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 For set inputs, they should be a permutation of
1794 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
1795 For map inputs, they should be a permutation of
1796 C<isl_dim_cst>, C<isl_dim_param>,
1797 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1799 The number of parameters, input, output or set dimensions can
1800 be obtained using the following functions.
1802 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1803 enum isl_dim_type type);
1804 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1805 enum isl_dim_type type);
1806 unsigned isl_set_dim(__isl_keep isl_set *set,
1807 enum isl_dim_type type);
1808 unsigned isl_map_dim(__isl_keep isl_map *map,
1809 enum isl_dim_type type);
1810 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1811 enum isl_dim_type type);
1813 Note that a C<isl_union_map> only has parameters.
1815 To check whether the description of a set or relation depends
1816 on one or more given dimensions, it is not necessary to iterate over all
1817 constraints. Instead the following functions can be used.
1819 int isl_basic_set_involves_dims(
1820 __isl_keep isl_basic_set *bset,
1821 enum isl_dim_type type, unsigned first, unsigned n);
1822 int isl_set_involves_dims(__isl_keep isl_set *set,
1823 enum isl_dim_type type, unsigned first, unsigned n);
1824 int isl_basic_map_involves_dims(
1825 __isl_keep isl_basic_map *bmap,
1826 enum isl_dim_type type, unsigned first, unsigned n);
1827 int isl_map_involves_dims(__isl_keep isl_map *map,
1828 enum isl_dim_type type, unsigned first, unsigned n);
1830 Similarly, the following functions can be used to check whether
1831 a given dimension is involved in any lower or upper bound.
1833 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1834 enum isl_dim_type type, unsigned pos);
1835 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1836 enum isl_dim_type type, unsigned pos);
1838 Note that these functions return true even if there is a bound on
1839 the dimension on only some of the basic sets of C<set>.
1840 To check if they have a bound for all of the basic sets in C<set>,
1841 use the following functions instead.
1843 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1844 enum isl_dim_type type, unsigned pos);
1845 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1846 enum isl_dim_type type, unsigned pos);
1848 The identifiers or names of the domain and range spaces of a set
1849 or relation can be read off or set using the following functions.
1851 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1852 __isl_take isl_basic_set *bset,
1853 __isl_take isl_id *id);
1854 __isl_give isl_set *isl_set_set_tuple_id(
1855 __isl_take isl_set *set, __isl_take isl_id *id);
1856 __isl_give isl_set *isl_set_reset_tuple_id(
1857 __isl_take isl_set *set);
1858 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1859 __isl_give isl_id *isl_set_get_tuple_id(
1860 __isl_keep isl_set *set);
1861 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1862 __isl_take isl_basic_map *bmap,
1863 enum isl_dim_type type, __isl_take isl_id *id);
1864 __isl_give isl_map *isl_map_set_tuple_id(
1865 __isl_take isl_map *map, enum isl_dim_type type,
1866 __isl_take isl_id *id);
1867 __isl_give isl_map *isl_map_reset_tuple_id(
1868 __isl_take isl_map *map, enum isl_dim_type type);
1869 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1870 enum isl_dim_type type);
1871 __isl_give isl_id *isl_map_get_tuple_id(
1872 __isl_keep isl_map *map, enum isl_dim_type type);
1874 const char *isl_basic_set_get_tuple_name(
1875 __isl_keep isl_basic_set *bset);
1876 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1877 __isl_take isl_basic_set *set, const char *s);
1878 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1879 const char *isl_set_get_tuple_name(
1880 __isl_keep isl_set *set);
1881 __isl_give isl_set *isl_set_set_tuple_name(
1882 __isl_take isl_set *set, const char *s);
1883 const char *isl_basic_map_get_tuple_name(
1884 __isl_keep isl_basic_map *bmap,
1885 enum isl_dim_type type);
1886 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1887 __isl_take isl_basic_map *bmap,
1888 enum isl_dim_type type, const char *s);
1889 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1890 enum isl_dim_type type);
1891 const char *isl_map_get_tuple_name(
1892 __isl_keep isl_map *map,
1893 enum isl_dim_type type);
1894 __isl_give isl_map *isl_map_set_tuple_name(
1895 __isl_take isl_map *map,
1896 enum isl_dim_type type, const char *s);
1898 As with C<isl_space_get_tuple_name>, the value returned points to
1899 an internal data structure.
1900 The identifiers, positions or names of individual dimensions can be
1901 read off using the following functions.
1903 __isl_give isl_id *isl_basic_set_get_dim_id(
1904 __isl_keep isl_basic_set *bset,
1905 enum isl_dim_type type, unsigned pos);
1906 __isl_give isl_set *isl_set_set_dim_id(
1907 __isl_take isl_set *set, enum isl_dim_type type,
1908 unsigned pos, __isl_take isl_id *id);
1909 int isl_set_has_dim_id(__isl_keep isl_set *set,
1910 enum isl_dim_type type, unsigned pos);
1911 __isl_give isl_id *isl_set_get_dim_id(
1912 __isl_keep isl_set *set, enum isl_dim_type type,
1914 int isl_basic_map_has_dim_id(
1915 __isl_keep isl_basic_map *bmap,
1916 enum isl_dim_type type, unsigned pos);
1917 __isl_give isl_map *isl_map_set_dim_id(
1918 __isl_take isl_map *map, enum isl_dim_type type,
1919 unsigned pos, __isl_take isl_id *id);
1920 int isl_map_has_dim_id(__isl_keep isl_map *map,
1921 enum isl_dim_type type, unsigned pos);
1922 __isl_give isl_id *isl_map_get_dim_id(
1923 __isl_keep isl_map *map, enum isl_dim_type type,
1925 __isl_give isl_id *isl_union_map_get_dim_id(
1926 __isl_keep isl_union_map *umap,
1927 enum isl_dim_type type, unsigned pos);
1929 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1930 enum isl_dim_type type, __isl_keep isl_id *id);
1931 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1932 enum isl_dim_type type, __isl_keep isl_id *id);
1933 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1934 enum isl_dim_type type, const char *name);
1935 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1936 enum isl_dim_type type, const char *name);
1938 const char *isl_constraint_get_dim_name(
1939 __isl_keep isl_constraint *constraint,
1940 enum isl_dim_type type, unsigned pos);
1941 const char *isl_basic_set_get_dim_name(
1942 __isl_keep isl_basic_set *bset,
1943 enum isl_dim_type type, unsigned pos);
1944 int isl_set_has_dim_name(__isl_keep isl_set *set,
1945 enum isl_dim_type type, unsigned pos);
1946 const char *isl_set_get_dim_name(
1947 __isl_keep isl_set *set,
1948 enum isl_dim_type type, unsigned pos);
1949 const char *isl_basic_map_get_dim_name(
1950 __isl_keep isl_basic_map *bmap,
1951 enum isl_dim_type type, unsigned pos);
1952 int isl_map_has_dim_name(__isl_keep isl_map *map,
1953 enum isl_dim_type type, unsigned pos);
1954 const char *isl_map_get_dim_name(
1955 __isl_keep isl_map *map,
1956 enum isl_dim_type type, unsigned pos);
1958 These functions are mostly useful to obtain the identifiers, positions
1959 or names of the parameters. Identifiers of individual dimensions are
1960 essentially only useful for printing. They are ignored by all other
1961 operations and may not be preserved across those operations.
1963 The user pointers on all parameters and tuples can be reset
1964 using the following functions.
1966 #include <isl/set.h>
1967 __isl_give isl_set *isl_set_reset_user(
1968 __isl_take isl_set *set);
1969 #include <isl/map.h>
1970 __isl_give isl_map *isl_map_reset_user(
1971 __isl_take isl_map *map);
1972 #include <isl/union_set.h>
1973 __isl_give isl_union_set *isl_union_set_reset_user(
1974 __isl_take isl_union_set *uset);
1975 #include <isl/union_map.h>
1976 __isl_give isl_union_map *isl_union_map_reset_user(
1977 __isl_take isl_union_map *umap);
1981 =head3 Unary Properties
1987 The following functions test whether the given set or relation
1988 contains any integer points. The ``plain'' variants do not perform
1989 any computations, but simply check if the given set or relation
1990 is already known to be empty.
1992 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1993 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1994 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1995 int isl_set_is_empty(__isl_keep isl_set *set);
1996 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1997 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1998 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1999 int isl_map_plain_is_empty(__isl_keep isl_map *map);
2000 int isl_map_is_empty(__isl_keep isl_map *map);
2001 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
2003 =item * Universality
2005 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
2006 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
2007 int isl_set_plain_is_universe(__isl_keep isl_set *set);
2009 =item * Single-valuedness
2011 int isl_basic_map_is_single_valued(
2012 __isl_keep isl_basic_map *bmap);
2013 int isl_map_plain_is_single_valued(
2014 __isl_keep isl_map *map);
2015 int isl_map_is_single_valued(__isl_keep isl_map *map);
2016 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
2020 int isl_map_plain_is_injective(__isl_keep isl_map *map);
2021 int isl_map_is_injective(__isl_keep isl_map *map);
2022 int isl_union_map_plain_is_injective(
2023 __isl_keep isl_union_map *umap);
2024 int isl_union_map_is_injective(
2025 __isl_keep isl_union_map *umap);
2029 int isl_map_is_bijective(__isl_keep isl_map *map);
2030 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
2034 __isl_give isl_val *
2035 isl_basic_map_plain_get_val_if_fixed(
2036 __isl_keep isl_basic_map *bmap,
2037 enum isl_dim_type type, unsigned pos);
2038 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
2039 __isl_keep isl_set *set,
2040 enum isl_dim_type type, unsigned pos);
2041 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
2042 __isl_keep isl_map *map,
2043 enum isl_dim_type type, unsigned pos);
2045 If the set or relation obviously lies on a hyperplane where the given dimension
2046 has a fixed value, then return that value.
2047 Otherwise return NaN.
2051 int isl_set_dim_residue_class_val(
2052 __isl_keep isl_set *set,
2053 int pos, __isl_give isl_val **modulo,
2054 __isl_give isl_val **residue);
2056 Check if the values of the given set dimension are equal to a fixed
2057 value modulo some integer value. If so, assign the modulo to C<*modulo>
2058 and the fixed value to C<*residue>. If the given dimension attains only
2059 a single value, then assign C<0> to C<*modulo> and the fixed value to
2061 If the dimension does not attain only a single value and if no modulo
2062 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
2066 To check whether a set is a parameter domain, use this function:
2068 int isl_set_is_params(__isl_keep isl_set *set);
2069 int isl_union_set_is_params(
2070 __isl_keep isl_union_set *uset);
2074 The following functions check whether the space of the given
2075 (basic) set or relation range is a wrapped relation.
2077 #include <isl/space.h>
2078 int isl_space_is_wrapping(
2079 __isl_keep isl_space *space);
2080 int isl_space_domain_is_wrapping(
2081 __isl_keep isl_space *space);
2082 int isl_space_range_is_wrapping(
2083 __isl_keep isl_space *space);
2085 #include <isl/set.h>
2086 int isl_basic_set_is_wrapping(
2087 __isl_keep isl_basic_set *bset);
2088 int isl_set_is_wrapping(__isl_keep isl_set *set);
2090 #include <isl/map.h>
2091 int isl_map_domain_is_wrapping(
2092 __isl_keep isl_map *map);
2093 int isl_map_range_is_wrapping(
2094 __isl_keep isl_map *map);
2096 The input to C<isl_space_is_wrapping> should
2097 be the space of a set, while that of
2098 C<isl_space_domain_is_wrapping> and
2099 C<isl_space_range_is_wrapping> should be the space of a relation.
2101 =item * Internal Product
2103 int isl_basic_map_can_zip(
2104 __isl_keep isl_basic_map *bmap);
2105 int isl_map_can_zip(__isl_keep isl_map *map);
2107 Check whether the product of domain and range of the given relation
2109 i.e., whether both domain and range are nested relations.
2113 int isl_basic_map_can_curry(
2114 __isl_keep isl_basic_map *bmap);
2115 int isl_map_can_curry(__isl_keep isl_map *map);
2117 Check whether the domain of the (basic) relation is a wrapped relation.
2119 int isl_basic_map_can_uncurry(
2120 __isl_keep isl_basic_map *bmap);
2121 int isl_map_can_uncurry(__isl_keep isl_map *map);
2123 Check whether the range of the (basic) relation is a wrapped relation.
2127 =head3 Binary Properties
2133 int isl_basic_set_plain_is_equal(
2134 __isl_keep isl_basic_set *bset1,
2135 __isl_keep isl_basic_set *bset2);
2136 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2137 __isl_keep isl_set *set2);
2138 int isl_set_is_equal(__isl_keep isl_set *set1,
2139 __isl_keep isl_set *set2);
2140 int isl_union_set_is_equal(
2141 __isl_keep isl_union_set *uset1,
2142 __isl_keep isl_union_set *uset2);
2143 int isl_basic_map_is_equal(
2144 __isl_keep isl_basic_map *bmap1,
2145 __isl_keep isl_basic_map *bmap2);
2146 int isl_map_is_equal(__isl_keep isl_map *map1,
2147 __isl_keep isl_map *map2);
2148 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2149 __isl_keep isl_map *map2);
2150 int isl_union_map_is_equal(
2151 __isl_keep isl_union_map *umap1,
2152 __isl_keep isl_union_map *umap2);
2154 =item * Disjointness
2156 int isl_basic_set_is_disjoint(
2157 __isl_keep isl_basic_set *bset1,
2158 __isl_keep isl_basic_set *bset2);
2159 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2160 __isl_keep isl_set *set2);
2161 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2162 __isl_keep isl_set *set2);
2163 int isl_basic_map_is_disjoint(
2164 __isl_keep isl_basic_map *bmap1,
2165 __isl_keep isl_basic_map *bmap2);
2166 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2167 __isl_keep isl_map *map2);
2171 int isl_basic_set_is_subset(
2172 __isl_keep isl_basic_set *bset1,
2173 __isl_keep isl_basic_set *bset2);
2174 int isl_set_is_subset(__isl_keep isl_set *set1,
2175 __isl_keep isl_set *set2);
2176 int isl_set_is_strict_subset(
2177 __isl_keep isl_set *set1,
2178 __isl_keep isl_set *set2);
2179 int isl_union_set_is_subset(
2180 __isl_keep isl_union_set *uset1,
2181 __isl_keep isl_union_set *uset2);
2182 int isl_union_set_is_strict_subset(
2183 __isl_keep isl_union_set *uset1,
2184 __isl_keep isl_union_set *uset2);
2185 int isl_basic_map_is_subset(
2186 __isl_keep isl_basic_map *bmap1,
2187 __isl_keep isl_basic_map *bmap2);
2188 int isl_basic_map_is_strict_subset(
2189 __isl_keep isl_basic_map *bmap1,
2190 __isl_keep isl_basic_map *bmap2);
2191 int isl_map_is_subset(
2192 __isl_keep isl_map *map1,
2193 __isl_keep isl_map *map2);
2194 int isl_map_is_strict_subset(
2195 __isl_keep isl_map *map1,
2196 __isl_keep isl_map *map2);
2197 int isl_union_map_is_subset(
2198 __isl_keep isl_union_map *umap1,
2199 __isl_keep isl_union_map *umap2);
2200 int isl_union_map_is_strict_subset(
2201 __isl_keep isl_union_map *umap1,
2202 __isl_keep isl_union_map *umap2);
2204 Check whether the first argument is a (strict) subset of the
2209 Every comparison function returns a negative value if the first
2210 argument is considered smaller than the second, a positive value
2211 if the first argument is considered greater and zero if the two
2212 constraints are considered the same by the comparison criterion.
2214 #include <isl/constraint.h>
2215 int isl_constraint_plain_cmp(
2216 __isl_keep isl_constraint *c1,
2217 __isl_keep isl_constraint *c2);
2219 This function is useful for sorting C<isl_constraint>s.
2220 The order depends on the internal representation of the inputs.
2221 The order is fixed over different calls to the function (assuming
2222 the internal representation of the inputs has not changed), but may
2223 change over different versions of C<isl>.
2225 #include <isl/constraint.h>
2226 int isl_constraint_cmp_last_non_zero(
2227 __isl_keep isl_constraint *c1,
2228 __isl_keep isl_constraint *c2);
2230 This function can be used to sort constraints that live in the same
2231 local space. Constraints that involve ``earlier'' dimensions or
2232 that have a smaller coefficient for the shared latest dimension
2233 are considered smaller than other constraints.
2234 This function only defines a B<partial> order.
2236 #include <isl/set.h>
2237 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2238 __isl_keep isl_set *set2);
2240 This function is useful for sorting C<isl_set>s.
2241 The order depends on the internal representation of the inputs.
2242 The order is fixed over different calls to the function (assuming
2243 the internal representation of the inputs has not changed), but may
2244 change over different versions of C<isl>.
2248 =head2 Unary Operations
2254 __isl_give isl_set *isl_set_complement(
2255 __isl_take isl_set *set);
2256 __isl_give isl_map *isl_map_complement(
2257 __isl_take isl_map *map);
2261 __isl_give isl_basic_map *isl_basic_map_reverse(
2262 __isl_take isl_basic_map *bmap);
2263 __isl_give isl_map *isl_map_reverse(
2264 __isl_take isl_map *map);
2265 __isl_give isl_union_map *isl_union_map_reverse(
2266 __isl_take isl_union_map *umap);
2270 #include <isl/local_space.h>
2271 __isl_give isl_local_space *isl_local_space_domain(
2272 __isl_take isl_local_space *ls);
2273 __isl_give isl_local_space *isl_local_space_range(
2274 __isl_take isl_local_space *ls);
2276 #include <isl/set.h>
2277 __isl_give isl_basic_set *isl_basic_set_project_out(
2278 __isl_take isl_basic_set *bset,
2279 enum isl_dim_type type, unsigned first, unsigned n);
2280 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2281 enum isl_dim_type type, unsigned first, unsigned n);
2282 __isl_give isl_basic_set *isl_basic_set_params(
2283 __isl_take isl_basic_set *bset);
2284 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2286 #include <isl/map.h>
2287 __isl_give isl_basic_map *isl_basic_map_project_out(
2288 __isl_take isl_basic_map *bmap,
2289 enum isl_dim_type type, unsigned first, unsigned n);
2290 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2291 enum isl_dim_type type, unsigned first, unsigned n);
2292 __isl_give isl_basic_set *isl_basic_map_domain(
2293 __isl_take isl_basic_map *bmap);
2294 __isl_give isl_basic_set *isl_basic_map_range(
2295 __isl_take isl_basic_map *bmap);
2296 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2297 __isl_give isl_set *isl_map_domain(
2298 __isl_take isl_map *bmap);
2299 __isl_give isl_set *isl_map_range(
2300 __isl_take isl_map *map);
2302 #include <isl/union_set.h>
2303 __isl_give isl_set *isl_union_set_params(
2304 __isl_take isl_union_set *uset);
2306 #include <isl/union_map.h>
2307 __isl_give isl_union_map *isl_union_map_project_out(
2308 __isl_take isl_union_map *umap,
2309 enum isl_dim_type type, unsigned first, unsigned n);
2310 __isl_give isl_set *isl_union_map_params(
2311 __isl_take isl_union_map *umap);
2312 __isl_give isl_union_set *isl_union_map_domain(
2313 __isl_take isl_union_map *umap);
2314 __isl_give isl_union_set *isl_union_map_range(
2315 __isl_take isl_union_map *umap);
2317 The function C<isl_union_map_project_out> can only project out
2320 #include <isl/map.h>
2321 __isl_give isl_basic_map *isl_basic_map_domain_map(
2322 __isl_take isl_basic_map *bmap);
2323 __isl_give isl_basic_map *isl_basic_map_range_map(
2324 __isl_take isl_basic_map *bmap);
2325 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2326 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2328 #include <isl/union_map.h>
2329 __isl_give isl_union_map *isl_union_map_domain_map(
2330 __isl_take isl_union_map *umap);
2331 __isl_give isl_union_map *isl_union_map_range_map(
2332 __isl_take isl_union_map *umap);
2334 The functions above construct a (basic, regular or union) relation
2335 that maps (a wrapped version of) the input relation to its domain or range.
2339 __isl_give isl_basic_set *isl_basic_set_eliminate(
2340 __isl_take isl_basic_set *bset,
2341 enum isl_dim_type type,
2342 unsigned first, unsigned n);
2343 __isl_give isl_set *isl_set_eliminate(
2344 __isl_take isl_set *set, enum isl_dim_type type,
2345 unsigned first, unsigned n);
2346 __isl_give isl_basic_map *isl_basic_map_eliminate(
2347 __isl_take isl_basic_map *bmap,
2348 enum isl_dim_type type,
2349 unsigned first, unsigned n);
2350 __isl_give isl_map *isl_map_eliminate(
2351 __isl_take isl_map *map, enum isl_dim_type type,
2352 unsigned first, unsigned n);
2354 Eliminate the coefficients for the given dimensions from the constraints,
2355 without removing the dimensions.
2357 =item * Constructing a relation from a set
2359 #include <isl/local_space.h>
2360 __isl_give isl_local_space *isl_local_space_from_domain(
2361 __isl_take isl_local_space *ls);
2363 #include <isl/map.h>
2364 __isl_give isl_map *isl_map_from_domain(
2365 __isl_take isl_set *set);
2366 __isl_give isl_map *isl_map_from_range(
2367 __isl_take isl_set *set);
2369 Create a relation with the given set as domain or range.
2370 The range or domain of the created relation is a zero-dimensional
2371 flat anonymous space.
2375 __isl_give isl_basic_set *isl_basic_set_fix_si(
2376 __isl_take isl_basic_set *bset,
2377 enum isl_dim_type type, unsigned pos, int value);
2378 __isl_give isl_basic_set *isl_basic_set_fix_val(
2379 __isl_take isl_basic_set *bset,
2380 enum isl_dim_type type, unsigned pos,
2381 __isl_take isl_val *v);
2382 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2383 enum isl_dim_type type, unsigned pos, int value);
2384 __isl_give isl_set *isl_set_fix_val(
2385 __isl_take isl_set *set,
2386 enum isl_dim_type type, unsigned pos,
2387 __isl_take isl_val *v);
2388 __isl_give isl_basic_map *isl_basic_map_fix_si(
2389 __isl_take isl_basic_map *bmap,
2390 enum isl_dim_type type, unsigned pos, int value);
2391 __isl_give isl_basic_map *isl_basic_map_fix_val(
2392 __isl_take isl_basic_map *bmap,
2393 enum isl_dim_type type, unsigned pos,
2394 __isl_take isl_val *v);
2395 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2396 enum isl_dim_type type, unsigned pos, int value);
2397 __isl_give isl_map *isl_map_fix_val(
2398 __isl_take isl_map *map,
2399 enum isl_dim_type type, unsigned pos,
2400 __isl_take isl_val *v);
2402 Intersect the set or relation with the hyperplane where the given
2403 dimension has the fixed given value.
2405 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2406 __isl_take isl_basic_map *bmap,
2407 enum isl_dim_type type, unsigned pos, int value);
2408 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2409 __isl_take isl_basic_map *bmap,
2410 enum isl_dim_type type, unsigned pos, int value);
2411 __isl_give isl_set *isl_set_lower_bound_si(
2412 __isl_take isl_set *set,
2413 enum isl_dim_type type, unsigned pos, int value);
2414 __isl_give isl_set *isl_set_lower_bound_val(
2415 __isl_take isl_set *set,
2416 enum isl_dim_type type, unsigned pos,
2417 __isl_take isl_val *value);
2418 __isl_give isl_map *isl_map_lower_bound_si(
2419 __isl_take isl_map *map,
2420 enum isl_dim_type type, unsigned pos, int value);
2421 __isl_give isl_set *isl_set_upper_bound_si(
2422 __isl_take isl_set *set,
2423 enum isl_dim_type type, unsigned pos, int value);
2424 __isl_give isl_set *isl_set_upper_bound_val(
2425 __isl_take isl_set *set,
2426 enum isl_dim_type type, unsigned pos,
2427 __isl_take isl_val *value);
2428 __isl_give isl_map *isl_map_upper_bound_si(
2429 __isl_take isl_map *map,
2430 enum isl_dim_type type, unsigned pos, int value);
2432 Intersect the set or relation with the half-space where the given
2433 dimension has a value bounded by the fixed given integer value.
2435 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2436 enum isl_dim_type type1, int pos1,
2437 enum isl_dim_type type2, int pos2);
2438 __isl_give isl_basic_map *isl_basic_map_equate(
2439 __isl_take isl_basic_map *bmap,
2440 enum isl_dim_type type1, int pos1,
2441 enum isl_dim_type type2, int pos2);
2442 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2443 enum isl_dim_type type1, int pos1,
2444 enum isl_dim_type type2, int pos2);
2446 Intersect the set or relation with the hyperplane where the given
2447 dimensions are equal to each other.
2449 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2450 enum isl_dim_type type1, int pos1,
2451 enum isl_dim_type type2, int pos2);
2453 Intersect the relation with the hyperplane where the given
2454 dimensions have opposite values.
2456 __isl_give isl_map *isl_map_order_le(
2457 __isl_take isl_map *map,
2458 enum isl_dim_type type1, int pos1,
2459 enum isl_dim_type type2, int pos2);
2460 __isl_give isl_basic_map *isl_basic_map_order_ge(
2461 __isl_take isl_basic_map *bmap,
2462 enum isl_dim_type type1, int pos1,
2463 enum isl_dim_type type2, int pos2);
2464 __isl_give isl_map *isl_map_order_ge(
2465 __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_map *isl_map_order_lt(__isl_take isl_map *map,
2469 enum isl_dim_type type1, int pos1,
2470 enum isl_dim_type type2, int pos2);
2471 __isl_give isl_basic_map *isl_basic_map_order_gt(
2472 __isl_take isl_basic_map *bmap,
2473 enum isl_dim_type type1, int pos1,
2474 enum isl_dim_type type2, int pos2);
2475 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2476 enum isl_dim_type type1, int pos1,
2477 enum isl_dim_type type2, int pos2);
2479 Intersect the relation with the half-space where the given
2480 dimensions satisfy the given ordering.
2484 __isl_give isl_map *isl_set_identity(
2485 __isl_take isl_set *set);
2486 __isl_give isl_union_map *isl_union_set_identity(
2487 __isl_take isl_union_set *uset);
2489 Construct an identity relation on the given (union) set.
2493 __isl_give isl_basic_set *isl_basic_map_deltas(
2494 __isl_take isl_basic_map *bmap);
2495 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2496 __isl_give isl_union_set *isl_union_map_deltas(
2497 __isl_take isl_union_map *umap);
2499 These functions return a (basic) set containing the differences
2500 between image elements and corresponding domain elements in the input.
2502 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2503 __isl_take isl_basic_map *bmap);
2504 __isl_give isl_map *isl_map_deltas_map(
2505 __isl_take isl_map *map);
2506 __isl_give isl_union_map *isl_union_map_deltas_map(
2507 __isl_take isl_union_map *umap);
2509 The functions above construct a (basic, regular or union) relation
2510 that maps (a wrapped version of) the input relation to its delta set.
2514 Simplify the representation of a set or relation by trying
2515 to combine pairs of basic sets or relations into a single
2516 basic set or relation.
2518 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2519 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2520 __isl_give isl_union_set *isl_union_set_coalesce(
2521 __isl_take isl_union_set *uset);
2522 __isl_give isl_union_map *isl_union_map_coalesce(
2523 __isl_take isl_union_map *umap);
2525 One of the methods for combining pairs of basic sets or relations
2526 can result in coefficients that are much larger than those that appear
2527 in the constraints of the input. By default, the coefficients are
2528 not allowed to grow larger, but this can be changed by unsetting
2529 the following option.
2531 int isl_options_set_coalesce_bounded_wrapping(
2532 isl_ctx *ctx, int val);
2533 int isl_options_get_coalesce_bounded_wrapping(
2536 =item * Detecting equalities
2538 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2539 __isl_take isl_basic_set *bset);
2540 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2541 __isl_take isl_basic_map *bmap);
2542 __isl_give isl_set *isl_set_detect_equalities(
2543 __isl_take isl_set *set);
2544 __isl_give isl_map *isl_map_detect_equalities(
2545 __isl_take isl_map *map);
2546 __isl_give isl_union_set *isl_union_set_detect_equalities(
2547 __isl_take isl_union_set *uset);
2548 __isl_give isl_union_map *isl_union_map_detect_equalities(
2549 __isl_take isl_union_map *umap);
2551 Simplify the representation of a set or relation by detecting implicit
2554 =item * Removing redundant constraints
2556 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2557 __isl_take isl_basic_set *bset);
2558 __isl_give isl_set *isl_set_remove_redundancies(
2559 __isl_take isl_set *set);
2560 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2561 __isl_take isl_basic_map *bmap);
2562 __isl_give isl_map *isl_map_remove_redundancies(
2563 __isl_take isl_map *map);
2567 __isl_give isl_basic_set *isl_set_convex_hull(
2568 __isl_take isl_set *set);
2569 __isl_give isl_basic_map *isl_map_convex_hull(
2570 __isl_take isl_map *map);
2572 If the input set or relation has any existentially quantified
2573 variables, then the result of these operations is currently undefined.
2577 #include <isl/set.h>
2578 __isl_give isl_basic_set *
2579 isl_set_unshifted_simple_hull(
2580 __isl_take isl_set *set);
2581 __isl_give isl_basic_set *isl_set_simple_hull(
2582 __isl_take isl_set *set);
2583 __isl_give isl_basic_set *
2584 isl_set_unshifted_simple_hull_from_set_list(
2585 __isl_take isl_set *set,
2586 __isl_take isl_set_list *list);
2588 #include <isl/map.h>
2589 __isl_give isl_basic_map *
2590 isl_map_unshifted_simple_hull(
2591 __isl_take isl_map *map);
2592 __isl_give isl_basic_map *isl_map_simple_hull(
2593 __isl_take isl_map *map);
2595 #include <isl/union_map.h>
2596 __isl_give isl_union_map *isl_union_map_simple_hull(
2597 __isl_take isl_union_map *umap);
2599 These functions compute a single basic set or relation
2600 that contains the whole input set or relation.
2601 In particular, the output is described by translates
2602 of the constraints describing the basic sets or relations in the input.
2603 In case of C<isl_set_unshifted_simple_hull>, only the original
2604 constraints are used, without any translation.
2605 In case of C<isl_set_unshifted_simple_hull_from_set_list>, the
2606 constraints are taken from the elements of the second argument.
2610 (See \autoref{s:simple hull}.)
2616 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2617 __isl_take isl_basic_set *bset);
2618 __isl_give isl_basic_set *isl_set_affine_hull(
2619 __isl_take isl_set *set);
2620 __isl_give isl_union_set *isl_union_set_affine_hull(
2621 __isl_take isl_union_set *uset);
2622 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2623 __isl_take isl_basic_map *bmap);
2624 __isl_give isl_basic_map *isl_map_affine_hull(
2625 __isl_take isl_map *map);
2626 __isl_give isl_union_map *isl_union_map_affine_hull(
2627 __isl_take isl_union_map *umap);
2629 In case of union sets and relations, the affine hull is computed
2632 =item * Polyhedral hull
2634 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2635 __isl_take isl_set *set);
2636 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2637 __isl_take isl_map *map);
2638 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2639 __isl_take isl_union_set *uset);
2640 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2641 __isl_take isl_union_map *umap);
2643 These functions compute a single basic set or relation
2644 not involving any existentially quantified variables
2645 that contains the whole input set or relation.
2646 In case of union sets and relations, the polyhedral hull is computed
2649 =item * Other approximations
2651 __isl_give isl_basic_set *
2652 isl_basic_set_drop_constraints_involving_dims(
2653 __isl_take isl_basic_set *bset,
2654 enum isl_dim_type type,
2655 unsigned first, unsigned n);
2656 __isl_give isl_basic_map *
2657 isl_basic_map_drop_constraints_involving_dims(
2658 __isl_take isl_basic_map *bmap,
2659 enum isl_dim_type type,
2660 unsigned first, unsigned n);
2661 __isl_give isl_basic_set *
2662 isl_basic_set_drop_constraints_not_involving_dims(
2663 __isl_take isl_basic_set *bset,
2664 enum isl_dim_type type,
2665 unsigned first, unsigned n);
2666 __isl_give isl_set *
2667 isl_set_drop_constraints_involving_dims(
2668 __isl_take isl_set *set,
2669 enum isl_dim_type type,
2670 unsigned first, unsigned n);
2671 __isl_give isl_map *
2672 isl_map_drop_constraints_involving_dims(
2673 __isl_take isl_map *map,
2674 enum isl_dim_type type,
2675 unsigned first, unsigned n);
2677 These functions drop any constraints (not) involving the specified dimensions.
2678 Note that the result depends on the representation of the input.
2682 __isl_give isl_basic_set *isl_basic_set_sample(
2683 __isl_take isl_basic_set *bset);
2684 __isl_give isl_basic_set *isl_set_sample(
2685 __isl_take isl_set *set);
2686 __isl_give isl_basic_map *isl_basic_map_sample(
2687 __isl_take isl_basic_map *bmap);
2688 __isl_give isl_basic_map *isl_map_sample(
2689 __isl_take isl_map *map);
2691 If the input (basic) set or relation is non-empty, then return
2692 a singleton subset of the input. Otherwise, return an empty set.
2694 =item * Optimization
2696 #include <isl/ilp.h>
2697 __isl_give isl_val *isl_basic_set_max_val(
2698 __isl_keep isl_basic_set *bset,
2699 __isl_keep isl_aff *obj);
2700 __isl_give isl_val *isl_set_min_val(
2701 __isl_keep isl_set *set,
2702 __isl_keep isl_aff *obj);
2703 __isl_give isl_val *isl_set_max_val(
2704 __isl_keep isl_set *set,
2705 __isl_keep isl_aff *obj);
2707 Compute the minimum or maximum of the integer affine expression C<obj>
2708 over the points in C<set>, returning the result in C<opt>.
2709 The result is C<NULL> in case of an error, the optimal value in case
2710 there is one, negative infinity or infinity if the problem is unbounded and
2711 NaN if the problem is empty.
2713 =item * Parametric optimization
2715 __isl_give isl_pw_aff *isl_set_dim_min(
2716 __isl_take isl_set *set, int pos);
2717 __isl_give isl_pw_aff *isl_set_dim_max(
2718 __isl_take isl_set *set, int pos);
2719 __isl_give isl_pw_aff *isl_map_dim_max(
2720 __isl_take isl_map *map, int pos);
2722 Compute the minimum or maximum of the given set or output dimension
2723 as a function of the parameters (and input dimensions), but independently
2724 of the other set or output dimensions.
2725 For lexicographic optimization, see L<"Lexicographic Optimization">.
2729 The following functions compute either the set of (rational) coefficient
2730 values of valid constraints for the given set or the set of (rational)
2731 values satisfying the constraints with coefficients from the given set.
2732 Internally, these two sets of functions perform essentially the
2733 same operations, except that the set of coefficients is assumed to
2734 be a cone, while the set of values may be any polyhedron.
2735 The current implementation is based on the Farkas lemma and
2736 Fourier-Motzkin elimination, but this may change or be made optional
2737 in future. In particular, future implementations may use different
2738 dualization algorithms or skip the elimination step.
2740 __isl_give isl_basic_set *isl_basic_set_coefficients(
2741 __isl_take isl_basic_set *bset);
2742 __isl_give isl_basic_set *isl_set_coefficients(
2743 __isl_take isl_set *set);
2744 __isl_give isl_union_set *isl_union_set_coefficients(
2745 __isl_take isl_union_set *bset);
2746 __isl_give isl_basic_set *isl_basic_set_solutions(
2747 __isl_take isl_basic_set *bset);
2748 __isl_give isl_basic_set *isl_set_solutions(
2749 __isl_take isl_set *set);
2750 __isl_give isl_union_set *isl_union_set_solutions(
2751 __isl_take isl_union_set *bset);
2755 __isl_give isl_map *isl_map_fixed_power_val(
2756 __isl_take isl_map *map,
2757 __isl_take isl_val *exp);
2758 __isl_give isl_union_map *
2759 isl_union_map_fixed_power_val(
2760 __isl_take isl_union_map *umap,
2761 __isl_take isl_val *exp);
2763 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2764 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2765 of C<map> is computed.
2767 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2769 __isl_give isl_union_map *isl_union_map_power(
2770 __isl_take isl_union_map *umap, int *exact);
2772 Compute a parametric representation for all positive powers I<k> of C<map>.
2773 The result maps I<k> to a nested relation corresponding to the
2774 I<k>th power of C<map>.
2775 The result may be an overapproximation. If the result is known to be exact,
2776 then C<*exact> is set to C<1>.
2778 =item * Transitive closure
2780 __isl_give isl_map *isl_map_transitive_closure(
2781 __isl_take isl_map *map, int *exact);
2782 __isl_give isl_union_map *isl_union_map_transitive_closure(
2783 __isl_take isl_union_map *umap, int *exact);
2785 Compute the transitive closure of C<map>.
2786 The result may be an overapproximation. If the result is known to be exact,
2787 then C<*exact> is set to C<1>.
2789 =item * Reaching path lengths
2791 __isl_give isl_map *isl_map_reaching_path_lengths(
2792 __isl_take isl_map *map, int *exact);
2794 Compute a relation that maps each element in the range of C<map>
2795 to the lengths of all paths composed of edges in C<map> that
2796 end up in the given element.
2797 The result may be an overapproximation. If the result is known to be exact,
2798 then C<*exact> is set to C<1>.
2799 To compute the I<maximal> path length, the resulting relation
2800 should be postprocessed by C<isl_map_lexmax>.
2801 In particular, if the input relation is a dependence relation
2802 (mapping sources to sinks), then the maximal path length corresponds
2803 to the free schedule.
2804 Note, however, that C<isl_map_lexmax> expects the maximum to be
2805 finite, so if the path lengths are unbounded (possibly due to
2806 the overapproximation), then you will get an error message.
2810 #include <isl/space.h>
2811 __isl_give isl_space *isl_space_wrap(
2812 __isl_take isl_space *space);
2813 __isl_give isl_space *isl_space_unwrap(
2814 __isl_take isl_space *space);
2816 #include <isl/set.h>
2817 __isl_give isl_basic_map *isl_basic_set_unwrap(
2818 __isl_take isl_basic_set *bset);
2819 __isl_give isl_map *isl_set_unwrap(
2820 __isl_take isl_set *set);
2822 #include <isl/map.h>
2823 __isl_give isl_basic_set *isl_basic_map_wrap(
2824 __isl_take isl_basic_map *bmap);
2825 __isl_give isl_set *isl_map_wrap(
2826 __isl_take isl_map *map);
2828 #include <isl/union_set.h>
2829 __isl_give isl_union_map *isl_union_set_unwrap(
2830 __isl_take isl_union_set *uset);
2832 #include <isl/union_map.h>
2833 __isl_give isl_union_set *isl_union_map_wrap(
2834 __isl_take isl_union_map *umap);
2836 The input to C<isl_space_unwrap> should
2837 be the space of a set, while that of
2838 C<isl_space_wrap> should be the space of a relation.
2839 Conversely, the output of C<isl_space_unwrap> is the space
2840 of a relation, while that of C<isl_space_wrap> is the space of a set.
2844 Remove any internal structure of domain (and range) of the given
2845 set or relation. If there is any such internal structure in the input,
2846 then the name of the space is also removed.
2848 #include <isl/local_space.h>
2849 __isl_give isl_local_space *
2850 isl_local_space_flatten_domain(
2851 __isl_take isl_local_space *ls);
2852 __isl_give isl_local_space *
2853 isl_local_space_flatten_range(
2854 __isl_take isl_local_space *ls);
2856 #include <isl/set.h>
2857 __isl_give isl_basic_set *isl_basic_set_flatten(
2858 __isl_take isl_basic_set *bset);
2859 __isl_give isl_set *isl_set_flatten(
2860 __isl_take isl_set *set);
2862 #include <isl/map.h>
2863 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2864 __isl_take isl_basic_map *bmap);
2865 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2866 __isl_take isl_basic_map *bmap);
2867 __isl_give isl_map *isl_map_flatten_range(
2868 __isl_take isl_map *map);
2869 __isl_give isl_map *isl_map_flatten_domain(
2870 __isl_take isl_map *map);
2871 __isl_give isl_basic_map *isl_basic_map_flatten(
2872 __isl_take isl_basic_map *bmap);
2873 __isl_give isl_map *isl_map_flatten(
2874 __isl_take isl_map *map);
2876 #include <isl/map.h>
2877 __isl_give isl_map *isl_set_flatten_map(
2878 __isl_take isl_set *set);
2880 The function above constructs a relation
2881 that maps the input set to a flattened version of the set.
2885 Lift the input set to a space with extra dimensions corresponding
2886 to the existentially quantified variables in the input.
2887 In particular, the result lives in a wrapped map where the domain
2888 is the original space and the range corresponds to the original
2889 existentially quantified variables.
2891 __isl_give isl_basic_set *isl_basic_set_lift(
2892 __isl_take isl_basic_set *bset);
2893 __isl_give isl_set *isl_set_lift(
2894 __isl_take isl_set *set);
2895 __isl_give isl_union_set *isl_union_set_lift(
2896 __isl_take isl_union_set *uset);
2898 Given a local space that contains the existentially quantified
2899 variables of a set, a basic relation that, when applied to
2900 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2901 can be constructed using the following function.
2903 #include <isl/local_space.h>
2904 __isl_give isl_basic_map *isl_local_space_lifting(
2905 __isl_take isl_local_space *ls);
2907 =item * Internal Product
2909 __isl_give isl_basic_map *isl_basic_map_zip(
2910 __isl_take isl_basic_map *bmap);
2911 __isl_give isl_map *isl_map_zip(
2912 __isl_take isl_map *map);
2913 __isl_give isl_union_map *isl_union_map_zip(
2914 __isl_take isl_union_map *umap);
2916 Given a relation with nested relations for domain and range,
2917 interchange the range of the domain with the domain of the range.
2921 __isl_give isl_basic_map *isl_basic_map_curry(
2922 __isl_take isl_basic_map *bmap);
2923 __isl_give isl_basic_map *isl_basic_map_uncurry(
2924 __isl_take isl_basic_map *bmap);
2925 __isl_give isl_map *isl_map_curry(
2926 __isl_take isl_map *map);
2927 __isl_give isl_map *isl_map_uncurry(
2928 __isl_take isl_map *map);
2929 __isl_give isl_union_map *isl_union_map_curry(
2930 __isl_take isl_union_map *umap);
2931 __isl_give isl_union_map *isl_union_map_uncurry(
2932 __isl_take isl_union_map *umap);
2934 Given a relation with a nested relation for domain,
2935 the C<curry> functions
2936 move the range of the nested relation out of the domain
2937 and use it as the domain of a nested relation in the range,
2938 with the original range as range of this nested relation.
2939 The C<uncurry> functions perform the inverse operation.
2941 =item * Aligning parameters
2943 __isl_give isl_basic_set *isl_basic_set_align_params(
2944 __isl_take isl_basic_set *bset,
2945 __isl_take isl_space *model);
2946 __isl_give isl_set *isl_set_align_params(
2947 __isl_take isl_set *set,
2948 __isl_take isl_space *model);
2949 __isl_give isl_basic_map *isl_basic_map_align_params(
2950 __isl_take isl_basic_map *bmap,
2951 __isl_take isl_space *model);
2952 __isl_give isl_map *isl_map_align_params(
2953 __isl_take isl_map *map,
2954 __isl_take isl_space *model);
2956 Change the order of the parameters of the given set or relation
2957 such that the first parameters match those of C<model>.
2958 This may involve the introduction of extra parameters.
2959 All parameters need to be named.
2961 =item * Dimension manipulation
2963 #include <isl/local_space.h>
2964 __isl_give isl_local_space *isl_local_space_add_dims(
2965 __isl_take isl_local_space *ls,
2966 enum isl_dim_type type, unsigned n);
2967 __isl_give isl_local_space *isl_local_space_insert_dims(
2968 __isl_take isl_local_space *ls,
2969 enum isl_dim_type type, unsigned first, unsigned n);
2970 __isl_give isl_local_space *isl_local_space_drop_dims(
2971 __isl_take isl_local_space *ls,
2972 enum isl_dim_type type, unsigned first, unsigned n);
2974 #include <isl/set.h>
2975 __isl_give isl_basic_set *isl_basic_set_add_dims(
2976 __isl_take isl_basic_set *bset,
2977 enum isl_dim_type type, unsigned n);
2978 __isl_give isl_set *isl_set_add_dims(
2979 __isl_take isl_set *set,
2980 enum isl_dim_type type, unsigned n);
2981 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2982 __isl_take isl_basic_set *bset,
2983 enum isl_dim_type type, unsigned pos,
2985 __isl_give isl_set *isl_set_insert_dims(
2986 __isl_take isl_set *set,
2987 enum isl_dim_type type, unsigned pos, unsigned n);
2988 __isl_give isl_basic_set *isl_basic_set_move_dims(
2989 __isl_take isl_basic_set *bset,
2990 enum isl_dim_type dst_type, unsigned dst_pos,
2991 enum isl_dim_type src_type, unsigned src_pos,
2993 __isl_give isl_set *isl_set_move_dims(
2994 __isl_take isl_set *set,
2995 enum isl_dim_type dst_type, unsigned dst_pos,
2996 enum isl_dim_type src_type, unsigned src_pos,
2999 #include <isl/map.h>
3000 __isl_give isl_map *isl_map_add_dims(
3001 __isl_take isl_map *map,
3002 enum isl_dim_type type, unsigned n);
3003 __isl_give isl_basic_map *isl_basic_map_insert_dims(
3004 __isl_take isl_basic_map *bmap,
3005 enum isl_dim_type type, unsigned pos,
3007 __isl_give isl_map *isl_map_insert_dims(
3008 __isl_take isl_map *map,
3009 enum isl_dim_type type, unsigned pos, unsigned n);
3010 __isl_give isl_basic_map *isl_basic_map_move_dims(
3011 __isl_take isl_basic_map *bmap,
3012 enum isl_dim_type dst_type, unsigned dst_pos,
3013 enum isl_dim_type src_type, unsigned src_pos,
3015 __isl_give isl_map *isl_map_move_dims(
3016 __isl_take isl_map *map,
3017 enum isl_dim_type dst_type, unsigned dst_pos,
3018 enum isl_dim_type src_type, unsigned src_pos,
3021 It is usually not advisable to directly change the (input or output)
3022 space of a set or a relation as this removes the name and the internal
3023 structure of the space. However, the above functions can be useful
3024 to add new parameters, assuming
3025 C<isl_set_align_params> and C<isl_map_align_params>
3030 =head2 Binary Operations
3032 The two arguments of a binary operation not only need to live
3033 in the same C<isl_ctx>, they currently also need to have
3034 the same (number of) parameters.
3036 =head3 Basic Operations
3040 =item * Intersection
3042 #include <isl/local_space.h>
3043 __isl_give isl_local_space *isl_local_space_intersect(
3044 __isl_take isl_local_space *ls1,
3045 __isl_take isl_local_space *ls2);
3047 #include <isl/set.h>
3048 __isl_give isl_basic_set *isl_basic_set_intersect_params(
3049 __isl_take isl_basic_set *bset1,
3050 __isl_take isl_basic_set *bset2);
3051 __isl_give isl_basic_set *isl_basic_set_intersect(
3052 __isl_take isl_basic_set *bset1,
3053 __isl_take isl_basic_set *bset2);
3054 __isl_give isl_basic_set *isl_basic_set_list_intersect(
3055 __isl_take struct isl_basic_set_list *list);
3056 __isl_give isl_set *isl_set_intersect_params(
3057 __isl_take isl_set *set,
3058 __isl_take isl_set *params);
3059 __isl_give isl_set *isl_set_intersect(
3060 __isl_take isl_set *set1,
3061 __isl_take isl_set *set2);
3063 #include <isl/map.h>
3064 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
3065 __isl_take isl_basic_map *bmap,
3066 __isl_take isl_basic_set *bset);
3067 __isl_give isl_basic_map *isl_basic_map_intersect_range(
3068 __isl_take isl_basic_map *bmap,
3069 __isl_take isl_basic_set *bset);
3070 __isl_give isl_basic_map *isl_basic_map_intersect(
3071 __isl_take isl_basic_map *bmap1,
3072 __isl_take isl_basic_map *bmap2);
3073 __isl_give isl_map *isl_map_intersect_params(
3074 __isl_take isl_map *map,
3075 __isl_take isl_set *params);
3076 __isl_give isl_map *isl_map_intersect_domain(
3077 __isl_take isl_map *map,
3078 __isl_take isl_set *set);
3079 __isl_give isl_map *isl_map_intersect_range(
3080 __isl_take isl_map *map,
3081 __isl_take isl_set *set);
3082 __isl_give isl_map *isl_map_intersect(
3083 __isl_take isl_map *map1,
3084 __isl_take isl_map *map2);
3086 #include <isl/union_set.h>
3087 __isl_give isl_union_set *isl_union_set_intersect_params(
3088 __isl_take isl_union_set *uset,
3089 __isl_take isl_set *set);
3090 __isl_give isl_union_set *isl_union_set_intersect(
3091 __isl_take isl_union_set *uset1,
3092 __isl_take isl_union_set *uset2);
3094 #include <isl/union_map.h>
3095 __isl_give isl_union_map *isl_union_map_intersect_params(
3096 __isl_take isl_union_map *umap,
3097 __isl_take isl_set *set);
3098 __isl_give isl_union_map *isl_union_map_intersect_domain(
3099 __isl_take isl_union_map *umap,
3100 __isl_take isl_union_set *uset);
3101 __isl_give isl_union_map *isl_union_map_intersect_range(
3102 __isl_take isl_union_map *umap,
3103 __isl_take isl_union_set *uset);
3104 __isl_give isl_union_map *isl_union_map_intersect(
3105 __isl_take isl_union_map *umap1,
3106 __isl_take isl_union_map *umap2);
3108 The second argument to the C<_params> functions needs to be
3109 a parametric (basic) set. For the other functions, a parametric set
3110 for either argument is only allowed if the other argument is
3111 a parametric set as well.
3112 The list passed to C<isl_basic_set_list_intersect> needs to have
3113 at least one element and all elements need to live in the same space.
3117 __isl_give isl_set *isl_basic_set_union(
3118 __isl_take isl_basic_set *bset1,
3119 __isl_take isl_basic_set *bset2);
3120 __isl_give isl_map *isl_basic_map_union(
3121 __isl_take isl_basic_map *bmap1,
3122 __isl_take isl_basic_map *bmap2);
3123 __isl_give isl_set *isl_set_union(
3124 __isl_take isl_set *set1,
3125 __isl_take isl_set *set2);
3126 __isl_give isl_map *isl_map_union(
3127 __isl_take isl_map *map1,
3128 __isl_take isl_map *map2);
3129 __isl_give isl_union_set *isl_union_set_union(
3130 __isl_take isl_union_set *uset1,
3131 __isl_take isl_union_set *uset2);
3132 __isl_give isl_union_map *isl_union_map_union(
3133 __isl_take isl_union_map *umap1,
3134 __isl_take isl_union_map *umap2);
3136 =item * Set difference
3138 __isl_give isl_set *isl_set_subtract(
3139 __isl_take isl_set *set1,
3140 __isl_take isl_set *set2);
3141 __isl_give isl_map *isl_map_subtract(
3142 __isl_take isl_map *map1,
3143 __isl_take isl_map *map2);
3144 __isl_give isl_map *isl_map_subtract_domain(
3145 __isl_take isl_map *map,
3146 __isl_take isl_set *dom);
3147 __isl_give isl_map *isl_map_subtract_range(
3148 __isl_take isl_map *map,
3149 __isl_take isl_set *dom);
3150 __isl_give isl_union_set *isl_union_set_subtract(
3151 __isl_take isl_union_set *uset1,
3152 __isl_take isl_union_set *uset2);
3153 __isl_give isl_union_map *isl_union_map_subtract(
3154 __isl_take isl_union_map *umap1,
3155 __isl_take isl_union_map *umap2);
3156 __isl_give isl_union_map *isl_union_map_subtract_domain(
3157 __isl_take isl_union_map *umap,
3158 __isl_take isl_union_set *dom);
3159 __isl_give isl_union_map *isl_union_map_subtract_range(
3160 __isl_take isl_union_map *umap,
3161 __isl_take isl_union_set *dom);
3165 __isl_give isl_basic_set *isl_basic_set_apply(
3166 __isl_take isl_basic_set *bset,
3167 __isl_take isl_basic_map *bmap);
3168 __isl_give isl_set *isl_set_apply(
3169 __isl_take isl_set *set,
3170 __isl_take isl_map *map);
3171 __isl_give isl_union_set *isl_union_set_apply(
3172 __isl_take isl_union_set *uset,
3173 __isl_take isl_union_map *umap);
3174 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3175 __isl_take isl_basic_map *bmap1,
3176 __isl_take isl_basic_map *bmap2);
3177 __isl_give isl_basic_map *isl_basic_map_apply_range(
3178 __isl_take isl_basic_map *bmap1,
3179 __isl_take isl_basic_map *bmap2);
3180 __isl_give isl_map *isl_map_apply_domain(
3181 __isl_take isl_map *map1,
3182 __isl_take isl_map *map2);
3183 __isl_give isl_union_map *isl_union_map_apply_domain(
3184 __isl_take isl_union_map *umap1,
3185 __isl_take isl_union_map *umap2);
3186 __isl_give isl_map *isl_map_apply_range(
3187 __isl_take isl_map *map1,
3188 __isl_take isl_map *map2);
3189 __isl_give isl_union_map *isl_union_map_apply_range(
3190 __isl_take isl_union_map *umap1,
3191 __isl_take isl_union_map *umap2);
3195 #include <isl/set.h>
3196 __isl_give isl_basic_set *
3197 isl_basic_set_preimage_multi_aff(
3198 __isl_take isl_basic_set *bset,
3199 __isl_take isl_multi_aff *ma);
3200 __isl_give isl_set *isl_set_preimage_multi_aff(
3201 __isl_take isl_set *set,
3202 __isl_take isl_multi_aff *ma);
3203 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3204 __isl_take isl_set *set,
3205 __isl_take isl_pw_multi_aff *pma);
3206 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
3207 __isl_take isl_set *set,
3208 __isl_take isl_multi_pw_aff *mpa);
3210 #include <isl/union_set.h>
3211 __isl_give isl_union_set *
3212 isl_union_set_preimage_multi_aff(
3213 __isl_take isl_union_set *uset,
3214 __isl_take isl_multi_aff *ma);
3215 __isl_give isl_union_set *
3216 isl_union_set_preimage_pw_multi_aff(
3217 __isl_take isl_union_set *uset,
3218 __isl_take isl_pw_multi_aff *pma);
3219 __isl_give isl_union_set *
3220 isl_union_set_preimage_union_pw_multi_aff(
3221 __isl_take isl_union_set *uset,
3222 __isl_take isl_union_pw_multi_aff *upma);
3224 #include <isl/map.h>
3225 __isl_give isl_basic_map *
3226 isl_basic_map_preimage_domain_multi_aff(
3227 __isl_take isl_basic_map *bmap,
3228 __isl_take isl_multi_aff *ma);
3229 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3230 __isl_take isl_map *map,
3231 __isl_take isl_multi_aff *ma);
3232 __isl_give isl_map *isl_map_preimage_range_multi_aff(
3233 __isl_take isl_map *map,
3234 __isl_take isl_multi_aff *ma);
3235 __isl_give isl_map *
3236 isl_map_preimage_domain_pw_multi_aff(
3237 __isl_take isl_map *map,
3238 __isl_take isl_pw_multi_aff *pma);
3239 __isl_give isl_map *
3240 isl_map_preimage_range_pw_multi_aff(
3241 __isl_take isl_map *map,
3242 __isl_take isl_pw_multi_aff *pma);
3243 __isl_give isl_map *
3244 isl_map_preimage_domain_multi_pw_aff(
3245 __isl_take isl_map *map,
3246 __isl_take isl_multi_pw_aff *mpa);
3247 __isl_give isl_basic_map *
3248 isl_basic_map_preimage_range_multi_aff(
3249 __isl_take isl_basic_map *bmap,
3250 __isl_take isl_multi_aff *ma);
3252 #include <isl/union_map.h>
3253 __isl_give isl_union_map *
3254 isl_union_map_preimage_domain_multi_aff(
3255 __isl_take isl_union_map *umap,
3256 __isl_take isl_multi_aff *ma);
3257 __isl_give isl_union_map *
3258 isl_union_map_preimage_range_multi_aff(
3259 __isl_take isl_union_map *umap,
3260 __isl_take isl_multi_aff *ma);
3261 __isl_give isl_union_map *
3262 isl_union_map_preimage_domain_pw_multi_aff(
3263 __isl_take isl_union_map *umap,
3264 __isl_take isl_pw_multi_aff *pma);
3265 __isl_give isl_union_map *
3266 isl_union_map_preimage_range_pw_multi_aff(
3267 __isl_take isl_union_map *umap,
3268 __isl_take isl_pw_multi_aff *pma);
3269 __isl_give isl_union_map *
3270 isl_union_map_preimage_domain_union_pw_multi_aff(
3271 __isl_take isl_union_map *umap,
3272 __isl_take isl_union_pw_multi_aff *upma);
3273 __isl_give isl_union_map *
3274 isl_union_map_preimage_range_union_pw_multi_aff(
3275 __isl_take isl_union_map *umap,
3276 __isl_take isl_union_pw_multi_aff *upma);
3278 These functions compute the preimage of the given set or map domain/range under
3279 the given function. In other words, the expression is plugged
3280 into the set description or into the domain/range of the map.
3281 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3282 L</"Piecewise Multiple Quasi Affine Expressions">.
3284 =item * Cartesian Product
3286 #include <isl/space.h>
3287 __isl_give isl_space *isl_space_product(
3288 __isl_take isl_space *space1,
3289 __isl_take isl_space *space2);
3290 __isl_give isl_space *isl_space_domain_product(
3291 __isl_take isl_space *space1,
3292 __isl_take isl_space *space2);
3293 __isl_give isl_space *isl_space_range_product(
3294 __isl_take isl_space *space1,
3295 __isl_take isl_space *space2);
3298 C<isl_space_product>, C<isl_space_domain_product>
3299 and C<isl_space_range_product> take pairs or relation spaces and
3300 produce a single relations space, where either the domain, the range
3301 or both domain and range are wrapped spaces of relations between
3302 the domains and/or ranges of the input spaces.
3303 If the product is only constructed over the domain or the range
3304 then the ranges or the domains of the inputs should be the same.
3305 The function C<isl_space_product> also accepts a pair of set spaces,
3306 in which case it returns a wrapped space of a relation between the
3309 #include <isl/set.h>
3310 __isl_give isl_set *isl_set_product(
3311 __isl_take isl_set *set1,
3312 __isl_take isl_set *set2);
3314 #include <isl/map.h>
3315 __isl_give isl_basic_map *isl_basic_map_domain_product(
3316 __isl_take isl_basic_map *bmap1,
3317 __isl_take isl_basic_map *bmap2);
3318 __isl_give isl_basic_map *isl_basic_map_range_product(
3319 __isl_take isl_basic_map *bmap1,
3320 __isl_take isl_basic_map *bmap2);
3321 __isl_give isl_basic_map *isl_basic_map_product(
3322 __isl_take isl_basic_map *bmap1,
3323 __isl_take isl_basic_map *bmap2);
3324 __isl_give isl_map *isl_map_domain_product(
3325 __isl_take isl_map *map1,
3326 __isl_take isl_map *map2);
3327 __isl_give isl_map *isl_map_range_product(
3328 __isl_take isl_map *map1,
3329 __isl_take isl_map *map2);
3330 __isl_give isl_map *isl_map_product(
3331 __isl_take isl_map *map1,
3332 __isl_take isl_map *map2);
3334 #include <isl/union_set.h>
3335 __isl_give isl_union_set *isl_union_set_product(
3336 __isl_take isl_union_set *uset1,
3337 __isl_take isl_union_set *uset2);
3339 #include <isl/union_map.h>
3340 __isl_give isl_union_map *isl_union_map_domain_product(
3341 __isl_take isl_union_map *umap1,
3342 __isl_take isl_union_map *umap2);
3343 __isl_give isl_union_map *isl_union_map_range_product(
3344 __isl_take isl_union_map *umap1,
3345 __isl_take isl_union_map *umap2);
3346 __isl_give isl_union_map *isl_union_map_product(
3347 __isl_take isl_union_map *umap1,
3348 __isl_take isl_union_map *umap2);
3350 The above functions compute the cross product of the given
3351 sets or relations. The domains and ranges of the results
3352 are wrapped maps between domains and ranges of the inputs.
3353 To obtain a ``flat'' product, use the following functions
3356 __isl_give isl_basic_set *isl_basic_set_flat_product(
3357 __isl_take isl_basic_set *bset1,
3358 __isl_take isl_basic_set *bset2);
3359 __isl_give isl_set *isl_set_flat_product(
3360 __isl_take isl_set *set1,
3361 __isl_take isl_set *set2);
3362 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3363 __isl_take isl_basic_map *bmap1,
3364 __isl_take isl_basic_map *bmap2);
3365 __isl_give isl_map *isl_map_flat_domain_product(
3366 __isl_take isl_map *map1,
3367 __isl_take isl_map *map2);
3368 __isl_give isl_map *isl_map_flat_range_product(
3369 __isl_take isl_map *map1,
3370 __isl_take isl_map *map2);
3371 __isl_give isl_union_map *isl_union_map_flat_range_product(
3372 __isl_take isl_union_map *umap1,
3373 __isl_take isl_union_map *umap2);
3374 __isl_give isl_basic_map *isl_basic_map_flat_product(
3375 __isl_take isl_basic_map *bmap1,
3376 __isl_take isl_basic_map *bmap2);
3377 __isl_give isl_map *isl_map_flat_product(
3378 __isl_take isl_map *map1,
3379 __isl_take isl_map *map2);
3381 #include <isl/space.h>
3382 __isl_give isl_space *isl_space_domain_factor_domain(
3383 __isl_take isl_space *space);
3384 __isl_give isl_space *isl_space_range_factor_domain(
3385 __isl_take isl_space *space);
3386 __isl_give isl_space *isl_space_range_factor_range(
3387 __isl_take isl_space *space);
3389 The functions C<isl_space_range_factor_domain> and
3390 C<isl_space_range_factor_range> extract the two arguments from
3391 the result of a call to C<isl_space_range_product>.
3393 The arguments of a call to C<isl_map_range_product> can be extracted
3394 from the result using the following two functions.
3396 #include <isl/map.h>
3397 __isl_give isl_map *isl_map_range_factor_domain(
3398 __isl_take isl_map *map);
3399 __isl_give isl_map *isl_map_range_factor_range(
3400 __isl_take isl_map *map);
3402 =item * Simplification
3404 __isl_give isl_basic_set *isl_basic_set_gist(
3405 __isl_take isl_basic_set *bset,
3406 __isl_take isl_basic_set *context);
3407 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3408 __isl_take isl_set *context);
3409 __isl_give isl_set *isl_set_gist_params(
3410 __isl_take isl_set *set,
3411 __isl_take isl_set *context);
3412 __isl_give isl_union_set *isl_union_set_gist(
3413 __isl_take isl_union_set *uset,
3414 __isl_take isl_union_set *context);
3415 __isl_give isl_union_set *isl_union_set_gist_params(
3416 __isl_take isl_union_set *uset,
3417 __isl_take isl_set *set);
3418 __isl_give isl_basic_map *isl_basic_map_gist(
3419 __isl_take isl_basic_map *bmap,
3420 __isl_take isl_basic_map *context);
3421 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3422 __isl_take isl_map *context);
3423 __isl_give isl_map *isl_map_gist_params(
3424 __isl_take isl_map *map,
3425 __isl_take isl_set *context);
3426 __isl_give isl_map *isl_map_gist_domain(
3427 __isl_take isl_map *map,
3428 __isl_take isl_set *context);
3429 __isl_give isl_map *isl_map_gist_range(
3430 __isl_take isl_map *map,
3431 __isl_take isl_set *context);
3432 __isl_give isl_union_map *isl_union_map_gist(
3433 __isl_take isl_union_map *umap,
3434 __isl_take isl_union_map *context);
3435 __isl_give isl_union_map *isl_union_map_gist_params(
3436 __isl_take isl_union_map *umap,
3437 __isl_take isl_set *set);
3438 __isl_give isl_union_map *isl_union_map_gist_domain(
3439 __isl_take isl_union_map *umap,
3440 __isl_take isl_union_set *uset);
3441 __isl_give isl_union_map *isl_union_map_gist_range(
3442 __isl_take isl_union_map *umap,
3443 __isl_take isl_union_set *uset);
3445 The gist operation returns a set or relation that has the
3446 same intersection with the context as the input set or relation.
3447 Any implicit equality in the intersection is made explicit in the result,
3448 while all inequalities that are redundant with respect to the intersection
3450 In case of union sets and relations, the gist operation is performed
3455 =head3 Lexicographic Optimization
3457 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3458 the following functions
3459 compute a set that contains the lexicographic minimum or maximum
3460 of the elements in C<set> (or C<bset>) for those values of the parameters
3461 that satisfy C<dom>.
3462 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3463 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3465 In other words, the union of the parameter values
3466 for which the result is non-empty and of C<*empty>
3469 __isl_give isl_set *isl_basic_set_partial_lexmin(
3470 __isl_take isl_basic_set *bset,
3471 __isl_take isl_basic_set *dom,
3472 __isl_give isl_set **empty);
3473 __isl_give isl_set *isl_basic_set_partial_lexmax(
3474 __isl_take isl_basic_set *bset,
3475 __isl_take isl_basic_set *dom,
3476 __isl_give isl_set **empty);
3477 __isl_give isl_set *isl_set_partial_lexmin(
3478 __isl_take isl_set *set, __isl_take isl_set *dom,
3479 __isl_give isl_set **empty);
3480 __isl_give isl_set *isl_set_partial_lexmax(
3481 __isl_take isl_set *set, __isl_take isl_set *dom,
3482 __isl_give isl_set **empty);
3484 Given a (basic) set C<set> (or C<bset>), the following functions simply
3485 return a set containing the lexicographic minimum or maximum
3486 of the elements in C<set> (or C<bset>).
3487 In case of union sets, the optimum is computed per space.
3489 __isl_give isl_set *isl_basic_set_lexmin(
3490 __isl_take isl_basic_set *bset);
3491 __isl_give isl_set *isl_basic_set_lexmax(
3492 __isl_take isl_basic_set *bset);
3493 __isl_give isl_set *isl_set_lexmin(
3494 __isl_take isl_set *set);
3495 __isl_give isl_set *isl_set_lexmax(
3496 __isl_take isl_set *set);
3497 __isl_give isl_union_set *isl_union_set_lexmin(
3498 __isl_take isl_union_set *uset);
3499 __isl_give isl_union_set *isl_union_set_lexmax(
3500 __isl_take isl_union_set *uset);
3502 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3503 the following functions
3504 compute a relation that maps each element of C<dom>
3505 to the single lexicographic minimum or maximum
3506 of the elements that are associated to that same
3507 element in C<map> (or C<bmap>).
3508 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3509 that contains the elements in C<dom> that do not map
3510 to any elements in C<map> (or C<bmap>).
3511 In other words, the union of the domain of the result and of C<*empty>
3514 __isl_give isl_map *isl_basic_map_partial_lexmax(
3515 __isl_take isl_basic_map *bmap,
3516 __isl_take isl_basic_set *dom,
3517 __isl_give isl_set **empty);
3518 __isl_give isl_map *isl_basic_map_partial_lexmin(
3519 __isl_take isl_basic_map *bmap,
3520 __isl_take isl_basic_set *dom,
3521 __isl_give isl_set **empty);
3522 __isl_give isl_map *isl_map_partial_lexmax(
3523 __isl_take isl_map *map, __isl_take isl_set *dom,
3524 __isl_give isl_set **empty);
3525 __isl_give isl_map *isl_map_partial_lexmin(
3526 __isl_take isl_map *map, __isl_take isl_set *dom,
3527 __isl_give isl_set **empty);
3529 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3530 return a map mapping each element in the domain of
3531 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3532 of all elements associated to that element.
3533 In case of union relations, the optimum is computed per space.
3535 __isl_give isl_map *isl_basic_map_lexmin(
3536 __isl_take isl_basic_map *bmap);
3537 __isl_give isl_map *isl_basic_map_lexmax(
3538 __isl_take isl_basic_map *bmap);
3539 __isl_give isl_map *isl_map_lexmin(
3540 __isl_take isl_map *map);
3541 __isl_give isl_map *isl_map_lexmax(
3542 __isl_take isl_map *map);
3543 __isl_give isl_union_map *isl_union_map_lexmin(
3544 __isl_take isl_union_map *umap);
3545 __isl_give isl_union_map *isl_union_map_lexmax(
3546 __isl_take isl_union_map *umap);
3548 The following functions return their result in the form of
3549 a piecewise multi-affine expression
3550 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3551 but are otherwise equivalent to the corresponding functions
3552 returning a basic set or relation.
3554 __isl_give isl_pw_multi_aff *
3555 isl_basic_map_lexmin_pw_multi_aff(
3556 __isl_take isl_basic_map *bmap);
3557 __isl_give isl_pw_multi_aff *
3558 isl_basic_set_partial_lexmin_pw_multi_aff(
3559 __isl_take isl_basic_set *bset,
3560 __isl_take isl_basic_set *dom,
3561 __isl_give isl_set **empty);
3562 __isl_give isl_pw_multi_aff *
3563 isl_basic_set_partial_lexmax_pw_multi_aff(
3564 __isl_take isl_basic_set *bset,
3565 __isl_take isl_basic_set *dom,
3566 __isl_give isl_set **empty);
3567 __isl_give isl_pw_multi_aff *
3568 isl_basic_map_partial_lexmin_pw_multi_aff(
3569 __isl_take isl_basic_map *bmap,
3570 __isl_take isl_basic_set *dom,
3571 __isl_give isl_set **empty);
3572 __isl_give isl_pw_multi_aff *
3573 isl_basic_map_partial_lexmax_pw_multi_aff(
3574 __isl_take isl_basic_map *bmap,
3575 __isl_take isl_basic_set *dom,
3576 __isl_give isl_set **empty);
3577 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3578 __isl_take isl_set *set);
3579 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3580 __isl_take isl_set *set);
3581 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3582 __isl_take isl_map *map);
3583 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3584 __isl_take isl_map *map);
3588 Lists are defined over several element types, including
3589 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3590 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3591 Here we take lists of C<isl_set>s as an example.
3592 Lists can be created, copied, modified and freed using the following functions.
3594 #include <isl/list.h>
3595 __isl_give isl_set_list *isl_set_list_from_set(
3596 __isl_take isl_set *el);
3597 __isl_give isl_set_list *isl_set_list_alloc(
3598 isl_ctx *ctx, int n);
3599 __isl_give isl_set_list *isl_set_list_copy(
3600 __isl_keep isl_set_list *list);
3601 __isl_give isl_set_list *isl_set_list_insert(
3602 __isl_take isl_set_list *list, unsigned pos,
3603 __isl_take isl_set *el);
3604 __isl_give isl_set_list *isl_set_list_add(
3605 __isl_take isl_set_list *list,
3606 __isl_take isl_set *el);
3607 __isl_give isl_set_list *isl_set_list_drop(
3608 __isl_take isl_set_list *list,
3609 unsigned first, unsigned n);
3610 __isl_give isl_set_list *isl_set_list_set_set(
3611 __isl_take isl_set_list *list, int index,
3612 __isl_take isl_set *set);
3613 __isl_give isl_set_list *isl_set_list_concat(
3614 __isl_take isl_set_list *list1,
3615 __isl_take isl_set_list *list2);
3616 __isl_give isl_set_list *isl_set_list_sort(
3617 __isl_take isl_set_list *list,
3618 int (*cmp)(__isl_keep isl_set *a,
3619 __isl_keep isl_set *b, void *user),
3621 __isl_null isl_set_list *isl_set_list_free(
3622 __isl_take isl_set_list *list);
3624 C<isl_set_list_alloc> creates an empty list with a capacity for
3625 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3628 Lists can be inspected using the following functions.
3630 #include <isl/list.h>
3631 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3632 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3633 __isl_give isl_set *isl_set_list_get_set(
3634 __isl_keep isl_set_list *list, int index);
3635 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3636 int (*fn)(__isl_take isl_set *el, void *user),
3638 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3639 int (*follows)(__isl_keep isl_set *a,
3640 __isl_keep isl_set *b, void *user),
3642 int (*fn)(__isl_take isl_set *el, void *user),
3645 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3646 strongly connected components of the graph with as vertices the elements
3647 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3648 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3649 should return C<-1> on error.
3651 Lists can be printed using
3653 #include <isl/list.h>
3654 __isl_give isl_printer *isl_printer_print_set_list(
3655 __isl_take isl_printer *p,
3656 __isl_keep isl_set_list *list);
3658 =head2 Associative arrays
3660 Associative arrays map isl objects of a specific type to isl objects
3661 of some (other) specific type. They are defined for several pairs
3662 of types, including (C<isl_map>, C<isl_basic_set>),
3663 (C<isl_id>, C<isl_ast_expr>) and.
3664 (C<isl_id>, C<isl_pw_aff>).
3665 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3668 Associative arrays can be created, copied and freed using
3669 the following functions.
3671 #include <isl/id_to_ast_expr.h>
3672 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3673 isl_ctx *ctx, int min_size);
3674 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3675 __isl_keep id_to_ast_expr *id2expr);
3676 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
3677 __isl_take id_to_ast_expr *id2expr);
3679 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3680 to specify the expected size of the associative array.
3681 The associative array will be grown automatically as needed.
3683 Associative arrays can be inspected using the following functions.
3685 #include <isl/id_to_ast_expr.h>
3686 isl_ctx *isl_id_to_ast_expr_get_ctx(
3687 __isl_keep id_to_ast_expr *id2expr);
3688 int isl_id_to_ast_expr_has(
3689 __isl_keep id_to_ast_expr *id2expr,
3690 __isl_keep isl_id *key);
3691 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3692 __isl_keep id_to_ast_expr *id2expr,
3693 __isl_take isl_id *key);
3694 int isl_id_to_ast_expr_foreach(
3695 __isl_keep id_to_ast_expr *id2expr,
3696 int (*fn)(__isl_take isl_id *key,
3697 __isl_take isl_ast_expr *val, void *user),
3700 They can be modified using the following function.
3702 #include <isl/id_to_ast_expr.h>
3703 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3704 __isl_take id_to_ast_expr *id2expr,
3705 __isl_take isl_id *key,
3706 __isl_take isl_ast_expr *val);
3707 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
3708 __isl_take id_to_ast_expr *id2expr,
3709 __isl_take isl_id *key);
3711 Associative arrays can be printed using the following function.
3713 #include <isl/id_to_ast_expr.h>
3714 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3715 __isl_take isl_printer *p,
3716 __isl_keep id_to_ast_expr *id2expr);
3718 =head2 Multiple Values
3720 An C<isl_multi_val> object represents a sequence of zero or more values,
3721 living in a set space.
3723 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3724 using the following function
3726 #include <isl/val.h>
3727 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3728 __isl_take isl_space *space,
3729 __isl_take isl_val_list *list);
3731 The zero multiple value (with value zero for each set dimension)
3732 can be created using the following function.
3734 #include <isl/val.h>
3735 __isl_give isl_multi_val *isl_multi_val_zero(
3736 __isl_take isl_space *space);
3738 Multiple values can be copied and freed using
3740 #include <isl/val.h>
3741 __isl_give isl_multi_val *isl_multi_val_copy(
3742 __isl_keep isl_multi_val *mv);
3743 __isl_null isl_multi_val *isl_multi_val_free(
3744 __isl_take isl_multi_val *mv);
3746 They can be inspected using
3748 #include <isl/val.h>
3749 isl_ctx *isl_multi_val_get_ctx(
3750 __isl_keep isl_multi_val *mv);
3751 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3752 enum isl_dim_type type);
3753 __isl_give isl_val *isl_multi_val_get_val(
3754 __isl_keep isl_multi_val *mv, int pos);
3755 int isl_multi_val_find_dim_by_id(
3756 __isl_keep isl_multi_val *mv,
3757 enum isl_dim_type type, __isl_keep isl_id *id);
3758 __isl_give isl_id *isl_multi_val_get_dim_id(
3759 __isl_keep isl_multi_val *mv,
3760 enum isl_dim_type type, unsigned pos);
3761 const char *isl_multi_val_get_tuple_name(
3762 __isl_keep isl_multi_val *mv,
3763 enum isl_dim_type type);
3764 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3765 enum isl_dim_type type);
3766 __isl_give isl_id *isl_multi_val_get_tuple_id(
3767 __isl_keep isl_multi_val *mv,
3768 enum isl_dim_type type);
3769 int isl_multi_val_range_is_wrapping(
3770 __isl_keep isl_multi_val *mv);
3772 They can be modified using
3774 #include <isl/val.h>
3775 __isl_give isl_multi_val *isl_multi_val_set_val(
3776 __isl_take isl_multi_val *mv, int pos,
3777 __isl_take isl_val *val);
3778 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3779 __isl_take isl_multi_val *mv,
3780 enum isl_dim_type type, unsigned pos, const char *s);
3781 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3782 __isl_take isl_multi_val *mv,
3783 enum isl_dim_type type, unsigned pos,
3784 __isl_take isl_id *id);
3785 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3786 __isl_take isl_multi_val *mv,
3787 enum isl_dim_type type, const char *s);
3788 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3789 __isl_take isl_multi_val *mv,
3790 enum isl_dim_type type, __isl_take isl_id *id);
3791 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3792 __isl_take isl_multi_val *mv,
3793 enum isl_dim_type type);
3794 __isl_give isl_multi_val *isl_multi_val_reset_user(
3795 __isl_take isl_multi_val *mv);
3797 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3798 __isl_take isl_multi_val *mv,
3799 enum isl_dim_type type, unsigned first, unsigned n);
3800 __isl_give isl_multi_val *isl_multi_val_add_dims(
3801 __isl_take isl_multi_val *mv,
3802 enum isl_dim_type type, unsigned n);
3803 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3804 __isl_take isl_multi_val *mv,
3805 enum isl_dim_type type, unsigned first, unsigned n);
3809 #include <isl/val.h>
3810 __isl_give isl_multi_val *isl_multi_val_align_params(
3811 __isl_take isl_multi_val *mv,
3812 __isl_take isl_space *model);
3813 __isl_give isl_multi_val *isl_multi_val_from_range(
3814 __isl_take isl_multi_val *mv);
3815 __isl_give isl_multi_val *isl_multi_val_range_splice(
3816 __isl_take isl_multi_val *mv1, unsigned pos,
3817 __isl_take isl_multi_val *mv2);
3818 __isl_give isl_multi_val *isl_multi_val_range_product(
3819 __isl_take isl_multi_val *mv1,
3820 __isl_take isl_multi_val *mv2);
3821 __isl_give isl_multi_val *
3822 isl_multi_val_range_factor_domain(
3823 __isl_take isl_multi_val *mv);
3824 __isl_give isl_multi_val *
3825 isl_multi_val_range_factor_range(
3826 __isl_take isl_multi_val *mv);
3827 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3828 __isl_take isl_multi_val *mv1,
3829 __isl_take isl_multi_aff *mv2);
3830 __isl_give isl_multi_val *isl_multi_val_product(
3831 __isl_take isl_multi_val *mv1,
3832 __isl_take isl_multi_val *mv2);
3833 __isl_give isl_multi_val *isl_multi_val_add_val(
3834 __isl_take isl_multi_val *mv,
3835 __isl_take isl_val *v);
3836 __isl_give isl_multi_val *isl_multi_val_mod_val(
3837 __isl_take isl_multi_val *mv,
3838 __isl_take isl_val *v);
3839 __isl_give isl_multi_val *isl_multi_val_scale_val(
3840 __isl_take isl_multi_val *mv,
3841 __isl_take isl_val *v);
3842 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3843 __isl_take isl_multi_val *mv1,
3844 __isl_take isl_multi_val *mv2);
3845 __isl_give isl_multi_val *
3846 isl_multi_val_scale_down_multi_val(
3847 __isl_take isl_multi_val *mv1,
3848 __isl_take isl_multi_val *mv2);
3850 A multiple value can be printed using
3852 __isl_give isl_printer *isl_printer_print_multi_val(
3853 __isl_take isl_printer *p,
3854 __isl_keep isl_multi_val *mv);
3858 Vectors can be created, copied and freed using the following functions.
3860 #include <isl/vec.h>
3861 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3863 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3864 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
3866 Note that the elements of a newly created vector may have arbitrary values.
3867 The elements can be changed and inspected using the following functions.
3869 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3870 int isl_vec_size(__isl_keep isl_vec *vec);
3871 __isl_give isl_val *isl_vec_get_element_val(
3872 __isl_keep isl_vec *vec, int pos);
3873 __isl_give isl_vec *isl_vec_set_element_si(
3874 __isl_take isl_vec *vec, int pos, int v);
3875 __isl_give isl_vec *isl_vec_set_element_val(
3876 __isl_take isl_vec *vec, int pos,
3877 __isl_take isl_val *v);
3878 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3880 __isl_give isl_vec *isl_vec_set_val(
3881 __isl_take isl_vec *vec, __isl_take isl_val *v);
3882 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3883 __isl_keep isl_vec *vec2, int pos);
3885 C<isl_vec_get_element> will return a negative value if anything went wrong.
3886 In that case, the value of C<*v> is undefined.
3888 The following function can be used to concatenate two vectors.
3890 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3891 __isl_take isl_vec *vec2);
3895 Matrices can be created, copied and freed using the following functions.
3897 #include <isl/mat.h>
3898 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3899 unsigned n_row, unsigned n_col);
3900 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3901 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
3903 Note that the elements of a newly created matrix may have arbitrary values.
3904 The elements can be changed and inspected using the following functions.
3906 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3907 int isl_mat_rows(__isl_keep isl_mat *mat);
3908 int isl_mat_cols(__isl_keep isl_mat *mat);
3909 __isl_give isl_val *isl_mat_get_element_val(
3910 __isl_keep isl_mat *mat, int row, int col);
3911 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3912 int row, int col, int v);
3913 __isl_give isl_mat *isl_mat_set_element_val(
3914 __isl_take isl_mat *mat, int row, int col,
3915 __isl_take isl_val *v);
3917 C<isl_mat_get_element> will return a negative value if anything went wrong.
3918 In that case, the value of C<*v> is undefined.
3920 The following function can be used to compute the (right) inverse
3921 of a matrix, i.e., a matrix such that the product of the original
3922 and the inverse (in that order) is a multiple of the identity matrix.
3923 The input matrix is assumed to be of full row-rank.
3925 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3927 The following function can be used to compute the (right) kernel
3928 (or null space) of a matrix, i.e., a matrix such that the product of
3929 the original and the kernel (in that order) is the zero matrix.
3931 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3933 =head2 Piecewise Quasi Affine Expressions
3935 The zero quasi affine expression or the quasi affine expression
3936 that is equal to a given value or
3937 a specified dimension on a given domain can be created using
3939 __isl_give isl_aff *isl_aff_zero_on_domain(
3940 __isl_take isl_local_space *ls);
3941 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3942 __isl_take isl_local_space *ls);
3943 __isl_give isl_aff *isl_aff_val_on_domain(
3944 __isl_take isl_local_space *ls,
3945 __isl_take isl_val *val);
3946 __isl_give isl_aff *isl_aff_var_on_domain(
3947 __isl_take isl_local_space *ls,
3948 enum isl_dim_type type, unsigned pos);
3949 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3950 __isl_take isl_local_space *ls,
3951 enum isl_dim_type type, unsigned pos);
3952 __isl_give isl_aff *isl_aff_nan_on_domain(
3953 __isl_take isl_local_space *ls);
3954 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3955 __isl_take isl_local_space *ls);
3957 Note that the space in which the resulting objects live is a map space
3958 with the given space as domain and a one-dimensional range.
3960 An empty piecewise quasi affine expression (one with no cells)
3961 or a piecewise quasi affine expression with a single cell can
3962 be created using the following functions.
3964 #include <isl/aff.h>
3965 __isl_give isl_pw_aff *isl_pw_aff_empty(
3966 __isl_take isl_space *space);
3967 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3968 __isl_take isl_set *set, __isl_take isl_aff *aff);
3969 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3970 __isl_take isl_aff *aff);
3972 A piecewise quasi affine expression that is equal to 1 on a set
3973 and 0 outside the set can be created using the following function.
3975 #include <isl/aff.h>
3976 __isl_give isl_pw_aff *isl_set_indicator_function(
3977 __isl_take isl_set *set);
3979 Quasi affine expressions can be copied and freed using
3981 #include <isl/aff.h>
3982 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3983 __isl_null isl_aff *isl_aff_free(__isl_take isl_aff *aff);
3985 __isl_give isl_pw_aff *isl_pw_aff_copy(
3986 __isl_keep isl_pw_aff *pwaff);
3987 __isl_null isl_pw_aff *isl_pw_aff_free(
3988 __isl_take isl_pw_aff *pwaff);
3990 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3991 using the following function. The constraint is required to have
3992 a non-zero coefficient for the specified dimension.
3994 #include <isl/constraint.h>
3995 __isl_give isl_aff *isl_constraint_get_bound(
3996 __isl_keep isl_constraint *constraint,
3997 enum isl_dim_type type, int pos);
3999 The entire affine expression of the constraint can also be extracted
4000 using the following function.
4002 #include <isl/constraint.h>
4003 __isl_give isl_aff *isl_constraint_get_aff(
4004 __isl_keep isl_constraint *constraint);
4006 Conversely, an equality constraint equating
4007 the affine expression to zero or an inequality constraint enforcing
4008 the affine expression to be non-negative, can be constructed using
4010 __isl_give isl_constraint *isl_equality_from_aff(
4011 __isl_take isl_aff *aff);
4012 __isl_give isl_constraint *isl_inequality_from_aff(
4013 __isl_take isl_aff *aff);
4015 The expression can be inspected using
4017 #include <isl/aff.h>
4018 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
4019 int isl_aff_dim(__isl_keep isl_aff *aff,
4020 enum isl_dim_type type);
4021 __isl_give isl_local_space *isl_aff_get_domain_local_space(
4022 __isl_keep isl_aff *aff);
4023 __isl_give isl_local_space *isl_aff_get_local_space(
4024 __isl_keep isl_aff *aff);
4025 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
4026 enum isl_dim_type type, unsigned pos);
4027 const char *isl_pw_aff_get_dim_name(
4028 __isl_keep isl_pw_aff *pa,
4029 enum isl_dim_type type, unsigned pos);
4030 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
4031 enum isl_dim_type type, unsigned pos);
4032 __isl_give isl_id *isl_pw_aff_get_dim_id(
4033 __isl_keep isl_pw_aff *pa,
4034 enum isl_dim_type type, unsigned pos);
4035 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
4036 enum isl_dim_type type);
4037 __isl_give isl_id *isl_pw_aff_get_tuple_id(
4038 __isl_keep isl_pw_aff *pa,
4039 enum isl_dim_type type);
4040 __isl_give isl_val *isl_aff_get_constant_val(
4041 __isl_keep isl_aff *aff);
4042 __isl_give isl_val *isl_aff_get_coefficient_val(
4043 __isl_keep isl_aff *aff,
4044 enum isl_dim_type type, int pos);
4045 __isl_give isl_val *isl_aff_get_denominator_val(
4046 __isl_keep isl_aff *aff);
4047 __isl_give isl_aff *isl_aff_get_div(
4048 __isl_keep isl_aff *aff, int pos);
4050 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
4051 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
4052 int (*fn)(__isl_take isl_set *set,
4053 __isl_take isl_aff *aff,
4054 void *user), void *user);
4056 int isl_aff_is_cst(__isl_keep isl_aff *aff);
4057 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4059 int isl_aff_is_nan(__isl_keep isl_aff *aff);
4060 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
4062 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
4063 enum isl_dim_type type, unsigned first, unsigned n);
4064 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
4065 enum isl_dim_type type, unsigned first, unsigned n);
4067 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
4068 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
4069 enum isl_dim_type type);
4070 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
4072 It can be modified using
4074 #include <isl/aff.h>
4075 __isl_give isl_aff *isl_aff_set_tuple_id(
4076 __isl_take isl_aff *aff,
4077 enum isl_dim_type type, __isl_take isl_id *id);
4078 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
4079 __isl_take isl_pw_aff *pwaff,
4080 enum isl_dim_type type, __isl_take isl_id *id);
4081 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
4082 __isl_take isl_pw_aff *pa,
4083 enum isl_dim_type type);
4084 __isl_give isl_aff *isl_aff_set_dim_name(
4085 __isl_take isl_aff *aff, enum isl_dim_type type,
4086 unsigned pos, const char *s);
4087 __isl_give isl_aff *isl_aff_set_dim_id(
4088 __isl_take isl_aff *aff, enum isl_dim_type type,
4089 unsigned pos, __isl_take isl_id *id);
4090 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
4091 __isl_take isl_pw_aff *pma,
4092 enum isl_dim_type type, unsigned pos,
4093 __isl_take isl_id *id);
4094 __isl_give isl_aff *isl_aff_set_constant_si(
4095 __isl_take isl_aff *aff, int v);
4096 __isl_give isl_aff *isl_aff_set_constant_val(
4097 __isl_take isl_aff *aff, __isl_take isl_val *v);
4098 __isl_give isl_aff *isl_aff_set_coefficient_si(
4099 __isl_take isl_aff *aff,
4100 enum isl_dim_type type, int pos, int v);
4101 __isl_give isl_aff *isl_aff_set_coefficient_val(
4102 __isl_take isl_aff *aff,
4103 enum isl_dim_type type, int pos,
4104 __isl_take isl_val *v);
4106 __isl_give isl_aff *isl_aff_add_constant_si(
4107 __isl_take isl_aff *aff, int v);
4108 __isl_give isl_aff *isl_aff_add_constant_val(
4109 __isl_take isl_aff *aff, __isl_take isl_val *v);
4110 __isl_give isl_aff *isl_aff_add_constant_num_si(
4111 __isl_take isl_aff *aff, int v);
4112 __isl_give isl_aff *isl_aff_add_coefficient_si(
4113 __isl_take isl_aff *aff,
4114 enum isl_dim_type type, int pos, int v);
4115 __isl_give isl_aff *isl_aff_add_coefficient_val(
4116 __isl_take isl_aff *aff,
4117 enum isl_dim_type type, int pos,
4118 __isl_take isl_val *v);
4120 __isl_give isl_aff *isl_aff_insert_dims(
4121 __isl_take isl_aff *aff,
4122 enum isl_dim_type type, unsigned first, unsigned n);
4123 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
4124 __isl_take isl_pw_aff *pwaff,
4125 enum isl_dim_type type, unsigned first, unsigned n);
4126 __isl_give isl_aff *isl_aff_add_dims(
4127 __isl_take isl_aff *aff,
4128 enum isl_dim_type type, unsigned n);
4129 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
4130 __isl_take isl_pw_aff *pwaff,
4131 enum isl_dim_type type, unsigned n);
4132 __isl_give isl_aff *isl_aff_drop_dims(
4133 __isl_take isl_aff *aff,
4134 enum isl_dim_type type, unsigned first, unsigned n);
4135 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
4136 __isl_take isl_pw_aff *pwaff,
4137 enum isl_dim_type type, unsigned first, unsigned n);
4138 __isl_give isl_aff *isl_aff_move_dims(
4139 __isl_take isl_aff *aff,
4140 enum isl_dim_type dst_type, unsigned dst_pos,
4141 enum isl_dim_type src_type, unsigned src_pos,
4143 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
4144 __isl_take isl_pw_aff *pa,
4145 enum isl_dim_type dst_type, unsigned dst_pos,
4146 enum isl_dim_type src_type, unsigned src_pos,
4149 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
4150 set the I<numerator> of the constant or coefficient, while
4151 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
4152 the constant or coefficient as a whole.
4153 The C<add_constant> and C<add_coefficient> functions add an integer
4154 or rational value to
4155 the possibly rational constant or coefficient.
4156 The C<add_constant_num> functions add an integer value to
4159 To check whether an affine expressions is obviously zero
4160 or (obviously) equal to some other affine expression, use
4162 #include <isl/aff.h>
4163 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
4164 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
4165 __isl_keep isl_aff *aff2);
4166 int isl_pw_aff_plain_is_equal(
4167 __isl_keep isl_pw_aff *pwaff1,
4168 __isl_keep isl_pw_aff *pwaff2);
4169 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
4170 __isl_keep isl_pw_aff *pa2);
4171 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4172 __isl_keep isl_pw_aff *pa2);
4174 The function C<isl_pw_aff_plain_cmp> can be used to sort
4175 C<isl_pw_aff>s. The order is not strictly defined.
4176 The current order sorts expressions that only involve
4177 earlier dimensions before those that involve later dimensions.
4181 #include <isl/aff.h>
4182 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
4183 __isl_take isl_aff *aff2);
4184 __isl_give isl_pw_aff *isl_pw_aff_add(
4185 __isl_take isl_pw_aff *pwaff1,
4186 __isl_take isl_pw_aff *pwaff2);
4187 __isl_give isl_pw_aff *isl_pw_aff_min(
4188 __isl_take isl_pw_aff *pwaff1,
4189 __isl_take isl_pw_aff *pwaff2);
4190 __isl_give isl_pw_aff *isl_pw_aff_max(
4191 __isl_take isl_pw_aff *pwaff1,
4192 __isl_take isl_pw_aff *pwaff2);
4193 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
4194 __isl_take isl_aff *aff2);
4195 __isl_give isl_pw_aff *isl_pw_aff_sub(
4196 __isl_take isl_pw_aff *pwaff1,
4197 __isl_take isl_pw_aff *pwaff2);
4198 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
4199 __isl_give isl_pw_aff *isl_pw_aff_neg(
4200 __isl_take isl_pw_aff *pwaff);
4201 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
4202 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4203 __isl_take isl_pw_aff *pwaff);
4204 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
4205 __isl_give isl_pw_aff *isl_pw_aff_floor(
4206 __isl_take isl_pw_aff *pwaff);
4207 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
4208 __isl_take isl_val *mod);
4209 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
4210 __isl_take isl_pw_aff *pa,
4211 __isl_take isl_val *mod);
4212 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
4213 __isl_take isl_val *v);
4214 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
4215 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
4216 __isl_give isl_aff *isl_aff_scale_down_ui(
4217 __isl_take isl_aff *aff, unsigned f);
4218 __isl_give isl_aff *isl_aff_scale_down_val(
4219 __isl_take isl_aff *aff, __isl_take isl_val *v);
4220 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
4221 __isl_take isl_pw_aff *pa,
4222 __isl_take isl_val *f);
4224 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4225 __isl_take isl_pw_aff_list *list);
4226 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4227 __isl_take isl_pw_aff_list *list);
4229 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4230 __isl_take isl_pw_aff *pwqp);
4232 __isl_give isl_aff *isl_aff_align_params(
4233 __isl_take isl_aff *aff,
4234 __isl_take isl_space *model);
4235 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4236 __isl_take isl_pw_aff *pwaff,
4237 __isl_take isl_space *model);
4239 __isl_give isl_aff *isl_aff_project_domain_on_params(
4240 __isl_take isl_aff *aff);
4241 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4242 __isl_take isl_pw_aff *pwa);
4244 __isl_give isl_aff *isl_aff_gist_params(
4245 __isl_take isl_aff *aff,
4246 __isl_take isl_set *context);
4247 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
4248 __isl_take isl_set *context);
4249 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
4250 __isl_take isl_pw_aff *pwaff,
4251 __isl_take isl_set *context);
4252 __isl_give isl_pw_aff *isl_pw_aff_gist(
4253 __isl_take isl_pw_aff *pwaff,
4254 __isl_take isl_set *context);
4256 __isl_give isl_set *isl_pw_aff_domain(
4257 __isl_take isl_pw_aff *pwaff);
4258 __isl_give isl_set *isl_pw_aff_params(
4259 __isl_take isl_pw_aff *pwa);
4260 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4261 __isl_take isl_pw_aff *pa,
4262 __isl_take isl_set *set);
4263 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4264 __isl_take isl_pw_aff *pa,
4265 __isl_take isl_set *set);
4267 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
4268 __isl_take isl_aff *aff2);
4269 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
4270 __isl_take isl_aff *aff2);
4271 __isl_give isl_pw_aff *isl_pw_aff_mul(
4272 __isl_take isl_pw_aff *pwaff1,
4273 __isl_take isl_pw_aff *pwaff2);
4274 __isl_give isl_pw_aff *isl_pw_aff_div(
4275 __isl_take isl_pw_aff *pa1,
4276 __isl_take isl_pw_aff *pa2);
4277 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
4278 __isl_take isl_pw_aff *pa1,
4279 __isl_take isl_pw_aff *pa2);
4280 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
4281 __isl_take isl_pw_aff *pa1,
4282 __isl_take isl_pw_aff *pa2);
4284 When multiplying two affine expressions, at least one of the two needs
4285 to be a constant. Similarly, when dividing an affine expression by another,
4286 the second expression needs to be a constant.
4287 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
4288 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
4291 #include <isl/aff.h>
4292 __isl_give isl_aff *isl_aff_pullback_aff(
4293 __isl_take isl_aff *aff1,
4294 __isl_take isl_aff *aff2);
4295 __isl_give isl_aff *isl_aff_pullback_multi_aff(
4296 __isl_take isl_aff *aff,
4297 __isl_take isl_multi_aff *ma);
4298 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
4299 __isl_take isl_pw_aff *pa,
4300 __isl_take isl_multi_aff *ma);
4301 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
4302 __isl_take isl_pw_aff *pa,
4303 __isl_take isl_pw_multi_aff *pma);
4304 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
4305 __isl_take isl_pw_aff *pa,
4306 __isl_take isl_multi_pw_aff *mpa);
4308 These functions precompose the input expression by the given
4309 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
4310 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
4311 into the (piecewise) affine expression.
4312 Objects of type C<isl_multi_aff> are described in
4313 L</"Piecewise Multiple Quasi Affine Expressions">.
4315 #include <isl/aff.h>
4316 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4317 __isl_take isl_aff *aff);
4318 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4319 __isl_take isl_aff *aff);
4320 __isl_give isl_basic_set *isl_aff_le_basic_set(
4321 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4322 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4323 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4324 __isl_give isl_set *isl_pw_aff_eq_set(
4325 __isl_take isl_pw_aff *pwaff1,
4326 __isl_take isl_pw_aff *pwaff2);
4327 __isl_give isl_set *isl_pw_aff_ne_set(
4328 __isl_take isl_pw_aff *pwaff1,
4329 __isl_take isl_pw_aff *pwaff2);
4330 __isl_give isl_set *isl_pw_aff_le_set(
4331 __isl_take isl_pw_aff *pwaff1,
4332 __isl_take isl_pw_aff *pwaff2);
4333 __isl_give isl_set *isl_pw_aff_lt_set(
4334 __isl_take isl_pw_aff *pwaff1,
4335 __isl_take isl_pw_aff *pwaff2);
4336 __isl_give isl_set *isl_pw_aff_ge_set(
4337 __isl_take isl_pw_aff *pwaff1,
4338 __isl_take isl_pw_aff *pwaff2);
4339 __isl_give isl_set *isl_pw_aff_gt_set(
4340 __isl_take isl_pw_aff *pwaff1,
4341 __isl_take isl_pw_aff *pwaff2);
4343 __isl_give isl_set *isl_pw_aff_list_eq_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_ne_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_le_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_lt_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_ge_set(
4356 __isl_take isl_pw_aff_list *list1,
4357 __isl_take isl_pw_aff_list *list2);
4358 __isl_give isl_set *isl_pw_aff_list_gt_set(
4359 __isl_take isl_pw_aff_list *list1,
4360 __isl_take isl_pw_aff_list *list2);
4362 The function C<isl_aff_neg_basic_set> returns a basic set
4363 containing those elements in the domain space
4364 of C<aff> where C<aff> is negative.
4365 The function C<isl_aff_ge_basic_set> returns a basic set
4366 containing those elements in the shared space
4367 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4368 The function C<isl_pw_aff_ge_set> returns a set
4369 containing those elements in the shared domain
4370 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4371 The functions operating on C<isl_pw_aff_list> apply the corresponding
4372 C<isl_pw_aff> function to each pair of elements in the two lists.
4374 #include <isl/aff.h>
4375 __isl_give isl_set *isl_pw_aff_nonneg_set(
4376 __isl_take isl_pw_aff *pwaff);
4377 __isl_give isl_set *isl_pw_aff_zero_set(
4378 __isl_take isl_pw_aff *pwaff);
4379 __isl_give isl_set *isl_pw_aff_non_zero_set(
4380 __isl_take isl_pw_aff *pwaff);
4382 The function C<isl_pw_aff_nonneg_set> returns a set
4383 containing those elements in the domain
4384 of C<pwaff> where C<pwaff> is non-negative.
4386 #include <isl/aff.h>
4387 __isl_give isl_pw_aff *isl_pw_aff_cond(
4388 __isl_take isl_pw_aff *cond,
4389 __isl_take isl_pw_aff *pwaff_true,
4390 __isl_take isl_pw_aff *pwaff_false);
4392 The function C<isl_pw_aff_cond> performs a conditional operator
4393 and returns an expression that is equal to C<pwaff_true>
4394 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4395 where C<cond> is zero.
4397 #include <isl/aff.h>
4398 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4399 __isl_take isl_pw_aff *pwaff1,
4400 __isl_take isl_pw_aff *pwaff2);
4401 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4402 __isl_take isl_pw_aff *pwaff1,
4403 __isl_take isl_pw_aff *pwaff2);
4404 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4405 __isl_take isl_pw_aff *pwaff1,
4406 __isl_take isl_pw_aff *pwaff2);
4408 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4409 expression with a domain that is the union of those of C<pwaff1> and
4410 C<pwaff2> and such that on each cell, the quasi-affine expression is
4411 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4412 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4413 associated expression is the defined one.
4415 An expression can be read from input using
4417 #include <isl/aff.h>
4418 __isl_give isl_aff *isl_aff_read_from_str(
4419 isl_ctx *ctx, const char *str);
4420 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4421 isl_ctx *ctx, const char *str);
4423 An expression can be printed using
4425 #include <isl/aff.h>
4426 __isl_give isl_printer *isl_printer_print_aff(
4427 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4429 __isl_give isl_printer *isl_printer_print_pw_aff(
4430 __isl_take isl_printer *p,
4431 __isl_keep isl_pw_aff *pwaff);
4433 =head2 Piecewise Multiple Quasi Affine Expressions
4435 An C<isl_multi_aff> object represents a sequence of
4436 zero or more affine expressions, all defined on the same domain space.
4437 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4438 zero or more piecewise affine expressions.
4440 An C<isl_multi_aff> can be constructed from a single
4441 C<isl_aff> or an C<isl_aff_list> using the
4442 following functions. Similarly for C<isl_multi_pw_aff>
4443 and C<isl_pw_multi_aff>.
4445 #include <isl/aff.h>
4446 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4447 __isl_take isl_aff *aff);
4448 __isl_give isl_multi_pw_aff *
4449 isl_multi_pw_aff_from_multi_aff(
4450 __isl_take isl_multi_aff *ma);
4451 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4452 __isl_take isl_pw_aff *pa);
4453 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4454 __isl_take isl_pw_aff *pa);
4455 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4456 __isl_take isl_space *space,
4457 __isl_take isl_aff_list *list);
4459 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4460 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4461 Note however that the domain
4462 of the result is the intersection of the domains of the input.
4463 The reverse conversion is exact.
4465 #include <isl/aff.h>
4466 __isl_give isl_pw_multi_aff *
4467 isl_pw_multi_aff_from_multi_pw_aff(
4468 __isl_take isl_multi_pw_aff *mpa);
4469 __isl_give isl_multi_pw_aff *
4470 isl_multi_pw_aff_from_pw_multi_aff(
4471 __isl_take isl_pw_multi_aff *pma);
4473 An empty piecewise multiple quasi affine expression (one with no cells),
4474 the zero piecewise multiple quasi affine expression (with value zero
4475 for each output dimension),
4476 a piecewise multiple quasi affine expression with a single cell (with
4477 either a universe or a specified domain) or
4478 a zero-dimensional piecewise multiple quasi affine expression
4480 can be created using the following functions.
4482 #include <isl/aff.h>
4483 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4484 __isl_take isl_space *space);
4485 __isl_give isl_multi_aff *isl_multi_aff_zero(
4486 __isl_take isl_space *space);
4487 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4488 __isl_take isl_space *space);
4489 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4490 __isl_take isl_space *space);
4491 __isl_give isl_multi_aff *isl_multi_aff_identity(
4492 __isl_take isl_space *space);
4493 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4494 __isl_take isl_space *space);
4495 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4496 __isl_take isl_space *space);
4497 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4498 __isl_take isl_space *space);
4499 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4500 __isl_take isl_space *space);
4501 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4502 __isl_take isl_space *space,
4503 enum isl_dim_type type,
4504 unsigned first, unsigned n);
4505 __isl_give isl_pw_multi_aff *
4506 isl_pw_multi_aff_project_out_map(
4507 __isl_take isl_space *space,
4508 enum isl_dim_type type,
4509 unsigned first, unsigned n);
4510 __isl_give isl_pw_multi_aff *
4511 isl_pw_multi_aff_from_multi_aff(
4512 __isl_take isl_multi_aff *ma);
4513 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4514 __isl_take isl_set *set,
4515 __isl_take isl_multi_aff *maff);
4516 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4517 __isl_take isl_set *set);
4519 __isl_give isl_union_pw_multi_aff *
4520 isl_union_pw_multi_aff_empty(
4521 __isl_take isl_space *space);
4522 __isl_give isl_union_pw_multi_aff *
4523 isl_union_pw_multi_aff_add_pw_multi_aff(
4524 __isl_take isl_union_pw_multi_aff *upma,
4525 __isl_take isl_pw_multi_aff *pma);
4526 __isl_give isl_union_pw_multi_aff *
4527 isl_union_pw_multi_aff_from_domain(
4528 __isl_take isl_union_set *uset);
4530 A piecewise multiple quasi affine expression can also be initialized
4531 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4532 and the C<isl_map> is single-valued.
4533 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4534 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4536 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4537 __isl_take isl_set *set);
4538 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4539 __isl_take isl_map *map);
4541 __isl_give isl_union_pw_multi_aff *
4542 isl_union_pw_multi_aff_from_union_set(
4543 __isl_take isl_union_set *uset);
4544 __isl_give isl_union_pw_multi_aff *
4545 isl_union_pw_multi_aff_from_union_map(
4546 __isl_take isl_union_map *umap);
4548 Multiple quasi affine expressions can be copied and freed using
4550 #include <isl/aff.h>
4551 __isl_give isl_multi_aff *isl_multi_aff_copy(
4552 __isl_keep isl_multi_aff *maff);
4553 __isl_null isl_multi_aff *isl_multi_aff_free(
4554 __isl_take isl_multi_aff *maff);
4556 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4557 __isl_keep isl_pw_multi_aff *pma);
4558 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
4559 __isl_take isl_pw_multi_aff *pma);
4561 __isl_give isl_union_pw_multi_aff *
4562 isl_union_pw_multi_aff_copy(
4563 __isl_keep isl_union_pw_multi_aff *upma);
4564 __isl_null isl_union_pw_multi_aff *
4565 isl_union_pw_multi_aff_free(
4566 __isl_take isl_union_pw_multi_aff *upma);
4568 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4569 __isl_keep isl_multi_pw_aff *mpa);
4570 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
4571 __isl_take isl_multi_pw_aff *mpa);
4573 The expression can be inspected using
4575 #include <isl/aff.h>
4576 isl_ctx *isl_multi_aff_get_ctx(
4577 __isl_keep isl_multi_aff *maff);
4578 isl_ctx *isl_pw_multi_aff_get_ctx(
4579 __isl_keep isl_pw_multi_aff *pma);
4580 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4581 __isl_keep isl_union_pw_multi_aff *upma);
4582 isl_ctx *isl_multi_pw_aff_get_ctx(
4583 __isl_keep isl_multi_pw_aff *mpa);
4585 int isl_multi_aff_involves_dims(
4586 __isl_keep isl_multi_aff *ma,
4587 enum isl_dim_type type, unsigned first, unsigned n);
4588 int isl_multi_pw_aff_involves_dims(
4589 __isl_keep isl_multi_pw_aff *mpa,
4590 enum isl_dim_type type, unsigned first, unsigned n);
4592 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4593 enum isl_dim_type type);
4594 unsigned isl_pw_multi_aff_dim(
4595 __isl_keep isl_pw_multi_aff *pma,
4596 enum isl_dim_type type);
4597 unsigned isl_multi_pw_aff_dim(
4598 __isl_keep isl_multi_pw_aff *mpa,
4599 enum isl_dim_type type);
4600 __isl_give isl_aff *isl_multi_aff_get_aff(
4601 __isl_keep isl_multi_aff *multi, int pos);
4602 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4603 __isl_keep isl_pw_multi_aff *pma, int pos);
4604 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4605 __isl_keep isl_multi_pw_aff *mpa, int pos);
4606 int isl_multi_aff_find_dim_by_id(
4607 __isl_keep isl_multi_aff *ma,
4608 enum isl_dim_type type, __isl_keep isl_id *id);
4609 int isl_multi_pw_aff_find_dim_by_id(
4610 __isl_keep isl_multi_pw_aff *mpa,
4611 enum isl_dim_type type, __isl_keep isl_id *id);
4612 const char *isl_pw_multi_aff_get_dim_name(
4613 __isl_keep isl_pw_multi_aff *pma,
4614 enum isl_dim_type type, unsigned pos);
4615 __isl_give isl_id *isl_multi_aff_get_dim_id(
4616 __isl_keep isl_multi_aff *ma,
4617 enum isl_dim_type type, unsigned pos);
4618 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4619 __isl_keep isl_pw_multi_aff *pma,
4620 enum isl_dim_type type, unsigned pos);
4621 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4622 __isl_keep isl_multi_pw_aff *mpa,
4623 enum isl_dim_type type, unsigned pos);
4624 const char *isl_multi_aff_get_tuple_name(
4625 __isl_keep isl_multi_aff *multi,
4626 enum isl_dim_type type);
4627 int isl_pw_multi_aff_has_tuple_name(
4628 __isl_keep isl_pw_multi_aff *pma,
4629 enum isl_dim_type type);
4630 const char *isl_pw_multi_aff_get_tuple_name(
4631 __isl_keep isl_pw_multi_aff *pma,
4632 enum isl_dim_type type);
4633 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4634 enum isl_dim_type type);
4635 int isl_pw_multi_aff_has_tuple_id(
4636 __isl_keep isl_pw_multi_aff *pma,
4637 enum isl_dim_type type);
4638 int isl_multi_pw_aff_has_tuple_id(
4639 __isl_keep isl_multi_pw_aff *mpa,
4640 enum isl_dim_type type);
4641 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4642 __isl_keep isl_multi_aff *ma,
4643 enum isl_dim_type type);
4644 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4645 __isl_keep isl_pw_multi_aff *pma,
4646 enum isl_dim_type type);
4647 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4648 __isl_keep isl_multi_pw_aff *mpa,
4649 enum isl_dim_type type);
4650 int isl_multi_aff_range_is_wrapping(
4651 __isl_keep isl_multi_aff *ma);
4652 int isl_multi_pw_aff_range_is_wrapping(
4653 __isl_keep isl_multi_pw_aff *mpa);
4655 int isl_pw_multi_aff_foreach_piece(
4656 __isl_keep isl_pw_multi_aff *pma,
4657 int (*fn)(__isl_take isl_set *set,
4658 __isl_take isl_multi_aff *maff,
4659 void *user), void *user);
4661 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4662 __isl_keep isl_union_pw_multi_aff *upma,
4663 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4664 void *user), void *user);
4666 It can be modified using
4668 #include <isl/aff.h>
4669 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4670 __isl_take isl_multi_aff *multi, int pos,
4671 __isl_take isl_aff *aff);
4672 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4673 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4674 __isl_take isl_pw_aff *pa);
4675 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4676 __isl_take isl_multi_aff *maff,
4677 enum isl_dim_type type, unsigned pos, const char *s);
4678 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4679 __isl_take isl_multi_aff *maff,
4680 enum isl_dim_type type, unsigned pos,
4681 __isl_take isl_id *id);
4682 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4683 __isl_take isl_multi_aff *maff,
4684 enum isl_dim_type type, const char *s);
4685 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4686 __isl_take isl_multi_aff *maff,
4687 enum isl_dim_type type, __isl_take isl_id *id);
4688 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4689 __isl_take isl_pw_multi_aff *pma,
4690 enum isl_dim_type type, __isl_take isl_id *id);
4691 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4692 __isl_take isl_multi_aff *ma,
4693 enum isl_dim_type type);
4694 __isl_give isl_multi_pw_aff *
4695 isl_multi_pw_aff_reset_tuple_id(
4696 __isl_take isl_multi_pw_aff *mpa,
4697 enum isl_dim_type type);
4698 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4699 __isl_take isl_multi_aff *ma);
4700 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4701 __isl_take isl_multi_pw_aff *mpa);
4703 __isl_give isl_multi_pw_aff *
4704 isl_multi_pw_aff_set_dim_name(
4705 __isl_take isl_multi_pw_aff *mpa,
4706 enum isl_dim_type type, unsigned pos, const char *s);
4707 __isl_give isl_multi_pw_aff *
4708 isl_multi_pw_aff_set_dim_id(
4709 __isl_take isl_multi_pw_aff *mpa,
4710 enum isl_dim_type type, unsigned pos,
4711 __isl_take isl_id *id);
4712 __isl_give isl_multi_pw_aff *
4713 isl_multi_pw_aff_set_tuple_name(
4714 __isl_take isl_multi_pw_aff *mpa,
4715 enum isl_dim_type type, const char *s);
4717 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4718 __isl_take isl_multi_aff *ma);
4720 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4721 __isl_take isl_multi_aff *ma,
4722 enum isl_dim_type type, unsigned first, unsigned n);
4723 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4724 __isl_take isl_multi_aff *ma,
4725 enum isl_dim_type type, unsigned n);
4726 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4727 __isl_take isl_multi_aff *maff,
4728 enum isl_dim_type type, unsigned first, unsigned n);
4729 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4730 __isl_take isl_pw_multi_aff *pma,
4731 enum isl_dim_type type, unsigned first, unsigned n);
4733 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4734 __isl_take isl_multi_pw_aff *mpa,
4735 enum isl_dim_type type, unsigned first, unsigned n);
4736 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4737 __isl_take isl_multi_pw_aff *mpa,
4738 enum isl_dim_type type, unsigned n);
4739 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4740 __isl_take isl_multi_pw_aff *pma,
4741 enum isl_dim_type dst_type, unsigned dst_pos,
4742 enum isl_dim_type src_type, unsigned src_pos,
4745 To check whether two multiple affine expressions are
4746 (obviously) equal to each other, use
4748 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4749 __isl_keep isl_multi_aff *maff2);
4750 int isl_pw_multi_aff_plain_is_equal(
4751 __isl_keep isl_pw_multi_aff *pma1,
4752 __isl_keep isl_pw_multi_aff *pma2);
4753 int isl_multi_pw_aff_plain_is_equal(
4754 __isl_keep isl_multi_pw_aff *mpa1,
4755 __isl_keep isl_multi_pw_aff *mpa2);
4756 int isl_multi_pw_aff_is_equal(
4757 __isl_keep isl_multi_pw_aff *mpa1,
4758 __isl_keep isl_multi_pw_aff *mpa2);
4762 #include <isl/aff.h>
4763 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4764 __isl_take isl_pw_multi_aff *pma1,
4765 __isl_take isl_pw_multi_aff *pma2);
4766 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4767 __isl_take isl_pw_multi_aff *pma1,
4768 __isl_take isl_pw_multi_aff *pma2);
4769 __isl_give isl_multi_aff *isl_multi_aff_floor(
4770 __isl_take isl_multi_aff *ma);
4771 __isl_give isl_multi_aff *isl_multi_aff_add(
4772 __isl_take isl_multi_aff *maff1,
4773 __isl_take isl_multi_aff *maff2);
4774 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4775 __isl_take isl_pw_multi_aff *pma1,
4776 __isl_take isl_pw_multi_aff *pma2);
4777 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4778 __isl_take isl_union_pw_multi_aff *upma1,
4779 __isl_take isl_union_pw_multi_aff *upma2);
4780 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4781 __isl_take isl_pw_multi_aff *pma1,
4782 __isl_take isl_pw_multi_aff *pma2);
4783 __isl_give isl_multi_aff *isl_multi_aff_sub(
4784 __isl_take isl_multi_aff *ma1,
4785 __isl_take isl_multi_aff *ma2);
4786 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4787 __isl_take isl_pw_multi_aff *pma1,
4788 __isl_take isl_pw_multi_aff *pma2);
4789 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4790 __isl_take isl_union_pw_multi_aff *upma1,
4791 __isl_take isl_union_pw_multi_aff *upma2);
4793 C<isl_multi_aff_sub> subtracts the second argument from the first.
4795 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4796 __isl_take isl_multi_aff *ma,
4797 __isl_take isl_val *v);
4798 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4799 __isl_take isl_pw_multi_aff *pma,
4800 __isl_take isl_val *v);
4801 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4802 __isl_take isl_multi_pw_aff *mpa,
4803 __isl_take isl_val *v);
4804 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4805 __isl_take isl_multi_aff *ma,
4806 __isl_take isl_multi_val *mv);
4807 __isl_give isl_pw_multi_aff *
4808 isl_pw_multi_aff_scale_multi_val(
4809 __isl_take isl_pw_multi_aff *pma,
4810 __isl_take isl_multi_val *mv);
4811 __isl_give isl_multi_pw_aff *
4812 isl_multi_pw_aff_scale_multi_val(
4813 __isl_take isl_multi_pw_aff *mpa,
4814 __isl_take isl_multi_val *mv);
4815 __isl_give isl_union_pw_multi_aff *
4816 isl_union_pw_multi_aff_scale_multi_val(
4817 __isl_take isl_union_pw_multi_aff *upma,
4818 __isl_take isl_multi_val *mv);
4819 __isl_give isl_multi_aff *
4820 isl_multi_aff_scale_down_multi_val(
4821 __isl_take isl_multi_aff *ma,
4822 __isl_take isl_multi_val *mv);
4823 __isl_give isl_multi_pw_aff *
4824 isl_multi_pw_aff_scale_down_multi_val(
4825 __isl_take isl_multi_pw_aff *mpa,
4826 __isl_take isl_multi_val *mv);
4828 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4829 by the corresponding elements of C<mv>.
4831 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4832 __isl_take isl_pw_multi_aff *pma,
4833 enum isl_dim_type type, unsigned pos, int value);
4834 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4835 __isl_take isl_pw_multi_aff *pma,
4836 __isl_take isl_set *set);
4837 __isl_give isl_set *isl_multi_pw_aff_domain(
4838 __isl_take isl_multi_pw_aff *mpa);
4839 __isl_give isl_multi_pw_aff *
4840 isl_multi_pw_aff_intersect_params(
4841 __isl_take isl_multi_pw_aff *mpa,
4842 __isl_take isl_set *set);
4843 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4844 __isl_take isl_pw_multi_aff *pma,
4845 __isl_take isl_set *set);
4846 __isl_give isl_multi_pw_aff *
4847 isl_multi_pw_aff_intersect_domain(
4848 __isl_take isl_multi_pw_aff *mpa,
4849 __isl_take isl_set *domain);
4850 __isl_give isl_union_pw_multi_aff *
4851 isl_union_pw_multi_aff_intersect_domain(
4852 __isl_take isl_union_pw_multi_aff *upma,
4853 __isl_take isl_union_set *uset);
4854 __isl_give isl_multi_aff *isl_multi_aff_lift(
4855 __isl_take isl_multi_aff *maff,
4856 __isl_give isl_local_space **ls);
4857 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4858 __isl_take isl_pw_multi_aff *pma);
4859 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4860 __isl_take isl_multi_pw_aff *mpa);
4861 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4862 __isl_take isl_multi_aff *multi,
4863 __isl_take isl_space *model);
4864 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4865 __isl_take isl_pw_multi_aff *pma,
4866 __isl_take isl_space *model);
4867 __isl_give isl_union_pw_multi_aff *
4868 isl_union_pw_multi_aff_align_params(
4869 __isl_take isl_union_pw_multi_aff *upma,
4870 __isl_take isl_space *model);
4871 __isl_give isl_pw_multi_aff *
4872 isl_pw_multi_aff_project_domain_on_params(
4873 __isl_take isl_pw_multi_aff *pma);
4874 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4875 __isl_take isl_multi_aff *maff,
4876 __isl_take isl_set *context);
4877 __isl_give isl_multi_aff *isl_multi_aff_gist(
4878 __isl_take isl_multi_aff *maff,
4879 __isl_take isl_set *context);
4880 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4881 __isl_take isl_pw_multi_aff *pma,
4882 __isl_take isl_set *set);
4883 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4884 __isl_take isl_pw_multi_aff *pma,
4885 __isl_take isl_set *set);
4886 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4887 __isl_take isl_multi_pw_aff *mpa,
4888 __isl_take isl_set *set);
4889 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4890 __isl_take isl_multi_pw_aff *mpa,
4891 __isl_take isl_set *set);
4892 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4893 __isl_take isl_multi_aff *ma);
4894 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4895 __isl_take isl_multi_pw_aff *mpa);
4896 __isl_give isl_set *isl_pw_multi_aff_domain(
4897 __isl_take isl_pw_multi_aff *pma);
4898 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4899 __isl_take isl_union_pw_multi_aff *upma);
4900 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4901 __isl_take isl_multi_aff *ma1, unsigned pos,
4902 __isl_take isl_multi_aff *ma2);
4903 __isl_give isl_multi_aff *isl_multi_aff_splice(
4904 __isl_take isl_multi_aff *ma1,
4905 unsigned in_pos, unsigned out_pos,
4906 __isl_take isl_multi_aff *ma2);
4907 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4908 __isl_take isl_multi_aff *ma1,
4909 __isl_take isl_multi_aff *ma2);
4910 __isl_give isl_multi_aff *
4911 isl_multi_aff_range_factor_domain(
4912 __isl_take isl_multi_aff *ma);
4913 __isl_give isl_multi_aff *
4914 isl_multi_aff_range_factor_range(
4915 __isl_take isl_multi_aff *ma);
4916 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4917 __isl_take isl_multi_aff *ma1,
4918 __isl_take isl_multi_aff *ma2);
4919 __isl_give isl_multi_aff *isl_multi_aff_product(
4920 __isl_take isl_multi_aff *ma1,
4921 __isl_take isl_multi_aff *ma2);
4922 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4923 __isl_take isl_multi_pw_aff *mpa1,
4924 __isl_take isl_multi_pw_aff *mpa2);
4925 __isl_give isl_pw_multi_aff *
4926 isl_pw_multi_aff_range_product(
4927 __isl_take isl_pw_multi_aff *pma1,
4928 __isl_take isl_pw_multi_aff *pma2);
4929 __isl_give isl_multi_pw_aff *
4930 isl_multi_pw_aff_range_factor_domain(
4931 __isl_take isl_multi_pw_aff *mpa);
4932 __isl_give isl_multi_pw_aff *
4933 isl_multi_pw_aff_range_factor_range(
4934 __isl_take isl_multi_pw_aff *mpa);
4935 __isl_give isl_pw_multi_aff *
4936 isl_pw_multi_aff_flat_range_product(
4937 __isl_take isl_pw_multi_aff *pma1,
4938 __isl_take isl_pw_multi_aff *pma2);
4939 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4940 __isl_take isl_pw_multi_aff *pma1,
4941 __isl_take isl_pw_multi_aff *pma2);
4942 __isl_give isl_union_pw_multi_aff *
4943 isl_union_pw_multi_aff_flat_range_product(
4944 __isl_take isl_union_pw_multi_aff *upma1,
4945 __isl_take isl_union_pw_multi_aff *upma2);
4946 __isl_give isl_multi_pw_aff *
4947 isl_multi_pw_aff_range_splice(
4948 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4949 __isl_take isl_multi_pw_aff *mpa2);
4950 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4951 __isl_take isl_multi_pw_aff *mpa1,
4952 unsigned in_pos, unsigned out_pos,
4953 __isl_take isl_multi_pw_aff *mpa2);
4954 __isl_give isl_multi_pw_aff *
4955 isl_multi_pw_aff_range_product(
4956 __isl_take isl_multi_pw_aff *mpa1,
4957 __isl_take isl_multi_pw_aff *mpa2);
4958 __isl_give isl_multi_pw_aff *
4959 isl_multi_pw_aff_flat_range_product(
4960 __isl_take isl_multi_pw_aff *mpa1,
4961 __isl_take isl_multi_pw_aff *mpa2);
4963 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4964 then it is assigned the local space that lies at the basis of
4965 the lifting applied.
4967 #include <isl/aff.h>
4968 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4969 __isl_take isl_multi_aff *ma1,
4970 __isl_take isl_multi_aff *ma2);
4971 __isl_give isl_pw_multi_aff *
4972 isl_pw_multi_aff_pullback_multi_aff(
4973 __isl_take isl_pw_multi_aff *pma,
4974 __isl_take isl_multi_aff *ma);
4975 __isl_give isl_multi_pw_aff *
4976 isl_multi_pw_aff_pullback_multi_aff(
4977 __isl_take isl_multi_pw_aff *mpa,
4978 __isl_take isl_multi_aff *ma);
4979 __isl_give isl_pw_multi_aff *
4980 isl_pw_multi_aff_pullback_pw_multi_aff(
4981 __isl_take isl_pw_multi_aff *pma1,
4982 __isl_take isl_pw_multi_aff *pma2);
4983 __isl_give isl_multi_pw_aff *
4984 isl_multi_pw_aff_pullback_pw_multi_aff(
4985 __isl_take isl_multi_pw_aff *mpa,
4986 __isl_take isl_pw_multi_aff *pma);
4987 __isl_give isl_multi_pw_aff *
4988 isl_multi_pw_aff_pullback_multi_pw_aff(
4989 __isl_take isl_multi_pw_aff *mpa1,
4990 __isl_take isl_multi_pw_aff *mpa2);
4992 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4993 In other words, C<ma2> is plugged
4996 __isl_give isl_set *isl_multi_aff_lex_le_set(
4997 __isl_take isl_multi_aff *ma1,
4998 __isl_take isl_multi_aff *ma2);
4999 __isl_give isl_set *isl_multi_aff_lex_ge_set(
5000 __isl_take isl_multi_aff *ma1,
5001 __isl_take isl_multi_aff *ma2);
5003 The function C<isl_multi_aff_lex_le_set> returns a set
5004 containing those elements in the shared domain space
5005 where C<ma1> is lexicographically smaller than or
5008 An expression can be read from input using
5010 #include <isl/aff.h>
5011 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
5012 isl_ctx *ctx, const char *str);
5013 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
5014 isl_ctx *ctx, const char *str);
5015 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
5016 isl_ctx *ctx, const char *str);
5017 __isl_give isl_union_pw_multi_aff *
5018 isl_union_pw_multi_aff_read_from_str(
5019 isl_ctx *ctx, const char *str);
5021 An expression can be printed using
5023 #include <isl/aff.h>
5024 __isl_give isl_printer *isl_printer_print_multi_aff(
5025 __isl_take isl_printer *p,
5026 __isl_keep isl_multi_aff *maff);
5027 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
5028 __isl_take isl_printer *p,
5029 __isl_keep isl_pw_multi_aff *pma);
5030 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
5031 __isl_take isl_printer *p,
5032 __isl_keep isl_union_pw_multi_aff *upma);
5033 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
5034 __isl_take isl_printer *p,
5035 __isl_keep isl_multi_pw_aff *mpa);
5039 Points are elements of a set. They can be used to construct
5040 simple sets (boxes) or they can be used to represent the
5041 individual elements of a set.
5042 The zero point (the origin) can be created using
5044 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
5046 The coordinates of a point can be inspected, set and changed
5049 __isl_give isl_val *isl_point_get_coordinate_val(
5050 __isl_keep isl_point *pnt,
5051 enum isl_dim_type type, int pos);
5052 __isl_give isl_point *isl_point_set_coordinate_val(
5053 __isl_take isl_point *pnt,
5054 enum isl_dim_type type, int pos,
5055 __isl_take isl_val *v);
5057 __isl_give isl_point *isl_point_add_ui(
5058 __isl_take isl_point *pnt,
5059 enum isl_dim_type type, int pos, unsigned val);
5060 __isl_give isl_point *isl_point_sub_ui(
5061 __isl_take isl_point *pnt,
5062 enum isl_dim_type type, int pos, unsigned val);
5064 Other properties can be obtained using
5066 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
5068 Points can be copied or freed using
5070 __isl_give isl_point *isl_point_copy(
5071 __isl_keep isl_point *pnt);
5072 void isl_point_free(__isl_take isl_point *pnt);
5074 A singleton set can be created from a point using
5076 __isl_give isl_basic_set *isl_basic_set_from_point(
5077 __isl_take isl_point *pnt);
5078 __isl_give isl_set *isl_set_from_point(
5079 __isl_take isl_point *pnt);
5081 and a box can be created from two opposite extremal points using
5083 __isl_give isl_basic_set *isl_basic_set_box_from_points(
5084 __isl_take isl_point *pnt1,
5085 __isl_take isl_point *pnt2);
5086 __isl_give isl_set *isl_set_box_from_points(
5087 __isl_take isl_point *pnt1,
5088 __isl_take isl_point *pnt2);
5090 All elements of a B<bounded> (union) set can be enumerated using
5091 the following functions.
5093 int isl_set_foreach_point(__isl_keep isl_set *set,
5094 int (*fn)(__isl_take isl_point *pnt, void *user),
5096 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
5097 int (*fn)(__isl_take isl_point *pnt, void *user),
5100 The function C<fn> is called for each integer point in
5101 C<set> with as second argument the last argument of
5102 the C<isl_set_foreach_point> call. The function C<fn>
5103 should return C<0> on success and C<-1> on failure.
5104 In the latter case, C<isl_set_foreach_point> will stop
5105 enumerating and return C<-1> as well.
5106 If the enumeration is performed successfully and to completion,
5107 then C<isl_set_foreach_point> returns C<0>.
5109 To obtain a single point of a (basic) set, use
5111 __isl_give isl_point *isl_basic_set_sample_point(
5112 __isl_take isl_basic_set *bset);
5113 __isl_give isl_point *isl_set_sample_point(
5114 __isl_take isl_set *set);
5116 If C<set> does not contain any (integer) points, then the
5117 resulting point will be ``void'', a property that can be
5120 int isl_point_is_void(__isl_keep isl_point *pnt);
5122 =head2 Piecewise Quasipolynomials
5124 A piecewise quasipolynomial is a particular kind of function that maps
5125 a parametric point to a rational value.
5126 More specifically, a quasipolynomial is a polynomial expression in greatest
5127 integer parts of affine expressions of parameters and variables.
5128 A piecewise quasipolynomial is a subdivision of a given parametric
5129 domain into disjoint cells with a quasipolynomial associated to
5130 each cell. The value of the piecewise quasipolynomial at a given
5131 point is the value of the quasipolynomial associated to the cell
5132 that contains the point. Outside of the union of cells,
5133 the value is assumed to be zero.
5134 For example, the piecewise quasipolynomial
5136 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
5138 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
5139 A given piecewise quasipolynomial has a fixed domain dimension.
5140 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
5141 defined over different domains.
5142 Piecewise quasipolynomials are mainly used by the C<barvinok>
5143 library for representing the number of elements in a parametric set or map.
5144 For example, the piecewise quasipolynomial above represents
5145 the number of points in the map
5147 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
5149 =head3 Input and Output
5151 Piecewise quasipolynomials can be read from input using
5153 __isl_give isl_union_pw_qpolynomial *
5154 isl_union_pw_qpolynomial_read_from_str(
5155 isl_ctx *ctx, const char *str);
5157 Quasipolynomials and piecewise quasipolynomials can be printed
5158 using the following functions.
5160 __isl_give isl_printer *isl_printer_print_qpolynomial(
5161 __isl_take isl_printer *p,
5162 __isl_keep isl_qpolynomial *qp);
5164 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
5165 __isl_take isl_printer *p,
5166 __isl_keep isl_pw_qpolynomial *pwqp);
5168 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
5169 __isl_take isl_printer *p,
5170 __isl_keep isl_union_pw_qpolynomial *upwqp);
5172 The output format of the printer
5173 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5174 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
5176 In case of printing in C<ISL_FORMAT_C>, the user may want
5177 to set the names of all dimensions
5179 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
5180 __isl_take isl_qpolynomial *qp,
5181 enum isl_dim_type type, unsigned pos,
5183 __isl_give isl_pw_qpolynomial *
5184 isl_pw_qpolynomial_set_dim_name(
5185 __isl_take isl_pw_qpolynomial *pwqp,
5186 enum isl_dim_type type, unsigned pos,
5189 =head3 Creating New (Piecewise) Quasipolynomials
5191 Some simple quasipolynomials can be created using the following functions.
5192 More complicated quasipolynomials can be created by applying
5193 operations such as addition and multiplication
5194 on the resulting quasipolynomials
5196 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
5197 __isl_take isl_space *domain);
5198 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
5199 __isl_take isl_space *domain);
5200 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
5201 __isl_take isl_space *domain);
5202 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
5203 __isl_take isl_space *domain);
5204 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
5205 __isl_take isl_space *domain);
5206 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
5207 __isl_take isl_space *domain,
5208 __isl_take isl_val *val);
5209 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
5210 __isl_take isl_space *domain,
5211 enum isl_dim_type type, unsigned pos);
5212 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
5213 __isl_take isl_aff *aff);
5215 Note that the space in which a quasipolynomial lives is a map space
5216 with a one-dimensional range. The C<domain> argument in some of
5217 the functions above corresponds to the domain of this map space.
5219 The zero piecewise quasipolynomial or a piecewise quasipolynomial
5220 with a single cell can be created using the following functions.
5221 Multiple of these single cell piecewise quasipolynomials can
5222 be combined to create more complicated piecewise quasipolynomials.
5224 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
5225 __isl_take isl_space *space);
5226 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
5227 __isl_take isl_set *set,
5228 __isl_take isl_qpolynomial *qp);
5229 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
5230 __isl_take isl_qpolynomial *qp);
5231 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
5232 __isl_take isl_pw_aff *pwaff);
5234 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
5235 __isl_take isl_space *space);
5236 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
5237 __isl_take isl_pw_qpolynomial *pwqp);
5238 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
5239 __isl_take isl_union_pw_qpolynomial *upwqp,
5240 __isl_take isl_pw_qpolynomial *pwqp);
5242 Quasipolynomials can be copied and freed again using the following
5245 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
5246 __isl_keep isl_qpolynomial *qp);
5247 __isl_null isl_qpolynomial *isl_qpolynomial_free(
5248 __isl_take isl_qpolynomial *qp);
5250 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
5251 __isl_keep isl_pw_qpolynomial *pwqp);
5252 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
5253 __isl_take isl_pw_qpolynomial *pwqp);
5255 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
5256 __isl_keep isl_union_pw_qpolynomial *upwqp);
5257 __isl_null isl_union_pw_qpolynomial *
5258 isl_union_pw_qpolynomial_free(
5259 __isl_take isl_union_pw_qpolynomial *upwqp);
5261 =head3 Inspecting (Piecewise) Quasipolynomials
5263 To iterate over all piecewise quasipolynomials in a union
5264 piecewise quasipolynomial, use the following function
5266 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
5267 __isl_keep isl_union_pw_qpolynomial *upwqp,
5268 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
5271 To extract the piecewise quasipolynomial in a given space from a union, use
5273 __isl_give isl_pw_qpolynomial *
5274 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
5275 __isl_keep isl_union_pw_qpolynomial *upwqp,
5276 __isl_take isl_space *space);
5278 To iterate over the cells in a piecewise quasipolynomial,
5279 use either of the following two functions
5281 int isl_pw_qpolynomial_foreach_piece(
5282 __isl_keep isl_pw_qpolynomial *pwqp,
5283 int (*fn)(__isl_take isl_set *set,
5284 __isl_take isl_qpolynomial *qp,
5285 void *user), void *user);
5286 int isl_pw_qpolynomial_foreach_lifted_piece(
5287 __isl_keep isl_pw_qpolynomial *pwqp,
5288 int (*fn)(__isl_take isl_set *set,
5289 __isl_take isl_qpolynomial *qp,
5290 void *user), void *user);
5292 As usual, the function C<fn> should return C<0> on success
5293 and C<-1> on failure. The difference between
5294 C<isl_pw_qpolynomial_foreach_piece> and
5295 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
5296 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
5297 compute unique representations for all existentially quantified
5298 variables and then turn these existentially quantified variables
5299 into extra set variables, adapting the associated quasipolynomial
5300 accordingly. This means that the C<set> passed to C<fn>
5301 will not have any existentially quantified variables, but that
5302 the dimensions of the sets may be different for different
5303 invocations of C<fn>.
5305 The constant term of a quasipolynomial can be extracted using
5307 __isl_give isl_val *isl_qpolynomial_get_constant_val(
5308 __isl_keep isl_qpolynomial *qp);
5310 To iterate over all terms in a quasipolynomial,
5313 int isl_qpolynomial_foreach_term(
5314 __isl_keep isl_qpolynomial *qp,
5315 int (*fn)(__isl_take isl_term *term,
5316 void *user), void *user);
5318 The terms themselves can be inspected and freed using
5321 unsigned isl_term_dim(__isl_keep isl_term *term,
5322 enum isl_dim_type type);
5323 __isl_give isl_val *isl_term_get_coefficient_val(
5324 __isl_keep isl_term *term);
5325 int isl_term_get_exp(__isl_keep isl_term *term,
5326 enum isl_dim_type type, unsigned pos);
5327 __isl_give isl_aff *isl_term_get_div(
5328 __isl_keep isl_term *term, unsigned pos);
5329 void isl_term_free(__isl_take isl_term *term);
5331 Each term is a product of parameters, set variables and
5332 integer divisions. The function C<isl_term_get_exp>
5333 returns the exponent of a given dimensions in the given term.
5335 =head3 Properties of (Piecewise) Quasipolynomials
5337 To check whether two union piecewise quasipolynomials are
5338 obviously equal, use
5340 int isl_union_pw_qpolynomial_plain_is_equal(
5341 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5342 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5344 =head3 Operations on (Piecewise) Quasipolynomials
5346 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5347 __isl_take isl_qpolynomial *qp,
5348 __isl_take isl_val *v);
5349 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5350 __isl_take isl_qpolynomial *qp);
5351 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5352 __isl_take isl_qpolynomial *qp1,
5353 __isl_take isl_qpolynomial *qp2);
5354 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5355 __isl_take isl_qpolynomial *qp1,
5356 __isl_take isl_qpolynomial *qp2);
5357 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5358 __isl_take isl_qpolynomial *qp1,
5359 __isl_take isl_qpolynomial *qp2);
5360 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5361 __isl_take isl_qpolynomial *qp, unsigned exponent);
5363 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5364 __isl_take isl_pw_qpolynomial *pwqp,
5365 enum isl_dim_type type, unsigned n,
5366 __isl_take isl_val *v);
5367 __isl_give isl_pw_qpolynomial *
5368 isl_pw_qpolynomial_scale_val(
5369 __isl_take isl_pw_qpolynomial *pwqp,
5370 __isl_take isl_val *v);
5371 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5372 __isl_take isl_pw_qpolynomial *pwqp1,
5373 __isl_take isl_pw_qpolynomial *pwqp2);
5374 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5375 __isl_take isl_pw_qpolynomial *pwqp1,
5376 __isl_take isl_pw_qpolynomial *pwqp2);
5377 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5378 __isl_take isl_pw_qpolynomial *pwqp1,
5379 __isl_take isl_pw_qpolynomial *pwqp2);
5380 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5381 __isl_take isl_pw_qpolynomial *pwqp);
5382 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5383 __isl_take isl_pw_qpolynomial *pwqp1,
5384 __isl_take isl_pw_qpolynomial *pwqp2);
5385 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5386 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5388 __isl_give isl_union_pw_qpolynomial *
5389 isl_union_pw_qpolynomial_scale_val(
5390 __isl_take isl_union_pw_qpolynomial *upwqp,
5391 __isl_take isl_val *v);
5392 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
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_sub(
5396 __isl_take isl_union_pw_qpolynomial *upwqp1,
5397 __isl_take isl_union_pw_qpolynomial *upwqp2);
5398 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5399 __isl_take isl_union_pw_qpolynomial *upwqp1,
5400 __isl_take isl_union_pw_qpolynomial *upwqp2);
5402 __isl_give isl_val *isl_pw_qpolynomial_eval(
5403 __isl_take isl_pw_qpolynomial *pwqp,
5404 __isl_take isl_point *pnt);
5406 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5407 __isl_take isl_union_pw_qpolynomial *upwqp,
5408 __isl_take isl_point *pnt);
5410 __isl_give isl_set *isl_pw_qpolynomial_domain(
5411 __isl_take isl_pw_qpolynomial *pwqp);
5412 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5413 __isl_take isl_pw_qpolynomial *pwpq,
5414 __isl_take isl_set *set);
5415 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5416 __isl_take isl_pw_qpolynomial *pwpq,
5417 __isl_take isl_set *set);
5419 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5420 __isl_take isl_union_pw_qpolynomial *upwqp);
5421 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5422 __isl_take isl_union_pw_qpolynomial *upwpq,
5423 __isl_take isl_union_set *uset);
5424 __isl_give isl_union_pw_qpolynomial *
5425 isl_union_pw_qpolynomial_intersect_params(
5426 __isl_take isl_union_pw_qpolynomial *upwpq,
5427 __isl_take isl_set *set);
5429 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5430 __isl_take isl_qpolynomial *qp,
5431 __isl_take isl_space *model);
5433 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5434 __isl_take isl_qpolynomial *qp);
5435 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5436 __isl_take isl_pw_qpolynomial *pwqp);
5438 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5439 __isl_take isl_union_pw_qpolynomial *upwqp);
5441 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5442 __isl_take isl_qpolynomial *qp,
5443 __isl_take isl_set *context);
5444 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5445 __isl_take isl_qpolynomial *qp,
5446 __isl_take isl_set *context);
5448 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5449 __isl_take isl_pw_qpolynomial *pwqp,
5450 __isl_take isl_set *context);
5451 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5452 __isl_take isl_pw_qpolynomial *pwqp,
5453 __isl_take isl_set *context);
5455 __isl_give isl_union_pw_qpolynomial *
5456 isl_union_pw_qpolynomial_gist_params(
5457 __isl_take isl_union_pw_qpolynomial *upwqp,
5458 __isl_take isl_set *context);
5459 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5460 __isl_take isl_union_pw_qpolynomial *upwqp,
5461 __isl_take isl_union_set *context);
5463 The gist operation applies the gist operation to each of
5464 the cells in the domain of the input piecewise quasipolynomial.
5465 The context is also exploited
5466 to simplify the quasipolynomials associated to each cell.
5468 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5469 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5470 __isl_give isl_union_pw_qpolynomial *
5471 isl_union_pw_qpolynomial_to_polynomial(
5472 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5474 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5475 the polynomial will be an overapproximation. If C<sign> is negative,
5476 it will be an underapproximation. If C<sign> is zero, the approximation
5477 will lie somewhere in between.
5479 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5481 A piecewise quasipolynomial reduction is a piecewise
5482 reduction (or fold) of quasipolynomials.
5483 In particular, the reduction can be maximum or a minimum.
5484 The objects are mainly used to represent the result of
5485 an upper or lower bound on a quasipolynomial over its domain,
5486 i.e., as the result of the following function.
5488 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5489 __isl_take isl_pw_qpolynomial *pwqp,
5490 enum isl_fold type, int *tight);
5492 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5493 __isl_take isl_union_pw_qpolynomial *upwqp,
5494 enum isl_fold type, int *tight);
5496 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5497 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5498 is the returned bound is known be tight, i.e., for each value
5499 of the parameters there is at least
5500 one element in the domain that reaches the bound.
5501 If the domain of C<pwqp> is not wrapping, then the bound is computed
5502 over all elements in that domain and the result has a purely parametric
5503 domain. If the domain of C<pwqp> is wrapping, then the bound is
5504 computed over the range of the wrapped relation. The domain of the
5505 wrapped relation becomes the domain of the result.
5507 A (piecewise) quasipolynomial reduction can be copied or freed using the
5508 following functions.
5510 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5511 __isl_keep isl_qpolynomial_fold *fold);
5512 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5513 __isl_keep isl_pw_qpolynomial_fold *pwf);
5514 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5515 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5516 void isl_qpolynomial_fold_free(
5517 __isl_take isl_qpolynomial_fold *fold);
5518 __isl_null isl_pw_qpolynomial_fold *
5519 isl_pw_qpolynomial_fold_free(
5520 __isl_take isl_pw_qpolynomial_fold *pwf);
5521 __isl_null isl_union_pw_qpolynomial_fold *
5522 isl_union_pw_qpolynomial_fold_free(
5523 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5525 =head3 Printing Piecewise Quasipolynomial Reductions
5527 Piecewise quasipolynomial reductions can be printed
5528 using the following function.
5530 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5531 __isl_take isl_printer *p,
5532 __isl_keep isl_pw_qpolynomial_fold *pwf);
5533 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5534 __isl_take isl_printer *p,
5535 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5537 For C<isl_printer_print_pw_qpolynomial_fold>,
5538 output format of the printer
5539 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5540 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5541 output format of the printer
5542 needs to be set to C<ISL_FORMAT_ISL>.
5543 In case of printing in C<ISL_FORMAT_C>, the user may want
5544 to set the names of all dimensions
5546 __isl_give isl_pw_qpolynomial_fold *
5547 isl_pw_qpolynomial_fold_set_dim_name(
5548 __isl_take isl_pw_qpolynomial_fold *pwf,
5549 enum isl_dim_type type, unsigned pos,
5552 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5554 To iterate over all piecewise quasipolynomial reductions in a union
5555 piecewise quasipolynomial reduction, use the following function
5557 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5558 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5559 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5560 void *user), void *user);
5562 To iterate over the cells in a piecewise quasipolynomial reduction,
5563 use either of the following two functions
5565 int isl_pw_qpolynomial_fold_foreach_piece(
5566 __isl_keep isl_pw_qpolynomial_fold *pwf,
5567 int (*fn)(__isl_take isl_set *set,
5568 __isl_take isl_qpolynomial_fold *fold,
5569 void *user), void *user);
5570 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5571 __isl_keep isl_pw_qpolynomial_fold *pwf,
5572 int (*fn)(__isl_take isl_set *set,
5573 __isl_take isl_qpolynomial_fold *fold,
5574 void *user), void *user);
5576 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5577 of the difference between these two functions.
5579 To iterate over all quasipolynomials in a reduction, use
5581 int isl_qpolynomial_fold_foreach_qpolynomial(
5582 __isl_keep isl_qpolynomial_fold *fold,
5583 int (*fn)(__isl_take isl_qpolynomial *qp,
5584 void *user), void *user);
5586 =head3 Properties of Piecewise Quasipolynomial Reductions
5588 To check whether two union piecewise quasipolynomial reductions are
5589 obviously equal, use
5591 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5592 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5593 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5595 =head3 Operations on Piecewise Quasipolynomial Reductions
5597 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5598 __isl_take isl_qpolynomial_fold *fold,
5599 __isl_take isl_val *v);
5600 __isl_give isl_pw_qpolynomial_fold *
5601 isl_pw_qpolynomial_fold_scale_val(
5602 __isl_take isl_pw_qpolynomial_fold *pwf,
5603 __isl_take isl_val *v);
5604 __isl_give isl_union_pw_qpolynomial_fold *
5605 isl_union_pw_qpolynomial_fold_scale_val(
5606 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5607 __isl_take isl_val *v);
5609 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5610 __isl_take isl_pw_qpolynomial_fold *pwf1,
5611 __isl_take isl_pw_qpolynomial_fold *pwf2);
5613 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5614 __isl_take isl_pw_qpolynomial_fold *pwf1,
5615 __isl_take isl_pw_qpolynomial_fold *pwf2);
5617 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5618 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5619 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5621 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5622 __isl_take isl_pw_qpolynomial_fold *pwf,
5623 __isl_take isl_point *pnt);
5625 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5626 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5627 __isl_take isl_point *pnt);
5629 __isl_give isl_pw_qpolynomial_fold *
5630 isl_pw_qpolynomial_fold_intersect_params(
5631 __isl_take isl_pw_qpolynomial_fold *pwf,
5632 __isl_take isl_set *set);
5634 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5635 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5636 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5637 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5638 __isl_take isl_union_set *uset);
5639 __isl_give isl_union_pw_qpolynomial_fold *
5640 isl_union_pw_qpolynomial_fold_intersect_params(
5641 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5642 __isl_take isl_set *set);
5644 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5645 __isl_take isl_pw_qpolynomial_fold *pwf);
5647 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5648 __isl_take isl_pw_qpolynomial_fold *pwf);
5650 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5651 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5653 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5654 __isl_take isl_qpolynomial_fold *fold,
5655 __isl_take isl_set *context);
5656 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5657 __isl_take isl_qpolynomial_fold *fold,
5658 __isl_take isl_set *context);
5660 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5661 __isl_take isl_pw_qpolynomial_fold *pwf,
5662 __isl_take isl_set *context);
5663 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5664 __isl_take isl_pw_qpolynomial_fold *pwf,
5665 __isl_take isl_set *context);
5667 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5668 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5669 __isl_take isl_union_set *context);
5670 __isl_give isl_union_pw_qpolynomial_fold *
5671 isl_union_pw_qpolynomial_fold_gist_params(
5672 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5673 __isl_take isl_set *context);
5675 The gist operation applies the gist operation to each of
5676 the cells in the domain of the input piecewise quasipolynomial reduction.
5677 In future, the operation will also exploit the context
5678 to simplify the quasipolynomial reductions associated to each cell.
5680 __isl_give isl_pw_qpolynomial_fold *
5681 isl_set_apply_pw_qpolynomial_fold(
5682 __isl_take isl_set *set,
5683 __isl_take isl_pw_qpolynomial_fold *pwf,
5685 __isl_give isl_pw_qpolynomial_fold *
5686 isl_map_apply_pw_qpolynomial_fold(
5687 __isl_take isl_map *map,
5688 __isl_take isl_pw_qpolynomial_fold *pwf,
5690 __isl_give isl_union_pw_qpolynomial_fold *
5691 isl_union_set_apply_union_pw_qpolynomial_fold(
5692 __isl_take isl_union_set *uset,
5693 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5695 __isl_give isl_union_pw_qpolynomial_fold *
5696 isl_union_map_apply_union_pw_qpolynomial_fold(
5697 __isl_take isl_union_map *umap,
5698 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5701 The functions taking a map
5702 compose the given map with the given piecewise quasipolynomial reduction.
5703 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5704 over all elements in the intersection of the range of the map
5705 and the domain of the piecewise quasipolynomial reduction
5706 as a function of an element in the domain of the map.
5707 The functions taking a set compute a bound over all elements in the
5708 intersection of the set and the domain of the
5709 piecewise quasipolynomial reduction.
5711 =head2 Parametric Vertex Enumeration
5713 The parametric vertex enumeration described in this section
5714 is mainly intended to be used internally and by the C<barvinok>
5717 #include <isl/vertices.h>
5718 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5719 __isl_keep isl_basic_set *bset);
5721 The function C<isl_basic_set_compute_vertices> performs the
5722 actual computation of the parametric vertices and the chamber
5723 decomposition and store the result in an C<isl_vertices> object.
5724 This information can be queried by either iterating over all
5725 the vertices or iterating over all the chambers or cells
5726 and then iterating over all vertices that are active on the chamber.
5728 int isl_vertices_foreach_vertex(
5729 __isl_keep isl_vertices *vertices,
5730 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5733 int isl_vertices_foreach_cell(
5734 __isl_keep isl_vertices *vertices,
5735 int (*fn)(__isl_take isl_cell *cell, void *user),
5737 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5738 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5741 Other operations that can be performed on an C<isl_vertices> object are
5744 isl_ctx *isl_vertices_get_ctx(
5745 __isl_keep isl_vertices *vertices);
5746 int isl_vertices_get_n_vertices(
5747 __isl_keep isl_vertices *vertices);
5748 void isl_vertices_free(__isl_take isl_vertices *vertices);
5750 Vertices can be inspected and destroyed using the following functions.
5752 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5753 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5754 __isl_give isl_basic_set *isl_vertex_get_domain(
5755 __isl_keep isl_vertex *vertex);
5756 __isl_give isl_multi_aff *isl_vertex_get_expr(
5757 __isl_keep isl_vertex *vertex);
5758 void isl_vertex_free(__isl_take isl_vertex *vertex);
5760 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
5761 describing the vertex in terms of the parameters,
5762 while C<isl_vertex_get_domain> returns the activity domain
5765 Chambers can be inspected and destroyed using the following functions.
5767 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5768 __isl_give isl_basic_set *isl_cell_get_domain(
5769 __isl_keep isl_cell *cell);
5770 void isl_cell_free(__isl_take isl_cell *cell);
5772 =head1 Polyhedral Compilation Library
5774 This section collects functionality in C<isl> that has been specifically
5775 designed for use during polyhedral compilation.
5777 =head2 Dependence Analysis
5779 C<isl> contains specialized functionality for performing
5780 array dataflow analysis. That is, given a I<sink> access relation
5781 and a collection of possible I<source> access relations,
5782 C<isl> can compute relations that describe
5783 for each iteration of the sink access, which iteration
5784 of which of the source access relations was the last
5785 to access the same data element before the given iteration
5787 The resulting dependence relations map source iterations
5788 to the corresponding sink iterations.
5789 To compute standard flow dependences, the sink should be
5790 a read, while the sources should be writes.
5791 If any of the source accesses are marked as being I<may>
5792 accesses, then there will be a dependence from the last
5793 I<must> access B<and> from any I<may> access that follows
5794 this last I<must> access.
5795 In particular, if I<all> sources are I<may> accesses,
5796 then memory based dependence analysis is performed.
5797 If, on the other hand, all sources are I<must> accesses,
5798 then value based dependence analysis is performed.
5800 #include <isl/flow.h>
5802 typedef int (*isl_access_level_before)(void *first, void *second);
5804 __isl_give isl_access_info *isl_access_info_alloc(
5805 __isl_take isl_map *sink,
5806 void *sink_user, isl_access_level_before fn,
5808 __isl_give isl_access_info *isl_access_info_add_source(
5809 __isl_take isl_access_info *acc,
5810 __isl_take isl_map *source, int must,
5812 __isl_null isl_access_info *isl_access_info_free(
5813 __isl_take isl_access_info *acc);
5815 __isl_give isl_flow *isl_access_info_compute_flow(
5816 __isl_take isl_access_info *acc);
5818 int isl_flow_foreach(__isl_keep isl_flow *deps,
5819 int (*fn)(__isl_take isl_map *dep, int must,
5820 void *dep_user, void *user),
5822 __isl_give isl_map *isl_flow_get_no_source(
5823 __isl_keep isl_flow *deps, int must);
5824 void isl_flow_free(__isl_take isl_flow *deps);
5826 The function C<isl_access_info_compute_flow> performs the actual
5827 dependence analysis. The other functions are used to construct
5828 the input for this function or to read off the output.
5830 The input is collected in an C<isl_access_info>, which can
5831 be created through a call to C<isl_access_info_alloc>.
5832 The arguments to this functions are the sink access relation
5833 C<sink>, a token C<sink_user> used to identify the sink
5834 access to the user, a callback function for specifying the
5835 relative order of source and sink accesses, and the number
5836 of source access relations that will be added.
5837 The callback function has type C<int (*)(void *first, void *second)>.
5838 The function is called with two user supplied tokens identifying
5839 either a source or the sink and it should return the shared nesting
5840 level and the relative order of the two accesses.
5841 In particular, let I<n> be the number of loops shared by
5842 the two accesses. If C<first> precedes C<second> textually,
5843 then the function should return I<2 * n + 1>; otherwise,
5844 it should return I<2 * n>.
5845 The sources can be added to the C<isl_access_info> by performing
5846 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5847 C<must> indicates whether the source is a I<must> access
5848 or a I<may> access. Note that a multi-valued access relation
5849 should only be marked I<must> if every iteration in the domain
5850 of the relation accesses I<all> elements in its image.
5851 The C<source_user> token is again used to identify
5852 the source access. The range of the source access relation
5853 C<source> should have the same dimension as the range
5854 of the sink access relation.
5855 The C<isl_access_info_free> function should usually not be
5856 called explicitly, because it is called implicitly by
5857 C<isl_access_info_compute_flow>.
5859 The result of the dependence analysis is collected in an
5860 C<isl_flow>. There may be elements of
5861 the sink access for which no preceding source access could be
5862 found or for which all preceding sources are I<may> accesses.
5863 The relations containing these elements can be obtained through
5864 calls to C<isl_flow_get_no_source>, the first with C<must> set
5865 and the second with C<must> unset.
5866 In the case of standard flow dependence analysis,
5867 with the sink a read and the sources I<must> writes,
5868 the first relation corresponds to the reads from uninitialized
5869 array elements and the second relation is empty.
5870 The actual flow dependences can be extracted using
5871 C<isl_flow_foreach>. This function will call the user-specified
5872 callback function C<fn> for each B<non-empty> dependence between
5873 a source and the sink. The callback function is called
5874 with four arguments, the actual flow dependence relation
5875 mapping source iterations to sink iterations, a boolean that
5876 indicates whether it is a I<must> or I<may> dependence, a token
5877 identifying the source and an additional C<void *> with value
5878 equal to the third argument of the C<isl_flow_foreach> call.
5879 A dependence is marked I<must> if it originates from a I<must>
5880 source and if it is not followed by any I<may> sources.
5882 After finishing with an C<isl_flow>, the user should call
5883 C<isl_flow_free> to free all associated memory.
5885 A higher-level interface to dependence analysis is provided
5886 by the following function.
5888 #include <isl/flow.h>
5890 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5891 __isl_take isl_union_map *must_source,
5892 __isl_take isl_union_map *may_source,
5893 __isl_take isl_union_map *schedule,
5894 __isl_give isl_union_map **must_dep,
5895 __isl_give isl_union_map **may_dep,
5896 __isl_give isl_union_map **must_no_source,
5897 __isl_give isl_union_map **may_no_source);
5899 The arrays are identified by the tuple names of the ranges
5900 of the accesses. The iteration domains by the tuple names
5901 of the domains of the accesses and of the schedule.
5902 The relative order of the iteration domains is given by the
5903 schedule. The relations returned through C<must_no_source>
5904 and C<may_no_source> are subsets of C<sink>.
5905 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5906 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5907 any of the other arguments is treated as an error.
5909 =head3 Interaction with Dependence Analysis
5911 During the dependence analysis, we frequently need to perform
5912 the following operation. Given a relation between sink iterations
5913 and potential source iterations from a particular source domain,
5914 what is the last potential source iteration corresponding to each
5915 sink iteration. It can sometimes be convenient to adjust
5916 the set of potential source iterations before or after each such operation.
5917 The prototypical example is fuzzy array dataflow analysis,
5918 where we need to analyze if, based on data-dependent constraints,
5919 the sink iteration can ever be executed without one or more of
5920 the corresponding potential source iterations being executed.
5921 If so, we can introduce extra parameters and select an unknown
5922 but fixed source iteration from the potential source iterations.
5923 To be able to perform such manipulations, C<isl> provides the following
5926 #include <isl/flow.h>
5928 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5929 __isl_keep isl_map *source_map,
5930 __isl_keep isl_set *sink, void *source_user,
5932 __isl_give isl_access_info *isl_access_info_set_restrict(
5933 __isl_take isl_access_info *acc,
5934 isl_access_restrict fn, void *user);
5936 The function C<isl_access_info_set_restrict> should be called
5937 before calling C<isl_access_info_compute_flow> and registers a callback function
5938 that will be called any time C<isl> is about to compute the last
5939 potential source. The first argument is the (reverse) proto-dependence,
5940 mapping sink iterations to potential source iterations.
5941 The second argument represents the sink iterations for which
5942 we want to compute the last source iteration.
5943 The third argument is the token corresponding to the source
5944 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5945 The callback is expected to return a restriction on either the input or
5946 the output of the operation computing the last potential source.
5947 If the input needs to be restricted then restrictions are needed
5948 for both the source and the sink iterations. The sink iterations
5949 and the potential source iterations will be intersected with these sets.
5950 If the output needs to be restricted then only a restriction on the source
5951 iterations is required.
5952 If any error occurs, the callback should return C<NULL>.
5953 An C<isl_restriction> object can be created, freed and inspected
5954 using the following functions.
5956 #include <isl/flow.h>
5958 __isl_give isl_restriction *isl_restriction_input(
5959 __isl_take isl_set *source_restr,
5960 __isl_take isl_set *sink_restr);
5961 __isl_give isl_restriction *isl_restriction_output(
5962 __isl_take isl_set *source_restr);
5963 __isl_give isl_restriction *isl_restriction_none(
5964 __isl_take isl_map *source_map);
5965 __isl_give isl_restriction *isl_restriction_empty(
5966 __isl_take isl_map *source_map);
5967 __isl_null isl_restriction *isl_restriction_free(
5968 __isl_take isl_restriction *restr);
5969 isl_ctx *isl_restriction_get_ctx(
5970 __isl_keep isl_restriction *restr);
5972 C<isl_restriction_none> and C<isl_restriction_empty> are special
5973 cases of C<isl_restriction_input>. C<isl_restriction_none>
5974 is essentially equivalent to
5976 isl_restriction_input(isl_set_universe(
5977 isl_space_range(isl_map_get_space(source_map))),
5979 isl_space_domain(isl_map_get_space(source_map))));
5981 whereas C<isl_restriction_empty> is essentially equivalent to
5983 isl_restriction_input(isl_set_empty(
5984 isl_space_range(isl_map_get_space(source_map))),
5986 isl_space_domain(isl_map_get_space(source_map))));
5990 B<The functionality described in this section is fairly new
5991 and may be subject to change.>
5993 #include <isl/schedule.h>
5994 __isl_give isl_schedule *
5995 isl_schedule_constraints_compute_schedule(
5996 __isl_take isl_schedule_constraints *sc);
5997 __isl_null isl_schedule *isl_schedule_free(
5998 __isl_take isl_schedule *sched);
6000 The function C<isl_schedule_constraints_compute_schedule> can be
6001 used to compute a schedule that satisfy the given schedule constraints.
6002 These schedule constraints include the iteration domain for which
6003 a schedule should be computed and dependences between pairs of
6004 iterations. In particular, these dependences include
6005 I<validity> dependences and I<proximity> dependences.
6006 By default, the algorithm used to construct the schedule is similar
6007 to that of C<Pluto>.
6008 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
6010 The generated schedule respects all validity dependences.
6011 That is, all dependence distances over these dependences in the
6012 scheduled space are lexicographically positive.
6013 The default algorithm tries to ensure that the dependence distances
6014 over coincidence constraints are zero and to minimize the
6015 dependence distances over proximity dependences.
6016 Moreover, it tries to obtain sequences (bands) of schedule dimensions
6017 for groups of domains where the dependence distances over validity
6018 dependences have only non-negative values.
6019 When using Feautrier's algorithm, the coincidence and proximity constraints
6020 are only taken into account during the extension to a
6021 full-dimensional schedule.
6023 An C<isl_schedule_constraints> object can be constructed
6024 and manipulated using the following functions.
6026 #include <isl/schedule.h>
6027 __isl_give isl_schedule_constraints *
6028 isl_schedule_constraints_copy(
6029 __isl_keep isl_schedule_constraints *sc);
6030 __isl_give isl_schedule_constraints *
6031 isl_schedule_constraints_on_domain(
6032 __isl_take isl_union_set *domain);
6033 isl_ctx *isl_schedule_constraints_get_ctx(
6034 __isl_keep isl_schedule_constraints *sc);
6035 __isl_give isl_schedule_constraints *
6036 isl_schedule_constraints_set_validity(
6037 __isl_take isl_schedule_constraints *sc,
6038 __isl_take isl_union_map *validity);
6039 __isl_give isl_schedule_constraints *
6040 isl_schedule_constraints_set_coincidence(
6041 __isl_take isl_schedule_constraints *sc,
6042 __isl_take isl_union_map *coincidence);
6043 __isl_give isl_schedule_constraints *
6044 isl_schedule_constraints_set_proximity(
6045 __isl_take isl_schedule_constraints *sc,
6046 __isl_take isl_union_map *proximity);
6047 __isl_give isl_schedule_constraints *
6048 isl_schedule_constraints_set_conditional_validity(
6049 __isl_take isl_schedule_constraints *sc,
6050 __isl_take isl_union_map *condition,
6051 __isl_take isl_union_map *validity);
6052 __isl_null isl_schedule_constraints *
6053 isl_schedule_constraints_free(
6054 __isl_take isl_schedule_constraints *sc);
6056 The initial C<isl_schedule_constraints> object created by
6057 C<isl_schedule_constraints_on_domain> does not impose any constraints.
6058 That is, it has an empty set of dependences.
6059 The function C<isl_schedule_constraints_set_validity> replaces the
6060 validity dependences, mapping domain elements I<i> to domain
6061 elements that should be scheduled after I<i>.
6062 The function C<isl_schedule_constraints_set_coincidence> replaces the
6063 coincidence dependences, mapping domain elements I<i> to domain
6064 elements that should be scheduled together with I<I>, if possible.
6065 The function C<isl_schedule_constraints_set_proximity> replaces the
6066 proximity dependences, mapping domain elements I<i> to domain
6067 elements that should be scheduled either before I<I>
6068 or as early as possible after I<i>.
6070 The function C<isl_schedule_constraints_set_conditional_validity>
6071 replaces the conditional validity constraints.
6072 A conditional validity constraint is only imposed when any of the corresponding
6073 conditions is satisfied, i.e., when any of them is non-zero.
6074 That is, the scheduler ensures that within each band if the dependence
6075 distances over the condition constraints are not all zero
6076 then all corresponding conditional validity constraints are respected.
6077 A conditional validity constraint corresponds to a condition
6078 if the two are adjacent, i.e., if the domain of one relation intersect
6079 the range of the other relation.
6080 The typical use case of conditional validity constraints is
6081 to allow order constraints between live ranges to be violated
6082 as long as the live ranges themselves are local to the band.
6083 To allow more fine-grained control over which conditions correspond
6084 to which conditional validity constraints, the domains and ranges
6085 of these relations may include I<tags>. That is, the domains and
6086 ranges of those relation may themselves be wrapped relations
6087 where the iteration domain appears in the domain of those wrapped relations
6088 and the range of the wrapped relations can be arbitrarily chosen
6089 by the user. Conditions and conditional validity constraints are only
6090 considere adjacent to each other if the entire wrapped relation matches.
6091 In particular, a relation with a tag will never be considered adjacent
6092 to a relation without a tag.
6094 The following function computes a schedule directly from
6095 an iteration domain and validity and proximity dependences
6096 and is implemented in terms of the functions described above.
6097 The use of C<isl_union_set_compute_schedule> is discouraged.
6099 #include <isl/schedule.h>
6100 __isl_give isl_schedule *isl_union_set_compute_schedule(
6101 __isl_take isl_union_set *domain,
6102 __isl_take isl_union_map *validity,
6103 __isl_take isl_union_map *proximity);
6105 A mapping from the domains to the scheduled space can be obtained
6106 from an C<isl_schedule> using the following function.
6108 __isl_give isl_union_map *isl_schedule_get_map(
6109 __isl_keep isl_schedule *sched);
6111 A representation of the schedule can be printed using
6113 __isl_give isl_printer *isl_printer_print_schedule(
6114 __isl_take isl_printer *p,
6115 __isl_keep isl_schedule *schedule);
6117 A representation of the schedule as a forest of bands can be obtained
6118 using the following function.
6120 __isl_give isl_band_list *isl_schedule_get_band_forest(
6121 __isl_keep isl_schedule *schedule);
6123 The individual bands can be visited in depth-first post-order
6124 using the following function.
6126 #include <isl/schedule.h>
6127 int isl_schedule_foreach_band(
6128 __isl_keep isl_schedule *sched,
6129 int (*fn)(__isl_keep isl_band *band, void *user),
6132 The list can be manipulated as explained in L<"Lists">.
6133 The bands inside the list can be copied and freed using the following
6136 #include <isl/band.h>
6137 __isl_give isl_band *isl_band_copy(
6138 __isl_keep isl_band *band);
6139 __isl_null isl_band *isl_band_free(
6140 __isl_take isl_band *band);
6142 Each band contains zero or more scheduling dimensions.
6143 These are referred to as the members of the band.
6144 The section of the schedule that corresponds to the band is
6145 referred to as the partial schedule of the band.
6146 For those nodes that participate in a band, the outer scheduling
6147 dimensions form the prefix schedule, while the inner scheduling
6148 dimensions form the suffix schedule.
6149 That is, if we take a cut of the band forest, then the union of
6150 the concatenations of the prefix, partial and suffix schedules of
6151 each band in the cut is equal to the entire schedule (modulo
6152 some possible padding at the end with zero scheduling dimensions).
6153 The properties of a band can be inspected using the following functions.
6155 #include <isl/band.h>
6156 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
6158 int isl_band_has_children(__isl_keep isl_band *band);
6159 __isl_give isl_band_list *isl_band_get_children(
6160 __isl_keep isl_band *band);
6162 __isl_give isl_union_map *isl_band_get_prefix_schedule(
6163 __isl_keep isl_band *band);
6164 __isl_give isl_union_map *isl_band_get_partial_schedule(
6165 __isl_keep isl_band *band);
6166 __isl_give isl_union_map *isl_band_get_suffix_schedule(
6167 __isl_keep isl_band *band);
6169 int isl_band_n_member(__isl_keep isl_band *band);
6170 int isl_band_member_is_coincident(
6171 __isl_keep isl_band *band, int pos);
6173 int isl_band_list_foreach_band(
6174 __isl_keep isl_band_list *list,
6175 int (*fn)(__isl_keep isl_band *band, void *user),
6178 Note that a scheduling dimension is considered to be ``coincident''
6179 if it satisfies the coincidence constraints within its band.
6180 That is, if the dependence distances of the coincidence
6181 constraints are all zero in that direction (for fixed
6182 iterations of outer bands).
6183 Like C<isl_schedule_foreach_band>,
6184 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
6185 in depth-first post-order.
6187 A band can be tiled using the following function.
6189 #include <isl/band.h>
6190 int isl_band_tile(__isl_keep isl_band *band,
6191 __isl_take isl_vec *sizes);
6193 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
6195 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
6196 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
6198 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
6200 The C<isl_band_tile> function tiles the band using the given tile sizes
6201 inside its schedule.
6202 A new child band is created to represent the point loops and it is
6203 inserted between the modified band and its children.
6204 The C<tile_scale_tile_loops> option specifies whether the tile
6205 loops iterators should be scaled by the tile sizes.
6206 If the C<tile_shift_point_loops> option is set, then the point loops
6207 are shifted to start at zero.
6209 A band can be split into two nested bands using the following function.
6211 int isl_band_split(__isl_keep isl_band *band, int pos);
6213 The resulting outer band contains the first C<pos> dimensions of C<band>
6214 while the inner band contains the remaining dimensions.
6216 A representation of the band can be printed using
6218 #include <isl/band.h>
6219 __isl_give isl_printer *isl_printer_print_band(
6220 __isl_take isl_printer *p,
6221 __isl_keep isl_band *band);
6225 #include <isl/schedule.h>
6226 int isl_options_set_schedule_max_coefficient(
6227 isl_ctx *ctx, int val);
6228 int isl_options_get_schedule_max_coefficient(
6230 int isl_options_set_schedule_max_constant_term(
6231 isl_ctx *ctx, int val);
6232 int isl_options_get_schedule_max_constant_term(
6234 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
6235 int isl_options_get_schedule_fuse(isl_ctx *ctx);
6236 int isl_options_set_schedule_maximize_band_depth(
6237 isl_ctx *ctx, int val);
6238 int isl_options_get_schedule_maximize_band_depth(
6240 int isl_options_set_schedule_outer_coincidence(
6241 isl_ctx *ctx, int val);
6242 int isl_options_get_schedule_outer_coincidence(
6244 int isl_options_set_schedule_split_scaled(
6245 isl_ctx *ctx, int val);
6246 int isl_options_get_schedule_split_scaled(
6248 int isl_options_set_schedule_algorithm(
6249 isl_ctx *ctx, int val);
6250 int isl_options_get_schedule_algorithm(
6252 int isl_options_set_schedule_separate_components(
6253 isl_ctx *ctx, int val);
6254 int isl_options_get_schedule_separate_components(
6259 =item * schedule_max_coefficient
6261 This option enforces that the coefficients for variable and parameter
6262 dimensions in the calculated schedule are not larger than the specified value.
6263 This option can significantly increase the speed of the scheduling calculation
6264 and may also prevent fusing of unrelated dimensions. A value of -1 means that
6265 this option does not introduce bounds on the variable or parameter
6268 =item * schedule_max_constant_term
6270 This option enforces that the constant coefficients in the calculated schedule
6271 are not larger than the maximal constant term. This option can significantly
6272 increase the speed of the scheduling calculation and may also prevent fusing of
6273 unrelated dimensions. A value of -1 means that this option does not introduce
6274 bounds on the constant coefficients.
6276 =item * schedule_fuse
6278 This option controls the level of fusion.
6279 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6280 resulting schedule will be distributed as much as possible.
6281 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6282 try to fuse loops in the resulting schedule.
6284 =item * schedule_maximize_band_depth
6286 If this option is set, we do not split bands at the point
6287 where we detect splitting is necessary. Instead, we
6288 backtrack and split bands as early as possible. This
6289 reduces the number of splits and maximizes the width of
6290 the bands. Wider bands give more possibilities for tiling.
6291 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6292 then bands will be split as early as possible, even if there is no need.
6293 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6295 =item * schedule_outer_coincidence
6297 If this option is set, then we try to construct schedules
6298 where the outermost scheduling dimension in each band
6299 satisfies the coincidence constraints.
6301 =item * schedule_split_scaled
6303 If this option is set, then we try to construct schedules in which the
6304 constant term is split off from the linear part if the linear parts of
6305 the scheduling rows for all nodes in the graphs have a common non-trivial
6307 The constant term is then placed in a separate band and the linear
6310 =item * schedule_algorithm
6312 Selects the scheduling algorithm to be used.
6313 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6314 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6316 =item * schedule_separate_components
6318 If at any point the dependence graph contains any (weakly connected) components,
6319 then these components are scheduled separately.
6320 If this option is not set, then some iterations of the domains
6321 in these components may be scheduled together.
6322 If this option is set, then the components are given consecutive
6327 =head2 AST Generation
6329 This section describes the C<isl> functionality for generating
6330 ASTs that visit all the elements
6331 in a domain in an order specified by a schedule.
6332 In particular, given a C<isl_union_map>, an AST is generated
6333 that visits all the elements in the domain of the C<isl_union_map>
6334 according to the lexicographic order of the corresponding image
6335 element(s). If the range of the C<isl_union_map> consists of
6336 elements in more than one space, then each of these spaces is handled
6337 separately in an arbitrary order.
6338 It should be noted that the image elements only specify the I<order>
6339 in which the corresponding domain elements should be visited.
6340 No direct relation between the image elements and the loop iterators
6341 in the generated AST should be assumed.
6343 Each AST is generated within a build. The initial build
6344 simply specifies the constraints on the parameters (if any)
6345 and can be created, inspected, copied and freed using the following functions.
6347 #include <isl/ast_build.h>
6348 __isl_give isl_ast_build *isl_ast_build_from_context(
6349 __isl_take isl_set *set);
6350 isl_ctx *isl_ast_build_get_ctx(
6351 __isl_keep isl_ast_build *build);
6352 __isl_give isl_ast_build *isl_ast_build_copy(
6353 __isl_keep isl_ast_build *build);
6354 __isl_null isl_ast_build *isl_ast_build_free(
6355 __isl_take isl_ast_build *build);
6357 The C<set> argument is usually a parameter set with zero or more parameters.
6358 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6359 and L</"Fine-grained Control over AST Generation">.
6360 Finally, the AST itself can be constructed using the following
6363 #include <isl/ast_build.h>
6364 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6365 __isl_keep isl_ast_build *build,
6366 __isl_take isl_union_map *schedule);
6368 =head3 Inspecting the AST
6370 The basic properties of an AST node can be obtained as follows.
6372 #include <isl/ast.h>
6373 isl_ctx *isl_ast_node_get_ctx(
6374 __isl_keep isl_ast_node *node);
6375 enum isl_ast_node_type isl_ast_node_get_type(
6376 __isl_keep isl_ast_node *node);
6378 The type of an AST node is one of
6379 C<isl_ast_node_for>,
6381 C<isl_ast_node_block> or
6382 C<isl_ast_node_user>.
6383 An C<isl_ast_node_for> represents a for node.
6384 An C<isl_ast_node_if> represents an if node.
6385 An C<isl_ast_node_block> represents a compound node.
6386 An C<isl_ast_node_user> represents an expression statement.
6387 An expression statement typically corresponds to a domain element, i.e.,
6388 one of the elements that is visited by the AST.
6390 Each type of node has its own additional properties.
6392 #include <isl/ast.h>
6393 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6394 __isl_keep isl_ast_node *node);
6395 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6396 __isl_keep isl_ast_node *node);
6397 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6398 __isl_keep isl_ast_node *node);
6399 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6400 __isl_keep isl_ast_node *node);
6401 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6402 __isl_keep isl_ast_node *node);
6403 int isl_ast_node_for_is_degenerate(
6404 __isl_keep isl_ast_node *node);
6406 An C<isl_ast_for> is considered degenerate if it is known to execute
6409 #include <isl/ast.h>
6410 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6411 __isl_keep isl_ast_node *node);
6412 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6413 __isl_keep isl_ast_node *node);
6414 int isl_ast_node_if_has_else(
6415 __isl_keep isl_ast_node *node);
6416 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6417 __isl_keep isl_ast_node *node);
6419 __isl_give isl_ast_node_list *
6420 isl_ast_node_block_get_children(
6421 __isl_keep isl_ast_node *node);
6423 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6424 __isl_keep isl_ast_node *node);
6426 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6427 the following functions.
6429 #include <isl/ast.h>
6430 isl_ctx *isl_ast_expr_get_ctx(
6431 __isl_keep isl_ast_expr *expr);
6432 enum isl_ast_expr_type isl_ast_expr_get_type(
6433 __isl_keep isl_ast_expr *expr);
6435 The type of an AST expression is one of
6437 C<isl_ast_expr_id> or
6438 C<isl_ast_expr_int>.
6439 An C<isl_ast_expr_op> represents the result of an operation.
6440 An C<isl_ast_expr_id> represents an identifier.
6441 An C<isl_ast_expr_int> represents an integer value.
6443 Each type of expression has its own additional properties.
6445 #include <isl/ast.h>
6446 enum isl_ast_op_type isl_ast_expr_get_op_type(
6447 __isl_keep isl_ast_expr *expr);
6448 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6449 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6450 __isl_keep isl_ast_expr *expr, int pos);
6451 int isl_ast_node_foreach_ast_op_type(
6452 __isl_keep isl_ast_node *node,
6453 int (*fn)(enum isl_ast_op_type type, void *user),
6456 C<isl_ast_expr_get_op_type> returns the type of the operation
6457 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6458 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6460 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6461 C<isl_ast_op_type> that appears in C<node>.
6462 The operation type is one of the following.
6466 =item C<isl_ast_op_and>
6468 Logical I<and> of two arguments.
6469 Both arguments can be evaluated.
6471 =item C<isl_ast_op_and_then>
6473 Logical I<and> of two arguments.
6474 The second argument can only be evaluated if the first evaluates to true.
6476 =item C<isl_ast_op_or>
6478 Logical I<or> of two arguments.
6479 Both arguments can be evaluated.
6481 =item C<isl_ast_op_or_else>
6483 Logical I<or> of two arguments.
6484 The second argument can only be evaluated if the first evaluates to false.
6486 =item C<isl_ast_op_max>
6488 Maximum of two or more arguments.
6490 =item C<isl_ast_op_min>
6492 Minimum of two or more arguments.
6494 =item C<isl_ast_op_minus>
6498 =item C<isl_ast_op_add>
6500 Sum of two arguments.
6502 =item C<isl_ast_op_sub>
6504 Difference of two arguments.
6506 =item C<isl_ast_op_mul>
6508 Product of two arguments.
6510 =item C<isl_ast_op_div>
6512 Exact division. That is, the result is known to be an integer.
6514 =item C<isl_ast_op_fdiv_q>
6516 Result of integer division, rounded towards negative
6519 =item C<isl_ast_op_pdiv_q>
6521 Result of integer division, where dividend is known to be non-negative.
6523 =item C<isl_ast_op_pdiv_r>
6525 Remainder of integer division, where dividend is known to be non-negative.
6527 =item C<isl_ast_op_cond>
6529 Conditional operator defined on three arguments.
6530 If the first argument evaluates to true, then the result
6531 is equal to the second argument. Otherwise, the result
6532 is equal to the third argument.
6533 The second and third argument may only be evaluated if
6534 the first argument evaluates to true and false, respectively.
6535 Corresponds to C<a ? b : c> in C.
6537 =item C<isl_ast_op_select>
6539 Conditional operator defined on three arguments.
6540 If the first argument evaluates to true, then the result
6541 is equal to the second argument. Otherwise, the result
6542 is equal to the third argument.
6543 The second and third argument may be evaluated independently
6544 of the value of the first argument.
6545 Corresponds to C<a * b + (1 - a) * c> in C.
6547 =item C<isl_ast_op_eq>
6551 =item C<isl_ast_op_le>
6553 Less than or equal relation.
6555 =item C<isl_ast_op_lt>
6559 =item C<isl_ast_op_ge>
6561 Greater than or equal relation.
6563 =item C<isl_ast_op_gt>
6565 Greater than relation.
6567 =item C<isl_ast_op_call>
6570 The number of arguments of the C<isl_ast_expr> is one more than
6571 the number of arguments in the function call, the first argument
6572 representing the function being called.
6574 =item C<isl_ast_op_access>
6577 The number of arguments of the C<isl_ast_expr> is one more than
6578 the number of index expressions in the array access, the first argument
6579 representing the array being accessed.
6581 =item C<isl_ast_op_member>
6584 This operation has two arguments, a structure and the name of
6585 the member of the structure being accessed.
6589 #include <isl/ast.h>
6590 __isl_give isl_id *isl_ast_expr_get_id(
6591 __isl_keep isl_ast_expr *expr);
6593 Return the identifier represented by the AST expression.
6595 #include <isl/ast.h>
6596 __isl_give isl_val *isl_ast_expr_get_val(
6597 __isl_keep isl_ast_expr *expr);
6599 Return the integer represented by the AST expression.
6601 =head3 Properties of ASTs
6603 #include <isl/ast.h>
6604 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6605 __isl_keep isl_ast_expr *expr2);
6607 Check if two C<isl_ast_expr>s are equal to each other.
6609 =head3 Manipulating and printing the AST
6611 AST nodes can be copied and freed using the following functions.
6613 #include <isl/ast.h>
6614 __isl_give isl_ast_node *isl_ast_node_copy(
6615 __isl_keep isl_ast_node *node);
6616 __isl_null isl_ast_node *isl_ast_node_free(
6617 __isl_take isl_ast_node *node);
6619 AST expressions can be copied and freed using the following functions.
6621 #include <isl/ast.h>
6622 __isl_give isl_ast_expr *isl_ast_expr_copy(
6623 __isl_keep isl_ast_expr *expr);
6624 __isl_null isl_ast_expr *isl_ast_expr_free(
6625 __isl_take isl_ast_expr *expr);
6627 New AST expressions can be created either directly or within
6628 the context of an C<isl_ast_build>.
6630 #include <isl/ast.h>
6631 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6632 __isl_take isl_val *v);
6633 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6634 __isl_take isl_id *id);
6635 __isl_give isl_ast_expr *isl_ast_expr_neg(
6636 __isl_take isl_ast_expr *expr);
6637 __isl_give isl_ast_expr *isl_ast_expr_add(
6638 __isl_take isl_ast_expr *expr1,
6639 __isl_take isl_ast_expr *expr2);
6640 __isl_give isl_ast_expr *isl_ast_expr_sub(
6641 __isl_take isl_ast_expr *expr1,
6642 __isl_take isl_ast_expr *expr2);
6643 __isl_give isl_ast_expr *isl_ast_expr_mul(
6644 __isl_take isl_ast_expr *expr1,
6645 __isl_take isl_ast_expr *expr2);
6646 __isl_give isl_ast_expr *isl_ast_expr_div(
6647 __isl_take isl_ast_expr *expr1,
6648 __isl_take isl_ast_expr *expr2);
6649 __isl_give isl_ast_expr *isl_ast_expr_and(
6650 __isl_take isl_ast_expr *expr1,
6651 __isl_take isl_ast_expr *expr2)
6652 __isl_give isl_ast_expr *isl_ast_expr_or(
6653 __isl_take isl_ast_expr *expr1,
6654 __isl_take isl_ast_expr *expr2)
6655 __isl_give isl_ast_expr *isl_ast_expr_access(
6656 __isl_take isl_ast_expr *array,
6657 __isl_take isl_ast_expr_list *indices);
6659 #include <isl/ast_build.h>
6660 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6661 __isl_keep isl_ast_build *build,
6662 __isl_take isl_pw_aff *pa);
6663 __isl_give isl_ast_expr *
6664 isl_ast_build_access_from_pw_multi_aff(
6665 __isl_keep isl_ast_build *build,
6666 __isl_take isl_pw_multi_aff *pma);
6667 __isl_give isl_ast_expr *
6668 isl_ast_build_access_from_multi_pw_aff(
6669 __isl_keep isl_ast_build *build,
6670 __isl_take isl_multi_pw_aff *mpa);
6671 __isl_give isl_ast_expr *
6672 isl_ast_build_call_from_pw_multi_aff(
6673 __isl_keep isl_ast_build *build,
6674 __isl_take isl_pw_multi_aff *pma);
6675 __isl_give isl_ast_expr *
6676 isl_ast_build_call_from_multi_pw_aff(
6677 __isl_keep isl_ast_build *build,
6678 __isl_take isl_multi_pw_aff *mpa);
6680 The domains of C<pa>, C<mpa> and C<pma> should correspond
6681 to the schedule space of C<build>.
6682 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6683 the function being called.
6684 If the accessed space is a nested relation, then it is taken
6685 to represent an access of the member specified by the range
6686 of this nested relation of the structure specified by the domain
6687 of the nested relation.
6689 The following functions can be used to modify an C<isl_ast_expr>.
6691 #include <isl/ast.h>
6692 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6693 __isl_take isl_ast_expr *expr, int pos,
6694 __isl_take isl_ast_expr *arg);
6696 Replace the argument of C<expr> at position C<pos> by C<arg>.
6698 #include <isl/ast.h>
6699 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6700 __isl_take isl_ast_expr *expr,
6701 __isl_take isl_id_to_ast_expr *id2expr);
6703 The function C<isl_ast_expr_substitute_ids> replaces the
6704 subexpressions of C<expr> of type C<isl_ast_expr_id>
6705 by the corresponding expression in C<id2expr>, if there is any.
6708 User specified data can be attached to an C<isl_ast_node> and obtained
6709 from the same C<isl_ast_node> using the following functions.
6711 #include <isl/ast.h>
6712 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6713 __isl_take isl_ast_node *node,
6714 __isl_take isl_id *annotation);
6715 __isl_give isl_id *isl_ast_node_get_annotation(
6716 __isl_keep isl_ast_node *node);
6718 Basic printing can be performed using the following functions.
6720 #include <isl/ast.h>
6721 __isl_give isl_printer *isl_printer_print_ast_expr(
6722 __isl_take isl_printer *p,
6723 __isl_keep isl_ast_expr *expr);
6724 __isl_give isl_printer *isl_printer_print_ast_node(
6725 __isl_take isl_printer *p,
6726 __isl_keep isl_ast_node *node);
6728 More advanced printing can be performed using the following functions.
6730 #include <isl/ast.h>
6731 __isl_give isl_printer *isl_ast_op_type_print_macro(
6732 enum isl_ast_op_type type,
6733 __isl_take isl_printer *p);
6734 __isl_give isl_printer *isl_ast_node_print_macros(
6735 __isl_keep isl_ast_node *node,
6736 __isl_take isl_printer *p);
6737 __isl_give isl_printer *isl_ast_node_print(
6738 __isl_keep isl_ast_node *node,
6739 __isl_take isl_printer *p,
6740 __isl_take isl_ast_print_options *options);
6741 __isl_give isl_printer *isl_ast_node_for_print(
6742 __isl_keep isl_ast_node *node,
6743 __isl_take isl_printer *p,
6744 __isl_take isl_ast_print_options *options);
6745 __isl_give isl_printer *isl_ast_node_if_print(
6746 __isl_keep isl_ast_node *node,
6747 __isl_take isl_printer *p,
6748 __isl_take isl_ast_print_options *options);
6750 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6751 C<isl> may print out an AST that makes use of macros such
6752 as C<floord>, C<min> and C<max>.
6753 C<isl_ast_op_type_print_macro> prints out the macro
6754 corresponding to a specific C<isl_ast_op_type>.
6755 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6756 for expressions where these macros would be used and prints
6757 out the required macro definitions.
6758 Essentially, C<isl_ast_node_print_macros> calls
6759 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6760 as function argument.
6761 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6762 C<isl_ast_node_if_print> print an C<isl_ast_node>
6763 in C<ISL_FORMAT_C>, but allow for some extra control
6764 through an C<isl_ast_print_options> object.
6765 This object can be created using the following functions.
6767 #include <isl/ast.h>
6768 __isl_give isl_ast_print_options *
6769 isl_ast_print_options_alloc(isl_ctx *ctx);
6770 __isl_give isl_ast_print_options *
6771 isl_ast_print_options_copy(
6772 __isl_keep isl_ast_print_options *options);
6773 __isl_null isl_ast_print_options *
6774 isl_ast_print_options_free(
6775 __isl_take isl_ast_print_options *options);
6777 __isl_give isl_ast_print_options *
6778 isl_ast_print_options_set_print_user(
6779 __isl_take isl_ast_print_options *options,
6780 __isl_give isl_printer *(*print_user)(
6781 __isl_take isl_printer *p,
6782 __isl_take isl_ast_print_options *options,
6783 __isl_keep isl_ast_node *node, void *user),
6785 __isl_give isl_ast_print_options *
6786 isl_ast_print_options_set_print_for(
6787 __isl_take isl_ast_print_options *options,
6788 __isl_give isl_printer *(*print_for)(
6789 __isl_take isl_printer *p,
6790 __isl_take isl_ast_print_options *options,
6791 __isl_keep isl_ast_node *node, void *user),
6794 The callback set by C<isl_ast_print_options_set_print_user>
6795 is called whenever a node of type C<isl_ast_node_user> needs to
6797 The callback set by C<isl_ast_print_options_set_print_for>
6798 is called whenever a node of type C<isl_ast_node_for> needs to
6800 Note that C<isl_ast_node_for_print> will I<not> call the
6801 callback set by C<isl_ast_print_options_set_print_for> on the node
6802 on which C<isl_ast_node_for_print> is called, but only on nested
6803 nodes of type C<isl_ast_node_for>. It is therefore safe to
6804 call C<isl_ast_node_for_print> from within the callback set by
6805 C<isl_ast_print_options_set_print_for>.
6807 The following option determines the type to be used for iterators
6808 while printing the AST.
6810 int isl_options_set_ast_iterator_type(
6811 isl_ctx *ctx, const char *val);
6812 const char *isl_options_get_ast_iterator_type(
6817 #include <isl/ast_build.h>
6818 int isl_options_set_ast_build_atomic_upper_bound(
6819 isl_ctx *ctx, int val);
6820 int isl_options_get_ast_build_atomic_upper_bound(
6822 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6824 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6825 int isl_options_set_ast_build_exploit_nested_bounds(
6826 isl_ctx *ctx, int val);
6827 int isl_options_get_ast_build_exploit_nested_bounds(
6829 int isl_options_set_ast_build_group_coscheduled(
6830 isl_ctx *ctx, int val);
6831 int isl_options_get_ast_build_group_coscheduled(
6833 int isl_options_set_ast_build_scale_strides(
6834 isl_ctx *ctx, int val);
6835 int isl_options_get_ast_build_scale_strides(
6837 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6839 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6840 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6842 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6846 =item * ast_build_atomic_upper_bound
6848 Generate loop upper bounds that consist of the current loop iterator,
6849 an operator and an expression not involving the iterator.
6850 If this option is not set, then the current loop iterator may appear
6851 several times in the upper bound.
6852 For example, when this option is turned off, AST generation
6855 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6859 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6862 When the option is turned on, the following AST is generated
6864 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6867 =item * ast_build_prefer_pdiv
6869 If this option is turned off, then the AST generation will
6870 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6871 operators, but no C<isl_ast_op_pdiv_q> or
6872 C<isl_ast_op_pdiv_r> operators.
6873 If this options is turned on, then C<isl> will try to convert
6874 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6875 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6877 =item * ast_build_exploit_nested_bounds
6879 Simplify conditions based on bounds of nested for loops.
6880 In particular, remove conditions that are implied by the fact
6881 that one or more nested loops have at least one iteration,
6882 meaning that the upper bound is at least as large as the lower bound.
6883 For example, when this option is turned off, AST generation
6886 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6892 for (int c0 = 0; c0 <= N; c0 += 1)
6893 for (int c1 = 0; c1 <= M; c1 += 1)
6896 When the option is turned on, the following AST is generated
6898 for (int c0 = 0; c0 <= N; c0 += 1)
6899 for (int c1 = 0; c1 <= M; c1 += 1)
6902 =item * ast_build_group_coscheduled
6904 If two domain elements are assigned the same schedule point, then
6905 they may be executed in any order and they may even appear in different
6906 loops. If this options is set, then the AST generator will make
6907 sure that coscheduled domain elements do not appear in separate parts
6908 of the AST. This is useful in case of nested AST generation
6909 if the outer AST generation is given only part of a schedule
6910 and the inner AST generation should handle the domains that are
6911 coscheduled by this initial part of the schedule together.
6912 For example if an AST is generated for a schedule
6914 { A[i] -> [0]; B[i] -> [0] }
6916 then the C<isl_ast_build_set_create_leaf> callback described
6917 below may get called twice, once for each domain.
6918 Setting this option ensures that the callback is only called once
6919 on both domains together.
6921 =item * ast_build_separation_bounds
6923 This option specifies which bounds to use during separation.
6924 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6925 then all (possibly implicit) bounds on the current dimension will
6926 be used during separation.
6927 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6928 then only those bounds that are explicitly available will
6929 be used during separation.
6931 =item * ast_build_scale_strides
6933 This option specifies whether the AST generator is allowed
6934 to scale down iterators of strided loops.
6936 =item * ast_build_allow_else
6938 This option specifies whether the AST generator is allowed
6939 to construct if statements with else branches.
6941 =item * ast_build_allow_or
6943 This option specifies whether the AST generator is allowed
6944 to construct if conditions with disjunctions.
6948 =head3 Fine-grained Control over AST Generation
6950 Besides specifying the constraints on the parameters,
6951 an C<isl_ast_build> object can be used to control
6952 various aspects of the AST generation process.
6953 The most prominent way of control is through ``options'',
6954 which can be set using the following function.
6956 #include <isl/ast_build.h>
6957 __isl_give isl_ast_build *
6958 isl_ast_build_set_options(
6959 __isl_take isl_ast_build *control,
6960 __isl_take isl_union_map *options);
6962 The options are encoded in an <isl_union_map>.
6963 The domain of this union relation refers to the schedule domain,
6964 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6965 In the case of nested AST generation (see L</"Nested AST Generation">),
6966 the domain of C<options> should refer to the extra piece of the schedule.
6967 That is, it should be equal to the range of the wrapped relation in the
6968 range of the schedule.
6969 The range of the options can consist of elements in one or more spaces,
6970 the names of which determine the effect of the option.
6971 The values of the range typically also refer to the schedule dimension
6972 to which the option applies. In case of nested AST generation
6973 (see L</"Nested AST Generation">), these values refer to the position
6974 of the schedule dimension within the innermost AST generation.
6975 The constraints on the domain elements of
6976 the option should only refer to this dimension and earlier dimensions.
6977 We consider the following spaces.
6981 =item C<separation_class>
6983 This space is a wrapped relation between two one dimensional spaces.
6984 The input space represents the schedule dimension to which the option
6985 applies and the output space represents the separation class.
6986 While constructing a loop corresponding to the specified schedule
6987 dimension(s), the AST generator will try to generate separate loops
6988 for domain elements that are assigned different classes.
6989 If only some of the elements are assigned a class, then those elements
6990 that are not assigned any class will be treated as belonging to a class
6991 that is separate from the explicitly assigned classes.
6992 The typical use case for this option is to separate full tiles from
6994 The other options, described below, are applied after the separation
6997 As an example, consider the separation into full and partial tiles
6998 of a tiling of a triangular domain.
6999 Take, for example, the domain
7001 { A[i,j] : 0 <= i,j and i + j <= 100 }
7003 and a tiling into tiles of 10 by 10. The input to the AST generator
7004 is then the schedule
7006 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
7009 Without any options, the following AST is generated
7011 for (int c0 = 0; c0 <= 10; c0 += 1)
7012 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
7013 for (int c2 = 10 * c0;
7014 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7016 for (int c3 = 10 * c1;
7017 c3 <= min(10 * c1 + 9, -c2 + 100);
7021 Separation into full and partial tiles can be obtained by assigning
7022 a class, say C<0>, to the full tiles. The full tiles are represented by those
7023 values of the first and second schedule dimensions for which there are
7024 values of the third and fourth dimensions to cover an entire tile.
7025 That is, we need to specify the following option
7027 { [a,b,c,d] -> separation_class[[0]->[0]] :
7028 exists b': 0 <= 10a,10b' and
7029 10a+9+10b'+9 <= 100;
7030 [a,b,c,d] -> separation_class[[1]->[0]] :
7031 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
7035 { [a, b, c, d] -> separation_class[[1] -> [0]] :
7036 a >= 0 and b >= 0 and b <= 8 - a;
7037 [a, b, c, d] -> separation_class[[0] -> [0]] :
7040 With this option, the generated AST is as follows
7043 for (int c0 = 0; c0 <= 8; c0 += 1) {
7044 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
7045 for (int c2 = 10 * c0;
7046 c2 <= 10 * c0 + 9; c2 += 1)
7047 for (int c3 = 10 * c1;
7048 c3 <= 10 * c1 + 9; c3 += 1)
7050 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
7051 for (int c2 = 10 * c0;
7052 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7054 for (int c3 = 10 * c1;
7055 c3 <= min(-c2 + 100, 10 * c1 + 9);
7059 for (int c0 = 9; c0 <= 10; c0 += 1)
7060 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
7061 for (int c2 = 10 * c0;
7062 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7064 for (int c3 = 10 * c1;
7065 c3 <= min(10 * c1 + 9, -c2 + 100);
7072 This is a single-dimensional space representing the schedule dimension(s)
7073 to which ``separation'' should be applied. Separation tries to split
7074 a loop into several pieces if this can avoid the generation of guards
7076 See also the C<atomic> option.
7080 This is a single-dimensional space representing the schedule dimension(s)
7081 for which the domains should be considered ``atomic''. That is, the
7082 AST generator will make sure that any given domain space will only appear
7083 in a single loop at the specified level.
7085 Consider the following schedule
7087 { a[i] -> [i] : 0 <= i < 10;
7088 b[i] -> [i+1] : 0 <= i < 10 }
7090 If the following option is specified
7092 { [i] -> separate[x] }
7094 then the following AST will be generated
7098 for (int c0 = 1; c0 <= 9; c0 += 1) {
7105 If, on the other hand, the following option is specified
7107 { [i] -> atomic[x] }
7109 then the following AST will be generated
7111 for (int c0 = 0; c0 <= 10; c0 += 1) {
7118 If neither C<atomic> nor C<separate> is specified, then the AST generator
7119 may produce either of these two results or some intermediate form.
7123 This is a single-dimensional space representing the schedule dimension(s)
7124 that should be I<completely> unrolled.
7125 To obtain a partial unrolling, the user should apply an additional
7126 strip-mining to the schedule and fully unroll the inner loop.
7130 Additional control is available through the following functions.
7132 #include <isl/ast_build.h>
7133 __isl_give isl_ast_build *
7134 isl_ast_build_set_iterators(
7135 __isl_take isl_ast_build *control,
7136 __isl_take isl_id_list *iterators);
7138 The function C<isl_ast_build_set_iterators> allows the user to
7139 specify a list of iterator C<isl_id>s to be used as iterators.
7140 If the input schedule is injective, then
7141 the number of elements in this list should be as large as the dimension
7142 of the schedule space, but no direct correspondence should be assumed
7143 between dimensions and elements.
7144 If the input schedule is not injective, then an additional number
7145 of C<isl_id>s equal to the largest dimension of the input domains
7147 If the number of provided C<isl_id>s is insufficient, then additional
7148 names are automatically generated.
7150 #include <isl/ast_build.h>
7151 __isl_give isl_ast_build *
7152 isl_ast_build_set_create_leaf(
7153 __isl_take isl_ast_build *control,
7154 __isl_give isl_ast_node *(*fn)(
7155 __isl_take isl_ast_build *build,
7156 void *user), void *user);
7159 C<isl_ast_build_set_create_leaf> function allows for the
7160 specification of a callback that should be called whenever the AST
7161 generator arrives at an element of the schedule domain.
7162 The callback should return an AST node that should be inserted
7163 at the corresponding position of the AST. The default action (when
7164 the callback is not set) is to continue generating parts of the AST to scan
7165 all the domain elements associated to the schedule domain element
7166 and to insert user nodes, ``calling'' the domain element, for each of them.
7167 The C<build> argument contains the current state of the C<isl_ast_build>.
7168 To ease nested AST generation (see L</"Nested AST Generation">),
7169 all control information that is
7170 specific to the current AST generation such as the options and
7171 the callbacks has been removed from this C<isl_ast_build>.
7172 The callback would typically return the result of a nested
7174 user defined node created using the following function.
7176 #include <isl/ast.h>
7177 __isl_give isl_ast_node *isl_ast_node_alloc_user(
7178 __isl_take isl_ast_expr *expr);
7180 #include <isl/ast_build.h>
7181 __isl_give isl_ast_build *
7182 isl_ast_build_set_at_each_domain(
7183 __isl_take isl_ast_build *build,
7184 __isl_give isl_ast_node *(*fn)(
7185 __isl_take isl_ast_node *node,
7186 __isl_keep isl_ast_build *build,
7187 void *user), void *user);
7188 __isl_give isl_ast_build *
7189 isl_ast_build_set_before_each_for(
7190 __isl_take isl_ast_build *build,
7191 __isl_give isl_id *(*fn)(
7192 __isl_keep isl_ast_build *build,
7193 void *user), void *user);
7194 __isl_give isl_ast_build *
7195 isl_ast_build_set_after_each_for(
7196 __isl_take isl_ast_build *build,
7197 __isl_give isl_ast_node *(*fn)(
7198 __isl_take isl_ast_node *node,
7199 __isl_keep isl_ast_build *build,
7200 void *user), void *user);
7202 The callback set by C<isl_ast_build_set_at_each_domain> will
7203 be called for each domain AST node.
7204 The callbacks set by C<isl_ast_build_set_before_each_for>
7205 and C<isl_ast_build_set_after_each_for> will be called
7206 for each for AST node. The first will be called in depth-first
7207 pre-order, while the second will be called in depth-first post-order.
7208 Since C<isl_ast_build_set_before_each_for> is called before the for
7209 node is actually constructed, it is only passed an C<isl_ast_build>.
7210 The returned C<isl_id> will be added as an annotation (using
7211 C<isl_ast_node_set_annotation>) to the constructed for node.
7212 In particular, if the user has also specified an C<after_each_for>
7213 callback, then the annotation can be retrieved from the node passed to
7214 that callback using C<isl_ast_node_get_annotation>.
7215 All callbacks should C<NULL> on failure.
7216 The given C<isl_ast_build> can be used to create new
7217 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
7218 or C<isl_ast_build_call_from_pw_multi_aff>.
7220 =head3 Nested AST Generation
7222 C<isl> allows the user to create an AST within the context
7223 of another AST. These nested ASTs are created using the
7224 same C<isl_ast_build_ast_from_schedule> function that is used to create the
7225 outer AST. The C<build> argument should be an C<isl_ast_build>
7226 passed to a callback set by
7227 C<isl_ast_build_set_create_leaf>.
7228 The space of the range of the C<schedule> argument should refer
7229 to this build. In particular, the space should be a wrapped
7230 relation and the domain of this wrapped relation should be the
7231 same as that of the range of the schedule returned by
7232 C<isl_ast_build_get_schedule> below.
7233 In practice, the new schedule is typically
7234 created by calling C<isl_union_map_range_product> on the old schedule
7235 and some extra piece of the schedule.
7236 The space of the schedule domain is also available from
7237 the C<isl_ast_build>.
7239 #include <isl/ast_build.h>
7240 __isl_give isl_union_map *isl_ast_build_get_schedule(
7241 __isl_keep isl_ast_build *build);
7242 __isl_give isl_space *isl_ast_build_get_schedule_space(
7243 __isl_keep isl_ast_build *build);
7244 __isl_give isl_ast_build *isl_ast_build_restrict(
7245 __isl_take isl_ast_build *build,
7246 __isl_take isl_set *set);
7248 The C<isl_ast_build_get_schedule> function returns a (partial)
7249 schedule for the domains elements for which part of the AST still needs to
7250 be generated in the current build.
7251 In particular, the domain elements are mapped to those iterations of the loops
7252 enclosing the current point of the AST generation inside which
7253 the domain elements are executed.
7254 No direct correspondence between
7255 the input schedule and this schedule should be assumed.
7256 The space obtained from C<isl_ast_build_get_schedule_space> can be used
7257 to create a set for C<isl_ast_build_restrict> to intersect
7258 with the current build. In particular, the set passed to
7259 C<isl_ast_build_restrict> can have additional parameters.
7260 The ids of the set dimensions in the space returned by
7261 C<isl_ast_build_get_schedule_space> correspond to the
7262 iterators of the already generated loops.
7263 The user should not rely on the ids of the output dimensions
7264 of the relations in the union relation returned by
7265 C<isl_ast_build_get_schedule> having any particular value.
7269 Although C<isl> is mainly meant to be used as a library,
7270 it also contains some basic applications that use some
7271 of the functionality of C<isl>.
7272 The input may be specified in either the L<isl format>
7273 or the L<PolyLib format>.
7275 =head2 C<isl_polyhedron_sample>
7277 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7278 an integer element of the polyhedron, if there is any.
7279 The first column in the output is the denominator and is always
7280 equal to 1. If the polyhedron contains no integer points,
7281 then a vector of length zero is printed.
7285 C<isl_pip> takes the same input as the C<example> program
7286 from the C<piplib> distribution, i.e., a set of constraints
7287 on the parameters, a line containing only -1 and finally a set
7288 of constraints on a parametric polyhedron.
7289 The coefficients of the parameters appear in the last columns
7290 (but before the final constant column).
7291 The output is the lexicographic minimum of the parametric polyhedron.
7292 As C<isl> currently does not have its own output format, the output
7293 is just a dump of the internal state.
7295 =head2 C<isl_polyhedron_minimize>
7297 C<isl_polyhedron_minimize> computes the minimum of some linear
7298 or affine objective function over the integer points in a polyhedron.
7299 If an affine objective function
7300 is given, then the constant should appear in the last column.
7302 =head2 C<isl_polytope_scan>
7304 Given a polytope, C<isl_polytope_scan> prints
7305 all integer points in the polytope.
7307 =head2 C<isl_codegen>
7309 Given a schedule, a context set and an options relation,
7310 C<isl_codegen> prints out an AST that scans the domain elements
7311 of the schedule in the order of their image(s) taking into account
7312 the constraints in the context set.