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_foreach_constraint(
1705 __isl_keep isl_basic_map *bmap,
1706 int (*fn)(__isl_take isl_constraint *c, void *user),
1708 __isl_null isl_constraint *isl_constraint_free(
1709 __isl_take isl_constraint *c);
1711 Again, the callback function C<fn> should return 0 if successful and
1712 -1 if an error occurs. In the latter case, or if any other error
1713 occurs, the above functions will return -1.
1714 The constraint C<c> represents either an equality or an inequality.
1715 Use the following function to find out whether a constraint
1716 represents an equality. If not, it represents an inequality.
1718 int isl_constraint_is_equality(
1719 __isl_keep isl_constraint *constraint);
1721 The coefficients of the constraints can be inspected using
1722 the following functions.
1724 int isl_constraint_is_lower_bound(
1725 __isl_keep isl_constraint *constraint,
1726 enum isl_dim_type type, unsigned pos);
1727 int isl_constraint_is_upper_bound(
1728 __isl_keep isl_constraint *constraint,
1729 enum isl_dim_type type, unsigned pos);
1730 __isl_give isl_val *isl_constraint_get_constant_val(
1731 __isl_keep isl_constraint *constraint);
1732 __isl_give isl_val *isl_constraint_get_coefficient_val(
1733 __isl_keep isl_constraint *constraint,
1734 enum isl_dim_type type, int pos);
1735 int isl_constraint_involves_dims(
1736 __isl_keep isl_constraint *constraint,
1737 enum isl_dim_type type, unsigned first, unsigned n);
1739 The explicit representations of the existentially quantified
1740 variables can be inspected using the following function.
1741 Note that the user is only allowed to use this function
1742 if the inspected set or map is the result of a call
1743 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1744 The existentially quantified variable is equal to the floor
1745 of the returned affine expression. The affine expression
1746 itself can be inspected using the functions in
1747 L<"Piecewise Quasi Affine Expressions">.
1749 __isl_give isl_aff *isl_constraint_get_div(
1750 __isl_keep isl_constraint *constraint, int pos);
1752 To obtain the constraints of a basic set or map in matrix
1753 form, use the following functions.
1755 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1756 __isl_keep isl_basic_set *bset,
1757 enum isl_dim_type c1, enum isl_dim_type c2,
1758 enum isl_dim_type c3, enum isl_dim_type c4);
1759 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1760 __isl_keep isl_basic_set *bset,
1761 enum isl_dim_type c1, enum isl_dim_type c2,
1762 enum isl_dim_type c3, enum isl_dim_type c4);
1763 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1764 __isl_keep isl_basic_map *bmap,
1765 enum isl_dim_type c1,
1766 enum isl_dim_type c2, enum isl_dim_type c3,
1767 enum isl_dim_type c4, enum isl_dim_type c5);
1768 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1769 __isl_keep isl_basic_map *bmap,
1770 enum isl_dim_type c1,
1771 enum isl_dim_type c2, enum isl_dim_type c3,
1772 enum isl_dim_type c4, enum isl_dim_type c5);
1774 The C<isl_dim_type> arguments dictate the order in which
1775 different kinds of variables appear in the resulting matrix
1776 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1777 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1779 The number of parameters, input, output or set dimensions can
1780 be obtained using the following functions.
1782 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1783 enum isl_dim_type type);
1784 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1785 enum isl_dim_type type);
1786 unsigned isl_set_dim(__isl_keep isl_set *set,
1787 enum isl_dim_type type);
1788 unsigned isl_map_dim(__isl_keep isl_map *map,
1789 enum isl_dim_type type);
1790 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1791 enum isl_dim_type type);
1793 Note that a C<isl_union_map> only has parameters.
1795 To check whether the description of a set or relation depends
1796 on one or more given dimensions, it is not necessary to iterate over all
1797 constraints. Instead the following functions can be used.
1799 int isl_basic_set_involves_dims(
1800 __isl_keep isl_basic_set *bset,
1801 enum isl_dim_type type, unsigned first, unsigned n);
1802 int isl_set_involves_dims(__isl_keep isl_set *set,
1803 enum isl_dim_type type, unsigned first, unsigned n);
1804 int isl_basic_map_involves_dims(
1805 __isl_keep isl_basic_map *bmap,
1806 enum isl_dim_type type, unsigned first, unsigned n);
1807 int isl_map_involves_dims(__isl_keep isl_map *map,
1808 enum isl_dim_type type, unsigned first, unsigned n);
1810 Similarly, the following functions can be used to check whether
1811 a given dimension is involved in any lower or upper bound.
1813 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1814 enum isl_dim_type type, unsigned pos);
1815 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1816 enum isl_dim_type type, unsigned pos);
1818 Note that these functions return true even if there is a bound on
1819 the dimension on only some of the basic sets of C<set>.
1820 To check if they have a bound for all of the basic sets in C<set>,
1821 use the following functions instead.
1823 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1824 enum isl_dim_type type, unsigned pos);
1825 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1826 enum isl_dim_type type, unsigned pos);
1828 The identifiers or names of the domain and range spaces of a set
1829 or relation can be read off or set using the following functions.
1831 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1832 __isl_take isl_basic_set *bset,
1833 __isl_take isl_id *id);
1834 __isl_give isl_set *isl_set_set_tuple_id(
1835 __isl_take isl_set *set, __isl_take isl_id *id);
1836 __isl_give isl_set *isl_set_reset_tuple_id(
1837 __isl_take isl_set *set);
1838 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1839 __isl_give isl_id *isl_set_get_tuple_id(
1840 __isl_keep isl_set *set);
1841 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1842 __isl_take isl_basic_map *bmap,
1843 enum isl_dim_type type, __isl_take isl_id *id);
1844 __isl_give isl_map *isl_map_set_tuple_id(
1845 __isl_take isl_map *map, enum isl_dim_type type,
1846 __isl_take isl_id *id);
1847 __isl_give isl_map *isl_map_reset_tuple_id(
1848 __isl_take isl_map *map, enum isl_dim_type type);
1849 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1850 enum isl_dim_type type);
1851 __isl_give isl_id *isl_map_get_tuple_id(
1852 __isl_keep isl_map *map, enum isl_dim_type type);
1854 const char *isl_basic_set_get_tuple_name(
1855 __isl_keep isl_basic_set *bset);
1856 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1857 __isl_take isl_basic_set *set, const char *s);
1858 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1859 const char *isl_set_get_tuple_name(
1860 __isl_keep isl_set *set);
1861 __isl_give isl_set *isl_set_set_tuple_name(
1862 __isl_take isl_set *set, const char *s);
1863 const char *isl_basic_map_get_tuple_name(
1864 __isl_keep isl_basic_map *bmap,
1865 enum isl_dim_type type);
1866 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1867 __isl_take isl_basic_map *bmap,
1868 enum isl_dim_type type, const char *s);
1869 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1870 enum isl_dim_type type);
1871 const char *isl_map_get_tuple_name(
1872 __isl_keep isl_map *map,
1873 enum isl_dim_type type);
1874 __isl_give isl_map *isl_map_set_tuple_name(
1875 __isl_take isl_map *map,
1876 enum isl_dim_type type, const char *s);
1878 As with C<isl_space_get_tuple_name>, the value returned points to
1879 an internal data structure.
1880 The identifiers, positions or names of individual dimensions can be
1881 read off using the following functions.
1883 __isl_give isl_id *isl_basic_set_get_dim_id(
1884 __isl_keep isl_basic_set *bset,
1885 enum isl_dim_type type, unsigned pos);
1886 __isl_give isl_set *isl_set_set_dim_id(
1887 __isl_take isl_set *set, enum isl_dim_type type,
1888 unsigned pos, __isl_take isl_id *id);
1889 int isl_set_has_dim_id(__isl_keep isl_set *set,
1890 enum isl_dim_type type, unsigned pos);
1891 __isl_give isl_id *isl_set_get_dim_id(
1892 __isl_keep isl_set *set, enum isl_dim_type type,
1894 int isl_basic_map_has_dim_id(
1895 __isl_keep isl_basic_map *bmap,
1896 enum isl_dim_type type, unsigned pos);
1897 __isl_give isl_map *isl_map_set_dim_id(
1898 __isl_take isl_map *map, enum isl_dim_type type,
1899 unsigned pos, __isl_take isl_id *id);
1900 int isl_map_has_dim_id(__isl_keep isl_map *map,
1901 enum isl_dim_type type, unsigned pos);
1902 __isl_give isl_id *isl_map_get_dim_id(
1903 __isl_keep isl_map *map, enum isl_dim_type type,
1905 __isl_give isl_id *isl_union_map_get_dim_id(
1906 __isl_keep isl_union_map *umap,
1907 enum isl_dim_type type, unsigned pos);
1909 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1910 enum isl_dim_type type, __isl_keep isl_id *id);
1911 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1912 enum isl_dim_type type, __isl_keep isl_id *id);
1913 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1914 enum isl_dim_type type, const char *name);
1915 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1916 enum isl_dim_type type, const char *name);
1918 const char *isl_constraint_get_dim_name(
1919 __isl_keep isl_constraint *constraint,
1920 enum isl_dim_type type, unsigned pos);
1921 const char *isl_basic_set_get_dim_name(
1922 __isl_keep isl_basic_set *bset,
1923 enum isl_dim_type type, unsigned pos);
1924 int isl_set_has_dim_name(__isl_keep isl_set *set,
1925 enum isl_dim_type type, unsigned pos);
1926 const char *isl_set_get_dim_name(
1927 __isl_keep isl_set *set,
1928 enum isl_dim_type type, unsigned pos);
1929 const char *isl_basic_map_get_dim_name(
1930 __isl_keep isl_basic_map *bmap,
1931 enum isl_dim_type type, unsigned pos);
1932 int isl_map_has_dim_name(__isl_keep isl_map *map,
1933 enum isl_dim_type type, unsigned pos);
1934 const char *isl_map_get_dim_name(
1935 __isl_keep isl_map *map,
1936 enum isl_dim_type type, unsigned pos);
1938 These functions are mostly useful to obtain the identifiers, positions
1939 or names of the parameters. Identifiers of individual dimensions are
1940 essentially only useful for printing. They are ignored by all other
1941 operations and may not be preserved across those operations.
1943 The user pointers on all parameters and tuples can be reset
1944 using the following functions.
1946 #include <isl/set.h>
1947 __isl_give isl_set *isl_set_reset_user(
1948 __isl_take isl_set *set);
1949 #include <isl/map.h>
1950 __isl_give isl_map *isl_map_reset_user(
1951 __isl_take isl_map *map);
1952 #include <isl/union_set.h>
1953 __isl_give isl_union_set *isl_union_set_reset_user(
1954 __isl_take isl_union_set *uset);
1955 #include <isl/union_map.h>
1956 __isl_give isl_union_map *isl_union_map_reset_user(
1957 __isl_take isl_union_map *umap);
1961 =head3 Unary Properties
1967 The following functions test whether the given set or relation
1968 contains any integer points. The ``plain'' variants do not perform
1969 any computations, but simply check if the given set or relation
1970 is already known to be empty.
1972 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1973 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1974 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1975 int isl_set_is_empty(__isl_keep isl_set *set);
1976 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1977 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1978 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1979 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1980 int isl_map_is_empty(__isl_keep isl_map *map);
1981 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1983 =item * Universality
1985 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1986 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1987 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1989 =item * Single-valuedness
1991 int isl_basic_map_is_single_valued(
1992 __isl_keep isl_basic_map *bmap);
1993 int isl_map_plain_is_single_valued(
1994 __isl_keep isl_map *map);
1995 int isl_map_is_single_valued(__isl_keep isl_map *map);
1996 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
2000 int isl_map_plain_is_injective(__isl_keep isl_map *map);
2001 int isl_map_is_injective(__isl_keep isl_map *map);
2002 int isl_union_map_plain_is_injective(
2003 __isl_keep isl_union_map *umap);
2004 int isl_union_map_is_injective(
2005 __isl_keep isl_union_map *umap);
2009 int isl_map_is_bijective(__isl_keep isl_map *map);
2010 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
2014 __isl_give isl_val *
2015 isl_basic_map_plain_get_val_if_fixed(
2016 __isl_keep isl_basic_map *bmap,
2017 enum isl_dim_type type, unsigned pos);
2018 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
2019 __isl_keep isl_set *set,
2020 enum isl_dim_type type, unsigned pos);
2021 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
2022 __isl_keep isl_map *map,
2023 enum isl_dim_type type, unsigned pos);
2025 If the set or relation obviously lies on a hyperplane where the given dimension
2026 has a fixed value, then return that value.
2027 Otherwise return NaN.
2031 int isl_set_dim_residue_class_val(
2032 __isl_keep isl_set *set,
2033 int pos, __isl_give isl_val **modulo,
2034 __isl_give isl_val **residue);
2036 Check if the values of the given set dimension are equal to a fixed
2037 value modulo some integer value. If so, assign the modulo to C<*modulo>
2038 and the fixed value to C<*residue>. If the given dimension attains only
2039 a single value, then assign C<0> to C<*modulo> and the fixed value to
2041 If the dimension does not attain only a single value and if no modulo
2042 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
2046 To check whether a set is a parameter domain, use this function:
2048 int isl_set_is_params(__isl_keep isl_set *set);
2049 int isl_union_set_is_params(
2050 __isl_keep isl_union_set *uset);
2054 The following functions check whether the space of the given
2055 (basic) set or relation range is a wrapped relation.
2057 #include <isl/space.h>
2058 int isl_space_is_wrapping(
2059 __isl_keep isl_space *space);
2060 int isl_space_domain_is_wrapping(
2061 __isl_keep isl_space *space);
2062 int isl_space_range_is_wrapping(
2063 __isl_keep isl_space *space);
2065 #include <isl/set.h>
2066 int isl_basic_set_is_wrapping(
2067 __isl_keep isl_basic_set *bset);
2068 int isl_set_is_wrapping(__isl_keep isl_set *set);
2070 #include <isl/map.h>
2071 int isl_map_domain_is_wrapping(
2072 __isl_keep isl_map *map);
2073 int isl_map_range_is_wrapping(
2074 __isl_keep isl_map *map);
2076 The input to C<isl_space_is_wrapping> should
2077 be the space of a set, while that of
2078 C<isl_space_domain_is_wrapping> and
2079 C<isl_space_range_is_wrapping> should be the space of a relation.
2081 =item * Internal Product
2083 int isl_basic_map_can_zip(
2084 __isl_keep isl_basic_map *bmap);
2085 int isl_map_can_zip(__isl_keep isl_map *map);
2087 Check whether the product of domain and range of the given relation
2089 i.e., whether both domain and range are nested relations.
2093 int isl_basic_map_can_curry(
2094 __isl_keep isl_basic_map *bmap);
2095 int isl_map_can_curry(__isl_keep isl_map *map);
2097 Check whether the domain of the (basic) relation is a wrapped relation.
2099 int isl_basic_map_can_uncurry(
2100 __isl_keep isl_basic_map *bmap);
2101 int isl_map_can_uncurry(__isl_keep isl_map *map);
2103 Check whether the range of the (basic) relation is a wrapped relation.
2107 =head3 Binary Properties
2113 int isl_basic_set_plain_is_equal(
2114 __isl_keep isl_basic_set *bset1,
2115 __isl_keep isl_basic_set *bset2);
2116 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2117 __isl_keep isl_set *set2);
2118 int isl_set_is_equal(__isl_keep isl_set *set1,
2119 __isl_keep isl_set *set2);
2120 int isl_union_set_is_equal(
2121 __isl_keep isl_union_set *uset1,
2122 __isl_keep isl_union_set *uset2);
2123 int isl_basic_map_is_equal(
2124 __isl_keep isl_basic_map *bmap1,
2125 __isl_keep isl_basic_map *bmap2);
2126 int isl_map_is_equal(__isl_keep isl_map *map1,
2127 __isl_keep isl_map *map2);
2128 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2129 __isl_keep isl_map *map2);
2130 int isl_union_map_is_equal(
2131 __isl_keep isl_union_map *umap1,
2132 __isl_keep isl_union_map *umap2);
2134 =item * Disjointness
2136 int isl_basic_set_is_disjoint(
2137 __isl_keep isl_basic_set *bset1,
2138 __isl_keep isl_basic_set *bset2);
2139 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2140 __isl_keep isl_set *set2);
2141 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2142 __isl_keep isl_set *set2);
2143 int isl_basic_map_is_disjoint(
2144 __isl_keep isl_basic_map *bmap1,
2145 __isl_keep isl_basic_map *bmap2);
2146 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2147 __isl_keep isl_map *map2);
2151 int isl_basic_set_is_subset(
2152 __isl_keep isl_basic_set *bset1,
2153 __isl_keep isl_basic_set *bset2);
2154 int isl_set_is_subset(__isl_keep isl_set *set1,
2155 __isl_keep isl_set *set2);
2156 int isl_set_is_strict_subset(
2157 __isl_keep isl_set *set1,
2158 __isl_keep isl_set *set2);
2159 int isl_union_set_is_subset(
2160 __isl_keep isl_union_set *uset1,
2161 __isl_keep isl_union_set *uset2);
2162 int isl_union_set_is_strict_subset(
2163 __isl_keep isl_union_set *uset1,
2164 __isl_keep isl_union_set *uset2);
2165 int isl_basic_map_is_subset(
2166 __isl_keep isl_basic_map *bmap1,
2167 __isl_keep isl_basic_map *bmap2);
2168 int isl_basic_map_is_strict_subset(
2169 __isl_keep isl_basic_map *bmap1,
2170 __isl_keep isl_basic_map *bmap2);
2171 int isl_map_is_subset(
2172 __isl_keep isl_map *map1,
2173 __isl_keep isl_map *map2);
2174 int isl_map_is_strict_subset(
2175 __isl_keep isl_map *map1,
2176 __isl_keep isl_map *map2);
2177 int isl_union_map_is_subset(
2178 __isl_keep isl_union_map *umap1,
2179 __isl_keep isl_union_map *umap2);
2180 int isl_union_map_is_strict_subset(
2181 __isl_keep isl_union_map *umap1,
2182 __isl_keep isl_union_map *umap2);
2184 Check whether the first argument is a (strict) subset of the
2189 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2190 __isl_keep isl_set *set2);
2192 This function is useful for sorting C<isl_set>s.
2193 The order depends on the internal representation of the inputs.
2194 The order is fixed over different calls to the function (assuming
2195 the internal representation of the inputs has not changed), but may
2196 change over different versions of C<isl>.
2200 =head2 Unary Operations
2206 __isl_give isl_set *isl_set_complement(
2207 __isl_take isl_set *set);
2208 __isl_give isl_map *isl_map_complement(
2209 __isl_take isl_map *map);
2213 __isl_give isl_basic_map *isl_basic_map_reverse(
2214 __isl_take isl_basic_map *bmap);
2215 __isl_give isl_map *isl_map_reverse(
2216 __isl_take isl_map *map);
2217 __isl_give isl_union_map *isl_union_map_reverse(
2218 __isl_take isl_union_map *umap);
2222 #include <isl/local_space.h>
2223 __isl_give isl_local_space *isl_local_space_domain(
2224 __isl_take isl_local_space *ls);
2225 __isl_give isl_local_space *isl_local_space_range(
2226 __isl_take isl_local_space *ls);
2228 #include <isl/set.h>
2229 __isl_give isl_basic_set *isl_basic_set_project_out(
2230 __isl_take isl_basic_set *bset,
2231 enum isl_dim_type type, unsigned first, unsigned n);
2232 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2233 enum isl_dim_type type, unsigned first, unsigned n);
2234 __isl_give isl_basic_set *isl_basic_set_params(
2235 __isl_take isl_basic_set *bset);
2236 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2238 #include <isl/map.h>
2239 __isl_give isl_basic_map *isl_basic_map_project_out(
2240 __isl_take isl_basic_map *bmap,
2241 enum isl_dim_type type, unsigned first, unsigned n);
2242 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2243 enum isl_dim_type type, unsigned first, unsigned n);
2244 __isl_give isl_basic_set *isl_basic_map_domain(
2245 __isl_take isl_basic_map *bmap);
2246 __isl_give isl_basic_set *isl_basic_map_range(
2247 __isl_take isl_basic_map *bmap);
2248 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2249 __isl_give isl_set *isl_map_domain(
2250 __isl_take isl_map *bmap);
2251 __isl_give isl_set *isl_map_range(
2252 __isl_take isl_map *map);
2254 #include <isl/union_set.h>
2255 __isl_give isl_set *isl_union_set_params(
2256 __isl_take isl_union_set *uset);
2258 #include <isl/union_map.h>
2259 __isl_give isl_union_map *isl_union_map_project_out(
2260 __isl_take isl_union_map *umap,
2261 enum isl_dim_type type, unsigned first, unsigned n);
2262 __isl_give isl_set *isl_union_map_params(
2263 __isl_take isl_union_map *umap);
2264 __isl_give isl_union_set *isl_union_map_domain(
2265 __isl_take isl_union_map *umap);
2266 __isl_give isl_union_set *isl_union_map_range(
2267 __isl_take isl_union_map *umap);
2269 The function C<isl_union_map_project_out> can only project out
2272 #include <isl/map.h>
2273 __isl_give isl_basic_map *isl_basic_map_domain_map(
2274 __isl_take isl_basic_map *bmap);
2275 __isl_give isl_basic_map *isl_basic_map_range_map(
2276 __isl_take isl_basic_map *bmap);
2277 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2278 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2280 #include <isl/union_map.h>
2281 __isl_give isl_union_map *isl_union_map_domain_map(
2282 __isl_take isl_union_map *umap);
2283 __isl_give isl_union_map *isl_union_map_range_map(
2284 __isl_take isl_union_map *umap);
2286 The functions above construct a (basic, regular or union) relation
2287 that maps (a wrapped version of) the input relation to its domain or range.
2291 __isl_give isl_basic_set *isl_basic_set_eliminate(
2292 __isl_take isl_basic_set *bset,
2293 enum isl_dim_type type,
2294 unsigned first, unsigned n);
2295 __isl_give isl_set *isl_set_eliminate(
2296 __isl_take isl_set *set, enum isl_dim_type type,
2297 unsigned first, unsigned n);
2298 __isl_give isl_basic_map *isl_basic_map_eliminate(
2299 __isl_take isl_basic_map *bmap,
2300 enum isl_dim_type type,
2301 unsigned first, unsigned n);
2302 __isl_give isl_map *isl_map_eliminate(
2303 __isl_take isl_map *map, enum isl_dim_type type,
2304 unsigned first, unsigned n);
2306 Eliminate the coefficients for the given dimensions from the constraints,
2307 without removing the dimensions.
2309 =item * Constructing a relation from a set
2311 #include <isl/local_space.h>
2312 __isl_give isl_local_space *isl_local_space_from_domain(
2313 __isl_take isl_local_space *ls);
2315 #include <isl/map.h>
2316 __isl_give isl_map *isl_map_from_domain(
2317 __isl_take isl_set *set);
2318 __isl_give isl_map *isl_map_from_range(
2319 __isl_take isl_set *set);
2321 Create a relation with the given set as domain or range.
2322 The range or domain of the created relation is a zero-dimensional
2323 flat anonymous space.
2327 __isl_give isl_basic_set *isl_basic_set_fix_si(
2328 __isl_take isl_basic_set *bset,
2329 enum isl_dim_type type, unsigned pos, int value);
2330 __isl_give isl_basic_set *isl_basic_set_fix_val(
2331 __isl_take isl_basic_set *bset,
2332 enum isl_dim_type type, unsigned pos,
2333 __isl_take isl_val *v);
2334 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2335 enum isl_dim_type type, unsigned pos, int value);
2336 __isl_give isl_set *isl_set_fix_val(
2337 __isl_take isl_set *set,
2338 enum isl_dim_type type, unsigned pos,
2339 __isl_take isl_val *v);
2340 __isl_give isl_basic_map *isl_basic_map_fix_si(
2341 __isl_take isl_basic_map *bmap,
2342 enum isl_dim_type type, unsigned pos, int value);
2343 __isl_give isl_basic_map *isl_basic_map_fix_val(
2344 __isl_take isl_basic_map *bmap,
2345 enum isl_dim_type type, unsigned pos,
2346 __isl_take isl_val *v);
2347 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2348 enum isl_dim_type type, unsigned pos, int value);
2349 __isl_give isl_map *isl_map_fix_val(
2350 __isl_take isl_map *map,
2351 enum isl_dim_type type, unsigned pos,
2352 __isl_take isl_val *v);
2354 Intersect the set or relation with the hyperplane where the given
2355 dimension has the fixed given value.
2357 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2358 __isl_take isl_basic_map *bmap,
2359 enum isl_dim_type type, unsigned pos, int value);
2360 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2361 __isl_take isl_basic_map *bmap,
2362 enum isl_dim_type type, unsigned pos, int value);
2363 __isl_give isl_set *isl_set_lower_bound_si(
2364 __isl_take isl_set *set,
2365 enum isl_dim_type type, unsigned pos, int value);
2366 __isl_give isl_set *isl_set_lower_bound_val(
2367 __isl_take isl_set *set,
2368 enum isl_dim_type type, unsigned pos,
2369 __isl_take isl_val *value);
2370 __isl_give isl_map *isl_map_lower_bound_si(
2371 __isl_take isl_map *map,
2372 enum isl_dim_type type, unsigned pos, int value);
2373 __isl_give isl_set *isl_set_upper_bound_si(
2374 __isl_take isl_set *set,
2375 enum isl_dim_type type, unsigned pos, int value);
2376 __isl_give isl_set *isl_set_upper_bound_val(
2377 __isl_take isl_set *set,
2378 enum isl_dim_type type, unsigned pos,
2379 __isl_take isl_val *value);
2380 __isl_give isl_map *isl_map_upper_bound_si(
2381 __isl_take isl_map *map,
2382 enum isl_dim_type type, unsigned pos, int value);
2384 Intersect the set or relation with the half-space where the given
2385 dimension has a value bounded by the fixed given integer value.
2387 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2388 enum isl_dim_type type1, int pos1,
2389 enum isl_dim_type type2, int pos2);
2390 __isl_give isl_basic_map *isl_basic_map_equate(
2391 __isl_take isl_basic_map *bmap,
2392 enum isl_dim_type type1, int pos1,
2393 enum isl_dim_type type2, int pos2);
2394 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2395 enum isl_dim_type type1, int pos1,
2396 enum isl_dim_type type2, int pos2);
2398 Intersect the set or relation with the hyperplane where the given
2399 dimensions are equal to each other.
2401 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2402 enum isl_dim_type type1, int pos1,
2403 enum isl_dim_type type2, int pos2);
2405 Intersect the relation with the hyperplane where the given
2406 dimensions have opposite values.
2408 __isl_give isl_map *isl_map_order_le(
2409 __isl_take isl_map *map,
2410 enum isl_dim_type type1, int pos1,
2411 enum isl_dim_type type2, int pos2);
2412 __isl_give isl_basic_map *isl_basic_map_order_ge(
2413 __isl_take isl_basic_map *bmap,
2414 enum isl_dim_type type1, int pos1,
2415 enum isl_dim_type type2, int pos2);
2416 __isl_give isl_map *isl_map_order_ge(
2417 __isl_take isl_map *map,
2418 enum isl_dim_type type1, int pos1,
2419 enum isl_dim_type type2, int pos2);
2420 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2421 enum isl_dim_type type1, int pos1,
2422 enum isl_dim_type type2, int pos2);
2423 __isl_give isl_basic_map *isl_basic_map_order_gt(
2424 __isl_take isl_basic_map *bmap,
2425 enum isl_dim_type type1, int pos1,
2426 enum isl_dim_type type2, int pos2);
2427 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2428 enum isl_dim_type type1, int pos1,
2429 enum isl_dim_type type2, int pos2);
2431 Intersect the relation with the half-space where the given
2432 dimensions satisfy the given ordering.
2436 __isl_give isl_map *isl_set_identity(
2437 __isl_take isl_set *set);
2438 __isl_give isl_union_map *isl_union_set_identity(
2439 __isl_take isl_union_set *uset);
2441 Construct an identity relation on the given (union) set.
2445 __isl_give isl_basic_set *isl_basic_map_deltas(
2446 __isl_take isl_basic_map *bmap);
2447 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2448 __isl_give isl_union_set *isl_union_map_deltas(
2449 __isl_take isl_union_map *umap);
2451 These functions return a (basic) set containing the differences
2452 between image elements and corresponding domain elements in the input.
2454 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2455 __isl_take isl_basic_map *bmap);
2456 __isl_give isl_map *isl_map_deltas_map(
2457 __isl_take isl_map *map);
2458 __isl_give isl_union_map *isl_union_map_deltas_map(
2459 __isl_take isl_union_map *umap);
2461 The functions above construct a (basic, regular or union) relation
2462 that maps (a wrapped version of) the input relation to its delta set.
2466 Simplify the representation of a set or relation by trying
2467 to combine pairs of basic sets or relations into a single
2468 basic set or relation.
2470 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2471 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2472 __isl_give isl_union_set *isl_union_set_coalesce(
2473 __isl_take isl_union_set *uset);
2474 __isl_give isl_union_map *isl_union_map_coalesce(
2475 __isl_take isl_union_map *umap);
2477 One of the methods for combining pairs of basic sets or relations
2478 can result in coefficients that are much larger than those that appear
2479 in the constraints of the input. By default, the coefficients are
2480 not allowed to grow larger, but this can be changed by unsetting
2481 the following option.
2483 int isl_options_set_coalesce_bounded_wrapping(
2484 isl_ctx *ctx, int val);
2485 int isl_options_get_coalesce_bounded_wrapping(
2488 =item * Detecting equalities
2490 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2491 __isl_take isl_basic_set *bset);
2492 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2493 __isl_take isl_basic_map *bmap);
2494 __isl_give isl_set *isl_set_detect_equalities(
2495 __isl_take isl_set *set);
2496 __isl_give isl_map *isl_map_detect_equalities(
2497 __isl_take isl_map *map);
2498 __isl_give isl_union_set *isl_union_set_detect_equalities(
2499 __isl_take isl_union_set *uset);
2500 __isl_give isl_union_map *isl_union_map_detect_equalities(
2501 __isl_take isl_union_map *umap);
2503 Simplify the representation of a set or relation by detecting implicit
2506 =item * Removing redundant constraints
2508 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2509 __isl_take isl_basic_set *bset);
2510 __isl_give isl_set *isl_set_remove_redundancies(
2511 __isl_take isl_set *set);
2512 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2513 __isl_take isl_basic_map *bmap);
2514 __isl_give isl_map *isl_map_remove_redundancies(
2515 __isl_take isl_map *map);
2519 __isl_give isl_basic_set *isl_set_convex_hull(
2520 __isl_take isl_set *set);
2521 __isl_give isl_basic_map *isl_map_convex_hull(
2522 __isl_take isl_map *map);
2524 If the input set or relation has any existentially quantified
2525 variables, then the result of these operations is currently undefined.
2529 __isl_give isl_basic_set *
2530 isl_set_unshifted_simple_hull(
2531 __isl_take isl_set *set);
2532 __isl_give isl_basic_map *
2533 isl_map_unshifted_simple_hull(
2534 __isl_take isl_map *map);
2535 __isl_give isl_basic_set *isl_set_simple_hull(
2536 __isl_take isl_set *set);
2537 __isl_give isl_basic_map *isl_map_simple_hull(
2538 __isl_take isl_map *map);
2539 __isl_give isl_union_map *isl_union_map_simple_hull(
2540 __isl_take isl_union_map *umap);
2542 These functions compute a single basic set or relation
2543 that contains the whole input set or relation.
2544 In particular, the output is described by translates
2545 of the constraints describing the basic sets or relations in the input.
2546 In case of C<isl_set_unshifted_simple_hull>, only the original
2547 constraints are used, without any translation.
2551 (See \autoref{s:simple hull}.)
2557 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2558 __isl_take isl_basic_set *bset);
2559 __isl_give isl_basic_set *isl_set_affine_hull(
2560 __isl_take isl_set *set);
2561 __isl_give isl_union_set *isl_union_set_affine_hull(
2562 __isl_take isl_union_set *uset);
2563 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2564 __isl_take isl_basic_map *bmap);
2565 __isl_give isl_basic_map *isl_map_affine_hull(
2566 __isl_take isl_map *map);
2567 __isl_give isl_union_map *isl_union_map_affine_hull(
2568 __isl_take isl_union_map *umap);
2570 In case of union sets and relations, the affine hull is computed
2573 =item * Polyhedral hull
2575 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2576 __isl_take isl_set *set);
2577 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2578 __isl_take isl_map *map);
2579 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2580 __isl_take isl_union_set *uset);
2581 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2582 __isl_take isl_union_map *umap);
2584 These functions compute a single basic set or relation
2585 not involving any existentially quantified variables
2586 that contains the whole input set or relation.
2587 In case of union sets and relations, the polyhedral hull is computed
2590 =item * Other approximations
2592 __isl_give isl_basic_set *
2593 isl_basic_set_drop_constraints_involving_dims(
2594 __isl_take isl_basic_set *bset,
2595 enum isl_dim_type type,
2596 unsigned first, unsigned n);
2597 __isl_give isl_basic_map *
2598 isl_basic_map_drop_constraints_involving_dims(
2599 __isl_take isl_basic_map *bmap,
2600 enum isl_dim_type type,
2601 unsigned first, unsigned n);
2602 __isl_give isl_basic_set *
2603 isl_basic_set_drop_constraints_not_involving_dims(
2604 __isl_take isl_basic_set *bset,
2605 enum isl_dim_type type,
2606 unsigned first, unsigned n);
2607 __isl_give isl_set *
2608 isl_set_drop_constraints_involving_dims(
2609 __isl_take isl_set *set,
2610 enum isl_dim_type type,
2611 unsigned first, unsigned n);
2612 __isl_give isl_map *
2613 isl_map_drop_constraints_involving_dims(
2614 __isl_take isl_map *map,
2615 enum isl_dim_type type,
2616 unsigned first, unsigned n);
2618 These functions drop any constraints (not) involving the specified dimensions.
2619 Note that the result depends on the representation of the input.
2623 __isl_give isl_basic_set *isl_basic_set_sample(
2624 __isl_take isl_basic_set *bset);
2625 __isl_give isl_basic_set *isl_set_sample(
2626 __isl_take isl_set *set);
2627 __isl_give isl_basic_map *isl_basic_map_sample(
2628 __isl_take isl_basic_map *bmap);
2629 __isl_give isl_basic_map *isl_map_sample(
2630 __isl_take isl_map *map);
2632 If the input (basic) set or relation is non-empty, then return
2633 a singleton subset of the input. Otherwise, return an empty set.
2635 =item * Optimization
2637 #include <isl/ilp.h>
2638 __isl_give isl_val *isl_basic_set_max_val(
2639 __isl_keep isl_basic_set *bset,
2640 __isl_keep isl_aff *obj);
2641 __isl_give isl_val *isl_set_min_val(
2642 __isl_keep isl_set *set,
2643 __isl_keep isl_aff *obj);
2644 __isl_give isl_val *isl_set_max_val(
2645 __isl_keep isl_set *set,
2646 __isl_keep isl_aff *obj);
2648 Compute the minimum or maximum of the integer affine expression C<obj>
2649 over the points in C<set>, returning the result in C<opt>.
2650 The result is C<NULL> in case of an error, the optimal value in case
2651 there is one, negative infinity or infinity if the problem is unbounded and
2652 NaN if the problem is empty.
2654 =item * Parametric optimization
2656 __isl_give isl_pw_aff *isl_set_dim_min(
2657 __isl_take isl_set *set, int pos);
2658 __isl_give isl_pw_aff *isl_set_dim_max(
2659 __isl_take isl_set *set, int pos);
2660 __isl_give isl_pw_aff *isl_map_dim_max(
2661 __isl_take isl_map *map, int pos);
2663 Compute the minimum or maximum of the given set or output dimension
2664 as a function of the parameters (and input dimensions), but independently
2665 of the other set or output dimensions.
2666 For lexicographic optimization, see L<"Lexicographic Optimization">.
2670 The following functions compute either the set of (rational) coefficient
2671 values of valid constraints for the given set or the set of (rational)
2672 values satisfying the constraints with coefficients from the given set.
2673 Internally, these two sets of functions perform essentially the
2674 same operations, except that the set of coefficients is assumed to
2675 be a cone, while the set of values may be any polyhedron.
2676 The current implementation is based on the Farkas lemma and
2677 Fourier-Motzkin elimination, but this may change or be made optional
2678 in future. In particular, future implementations may use different
2679 dualization algorithms or skip the elimination step.
2681 __isl_give isl_basic_set *isl_basic_set_coefficients(
2682 __isl_take isl_basic_set *bset);
2683 __isl_give isl_basic_set *isl_set_coefficients(
2684 __isl_take isl_set *set);
2685 __isl_give isl_union_set *isl_union_set_coefficients(
2686 __isl_take isl_union_set *bset);
2687 __isl_give isl_basic_set *isl_basic_set_solutions(
2688 __isl_take isl_basic_set *bset);
2689 __isl_give isl_basic_set *isl_set_solutions(
2690 __isl_take isl_set *set);
2691 __isl_give isl_union_set *isl_union_set_solutions(
2692 __isl_take isl_union_set *bset);
2696 __isl_give isl_map *isl_map_fixed_power_val(
2697 __isl_take isl_map *map,
2698 __isl_take isl_val *exp);
2699 __isl_give isl_union_map *
2700 isl_union_map_fixed_power_val(
2701 __isl_take isl_union_map *umap,
2702 __isl_take isl_val *exp);
2704 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2705 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2706 of C<map> is computed.
2708 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2710 __isl_give isl_union_map *isl_union_map_power(
2711 __isl_take isl_union_map *umap, int *exact);
2713 Compute a parametric representation for all positive powers I<k> of C<map>.
2714 The result maps I<k> to a nested relation corresponding to the
2715 I<k>th power of C<map>.
2716 The result may be an overapproximation. If the result is known to be exact,
2717 then C<*exact> is set to C<1>.
2719 =item * Transitive closure
2721 __isl_give isl_map *isl_map_transitive_closure(
2722 __isl_take isl_map *map, int *exact);
2723 __isl_give isl_union_map *isl_union_map_transitive_closure(
2724 __isl_take isl_union_map *umap, int *exact);
2726 Compute the transitive closure of C<map>.
2727 The result may be an overapproximation. If the result is known to be exact,
2728 then C<*exact> is set to C<1>.
2730 =item * Reaching path lengths
2732 __isl_give isl_map *isl_map_reaching_path_lengths(
2733 __isl_take isl_map *map, int *exact);
2735 Compute a relation that maps each element in the range of C<map>
2736 to the lengths of all paths composed of edges in C<map> that
2737 end up in the given element.
2738 The result may be an overapproximation. If the result is known to be exact,
2739 then C<*exact> is set to C<1>.
2740 To compute the I<maximal> path length, the resulting relation
2741 should be postprocessed by C<isl_map_lexmax>.
2742 In particular, if the input relation is a dependence relation
2743 (mapping sources to sinks), then the maximal path length corresponds
2744 to the free schedule.
2745 Note, however, that C<isl_map_lexmax> expects the maximum to be
2746 finite, so if the path lengths are unbounded (possibly due to
2747 the overapproximation), then you will get an error message.
2751 #include <isl/space.h>
2752 __isl_give isl_space *isl_space_wrap(
2753 __isl_take isl_space *space);
2754 __isl_give isl_space *isl_space_unwrap(
2755 __isl_take isl_space *space);
2757 #include <isl/set.h>
2758 __isl_give isl_basic_map *isl_basic_set_unwrap(
2759 __isl_take isl_basic_set *bset);
2760 __isl_give isl_map *isl_set_unwrap(
2761 __isl_take isl_set *set);
2763 #include <isl/map.h>
2764 __isl_give isl_basic_set *isl_basic_map_wrap(
2765 __isl_take isl_basic_map *bmap);
2766 __isl_give isl_set *isl_map_wrap(
2767 __isl_take isl_map *map);
2769 #include <isl/union_set.h>
2770 __isl_give isl_union_map *isl_union_set_unwrap(
2771 __isl_take isl_union_set *uset);
2773 #include <isl/union_map.h>
2774 __isl_give isl_union_set *isl_union_map_wrap(
2775 __isl_take isl_union_map *umap);
2777 The input to C<isl_space_unwrap> should
2778 be the space of a set, while that of
2779 C<isl_space_wrap> should be the space of a relation.
2780 Conversely, the output of C<isl_space_unwrap> is the space
2781 of a relation, while that of C<isl_space_wrap> is the space of a set.
2785 Remove any internal structure of domain (and range) of the given
2786 set or relation. If there is any such internal structure in the input,
2787 then the name of the space is also removed.
2789 #include <isl/local_space.h>
2790 __isl_give isl_local_space *
2791 isl_local_space_flatten_domain(
2792 __isl_take isl_local_space *ls);
2793 __isl_give isl_local_space *
2794 isl_local_space_flatten_range(
2795 __isl_take isl_local_space *ls);
2797 #include <isl/set.h>
2798 __isl_give isl_basic_set *isl_basic_set_flatten(
2799 __isl_take isl_basic_set *bset);
2800 __isl_give isl_set *isl_set_flatten(
2801 __isl_take isl_set *set);
2803 #include <isl/map.h>
2804 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2805 __isl_take isl_basic_map *bmap);
2806 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2807 __isl_take isl_basic_map *bmap);
2808 __isl_give isl_map *isl_map_flatten_range(
2809 __isl_take isl_map *map);
2810 __isl_give isl_map *isl_map_flatten_domain(
2811 __isl_take isl_map *map);
2812 __isl_give isl_basic_map *isl_basic_map_flatten(
2813 __isl_take isl_basic_map *bmap);
2814 __isl_give isl_map *isl_map_flatten(
2815 __isl_take isl_map *map);
2817 #include <isl/map.h>
2818 __isl_give isl_map *isl_set_flatten_map(
2819 __isl_take isl_set *set);
2821 The function above constructs a relation
2822 that maps the input set to a flattened version of the set.
2826 Lift the input set to a space with extra dimensions corresponding
2827 to the existentially quantified variables in the input.
2828 In particular, the result lives in a wrapped map where the domain
2829 is the original space and the range corresponds to the original
2830 existentially quantified variables.
2832 __isl_give isl_basic_set *isl_basic_set_lift(
2833 __isl_take isl_basic_set *bset);
2834 __isl_give isl_set *isl_set_lift(
2835 __isl_take isl_set *set);
2836 __isl_give isl_union_set *isl_union_set_lift(
2837 __isl_take isl_union_set *uset);
2839 Given a local space that contains the existentially quantified
2840 variables of a set, a basic relation that, when applied to
2841 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2842 can be constructed using the following function.
2844 #include <isl/local_space.h>
2845 __isl_give isl_basic_map *isl_local_space_lifting(
2846 __isl_take isl_local_space *ls);
2848 =item * Internal Product
2850 __isl_give isl_basic_map *isl_basic_map_zip(
2851 __isl_take isl_basic_map *bmap);
2852 __isl_give isl_map *isl_map_zip(
2853 __isl_take isl_map *map);
2854 __isl_give isl_union_map *isl_union_map_zip(
2855 __isl_take isl_union_map *umap);
2857 Given a relation with nested relations for domain and range,
2858 interchange the range of the domain with the domain of the range.
2862 __isl_give isl_basic_map *isl_basic_map_curry(
2863 __isl_take isl_basic_map *bmap);
2864 __isl_give isl_basic_map *isl_basic_map_uncurry(
2865 __isl_take isl_basic_map *bmap);
2866 __isl_give isl_map *isl_map_curry(
2867 __isl_take isl_map *map);
2868 __isl_give isl_map *isl_map_uncurry(
2869 __isl_take isl_map *map);
2870 __isl_give isl_union_map *isl_union_map_curry(
2871 __isl_take isl_union_map *umap);
2872 __isl_give isl_union_map *isl_union_map_uncurry(
2873 __isl_take isl_union_map *umap);
2875 Given a relation with a nested relation for domain,
2876 the C<curry> functions
2877 move the range of the nested relation out of the domain
2878 and use it as the domain of a nested relation in the range,
2879 with the original range as range of this nested relation.
2880 The C<uncurry> functions perform the inverse operation.
2882 =item * Aligning parameters
2884 __isl_give isl_basic_set *isl_basic_set_align_params(
2885 __isl_take isl_basic_set *bset,
2886 __isl_take isl_space *model);
2887 __isl_give isl_set *isl_set_align_params(
2888 __isl_take isl_set *set,
2889 __isl_take isl_space *model);
2890 __isl_give isl_basic_map *isl_basic_map_align_params(
2891 __isl_take isl_basic_map *bmap,
2892 __isl_take isl_space *model);
2893 __isl_give isl_map *isl_map_align_params(
2894 __isl_take isl_map *map,
2895 __isl_take isl_space *model);
2897 Change the order of the parameters of the given set or relation
2898 such that the first parameters match those of C<model>.
2899 This may involve the introduction of extra parameters.
2900 All parameters need to be named.
2902 =item * Dimension manipulation
2904 #include <isl/local_space.h>
2905 __isl_give isl_local_space *isl_local_space_add_dims(
2906 __isl_take isl_local_space *ls,
2907 enum isl_dim_type type, unsigned n);
2908 __isl_give isl_local_space *isl_local_space_insert_dims(
2909 __isl_take isl_local_space *ls,
2910 enum isl_dim_type type, unsigned first, unsigned n);
2911 __isl_give isl_local_space *isl_local_space_drop_dims(
2912 __isl_take isl_local_space *ls,
2913 enum isl_dim_type type, unsigned first, unsigned n);
2915 #include <isl/set.h>
2916 __isl_give isl_basic_set *isl_basic_set_add_dims(
2917 __isl_take isl_basic_set *bset,
2918 enum isl_dim_type type, unsigned n);
2919 __isl_give isl_set *isl_set_add_dims(
2920 __isl_take isl_set *set,
2921 enum isl_dim_type type, unsigned n);
2922 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2923 __isl_take isl_basic_set *bset,
2924 enum isl_dim_type type, unsigned pos,
2926 __isl_give isl_set *isl_set_insert_dims(
2927 __isl_take isl_set *set,
2928 enum isl_dim_type type, unsigned pos, unsigned n);
2929 __isl_give isl_basic_set *isl_basic_set_move_dims(
2930 __isl_take isl_basic_set *bset,
2931 enum isl_dim_type dst_type, unsigned dst_pos,
2932 enum isl_dim_type src_type, unsigned src_pos,
2934 __isl_give isl_set *isl_set_move_dims(
2935 __isl_take isl_set *set,
2936 enum isl_dim_type dst_type, unsigned dst_pos,
2937 enum isl_dim_type src_type, unsigned src_pos,
2940 #include <isl/map.h>
2941 __isl_give isl_map *isl_map_add_dims(
2942 __isl_take isl_map *map,
2943 enum isl_dim_type type, unsigned n);
2944 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2945 __isl_take isl_basic_map *bmap,
2946 enum isl_dim_type type, unsigned pos,
2948 __isl_give isl_map *isl_map_insert_dims(
2949 __isl_take isl_map *map,
2950 enum isl_dim_type type, unsigned pos, unsigned n);
2951 __isl_give isl_basic_map *isl_basic_map_move_dims(
2952 __isl_take isl_basic_map *bmap,
2953 enum isl_dim_type dst_type, unsigned dst_pos,
2954 enum isl_dim_type src_type, unsigned src_pos,
2956 __isl_give isl_map *isl_map_move_dims(
2957 __isl_take isl_map *map,
2958 enum isl_dim_type dst_type, unsigned dst_pos,
2959 enum isl_dim_type src_type, unsigned src_pos,
2962 It is usually not advisable to directly change the (input or output)
2963 space of a set or a relation as this removes the name and the internal
2964 structure of the space. However, the above functions can be useful
2965 to add new parameters, assuming
2966 C<isl_set_align_params> and C<isl_map_align_params>
2971 =head2 Binary Operations
2973 The two arguments of a binary operation not only need to live
2974 in the same C<isl_ctx>, they currently also need to have
2975 the same (number of) parameters.
2977 =head3 Basic Operations
2981 =item * Intersection
2983 #include <isl/local_space.h>
2984 __isl_give isl_local_space *isl_local_space_intersect(
2985 __isl_take isl_local_space *ls1,
2986 __isl_take isl_local_space *ls2);
2988 #include <isl/set.h>
2989 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2990 __isl_take isl_basic_set *bset1,
2991 __isl_take isl_basic_set *bset2);
2992 __isl_give isl_basic_set *isl_basic_set_intersect(
2993 __isl_take isl_basic_set *bset1,
2994 __isl_take isl_basic_set *bset2);
2995 __isl_give isl_set *isl_set_intersect_params(
2996 __isl_take isl_set *set,
2997 __isl_take isl_set *params);
2998 __isl_give isl_set *isl_set_intersect(
2999 __isl_take isl_set *set1,
3000 __isl_take isl_set *set2);
3002 #include <isl/map.h>
3003 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
3004 __isl_take isl_basic_map *bmap,
3005 __isl_take isl_basic_set *bset);
3006 __isl_give isl_basic_map *isl_basic_map_intersect_range(
3007 __isl_take isl_basic_map *bmap,
3008 __isl_take isl_basic_set *bset);
3009 __isl_give isl_basic_map *isl_basic_map_intersect(
3010 __isl_take isl_basic_map *bmap1,
3011 __isl_take isl_basic_map *bmap2);
3012 __isl_give isl_map *isl_map_intersect_params(
3013 __isl_take isl_map *map,
3014 __isl_take isl_set *params);
3015 __isl_give isl_map *isl_map_intersect_domain(
3016 __isl_take isl_map *map,
3017 __isl_take isl_set *set);
3018 __isl_give isl_map *isl_map_intersect_range(
3019 __isl_take isl_map *map,
3020 __isl_take isl_set *set);
3021 __isl_give isl_map *isl_map_intersect(
3022 __isl_take isl_map *map1,
3023 __isl_take isl_map *map2);
3025 #include <isl/union_set.h>
3026 __isl_give isl_union_set *isl_union_set_intersect_params(
3027 __isl_take isl_union_set *uset,
3028 __isl_take isl_set *set);
3029 __isl_give isl_union_set *isl_union_set_intersect(
3030 __isl_take isl_union_set *uset1,
3031 __isl_take isl_union_set *uset2);
3033 #include <isl/union_map.h>
3034 __isl_give isl_union_map *isl_union_map_intersect_params(
3035 __isl_take isl_union_map *umap,
3036 __isl_take isl_set *set);
3037 __isl_give isl_union_map *isl_union_map_intersect_domain(
3038 __isl_take isl_union_map *umap,
3039 __isl_take isl_union_set *uset);
3040 __isl_give isl_union_map *isl_union_map_intersect_range(
3041 __isl_take isl_union_map *umap,
3042 __isl_take isl_union_set *uset);
3043 __isl_give isl_union_map *isl_union_map_intersect(
3044 __isl_take isl_union_map *umap1,
3045 __isl_take isl_union_map *umap2);
3047 The second argument to the C<_params> functions needs to be
3048 a parametric (basic) set. For the other functions, a parametric set
3049 for either argument is only allowed if the other argument is
3050 a parametric set as well.
3054 __isl_give isl_set *isl_basic_set_union(
3055 __isl_take isl_basic_set *bset1,
3056 __isl_take isl_basic_set *bset2);
3057 __isl_give isl_map *isl_basic_map_union(
3058 __isl_take isl_basic_map *bmap1,
3059 __isl_take isl_basic_map *bmap2);
3060 __isl_give isl_set *isl_set_union(
3061 __isl_take isl_set *set1,
3062 __isl_take isl_set *set2);
3063 __isl_give isl_map *isl_map_union(
3064 __isl_take isl_map *map1,
3065 __isl_take isl_map *map2);
3066 __isl_give isl_union_set *isl_union_set_union(
3067 __isl_take isl_union_set *uset1,
3068 __isl_take isl_union_set *uset2);
3069 __isl_give isl_union_map *isl_union_map_union(
3070 __isl_take isl_union_map *umap1,
3071 __isl_take isl_union_map *umap2);
3073 =item * Set difference
3075 __isl_give isl_set *isl_set_subtract(
3076 __isl_take isl_set *set1,
3077 __isl_take isl_set *set2);
3078 __isl_give isl_map *isl_map_subtract(
3079 __isl_take isl_map *map1,
3080 __isl_take isl_map *map2);
3081 __isl_give isl_map *isl_map_subtract_domain(
3082 __isl_take isl_map *map,
3083 __isl_take isl_set *dom);
3084 __isl_give isl_map *isl_map_subtract_range(
3085 __isl_take isl_map *map,
3086 __isl_take isl_set *dom);
3087 __isl_give isl_union_set *isl_union_set_subtract(
3088 __isl_take isl_union_set *uset1,
3089 __isl_take isl_union_set *uset2);
3090 __isl_give isl_union_map *isl_union_map_subtract(
3091 __isl_take isl_union_map *umap1,
3092 __isl_take isl_union_map *umap2);
3093 __isl_give isl_union_map *isl_union_map_subtract_domain(
3094 __isl_take isl_union_map *umap,
3095 __isl_take isl_union_set *dom);
3096 __isl_give isl_union_map *isl_union_map_subtract_range(
3097 __isl_take isl_union_map *umap,
3098 __isl_take isl_union_set *dom);
3102 __isl_give isl_basic_set *isl_basic_set_apply(
3103 __isl_take isl_basic_set *bset,
3104 __isl_take isl_basic_map *bmap);
3105 __isl_give isl_set *isl_set_apply(
3106 __isl_take isl_set *set,
3107 __isl_take isl_map *map);
3108 __isl_give isl_union_set *isl_union_set_apply(
3109 __isl_take isl_union_set *uset,
3110 __isl_take isl_union_map *umap);
3111 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3112 __isl_take isl_basic_map *bmap1,
3113 __isl_take isl_basic_map *bmap2);
3114 __isl_give isl_basic_map *isl_basic_map_apply_range(
3115 __isl_take isl_basic_map *bmap1,
3116 __isl_take isl_basic_map *bmap2);
3117 __isl_give isl_map *isl_map_apply_domain(
3118 __isl_take isl_map *map1,
3119 __isl_take isl_map *map2);
3120 __isl_give isl_union_map *isl_union_map_apply_domain(
3121 __isl_take isl_union_map *umap1,
3122 __isl_take isl_union_map *umap2);
3123 __isl_give isl_map *isl_map_apply_range(
3124 __isl_take isl_map *map1,
3125 __isl_take isl_map *map2);
3126 __isl_give isl_union_map *isl_union_map_apply_range(
3127 __isl_take isl_union_map *umap1,
3128 __isl_take isl_union_map *umap2);
3132 #include <isl/set.h>
3133 __isl_give isl_basic_set *
3134 isl_basic_set_preimage_multi_aff(
3135 __isl_take isl_basic_set *bset,
3136 __isl_take isl_multi_aff *ma);
3137 __isl_give isl_set *isl_set_preimage_multi_aff(
3138 __isl_take isl_set *set,
3139 __isl_take isl_multi_aff *ma);
3140 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3141 __isl_take isl_set *set,
3142 __isl_take isl_pw_multi_aff *pma);
3143 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
3144 __isl_take isl_set *set,
3145 __isl_take isl_multi_pw_aff *mpa);
3147 #include <isl/union_set.h>
3148 __isl_give isl_union_set *
3149 isl_union_set_preimage_multi_aff(
3150 __isl_take isl_union_set *uset,
3151 __isl_take isl_multi_aff *ma);
3152 __isl_give isl_union_set *
3153 isl_union_set_preimage_pw_multi_aff(
3154 __isl_take isl_union_set *uset,
3155 __isl_take isl_pw_multi_aff *pma);
3156 __isl_give isl_union_set *
3157 isl_union_set_preimage_union_pw_multi_aff(
3158 __isl_take isl_union_set *uset,
3159 __isl_take isl_union_pw_multi_aff *upma);
3161 #include <isl/map.h>
3162 __isl_give isl_basic_map *
3163 isl_basic_map_preimage_domain_multi_aff(
3164 __isl_take isl_basic_map *bmap,
3165 __isl_take isl_multi_aff *ma);
3166 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3167 __isl_take isl_map *map,
3168 __isl_take isl_multi_aff *ma);
3169 __isl_give isl_map *isl_map_preimage_range_multi_aff(
3170 __isl_take isl_map *map,
3171 __isl_take isl_multi_aff *ma);
3172 __isl_give isl_map *
3173 isl_map_preimage_domain_pw_multi_aff(
3174 __isl_take isl_map *map,
3175 __isl_take isl_pw_multi_aff *pma);
3176 __isl_give isl_map *
3177 isl_map_preimage_range_pw_multi_aff(
3178 __isl_take isl_map *map,
3179 __isl_take isl_pw_multi_aff *pma);
3180 __isl_give isl_map *
3181 isl_map_preimage_domain_multi_pw_aff(
3182 __isl_take isl_map *map,
3183 __isl_take isl_multi_pw_aff *mpa);
3184 __isl_give isl_basic_map *
3185 isl_basic_map_preimage_range_multi_aff(
3186 __isl_take isl_basic_map *bmap,
3187 __isl_take isl_multi_aff *ma);
3189 #include <isl/union_map.h>
3190 __isl_give isl_union_map *
3191 isl_union_map_preimage_domain_multi_aff(
3192 __isl_take isl_union_map *umap,
3193 __isl_take isl_multi_aff *ma);
3194 __isl_give isl_union_map *
3195 isl_union_map_preimage_range_multi_aff(
3196 __isl_take isl_union_map *umap,
3197 __isl_take isl_multi_aff *ma);
3198 __isl_give isl_union_map *
3199 isl_union_map_preimage_domain_pw_multi_aff(
3200 __isl_take isl_union_map *umap,
3201 __isl_take isl_pw_multi_aff *pma);
3202 __isl_give isl_union_map *
3203 isl_union_map_preimage_range_pw_multi_aff(
3204 __isl_take isl_union_map *umap,
3205 __isl_take isl_pw_multi_aff *pma);
3206 __isl_give isl_union_map *
3207 isl_union_map_preimage_domain_union_pw_multi_aff(
3208 __isl_take isl_union_map *umap,
3209 __isl_take isl_union_pw_multi_aff *upma);
3210 __isl_give isl_union_map *
3211 isl_union_map_preimage_range_union_pw_multi_aff(
3212 __isl_take isl_union_map *umap,
3213 __isl_take isl_union_pw_multi_aff *upma);
3215 These functions compute the preimage of the given set or map domain/range under
3216 the given function. In other words, the expression is plugged
3217 into the set description or into the domain/range of the map.
3218 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3219 L</"Piecewise Multiple Quasi Affine Expressions">.
3221 =item * Cartesian Product
3223 #include <isl/space.h>
3224 __isl_give isl_space *isl_space_product(
3225 __isl_take isl_space *space1,
3226 __isl_take isl_space *space2);
3227 __isl_give isl_space *isl_space_domain_product(
3228 __isl_take isl_space *space1,
3229 __isl_take isl_space *space2);
3230 __isl_give isl_space *isl_space_range_product(
3231 __isl_take isl_space *space1,
3232 __isl_take isl_space *space2);
3235 C<isl_space_product>, C<isl_space_domain_product>
3236 and C<isl_space_range_product> take pairs or relation spaces and
3237 produce a single relations space, where either the domain, the range
3238 or both domain and range are wrapped spaces of relations between
3239 the domains and/or ranges of the input spaces.
3240 If the product is only constructed over the domain or the range
3241 then the ranges or the domains of the inputs should be the same.
3242 The function C<isl_space_product> also accepts a pair of set spaces,
3243 in which case it returns a wrapped space of a relation between the
3246 #include <isl/set.h>
3247 __isl_give isl_set *isl_set_product(
3248 __isl_take isl_set *set1,
3249 __isl_take isl_set *set2);
3251 #include <isl/map.h>
3252 __isl_give isl_basic_map *isl_basic_map_domain_product(
3253 __isl_take isl_basic_map *bmap1,
3254 __isl_take isl_basic_map *bmap2);
3255 __isl_give isl_basic_map *isl_basic_map_range_product(
3256 __isl_take isl_basic_map *bmap1,
3257 __isl_take isl_basic_map *bmap2);
3258 __isl_give isl_basic_map *isl_basic_map_product(
3259 __isl_take isl_basic_map *bmap1,
3260 __isl_take isl_basic_map *bmap2);
3261 __isl_give isl_map *isl_map_domain_product(
3262 __isl_take isl_map *map1,
3263 __isl_take isl_map *map2);
3264 __isl_give isl_map *isl_map_range_product(
3265 __isl_take isl_map *map1,
3266 __isl_take isl_map *map2);
3267 __isl_give isl_map *isl_map_product(
3268 __isl_take isl_map *map1,
3269 __isl_take isl_map *map2);
3271 #include <isl/union_set.h>
3272 __isl_give isl_union_set *isl_union_set_product(
3273 __isl_take isl_union_set *uset1,
3274 __isl_take isl_union_set *uset2);
3276 #include <isl/union_map.h>
3277 __isl_give isl_union_map *isl_union_map_domain_product(
3278 __isl_take isl_union_map *umap1,
3279 __isl_take isl_union_map *umap2);
3280 __isl_give isl_union_map *isl_union_map_range_product(
3281 __isl_take isl_union_map *umap1,
3282 __isl_take isl_union_map *umap2);
3283 __isl_give isl_union_map *isl_union_map_product(
3284 __isl_take isl_union_map *umap1,
3285 __isl_take isl_union_map *umap2);
3287 The above functions compute the cross product of the given
3288 sets or relations. The domains and ranges of the results
3289 are wrapped maps between domains and ranges of the inputs.
3290 To obtain a ``flat'' product, use the following functions
3293 __isl_give isl_basic_set *isl_basic_set_flat_product(
3294 __isl_take isl_basic_set *bset1,
3295 __isl_take isl_basic_set *bset2);
3296 __isl_give isl_set *isl_set_flat_product(
3297 __isl_take isl_set *set1,
3298 __isl_take isl_set *set2);
3299 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3300 __isl_take isl_basic_map *bmap1,
3301 __isl_take isl_basic_map *bmap2);
3302 __isl_give isl_map *isl_map_flat_domain_product(
3303 __isl_take isl_map *map1,
3304 __isl_take isl_map *map2);
3305 __isl_give isl_map *isl_map_flat_range_product(
3306 __isl_take isl_map *map1,
3307 __isl_take isl_map *map2);
3308 __isl_give isl_union_map *isl_union_map_flat_range_product(
3309 __isl_take isl_union_map *umap1,
3310 __isl_take isl_union_map *umap2);
3311 __isl_give isl_basic_map *isl_basic_map_flat_product(
3312 __isl_take isl_basic_map *bmap1,
3313 __isl_take isl_basic_map *bmap2);
3314 __isl_give isl_map *isl_map_flat_product(
3315 __isl_take isl_map *map1,
3316 __isl_take isl_map *map2);
3318 #include <isl/space.h>
3319 __isl_give isl_space *isl_space_domain_factor_domain(
3320 __isl_take isl_space *space);
3321 __isl_give isl_space *isl_space_range_factor_domain(
3322 __isl_take isl_space *space);
3323 __isl_give isl_space *isl_space_range_factor_range(
3324 __isl_take isl_space *space);
3326 The functions C<isl_space_range_factor_domain> and
3327 C<isl_space_range_factor_range> extract the two arguments from
3328 the result of a call to C<isl_space_range_product>.
3330 The arguments of a call to C<isl_map_range_product> can be extracted
3331 from the result using the following two functions.
3333 #include <isl/map.h>
3334 __isl_give isl_map *isl_map_range_factor_domain(
3335 __isl_take isl_map *map);
3336 __isl_give isl_map *isl_map_range_factor_range(
3337 __isl_take isl_map *map);
3339 =item * Simplification
3341 __isl_give isl_basic_set *isl_basic_set_gist(
3342 __isl_take isl_basic_set *bset,
3343 __isl_take isl_basic_set *context);
3344 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3345 __isl_take isl_set *context);
3346 __isl_give isl_set *isl_set_gist_params(
3347 __isl_take isl_set *set,
3348 __isl_take isl_set *context);
3349 __isl_give isl_union_set *isl_union_set_gist(
3350 __isl_take isl_union_set *uset,
3351 __isl_take isl_union_set *context);
3352 __isl_give isl_union_set *isl_union_set_gist_params(
3353 __isl_take isl_union_set *uset,
3354 __isl_take isl_set *set);
3355 __isl_give isl_basic_map *isl_basic_map_gist(
3356 __isl_take isl_basic_map *bmap,
3357 __isl_take isl_basic_map *context);
3358 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3359 __isl_take isl_map *context);
3360 __isl_give isl_map *isl_map_gist_params(
3361 __isl_take isl_map *map,
3362 __isl_take isl_set *context);
3363 __isl_give isl_map *isl_map_gist_domain(
3364 __isl_take isl_map *map,
3365 __isl_take isl_set *context);
3366 __isl_give isl_map *isl_map_gist_range(
3367 __isl_take isl_map *map,
3368 __isl_take isl_set *context);
3369 __isl_give isl_union_map *isl_union_map_gist(
3370 __isl_take isl_union_map *umap,
3371 __isl_take isl_union_map *context);
3372 __isl_give isl_union_map *isl_union_map_gist_params(
3373 __isl_take isl_union_map *umap,
3374 __isl_take isl_set *set);
3375 __isl_give isl_union_map *isl_union_map_gist_domain(
3376 __isl_take isl_union_map *umap,
3377 __isl_take isl_union_set *uset);
3378 __isl_give isl_union_map *isl_union_map_gist_range(
3379 __isl_take isl_union_map *umap,
3380 __isl_take isl_union_set *uset);
3382 The gist operation returns a set or relation that has the
3383 same intersection with the context as the input set or relation.
3384 Any implicit equality in the intersection is made explicit in the result,
3385 while all inequalities that are redundant with respect to the intersection
3387 In case of union sets and relations, the gist operation is performed
3392 =head3 Lexicographic Optimization
3394 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3395 the following functions
3396 compute a set that contains the lexicographic minimum or maximum
3397 of the elements in C<set> (or C<bset>) for those values of the parameters
3398 that satisfy C<dom>.
3399 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3400 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3402 In other words, the union of the parameter values
3403 for which the result is non-empty and of C<*empty>
3406 __isl_give isl_set *isl_basic_set_partial_lexmin(
3407 __isl_take isl_basic_set *bset,
3408 __isl_take isl_basic_set *dom,
3409 __isl_give isl_set **empty);
3410 __isl_give isl_set *isl_basic_set_partial_lexmax(
3411 __isl_take isl_basic_set *bset,
3412 __isl_take isl_basic_set *dom,
3413 __isl_give isl_set **empty);
3414 __isl_give isl_set *isl_set_partial_lexmin(
3415 __isl_take isl_set *set, __isl_take isl_set *dom,
3416 __isl_give isl_set **empty);
3417 __isl_give isl_set *isl_set_partial_lexmax(
3418 __isl_take isl_set *set, __isl_take isl_set *dom,
3419 __isl_give isl_set **empty);
3421 Given a (basic) set C<set> (or C<bset>), the following functions simply
3422 return a set containing the lexicographic minimum or maximum
3423 of the elements in C<set> (or C<bset>).
3424 In case of union sets, the optimum is computed per space.
3426 __isl_give isl_set *isl_basic_set_lexmin(
3427 __isl_take isl_basic_set *bset);
3428 __isl_give isl_set *isl_basic_set_lexmax(
3429 __isl_take isl_basic_set *bset);
3430 __isl_give isl_set *isl_set_lexmin(
3431 __isl_take isl_set *set);
3432 __isl_give isl_set *isl_set_lexmax(
3433 __isl_take isl_set *set);
3434 __isl_give isl_union_set *isl_union_set_lexmin(
3435 __isl_take isl_union_set *uset);
3436 __isl_give isl_union_set *isl_union_set_lexmax(
3437 __isl_take isl_union_set *uset);
3439 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3440 the following functions
3441 compute a relation that maps each element of C<dom>
3442 to the single lexicographic minimum or maximum
3443 of the elements that are associated to that same
3444 element in C<map> (or C<bmap>).
3445 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3446 that contains the elements in C<dom> that do not map
3447 to any elements in C<map> (or C<bmap>).
3448 In other words, the union of the domain of the result and of C<*empty>
3451 __isl_give isl_map *isl_basic_map_partial_lexmax(
3452 __isl_take isl_basic_map *bmap,
3453 __isl_take isl_basic_set *dom,
3454 __isl_give isl_set **empty);
3455 __isl_give isl_map *isl_basic_map_partial_lexmin(
3456 __isl_take isl_basic_map *bmap,
3457 __isl_take isl_basic_set *dom,
3458 __isl_give isl_set **empty);
3459 __isl_give isl_map *isl_map_partial_lexmax(
3460 __isl_take isl_map *map, __isl_take isl_set *dom,
3461 __isl_give isl_set **empty);
3462 __isl_give isl_map *isl_map_partial_lexmin(
3463 __isl_take isl_map *map, __isl_take isl_set *dom,
3464 __isl_give isl_set **empty);
3466 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3467 return a map mapping each element in the domain of
3468 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3469 of all elements associated to that element.
3470 In case of union relations, the optimum is computed per space.
3472 __isl_give isl_map *isl_basic_map_lexmin(
3473 __isl_take isl_basic_map *bmap);
3474 __isl_give isl_map *isl_basic_map_lexmax(
3475 __isl_take isl_basic_map *bmap);
3476 __isl_give isl_map *isl_map_lexmin(
3477 __isl_take isl_map *map);
3478 __isl_give isl_map *isl_map_lexmax(
3479 __isl_take isl_map *map);
3480 __isl_give isl_union_map *isl_union_map_lexmin(
3481 __isl_take isl_union_map *umap);
3482 __isl_give isl_union_map *isl_union_map_lexmax(
3483 __isl_take isl_union_map *umap);
3485 The following functions return their result in the form of
3486 a piecewise multi-affine expression
3487 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3488 but are otherwise equivalent to the corresponding functions
3489 returning a basic set or relation.
3491 __isl_give isl_pw_multi_aff *
3492 isl_basic_map_lexmin_pw_multi_aff(
3493 __isl_take isl_basic_map *bmap);
3494 __isl_give isl_pw_multi_aff *
3495 isl_basic_set_partial_lexmin_pw_multi_aff(
3496 __isl_take isl_basic_set *bset,
3497 __isl_take isl_basic_set *dom,
3498 __isl_give isl_set **empty);
3499 __isl_give isl_pw_multi_aff *
3500 isl_basic_set_partial_lexmax_pw_multi_aff(
3501 __isl_take isl_basic_set *bset,
3502 __isl_take isl_basic_set *dom,
3503 __isl_give isl_set **empty);
3504 __isl_give isl_pw_multi_aff *
3505 isl_basic_map_partial_lexmin_pw_multi_aff(
3506 __isl_take isl_basic_map *bmap,
3507 __isl_take isl_basic_set *dom,
3508 __isl_give isl_set **empty);
3509 __isl_give isl_pw_multi_aff *
3510 isl_basic_map_partial_lexmax_pw_multi_aff(
3511 __isl_take isl_basic_map *bmap,
3512 __isl_take isl_basic_set *dom,
3513 __isl_give isl_set **empty);
3514 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3515 __isl_take isl_set *set);
3516 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3517 __isl_take isl_set *set);
3518 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3519 __isl_take isl_map *map);
3520 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3521 __isl_take isl_map *map);
3525 Lists are defined over several element types, including
3526 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3527 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3528 Here we take lists of C<isl_set>s as an example.
3529 Lists can be created, copied, modified and freed using the following functions.
3531 #include <isl/list.h>
3532 __isl_give isl_set_list *isl_set_list_from_set(
3533 __isl_take isl_set *el);
3534 __isl_give isl_set_list *isl_set_list_alloc(
3535 isl_ctx *ctx, int n);
3536 __isl_give isl_set_list *isl_set_list_copy(
3537 __isl_keep isl_set_list *list);
3538 __isl_give isl_set_list *isl_set_list_insert(
3539 __isl_take isl_set_list *list, unsigned pos,
3540 __isl_take isl_set *el);
3541 __isl_give isl_set_list *isl_set_list_add(
3542 __isl_take isl_set_list *list,
3543 __isl_take isl_set *el);
3544 __isl_give isl_set_list *isl_set_list_drop(
3545 __isl_take isl_set_list *list,
3546 unsigned first, unsigned n);
3547 __isl_give isl_set_list *isl_set_list_set_set(
3548 __isl_take isl_set_list *list, int index,
3549 __isl_take isl_set *set);
3550 __isl_give isl_set_list *isl_set_list_concat(
3551 __isl_take isl_set_list *list1,
3552 __isl_take isl_set_list *list2);
3553 __isl_give isl_set_list *isl_set_list_sort(
3554 __isl_take isl_set_list *list,
3555 int (*cmp)(__isl_keep isl_set *a,
3556 __isl_keep isl_set *b, void *user),
3558 __isl_null isl_set_list *isl_set_list_free(
3559 __isl_take isl_set_list *list);
3561 C<isl_set_list_alloc> creates an empty list with a capacity for
3562 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3565 Lists can be inspected using the following functions.
3567 #include <isl/list.h>
3568 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3569 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3570 __isl_give isl_set *isl_set_list_get_set(
3571 __isl_keep isl_set_list *list, int index);
3572 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3573 int (*fn)(__isl_take isl_set *el, void *user),
3575 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3576 int (*follows)(__isl_keep isl_set *a,
3577 __isl_keep isl_set *b, void *user),
3579 int (*fn)(__isl_take isl_set *el, void *user),
3582 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3583 strongly connected components of the graph with as vertices the elements
3584 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3585 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3586 should return C<-1> on error.
3588 Lists can be printed using
3590 #include <isl/list.h>
3591 __isl_give isl_printer *isl_printer_print_set_list(
3592 __isl_take isl_printer *p,
3593 __isl_keep isl_set_list *list);
3595 =head2 Associative arrays
3597 Associative arrays map isl objects of a specific type to isl objects
3598 of some (other) specific type. They are defined for several pairs
3599 of types, including (C<isl_map>, C<isl_basic_set>),
3600 (C<isl_id>, C<isl_ast_expr>) and.
3601 (C<isl_id>, C<isl_pw_aff>).
3602 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3605 Associative arrays can be created, copied and freed using
3606 the following functions.
3608 #include <isl/id_to_ast_expr.h>
3609 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3610 isl_ctx *ctx, int min_size);
3611 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3612 __isl_keep id_to_ast_expr *id2expr);
3613 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
3614 __isl_take id_to_ast_expr *id2expr);
3616 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3617 to specify the expected size of the associative array.
3618 The associative array will be grown automatically as needed.
3620 Associative arrays can be inspected using the following functions.
3622 #include <isl/id_to_ast_expr.h>
3623 isl_ctx *isl_id_to_ast_expr_get_ctx(
3624 __isl_keep id_to_ast_expr *id2expr);
3625 int isl_id_to_ast_expr_has(
3626 __isl_keep id_to_ast_expr *id2expr,
3627 __isl_keep isl_id *key);
3628 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3629 __isl_keep id_to_ast_expr *id2expr,
3630 __isl_take isl_id *key);
3631 int isl_id_to_ast_expr_foreach(
3632 __isl_keep id_to_ast_expr *id2expr,
3633 int (*fn)(__isl_take isl_id *key,
3634 __isl_take isl_ast_expr *val, void *user),
3637 They can be modified using the following function.
3639 #include <isl/id_to_ast_expr.h>
3640 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3641 __isl_take id_to_ast_expr *id2expr,
3642 __isl_take isl_id *key,
3643 __isl_take isl_ast_expr *val);
3644 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
3645 __isl_take id_to_ast_expr *id2expr,
3646 __isl_take isl_id *key);
3648 Associative arrays can be printed using the following function.
3650 #include <isl/id_to_ast_expr.h>
3651 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3652 __isl_take isl_printer *p,
3653 __isl_keep id_to_ast_expr *id2expr);
3655 =head2 Multiple Values
3657 An C<isl_multi_val> object represents a sequence of zero or more values,
3658 living in a set space.
3660 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3661 using the following function
3663 #include <isl/val.h>
3664 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3665 __isl_take isl_space *space,
3666 __isl_take isl_val_list *list);
3668 The zero multiple value (with value zero for each set dimension)
3669 can be created using the following function.
3671 #include <isl/val.h>
3672 __isl_give isl_multi_val *isl_multi_val_zero(
3673 __isl_take isl_space *space);
3675 Multiple values can be copied and freed using
3677 #include <isl/val.h>
3678 __isl_give isl_multi_val *isl_multi_val_copy(
3679 __isl_keep isl_multi_val *mv);
3680 __isl_null isl_multi_val *isl_multi_val_free(
3681 __isl_take isl_multi_val *mv);
3683 They can be inspected using
3685 #include <isl/val.h>
3686 isl_ctx *isl_multi_val_get_ctx(
3687 __isl_keep isl_multi_val *mv);
3688 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3689 enum isl_dim_type type);
3690 __isl_give isl_val *isl_multi_val_get_val(
3691 __isl_keep isl_multi_val *mv, int pos);
3692 int isl_multi_val_find_dim_by_id(
3693 __isl_keep isl_multi_val *mv,
3694 enum isl_dim_type type, __isl_keep isl_id *id);
3695 __isl_give isl_id *isl_multi_val_get_dim_id(
3696 __isl_keep isl_multi_val *mv,
3697 enum isl_dim_type type, unsigned pos);
3698 const char *isl_multi_val_get_tuple_name(
3699 __isl_keep isl_multi_val *mv,
3700 enum isl_dim_type type);
3701 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3702 enum isl_dim_type type);
3703 __isl_give isl_id *isl_multi_val_get_tuple_id(
3704 __isl_keep isl_multi_val *mv,
3705 enum isl_dim_type type);
3706 int isl_multi_val_range_is_wrapping(
3707 __isl_keep isl_multi_val *mv);
3709 They can be modified using
3711 #include <isl/val.h>
3712 __isl_give isl_multi_val *isl_multi_val_set_val(
3713 __isl_take isl_multi_val *mv, int pos,
3714 __isl_take isl_val *val);
3715 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3716 __isl_take isl_multi_val *mv,
3717 enum isl_dim_type type, unsigned pos, const char *s);
3718 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3719 __isl_take isl_multi_val *mv,
3720 enum isl_dim_type type, unsigned pos,
3721 __isl_take isl_id *id);
3722 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3723 __isl_take isl_multi_val *mv,
3724 enum isl_dim_type type, const char *s);
3725 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3726 __isl_take isl_multi_val *mv,
3727 enum isl_dim_type type, __isl_take isl_id *id);
3728 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3729 __isl_take isl_multi_val *mv,
3730 enum isl_dim_type type);
3731 __isl_give isl_multi_val *isl_multi_val_reset_user(
3732 __isl_take isl_multi_val *mv);
3734 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3735 __isl_take isl_multi_val *mv,
3736 enum isl_dim_type type, unsigned first, unsigned n);
3737 __isl_give isl_multi_val *isl_multi_val_add_dims(
3738 __isl_take isl_multi_val *mv,
3739 enum isl_dim_type type, unsigned n);
3740 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3741 __isl_take isl_multi_val *mv,
3742 enum isl_dim_type type, unsigned first, unsigned n);
3746 #include <isl/val.h>
3747 __isl_give isl_multi_val *isl_multi_val_align_params(
3748 __isl_take isl_multi_val *mv,
3749 __isl_take isl_space *model);
3750 __isl_give isl_multi_val *isl_multi_val_from_range(
3751 __isl_take isl_multi_val *mv);
3752 __isl_give isl_multi_val *isl_multi_val_range_splice(
3753 __isl_take isl_multi_val *mv1, unsigned pos,
3754 __isl_take isl_multi_val *mv2);
3755 __isl_give isl_multi_val *isl_multi_val_range_product(
3756 __isl_take isl_multi_val *mv1,
3757 __isl_take isl_multi_val *mv2);
3758 __isl_give isl_multi_val *
3759 isl_multi_val_range_factor_domain(
3760 __isl_take isl_multi_val *mv);
3761 __isl_give isl_multi_val *
3762 isl_multi_val_range_factor_range(
3763 __isl_take isl_multi_val *mv);
3764 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3765 __isl_take isl_multi_val *mv1,
3766 __isl_take isl_multi_aff *mv2);
3767 __isl_give isl_multi_val *isl_multi_val_product(
3768 __isl_take isl_multi_val *mv1,
3769 __isl_take isl_multi_val *mv2);
3770 __isl_give isl_multi_val *isl_multi_val_add_val(
3771 __isl_take isl_multi_val *mv,
3772 __isl_take isl_val *v);
3773 __isl_give isl_multi_val *isl_multi_val_mod_val(
3774 __isl_take isl_multi_val *mv,
3775 __isl_take isl_val *v);
3776 __isl_give isl_multi_val *isl_multi_val_scale_val(
3777 __isl_take isl_multi_val *mv,
3778 __isl_take isl_val *v);
3779 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3780 __isl_take isl_multi_val *mv1,
3781 __isl_take isl_multi_val *mv2);
3782 __isl_give isl_multi_val *
3783 isl_multi_val_scale_down_multi_val(
3784 __isl_take isl_multi_val *mv1,
3785 __isl_take isl_multi_val *mv2);
3787 A multiple value can be printed using
3789 __isl_give isl_printer *isl_printer_print_multi_val(
3790 __isl_take isl_printer *p,
3791 __isl_keep isl_multi_val *mv);
3795 Vectors can be created, copied and freed using the following functions.
3797 #include <isl/vec.h>
3798 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3800 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3801 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
3803 Note that the elements of a newly created vector may have arbitrary values.
3804 The elements can be changed and inspected using the following functions.
3806 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3807 int isl_vec_size(__isl_keep isl_vec *vec);
3808 __isl_give isl_val *isl_vec_get_element_val(
3809 __isl_keep isl_vec *vec, int pos);
3810 __isl_give isl_vec *isl_vec_set_element_si(
3811 __isl_take isl_vec *vec, int pos, int v);
3812 __isl_give isl_vec *isl_vec_set_element_val(
3813 __isl_take isl_vec *vec, int pos,
3814 __isl_take isl_val *v);
3815 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3817 __isl_give isl_vec *isl_vec_set_val(
3818 __isl_take isl_vec *vec, __isl_take isl_val *v);
3819 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3820 __isl_keep isl_vec *vec2, int pos);
3822 C<isl_vec_get_element> will return a negative value if anything went wrong.
3823 In that case, the value of C<*v> is undefined.
3825 The following function can be used to concatenate two vectors.
3827 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3828 __isl_take isl_vec *vec2);
3832 Matrices can be created, copied and freed using the following functions.
3834 #include <isl/mat.h>
3835 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3836 unsigned n_row, unsigned n_col);
3837 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3838 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
3840 Note that the elements of a newly created matrix may have arbitrary values.
3841 The elements can be changed and inspected using the following functions.
3843 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3844 int isl_mat_rows(__isl_keep isl_mat *mat);
3845 int isl_mat_cols(__isl_keep isl_mat *mat);
3846 __isl_give isl_val *isl_mat_get_element_val(
3847 __isl_keep isl_mat *mat, int row, int col);
3848 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3849 int row, int col, int v);
3850 __isl_give isl_mat *isl_mat_set_element_val(
3851 __isl_take isl_mat *mat, int row, int col,
3852 __isl_take isl_val *v);
3854 C<isl_mat_get_element> will return a negative value if anything went wrong.
3855 In that case, the value of C<*v> is undefined.
3857 The following function can be used to compute the (right) inverse
3858 of a matrix, i.e., a matrix such that the product of the original
3859 and the inverse (in that order) is a multiple of the identity matrix.
3860 The input matrix is assumed to be of full row-rank.
3862 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3864 The following function can be used to compute the (right) kernel
3865 (or null space) of a matrix, i.e., a matrix such that the product of
3866 the original and the kernel (in that order) is the zero matrix.
3868 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3870 =head2 Piecewise Quasi Affine Expressions
3872 The zero quasi affine expression or the quasi affine expression
3873 that is equal to a given value or
3874 a specified dimension on a given domain can be created using
3876 __isl_give isl_aff *isl_aff_zero_on_domain(
3877 __isl_take isl_local_space *ls);
3878 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3879 __isl_take isl_local_space *ls);
3880 __isl_give isl_aff *isl_aff_val_on_domain(
3881 __isl_take isl_local_space *ls,
3882 __isl_take isl_val *val);
3883 __isl_give isl_aff *isl_aff_var_on_domain(
3884 __isl_take isl_local_space *ls,
3885 enum isl_dim_type type, unsigned pos);
3886 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3887 __isl_take isl_local_space *ls,
3888 enum isl_dim_type type, unsigned pos);
3889 __isl_give isl_aff *isl_aff_nan_on_domain(
3890 __isl_take isl_local_space *ls);
3891 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3892 __isl_take isl_local_space *ls);
3894 Note that the space in which the resulting objects live is a map space
3895 with the given space as domain and a one-dimensional range.
3897 An empty piecewise quasi affine expression (one with no cells)
3898 or a piecewise quasi affine expression with a single cell can
3899 be created using the following functions.
3901 #include <isl/aff.h>
3902 __isl_give isl_pw_aff *isl_pw_aff_empty(
3903 __isl_take isl_space *space);
3904 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3905 __isl_take isl_set *set, __isl_take isl_aff *aff);
3906 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3907 __isl_take isl_aff *aff);
3909 A piecewise quasi affine expression that is equal to 1 on a set
3910 and 0 outside the set can be created using the following function.
3912 #include <isl/aff.h>
3913 __isl_give isl_pw_aff *isl_set_indicator_function(
3914 __isl_take isl_set *set);
3916 Quasi affine expressions can be copied and freed using
3918 #include <isl/aff.h>
3919 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3920 __isl_null isl_aff *isl_aff_free(__isl_take isl_aff *aff);
3922 __isl_give isl_pw_aff *isl_pw_aff_copy(
3923 __isl_keep isl_pw_aff *pwaff);
3924 __isl_null isl_pw_aff *isl_pw_aff_free(
3925 __isl_take isl_pw_aff *pwaff);
3927 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3928 using the following function. The constraint is required to have
3929 a non-zero coefficient for the specified dimension.
3931 #include <isl/constraint.h>
3932 __isl_give isl_aff *isl_constraint_get_bound(
3933 __isl_keep isl_constraint *constraint,
3934 enum isl_dim_type type, int pos);
3936 The entire affine expression of the constraint can also be extracted
3937 using the following function.
3939 #include <isl/constraint.h>
3940 __isl_give isl_aff *isl_constraint_get_aff(
3941 __isl_keep isl_constraint *constraint);
3943 Conversely, an equality constraint equating
3944 the affine expression to zero or an inequality constraint enforcing
3945 the affine expression to be non-negative, can be constructed using
3947 __isl_give isl_constraint *isl_equality_from_aff(
3948 __isl_take isl_aff *aff);
3949 __isl_give isl_constraint *isl_inequality_from_aff(
3950 __isl_take isl_aff *aff);
3952 The expression can be inspected using
3954 #include <isl/aff.h>
3955 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3956 int isl_aff_dim(__isl_keep isl_aff *aff,
3957 enum isl_dim_type type);
3958 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3959 __isl_keep isl_aff *aff);
3960 __isl_give isl_local_space *isl_aff_get_local_space(
3961 __isl_keep isl_aff *aff);
3962 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3963 enum isl_dim_type type, unsigned pos);
3964 const char *isl_pw_aff_get_dim_name(
3965 __isl_keep isl_pw_aff *pa,
3966 enum isl_dim_type type, unsigned pos);
3967 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3968 enum isl_dim_type type, unsigned pos);
3969 __isl_give isl_id *isl_pw_aff_get_dim_id(
3970 __isl_keep isl_pw_aff *pa,
3971 enum isl_dim_type type, unsigned pos);
3972 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
3973 enum isl_dim_type type);
3974 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3975 __isl_keep isl_pw_aff *pa,
3976 enum isl_dim_type type);
3977 __isl_give isl_val *isl_aff_get_constant_val(
3978 __isl_keep isl_aff *aff);
3979 __isl_give isl_val *isl_aff_get_coefficient_val(
3980 __isl_keep isl_aff *aff,
3981 enum isl_dim_type type, int pos);
3982 __isl_give isl_val *isl_aff_get_denominator_val(
3983 __isl_keep isl_aff *aff);
3984 __isl_give isl_aff *isl_aff_get_div(
3985 __isl_keep isl_aff *aff, int pos);
3987 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3988 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3989 int (*fn)(__isl_take isl_set *set,
3990 __isl_take isl_aff *aff,
3991 void *user), void *user);
3993 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3994 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3996 int isl_aff_is_nan(__isl_keep isl_aff *aff);
3997 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
3999 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
4000 enum isl_dim_type type, unsigned first, unsigned n);
4001 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
4002 enum isl_dim_type type, unsigned first, unsigned n);
4004 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
4005 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
4006 enum isl_dim_type type);
4007 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
4009 It can be modified using
4011 #include <isl/aff.h>
4012 __isl_give isl_aff *isl_aff_set_tuple_id(
4013 __isl_take isl_aff *aff,
4014 enum isl_dim_type type, __isl_take isl_id *id);
4015 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
4016 __isl_take isl_pw_aff *pwaff,
4017 enum isl_dim_type type, __isl_take isl_id *id);
4018 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
4019 __isl_take isl_pw_aff *pa,
4020 enum isl_dim_type type);
4021 __isl_give isl_aff *isl_aff_set_dim_name(
4022 __isl_take isl_aff *aff, enum isl_dim_type type,
4023 unsigned pos, const char *s);
4024 __isl_give isl_aff *isl_aff_set_dim_id(
4025 __isl_take isl_aff *aff, enum isl_dim_type type,
4026 unsigned pos, __isl_take isl_id *id);
4027 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
4028 __isl_take isl_pw_aff *pma,
4029 enum isl_dim_type type, unsigned pos,
4030 __isl_take isl_id *id);
4031 __isl_give isl_aff *isl_aff_set_constant_si(
4032 __isl_take isl_aff *aff, int v);
4033 __isl_give isl_aff *isl_aff_set_constant_val(
4034 __isl_take isl_aff *aff, __isl_take isl_val *v);
4035 __isl_give isl_aff *isl_aff_set_coefficient_si(
4036 __isl_take isl_aff *aff,
4037 enum isl_dim_type type, int pos, int v);
4038 __isl_give isl_aff *isl_aff_set_coefficient_val(
4039 __isl_take isl_aff *aff,
4040 enum isl_dim_type type, int pos,
4041 __isl_take isl_val *v);
4043 __isl_give isl_aff *isl_aff_add_constant_si(
4044 __isl_take isl_aff *aff, int v);
4045 __isl_give isl_aff *isl_aff_add_constant_val(
4046 __isl_take isl_aff *aff, __isl_take isl_val *v);
4047 __isl_give isl_aff *isl_aff_add_constant_num_si(
4048 __isl_take isl_aff *aff, int v);
4049 __isl_give isl_aff *isl_aff_add_coefficient_si(
4050 __isl_take isl_aff *aff,
4051 enum isl_dim_type type, int pos, int v);
4052 __isl_give isl_aff *isl_aff_add_coefficient_val(
4053 __isl_take isl_aff *aff,
4054 enum isl_dim_type type, int pos,
4055 __isl_take isl_val *v);
4057 __isl_give isl_aff *isl_aff_insert_dims(
4058 __isl_take isl_aff *aff,
4059 enum isl_dim_type type, unsigned first, unsigned n);
4060 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
4061 __isl_take isl_pw_aff *pwaff,
4062 enum isl_dim_type type, unsigned first, unsigned n);
4063 __isl_give isl_aff *isl_aff_add_dims(
4064 __isl_take isl_aff *aff,
4065 enum isl_dim_type type, unsigned n);
4066 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
4067 __isl_take isl_pw_aff *pwaff,
4068 enum isl_dim_type type, unsigned n);
4069 __isl_give isl_aff *isl_aff_drop_dims(
4070 __isl_take isl_aff *aff,
4071 enum isl_dim_type type, unsigned first, unsigned n);
4072 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
4073 __isl_take isl_pw_aff *pwaff,
4074 enum isl_dim_type type, unsigned first, unsigned n);
4075 __isl_give isl_aff *isl_aff_move_dims(
4076 __isl_take isl_aff *aff,
4077 enum isl_dim_type dst_type, unsigned dst_pos,
4078 enum isl_dim_type src_type, unsigned src_pos,
4080 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
4081 __isl_take isl_pw_aff *pa,
4082 enum isl_dim_type dst_type, unsigned dst_pos,
4083 enum isl_dim_type src_type, unsigned src_pos,
4086 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
4087 set the I<numerator> of the constant or coefficient, while
4088 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
4089 the constant or coefficient as a whole.
4090 The C<add_constant> and C<add_coefficient> functions add an integer
4091 or rational value to
4092 the possibly rational constant or coefficient.
4093 The C<add_constant_num> functions add an integer value to
4096 To check whether an affine expressions is obviously zero
4097 or (obviously) equal to some other affine expression, use
4099 #include <isl/aff.h>
4100 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
4101 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
4102 __isl_keep isl_aff *aff2);
4103 int isl_pw_aff_plain_is_equal(
4104 __isl_keep isl_pw_aff *pwaff1,
4105 __isl_keep isl_pw_aff *pwaff2);
4106 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
4107 __isl_keep isl_pw_aff *pa2);
4108 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4109 __isl_keep isl_pw_aff *pa2);
4111 The function C<isl_pw_aff_plain_cmp> can be used to sort
4112 C<isl_pw_aff>s. The order is not strictly defined.
4113 The current order sorts expressions that only involve
4114 earlier dimensions before those that involve later dimensions.
4118 #include <isl/aff.h>
4119 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
4120 __isl_take isl_aff *aff2);
4121 __isl_give isl_pw_aff *isl_pw_aff_add(
4122 __isl_take isl_pw_aff *pwaff1,
4123 __isl_take isl_pw_aff *pwaff2);
4124 __isl_give isl_pw_aff *isl_pw_aff_min(
4125 __isl_take isl_pw_aff *pwaff1,
4126 __isl_take isl_pw_aff *pwaff2);
4127 __isl_give isl_pw_aff *isl_pw_aff_max(
4128 __isl_take isl_pw_aff *pwaff1,
4129 __isl_take isl_pw_aff *pwaff2);
4130 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
4131 __isl_take isl_aff *aff2);
4132 __isl_give isl_pw_aff *isl_pw_aff_sub(
4133 __isl_take isl_pw_aff *pwaff1,
4134 __isl_take isl_pw_aff *pwaff2);
4135 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
4136 __isl_give isl_pw_aff *isl_pw_aff_neg(
4137 __isl_take isl_pw_aff *pwaff);
4138 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
4139 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4140 __isl_take isl_pw_aff *pwaff);
4141 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
4142 __isl_give isl_pw_aff *isl_pw_aff_floor(
4143 __isl_take isl_pw_aff *pwaff);
4144 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
4145 __isl_take isl_val *mod);
4146 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
4147 __isl_take isl_pw_aff *pa,
4148 __isl_take isl_val *mod);
4149 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
4150 __isl_take isl_val *v);
4151 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
4152 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
4153 __isl_give isl_aff *isl_aff_scale_down_ui(
4154 __isl_take isl_aff *aff, unsigned f);
4155 __isl_give isl_aff *isl_aff_scale_down_val(
4156 __isl_take isl_aff *aff, __isl_take isl_val *v);
4157 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
4158 __isl_take isl_pw_aff *pa,
4159 __isl_take isl_val *f);
4161 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4162 __isl_take isl_pw_aff_list *list);
4163 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4164 __isl_take isl_pw_aff_list *list);
4166 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4167 __isl_take isl_pw_aff *pwqp);
4169 __isl_give isl_aff *isl_aff_align_params(
4170 __isl_take isl_aff *aff,
4171 __isl_take isl_space *model);
4172 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4173 __isl_take isl_pw_aff *pwaff,
4174 __isl_take isl_space *model);
4176 __isl_give isl_aff *isl_aff_project_domain_on_params(
4177 __isl_take isl_aff *aff);
4178 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4179 __isl_take isl_pw_aff *pwa);
4181 __isl_give isl_aff *isl_aff_gist_params(
4182 __isl_take isl_aff *aff,
4183 __isl_take isl_set *context);
4184 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
4185 __isl_take isl_set *context);
4186 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
4187 __isl_take isl_pw_aff *pwaff,
4188 __isl_take isl_set *context);
4189 __isl_give isl_pw_aff *isl_pw_aff_gist(
4190 __isl_take isl_pw_aff *pwaff,
4191 __isl_take isl_set *context);
4193 __isl_give isl_set *isl_pw_aff_domain(
4194 __isl_take isl_pw_aff *pwaff);
4195 __isl_give isl_set *isl_pw_aff_params(
4196 __isl_take isl_pw_aff *pwa);
4197 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4198 __isl_take isl_pw_aff *pa,
4199 __isl_take isl_set *set);
4200 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4201 __isl_take isl_pw_aff *pa,
4202 __isl_take isl_set *set);
4204 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
4205 __isl_take isl_aff *aff2);
4206 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
4207 __isl_take isl_aff *aff2);
4208 __isl_give isl_pw_aff *isl_pw_aff_mul(
4209 __isl_take isl_pw_aff *pwaff1,
4210 __isl_take isl_pw_aff *pwaff2);
4211 __isl_give isl_pw_aff *isl_pw_aff_div(
4212 __isl_take isl_pw_aff *pa1,
4213 __isl_take isl_pw_aff *pa2);
4214 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
4215 __isl_take isl_pw_aff *pa1,
4216 __isl_take isl_pw_aff *pa2);
4217 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
4218 __isl_take isl_pw_aff *pa1,
4219 __isl_take isl_pw_aff *pa2);
4221 When multiplying two affine expressions, at least one of the two needs
4222 to be a constant. Similarly, when dividing an affine expression by another,
4223 the second expression needs to be a constant.
4224 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
4225 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
4228 #include <isl/aff.h>
4229 __isl_give isl_aff *isl_aff_pullback_aff(
4230 __isl_take isl_aff *aff1,
4231 __isl_take isl_aff *aff2);
4232 __isl_give isl_aff *isl_aff_pullback_multi_aff(
4233 __isl_take isl_aff *aff,
4234 __isl_take isl_multi_aff *ma);
4235 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
4236 __isl_take isl_pw_aff *pa,
4237 __isl_take isl_multi_aff *ma);
4238 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
4239 __isl_take isl_pw_aff *pa,
4240 __isl_take isl_pw_multi_aff *pma);
4241 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
4242 __isl_take isl_pw_aff *pa,
4243 __isl_take isl_multi_pw_aff *mpa);
4245 These functions precompose the input expression by the given
4246 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
4247 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
4248 into the (piecewise) affine expression.
4249 Objects of type C<isl_multi_aff> are described in
4250 L</"Piecewise Multiple Quasi Affine Expressions">.
4252 #include <isl/aff.h>
4253 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4254 __isl_take isl_aff *aff);
4255 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4256 __isl_take isl_aff *aff);
4257 __isl_give isl_basic_set *isl_aff_le_basic_set(
4258 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4259 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4260 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4261 __isl_give isl_set *isl_pw_aff_eq_set(
4262 __isl_take isl_pw_aff *pwaff1,
4263 __isl_take isl_pw_aff *pwaff2);
4264 __isl_give isl_set *isl_pw_aff_ne_set(
4265 __isl_take isl_pw_aff *pwaff1,
4266 __isl_take isl_pw_aff *pwaff2);
4267 __isl_give isl_set *isl_pw_aff_le_set(
4268 __isl_take isl_pw_aff *pwaff1,
4269 __isl_take isl_pw_aff *pwaff2);
4270 __isl_give isl_set *isl_pw_aff_lt_set(
4271 __isl_take isl_pw_aff *pwaff1,
4272 __isl_take isl_pw_aff *pwaff2);
4273 __isl_give isl_set *isl_pw_aff_ge_set(
4274 __isl_take isl_pw_aff *pwaff1,
4275 __isl_take isl_pw_aff *pwaff2);
4276 __isl_give isl_set *isl_pw_aff_gt_set(
4277 __isl_take isl_pw_aff *pwaff1,
4278 __isl_take isl_pw_aff *pwaff2);
4280 __isl_give isl_set *isl_pw_aff_list_eq_set(
4281 __isl_take isl_pw_aff_list *list1,
4282 __isl_take isl_pw_aff_list *list2);
4283 __isl_give isl_set *isl_pw_aff_list_ne_set(
4284 __isl_take isl_pw_aff_list *list1,
4285 __isl_take isl_pw_aff_list *list2);
4286 __isl_give isl_set *isl_pw_aff_list_le_set(
4287 __isl_take isl_pw_aff_list *list1,
4288 __isl_take isl_pw_aff_list *list2);
4289 __isl_give isl_set *isl_pw_aff_list_lt_set(
4290 __isl_take isl_pw_aff_list *list1,
4291 __isl_take isl_pw_aff_list *list2);
4292 __isl_give isl_set *isl_pw_aff_list_ge_set(
4293 __isl_take isl_pw_aff_list *list1,
4294 __isl_take isl_pw_aff_list *list2);
4295 __isl_give isl_set *isl_pw_aff_list_gt_set(
4296 __isl_take isl_pw_aff_list *list1,
4297 __isl_take isl_pw_aff_list *list2);
4299 The function C<isl_aff_neg_basic_set> returns a basic set
4300 containing those elements in the domain space
4301 of C<aff> where C<aff> is negative.
4302 The function C<isl_aff_ge_basic_set> returns a basic set
4303 containing those elements in the shared space
4304 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4305 The function C<isl_pw_aff_ge_set> returns a set
4306 containing those elements in the shared domain
4307 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4308 The functions operating on C<isl_pw_aff_list> apply the corresponding
4309 C<isl_pw_aff> function to each pair of elements in the two lists.
4311 #include <isl/aff.h>
4312 __isl_give isl_set *isl_pw_aff_nonneg_set(
4313 __isl_take isl_pw_aff *pwaff);
4314 __isl_give isl_set *isl_pw_aff_zero_set(
4315 __isl_take isl_pw_aff *pwaff);
4316 __isl_give isl_set *isl_pw_aff_non_zero_set(
4317 __isl_take isl_pw_aff *pwaff);
4319 The function C<isl_pw_aff_nonneg_set> returns a set
4320 containing those elements in the domain
4321 of C<pwaff> where C<pwaff> is non-negative.
4323 #include <isl/aff.h>
4324 __isl_give isl_pw_aff *isl_pw_aff_cond(
4325 __isl_take isl_pw_aff *cond,
4326 __isl_take isl_pw_aff *pwaff_true,
4327 __isl_take isl_pw_aff *pwaff_false);
4329 The function C<isl_pw_aff_cond> performs a conditional operator
4330 and returns an expression that is equal to C<pwaff_true>
4331 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4332 where C<cond> is zero.
4334 #include <isl/aff.h>
4335 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4336 __isl_take isl_pw_aff *pwaff1,
4337 __isl_take isl_pw_aff *pwaff2);
4338 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4339 __isl_take isl_pw_aff *pwaff1,
4340 __isl_take isl_pw_aff *pwaff2);
4341 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4342 __isl_take isl_pw_aff *pwaff1,
4343 __isl_take isl_pw_aff *pwaff2);
4345 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4346 expression with a domain that is the union of those of C<pwaff1> and
4347 C<pwaff2> and such that on each cell, the quasi-affine expression is
4348 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4349 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4350 associated expression is the defined one.
4352 An expression can be read from input using
4354 #include <isl/aff.h>
4355 __isl_give isl_aff *isl_aff_read_from_str(
4356 isl_ctx *ctx, const char *str);
4357 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4358 isl_ctx *ctx, const char *str);
4360 An expression can be printed using
4362 #include <isl/aff.h>
4363 __isl_give isl_printer *isl_printer_print_aff(
4364 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4366 __isl_give isl_printer *isl_printer_print_pw_aff(
4367 __isl_take isl_printer *p,
4368 __isl_keep isl_pw_aff *pwaff);
4370 =head2 Piecewise Multiple Quasi Affine Expressions
4372 An C<isl_multi_aff> object represents a sequence of
4373 zero or more affine expressions, all defined on the same domain space.
4374 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4375 zero or more piecewise affine expressions.
4377 An C<isl_multi_aff> can be constructed from a single
4378 C<isl_aff> or an C<isl_aff_list> using the
4379 following functions. Similarly for C<isl_multi_pw_aff>
4380 and C<isl_pw_multi_aff>.
4382 #include <isl/aff.h>
4383 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4384 __isl_take isl_aff *aff);
4385 __isl_give isl_multi_pw_aff *
4386 isl_multi_pw_aff_from_multi_aff(
4387 __isl_take isl_multi_aff *ma);
4388 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4389 __isl_take isl_pw_aff *pa);
4390 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4391 __isl_take isl_pw_aff *pa);
4392 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4393 __isl_take isl_space *space,
4394 __isl_take isl_aff_list *list);
4396 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4397 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4398 Note however that the domain
4399 of the result is the intersection of the domains of the input.
4400 The reverse conversion is exact.
4402 #include <isl/aff.h>
4403 __isl_give isl_pw_multi_aff *
4404 isl_pw_multi_aff_from_multi_pw_aff(
4405 __isl_take isl_multi_pw_aff *mpa);
4406 __isl_give isl_multi_pw_aff *
4407 isl_multi_pw_aff_from_pw_multi_aff(
4408 __isl_take isl_pw_multi_aff *pma);
4410 An empty piecewise multiple quasi affine expression (one with no cells),
4411 the zero piecewise multiple quasi affine expression (with value zero
4412 for each output dimension),
4413 a piecewise multiple quasi affine expression with a single cell (with
4414 either a universe or a specified domain) or
4415 a zero-dimensional piecewise multiple quasi affine expression
4417 can be created using the following functions.
4419 #include <isl/aff.h>
4420 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4421 __isl_take isl_space *space);
4422 __isl_give isl_multi_aff *isl_multi_aff_zero(
4423 __isl_take isl_space *space);
4424 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4425 __isl_take isl_space *space);
4426 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4427 __isl_take isl_space *space);
4428 __isl_give isl_multi_aff *isl_multi_aff_identity(
4429 __isl_take isl_space *space);
4430 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4431 __isl_take isl_space *space);
4432 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4433 __isl_take isl_space *space);
4434 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4435 __isl_take isl_space *space);
4436 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4437 __isl_take isl_space *space);
4438 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4439 __isl_take isl_space *space,
4440 enum isl_dim_type type,
4441 unsigned first, unsigned n);
4442 __isl_give isl_pw_multi_aff *
4443 isl_pw_multi_aff_project_out_map(
4444 __isl_take isl_space *space,
4445 enum isl_dim_type type,
4446 unsigned first, unsigned n);
4447 __isl_give isl_pw_multi_aff *
4448 isl_pw_multi_aff_from_multi_aff(
4449 __isl_take isl_multi_aff *ma);
4450 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4451 __isl_take isl_set *set,
4452 __isl_take isl_multi_aff *maff);
4453 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4454 __isl_take isl_set *set);
4456 __isl_give isl_union_pw_multi_aff *
4457 isl_union_pw_multi_aff_empty(
4458 __isl_take isl_space *space);
4459 __isl_give isl_union_pw_multi_aff *
4460 isl_union_pw_multi_aff_add_pw_multi_aff(
4461 __isl_take isl_union_pw_multi_aff *upma,
4462 __isl_take isl_pw_multi_aff *pma);
4463 __isl_give isl_union_pw_multi_aff *
4464 isl_union_pw_multi_aff_from_domain(
4465 __isl_take isl_union_set *uset);
4467 A piecewise multiple quasi affine expression can also be initialized
4468 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4469 and the C<isl_map> is single-valued.
4470 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4471 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4473 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4474 __isl_take isl_set *set);
4475 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4476 __isl_take isl_map *map);
4478 __isl_give isl_union_pw_multi_aff *
4479 isl_union_pw_multi_aff_from_union_set(
4480 __isl_take isl_union_set *uset);
4481 __isl_give isl_union_pw_multi_aff *
4482 isl_union_pw_multi_aff_from_union_map(
4483 __isl_take isl_union_map *umap);
4485 Multiple quasi affine expressions can be copied and freed using
4487 #include <isl/aff.h>
4488 __isl_give isl_multi_aff *isl_multi_aff_copy(
4489 __isl_keep isl_multi_aff *maff);
4490 __isl_null isl_multi_aff *isl_multi_aff_free(
4491 __isl_take isl_multi_aff *maff);
4493 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4494 __isl_keep isl_pw_multi_aff *pma);
4495 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
4496 __isl_take isl_pw_multi_aff *pma);
4498 __isl_give isl_union_pw_multi_aff *
4499 isl_union_pw_multi_aff_copy(
4500 __isl_keep isl_union_pw_multi_aff *upma);
4501 __isl_null isl_union_pw_multi_aff *
4502 isl_union_pw_multi_aff_free(
4503 __isl_take isl_union_pw_multi_aff *upma);
4505 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4506 __isl_keep isl_multi_pw_aff *mpa);
4507 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
4508 __isl_take isl_multi_pw_aff *mpa);
4510 The expression can be inspected using
4512 #include <isl/aff.h>
4513 isl_ctx *isl_multi_aff_get_ctx(
4514 __isl_keep isl_multi_aff *maff);
4515 isl_ctx *isl_pw_multi_aff_get_ctx(
4516 __isl_keep isl_pw_multi_aff *pma);
4517 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4518 __isl_keep isl_union_pw_multi_aff *upma);
4519 isl_ctx *isl_multi_pw_aff_get_ctx(
4520 __isl_keep isl_multi_pw_aff *mpa);
4522 int isl_multi_aff_involves_dims(
4523 __isl_keep isl_multi_aff *ma,
4524 enum isl_dim_type type, unsigned first, unsigned n);
4525 int isl_multi_pw_aff_involves_dims(
4526 __isl_keep isl_multi_pw_aff *mpa,
4527 enum isl_dim_type type, unsigned first, unsigned n);
4529 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4530 enum isl_dim_type type);
4531 unsigned isl_pw_multi_aff_dim(
4532 __isl_keep isl_pw_multi_aff *pma,
4533 enum isl_dim_type type);
4534 unsigned isl_multi_pw_aff_dim(
4535 __isl_keep isl_multi_pw_aff *mpa,
4536 enum isl_dim_type type);
4537 __isl_give isl_aff *isl_multi_aff_get_aff(
4538 __isl_keep isl_multi_aff *multi, int pos);
4539 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4540 __isl_keep isl_pw_multi_aff *pma, int pos);
4541 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4542 __isl_keep isl_multi_pw_aff *mpa, int pos);
4543 int isl_multi_aff_find_dim_by_id(
4544 __isl_keep isl_multi_aff *ma,
4545 enum isl_dim_type type, __isl_keep isl_id *id);
4546 int isl_multi_pw_aff_find_dim_by_id(
4547 __isl_keep isl_multi_pw_aff *mpa,
4548 enum isl_dim_type type, __isl_keep isl_id *id);
4549 const char *isl_pw_multi_aff_get_dim_name(
4550 __isl_keep isl_pw_multi_aff *pma,
4551 enum isl_dim_type type, unsigned pos);
4552 __isl_give isl_id *isl_multi_aff_get_dim_id(
4553 __isl_keep isl_multi_aff *ma,
4554 enum isl_dim_type type, unsigned pos);
4555 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4556 __isl_keep isl_pw_multi_aff *pma,
4557 enum isl_dim_type type, unsigned pos);
4558 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4559 __isl_keep isl_multi_pw_aff *mpa,
4560 enum isl_dim_type type, unsigned pos);
4561 const char *isl_multi_aff_get_tuple_name(
4562 __isl_keep isl_multi_aff *multi,
4563 enum isl_dim_type type);
4564 int isl_pw_multi_aff_has_tuple_name(
4565 __isl_keep isl_pw_multi_aff *pma,
4566 enum isl_dim_type type);
4567 const char *isl_pw_multi_aff_get_tuple_name(
4568 __isl_keep isl_pw_multi_aff *pma,
4569 enum isl_dim_type type);
4570 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4571 enum isl_dim_type type);
4572 int isl_pw_multi_aff_has_tuple_id(
4573 __isl_keep isl_pw_multi_aff *pma,
4574 enum isl_dim_type type);
4575 int isl_multi_pw_aff_has_tuple_id(
4576 __isl_keep isl_multi_pw_aff *mpa,
4577 enum isl_dim_type type);
4578 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4579 __isl_keep isl_multi_aff *ma,
4580 enum isl_dim_type type);
4581 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4582 __isl_keep isl_pw_multi_aff *pma,
4583 enum isl_dim_type type);
4584 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4585 __isl_keep isl_multi_pw_aff *mpa,
4586 enum isl_dim_type type);
4587 int isl_multi_aff_range_is_wrapping(
4588 __isl_keep isl_multi_aff *ma);
4589 int isl_multi_pw_aff_range_is_wrapping(
4590 __isl_keep isl_multi_pw_aff *mpa);
4592 int isl_pw_multi_aff_foreach_piece(
4593 __isl_keep isl_pw_multi_aff *pma,
4594 int (*fn)(__isl_take isl_set *set,
4595 __isl_take isl_multi_aff *maff,
4596 void *user), void *user);
4598 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4599 __isl_keep isl_union_pw_multi_aff *upma,
4600 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4601 void *user), void *user);
4603 It can be modified using
4605 #include <isl/aff.h>
4606 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4607 __isl_take isl_multi_aff *multi, int pos,
4608 __isl_take isl_aff *aff);
4609 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4610 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4611 __isl_take isl_pw_aff *pa);
4612 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4613 __isl_take isl_multi_aff *maff,
4614 enum isl_dim_type type, unsigned pos, const char *s);
4615 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4616 __isl_take isl_multi_aff *maff,
4617 enum isl_dim_type type, unsigned pos,
4618 __isl_take isl_id *id);
4619 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4620 __isl_take isl_multi_aff *maff,
4621 enum isl_dim_type type, const char *s);
4622 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4623 __isl_take isl_multi_aff *maff,
4624 enum isl_dim_type type, __isl_take isl_id *id);
4625 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4626 __isl_take isl_pw_multi_aff *pma,
4627 enum isl_dim_type type, __isl_take isl_id *id);
4628 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4629 __isl_take isl_multi_aff *ma,
4630 enum isl_dim_type type);
4631 __isl_give isl_multi_pw_aff *
4632 isl_multi_pw_aff_reset_tuple_id(
4633 __isl_take isl_multi_pw_aff *mpa,
4634 enum isl_dim_type type);
4635 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4636 __isl_take isl_multi_aff *ma);
4637 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4638 __isl_take isl_multi_pw_aff *mpa);
4640 __isl_give isl_multi_pw_aff *
4641 isl_multi_pw_aff_set_dim_name(
4642 __isl_take isl_multi_pw_aff *mpa,
4643 enum isl_dim_type type, unsigned pos, const char *s);
4644 __isl_give isl_multi_pw_aff *
4645 isl_multi_pw_aff_set_dim_id(
4646 __isl_take isl_multi_pw_aff *mpa,
4647 enum isl_dim_type type, unsigned pos,
4648 __isl_take isl_id *id);
4649 __isl_give isl_multi_pw_aff *
4650 isl_multi_pw_aff_set_tuple_name(
4651 __isl_take isl_multi_pw_aff *mpa,
4652 enum isl_dim_type type, const char *s);
4654 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4655 __isl_take isl_multi_aff *ma);
4657 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4658 __isl_take isl_multi_aff *ma,
4659 enum isl_dim_type type, unsigned first, unsigned n);
4660 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4661 __isl_take isl_multi_aff *ma,
4662 enum isl_dim_type type, unsigned n);
4663 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4664 __isl_take isl_multi_aff *maff,
4665 enum isl_dim_type type, unsigned first, unsigned n);
4666 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4667 __isl_take isl_pw_multi_aff *pma,
4668 enum isl_dim_type type, unsigned first, unsigned n);
4670 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4671 __isl_take isl_multi_pw_aff *mpa,
4672 enum isl_dim_type type, unsigned first, unsigned n);
4673 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4674 __isl_take isl_multi_pw_aff *mpa,
4675 enum isl_dim_type type, unsigned n);
4676 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4677 __isl_take isl_multi_pw_aff *pma,
4678 enum isl_dim_type dst_type, unsigned dst_pos,
4679 enum isl_dim_type src_type, unsigned src_pos,
4682 To check whether two multiple affine expressions are
4683 (obviously) equal to each other, use
4685 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4686 __isl_keep isl_multi_aff *maff2);
4687 int isl_pw_multi_aff_plain_is_equal(
4688 __isl_keep isl_pw_multi_aff *pma1,
4689 __isl_keep isl_pw_multi_aff *pma2);
4690 int isl_multi_pw_aff_plain_is_equal(
4691 __isl_keep isl_multi_pw_aff *mpa1,
4692 __isl_keep isl_multi_pw_aff *mpa2);
4693 int isl_multi_pw_aff_is_equal(
4694 __isl_keep isl_multi_pw_aff *mpa1,
4695 __isl_keep isl_multi_pw_aff *mpa2);
4699 #include <isl/aff.h>
4700 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4701 __isl_take isl_pw_multi_aff *pma1,
4702 __isl_take isl_pw_multi_aff *pma2);
4703 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4704 __isl_take isl_pw_multi_aff *pma1,
4705 __isl_take isl_pw_multi_aff *pma2);
4706 __isl_give isl_multi_aff *isl_multi_aff_floor(
4707 __isl_take isl_multi_aff *ma);
4708 __isl_give isl_multi_aff *isl_multi_aff_add(
4709 __isl_take isl_multi_aff *maff1,
4710 __isl_take isl_multi_aff *maff2);
4711 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4712 __isl_take isl_pw_multi_aff *pma1,
4713 __isl_take isl_pw_multi_aff *pma2);
4714 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4715 __isl_take isl_union_pw_multi_aff *upma1,
4716 __isl_take isl_union_pw_multi_aff *upma2);
4717 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4718 __isl_take isl_pw_multi_aff *pma1,
4719 __isl_take isl_pw_multi_aff *pma2);
4720 __isl_give isl_multi_aff *isl_multi_aff_sub(
4721 __isl_take isl_multi_aff *ma1,
4722 __isl_take isl_multi_aff *ma2);
4723 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4724 __isl_take isl_pw_multi_aff *pma1,
4725 __isl_take isl_pw_multi_aff *pma2);
4726 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4727 __isl_take isl_union_pw_multi_aff *upma1,
4728 __isl_take isl_union_pw_multi_aff *upma2);
4730 C<isl_multi_aff_sub> subtracts the second argument from the first.
4732 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4733 __isl_take isl_multi_aff *ma,
4734 __isl_take isl_val *v);
4735 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4736 __isl_take isl_pw_multi_aff *pma,
4737 __isl_take isl_val *v);
4738 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4739 __isl_take isl_multi_pw_aff *mpa,
4740 __isl_take isl_val *v);
4741 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4742 __isl_take isl_multi_aff *ma,
4743 __isl_take isl_multi_val *mv);
4744 __isl_give isl_pw_multi_aff *
4745 isl_pw_multi_aff_scale_multi_val(
4746 __isl_take isl_pw_multi_aff *pma,
4747 __isl_take isl_multi_val *mv);
4748 __isl_give isl_multi_pw_aff *
4749 isl_multi_pw_aff_scale_multi_val(
4750 __isl_take isl_multi_pw_aff *mpa,
4751 __isl_take isl_multi_val *mv);
4752 __isl_give isl_union_pw_multi_aff *
4753 isl_union_pw_multi_aff_scale_multi_val(
4754 __isl_take isl_union_pw_multi_aff *upma,
4755 __isl_take isl_multi_val *mv);
4756 __isl_give isl_multi_aff *
4757 isl_multi_aff_scale_down_multi_val(
4758 __isl_take isl_multi_aff *ma,
4759 __isl_take isl_multi_val *mv);
4760 __isl_give isl_multi_pw_aff *
4761 isl_multi_pw_aff_scale_down_multi_val(
4762 __isl_take isl_multi_pw_aff *mpa,
4763 __isl_take isl_multi_val *mv);
4765 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4766 by the corresponding elements of C<mv>.
4768 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4769 __isl_take isl_pw_multi_aff *pma,
4770 enum isl_dim_type type, unsigned pos, int value);
4771 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4772 __isl_take isl_pw_multi_aff *pma,
4773 __isl_take isl_set *set);
4774 __isl_give isl_set *isl_multi_pw_aff_domain(
4775 __isl_take isl_multi_pw_aff *mpa);
4776 __isl_give isl_multi_pw_aff *
4777 isl_multi_pw_aff_intersect_params(
4778 __isl_take isl_multi_pw_aff *mpa,
4779 __isl_take isl_set *set);
4780 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4781 __isl_take isl_pw_multi_aff *pma,
4782 __isl_take isl_set *set);
4783 __isl_give isl_multi_pw_aff *
4784 isl_multi_pw_aff_intersect_domain(
4785 __isl_take isl_multi_pw_aff *mpa,
4786 __isl_take isl_set *domain);
4787 __isl_give isl_union_pw_multi_aff *
4788 isl_union_pw_multi_aff_intersect_domain(
4789 __isl_take isl_union_pw_multi_aff *upma,
4790 __isl_take isl_union_set *uset);
4791 __isl_give isl_multi_aff *isl_multi_aff_lift(
4792 __isl_take isl_multi_aff *maff,
4793 __isl_give isl_local_space **ls);
4794 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4795 __isl_take isl_pw_multi_aff *pma);
4796 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4797 __isl_take isl_multi_pw_aff *mpa);
4798 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4799 __isl_take isl_multi_aff *multi,
4800 __isl_take isl_space *model);
4801 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4802 __isl_take isl_pw_multi_aff *pma,
4803 __isl_take isl_space *model);
4804 __isl_give isl_union_pw_multi_aff *
4805 isl_union_pw_multi_aff_align_params(
4806 __isl_take isl_union_pw_multi_aff *upma,
4807 __isl_take isl_space *model);
4808 __isl_give isl_pw_multi_aff *
4809 isl_pw_multi_aff_project_domain_on_params(
4810 __isl_take isl_pw_multi_aff *pma);
4811 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4812 __isl_take isl_multi_aff *maff,
4813 __isl_take isl_set *context);
4814 __isl_give isl_multi_aff *isl_multi_aff_gist(
4815 __isl_take isl_multi_aff *maff,
4816 __isl_take isl_set *context);
4817 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4818 __isl_take isl_pw_multi_aff *pma,
4819 __isl_take isl_set *set);
4820 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4821 __isl_take isl_pw_multi_aff *pma,
4822 __isl_take isl_set *set);
4823 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4824 __isl_take isl_multi_pw_aff *mpa,
4825 __isl_take isl_set *set);
4826 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4827 __isl_take isl_multi_pw_aff *mpa,
4828 __isl_take isl_set *set);
4829 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4830 __isl_take isl_multi_aff *ma);
4831 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4832 __isl_take isl_multi_pw_aff *mpa);
4833 __isl_give isl_set *isl_pw_multi_aff_domain(
4834 __isl_take isl_pw_multi_aff *pma);
4835 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4836 __isl_take isl_union_pw_multi_aff *upma);
4837 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4838 __isl_take isl_multi_aff *ma1, unsigned pos,
4839 __isl_take isl_multi_aff *ma2);
4840 __isl_give isl_multi_aff *isl_multi_aff_splice(
4841 __isl_take isl_multi_aff *ma1,
4842 unsigned in_pos, unsigned out_pos,
4843 __isl_take isl_multi_aff *ma2);
4844 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4845 __isl_take isl_multi_aff *ma1,
4846 __isl_take isl_multi_aff *ma2);
4847 __isl_give isl_multi_aff *
4848 isl_multi_aff_range_factor_domain(
4849 __isl_take isl_multi_aff *ma);
4850 __isl_give isl_multi_aff *
4851 isl_multi_aff_range_factor_range(
4852 __isl_take isl_multi_aff *ma);
4853 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4854 __isl_take isl_multi_aff *ma1,
4855 __isl_take isl_multi_aff *ma2);
4856 __isl_give isl_multi_aff *isl_multi_aff_product(
4857 __isl_take isl_multi_aff *ma1,
4858 __isl_take isl_multi_aff *ma2);
4859 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4860 __isl_take isl_multi_pw_aff *mpa1,
4861 __isl_take isl_multi_pw_aff *mpa2);
4862 __isl_give isl_pw_multi_aff *
4863 isl_pw_multi_aff_range_product(
4864 __isl_take isl_pw_multi_aff *pma1,
4865 __isl_take isl_pw_multi_aff *pma2);
4866 __isl_give isl_multi_pw_aff *
4867 isl_multi_pw_aff_range_factor_domain(
4868 __isl_take isl_multi_pw_aff *mpa);
4869 __isl_give isl_multi_pw_aff *
4870 isl_multi_pw_aff_range_factor_range(
4871 __isl_take isl_multi_pw_aff *mpa);
4872 __isl_give isl_pw_multi_aff *
4873 isl_pw_multi_aff_flat_range_product(
4874 __isl_take isl_pw_multi_aff *pma1,
4875 __isl_take isl_pw_multi_aff *pma2);
4876 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4877 __isl_take isl_pw_multi_aff *pma1,
4878 __isl_take isl_pw_multi_aff *pma2);
4879 __isl_give isl_union_pw_multi_aff *
4880 isl_union_pw_multi_aff_flat_range_product(
4881 __isl_take isl_union_pw_multi_aff *upma1,
4882 __isl_take isl_union_pw_multi_aff *upma2);
4883 __isl_give isl_multi_pw_aff *
4884 isl_multi_pw_aff_range_splice(
4885 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4886 __isl_take isl_multi_pw_aff *mpa2);
4887 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4888 __isl_take isl_multi_pw_aff *mpa1,
4889 unsigned in_pos, unsigned out_pos,
4890 __isl_take isl_multi_pw_aff *mpa2);
4891 __isl_give isl_multi_pw_aff *
4892 isl_multi_pw_aff_range_product(
4893 __isl_take isl_multi_pw_aff *mpa1,
4894 __isl_take isl_multi_pw_aff *mpa2);
4895 __isl_give isl_multi_pw_aff *
4896 isl_multi_pw_aff_flat_range_product(
4897 __isl_take isl_multi_pw_aff *mpa1,
4898 __isl_take isl_multi_pw_aff *mpa2);
4900 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4901 then it is assigned the local space that lies at the basis of
4902 the lifting applied.
4904 #include <isl/aff.h>
4905 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4906 __isl_take isl_multi_aff *ma1,
4907 __isl_take isl_multi_aff *ma2);
4908 __isl_give isl_pw_multi_aff *
4909 isl_pw_multi_aff_pullback_multi_aff(
4910 __isl_take isl_pw_multi_aff *pma,
4911 __isl_take isl_multi_aff *ma);
4912 __isl_give isl_multi_pw_aff *
4913 isl_multi_pw_aff_pullback_multi_aff(
4914 __isl_take isl_multi_pw_aff *mpa,
4915 __isl_take isl_multi_aff *ma);
4916 __isl_give isl_pw_multi_aff *
4917 isl_pw_multi_aff_pullback_pw_multi_aff(
4918 __isl_take isl_pw_multi_aff *pma1,
4919 __isl_take isl_pw_multi_aff *pma2);
4920 __isl_give isl_multi_pw_aff *
4921 isl_multi_pw_aff_pullback_pw_multi_aff(
4922 __isl_take isl_multi_pw_aff *mpa,
4923 __isl_take isl_pw_multi_aff *pma);
4924 __isl_give isl_multi_pw_aff *
4925 isl_multi_pw_aff_pullback_multi_pw_aff(
4926 __isl_take isl_multi_pw_aff *mpa1,
4927 __isl_take isl_multi_pw_aff *mpa2);
4929 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4930 In other words, C<ma2> is plugged
4933 __isl_give isl_set *isl_multi_aff_lex_le_set(
4934 __isl_take isl_multi_aff *ma1,
4935 __isl_take isl_multi_aff *ma2);
4936 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4937 __isl_take isl_multi_aff *ma1,
4938 __isl_take isl_multi_aff *ma2);
4940 The function C<isl_multi_aff_lex_le_set> returns a set
4941 containing those elements in the shared domain space
4942 where C<ma1> is lexicographically smaller than or
4945 An expression can be read from input using
4947 #include <isl/aff.h>
4948 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4949 isl_ctx *ctx, const char *str);
4950 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4951 isl_ctx *ctx, const char *str);
4952 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4953 isl_ctx *ctx, const char *str);
4954 __isl_give isl_union_pw_multi_aff *
4955 isl_union_pw_multi_aff_read_from_str(
4956 isl_ctx *ctx, const char *str);
4958 An expression can be printed using
4960 #include <isl/aff.h>
4961 __isl_give isl_printer *isl_printer_print_multi_aff(
4962 __isl_take isl_printer *p,
4963 __isl_keep isl_multi_aff *maff);
4964 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4965 __isl_take isl_printer *p,
4966 __isl_keep isl_pw_multi_aff *pma);
4967 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4968 __isl_take isl_printer *p,
4969 __isl_keep isl_union_pw_multi_aff *upma);
4970 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4971 __isl_take isl_printer *p,
4972 __isl_keep isl_multi_pw_aff *mpa);
4976 Points are elements of a set. They can be used to construct
4977 simple sets (boxes) or they can be used to represent the
4978 individual elements of a set.
4979 The zero point (the origin) can be created using
4981 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4983 The coordinates of a point can be inspected, set and changed
4986 __isl_give isl_val *isl_point_get_coordinate_val(
4987 __isl_keep isl_point *pnt,
4988 enum isl_dim_type type, int pos);
4989 __isl_give isl_point *isl_point_set_coordinate_val(
4990 __isl_take isl_point *pnt,
4991 enum isl_dim_type type, int pos,
4992 __isl_take isl_val *v);
4994 __isl_give isl_point *isl_point_add_ui(
4995 __isl_take isl_point *pnt,
4996 enum isl_dim_type type, int pos, unsigned val);
4997 __isl_give isl_point *isl_point_sub_ui(
4998 __isl_take isl_point *pnt,
4999 enum isl_dim_type type, int pos, unsigned val);
5001 Other properties can be obtained using
5003 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
5005 Points can be copied or freed using
5007 __isl_give isl_point *isl_point_copy(
5008 __isl_keep isl_point *pnt);
5009 void isl_point_free(__isl_take isl_point *pnt);
5011 A singleton set can be created from a point using
5013 __isl_give isl_basic_set *isl_basic_set_from_point(
5014 __isl_take isl_point *pnt);
5015 __isl_give isl_set *isl_set_from_point(
5016 __isl_take isl_point *pnt);
5018 and a box can be created from two opposite extremal points using
5020 __isl_give isl_basic_set *isl_basic_set_box_from_points(
5021 __isl_take isl_point *pnt1,
5022 __isl_take isl_point *pnt2);
5023 __isl_give isl_set *isl_set_box_from_points(
5024 __isl_take isl_point *pnt1,
5025 __isl_take isl_point *pnt2);
5027 All elements of a B<bounded> (union) set can be enumerated using
5028 the following functions.
5030 int isl_set_foreach_point(__isl_keep isl_set *set,
5031 int (*fn)(__isl_take isl_point *pnt, void *user),
5033 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
5034 int (*fn)(__isl_take isl_point *pnt, void *user),
5037 The function C<fn> is called for each integer point in
5038 C<set> with as second argument the last argument of
5039 the C<isl_set_foreach_point> call. The function C<fn>
5040 should return C<0> on success and C<-1> on failure.
5041 In the latter case, C<isl_set_foreach_point> will stop
5042 enumerating and return C<-1> as well.
5043 If the enumeration is performed successfully and to completion,
5044 then C<isl_set_foreach_point> returns C<0>.
5046 To obtain a single point of a (basic) set, use
5048 __isl_give isl_point *isl_basic_set_sample_point(
5049 __isl_take isl_basic_set *bset);
5050 __isl_give isl_point *isl_set_sample_point(
5051 __isl_take isl_set *set);
5053 If C<set> does not contain any (integer) points, then the
5054 resulting point will be ``void'', a property that can be
5057 int isl_point_is_void(__isl_keep isl_point *pnt);
5059 =head2 Piecewise Quasipolynomials
5061 A piecewise quasipolynomial is a particular kind of function that maps
5062 a parametric point to a rational value.
5063 More specifically, a quasipolynomial is a polynomial expression in greatest
5064 integer parts of affine expressions of parameters and variables.
5065 A piecewise quasipolynomial is a subdivision of a given parametric
5066 domain into disjoint cells with a quasipolynomial associated to
5067 each cell. The value of the piecewise quasipolynomial at a given
5068 point is the value of the quasipolynomial associated to the cell
5069 that contains the point. Outside of the union of cells,
5070 the value is assumed to be zero.
5071 For example, the piecewise quasipolynomial
5073 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
5075 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
5076 A given piecewise quasipolynomial has a fixed domain dimension.
5077 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
5078 defined over different domains.
5079 Piecewise quasipolynomials are mainly used by the C<barvinok>
5080 library for representing the number of elements in a parametric set or map.
5081 For example, the piecewise quasipolynomial above represents
5082 the number of points in the map
5084 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
5086 =head3 Input and Output
5088 Piecewise quasipolynomials can be read from input using
5090 __isl_give isl_union_pw_qpolynomial *
5091 isl_union_pw_qpolynomial_read_from_str(
5092 isl_ctx *ctx, const char *str);
5094 Quasipolynomials and piecewise quasipolynomials can be printed
5095 using the following functions.
5097 __isl_give isl_printer *isl_printer_print_qpolynomial(
5098 __isl_take isl_printer *p,
5099 __isl_keep isl_qpolynomial *qp);
5101 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
5102 __isl_take isl_printer *p,
5103 __isl_keep isl_pw_qpolynomial *pwqp);
5105 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
5106 __isl_take isl_printer *p,
5107 __isl_keep isl_union_pw_qpolynomial *upwqp);
5109 The output format of the printer
5110 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5111 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
5113 In case of printing in C<ISL_FORMAT_C>, the user may want
5114 to set the names of all dimensions
5116 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
5117 __isl_take isl_qpolynomial *qp,
5118 enum isl_dim_type type, unsigned pos,
5120 __isl_give isl_pw_qpolynomial *
5121 isl_pw_qpolynomial_set_dim_name(
5122 __isl_take isl_pw_qpolynomial *pwqp,
5123 enum isl_dim_type type, unsigned pos,
5126 =head3 Creating New (Piecewise) Quasipolynomials
5128 Some simple quasipolynomials can be created using the following functions.
5129 More complicated quasipolynomials can be created by applying
5130 operations such as addition and multiplication
5131 on the resulting quasipolynomials
5133 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
5134 __isl_take isl_space *domain);
5135 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
5136 __isl_take isl_space *domain);
5137 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
5138 __isl_take isl_space *domain);
5139 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
5140 __isl_take isl_space *domain);
5141 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
5142 __isl_take isl_space *domain);
5143 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
5144 __isl_take isl_space *domain,
5145 __isl_take isl_val *val);
5146 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
5147 __isl_take isl_space *domain,
5148 enum isl_dim_type type, unsigned pos);
5149 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
5150 __isl_take isl_aff *aff);
5152 Note that the space in which a quasipolynomial lives is a map space
5153 with a one-dimensional range. The C<domain> argument in some of
5154 the functions above corresponds to the domain of this map space.
5156 The zero piecewise quasipolynomial or a piecewise quasipolynomial
5157 with a single cell can be created using the following functions.
5158 Multiple of these single cell piecewise quasipolynomials can
5159 be combined to create more complicated piecewise quasipolynomials.
5161 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
5162 __isl_take isl_space *space);
5163 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
5164 __isl_take isl_set *set,
5165 __isl_take isl_qpolynomial *qp);
5166 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
5167 __isl_take isl_qpolynomial *qp);
5168 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
5169 __isl_take isl_pw_aff *pwaff);
5171 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
5172 __isl_take isl_space *space);
5173 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
5174 __isl_take isl_pw_qpolynomial *pwqp);
5175 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
5176 __isl_take isl_union_pw_qpolynomial *upwqp,
5177 __isl_take isl_pw_qpolynomial *pwqp);
5179 Quasipolynomials can be copied and freed again using the following
5182 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
5183 __isl_keep isl_qpolynomial *qp);
5184 __isl_null isl_qpolynomial *isl_qpolynomial_free(
5185 __isl_take isl_qpolynomial *qp);
5187 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
5188 __isl_keep isl_pw_qpolynomial *pwqp);
5189 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
5190 __isl_take isl_pw_qpolynomial *pwqp);
5192 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
5193 __isl_keep isl_union_pw_qpolynomial *upwqp);
5194 __isl_null isl_union_pw_qpolynomial *
5195 isl_union_pw_qpolynomial_free(
5196 __isl_take isl_union_pw_qpolynomial *upwqp);
5198 =head3 Inspecting (Piecewise) Quasipolynomials
5200 To iterate over all piecewise quasipolynomials in a union
5201 piecewise quasipolynomial, use the following function
5203 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
5204 __isl_keep isl_union_pw_qpolynomial *upwqp,
5205 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
5208 To extract the piecewise quasipolynomial in a given space from a union, use
5210 __isl_give isl_pw_qpolynomial *
5211 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
5212 __isl_keep isl_union_pw_qpolynomial *upwqp,
5213 __isl_take isl_space *space);
5215 To iterate over the cells in a piecewise quasipolynomial,
5216 use either of the following two functions
5218 int isl_pw_qpolynomial_foreach_piece(
5219 __isl_keep isl_pw_qpolynomial *pwqp,
5220 int (*fn)(__isl_take isl_set *set,
5221 __isl_take isl_qpolynomial *qp,
5222 void *user), void *user);
5223 int isl_pw_qpolynomial_foreach_lifted_piece(
5224 __isl_keep isl_pw_qpolynomial *pwqp,
5225 int (*fn)(__isl_take isl_set *set,
5226 __isl_take isl_qpolynomial *qp,
5227 void *user), void *user);
5229 As usual, the function C<fn> should return C<0> on success
5230 and C<-1> on failure. The difference between
5231 C<isl_pw_qpolynomial_foreach_piece> and
5232 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
5233 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
5234 compute unique representations for all existentially quantified
5235 variables and then turn these existentially quantified variables
5236 into extra set variables, adapting the associated quasipolynomial
5237 accordingly. This means that the C<set> passed to C<fn>
5238 will not have any existentially quantified variables, but that
5239 the dimensions of the sets may be different for different
5240 invocations of C<fn>.
5242 The constant term of a quasipolynomial can be extracted using
5244 __isl_give isl_val *isl_qpolynomial_get_constant_val(
5245 __isl_keep isl_qpolynomial *qp);
5247 To iterate over all terms in a quasipolynomial,
5250 int isl_qpolynomial_foreach_term(
5251 __isl_keep isl_qpolynomial *qp,
5252 int (*fn)(__isl_take isl_term *term,
5253 void *user), void *user);
5255 The terms themselves can be inspected and freed using
5258 unsigned isl_term_dim(__isl_keep isl_term *term,
5259 enum isl_dim_type type);
5260 __isl_give isl_val *isl_term_get_coefficient_val(
5261 __isl_keep isl_term *term);
5262 int isl_term_get_exp(__isl_keep isl_term *term,
5263 enum isl_dim_type type, unsigned pos);
5264 __isl_give isl_aff *isl_term_get_div(
5265 __isl_keep isl_term *term, unsigned pos);
5266 void isl_term_free(__isl_take isl_term *term);
5268 Each term is a product of parameters, set variables and
5269 integer divisions. The function C<isl_term_get_exp>
5270 returns the exponent of a given dimensions in the given term.
5272 =head3 Properties of (Piecewise) Quasipolynomials
5274 To check whether two union piecewise quasipolynomials are
5275 obviously equal, use
5277 int isl_union_pw_qpolynomial_plain_is_equal(
5278 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5279 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5281 =head3 Operations on (Piecewise) Quasipolynomials
5283 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5284 __isl_take isl_qpolynomial *qp,
5285 __isl_take isl_val *v);
5286 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5287 __isl_take isl_qpolynomial *qp);
5288 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5289 __isl_take isl_qpolynomial *qp1,
5290 __isl_take isl_qpolynomial *qp2);
5291 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5292 __isl_take isl_qpolynomial *qp1,
5293 __isl_take isl_qpolynomial *qp2);
5294 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5295 __isl_take isl_qpolynomial *qp1,
5296 __isl_take isl_qpolynomial *qp2);
5297 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5298 __isl_take isl_qpolynomial *qp, unsigned exponent);
5300 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5301 __isl_take isl_pw_qpolynomial *pwqp,
5302 enum isl_dim_type type, unsigned n,
5303 __isl_take isl_val *v);
5304 __isl_give isl_pw_qpolynomial *
5305 isl_pw_qpolynomial_scale_val(
5306 __isl_take isl_pw_qpolynomial *pwqp,
5307 __isl_take isl_val *v);
5308 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5309 __isl_take isl_pw_qpolynomial *pwqp1,
5310 __isl_take isl_pw_qpolynomial *pwqp2);
5311 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5312 __isl_take isl_pw_qpolynomial *pwqp1,
5313 __isl_take isl_pw_qpolynomial *pwqp2);
5314 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5315 __isl_take isl_pw_qpolynomial *pwqp1,
5316 __isl_take isl_pw_qpolynomial *pwqp2);
5317 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5318 __isl_take isl_pw_qpolynomial *pwqp);
5319 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5320 __isl_take isl_pw_qpolynomial *pwqp1,
5321 __isl_take isl_pw_qpolynomial *pwqp2);
5322 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5323 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5325 __isl_give isl_union_pw_qpolynomial *
5326 isl_union_pw_qpolynomial_scale_val(
5327 __isl_take isl_union_pw_qpolynomial *upwqp,
5328 __isl_take isl_val *v);
5329 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5330 __isl_take isl_union_pw_qpolynomial *upwqp1,
5331 __isl_take isl_union_pw_qpolynomial *upwqp2);
5332 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5333 __isl_take isl_union_pw_qpolynomial *upwqp1,
5334 __isl_take isl_union_pw_qpolynomial *upwqp2);
5335 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5336 __isl_take isl_union_pw_qpolynomial *upwqp1,
5337 __isl_take isl_union_pw_qpolynomial *upwqp2);
5339 __isl_give isl_val *isl_pw_qpolynomial_eval(
5340 __isl_take isl_pw_qpolynomial *pwqp,
5341 __isl_take isl_point *pnt);
5343 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5344 __isl_take isl_union_pw_qpolynomial *upwqp,
5345 __isl_take isl_point *pnt);
5347 __isl_give isl_set *isl_pw_qpolynomial_domain(
5348 __isl_take isl_pw_qpolynomial *pwqp);
5349 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5350 __isl_take isl_pw_qpolynomial *pwpq,
5351 __isl_take isl_set *set);
5352 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5353 __isl_take isl_pw_qpolynomial *pwpq,
5354 __isl_take isl_set *set);
5356 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5357 __isl_take isl_union_pw_qpolynomial *upwqp);
5358 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5359 __isl_take isl_union_pw_qpolynomial *upwpq,
5360 __isl_take isl_union_set *uset);
5361 __isl_give isl_union_pw_qpolynomial *
5362 isl_union_pw_qpolynomial_intersect_params(
5363 __isl_take isl_union_pw_qpolynomial *upwpq,
5364 __isl_take isl_set *set);
5366 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5367 __isl_take isl_qpolynomial *qp,
5368 __isl_take isl_space *model);
5370 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5371 __isl_take isl_qpolynomial *qp);
5372 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5373 __isl_take isl_pw_qpolynomial *pwqp);
5375 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5376 __isl_take isl_union_pw_qpolynomial *upwqp);
5378 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5379 __isl_take isl_qpolynomial *qp,
5380 __isl_take isl_set *context);
5381 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5382 __isl_take isl_qpolynomial *qp,
5383 __isl_take isl_set *context);
5385 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5386 __isl_take isl_pw_qpolynomial *pwqp,
5387 __isl_take isl_set *context);
5388 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5389 __isl_take isl_pw_qpolynomial *pwqp,
5390 __isl_take isl_set *context);
5392 __isl_give isl_union_pw_qpolynomial *
5393 isl_union_pw_qpolynomial_gist_params(
5394 __isl_take isl_union_pw_qpolynomial *upwqp,
5395 __isl_take isl_set *context);
5396 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5397 __isl_take isl_union_pw_qpolynomial *upwqp,
5398 __isl_take isl_union_set *context);
5400 The gist operation applies the gist operation to each of
5401 the cells in the domain of the input piecewise quasipolynomial.
5402 The context is also exploited
5403 to simplify the quasipolynomials associated to each cell.
5405 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5406 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5407 __isl_give isl_union_pw_qpolynomial *
5408 isl_union_pw_qpolynomial_to_polynomial(
5409 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5411 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5412 the polynomial will be an overapproximation. If C<sign> is negative,
5413 it will be an underapproximation. If C<sign> is zero, the approximation
5414 will lie somewhere in between.
5416 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5418 A piecewise quasipolynomial reduction is a piecewise
5419 reduction (or fold) of quasipolynomials.
5420 In particular, the reduction can be maximum or a minimum.
5421 The objects are mainly used to represent the result of
5422 an upper or lower bound on a quasipolynomial over its domain,
5423 i.e., as the result of the following function.
5425 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5426 __isl_take isl_pw_qpolynomial *pwqp,
5427 enum isl_fold type, int *tight);
5429 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5430 __isl_take isl_union_pw_qpolynomial *upwqp,
5431 enum isl_fold type, int *tight);
5433 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5434 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5435 is the returned bound is known be tight, i.e., for each value
5436 of the parameters there is at least
5437 one element in the domain that reaches the bound.
5438 If the domain of C<pwqp> is not wrapping, then the bound is computed
5439 over all elements in that domain and the result has a purely parametric
5440 domain. If the domain of C<pwqp> is wrapping, then the bound is
5441 computed over the range of the wrapped relation. The domain of the
5442 wrapped relation becomes the domain of the result.
5444 A (piecewise) quasipolynomial reduction can be copied or freed using the
5445 following functions.
5447 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5448 __isl_keep isl_qpolynomial_fold *fold);
5449 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5450 __isl_keep isl_pw_qpolynomial_fold *pwf);
5451 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5452 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5453 void isl_qpolynomial_fold_free(
5454 __isl_take isl_qpolynomial_fold *fold);
5455 __isl_null isl_pw_qpolynomial_fold *
5456 isl_pw_qpolynomial_fold_free(
5457 __isl_take isl_pw_qpolynomial_fold *pwf);
5458 __isl_null isl_union_pw_qpolynomial_fold *
5459 isl_union_pw_qpolynomial_fold_free(
5460 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5462 =head3 Printing Piecewise Quasipolynomial Reductions
5464 Piecewise quasipolynomial reductions can be printed
5465 using the following function.
5467 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5468 __isl_take isl_printer *p,
5469 __isl_keep isl_pw_qpolynomial_fold *pwf);
5470 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5471 __isl_take isl_printer *p,
5472 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5474 For C<isl_printer_print_pw_qpolynomial_fold>,
5475 output format of the printer
5476 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5477 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5478 output format of the printer
5479 needs to be set to C<ISL_FORMAT_ISL>.
5480 In case of printing in C<ISL_FORMAT_C>, the user may want
5481 to set the names of all dimensions
5483 __isl_give isl_pw_qpolynomial_fold *
5484 isl_pw_qpolynomial_fold_set_dim_name(
5485 __isl_take isl_pw_qpolynomial_fold *pwf,
5486 enum isl_dim_type type, unsigned pos,
5489 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5491 To iterate over all piecewise quasipolynomial reductions in a union
5492 piecewise quasipolynomial reduction, use the following function
5494 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5495 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5496 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5497 void *user), void *user);
5499 To iterate over the cells in a piecewise quasipolynomial reduction,
5500 use either of the following two functions
5502 int isl_pw_qpolynomial_fold_foreach_piece(
5503 __isl_keep isl_pw_qpolynomial_fold *pwf,
5504 int (*fn)(__isl_take isl_set *set,
5505 __isl_take isl_qpolynomial_fold *fold,
5506 void *user), void *user);
5507 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5508 __isl_keep isl_pw_qpolynomial_fold *pwf,
5509 int (*fn)(__isl_take isl_set *set,
5510 __isl_take isl_qpolynomial_fold *fold,
5511 void *user), void *user);
5513 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5514 of the difference between these two functions.
5516 To iterate over all quasipolynomials in a reduction, use
5518 int isl_qpolynomial_fold_foreach_qpolynomial(
5519 __isl_keep isl_qpolynomial_fold *fold,
5520 int (*fn)(__isl_take isl_qpolynomial *qp,
5521 void *user), void *user);
5523 =head3 Properties of Piecewise Quasipolynomial Reductions
5525 To check whether two union piecewise quasipolynomial reductions are
5526 obviously equal, use
5528 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5529 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5530 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5532 =head3 Operations on Piecewise Quasipolynomial Reductions
5534 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5535 __isl_take isl_qpolynomial_fold *fold,
5536 __isl_take isl_val *v);
5537 __isl_give isl_pw_qpolynomial_fold *
5538 isl_pw_qpolynomial_fold_scale_val(
5539 __isl_take isl_pw_qpolynomial_fold *pwf,
5540 __isl_take isl_val *v);
5541 __isl_give isl_union_pw_qpolynomial_fold *
5542 isl_union_pw_qpolynomial_fold_scale_val(
5543 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5544 __isl_take isl_val *v);
5546 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5547 __isl_take isl_pw_qpolynomial_fold *pwf1,
5548 __isl_take isl_pw_qpolynomial_fold *pwf2);
5550 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5551 __isl_take isl_pw_qpolynomial_fold *pwf1,
5552 __isl_take isl_pw_qpolynomial_fold *pwf2);
5554 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5555 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5556 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5558 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5559 __isl_take isl_pw_qpolynomial_fold *pwf,
5560 __isl_take isl_point *pnt);
5562 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5563 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5564 __isl_take isl_point *pnt);
5566 __isl_give isl_pw_qpolynomial_fold *
5567 isl_pw_qpolynomial_fold_intersect_params(
5568 __isl_take isl_pw_qpolynomial_fold *pwf,
5569 __isl_take isl_set *set);
5571 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5572 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5573 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5574 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5575 __isl_take isl_union_set *uset);
5576 __isl_give isl_union_pw_qpolynomial_fold *
5577 isl_union_pw_qpolynomial_fold_intersect_params(
5578 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5579 __isl_take isl_set *set);
5581 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5582 __isl_take isl_pw_qpolynomial_fold *pwf);
5584 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5585 __isl_take isl_pw_qpolynomial_fold *pwf);
5587 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5588 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5590 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5591 __isl_take isl_qpolynomial_fold *fold,
5592 __isl_take isl_set *context);
5593 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5594 __isl_take isl_qpolynomial_fold *fold,
5595 __isl_take isl_set *context);
5597 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5598 __isl_take isl_pw_qpolynomial_fold *pwf,
5599 __isl_take isl_set *context);
5600 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5601 __isl_take isl_pw_qpolynomial_fold *pwf,
5602 __isl_take isl_set *context);
5604 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5605 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5606 __isl_take isl_union_set *context);
5607 __isl_give isl_union_pw_qpolynomial_fold *
5608 isl_union_pw_qpolynomial_fold_gist_params(
5609 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5610 __isl_take isl_set *context);
5612 The gist operation applies the gist operation to each of
5613 the cells in the domain of the input piecewise quasipolynomial reduction.
5614 In future, the operation will also exploit the context
5615 to simplify the quasipolynomial reductions associated to each cell.
5617 __isl_give isl_pw_qpolynomial_fold *
5618 isl_set_apply_pw_qpolynomial_fold(
5619 __isl_take isl_set *set,
5620 __isl_take isl_pw_qpolynomial_fold *pwf,
5622 __isl_give isl_pw_qpolynomial_fold *
5623 isl_map_apply_pw_qpolynomial_fold(
5624 __isl_take isl_map *map,
5625 __isl_take isl_pw_qpolynomial_fold *pwf,
5627 __isl_give isl_union_pw_qpolynomial_fold *
5628 isl_union_set_apply_union_pw_qpolynomial_fold(
5629 __isl_take isl_union_set *uset,
5630 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5632 __isl_give isl_union_pw_qpolynomial_fold *
5633 isl_union_map_apply_union_pw_qpolynomial_fold(
5634 __isl_take isl_union_map *umap,
5635 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5638 The functions taking a map
5639 compose the given map with the given piecewise quasipolynomial reduction.
5640 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5641 over all elements in the intersection of the range of the map
5642 and the domain of the piecewise quasipolynomial reduction
5643 as a function of an element in the domain of the map.
5644 The functions taking a set compute a bound over all elements in the
5645 intersection of the set and the domain of the
5646 piecewise quasipolynomial reduction.
5648 =head2 Parametric Vertex Enumeration
5650 The parametric vertex enumeration described in this section
5651 is mainly intended to be used internally and by the C<barvinok>
5654 #include <isl/vertices.h>
5655 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5656 __isl_keep isl_basic_set *bset);
5658 The function C<isl_basic_set_compute_vertices> performs the
5659 actual computation of the parametric vertices and the chamber
5660 decomposition and store the result in an C<isl_vertices> object.
5661 This information can be queried by either iterating over all
5662 the vertices or iterating over all the chambers or cells
5663 and then iterating over all vertices that are active on the chamber.
5665 int isl_vertices_foreach_vertex(
5666 __isl_keep isl_vertices *vertices,
5667 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5670 int isl_vertices_foreach_cell(
5671 __isl_keep isl_vertices *vertices,
5672 int (*fn)(__isl_take isl_cell *cell, void *user),
5674 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5675 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5678 Other operations that can be performed on an C<isl_vertices> object are
5681 isl_ctx *isl_vertices_get_ctx(
5682 __isl_keep isl_vertices *vertices);
5683 int isl_vertices_get_n_vertices(
5684 __isl_keep isl_vertices *vertices);
5685 void isl_vertices_free(__isl_take isl_vertices *vertices);
5687 Vertices can be inspected and destroyed using the following functions.
5689 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5690 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5691 __isl_give isl_basic_set *isl_vertex_get_domain(
5692 __isl_keep isl_vertex *vertex);
5693 __isl_give isl_multi_aff *isl_vertex_get_expr(
5694 __isl_keep isl_vertex *vertex);
5695 void isl_vertex_free(__isl_take isl_vertex *vertex);
5697 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
5698 describing the vertex in terms of the parameters,
5699 while C<isl_vertex_get_domain> returns the activity domain
5702 Chambers can be inspected and destroyed using the following functions.
5704 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5705 __isl_give isl_basic_set *isl_cell_get_domain(
5706 __isl_keep isl_cell *cell);
5707 void isl_cell_free(__isl_take isl_cell *cell);
5709 =head1 Polyhedral Compilation Library
5711 This section collects functionality in C<isl> that has been specifically
5712 designed for use during polyhedral compilation.
5714 =head2 Dependence Analysis
5716 C<isl> contains specialized functionality for performing
5717 array dataflow analysis. That is, given a I<sink> access relation
5718 and a collection of possible I<source> access relations,
5719 C<isl> can compute relations that describe
5720 for each iteration of the sink access, which iteration
5721 of which of the source access relations was the last
5722 to access the same data element before the given iteration
5724 The resulting dependence relations map source iterations
5725 to the corresponding sink iterations.
5726 To compute standard flow dependences, the sink should be
5727 a read, while the sources should be writes.
5728 If any of the source accesses are marked as being I<may>
5729 accesses, then there will be a dependence from the last
5730 I<must> access B<and> from any I<may> access that follows
5731 this last I<must> access.
5732 In particular, if I<all> sources are I<may> accesses,
5733 then memory based dependence analysis is performed.
5734 If, on the other hand, all sources are I<must> accesses,
5735 then value based dependence analysis is performed.
5737 #include <isl/flow.h>
5739 typedef int (*isl_access_level_before)(void *first, void *second);
5741 __isl_give isl_access_info *isl_access_info_alloc(
5742 __isl_take isl_map *sink,
5743 void *sink_user, isl_access_level_before fn,
5745 __isl_give isl_access_info *isl_access_info_add_source(
5746 __isl_take isl_access_info *acc,
5747 __isl_take isl_map *source, int must,
5749 __isl_null isl_access_info *isl_access_info_free(
5750 __isl_take isl_access_info *acc);
5752 __isl_give isl_flow *isl_access_info_compute_flow(
5753 __isl_take isl_access_info *acc);
5755 int isl_flow_foreach(__isl_keep isl_flow *deps,
5756 int (*fn)(__isl_take isl_map *dep, int must,
5757 void *dep_user, void *user),
5759 __isl_give isl_map *isl_flow_get_no_source(
5760 __isl_keep isl_flow *deps, int must);
5761 void isl_flow_free(__isl_take isl_flow *deps);
5763 The function C<isl_access_info_compute_flow> performs the actual
5764 dependence analysis. The other functions are used to construct
5765 the input for this function or to read off the output.
5767 The input is collected in an C<isl_access_info>, which can
5768 be created through a call to C<isl_access_info_alloc>.
5769 The arguments to this functions are the sink access relation
5770 C<sink>, a token C<sink_user> used to identify the sink
5771 access to the user, a callback function for specifying the
5772 relative order of source and sink accesses, and the number
5773 of source access relations that will be added.
5774 The callback function has type C<int (*)(void *first, void *second)>.
5775 The function is called with two user supplied tokens identifying
5776 either a source or the sink and it should return the shared nesting
5777 level and the relative order of the two accesses.
5778 In particular, let I<n> be the number of loops shared by
5779 the two accesses. If C<first> precedes C<second> textually,
5780 then the function should return I<2 * n + 1>; otherwise,
5781 it should return I<2 * n>.
5782 The sources can be added to the C<isl_access_info> by performing
5783 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5784 C<must> indicates whether the source is a I<must> access
5785 or a I<may> access. Note that a multi-valued access relation
5786 should only be marked I<must> if every iteration in the domain
5787 of the relation accesses I<all> elements in its image.
5788 The C<source_user> token is again used to identify
5789 the source access. The range of the source access relation
5790 C<source> should have the same dimension as the range
5791 of the sink access relation.
5792 The C<isl_access_info_free> function should usually not be
5793 called explicitly, because it is called implicitly by
5794 C<isl_access_info_compute_flow>.
5796 The result of the dependence analysis is collected in an
5797 C<isl_flow>. There may be elements of
5798 the sink access for which no preceding source access could be
5799 found or for which all preceding sources are I<may> accesses.
5800 The relations containing these elements can be obtained through
5801 calls to C<isl_flow_get_no_source>, the first with C<must> set
5802 and the second with C<must> unset.
5803 In the case of standard flow dependence analysis,
5804 with the sink a read and the sources I<must> writes,
5805 the first relation corresponds to the reads from uninitialized
5806 array elements and the second relation is empty.
5807 The actual flow dependences can be extracted using
5808 C<isl_flow_foreach>. This function will call the user-specified
5809 callback function C<fn> for each B<non-empty> dependence between
5810 a source and the sink. The callback function is called
5811 with four arguments, the actual flow dependence relation
5812 mapping source iterations to sink iterations, a boolean that
5813 indicates whether it is a I<must> or I<may> dependence, a token
5814 identifying the source and an additional C<void *> with value
5815 equal to the third argument of the C<isl_flow_foreach> call.
5816 A dependence is marked I<must> if it originates from a I<must>
5817 source and if it is not followed by any I<may> sources.
5819 After finishing with an C<isl_flow>, the user should call
5820 C<isl_flow_free> to free all associated memory.
5822 A higher-level interface to dependence analysis is provided
5823 by the following function.
5825 #include <isl/flow.h>
5827 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5828 __isl_take isl_union_map *must_source,
5829 __isl_take isl_union_map *may_source,
5830 __isl_take isl_union_map *schedule,
5831 __isl_give isl_union_map **must_dep,
5832 __isl_give isl_union_map **may_dep,
5833 __isl_give isl_union_map **must_no_source,
5834 __isl_give isl_union_map **may_no_source);
5836 The arrays are identified by the tuple names of the ranges
5837 of the accesses. The iteration domains by the tuple names
5838 of the domains of the accesses and of the schedule.
5839 The relative order of the iteration domains is given by the
5840 schedule. The relations returned through C<must_no_source>
5841 and C<may_no_source> are subsets of C<sink>.
5842 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5843 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5844 any of the other arguments is treated as an error.
5846 =head3 Interaction with Dependence Analysis
5848 During the dependence analysis, we frequently need to perform
5849 the following operation. Given a relation between sink iterations
5850 and potential source iterations from a particular source domain,
5851 what is the last potential source iteration corresponding to each
5852 sink iteration. It can sometimes be convenient to adjust
5853 the set of potential source iterations before or after each such operation.
5854 The prototypical example is fuzzy array dataflow analysis,
5855 where we need to analyze if, based on data-dependent constraints,
5856 the sink iteration can ever be executed without one or more of
5857 the corresponding potential source iterations being executed.
5858 If so, we can introduce extra parameters and select an unknown
5859 but fixed source iteration from the potential source iterations.
5860 To be able to perform such manipulations, C<isl> provides the following
5863 #include <isl/flow.h>
5865 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5866 __isl_keep isl_map *source_map,
5867 __isl_keep isl_set *sink, void *source_user,
5869 __isl_give isl_access_info *isl_access_info_set_restrict(
5870 __isl_take isl_access_info *acc,
5871 isl_access_restrict fn, void *user);
5873 The function C<isl_access_info_set_restrict> should be called
5874 before calling C<isl_access_info_compute_flow> and registers a callback function
5875 that will be called any time C<isl> is about to compute the last
5876 potential source. The first argument is the (reverse) proto-dependence,
5877 mapping sink iterations to potential source iterations.
5878 The second argument represents the sink iterations for which
5879 we want to compute the last source iteration.
5880 The third argument is the token corresponding to the source
5881 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5882 The callback is expected to return a restriction on either the input or
5883 the output of the operation computing the last potential source.
5884 If the input needs to be restricted then restrictions are needed
5885 for both the source and the sink iterations. The sink iterations
5886 and the potential source iterations will be intersected with these sets.
5887 If the output needs to be restricted then only a restriction on the source
5888 iterations is required.
5889 If any error occurs, the callback should return C<NULL>.
5890 An C<isl_restriction> object can be created, freed and inspected
5891 using the following functions.
5893 #include <isl/flow.h>
5895 __isl_give isl_restriction *isl_restriction_input(
5896 __isl_take isl_set *source_restr,
5897 __isl_take isl_set *sink_restr);
5898 __isl_give isl_restriction *isl_restriction_output(
5899 __isl_take isl_set *source_restr);
5900 __isl_give isl_restriction *isl_restriction_none(
5901 __isl_take isl_map *source_map);
5902 __isl_give isl_restriction *isl_restriction_empty(
5903 __isl_take isl_map *source_map);
5904 __isl_null isl_restriction *isl_restriction_free(
5905 __isl_take isl_restriction *restr);
5906 isl_ctx *isl_restriction_get_ctx(
5907 __isl_keep isl_restriction *restr);
5909 C<isl_restriction_none> and C<isl_restriction_empty> are special
5910 cases of C<isl_restriction_input>. C<isl_restriction_none>
5911 is essentially equivalent to
5913 isl_restriction_input(isl_set_universe(
5914 isl_space_range(isl_map_get_space(source_map))),
5916 isl_space_domain(isl_map_get_space(source_map))));
5918 whereas C<isl_restriction_empty> is essentially equivalent to
5920 isl_restriction_input(isl_set_empty(
5921 isl_space_range(isl_map_get_space(source_map))),
5923 isl_space_domain(isl_map_get_space(source_map))));
5927 B<The functionality described in this section is fairly new
5928 and may be subject to change.>
5930 #include <isl/schedule.h>
5931 __isl_give isl_schedule *
5932 isl_schedule_constraints_compute_schedule(
5933 __isl_take isl_schedule_constraints *sc);
5934 __isl_null isl_schedule *isl_schedule_free(
5935 __isl_take isl_schedule *sched);
5937 The function C<isl_schedule_constraints_compute_schedule> can be
5938 used to compute a schedule that satisfy the given schedule constraints.
5939 These schedule constraints include the iteration domain for which
5940 a schedule should be computed and dependences between pairs of
5941 iterations. In particular, these dependences include
5942 I<validity> dependences and I<proximity> dependences.
5943 By default, the algorithm used to construct the schedule is similar
5944 to that of C<Pluto>.
5945 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5947 The generated schedule respects all validity dependences.
5948 That is, all dependence distances over these dependences in the
5949 scheduled space are lexicographically positive.
5950 The default algorithm tries to ensure that the dependence distances
5951 over coincidence constraints are zero and to minimize the
5952 dependence distances over proximity dependences.
5953 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5954 for groups of domains where the dependence distances over validity
5955 dependences have only non-negative values.
5956 When using Feautrier's algorithm, the coincidence and proximity constraints
5957 are only taken into account during the extension to a
5958 full-dimensional schedule.
5960 An C<isl_schedule_constraints> object can be constructed
5961 and manipulated using the following functions.
5963 #include <isl/schedule.h>
5964 __isl_give isl_schedule_constraints *
5965 isl_schedule_constraints_copy(
5966 __isl_keep isl_schedule_constraints *sc);
5967 __isl_give isl_schedule_constraints *
5968 isl_schedule_constraints_on_domain(
5969 __isl_take isl_union_set *domain);
5970 isl_ctx *isl_schedule_constraints_get_ctx(
5971 __isl_keep isl_schedule_constraints *sc);
5972 __isl_give isl_schedule_constraints *
5973 isl_schedule_constraints_set_validity(
5974 __isl_take isl_schedule_constraints *sc,
5975 __isl_take isl_union_map *validity);
5976 __isl_give isl_schedule_constraints *
5977 isl_schedule_constraints_set_coincidence(
5978 __isl_take isl_schedule_constraints *sc,
5979 __isl_take isl_union_map *coincidence);
5980 __isl_give isl_schedule_constraints *
5981 isl_schedule_constraints_set_proximity(
5982 __isl_take isl_schedule_constraints *sc,
5983 __isl_take isl_union_map *proximity);
5984 __isl_give isl_schedule_constraints *
5985 isl_schedule_constraints_set_conditional_validity(
5986 __isl_take isl_schedule_constraints *sc,
5987 __isl_take isl_union_map *condition,
5988 __isl_take isl_union_map *validity);
5989 __isl_null isl_schedule_constraints *
5990 isl_schedule_constraints_free(
5991 __isl_take isl_schedule_constraints *sc);
5993 The initial C<isl_schedule_constraints> object created by
5994 C<isl_schedule_constraints_on_domain> does not impose any constraints.
5995 That is, it has an empty set of dependences.
5996 The function C<isl_schedule_constraints_set_validity> replaces the
5997 validity dependences, mapping domain elements I<i> to domain
5998 elements that should be scheduled after I<i>.
5999 The function C<isl_schedule_constraints_set_coincidence> replaces the
6000 coincidence dependences, mapping domain elements I<i> to domain
6001 elements that should be scheduled together with I<I>, if possible.
6002 The function C<isl_schedule_constraints_set_proximity> replaces the
6003 proximity dependences, mapping domain elements I<i> to domain
6004 elements that should be scheduled either before I<I>
6005 or as early as possible after I<i>.
6007 The function C<isl_schedule_constraints_set_conditional_validity>
6008 replaces the conditional validity constraints.
6009 A conditional validity constraint is only imposed when any of the corresponding
6010 conditions is satisfied, i.e., when any of them is non-zero.
6011 That is, the scheduler ensures that within each band if the dependence
6012 distances over the condition constraints are not all zero
6013 then all corresponding conditional validity constraints are respected.
6014 A conditional validity constraint corresponds to a condition
6015 if the two are adjacent, i.e., if the domain of one relation intersect
6016 the range of the other relation.
6017 The typical use case of conditional validity constraints is
6018 to allow order constraints between live ranges to be violated
6019 as long as the live ranges themselves are local to the band.
6020 To allow more fine-grained control over which conditions correspond
6021 to which conditional validity constraints, the domains and ranges
6022 of these relations may include I<tags>. That is, the domains and
6023 ranges of those relation may themselves be wrapped relations
6024 where the iteration domain appears in the domain of those wrapped relations
6025 and the range of the wrapped relations can be arbitrarily chosen
6026 by the user. Conditions and conditional validity constraints are only
6027 considere adjacent to each other if the entire wrapped relation matches.
6028 In particular, a relation with a tag will never be considered adjacent
6029 to a relation without a tag.
6031 The following function computes a schedule directly from
6032 an iteration domain and validity and proximity dependences
6033 and is implemented in terms of the functions described above.
6034 The use of C<isl_union_set_compute_schedule> is discouraged.
6036 #include <isl/schedule.h>
6037 __isl_give isl_schedule *isl_union_set_compute_schedule(
6038 __isl_take isl_union_set *domain,
6039 __isl_take isl_union_map *validity,
6040 __isl_take isl_union_map *proximity);
6042 A mapping from the domains to the scheduled space can be obtained
6043 from an C<isl_schedule> using the following function.
6045 __isl_give isl_union_map *isl_schedule_get_map(
6046 __isl_keep isl_schedule *sched);
6048 A representation of the schedule can be printed using
6050 __isl_give isl_printer *isl_printer_print_schedule(
6051 __isl_take isl_printer *p,
6052 __isl_keep isl_schedule *schedule);
6054 A representation of the schedule as a forest of bands can be obtained
6055 using the following function.
6057 __isl_give isl_band_list *isl_schedule_get_band_forest(
6058 __isl_keep isl_schedule *schedule);
6060 The individual bands can be visited in depth-first post-order
6061 using the following function.
6063 #include <isl/schedule.h>
6064 int isl_schedule_foreach_band(
6065 __isl_keep isl_schedule *sched,
6066 int (*fn)(__isl_keep isl_band *band, void *user),
6069 The list can be manipulated as explained in L<"Lists">.
6070 The bands inside the list can be copied and freed using the following
6073 #include <isl/band.h>
6074 __isl_give isl_band *isl_band_copy(
6075 __isl_keep isl_band *band);
6076 __isl_null isl_band *isl_band_free(
6077 __isl_take isl_band *band);
6079 Each band contains zero or more scheduling dimensions.
6080 These are referred to as the members of the band.
6081 The section of the schedule that corresponds to the band is
6082 referred to as the partial schedule of the band.
6083 For those nodes that participate in a band, the outer scheduling
6084 dimensions form the prefix schedule, while the inner scheduling
6085 dimensions form the suffix schedule.
6086 That is, if we take a cut of the band forest, then the union of
6087 the concatenations of the prefix, partial and suffix schedules of
6088 each band in the cut is equal to the entire schedule (modulo
6089 some possible padding at the end with zero scheduling dimensions).
6090 The properties of a band can be inspected using the following functions.
6092 #include <isl/band.h>
6093 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
6095 int isl_band_has_children(__isl_keep isl_band *band);
6096 __isl_give isl_band_list *isl_band_get_children(
6097 __isl_keep isl_band *band);
6099 __isl_give isl_union_map *isl_band_get_prefix_schedule(
6100 __isl_keep isl_band *band);
6101 __isl_give isl_union_map *isl_band_get_partial_schedule(
6102 __isl_keep isl_band *band);
6103 __isl_give isl_union_map *isl_band_get_suffix_schedule(
6104 __isl_keep isl_band *band);
6106 int isl_band_n_member(__isl_keep isl_band *band);
6107 int isl_band_member_is_coincident(
6108 __isl_keep isl_band *band, int pos);
6110 int isl_band_list_foreach_band(
6111 __isl_keep isl_band_list *list,
6112 int (*fn)(__isl_keep isl_band *band, void *user),
6115 Note that a scheduling dimension is considered to be ``coincident''
6116 if it satisfies the coincidence constraints within its band.
6117 That is, if the dependence distances of the coincidence
6118 constraints are all zero in that direction (for fixed
6119 iterations of outer bands).
6120 Like C<isl_schedule_foreach_band>,
6121 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
6122 in depth-first post-order.
6124 A band can be tiled using the following function.
6126 #include <isl/band.h>
6127 int isl_band_tile(__isl_keep isl_band *band,
6128 __isl_take isl_vec *sizes);
6130 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
6132 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
6133 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
6135 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
6137 The C<isl_band_tile> function tiles the band using the given tile sizes
6138 inside its schedule.
6139 A new child band is created to represent the point loops and it is
6140 inserted between the modified band and its children.
6141 The C<tile_scale_tile_loops> option specifies whether the tile
6142 loops iterators should be scaled by the tile sizes.
6143 If the C<tile_shift_point_loops> option is set, then the point loops
6144 are shifted to start at zero.
6146 A band can be split into two nested bands using the following function.
6148 int isl_band_split(__isl_keep isl_band *band, int pos);
6150 The resulting outer band contains the first C<pos> dimensions of C<band>
6151 while the inner band contains the remaining dimensions.
6153 A representation of the band can be printed using
6155 #include <isl/band.h>
6156 __isl_give isl_printer *isl_printer_print_band(
6157 __isl_take isl_printer *p,
6158 __isl_keep isl_band *band);
6162 #include <isl/schedule.h>
6163 int isl_options_set_schedule_max_coefficient(
6164 isl_ctx *ctx, int val);
6165 int isl_options_get_schedule_max_coefficient(
6167 int isl_options_set_schedule_max_constant_term(
6168 isl_ctx *ctx, int val);
6169 int isl_options_get_schedule_max_constant_term(
6171 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
6172 int isl_options_get_schedule_fuse(isl_ctx *ctx);
6173 int isl_options_set_schedule_maximize_band_depth(
6174 isl_ctx *ctx, int val);
6175 int isl_options_get_schedule_maximize_band_depth(
6177 int isl_options_set_schedule_outer_coincidence(
6178 isl_ctx *ctx, int val);
6179 int isl_options_get_schedule_outer_coincidence(
6181 int isl_options_set_schedule_split_scaled(
6182 isl_ctx *ctx, int val);
6183 int isl_options_get_schedule_split_scaled(
6185 int isl_options_set_schedule_algorithm(
6186 isl_ctx *ctx, int val);
6187 int isl_options_get_schedule_algorithm(
6189 int isl_options_set_schedule_separate_components(
6190 isl_ctx *ctx, int val);
6191 int isl_options_get_schedule_separate_components(
6196 =item * schedule_max_coefficient
6198 This option enforces that the coefficients for variable and parameter
6199 dimensions in the calculated schedule are not larger than the specified value.
6200 This option can significantly increase the speed of the scheduling calculation
6201 and may also prevent fusing of unrelated dimensions. A value of -1 means that
6202 this option does not introduce bounds on the variable or parameter
6205 =item * schedule_max_constant_term
6207 This option enforces that the constant coefficients in the calculated schedule
6208 are not larger than the maximal constant term. This option can significantly
6209 increase the speed of the scheduling calculation and may also prevent fusing of
6210 unrelated dimensions. A value of -1 means that this option does not introduce
6211 bounds on the constant coefficients.
6213 =item * schedule_fuse
6215 This option controls the level of fusion.
6216 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6217 resulting schedule will be distributed as much as possible.
6218 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6219 try to fuse loops in the resulting schedule.
6221 =item * schedule_maximize_band_depth
6223 If this option is set, we do not split bands at the point
6224 where we detect splitting is necessary. Instead, we
6225 backtrack and split bands as early as possible. This
6226 reduces the number of splits and maximizes the width of
6227 the bands. Wider bands give more possibilities for tiling.
6228 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6229 then bands will be split as early as possible, even if there is no need.
6230 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6232 =item * schedule_outer_coincidence
6234 If this option is set, then we try to construct schedules
6235 where the outermost scheduling dimension in each band
6236 satisfies the coincidence constraints.
6238 =item * schedule_split_scaled
6240 If this option is set, then we try to construct schedules in which the
6241 constant term is split off from the linear part if the linear parts of
6242 the scheduling rows for all nodes in the graphs have a common non-trivial
6244 The constant term is then placed in a separate band and the linear
6247 =item * schedule_algorithm
6249 Selects the scheduling algorithm to be used.
6250 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6251 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6253 =item * schedule_separate_components
6255 If at any point the dependence graph contains any (weakly connected) components,
6256 then these components are scheduled separately.
6257 If this option is not set, then some iterations of the domains
6258 in these components may be scheduled together.
6259 If this option is set, then the components are given consecutive
6264 =head2 AST Generation
6266 This section describes the C<isl> functionality for generating
6267 ASTs that visit all the elements
6268 in a domain in an order specified by a schedule.
6269 In particular, given a C<isl_union_map>, an AST is generated
6270 that visits all the elements in the domain of the C<isl_union_map>
6271 according to the lexicographic order of the corresponding image
6272 element(s). If the range of the C<isl_union_map> consists of
6273 elements in more than one space, then each of these spaces is handled
6274 separately in an arbitrary order.
6275 It should be noted that the image elements only specify the I<order>
6276 in which the corresponding domain elements should be visited.
6277 No direct relation between the image elements and the loop iterators
6278 in the generated AST should be assumed.
6280 Each AST is generated within a build. The initial build
6281 simply specifies the constraints on the parameters (if any)
6282 and can be created, inspected, copied and freed using the following functions.
6284 #include <isl/ast_build.h>
6285 __isl_give isl_ast_build *isl_ast_build_from_context(
6286 __isl_take isl_set *set);
6287 isl_ctx *isl_ast_build_get_ctx(
6288 __isl_keep isl_ast_build *build);
6289 __isl_give isl_ast_build *isl_ast_build_copy(
6290 __isl_keep isl_ast_build *build);
6291 __isl_null isl_ast_build *isl_ast_build_free(
6292 __isl_take isl_ast_build *build);
6294 The C<set> argument is usually a parameter set with zero or more parameters.
6295 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6296 and L</"Fine-grained Control over AST Generation">.
6297 Finally, the AST itself can be constructed using the following
6300 #include <isl/ast_build.h>
6301 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6302 __isl_keep isl_ast_build *build,
6303 __isl_take isl_union_map *schedule);
6305 =head3 Inspecting the AST
6307 The basic properties of an AST node can be obtained as follows.
6309 #include <isl/ast.h>
6310 isl_ctx *isl_ast_node_get_ctx(
6311 __isl_keep isl_ast_node *node);
6312 enum isl_ast_node_type isl_ast_node_get_type(
6313 __isl_keep isl_ast_node *node);
6315 The type of an AST node is one of
6316 C<isl_ast_node_for>,
6318 C<isl_ast_node_block> or
6319 C<isl_ast_node_user>.
6320 An C<isl_ast_node_for> represents a for node.
6321 An C<isl_ast_node_if> represents an if node.
6322 An C<isl_ast_node_block> represents a compound node.
6323 An C<isl_ast_node_user> represents an expression statement.
6324 An expression statement typically corresponds to a domain element, i.e.,
6325 one of the elements that is visited by the AST.
6327 Each type of node has its own additional properties.
6329 #include <isl/ast.h>
6330 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6331 __isl_keep isl_ast_node *node);
6332 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6333 __isl_keep isl_ast_node *node);
6334 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6335 __isl_keep isl_ast_node *node);
6336 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6337 __isl_keep isl_ast_node *node);
6338 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6339 __isl_keep isl_ast_node *node);
6340 int isl_ast_node_for_is_degenerate(
6341 __isl_keep isl_ast_node *node);
6343 An C<isl_ast_for> is considered degenerate if it is known to execute
6346 #include <isl/ast.h>
6347 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6348 __isl_keep isl_ast_node *node);
6349 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6350 __isl_keep isl_ast_node *node);
6351 int isl_ast_node_if_has_else(
6352 __isl_keep isl_ast_node *node);
6353 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6354 __isl_keep isl_ast_node *node);
6356 __isl_give isl_ast_node_list *
6357 isl_ast_node_block_get_children(
6358 __isl_keep isl_ast_node *node);
6360 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6361 __isl_keep isl_ast_node *node);
6363 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6364 the following functions.
6366 #include <isl/ast.h>
6367 isl_ctx *isl_ast_expr_get_ctx(
6368 __isl_keep isl_ast_expr *expr);
6369 enum isl_ast_expr_type isl_ast_expr_get_type(
6370 __isl_keep isl_ast_expr *expr);
6372 The type of an AST expression is one of
6374 C<isl_ast_expr_id> or
6375 C<isl_ast_expr_int>.
6376 An C<isl_ast_expr_op> represents the result of an operation.
6377 An C<isl_ast_expr_id> represents an identifier.
6378 An C<isl_ast_expr_int> represents an integer value.
6380 Each type of expression has its own additional properties.
6382 #include <isl/ast.h>
6383 enum isl_ast_op_type isl_ast_expr_get_op_type(
6384 __isl_keep isl_ast_expr *expr);
6385 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6386 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6387 __isl_keep isl_ast_expr *expr, int pos);
6388 int isl_ast_node_foreach_ast_op_type(
6389 __isl_keep isl_ast_node *node,
6390 int (*fn)(enum isl_ast_op_type type, void *user),
6393 C<isl_ast_expr_get_op_type> returns the type of the operation
6394 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6395 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6397 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6398 C<isl_ast_op_type> that appears in C<node>.
6399 The operation type is one of the following.
6403 =item C<isl_ast_op_and>
6405 Logical I<and> of two arguments.
6406 Both arguments can be evaluated.
6408 =item C<isl_ast_op_and_then>
6410 Logical I<and> of two arguments.
6411 The second argument can only be evaluated if the first evaluates to true.
6413 =item C<isl_ast_op_or>
6415 Logical I<or> of two arguments.
6416 Both arguments can be evaluated.
6418 =item C<isl_ast_op_or_else>
6420 Logical I<or> of two arguments.
6421 The second argument can only be evaluated if the first evaluates to false.
6423 =item C<isl_ast_op_max>
6425 Maximum of two or more arguments.
6427 =item C<isl_ast_op_min>
6429 Minimum of two or more arguments.
6431 =item C<isl_ast_op_minus>
6435 =item C<isl_ast_op_add>
6437 Sum of two arguments.
6439 =item C<isl_ast_op_sub>
6441 Difference of two arguments.
6443 =item C<isl_ast_op_mul>
6445 Product of two arguments.
6447 =item C<isl_ast_op_div>
6449 Exact division. That is, the result is known to be an integer.
6451 =item C<isl_ast_op_fdiv_q>
6453 Result of integer division, rounded towards negative
6456 =item C<isl_ast_op_pdiv_q>
6458 Result of integer division, where dividend is known to be non-negative.
6460 =item C<isl_ast_op_pdiv_r>
6462 Remainder of integer division, where dividend is known to be non-negative.
6464 =item C<isl_ast_op_cond>
6466 Conditional operator defined on three arguments.
6467 If the first argument evaluates to true, then the result
6468 is equal to the second argument. Otherwise, the result
6469 is equal to the third argument.
6470 The second and third argument may only be evaluated if
6471 the first argument evaluates to true and false, respectively.
6472 Corresponds to C<a ? b : c> in C.
6474 =item C<isl_ast_op_select>
6476 Conditional operator defined on three arguments.
6477 If the first argument evaluates to true, then the result
6478 is equal to the second argument. Otherwise, the result
6479 is equal to the third argument.
6480 The second and third argument may be evaluated independently
6481 of the value of the first argument.
6482 Corresponds to C<a * b + (1 - a) * c> in C.
6484 =item C<isl_ast_op_eq>
6488 =item C<isl_ast_op_le>
6490 Less than or equal relation.
6492 =item C<isl_ast_op_lt>
6496 =item C<isl_ast_op_ge>
6498 Greater than or equal relation.
6500 =item C<isl_ast_op_gt>
6502 Greater than relation.
6504 =item C<isl_ast_op_call>
6507 The number of arguments of the C<isl_ast_expr> is one more than
6508 the number of arguments in the function call, the first argument
6509 representing the function being called.
6511 =item C<isl_ast_op_access>
6514 The number of arguments of the C<isl_ast_expr> is one more than
6515 the number of index expressions in the array access, the first argument
6516 representing the array being accessed.
6518 =item C<isl_ast_op_member>
6521 This operation has two arguments, a structure and the name of
6522 the member of the structure being accessed.
6526 #include <isl/ast.h>
6527 __isl_give isl_id *isl_ast_expr_get_id(
6528 __isl_keep isl_ast_expr *expr);
6530 Return the identifier represented by the AST expression.
6532 #include <isl/ast.h>
6533 __isl_give isl_val *isl_ast_expr_get_val(
6534 __isl_keep isl_ast_expr *expr);
6536 Return the integer represented by the AST expression.
6538 =head3 Properties of ASTs
6540 #include <isl/ast.h>
6541 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6542 __isl_keep isl_ast_expr *expr2);
6544 Check if two C<isl_ast_expr>s are equal to each other.
6546 =head3 Manipulating and printing the AST
6548 AST nodes can be copied and freed using the following functions.
6550 #include <isl/ast.h>
6551 __isl_give isl_ast_node *isl_ast_node_copy(
6552 __isl_keep isl_ast_node *node);
6553 __isl_null isl_ast_node *isl_ast_node_free(
6554 __isl_take isl_ast_node *node);
6556 AST expressions can be copied and freed using the following functions.
6558 #include <isl/ast.h>
6559 __isl_give isl_ast_expr *isl_ast_expr_copy(
6560 __isl_keep isl_ast_expr *expr);
6561 __isl_null isl_ast_expr *isl_ast_expr_free(
6562 __isl_take isl_ast_expr *expr);
6564 New AST expressions can be created either directly or within
6565 the context of an C<isl_ast_build>.
6567 #include <isl/ast.h>
6568 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6569 __isl_take isl_val *v);
6570 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6571 __isl_take isl_id *id);
6572 __isl_give isl_ast_expr *isl_ast_expr_neg(
6573 __isl_take isl_ast_expr *expr);
6574 __isl_give isl_ast_expr *isl_ast_expr_add(
6575 __isl_take isl_ast_expr *expr1,
6576 __isl_take isl_ast_expr *expr2);
6577 __isl_give isl_ast_expr *isl_ast_expr_sub(
6578 __isl_take isl_ast_expr *expr1,
6579 __isl_take isl_ast_expr *expr2);
6580 __isl_give isl_ast_expr *isl_ast_expr_mul(
6581 __isl_take isl_ast_expr *expr1,
6582 __isl_take isl_ast_expr *expr2);
6583 __isl_give isl_ast_expr *isl_ast_expr_div(
6584 __isl_take isl_ast_expr *expr1,
6585 __isl_take isl_ast_expr *expr2);
6586 __isl_give isl_ast_expr *isl_ast_expr_and(
6587 __isl_take isl_ast_expr *expr1,
6588 __isl_take isl_ast_expr *expr2)
6589 __isl_give isl_ast_expr *isl_ast_expr_or(
6590 __isl_take isl_ast_expr *expr1,
6591 __isl_take isl_ast_expr *expr2)
6592 __isl_give isl_ast_expr *isl_ast_expr_access(
6593 __isl_take isl_ast_expr *array,
6594 __isl_take isl_ast_expr_list *indices);
6596 #include <isl/ast_build.h>
6597 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6598 __isl_keep isl_ast_build *build,
6599 __isl_take isl_pw_aff *pa);
6600 __isl_give isl_ast_expr *
6601 isl_ast_build_access_from_pw_multi_aff(
6602 __isl_keep isl_ast_build *build,
6603 __isl_take isl_pw_multi_aff *pma);
6604 __isl_give isl_ast_expr *
6605 isl_ast_build_access_from_multi_pw_aff(
6606 __isl_keep isl_ast_build *build,
6607 __isl_take isl_multi_pw_aff *mpa);
6608 __isl_give isl_ast_expr *
6609 isl_ast_build_call_from_pw_multi_aff(
6610 __isl_keep isl_ast_build *build,
6611 __isl_take isl_pw_multi_aff *pma);
6612 __isl_give isl_ast_expr *
6613 isl_ast_build_call_from_multi_pw_aff(
6614 __isl_keep isl_ast_build *build,
6615 __isl_take isl_multi_pw_aff *mpa);
6617 The domains of C<pa>, C<mpa> and C<pma> should correspond
6618 to the schedule space of C<build>.
6619 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6620 the function being called.
6621 If the accessed space is a nested relation, then it is taken
6622 to represent an access of the member specified by the range
6623 of this nested relation of the structure specified by the domain
6624 of the nested relation.
6626 The following functions can be used to modify an C<isl_ast_expr>.
6628 #include <isl/ast.h>
6629 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6630 __isl_take isl_ast_expr *expr, int pos,
6631 __isl_take isl_ast_expr *arg);
6633 Replace the argument of C<expr> at position C<pos> by C<arg>.
6635 #include <isl/ast.h>
6636 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6637 __isl_take isl_ast_expr *expr,
6638 __isl_take isl_id_to_ast_expr *id2expr);
6640 The function C<isl_ast_expr_substitute_ids> replaces the
6641 subexpressions of C<expr> of type C<isl_ast_expr_id>
6642 by the corresponding expression in C<id2expr>, if there is any.
6645 User specified data can be attached to an C<isl_ast_node> and obtained
6646 from the same C<isl_ast_node> using the following functions.
6648 #include <isl/ast.h>
6649 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6650 __isl_take isl_ast_node *node,
6651 __isl_take isl_id *annotation);
6652 __isl_give isl_id *isl_ast_node_get_annotation(
6653 __isl_keep isl_ast_node *node);
6655 Basic printing can be performed using the following functions.
6657 #include <isl/ast.h>
6658 __isl_give isl_printer *isl_printer_print_ast_expr(
6659 __isl_take isl_printer *p,
6660 __isl_keep isl_ast_expr *expr);
6661 __isl_give isl_printer *isl_printer_print_ast_node(
6662 __isl_take isl_printer *p,
6663 __isl_keep isl_ast_node *node);
6665 More advanced printing can be performed using the following functions.
6667 #include <isl/ast.h>
6668 __isl_give isl_printer *isl_ast_op_type_print_macro(
6669 enum isl_ast_op_type type,
6670 __isl_take isl_printer *p);
6671 __isl_give isl_printer *isl_ast_node_print_macros(
6672 __isl_keep isl_ast_node *node,
6673 __isl_take isl_printer *p);
6674 __isl_give isl_printer *isl_ast_node_print(
6675 __isl_keep isl_ast_node *node,
6676 __isl_take isl_printer *p,
6677 __isl_take isl_ast_print_options *options);
6678 __isl_give isl_printer *isl_ast_node_for_print(
6679 __isl_keep isl_ast_node *node,
6680 __isl_take isl_printer *p,
6681 __isl_take isl_ast_print_options *options);
6682 __isl_give isl_printer *isl_ast_node_if_print(
6683 __isl_keep isl_ast_node *node,
6684 __isl_take isl_printer *p,
6685 __isl_take isl_ast_print_options *options);
6687 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6688 C<isl> may print out an AST that makes use of macros such
6689 as C<floord>, C<min> and C<max>.
6690 C<isl_ast_op_type_print_macro> prints out the macro
6691 corresponding to a specific C<isl_ast_op_type>.
6692 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6693 for expressions where these macros would be used and prints
6694 out the required macro definitions.
6695 Essentially, C<isl_ast_node_print_macros> calls
6696 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6697 as function argument.
6698 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6699 C<isl_ast_node_if_print> print an C<isl_ast_node>
6700 in C<ISL_FORMAT_C>, but allow for some extra control
6701 through an C<isl_ast_print_options> object.
6702 This object can be created using the following functions.
6704 #include <isl/ast.h>
6705 __isl_give isl_ast_print_options *
6706 isl_ast_print_options_alloc(isl_ctx *ctx);
6707 __isl_give isl_ast_print_options *
6708 isl_ast_print_options_copy(
6709 __isl_keep isl_ast_print_options *options);
6710 __isl_null isl_ast_print_options *
6711 isl_ast_print_options_free(
6712 __isl_take isl_ast_print_options *options);
6714 __isl_give isl_ast_print_options *
6715 isl_ast_print_options_set_print_user(
6716 __isl_take isl_ast_print_options *options,
6717 __isl_give isl_printer *(*print_user)(
6718 __isl_take isl_printer *p,
6719 __isl_take isl_ast_print_options *options,
6720 __isl_keep isl_ast_node *node, void *user),
6722 __isl_give isl_ast_print_options *
6723 isl_ast_print_options_set_print_for(
6724 __isl_take isl_ast_print_options *options,
6725 __isl_give isl_printer *(*print_for)(
6726 __isl_take isl_printer *p,
6727 __isl_take isl_ast_print_options *options,
6728 __isl_keep isl_ast_node *node, void *user),
6731 The callback set by C<isl_ast_print_options_set_print_user>
6732 is called whenever a node of type C<isl_ast_node_user> needs to
6734 The callback set by C<isl_ast_print_options_set_print_for>
6735 is called whenever a node of type C<isl_ast_node_for> needs to
6737 Note that C<isl_ast_node_for_print> will I<not> call the
6738 callback set by C<isl_ast_print_options_set_print_for> on the node
6739 on which C<isl_ast_node_for_print> is called, but only on nested
6740 nodes of type C<isl_ast_node_for>. It is therefore safe to
6741 call C<isl_ast_node_for_print> from within the callback set by
6742 C<isl_ast_print_options_set_print_for>.
6744 The following option determines the type to be used for iterators
6745 while printing the AST.
6747 int isl_options_set_ast_iterator_type(
6748 isl_ctx *ctx, const char *val);
6749 const char *isl_options_get_ast_iterator_type(
6754 #include <isl/ast_build.h>
6755 int isl_options_set_ast_build_atomic_upper_bound(
6756 isl_ctx *ctx, int val);
6757 int isl_options_get_ast_build_atomic_upper_bound(
6759 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6761 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6762 int isl_options_set_ast_build_exploit_nested_bounds(
6763 isl_ctx *ctx, int val);
6764 int isl_options_get_ast_build_exploit_nested_bounds(
6766 int isl_options_set_ast_build_group_coscheduled(
6767 isl_ctx *ctx, int val);
6768 int isl_options_get_ast_build_group_coscheduled(
6770 int isl_options_set_ast_build_scale_strides(
6771 isl_ctx *ctx, int val);
6772 int isl_options_get_ast_build_scale_strides(
6774 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6776 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6777 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6779 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6783 =item * ast_build_atomic_upper_bound
6785 Generate loop upper bounds that consist of the current loop iterator,
6786 an operator and an expression not involving the iterator.
6787 If this option is not set, then the current loop iterator may appear
6788 several times in the upper bound.
6789 For example, when this option is turned off, AST generation
6792 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6796 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6799 When the option is turned on, the following AST is generated
6801 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6804 =item * ast_build_prefer_pdiv
6806 If this option is turned off, then the AST generation will
6807 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6808 operators, but no C<isl_ast_op_pdiv_q> or
6809 C<isl_ast_op_pdiv_r> operators.
6810 If this options is turned on, then C<isl> will try to convert
6811 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6812 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6814 =item * ast_build_exploit_nested_bounds
6816 Simplify conditions based on bounds of nested for loops.
6817 In particular, remove conditions that are implied by the fact
6818 that one or more nested loops have at least one iteration,
6819 meaning that the upper bound is at least as large as the lower bound.
6820 For example, when this option is turned off, AST generation
6823 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6829 for (int c0 = 0; c0 <= N; c0 += 1)
6830 for (int c1 = 0; c1 <= M; c1 += 1)
6833 When the option is turned on, the following AST is generated
6835 for (int c0 = 0; c0 <= N; c0 += 1)
6836 for (int c1 = 0; c1 <= M; c1 += 1)
6839 =item * ast_build_group_coscheduled
6841 If two domain elements are assigned the same schedule point, then
6842 they may be executed in any order and they may even appear in different
6843 loops. If this options is set, then the AST generator will make
6844 sure that coscheduled domain elements do not appear in separate parts
6845 of the AST. This is useful in case of nested AST generation
6846 if the outer AST generation is given only part of a schedule
6847 and the inner AST generation should handle the domains that are
6848 coscheduled by this initial part of the schedule together.
6849 For example if an AST is generated for a schedule
6851 { A[i] -> [0]; B[i] -> [0] }
6853 then the C<isl_ast_build_set_create_leaf> callback described
6854 below may get called twice, once for each domain.
6855 Setting this option ensures that the callback is only called once
6856 on both domains together.
6858 =item * ast_build_separation_bounds
6860 This option specifies which bounds to use during separation.
6861 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6862 then all (possibly implicit) bounds on the current dimension will
6863 be used during separation.
6864 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6865 then only those bounds that are explicitly available will
6866 be used during separation.
6868 =item * ast_build_scale_strides
6870 This option specifies whether the AST generator is allowed
6871 to scale down iterators of strided loops.
6873 =item * ast_build_allow_else
6875 This option specifies whether the AST generator is allowed
6876 to construct if statements with else branches.
6878 =item * ast_build_allow_or
6880 This option specifies whether the AST generator is allowed
6881 to construct if conditions with disjunctions.
6885 =head3 Fine-grained Control over AST Generation
6887 Besides specifying the constraints on the parameters,
6888 an C<isl_ast_build> object can be used to control
6889 various aspects of the AST generation process.
6890 The most prominent way of control is through ``options'',
6891 which can be set using the following function.
6893 #include <isl/ast_build.h>
6894 __isl_give isl_ast_build *
6895 isl_ast_build_set_options(
6896 __isl_take isl_ast_build *control,
6897 __isl_take isl_union_map *options);
6899 The options are encoded in an <isl_union_map>.
6900 The domain of this union relation refers to the schedule domain,
6901 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6902 In the case of nested AST generation (see L</"Nested AST Generation">),
6903 the domain of C<options> should refer to the extra piece of the schedule.
6904 That is, it should be equal to the range of the wrapped relation in the
6905 range of the schedule.
6906 The range of the options can consist of elements in one or more spaces,
6907 the names of which determine the effect of the option.
6908 The values of the range typically also refer to the schedule dimension
6909 to which the option applies. In case of nested AST generation
6910 (see L</"Nested AST Generation">), these values refer to the position
6911 of the schedule dimension within the innermost AST generation.
6912 The constraints on the domain elements of
6913 the option should only refer to this dimension and earlier dimensions.
6914 We consider the following spaces.
6918 =item C<separation_class>
6920 This space is a wrapped relation between two one dimensional spaces.
6921 The input space represents the schedule dimension to which the option
6922 applies and the output space represents the separation class.
6923 While constructing a loop corresponding to the specified schedule
6924 dimension(s), the AST generator will try to generate separate loops
6925 for domain elements that are assigned different classes.
6926 If only some of the elements are assigned a class, then those elements
6927 that are not assigned any class will be treated as belonging to a class
6928 that is separate from the explicitly assigned classes.
6929 The typical use case for this option is to separate full tiles from
6931 The other options, described below, are applied after the separation
6934 As an example, consider the separation into full and partial tiles
6935 of a tiling of a triangular domain.
6936 Take, for example, the domain
6938 { A[i,j] : 0 <= i,j and i + j <= 100 }
6940 and a tiling into tiles of 10 by 10. The input to the AST generator
6941 is then the schedule
6943 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6946 Without any options, the following AST is generated
6948 for (int c0 = 0; c0 <= 10; c0 += 1)
6949 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6950 for (int c2 = 10 * c0;
6951 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6953 for (int c3 = 10 * c1;
6954 c3 <= min(10 * c1 + 9, -c2 + 100);
6958 Separation into full and partial tiles can be obtained by assigning
6959 a class, say C<0>, to the full tiles. The full tiles are represented by those
6960 values of the first and second schedule dimensions for which there are
6961 values of the third and fourth dimensions to cover an entire tile.
6962 That is, we need to specify the following option
6964 { [a,b,c,d] -> separation_class[[0]->[0]] :
6965 exists b': 0 <= 10a,10b' and
6966 10a+9+10b'+9 <= 100;
6967 [a,b,c,d] -> separation_class[[1]->[0]] :
6968 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6972 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6973 a >= 0 and b >= 0 and b <= 8 - a;
6974 [a, b, c, d] -> separation_class[[0] -> [0]] :
6977 With this option, the generated AST is as follows
6980 for (int c0 = 0; c0 <= 8; c0 += 1) {
6981 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6982 for (int c2 = 10 * c0;
6983 c2 <= 10 * c0 + 9; c2 += 1)
6984 for (int c3 = 10 * c1;
6985 c3 <= 10 * c1 + 9; c3 += 1)
6987 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6988 for (int c2 = 10 * c0;
6989 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6991 for (int c3 = 10 * c1;
6992 c3 <= min(-c2 + 100, 10 * c1 + 9);
6996 for (int c0 = 9; c0 <= 10; c0 += 1)
6997 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6998 for (int c2 = 10 * c0;
6999 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7001 for (int c3 = 10 * c1;
7002 c3 <= min(10 * c1 + 9, -c2 + 100);
7009 This is a single-dimensional space representing the schedule dimension(s)
7010 to which ``separation'' should be applied. Separation tries to split
7011 a loop into several pieces if this can avoid the generation of guards
7013 See also the C<atomic> option.
7017 This is a single-dimensional space representing the schedule dimension(s)
7018 for which the domains should be considered ``atomic''. That is, the
7019 AST generator will make sure that any given domain space will only appear
7020 in a single loop at the specified level.
7022 Consider the following schedule
7024 { a[i] -> [i] : 0 <= i < 10;
7025 b[i] -> [i+1] : 0 <= i < 10 }
7027 If the following option is specified
7029 { [i] -> separate[x] }
7031 then the following AST will be generated
7035 for (int c0 = 1; c0 <= 9; c0 += 1) {
7042 If, on the other hand, the following option is specified
7044 { [i] -> atomic[x] }
7046 then the following AST will be generated
7048 for (int c0 = 0; c0 <= 10; c0 += 1) {
7055 If neither C<atomic> nor C<separate> is specified, then the AST generator
7056 may produce either of these two results or some intermediate form.
7060 This is a single-dimensional space representing the schedule dimension(s)
7061 that should be I<completely> unrolled.
7062 To obtain a partial unrolling, the user should apply an additional
7063 strip-mining to the schedule and fully unroll the inner loop.
7067 Additional control is available through the following functions.
7069 #include <isl/ast_build.h>
7070 __isl_give isl_ast_build *
7071 isl_ast_build_set_iterators(
7072 __isl_take isl_ast_build *control,
7073 __isl_take isl_id_list *iterators);
7075 The function C<isl_ast_build_set_iterators> allows the user to
7076 specify a list of iterator C<isl_id>s to be used as iterators.
7077 If the input schedule is injective, then
7078 the number of elements in this list should be as large as the dimension
7079 of the schedule space, but no direct correspondence should be assumed
7080 between dimensions and elements.
7081 If the input schedule is not injective, then an additional number
7082 of C<isl_id>s equal to the largest dimension of the input domains
7084 If the number of provided C<isl_id>s is insufficient, then additional
7085 names are automatically generated.
7087 #include <isl/ast_build.h>
7088 __isl_give isl_ast_build *
7089 isl_ast_build_set_create_leaf(
7090 __isl_take isl_ast_build *control,
7091 __isl_give isl_ast_node *(*fn)(
7092 __isl_take isl_ast_build *build,
7093 void *user), void *user);
7096 C<isl_ast_build_set_create_leaf> function allows for the
7097 specification of a callback that should be called whenever the AST
7098 generator arrives at an element of the schedule domain.
7099 The callback should return an AST node that should be inserted
7100 at the corresponding position of the AST. The default action (when
7101 the callback is not set) is to continue generating parts of the AST to scan
7102 all the domain elements associated to the schedule domain element
7103 and to insert user nodes, ``calling'' the domain element, for each of them.
7104 The C<build> argument contains the current state of the C<isl_ast_build>.
7105 To ease nested AST generation (see L</"Nested AST Generation">),
7106 all control information that is
7107 specific to the current AST generation such as the options and
7108 the callbacks has been removed from this C<isl_ast_build>.
7109 The callback would typically return the result of a nested
7111 user defined node created using the following function.
7113 #include <isl/ast.h>
7114 __isl_give isl_ast_node *isl_ast_node_alloc_user(
7115 __isl_take isl_ast_expr *expr);
7117 #include <isl/ast_build.h>
7118 __isl_give isl_ast_build *
7119 isl_ast_build_set_at_each_domain(
7120 __isl_take isl_ast_build *build,
7121 __isl_give isl_ast_node *(*fn)(
7122 __isl_take isl_ast_node *node,
7123 __isl_keep isl_ast_build *build,
7124 void *user), void *user);
7125 __isl_give isl_ast_build *
7126 isl_ast_build_set_before_each_for(
7127 __isl_take isl_ast_build *build,
7128 __isl_give isl_id *(*fn)(
7129 __isl_keep isl_ast_build *build,
7130 void *user), void *user);
7131 __isl_give isl_ast_build *
7132 isl_ast_build_set_after_each_for(
7133 __isl_take isl_ast_build *build,
7134 __isl_give isl_ast_node *(*fn)(
7135 __isl_take isl_ast_node *node,
7136 __isl_keep isl_ast_build *build,
7137 void *user), void *user);
7139 The callback set by C<isl_ast_build_set_at_each_domain> will
7140 be called for each domain AST node.
7141 The callbacks set by C<isl_ast_build_set_before_each_for>
7142 and C<isl_ast_build_set_after_each_for> will be called
7143 for each for AST node. The first will be called in depth-first
7144 pre-order, while the second will be called in depth-first post-order.
7145 Since C<isl_ast_build_set_before_each_for> is called before the for
7146 node is actually constructed, it is only passed an C<isl_ast_build>.
7147 The returned C<isl_id> will be added as an annotation (using
7148 C<isl_ast_node_set_annotation>) to the constructed for node.
7149 In particular, if the user has also specified an C<after_each_for>
7150 callback, then the annotation can be retrieved from the node passed to
7151 that callback using C<isl_ast_node_get_annotation>.
7152 All callbacks should C<NULL> on failure.
7153 The given C<isl_ast_build> can be used to create new
7154 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
7155 or C<isl_ast_build_call_from_pw_multi_aff>.
7157 =head3 Nested AST Generation
7159 C<isl> allows the user to create an AST within the context
7160 of another AST. These nested ASTs are created using the
7161 same C<isl_ast_build_ast_from_schedule> function that is used to create the
7162 outer AST. The C<build> argument should be an C<isl_ast_build>
7163 passed to a callback set by
7164 C<isl_ast_build_set_create_leaf>.
7165 The space of the range of the C<schedule> argument should refer
7166 to this build. In particular, the space should be a wrapped
7167 relation and the domain of this wrapped relation should be the
7168 same as that of the range of the schedule returned by
7169 C<isl_ast_build_get_schedule> below.
7170 In practice, the new schedule is typically
7171 created by calling C<isl_union_map_range_product> on the old schedule
7172 and some extra piece of the schedule.
7173 The space of the schedule domain is also available from
7174 the C<isl_ast_build>.
7176 #include <isl/ast_build.h>
7177 __isl_give isl_union_map *isl_ast_build_get_schedule(
7178 __isl_keep isl_ast_build *build);
7179 __isl_give isl_space *isl_ast_build_get_schedule_space(
7180 __isl_keep isl_ast_build *build);
7181 __isl_give isl_ast_build *isl_ast_build_restrict(
7182 __isl_take isl_ast_build *build,
7183 __isl_take isl_set *set);
7185 The C<isl_ast_build_get_schedule> function returns a (partial)
7186 schedule for the domains elements for which part of the AST still needs to
7187 be generated in the current build.
7188 In particular, the domain elements are mapped to those iterations of the loops
7189 enclosing the current point of the AST generation inside which
7190 the domain elements are executed.
7191 No direct correspondence between
7192 the input schedule and this schedule should be assumed.
7193 The space obtained from C<isl_ast_build_get_schedule_space> can be used
7194 to create a set for C<isl_ast_build_restrict> to intersect
7195 with the current build. In particular, the set passed to
7196 C<isl_ast_build_restrict> can have additional parameters.
7197 The ids of the set dimensions in the space returned by
7198 C<isl_ast_build_get_schedule_space> correspond to the
7199 iterators of the already generated loops.
7200 The user should not rely on the ids of the output dimensions
7201 of the relations in the union relation returned by
7202 C<isl_ast_build_get_schedule> having any particular value.
7206 Although C<isl> is mainly meant to be used as a library,
7207 it also contains some basic applications that use some
7208 of the functionality of C<isl>.
7209 The input may be specified in either the L<isl format>
7210 or the L<PolyLib format>.
7212 =head2 C<isl_polyhedron_sample>
7214 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7215 an integer element of the polyhedron, if there is any.
7216 The first column in the output is the denominator and is always
7217 equal to 1. If the polyhedron contains no integer points,
7218 then a vector of length zero is printed.
7222 C<isl_pip> takes the same input as the C<example> program
7223 from the C<piplib> distribution, i.e., a set of constraints
7224 on the parameters, a line containing only -1 and finally a set
7225 of constraints on a parametric polyhedron.
7226 The coefficients of the parameters appear in the last columns
7227 (but before the final constant column).
7228 The output is the lexicographic minimum of the parametric polyhedron.
7229 As C<isl> currently does not have its own output format, the output
7230 is just a dump of the internal state.
7232 =head2 C<isl_polyhedron_minimize>
7234 C<isl_polyhedron_minimize> computes the minimum of some linear
7235 or affine objective function over the integer points in a polyhedron.
7236 If an affine objective function
7237 is given, then the constant should appear in the last column.
7239 =head2 C<isl_polytope_scan>
7241 Given a polytope, C<isl_polytope_scan> prints
7242 all integer points in the polytope.
7244 =head2 C<isl_codegen>
7246 Given a schedule, a context set and an options relation,
7247 C<isl_codegen> prints out an AST that scans the domain elements
7248 of the schedule in the order of their image(s) taking into account
7249 the constraints in the context set.