qp2);
5354 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5355 __isl_take isl_qpolynomial *qp1,
5356 __isl_take isl_qpolynomial *qp2);
5357 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5358 __isl_take isl_qpolynomial *qp, unsigned exponent);
5360 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5361 __isl_take isl_pw_qpolynomial *pwqp,
5362 enum isl_dim_type type, unsigned n,
5363 __isl_take isl_val *v);
5364 __isl_give isl_pw_qpolynomial *
5365 isl_pw_qpolynomial_scale_val(
5366 __isl_take isl_pw_qpolynomial *pwqp,
5367 __isl_take isl_val *v);
5368 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5369 __isl_take isl_pw_qpolynomial *pwqp1,
5370 __isl_take isl_pw_qpolynomial *pwqp2);
5371 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5372 __isl_take isl_pw_qpolynomial *pwqp1,
5373 __isl_take isl_pw_qpolynomial *pwqp2);
5374 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5375 __isl_take isl_pw_qpolynomial *pwqp1,
5376 __isl_take isl_pw_qpolynomial *pwqp2);
5377 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5378 __isl_take isl_pw_qpolynomial *pwqp);
5379 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5380 __isl_take isl_pw_qpolynomial *pwqp1,
5381 __isl_take isl_pw_qpolynomial *pwqp2);
5382 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5383 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5385 __isl_give isl_union_pw_qpolynomial *
5386 isl_union_pw_qpolynomial_scale_val(
5387 __isl_take isl_union_pw_qpolynomial *upwqp,
5388 __isl_take isl_val *v);
5389 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5390 __isl_take isl_union_pw_qpolynomial *upwqp1,
5391 __isl_take isl_union_pw_qpolynomial *upwqp2);
5392 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5393 __isl_take isl_union_pw_qpolynomial *upwqp1,
5394 __isl_take isl_union_pw_qpolynomial *upwqp2);
5395 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5396 __isl_take isl_union_pw_qpolynomial *upwqp1,
5397 __isl_take isl_union_pw_qpolynomial *upwqp2);
5399 __isl_give isl_val *isl_pw_qpolynomial_eval(
5400 __isl_take isl_pw_qpolynomial *pwqp,
5401 __isl_take isl_point *pnt);
5403 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5404 __isl_take isl_union_pw_qpolynomial *upwqp,
5405 __isl_take isl_point *pnt);
5407 __isl_give isl_set *isl_pw_qpolynomial_domain(
5408 __isl_take isl_pw_qpolynomial *pwqp);
5409 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5410 __isl_take isl_pw_qpolynomial *pwpq,
5411 __isl_take isl_set *set);
5412 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5413 __isl_take isl_pw_qpolynomial *pwpq,
5414 __isl_take isl_set *set);
5416 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5417 __isl_take isl_union_pw_qpolynomial *upwqp);
5418 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5419 __isl_take isl_union_pw_qpolynomial *upwpq,
5420 __isl_take isl_union_set *uset);
5421 __isl_give isl_union_pw_qpolynomial *
5422 isl_union_pw_qpolynomial_intersect_params(
5423 __isl_take isl_union_pw_qpolynomial *upwpq,
5424 __isl_take isl_set *set);
5426 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5427 __isl_take isl_qpolynomial *qp,
5428 __isl_take isl_space *model);
5430 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5431 __isl_take isl_qpolynomial *qp);
5432 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5433 __isl_take isl_pw_qpolynomial *pwqp);
5435 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5436 __isl_take isl_union_pw_qpolynomial *upwqp);
5438 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5439 __isl_take isl_qpolynomial *qp,
5440 __isl_take isl_set *context);
5441 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5442 __isl_take isl_qpolynomial *qp,
5443 __isl_take isl_set *context);
5445 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5446 __isl_take isl_pw_qpolynomial *pwqp,
5447 __isl_take isl_set *context);
5448 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5449 __isl_take isl_pw_qpolynomial *pwqp,
5450 __isl_take isl_set *context);
5452 __isl_give isl_union_pw_qpolynomial *
5453 isl_union_pw_qpolynomial_gist_params(
5454 __isl_take isl_union_pw_qpolynomial *upwqp,
5455 __isl_take isl_set *context);
5456 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5457 __isl_take isl_union_pw_qpolynomial *upwqp,
5458 __isl_take isl_union_set *context);
5460 The gist operation applies the gist operation to each of
5461 the cells in the domain of the input piecewise quasipolynomial.
5462 The context is also exploited
5463 to simplify the quasipolynomials associated to each cell.
5465 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5466 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5467 __isl_give isl_union_pw_qpolynomial *
5468 isl_union_pw_qpolynomial_to_polynomial(
5469 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5471 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5472 the polynomial will be an overapproximation. If C<sign> is negative,
5473 it will be an underapproximation. If C<sign> is zero, the approximation
5474 will lie somewhere in between.
5476 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5478 A piecewise quasipolynomial reduction is a piecewise
5479 reduction (or fold) of quasipolynomials.
5480 In particular, the reduction can be maximum or a minimum.
5481 The objects are mainly used to represent the result of
5482 an upper or lower bound on a quasipolynomial over its domain,
5483 i.e., as the result of the following function.
5485 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5486 __isl_take isl_pw_qpolynomial *pwqp,
5487 enum isl_fold type, int *tight);
5489 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5490 __isl_take isl_union_pw_qpolynomial *upwqp,
5491 enum isl_fold type, int *tight);
5493 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5494 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5495 is the returned bound is known be tight, i.e., for each value
5496 of the parameters there is at least
5497 one element in the domain that reaches the bound.
5498 If the domain of C<pwqp> is not wrapping, then the bound is computed
5499 over all elements in that domain and the result has a purely parametric
5500 domain. If the domain of C<pwqp> is wrapping, then the bound is
5501 computed over the range of the wrapped relation. The domain of the
5502 wrapped relation becomes the domain of the result.
5504 A (piecewise) quasipolynomial reduction can be copied or freed using the
5505 following functions.
5507 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5508 __isl_keep isl_qpolynomial_fold *fold);
5509 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5510 __isl_keep isl_pw_qpolynomial_fold *pwf);
5511 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5512 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5513 void isl_qpolynomial_fold_free(
5514 __isl_take isl_qpolynomial_fold *fold);
5515 __isl_null isl_pw_qpolynomial_fold *
5516 isl_pw_qpolynomial_fold_free(
5517 __isl_take isl_pw_qpolynomial_fold *pwf);
5518 __isl_null isl_union_pw_qpolynomial_fold *
5519 isl_union_pw_qpolynomial_fold_free(
5520 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5522 =head3 Printing Piecewise Quasipolynomial Reductions
5524 Piecewise quasipolynomial reductions can be printed
5525 using the following function.
5527 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5528 __isl_take isl_printer *p,
5529 __isl_keep isl_pw_qpolynomial_fold *pwf);
5530 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5531 __isl_take isl_printer *p,
5532 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5534 For C<isl_printer_print_pw_qpolynomial_fold>,
5535 output format of the printer
5536 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5537 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5538 output format of the printer
5539 needs to be set to C<ISL_FORMAT_ISL>.
5540 In case of printing in C<ISL_FORMAT_C>, the user may want
5541 to set the names of all dimensions
5543 __isl_give isl_pw_qpolynomial_fold *
5544 isl_pw_qpolynomial_fold_set_dim_name(
5545 __isl_take isl_pw_qpolynomial_fold *pwf,
5546 enum isl_dim_type type, unsigned pos,
5549 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5551 To iterate over all piecewise quasipolynomial reductions in a union
5552 piecewise quasipolynomial reduction, use the following function
5554 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5555 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5556 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5557 void *user), void *user);
5559 To iterate over the cells in a piecewise quasipolynomial reduction,
5560 use either of the following two functions
5562 int isl_pw_qpolynomial_fold_foreach_piece(
5563 __isl_keep isl_pw_qpolynomial_fold *pwf,
5564 int (*fn)(__isl_take isl_set *set,
5565 __isl_take isl_qpolynomial_fold *fold,
5566 void *user), void *user);
5567 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5568 __isl_keep isl_pw_qpolynomial_fold *pwf,
5569 int (*fn)(__isl_take isl_set *set,
5570 __isl_take isl_qpolynomial_fold *fold,
5571 void *user), void *user);
5573 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5574 of the difference between these two functions.
5576 To iterate over all quasipolynomials in a reduction, use
5578 int isl_qpolynomial_fold_foreach_qpolynomial(
5579 __isl_keep isl_qpolynomial_fold *fold,
5580 int (*fn)(__isl_take isl_qpolynomial *qp,
5581 void *user), void *user);
5583 =head3 Properties of Piecewise Quasipolynomial Reductions
5585 To check whether two union piecewise quasipolynomial reductions are
5586 obviously equal, use
5588 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5589 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5590 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5592 =head3 Operations on Piecewise Quasipolynomial Reductions
5594 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5595 __isl_take isl_qpolynomial_fold *fold,
5596 __isl_take isl_val *v);
5597 __isl_give isl_pw_qpolynomial_fold *
5598 isl_pw_qpolynomial_fold_scale_val(
5599 __isl_take isl_pw_qpolynomial_fold *pwf,
5600 __isl_take isl_val *v);
5601 __isl_give isl_union_pw_qpolynomial_fold *
5602 isl_union_pw_qpolynomial_fold_scale_val(
5603 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5604 __isl_take isl_val *v);
5606 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5607 __isl_take isl_pw_qpolynomial_fold *pwf1,
5608 __isl_take isl_pw_qpolynomial_fold *pwf2);
5610 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5611 __isl_take isl_pw_qpolynomial_fold *pwf1,
5612 __isl_take isl_pw_qpolynomial_fold *pwf2);
5614 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5615 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5616 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5618 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5619 __isl_take isl_pw_qpolynomial_fold *pwf,
5620 __isl_take isl_point *pnt);
5622 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5623 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5624 __isl_take isl_point *pnt);
5626 __isl_give isl_pw_qpolynomial_fold *
5627 isl_pw_qpolynomial_fold_intersect_params(
5628 __isl_take isl_pw_qpolynomial_fold *pwf,
5629 __isl_take isl_set *set);
5631 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5632 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5633 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5634 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5635 __isl_take isl_union_set *uset);
5636 __isl_give isl_union_pw_qpolynomial_fold *
5637 isl_union_pw_qpolynomial_fold_intersect_params(
5638 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5639 __isl_take isl_set *set);
5641 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5642 __isl_take isl_pw_qpolynomial_fold *pwf);
5644 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5645 __isl_take isl_pw_qpolynomial_fold *pwf);
5647 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5648 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5650 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5651 __isl_take isl_qpolynomial_fold *fold,
5652 __isl_take isl_set *context);
5653 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5654 __isl_take isl_qpolynomial_fold *fold,
5655 __isl_take isl_set *context);
5657 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5658 __isl_take isl_pw_qpolynomial_fold *pwf,
5659 __isl_take isl_set *context);
5660 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5661 __isl_take isl_pw_qpolynomial_fold *pwf,
5662 __isl_take isl_set *context);
5664 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5665 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5666 __isl_take isl_union_set *context);
5667 __isl_give isl_union_pw_qpolynomial_fold *
5668 isl_union_pw_qpolynomial_fold_gist_params(
5669 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5670 __isl_take isl_set *context);
5672 The gist operation applies the gist operation to each of
5673 the cells in the domain of the input piecewise quasipolynomial reduction.
5674 In future, the operation will also exploit the context
5675 to simplify the quasipolynomial reductions associated to each cell.
5677 __isl_give isl_pw_qpolynomial_fold *
5678 isl_set_apply_pw_qpolynomial_fold(
5679 __isl_take isl_set *set,
5680 __isl_take isl_pw_qpolynomial_fold *pwf,
5682 __isl_give isl_pw_qpolynomial_fold *
5683 isl_map_apply_pw_qpolynomial_fold(
5684 __isl_take isl_map *map,
5685 __isl_take isl_pw_qpolynomial_fold *pwf,
5687 __isl_give isl_union_pw_qpolynomial_fold *
5688 isl_union_set_apply_union_pw_qpolynomial_fold(
5689 __isl_take isl_union_set *uset,
5690 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5692 __isl_give isl_union_pw_qpolynomial_fold *
5693 isl_union_map_apply_union_pw_qpolynomial_fold(
5694 __isl_take isl_union_map *umap,
5695 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5698 The functions taking a map
5699 compose the given map with the given piecewise quasipolynomial reduction.
5700 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5701 over all elements in the intersection of the range of the map
5702 and the domain of the piecewise quasipolynomial reduction
5703 as a function of an element in the domain of the map.
5704 The functions taking a set compute a bound over all elements in the
5705 intersection of the set and the domain of the
5706 piecewise quasipolynomial reduction.
5708 =head2 Parametric Vertex Enumeration
5710 The parametric vertex enumeration described in this section
5711 is mainly intended to be used internally and by the C<barvinok>
5714 #include <isl/vertices.h>
5715 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5716 __isl_keep isl_basic_set *bset);
5718 The function C<isl_basic_set_compute_vertices> performs the
5719 actual computation of the parametric vertices and the chamber
5720 decomposition and store the result in an C<isl_vertices> object.
5721 This information can be queried by either iterating over all
5722 the vertices or iterating over all the chambers or cells
5723 and then iterating over all vertices that are active on the chamber.
5725 int isl_vertices_foreach_vertex(
5726 __isl_keep isl_vertices *vertices,
5727 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5730 int isl_vertices_foreach_cell(
5731 __isl_keep isl_vertices *vertices,
5732 int (*fn)(__isl_take isl_cell *cell, void *user),
5734 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5735 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5738 Other operations that can be performed on an C<isl_vertices> object are
5741 isl_ctx *isl_vertices_get_ctx(
5742 __isl_keep isl_vertices *vertices);
5743 int isl_vertices_get_n_vertices(
5744 __isl_keep isl_vertices *vertices);
5745 void isl_vertices_free(__isl_take isl_vertices *vertices);
5747 Vertices can be inspected and destroyed using the following functions.
5749 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5750 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5751 __isl_give isl_basic_set *isl_vertex_get_domain(
5752 __isl_keep isl_vertex *vertex);
5753 __isl_give isl_multi_aff *isl_vertex_get_expr(
5754 __isl_keep isl_vertex *vertex);
5755 void isl_vertex_free(__isl_take isl_vertex *vertex);
5757 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
5758 describing the vertex in terms of the parameters,
5759 while C<isl_vertex_get_domain> returns the activity domain
5762 Chambers can be inspected and destroyed using the following functions.
5764 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5765 __isl_give isl_basic_set *isl_cell_get_domain(
5766 __isl_keep isl_cell *cell);
5767 void isl_cell_free(__isl_take isl_cell *cell);
5769 =head1 Polyhedral Compilation Library
5771 This section collects functionality in C<isl> that has been specifically
5772 designed for use during polyhedral compilation.
5774 =head2 Dependence Analysis
5776 C<isl> contains specialized functionality for performing
5777 array dataflow analysis. That is, given a I<sink> access relation
5778 and a collection of possible I<source> access relations,
5779 C<isl> can compute relations that describe
5780 for each iteration of the sink access, which iteration
5781 of which of the source access relations was the last
5782 to access the same data element before the given iteration
5784 The resulting dependence relations map source iterations
5785 to the corresponding sink iterations.
5786 To compute standard flow dependences, the sink should be
5787 a read, while the sources should be writes.
5788 If any of the source accesses are marked as being I<may>
5789 accesses, then there will be a dependence from the last
5790 I<must> access B<and> from any I<may> access that follows
5791 this last I<must> access.
5792 In particular, if I<all> sources are I<may> accesses,
5793 then memory based dependence analysis is performed.
5794 If, on the other hand, all sources are I<must> accesses,
5795 then value based dependence analysis is performed.
5797 #include <isl/flow.h>
5799 typedef int (*isl_access_level_before)(void *first, void *second);
5801 __isl_give isl_access_info *isl_access_info_alloc(
5802 __isl_take isl_map *sink,
5803 void *sink_user, isl_access_level_before fn,
5805 __isl_give isl_access_info *isl_access_info_add_source(
5806 __isl_take isl_access_info *acc,
5807 __isl_take isl_map *source, int must,
5809 __isl_null isl_access_info *isl_access_info_free(
5810 __isl_take isl_access_info *acc);
5812 __isl_give isl_flow *isl_access_info_compute_flow(
5813 __isl_take isl_access_info *acc);
5815 int isl_flow_foreach(__isl_keep isl_flow *deps,
5816 int (*fn)(__isl_take isl_map *dep, int must,
5817 void *dep_user, void *user),
5819 __isl_give isl_map *isl_flow_get_no_source(
5820 __isl_keep isl_flow *deps, int must);
5821 void isl_flow_free(__isl_take isl_flow *deps);
5823 The function C<isl_access_info_compute_flow> performs the actual
5824 dependence analysis. The other functions are used to construct
5825 the input for this function or to read off the output.
5827 The input is collected in an C<isl_access_info>, which can
5828 be created through a call to C<isl_access_info_alloc>.
5829 The arguments to this functions are the sink access relation
5830 C<sink>, a token C<sink_user> used to identify the sink
5831 access to the user, a callback function for specifying the
5832 relative order of source and sink accesses, and the number
5833 of source access relations that will be added.
5834 The callback function has type C<int (*)(void *first, void *second)>.
5835 The function is called with two user supplied tokens identifying
5836 either a source or the sink and it should return the shared nesting
5837 level and the relative order of the two accesses.
5838 In particular, let I<n> be the number of loops shared by
5839 the two accesses. If C<first> precedes C<second> textually,
5840 then the function should return I<2 * n + 1>; otherwise,
5841 it should return I<2 * n>.
5842 The sources can be added to the C<isl_access_info> by performing
5843 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5844 C<must> indicates whether the source is a I<must> access
5845 or a I<may> access. Note that a multi-valued access relation
5846 should only be marked I<must> if every iteration in the domain
5847 of the relation accesses I<all> elements in its image.
5848 The C<source_user> token is again used to identify
5849 the source access. The range of the source access relation
5850 C<source> should have the same dimension as the range
5851 of the sink access relation.
5852 The C<isl_access_info_free> function should usually not be
5853 called explicitly, because it is called implicitly by
5854 C<isl_access_info_compute_flow>.
5856 The result of the dependence analysis is collected in an
5857 C<isl_flow>. There may be elements of
5858 the sink access for which no preceding source access could be
5859 found or for which all preceding sources are I<may> accesses.
5860 The relations containing these elements can be obtained through
5861 calls to C<isl_flow_get_no_source>, the first with C<must> set
5862 and the second with C<must> unset.
5863 In the case of standard flow dependence analysis,
5864 with the sink a read and the sources I<must> writes,
5865 the first relation corresponds to the reads from uninitialized
5866 array elements and the second relation is empty.
5867 The actual flow dependences can be extracted using
5868 C<isl_flow_foreach>. This function will call the user-specified
5869 callback function C<fn> for each B<non-empty> dependence between
5870 a source and the sink. The callback function is called
5871 with four arguments, the actual flow dependence relation
5872 mapping source iterations to sink iterations, a boolean that
5873 indicates whether it is a I<must> or I<may> dependence, a token
5874 identifying the source and an additional C<void *> with value
5875 equal to the third argument of the C<isl_flow_foreach> call.
5876 A dependence is marked I<must> if it originates from a I<must>
5877 source and if it is not followed by any I<may> sources.
5879 After finishing with an C<isl_flow>, the user should call
5880 C<isl_flow_free> to free all associated memory.
5882 A higher-level interface to dependence analysis is provided
5883 by the following function.
5885 #include <isl/flow.h>
5887 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5888 __isl_take isl_union_map *must_source,
5889 __isl_take isl_union_map *may_source,
5890 __isl_take isl_union_map *schedule,
5891 __isl_give isl_union_map **must_dep,
5892 __isl_give isl_union_map **may_dep,
5893 __isl_give isl_union_map **must_no_source,
5894 __isl_give isl_union_map **may_no_source);
5896 The arrays are identified by the tuple names of the ranges
5897 of the accesses. The iteration domains by the tuple names
5898 of the domains of the accesses and of the schedule.
5899 The relative order of the iteration domains is given by the
5900 schedule. The relations returned through C<must_no_source>
5901 and C<may_no_source> are subsets of C<sink>.
5902 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5903 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5904 any of the other arguments is treated as an error.
5906 =head3 Interaction with Dependence Analysis
5908 During the dependence analysis, we frequently need to perform
5909 the following operation. Given a relation between sink iterations
5910 and potential source iterations from a particular source domain,
5911 what is the last potential source iteration corresponding to each
5912 sink iteration. It can sometimes be convenient to adjust
5913 the set of potential source iterations before or after each such operation.
5914 The prototypical example is fuzzy array dataflow analysis,
5915 where we need to analyze if, based on data-dependent constraints,
5916 the sink iteration can ever be executed without one or more of
5917 the corresponding potential source iterations being executed.
5918 If so, we can introduce extra parameters and select an unknown
5919 but fixed source iteration from the potential source iterations.
5920 To be able to perform such manipulations, C<isl> provides the following
5923 #include <isl/flow.h>
5925 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5926 __isl_keep isl_map *source_map,
5927 __isl_keep isl_set *sink, void *source_user,
5929 __isl_give isl_access_info *isl_access_info_set_restrict(
5930 __isl_take isl_access_info *acc,
5931 isl_access_restrict fn, void *user);
5933 The function C<isl_access_info_set_restrict> should be called
5934 before calling C<isl_access_info_compute_flow> and registers a callback function
5935 that will be called any time C<isl> is about to compute the last
5936 potential source. The first argument is the (reverse) proto-dependence,
5937 mapping sink iterations to potential source iterations.
5938 The second argument represents the sink iterations for which
5939 we want to compute the last source iteration.
5940 The third argument is the token corresponding to the source
5941 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5942 The callback is expected to return a restriction on either the input or
5943 the output of the operation computing the last potential source.
5944 If the input needs to be restricted then restrictions are needed
5945 for both the source and the sink iterations. The sink iterations
5946 and the potential source iterations will be intersected with these sets.
5947 If the output needs to be restricted then only a restriction on the source
5948 iterations is required.
5949 If any error occurs, the callback should return C<NULL>.
5950 An C<isl_restriction> object can be created, freed and inspected
5951 using the following functions.
5953 #include <isl/flow.h>
5955 __isl_give isl_restriction *isl_restriction_input(
5956 __isl_take isl_set *source_restr,
5957 __isl_take isl_set *sink_restr);
5958 __isl_give isl_restriction *isl_restriction_output(
5959 __isl_take isl_set *source_restr);
5960 __isl_give isl_restriction *isl_restriction_none(
5961 __isl_take isl_map *source_map);
5962 __isl_give isl_restriction *isl_restriction_empty(
5963 __isl_take isl_map *source_map);
5964 __isl_null isl_restriction *isl_restriction_free(
5965 __isl_take isl_restriction *restr);
5966 isl_ctx *isl_restriction_get_ctx(
5967 __isl_keep isl_restriction *restr);
5969 C<isl_restriction_none> and C<isl_restriction_empty> are special
5970 cases of C<isl_restriction_input>. C<isl_restriction_none>
5971 is essentially equivalent to
5973 isl_restriction_input(isl_set_universe(
5974 isl_space_range(isl_map_get_space(source_map))),
5976 isl_space_domain(isl_map_get_space(source_map))));
5978 whereas C<isl_restriction_empty> is essentially equivalent to
5980 isl_restriction_input(isl_set_empty(
5981 isl_space_range(isl_map_get_space(source_map))),
5983 isl_space_domain(isl_map_get_space(source_map))));
5987 B<The functionality described in this section is fairly new
5988 and may be subject to change.>
5990 #include <isl/schedule.h>
5991 __isl_give isl_schedule *
5992 isl_schedule_constraints_compute_schedule(
5993 __isl_take isl_schedule_constraints *sc);
5994 __isl_null isl_schedule *isl_schedule_free(
5995 __isl_take isl_schedule *sched);
5997 The function C<isl_schedule_constraints_compute_schedule> can be
5998 used to compute a schedule that satisfy the given schedule constraints.
5999 These schedule constraints include the iteration domain for which
6000 a schedule should be computed and dependences between pairs of
6001 iterations. In particular, these dependences include
6002 I<validity> dependences and I<proximity> dependences.
6003 By default, the algorithm used to construct the schedule is similar
6004 to that of C<Pluto>.
6005 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
6007 The generated schedule respects all validity dependences.
6008 That is, all dependence distances over these dependences in the
6009 scheduled space are lexicographically positive.
6010 The default algorithm tries to ensure that the dependence distances
6011 over coincidence constraints are zero and to minimize the
6012 dependence distances over proximity dependences.
6013 Moreover, it tries to obtain sequences (bands) of schedule dimensions
6014 for groups of domains where the dependence distances over validity
6015 dependences have only non-negative values.
6016 When using Feautrier's algorithm, the coincidence and proximity constraints
6017 are only taken into account during the extension to a
6018 full-dimensional schedule.
6020 An C<isl_schedule_constraints> object can be constructed
6021 and manipulated using the following functions.
6023 #include <isl/schedule.h>
6024 __isl_give isl_schedule_constraints *
6025 isl_schedule_constraints_copy(
6026 __isl_keep isl_schedule_constraints *sc);
6027 __isl_give isl_schedule_constraints *
6028 isl_schedule_constraints_on_domain(
6029 __isl_take isl_union_set *domain);
6030 isl_ctx *isl_schedule_constraints_get_ctx(
6031 __isl_keep isl_schedule_constraints *sc);
6032 __isl_give isl_schedule_constraints *
6033 isl_schedule_constraints_set_validity(
6034 __isl_take isl_schedule_constraints *sc,
6035 __isl_take isl_union_map *validity);
6036 __isl_give isl_schedule_constraints *
6037 isl_schedule_constraints_set_coincidence(
6038 __isl_take isl_schedule_constraints *sc,
6039 __isl_take isl_union_map *coincidence);
6040 __isl_give isl_schedule_constraints *
6041 isl_schedule_constraints_set_proximity(
6042 __isl_take isl_schedule_constraints *sc,
6043 __isl_take isl_union_map *proximity);
6044 __isl_give isl_schedule_constraints *
6045 isl_schedule_constraints_set_conditional_validity(
6046 __isl_take isl_schedule_constraints *sc,
6047 __isl_take isl_union_map *condition,
6048 __isl_take isl_union_map *validity);
6049 __isl_null isl_schedule_constraints *
6050 isl_schedule_constraints_free(
6051 __isl_take isl_schedule_constraints *sc);
6053 The initial C<isl_schedule_constraints> object created by
6054 C<isl_schedule_constraints_on_domain> does not impose any constraints.
6055 That is, it has an empty set of dependences.
6056 The function C<isl_schedule_constraints_set_validity> replaces the
6057 validity dependences, mapping domain elements I<i> to domain
6058 elements that should be scheduled after I<i>.
6059 The function C<isl_schedule_constraints_set_coincidence> replaces the
6060 coincidence dependences, mapping domain elements I<i> to domain
6061 elements that should be scheduled together with I<I>, if possible.
6062 The function C<isl_schedule_constraints_set_proximity> replaces the
6063 proximity dependences, mapping domain elements I<i> to domain
6064 elements that should be scheduled either before I<I>
6065 or as early as possible after I<i>.
6067 The function C<isl_schedule_constraints_set_conditional_validity>
6068 replaces the conditional validity constraints.
6069 A conditional validity constraint is only imposed when any of the corresponding
6070 conditions is satisfied, i.e., when any of them is non-zero.
6071 That is, the scheduler ensures that within each band if the dependence
6072 distances over the condition constraints are not all zero
6073 then all corresponding conditional validity constraints are respected.
6074 A conditional validity constraint corresponds to a condition
6075 if the two are adjacent, i.e., if the domain of one relation intersect
6076 the range of the other relation.
6077 The typical use case of conditional validity constraints is
6078 to allow order constraints between live ranges to be violated
6079 as long as the live ranges themselves are local to the band.
6080 To allow more fine-grained control over which conditions correspond
6081 to which conditional validity constraints, the domains and ranges
6082 of these relations may include I<tags>. That is, the domains and
6083 ranges of those relation may themselves be wrapped relations
6084 where the iteration domain appears in the domain of those wrapped relations
6085 and the range of the wrapped relations can be arbitrarily chosen
6086 by the user. Conditions and conditional validity constraints are only
6087 considere adjacent to each other if the entire wrapped relation matches.
6088 In particular, a relation with a tag will never be considered adjacent
6089 to a relation without a tag.
6091 The following function computes a schedule directly from
6092 an iteration domain and validity and proximity dependences
6093 and is implemented in terms of the functions described above.
6094 The use of C<isl_union_set_compute_schedule> is discouraged.
6096 #include <isl/schedule.h>
6097 __isl_give isl_schedule *isl_union_set_compute_schedule(
6098 __isl_take isl_union_set *domain,
6099 __isl_take isl_union_map *validity,
6100 __isl_take isl_union_map *proximity);
6102 A mapping from the domains to the scheduled space can be obtained
6103 from an C<isl_schedule> using the following function.
6105 __isl_give isl_union_map *isl_schedule_get_map(
6106 __isl_keep isl_schedule *sched);
6108 A representation of the schedule can be printed using
6110 __isl_give isl_printer *isl_printer_print_schedule(
6111 __isl_take isl_printer *p,
6112 __isl_keep isl_schedule *schedule);
6114 A representation of the schedule as a forest of bands can be obtained
6115 using the following function.
6117 __isl_give isl_band_list *isl_schedule_get_band_forest(
6118 __isl_keep isl_schedule *schedule);
6120 The individual bands can be visited in depth-first post-order
6121 using the following function.
6123 #include <isl/schedule.h>
6124 int isl_schedule_foreach_band(
6125 __isl_keep isl_schedule *sched,
6126 int (*fn)(__isl_keep isl_band *band, void *user),
6129 The list can be manipulated as explained in L<"Lists">.
6130 The bands inside the list can be copied and freed using the following
6133 #include <isl/band.h>
6134 __isl_give isl_band *isl_band_copy(
6135 __isl_keep isl_band *band);
6136 __isl_null isl_band *isl_band_free(
6137 __isl_take isl_band *band);
6139 Each band contains zero or more scheduling dimensions.
6140 These are referred to as the members of the band.
6141 The section of the schedule that corresponds to the band is
6142 referred to as the partial schedule of the band.
6143 For those nodes that participate in a band, the outer scheduling
6144 dimensions form the prefix schedule, while the inner scheduling
6145 dimensions form the suffix schedule.
6146 That is, if we take a cut of the band forest, then the union of
6147 the concatenations of the prefix, partial and suffix schedules of
6148 each band in the cut is equal to the entire schedule (modulo
6149 some possible padding at the end with zero scheduling dimensions).
6150 The properties of a band can be inspected using the following functions.
6152 #include <isl/band.h>
6153 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
6155 int isl_band_has_children(__isl_keep isl_band *band);
6156 __isl_give isl_band_list *isl_band_get_children(
6157 __isl_keep isl_band *band);
6159 __isl_give isl_union_map *isl_band_get_prefix_schedule(
6160 __isl_keep isl_band *band);
6161 __isl_give isl_union_map *isl_band_get_partial_schedule(
6162 __isl_keep isl_band *band);
6163 __isl_give isl_union_map *isl_band_get_suffix_schedule(
6164 __isl_keep isl_band *band);
6166 int isl_band_n_member(__isl_keep isl_band *band);
6167 int isl_band_member_is_coincident(
6168 __isl_keep isl_band *band, int pos);
6170 int isl_band_list_foreach_band(
6171 __isl_keep isl_band_list *list,
6172 int (*fn)(__isl_keep isl_band *band, void *user),
6175 Note that a scheduling dimension is considered to be ``coincident''
6176 if it satisfies the coincidence constraints within its band.
6177 That is, if the dependence distances of the coincidence
6178 constraints are all zero in that direction (for fixed
6179 iterations of outer bands).
6180 Like C<isl_schedule_foreach_band>,
6181 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
6182 in depth-first post-order.
6184 A band can be tiled using the following function.
6186 #include <isl/band.h>
6187 int isl_band_tile(__isl_keep isl_band *band,
6188 __isl_take isl_vec *sizes);
6190 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
6192 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
6193 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
6195 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
6197 The C<isl_band_tile> function tiles the band using the given tile sizes
6198 inside its schedule.
6199 A new child band is created to represent the point loops and it is
6200 inserted between the modified band and its children.
6201 The C<tile_scale_tile_loops> option specifies whether the tile
6202 loops iterators should be scaled by the tile sizes.
6203 If the C<tile_shift_point_loops> option is set, then the point loops
6204 are shifted to start at zero.
6206 A band can be split into two nested bands using the following function.
6208 int isl_band_split(__isl_keep isl_band *band, int pos);
6210 The resulting outer band contains the first C<pos> dimensions of C<band>
6211 while the inner band contains the remaining dimensions.
6213 A representation of the band can be printed using
6215 #include <isl/band.h>
6216 __isl_give isl_printer *isl_printer_print_band(
6217 __isl_take isl_printer *p,
6218 __isl_keep isl_band *band);
6222 #include <isl/schedule.h>
6223 int isl_options_set_schedule_max_coefficient(
6224 isl_ctx *ctx, int val);
6225 int isl_options_get_schedule_max_coefficient(
6227 int isl_options_set_schedule_max_constant_term(
6228 isl_ctx *ctx, int val);
6229 int isl_options_get_schedule_max_constant_term(
6231 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
6232 int isl_options_get_schedule_fuse(isl_ctx *ctx);
6233 int isl_options_set_schedule_maximize_band_depth(
6234 isl_ctx *ctx, int val);
6235 int isl_options_get_schedule_maximize_band_depth(
6237 int isl_options_set_schedule_outer_coincidence(
6238 isl_ctx *ctx, int val);
6239 int isl_options_get_schedule_outer_coincidence(
6241 int isl_options_set_schedule_split_scaled(
6242 isl_ctx *ctx, int val);
6243 int isl_options_get_schedule_split_scaled(
6245 int isl_options_set_schedule_algorithm(
6246 isl_ctx *ctx, int val);
6247 int isl_options_get_schedule_algorithm(
6249 int isl_options_set_schedule_separate_components(
6250 isl_ctx *ctx, int val);
6251 int isl_options_get_schedule_separate_components(
6256 =item * schedule_max_coefficient
6258 This option enforces that the coefficients for variable and parameter
6259 dimensions in the calculated schedule are not larger than the specified value.
6260 This option can significantly increase the speed of the scheduling calculation
6261 and may also prevent fusing of unrelated dimensions. A value of -1 means that
6262 this option does not introduce bounds on the variable or parameter
6265 =item * schedule_max_constant_term
6267 This option enforces that the constant coefficients in the calculated schedule
6268 are not larger than the maximal constant term. This option can significantly
6269 increase the speed of the scheduling calculation and may also prevent fusing of
6270 unrelated dimensions. A value of -1 means that this option does not introduce
6271 bounds on the constant coefficients.
6273 =item * schedule_fuse
6275 This option controls the level of fusion.
6276 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6277 resulting schedule will be distributed as much as possible.
6278 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6279 try to fuse loops in the resulting schedule.
6281 =item * schedule_maximize_band_depth
6283 If this option is set, we do not split bands at the point
6284 where we detect splitting is necessary. Instead, we
6285 backtrack and split bands as early as possible. This
6286 reduces the number of splits and maximizes the width of
6287 the bands. Wider bands give more possibilities for tiling.
6288 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6289 then bands will be split as early as possible, even if there is no need.
6290 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6292 =item * schedule_outer_coincidence
6294 If this option is set, then we try to construct schedules
6295 where the outermost scheduling dimension in each band
6296 satisfies the coincidence constraints.
6298 =item * schedule_split_scaled
6300 If this option is set, then we try to construct schedules in which the
6301 constant term is split off from the linear part if the linear parts of
6302 the scheduling rows for all nodes in the graphs have a common non-trivial
6304 The constant term is then placed in a separate band and the linear
6307 =item * schedule_algorithm
6309 Selects the scheduling algorithm to be used.
6310 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6311 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6313 =item * schedule_separate_components
6315 If at any point the dependence graph contains any (weakly connected) components,
6316 then these components are scheduled separately.
6317 If this option is not set, then some iterations of the domains
6318 in these components may be scheduled together.
6319 If this option is set, then the components are given consecutive
6324 =head2 AST Generation
6326 This section describes the C<isl> functionality for generating
6327 ASTs that visit all the elements
6328 in a domain in an order specified by a schedule.
6329 In particular, given a C<isl_union_map>, an AST is generated
6330 that visits all the elements in the domain of the C<isl_union_map>
6331 according to the lexicographic order of the corresponding image
6332 element(s). If the range of the C<isl_union_map> consists of
6333 elements in more than one space, then each of these spaces is handled
6334 separately in an arbitrary order.
6335 It should be noted that the image elements only specify the I<order>
6336 in which the corresponding domain elements should be visited.
6337 No direct relation between the image elements and the loop iterators
6338 in the generated AST should be assumed.
6340 Each AST is generated within a build. The initial build
6341 simply specifies the constraints on the parameters (if any)
6342 and can be created, inspected, copied and freed using the following functions.
6344 #include <isl/ast_build.h>
6345 __isl_give isl_ast_build *isl_ast_build_from_context(
6346 __isl_take isl_set *set);
6347 isl_ctx *isl_ast_build_get_ctx(
6348 __isl_keep isl_ast_build *build);
6349 __isl_give isl_ast_build *isl_ast_build_copy(
6350 __isl_keep isl_ast_build *build);
6351 __isl_null isl_ast_build *isl_ast_build_free(
6352 __isl_take isl_ast_build *build);
6354 The C<set> argument is usually a parameter set with zero or more parameters.
6355 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6356 and L</"Fine-grained Control over AST Generation">.
6357 Finally, the AST itself can be constructed using the following
6360 #include <isl/ast_build.h>
6361 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6362 __isl_keep isl_ast_build *build,
6363 __isl_take isl_union_map *schedule);
6365 =head3 Inspecting the AST
6367 The basic properties of an AST node can be obtained as follows.
6369 #include <isl/ast.h>
6370 isl_ctx *isl_ast_node_get_ctx(
6371 __isl_keep isl_ast_node *node);
6372 enum isl_ast_node_type isl_ast_node_get_type(
6373 __isl_keep isl_ast_node *node);
6375 The type of an AST node is one of
6376 C<isl_ast_node_for>,
6378 C<isl_ast_node_block> or
6379 C<isl_ast_node_user>.
6380 An C<isl_ast_node_for> represents a for node.
6381 An C<isl_ast_node_if> represents an if node.
6382 An C<isl_ast_node_block> represents a compound node.
6383 An C<isl_ast_node_user> represents an expression statement.
6384 An expression statement typically corresponds to a domain element, i.e.,
6385 one of the elements that is visited by the AST.
6387 Each type of node has its own additional properties.
6389 #include <isl/ast.h>
6390 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6391 __isl_keep isl_ast_node *node);
6392 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6393 __isl_keep isl_ast_node *node);
6394 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6395 __isl_keep isl_ast_node *node);
6396 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6397 __isl_keep isl_ast_node *node);
6398 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6399 __isl_keep isl_ast_node *node);
6400 int isl_ast_node_for_is_degenerate(
6401 __isl_keep isl_ast_node *node);
6403 An C<isl_ast_for> is considered degenerate if it is known to execute
6406 #include <isl/ast.h>
6407 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6408 __isl_keep isl_ast_node *node);
6409 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6410 __isl_keep isl_ast_node *node);
6411 int isl_ast_node_if_has_else(
6412 __isl_keep isl_ast_node *node);
6413 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6414 __isl_keep isl_ast_node *node);
6416 __isl_give isl_ast_node_list *
6417 isl_ast_node_block_get_children(
6418 __isl_keep isl_ast_node *node);
6420 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6421 __isl_keep isl_ast_node *node);
6423 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6424 the following functions.
6426 #include <isl/ast.h>
6427 isl_ctx *isl_ast_expr_get_ctx(
6428 __isl_keep isl_ast_expr *expr);
6429 enum isl_ast_expr_type isl_ast_expr_get_type(
6430 __isl_keep isl_ast_expr *expr);
6432 The type of an AST expression is one of
6434 C<isl_ast_expr_id> or
6435 C<isl_ast_expr_int>.
6436 An C<isl_ast_expr_op> represents the result of an operation.
6437 An C<isl_ast_expr_id> represents an identifier.
6438 An C<isl_ast_expr_int> represents an integer value.
6440 Each type of expression has its own additional properties.
6442 #include <isl/ast.h>
6443 enum isl_ast_op_type isl_ast_expr_get_op_type(
6444 __isl_keep isl_ast_expr *expr);
6445 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6446 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6447 __isl_keep isl_ast_expr *expr, int pos);
6448 int isl_ast_node_foreach_ast_op_type(
6449 __isl_keep isl_ast_node *node,
6450 int (*fn)(enum isl_ast_op_type type, void *user),
6453 C<isl_ast_expr_get_op_type> returns the type of the operation
6454 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6455 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6457 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6458 C<isl_ast_op_type> that appears in C<node>.
6459 The operation type is one of the following.
6463 =item C<isl_ast_op_and>
6465 Logical I<and> of two arguments.
6466 Both arguments can be evaluated.
6468 =item C<isl_ast_op_and_then>
6470 Logical I<and> of two arguments.
6471 The second argument can only be evaluated if the first evaluates to true.
6473 =item C<isl_ast_op_or>
6475 Logical I<or> of two arguments.
6476 Both arguments can be evaluated.
6478 =item C<isl_ast_op_or_else>
6480 Logical I<or> of two arguments.
6481 The second argument can only be evaluated if the first evaluates to false.
6483 =item C<isl_ast_op_max>
6485 Maximum of two or more arguments.
6487 =item C<isl_ast_op_min>
6489 Minimum of two or more arguments.
6491 =item C<isl_ast_op_minus>
6495 =item C<isl_ast_op_add>
6497 Sum of two arguments.
6499 =item C<isl_ast_op_sub>
6501 Difference of two arguments.
6503 =item C<isl_ast_op_mul>
6505 Product of two arguments.
6507 =item C<isl_ast_op_div>
6509 Exact division. That is, the result is known to be an integer.
6511 =item C<isl_ast_op_fdiv_q>
6513 Result of integer division, rounded towards negative
6516 =item C<isl_ast_op_pdiv_q>
6518 Result of integer division, where dividend is known to be non-negative.
6520 =item C<isl_ast_op_pdiv_r>
6522 Remainder of integer division, where dividend is known to be non-negative.
6524 =item C<isl_ast_op_cond>
6526 Conditional operator defined on three arguments.
6527 If the first argument evaluates to true, then the result
6528 is equal to the second argument. Otherwise, the result
6529 is equal to the third argument.
6530 The second and third argument may only be evaluated if
6531 the first argument evaluates to true and false, respectively.
6532 Corresponds to C<a ? b : c> in C.
6534 =item C<isl_ast_op_select>
6536 Conditional operator defined on three arguments.
6537 If the first argument evaluates to true, then the result
6538 is equal to the second argument. Otherwise, the result
6539 is equal to the third argument.
6540 The second and third argument may be evaluated independently
6541 of the value of the first argument.
6542 Corresponds to C<a * b + (1 - a) * c> in C.
6544 =item C<isl_ast_op_eq>
6548 =item C<isl_ast_op_le>
6550 Less than or equal relation.
6552 =item C<isl_ast_op_lt>
6556 =item C<isl_ast_op_ge>
6558 Greater than or equal relation.
6560 =item C<isl_ast_op_gt>
6562 Greater than relation.
6564 =item C<isl_ast_op_call>
6567 The number of arguments of the C<isl_ast_expr> is one more than
6568 the number of arguments in the function call, the first argument
6569 representing the function being called.
6571 =item C<isl_ast_op_access>
6574 The number of arguments of the C<isl_ast_expr> is one more than
6575 the number of index expressions in the array access, the first argument
6576 representing the array being accessed.
6578 =item C<isl_ast_op_member>
6581 This operation has two arguments, a structure and the name of
6582 the member of the structure being accessed.
6586 #include <isl/ast.h>
6587 __isl_give isl_id *isl_ast_expr_get_id(
6588 __isl_keep isl_ast_expr *expr);
6590 Return the identifier represented by the AST expression.
6592 #include <isl/ast.h>
6593 __isl_give isl_val *isl_ast_expr_get_val(
6594 __isl_keep isl_ast_expr *expr);
6596 Return the integer represented by the AST expression.
6598 =head3 Properties of ASTs
6600 #include <isl/ast.h>
6601 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6602 __isl_keep isl_ast_expr *expr2);
6604 Check if two C<isl_ast_expr>s are equal to each other.
6606 =head3 Manipulating and printing the AST
6608 AST nodes can be copied and freed using the following functions.
6610 #include <isl/ast.h>
6611 __isl_give isl_ast_node *isl_ast_node_copy(
6612 __isl_keep isl_ast_node *node);
6613 __isl_null isl_ast_node *isl_ast_node_free(
6614 __isl_take isl_ast_node *node);
6616 AST expressions can be copied and freed using the following functions.
6618 #include <isl/ast.h>
6619 __isl_give isl_ast_expr *isl_ast_expr_copy(
6620 __isl_keep isl_ast_expr *expr);
6621 __isl_null isl_ast_expr *isl_ast_expr_free(
6622 __isl_take isl_ast_expr *expr);
6624 New AST expressions can be created either directly or within
6625 the context of an C<isl_ast_build>.
6627 #include <isl/ast.h>
6628 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6629 __isl_take isl_val *v);
6630 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6631 __isl_take isl_id *id);
6632 __isl_give isl_ast_expr *isl_ast_expr_neg(
6633 __isl_take isl_ast_expr *expr);
6634 __isl_give isl_ast_expr *isl_ast_expr_add(
6635 __isl_take isl_ast_expr *expr1,
6636 __isl_take isl_ast_expr *expr2);
6637 __isl_give isl_ast_expr *isl_ast_expr_sub(
6638 __isl_take isl_ast_expr *expr1,
6639 __isl_take isl_ast_expr *expr2);
6640 __isl_give isl_ast_expr *isl_ast_expr_mul(
6641 __isl_take isl_ast_expr *expr1,
6642 __isl_take isl_ast_expr *expr2);
6643 __isl_give isl_ast_expr *isl_ast_expr_div(
6644 __isl_take isl_ast_expr *expr1,
6645 __isl_take isl_ast_expr *expr2);
6646 __isl_give isl_ast_expr *isl_ast_expr_and(
6647 __isl_take isl_ast_expr *expr1,
6648 __isl_take isl_ast_expr *expr2)
6649 __isl_give isl_ast_expr *isl_ast_expr_or(
6650 __isl_take isl_ast_expr *expr1,
6651 __isl_take isl_ast_expr *expr2)
6652 __isl_give isl_ast_expr *isl_ast_expr_access(
6653 __isl_take isl_ast_expr *array,
6654 __isl_take isl_ast_expr_list *indices);
6656 #include <isl/ast_build.h>
6657 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6658 __isl_keep isl_ast_build *build,
6659 __isl_take isl_pw_aff *pa);
6660 __isl_give isl_ast_expr *
6661 isl_ast_build_access_from_pw_multi_aff(
6662 __isl_keep isl_ast_build *build,
6663 __isl_take isl_pw_multi_aff *pma);
6664 __isl_give isl_ast_expr *
6665 isl_ast_build_access_from_multi_pw_aff(
6666 __isl_keep isl_ast_build *build,
6667 __isl_take isl_multi_pw_aff *mpa);
6668 __isl_give isl_ast_expr *
6669 isl_ast_build_call_from_pw_multi_aff(
6670 __isl_keep isl_ast_build *build,
6671 __isl_take isl_pw_multi_aff *pma);
6672 __isl_give isl_ast_expr *
6673 isl_ast_build_call_from_multi_pw_aff(
6674 __isl_keep isl_ast_build *build,
6675 __isl_take isl_multi_pw_aff *mpa);
6677 The domains of C<pa>, C<mpa> and C<pma> should correspond
6678 to the schedule space of C<build>.
6679 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6680 the function being called.
6681 If the accessed space is a nested relation, then it is taken
6682 to represent an access of the member specified by the range
6683 of this nested relation of the structure specified by the domain
6684 of the nested relation.
6686 The following functions can be used to modify an C<isl_ast_expr>.
6688 #include <isl/ast.h>
6689 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6690 __isl_take isl_ast_expr *expr, int pos,
6691 __isl_take isl_ast_expr *arg);
6693 Replace the argument of C<expr> at position C<pos> by C<arg>.
6695 #include <isl/ast.h>
6696 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6697 __isl_take isl_ast_expr *expr,
6698 __isl_take isl_id_to_ast_expr *id2expr);
6700 The function C<isl_ast_expr_substitute_ids> replaces the
6701 subexpressions of C<expr> of type C<isl_ast_expr_id>
6702 by the corresponding expression in C<id2expr>, if there is any.
6705 User specified data can be attached to an C<isl_ast_node> and obtained
6706 from the same C<isl_ast_node> using the following functions.
6708 #include <isl/ast.h>
6709 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6710 __isl_take isl_ast_node *node,
6711 __isl_take isl_id *annotation);
6712 __isl_give isl_id *isl_ast_node_get_annotation(
6713 __isl_keep isl_ast_node *node);
6715 Basic printing can be performed using the following functions.
6717 #include <isl/ast.h>
6718 __isl_give isl_printer *isl_printer_print_ast_expr(
6719 __isl_take isl_printer *p,
6720 __isl_keep isl_ast_expr *expr);
6721 __isl_give isl_printer *isl_printer_print_ast_node(
6722 __isl_take isl_printer *p,
6723 __isl_keep isl_ast_node *node);
6725 More advanced printing can be performed using the following functions.
6727 #include <isl/ast.h>
6728 __isl_give isl_printer *isl_ast_op_type_print_macro(
6729 enum isl_ast_op_type type,
6730 __isl_take isl_printer *p);
6731 __isl_give isl_printer *isl_ast_node_print_macros(
6732 __isl_keep isl_ast_node *node,
6733 __isl_take isl_printer *p);
6734 __isl_give isl_printer *isl_ast_node_print(
6735 __isl_keep isl_ast_node *node,
6736 __isl_take isl_printer *p,
6737 __isl_take isl_ast_print_options *options);
6738 __isl_give isl_printer *isl_ast_node_for_print(
6739 __isl_keep isl_ast_node *node,
6740 __isl_take isl_printer *p,
6741 __isl_take isl_ast_print_options *options);
6742 __isl_give isl_printer *isl_ast_node_if_print(
6743 __isl_keep isl_ast_node *node,
6744 __isl_take isl_printer *p,
6745 __isl_take isl_ast_print_options *options);
6747 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6748 C<isl> may print out an AST that makes use of macros such
6749 as C<floord>, C<min> and C<max>.
6750 C<isl_ast_op_type_print_macro> prints out the macro
6751 corresponding to a specific C<isl_ast_op_type>.
6752 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6753 for expressions where these macros would be used and prints
6754 out the required macro definitions.
6755 Essentially, C<isl_ast_node_print_macros> calls
6756 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6757 as function argument.
6758 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6759 C<isl_ast_node_if_print> print an C<isl_ast_node>
6760 in C<ISL_FORMAT_C>, but allow for some extra control
6761 through an C<isl_ast_print_options> object.
6762 This object can be created using the following functions.
6764 #include <isl/ast.h>
6765 __isl_give isl_ast_print_options *
6766 isl_ast_print_options_alloc(isl_ctx *ctx);
6767 __isl_give isl_ast_print_options *
6768 isl_ast_print_options_copy(
6769 __isl_keep isl_ast_print_options *options);
6770 __isl_null isl_ast_print_options *
6771 isl_ast_print_options_free(
6772 __isl_take isl_ast_print_options *options);
6774 __isl_give isl_ast_print_options *
6775 isl_ast_print_options_set_print_user(
6776 __isl_take isl_ast_print_options *options,
6777 __isl_give isl_printer *(*print_user)(
6778 __isl_take isl_printer *p,
6779 __isl_take isl_ast_print_options *options,
6780 __isl_keep isl_ast_node *node, void *user),
6782 __isl_give isl_ast_print_options *
6783 isl_ast_print_options_set_print_for(
6784 __isl_take isl_ast_print_options *options,
6785 __isl_give isl_printer *(*print_for)(
6786 __isl_take isl_printer *p,
6787 __isl_take isl_ast_print_options *options,
6788 __isl_keep isl_ast_node *node, void *user),
6791 The callback set by C<isl_ast_print_options_set_print_user>
6792 is called whenever a node of type C<isl_ast_node_user> needs to
6794 The callback set by C<isl_ast_print_options_set_print_for>
6795 is called whenever a node of type C<isl_ast_node_for> needs to
6797 Note that C<isl_ast_node_for_print> will I<not> call the
6798 callback set by C<isl_ast_print_options_set_print_for> on the node
6799 on which C<isl_ast_node_for_print> is called, but only on nested
6800 nodes of type C<isl_ast_node_for>. It is therefore safe to
6801 call C<isl_ast_node_for_print> from within the callback set by
6802 C<isl_ast_print_options_set_print_for>.
6804 The following option determines the type to be used for iterators
6805 while printing the AST.
6807 int isl_options_set_ast_iterator_type(
6808 isl_ctx *ctx, const char *val);
6809 const char *isl_options_get_ast_iterator_type(
6814 #include <isl/ast_build.h>
6815 int isl_options_set_ast_build_atomic_upper_bound(
6816 isl_ctx *ctx, int val);
6817 int isl_options_get_ast_build_atomic_upper_bound(
6819 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6821 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6822 int isl_options_set_ast_build_exploit_nested_bounds(
6823 isl_ctx *ctx, int val);
6824 int isl_options_get_ast_build_exploit_nested_bounds(
6826 int isl_options_set_ast_build_group_coscheduled(
6827 isl_ctx *ctx, int val);
6828 int isl_options_get_ast_build_group_coscheduled(
6830 int isl_options_set_ast_build_scale_strides(
6831 isl_ctx *ctx, int val);
6832 int isl_options_get_ast_build_scale_strides(
6834 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6836 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6837 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6839 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6843 =item * ast_build_atomic_upper_bound
6845 Generate loop upper bounds that consist of the current loop iterator,
6846 an operator and an expression not involving the iterator.
6847 If this option is not set, then the current loop iterator may appear
6848 several times in the upper bound.
6849 For example, when this option is turned off, AST generation
6852 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6856 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6859 When the option is turned on, the following AST is generated
6861 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6864 =item * ast_build_prefer_pdiv
6866 If this option is turned off, then the AST generation will
6867 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6868 operators, but no C<isl_ast_op_pdiv_q> or
6869 C<isl_ast_op_pdiv_r> operators.
6870 If this options is turned on, then C<isl> will try to convert
6871 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6872 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6874 =item * ast_build_exploit_nested_bounds
6876 Simplify conditions based on bounds of nested for loops.
6877 In particular, remove conditions that are implied by the fact
6878 that one or more nested loops have at least one iteration,
6879 meaning that the upper bound is at least as large as the lower bound.
6880 For example, when this option is turned off, AST generation
6883 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6889 for (int c0 = 0; c0 <= N; c0 += 1)
6890 for (int c1 = 0; c1 <= M; c1 += 1)
6893 When the option is turned on, the following AST is generated
6895 for (int c0 = 0; c0 <= N; c0 += 1)
6896 for (int c1 = 0; c1 <= M; c1 += 1)
6899 =item * ast_build_group_coscheduled
6901 If two domain elements are assigned the same schedule point, then
6902 they may be executed in any order and they may even appear in different
6903 loops. If this options is set, then the AST generator will make
6904 sure that coscheduled domain elements do not appear in separate parts
6905 of the AST. This is useful in case of nested AST generation
6906 if the outer AST generation is given only part of a schedule
6907 and the inner AST generation should handle the domains that are
6908 coscheduled by this initial part of the schedule together.
6909 For example if an AST is generated for a schedule
6911 { A[i] -> [0]; B[i] -> [0] }
6913 then the C<isl_ast_build_set_create_leaf> callback described
6914 below may get called twice, once for each domain.
6915 Setting this option ensures that the callback is only called once
6916 on both domains together.
6918 =item * ast_build_separation_bounds
6920 This option specifies which bounds to use during separation.
6921 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6922 then all (possibly implicit) bounds on the current dimension will
6923 be used during separation.
6924 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6925 then only those bounds that are explicitly available will
6926 be used during separation.
6928 =item * ast_build_scale_strides
6930 This option specifies whether the AST generator is allowed
6931 to scale down iterators of strided loops.
6933 =item * ast_build_allow_else
6935 This option specifies whether the AST generator is allowed
6936 to construct if statements with else branches.
6938 =item * ast_build_allow_or
6940 This option specifies whether the AST generator is allowed
6941 to construct if conditions with disjunctions.
6945 =head3 Fine-grained Control over AST Generation
6947 Besides specifying the constraints on the parameters,
6948 an C<isl_ast_build> object can be used to control
6949 various aspects of the AST generation process.
6950 The most prominent way of control is through ``options'',
6951 which can be set using the following function.
6953 #include <isl/ast_build.h>
6954 __isl_give isl_ast_build *
6955 isl_ast_build_set_options(
6956 __isl_take isl_ast_build *control,
6957 __isl_take isl_union_map *options);
6959 The options are encoded in an <isl_union_map>.
6960 The domain of this union relation refers to the schedule domain,
6961 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6962 In the case of nested AST generation (see L</"Nested AST Generation">),
6963 the domain of C<options> should refer to the extra piece of the schedule.
6964 That is, it should be equal to the range of the wrapped relation in the
6965 range of the schedule.
6966 The range of the options can consist of elements in one or more spaces,
6967 the names of which determine the effect of the option.
6968 The values of the range typically also refer to the schedule dimension
6969 to which the option applies. In case of nested AST generation
6970 (see L</"Nested AST Generation">), these values refer to the position
6971 of the schedule dimension within the innermost AST generation.
6972 The constraints on the domain elements of
6973 the option should only refer to this dimension and earlier dimensions.
6974 We consider the following spaces.
6978 =item C<separation_class>
6980 This space is a wrapped relation between two one dimensional spaces.
6981 The input space represents the schedule dimension to which the option
6982 applies and the output space represents the separation class.
6983 While constructing a loop corresponding to the specified schedule
6984 dimension(s), the AST generator will try to generate separate loops
6985 for domain elements that are assigned different classes.
6986 If only some of the elements are assigned a class, then those elements
6987 that are not assigned any class will be treated as belonging to a class
6988 that is separate from the explicitly assigned classes.
6989 The typical use case for this option is to separate full tiles from
6991 The other options, described below, are applied after the separation
6994 As an example, consider the separation into full and partial tiles
6995 of a tiling of a triangular domain.
6996 Take, for example, the domain
6998 { A[i,j] : 0 <= i,j and i + j <= 100 }
7000 and a tiling into tiles of 10 by 10. The input to the AST generator
7001 is then the schedule
7003 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
7006 Without any options, the following AST is generated
7008 for (int c0 = 0; c0 <= 10; c0 += 1)
7009 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
7010 for (int c2 = 10 * c0;
7011 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7013 for (int c3 = 10 * c1;
7014 c3 <= min(10 * c1 + 9, -c2 + 100);
7018 Separation into full and partial tiles can be obtained by assigning
7019 a class, say C<0>, to the full tiles. The full tiles are represented by those
7020 values of the first and second schedule dimensions for which there are
7021 values of the third and fourth dimensions to cover an entire tile.
7022 That is, we need to specify the following option
7024 { [a,b,c,d] -> separation_class[[0]->[0]] :
7025 exists b': 0 <= 10a,10b' and
7026 10a+9+10b'+9 <= 100;
7027 [a,b,c,d] -> separation_class[[1]->[0]] :
7028 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
7032 { [a, b, c, d] -> separation_class[[1] -> [0]] :
7033 a >= 0 and b >= 0 and b <= 8 - a;
7034 [a, b, c, d] -> separation_class[[0] -> [0]] :
7037 With this option, the generated AST is as follows
7040 for (int c0 = 0; c0 <= 8; c0 += 1) {
7041 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
7042 for (int c2 = 10 * c0;
7043 c2 <= 10 * c0 + 9; c2 += 1)
7044 for (int c3 = 10 * c1;
7045 c3 <= 10 * c1 + 9; c3 += 1)
7047 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
7048 for (int c2 = 10 * c0;
7049 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7051 for (int c3 = 10 * c1;
7052 c3 <= min(-c2 + 100, 10 * c1 + 9);
7056 for (int c0 = 9; c0 <= 10; c0 += 1)
7057 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
7058 for (int c2 = 10 * c0;
7059 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7061 for (int c3 = 10 * c1;
7062 c3 <= min(10 * c1 + 9, -c2 + 100);
7069 This is a single-dimensional space representing the schedule dimension(s)
7070 to which ``separation'' should be applied. Separation tries to split
7071 a loop into several pieces if this can avoid the generation of guards
7073 See also the C<atomic> option.
7077 This is a single-dimensional space representing the schedule dimension(s)
7078 for which the domains should be considered ``atomic''. That is, the
7079 AST generator will make sure that any given domain space will only appear
7080 in a single loop at the specified level.
7082 Consider the following schedule
7084 { a[i] -> [i] : 0 <= i < 10;
7085 b[i] -> [i+1] : 0 <= i < 10 }
7087 If the following option is specified
7089 { [i] -> separate[x] }
7091 then the following AST will be generated
7095 for (int c0 = 1; c0 <= 9; c0 += 1) {
7102 If, on the other hand, the following option is specified
7104 { [i] -> atomic[x] }
7106 then the following AST will be generated
7108 for (int c0 = 0; c0 <= 10; c0 += 1) {
7115 If neither C<atomic> nor C<separate> is specified, then the AST generator
7116 may produce either of these two results or some intermediate form.
7120 This is a single-dimensional space representing the schedule dimension(s)
7121 that should be I<completely> unrolled.
7122 To obtain a partial unrolling, the user should apply an additional
7123 strip-mining to the schedule and fully unroll the inner loop.
7127 Additional control is available through the following functions.
7129 #include <isl/ast_build.h>
7130 __isl_give isl_ast_build *
7131 isl_ast_build_set_iterators(
7132 __isl_take isl_ast_build *control,
7133 __isl_take isl_id_list *iterators);
7135 The function C<isl_ast_build_set_iterators> allows the user to
7136 specify a list of iterator C<isl_id>s to be used as iterators.
7137 If the input schedule is injective, then
7138 the number of elements in this list should be as large as the dimension
7139 of the schedule space, but no direct correspondence should be assumed
7140 between dimensions and elements.
7141 If the input schedule is not injective, then an additional number
7142 of C<isl_id>s equal to the largest dimension of the input domains
7144 If the number of provided C<isl_id>s is insufficient, then additional
7145 names are automatically generated.
7147 #include <isl/ast_build.h>
7148 __isl_give isl_ast_build *
7149 isl_ast_build_set_create_leaf(
7150 __isl_take isl_ast_build *control,
7151 __isl_give isl_ast_node *(*fn)(
7152 __isl_take isl_ast_build *build,
7153 void *user), void *user);
7156 C<isl_ast_build_set_create_leaf> function allows for the
7157 specification of a callback that should be called whenever the AST
7158 generator arrives at an element of the schedule domain.
7159 The callback should return an AST node that should be inserted
7160 at the corresponding position of the AST. The default action (when
7161 the callback is not set) is to continue generating parts of the AST to scan
7162 all the domain elements associated to the schedule domain element
7163 and to insert user nodes, ``calling'' the domain element, for each of them.
7164 The C<build> argument contains the current state of the C<isl_ast_build>.
7165 To ease nested AST generation (see L</"Nested AST Generation">),
7166 all control information that is
7167 specific to the current AST generation such as the options and
7168 the callbacks has been removed from this C<isl_ast_build>.
7169 The callback would typically return the result of a nested
7171 user defined node created using the following function.
7173 #include <isl/ast.h>
7174 __isl_give isl_ast_node *isl_ast_node_alloc_user(
7175 __isl_take isl_ast_expr *expr);
7177 #include <isl/ast_build.h>
7178 __isl_give isl_ast_build *
7179 isl_ast_build_set_at_each_domain(
7180 __isl_take isl_ast_build *build,
7181 __isl_give isl_ast_node *(*fn)(
7182 __isl_take isl_ast_node *node,
7183 __isl_keep isl_ast_build *build,
7184 void *user), void *user);
7185 __isl_give isl_ast_build *
7186 isl_ast_build_set_before_each_for(
7187 __isl_take isl_ast_build *build,
7188 __isl_give isl_id *(*fn)(
7189 __isl_keep isl_ast_build *build,
7190 void *user), void *user);
7191 __isl_give isl_ast_build *
7192 isl_ast_build_set_after_each_for(
7193 __isl_take isl_ast_build *build,
7194 __isl_give isl_ast_node *(*fn)(
7195 __isl_take isl_ast_node *node,
7196 __isl_keep isl_ast_build *build,
7197 void *user), void *user);
7199 The callback set by C<isl_ast_build_set_at_each_domain> will
7200 be called for each domain AST node.
7201 The callbacks set by C<isl_ast_build_set_before_each_for>
7202 and C<isl_ast_build_set_after_each_for> will be called
7203 for each for AST node. The first will be called in depth-first
7204 pre-order, while the second will be called in depth-first post-order.
7205 Since C<isl_ast_build_set_before_each_for> is called before the for
7206 node is actually constructed, it is only passed an C<isl_ast_build>.
7207 The returned C<isl_id> will be added as an annotation (using
7208 C<isl_ast_node_set_annotation>) to the constructed for node.
7209 In particular, if the user has also specified an C<after_each_for>
7210 callback, then the annotation can be retrieved from the node passed to
7211 that callback using C<isl_ast_node_get_annotation>.
7212 All callbacks should C<NULL> on failure.
7213 The given C<isl_ast_build> can be used to create new
7214 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
7215 or C<isl_ast_build_call_from_pw_multi_aff>.
7217 =head3 Nested AST Generation
7219 C<isl> allows the user to create an AST within the context
7220 of another AST. These nested ASTs are created using the
7221 same C<isl_ast_build_ast_from_schedule> function that is used to create the
7222 outer AST. The C<build> argument should be an C<isl_ast_build>
7223 passed to a callback set by
7224 C<isl_ast_build_set_create_leaf>.
7225 The space of the range of the C<schedule> argument should refer
7226 to this build. In particular, the space should be a wrapped
7227 relation and the domain of this wrapped relation should be the
7228 same as that of the range of the schedule returned by
7229 C<isl_ast_build_get_schedule> below.
7230 In practice, the new schedule is typically
7231 created by calling C<isl_union_map_range_product> on the old schedule
7232 and some extra piece of the schedule.
7233 The space of the schedule domain is also available from
7234 the C<isl_ast_build>.
7236 #include <isl/ast_build.h>
7237 __isl_give isl_union_map *isl_ast_build_get_schedule(
7238 __isl_keep isl_ast_build *build);
7239 __isl_give isl_space *isl_ast_build_get_schedule_space(
7240 __isl_keep isl_ast_build *build);
7241 __isl_give isl_ast_build *isl_ast_build_restrict(
7242 __isl_take isl_ast_build *build,
7243 __isl_take isl_set *set);
7245 The C<isl_ast_build_get_schedule> function returns a (partial)
7246 schedule for the domains elements for which part of the AST still needs to
7247 be generated in the current build.
7248 In particular, the domain elements are mapped to those iterations of the loops
7249 enclosing the current point of the AST generation inside which
7250 the domain elements are executed.
7251 No direct correspondence between
7252 the input schedule and this schedule should be assumed.
7253 The space obtained from C<isl_ast_build_get_schedule_space> can be used
7254 to create a set for C<isl_ast_build_restrict> to intersect
7255 with the current build. In particular, the set passed to
7256 C<isl_ast_build_restrict> can have additional parameters.
7257 The ids of the set dimensions in the space returned by
7258 C<isl_ast_build_get_schedule_space> correspond to the
7259 iterators of the already generated loops.
7260 The user should not rely on the ids of the output dimensions
7261 of the relations in the union relation returned by
7262 C<isl_ast_build_get_schedule> having any particular value.
7266 Although C<isl> is mainly meant to be used as a library,
7267 it also contains some basic applications that use some
7268 of the functionality of C<isl>.
7269 The input may be specified in either the L<isl format>
7270 or the L<PolyLib format>.
7272 =head2 C<isl_polyhedron_sample>
7274 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7275 an integer element of the polyhedron, if there is any.
7276 The first column in the output is the denominator and is always
7277 equal to 1. If the polyhedron contains no integer points,
7278 then a vector of length zero is printed.
7282 C<isl_pip> takes the same input as the C<example> program
7283 from the C<piplib> distribution, i.e., a set of constraints
7284 on the parameters, a line containing only -1 and finally a set
7285 of constraints on a parametric polyhedron.
7286 The coefficients of the parameters appear in the last columns
7287 (but before the final constant column).
7288 The output is the lexicographic minimum of the parametric polyhedron.
7289 As C<isl> currently does not have its own output format, the output
7290 is just a dump of the internal state.
7292 =head2 C<isl_polyhedron_minimize>
7294 C<isl_polyhedron_minimize> computes the minimum of some linear
7295 or affine objective function over the integer points in a polyhedron.
7296 If an affine objective function
7297 is given, then the constant should appear in the last column.
7299 =head2 C<isl_polytope_scan>
7301 Given a polytope, C<isl_polytope_scan> prints
7302 all integer points in the polytope.
7304 =head2 C<isl_codegen>
7306 Given a schedule, a context set and an options relation,
7307 C<isl_codegen> prints out an AST that scans the domain elements
7308 of the schedule in the order of their image(s) taking into account
7309 the constraints in the context set.