3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
8 using C<GMP> or C<imath>.
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
184 =head3 Changes since isl-0.12
188 =item * C<isl_int> has been replaced by C<isl_val>.
189 Some of the old functions are still available in C<isl/deprecated/*.h>
190 but they will be removed in the future.
192 =item * The functions C<isl_pw_qpolynomial_eval>,
193 C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval>
194 and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return
195 an C<isl_val> instead of an C<isl_qpolynomial>.
197 =item * The function C<isl_band_member_is_zero_distance>
198 has been removed. Essentially the same functionality is available
199 through C<isl_band_member_is_coincident>, except that is requires
200 setting up coincidence constraints.
201 The option C<schedule_outer_zero_distance> has accordingly been
202 replaced by the option C<schedule_outer_coincidence>.
204 =item * The function C<isl_vertex_get_expr> has been changed
205 to return an C<isl_multi_aff> instead of a rational C<isl_basic_set>.
206 The function C<isl_vertex_get_domain> has been changed to return
207 a regular basic set, rather than a rational basic set.
213 C<isl> is released under the MIT license.
217 Permission is hereby granted, free of charge, to any person obtaining a copy of
218 this software and associated documentation files (the "Software"), to deal in
219 the Software without restriction, including without limitation the rights to
220 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
221 of the Software, and to permit persons to whom the Software is furnished to do
222 so, subject to the following conditions:
224 The above copyright notice and this permission notice shall be included in all
225 copies or substantial portions of the Software.
227 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
228 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
229 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
230 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
231 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
232 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
237 Note that by default C<isl> requires C<GMP>, which is released
238 under the GNU Lesser General Public License (LGPL). This means
239 that code linked against C<isl> is also linked against LGPL code.
241 When configuring with C<--with-int=imath>, C<isl> will link against C<imath>, a
242 library for exact integer arithmetic released under the MIT license.
246 The source of C<isl> can be obtained either as a tarball
247 or from the git repository. Both are available from
248 L<http://freshmeat.net/projects/isl/>.
249 The installation process depends on how you obtained
252 =head2 Installation from the git repository
256 =item 1 Clone or update the repository
258 The first time the source is obtained, you need to clone
261 git clone git://repo.or.cz/isl.git
263 To obtain updates, you need to pull in the latest changes
267 =item 2 Optionally get C<imath> submodule
269 To build C<isl> with C<imath>, you need to obtain the C<imath>
270 submodule by running in the git source tree of C<isl>
275 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
277 =item 2 Generate C<configure>
283 After performing the above steps, continue
284 with the L<Common installation instructions>.
286 =head2 Common installation instructions
290 =item 1 Obtain C<GMP>
292 By default, building C<isl> requires C<GMP>, including its headers files.
293 Your distribution may not provide these header files by default
294 and you may need to install a package called C<gmp-devel> or something
295 similar. Alternatively, C<GMP> can be built from
296 source, available from L<http://gmplib.org/>.
297 C<GMP> is not needed if you build C<isl> with C<imath>.
301 C<isl> uses the standard C<autoconf> C<configure> script.
306 optionally followed by some configure options.
307 A complete list of options can be obtained by running
311 Below we discuss some of the more common options.
317 Installation prefix for C<isl>
319 =item C<--with-int=[gmp|imath]>
321 Select the integer library to be used by C<isl>, the default is C<gmp>.
322 Note that C<isl> may run significantly slower if you use C<imath>.
324 =item C<--with-gmp-prefix>
326 Installation prefix for C<GMP> (architecture-independent files).
328 =item C<--with-gmp-exec-prefix>
330 Installation prefix for C<GMP> (architecture-dependent files).
338 =item 4 Install (optional)
344 =head1 Integer Set Library
346 =head2 Initialization
348 All manipulations of integer sets and relations occur within
349 the context of an C<isl_ctx>.
350 A given C<isl_ctx> can only be used within a single thread.
351 All arguments of a function are required to have been allocated
352 within the same context.
353 There are currently no functions available for moving an object
354 from one C<isl_ctx> to another C<isl_ctx>. This means that
355 there is currently no way of safely moving an object from one
356 thread to another, unless the whole C<isl_ctx> is moved.
358 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
359 freed using C<isl_ctx_free>.
360 All objects allocated within an C<isl_ctx> should be freed
361 before the C<isl_ctx> itself is freed.
363 isl_ctx *isl_ctx_alloc();
364 void isl_ctx_free(isl_ctx *ctx);
366 The user can impose a bound on the number of low-level I<operations>
367 that can be performed by an C<isl_ctx>. This bound can be set and
368 retrieved using the following functions. A bound of zero means that
369 no bound is imposed. The number of operations performed can be
370 reset using C<isl_ctx_reset_operations>. Note that the number
371 of low-level operations needed to perform a high-level computation
372 may differ significantly across different versions
373 of C<isl>, but it should be the same across different platforms
374 for the same version of C<isl>.
376 Warning: This feature is experimental. C<isl> has good support to abort and
377 bail out during the computation, but this feature may exercise error code paths
378 that are normally not used that much. Consequently, it is not unlikely that
379 hidden bugs will be exposed.
381 void isl_ctx_set_max_operations(isl_ctx *ctx,
382 unsigned long max_operations);
383 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
384 void isl_ctx_reset_operations(isl_ctx *ctx);
386 =head2 Memory Management
388 Since a high-level operation on isl objects usually involves
389 several substeps and since the user is usually not interested in
390 the intermediate results, most functions that return a new object
391 will also release all the objects passed as arguments.
392 If the user still wants to use one or more of these arguments
393 after the function call, she should pass along a copy of the
394 object rather than the object itself.
395 The user is then responsible for making sure that the original
396 object gets used somewhere else or is explicitly freed.
398 The arguments and return values of all documented functions are
399 annotated to make clear which arguments are released and which
400 arguments are preserved. In particular, the following annotations
407 C<__isl_give> means that a new object is returned.
408 The user should make sure that the returned pointer is
409 used exactly once as a value for an C<__isl_take> argument.
410 In between, it can be used as a value for as many
411 C<__isl_keep> arguments as the user likes.
412 There is one exception, and that is the case where the
413 pointer returned is C<NULL>. Is this case, the user
414 is free to use it as an C<__isl_take> argument or not.
418 C<__isl_null> means that a C<NULL> value is returned.
422 C<__isl_take> means that the object the argument points to
423 is taken over by the function and may no longer be used
424 by the user as an argument to any other function.
425 The pointer value must be one returned by a function
426 returning an C<__isl_give> pointer.
427 If the user passes in a C<NULL> value, then this will
428 be treated as an error in the sense that the function will
429 not perform its usual operation. However, it will still
430 make sure that all the other C<__isl_take> arguments
435 C<__isl_keep> means that the function will only use the object
436 temporarily. After the function has finished, the user
437 can still use it as an argument to other functions.
438 A C<NULL> value will be treated in the same way as
439 a C<NULL> value for an C<__isl_take> argument.
445 An C<isl_val> represents an integer value, a rational value
446 or one of three special values, infinity, negative infinity and NaN.
447 Some predefined values can be created using the following functions.
450 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
451 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
452 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
453 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
454 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
455 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
457 Specific integer values can be created using the following functions.
460 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
462 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
464 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
465 size_t n, size_t size, const void *chunks);
467 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
468 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
469 The least significant digit is assumed to be stored first.
471 Value objects can be copied and freed using the following functions.
474 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
475 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
477 They can be inspected using the following functions.
480 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
481 long isl_val_get_num_si(__isl_keep isl_val *v);
482 long isl_val_get_den_si(__isl_keep isl_val *v);
483 double isl_val_get_d(__isl_keep isl_val *v);
484 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
486 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
487 size_t size, void *chunks);
489 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
490 of C<size> bytes needed to store the absolute value of the
492 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
493 which is assumed to have been preallocated by the caller.
494 The least significant digit is stored first.
495 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
496 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
497 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
499 An C<isl_val> can be modified using the following function.
502 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
505 The following unary properties are defined on C<isl_val>s.
508 int isl_val_sgn(__isl_keep isl_val *v);
509 int isl_val_is_zero(__isl_keep isl_val *v);
510 int isl_val_is_one(__isl_keep isl_val *v);
511 int isl_val_is_negone(__isl_keep isl_val *v);
512 int isl_val_is_nonneg(__isl_keep isl_val *v);
513 int isl_val_is_nonpos(__isl_keep isl_val *v);
514 int isl_val_is_pos(__isl_keep isl_val *v);
515 int isl_val_is_neg(__isl_keep isl_val *v);
516 int isl_val_is_int(__isl_keep isl_val *v);
517 int isl_val_is_rat(__isl_keep isl_val *v);
518 int isl_val_is_nan(__isl_keep isl_val *v);
519 int isl_val_is_infty(__isl_keep isl_val *v);
520 int isl_val_is_neginfty(__isl_keep isl_val *v);
522 Note that the sign of NaN is undefined.
524 The following binary properties are defined on pairs of C<isl_val>s.
527 int isl_val_lt(__isl_keep isl_val *v1,
528 __isl_keep isl_val *v2);
529 int isl_val_le(__isl_keep isl_val *v1,
530 __isl_keep isl_val *v2);
531 int isl_val_gt(__isl_keep isl_val *v1,
532 __isl_keep isl_val *v2);
533 int isl_val_ge(__isl_keep isl_val *v1,
534 __isl_keep isl_val *v2);
535 int isl_val_eq(__isl_keep isl_val *v1,
536 __isl_keep isl_val *v2);
537 int isl_val_ne(__isl_keep isl_val *v1,
538 __isl_keep isl_val *v2);
540 For integer C<isl_val>s we additionally have the following binary property.
543 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
544 __isl_keep isl_val *v2);
546 An C<isl_val> can also be compared to an integer using the following
547 function. The result is undefined for NaN.
550 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
552 The following unary operations are available on C<isl_val>s.
555 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
556 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
557 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
558 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
559 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
561 The following binary operations are available on C<isl_val>s.
564 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
565 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
566 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
567 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
568 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
569 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
570 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
571 __isl_take isl_val *v2);
572 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
573 __isl_take isl_val *v2);
574 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
575 __isl_take isl_val *v2);
576 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
578 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
579 __isl_take isl_val *v2);
580 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
582 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
583 __isl_take isl_val *v2);
584 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
586 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
587 __isl_take isl_val *v2);
589 On integer values, we additionally have the following operations.
592 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
593 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
594 __isl_take isl_val *v2);
595 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
596 __isl_take isl_val *v2);
597 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
598 __isl_take isl_val *v2, __isl_give isl_val **x,
599 __isl_give isl_val **y);
601 The function C<isl_val_gcdext> returns the greatest common divisor g
602 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
603 that C<*x> * C<v1> + C<*y> * C<v2> = g.
605 A value can be read from input using
608 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
611 A value can be printed using
614 __isl_give isl_printer *isl_printer_print_val(
615 __isl_take isl_printer *p, __isl_keep isl_val *v);
617 =head3 GMP specific functions
619 These functions are only available if C<isl> has been compiled with C<GMP>
622 Specific integer and rational values can be created from C<GMP> values using
623 the following functions.
625 #include <isl/val_gmp.h>
626 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
628 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
629 const mpz_t n, const mpz_t d);
631 The numerator and denominator of a rational value can be extracted as
632 C<GMP> values using the following functions.
634 #include <isl/val_gmp.h>
635 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
636 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
638 =head2 Sets and Relations
640 C<isl> uses six types of objects for representing sets and relations,
641 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
642 C<isl_union_set> and C<isl_union_map>.
643 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
644 can be described as a conjunction of affine constraints, while
645 C<isl_set> and C<isl_map> represent unions of
646 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
647 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
648 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
649 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
650 where spaces are considered different if they have a different number
651 of dimensions and/or different names (see L<"Spaces">).
652 The difference between sets and relations (maps) is that sets have
653 one set of variables, while relations have two sets of variables,
654 input variables and output variables.
656 =head2 Error Handling
658 C<isl> supports different ways to react in case a runtime error is triggered.
659 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
660 with two maps that have incompatible spaces. There are three possible ways
661 to react on error: to warn, to continue or to abort.
663 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
664 the last error in the corresponding C<isl_ctx> and the function in which the
665 error was triggered returns C<NULL>. An error does not corrupt internal state,
666 such that isl can continue to be used. C<isl> also provides functions to
667 read the last error and to reset the memory that stores the last error. The
668 last error is only stored for information purposes. Its presence does not
669 change the behavior of C<isl>. Hence, resetting an error is not required to
670 continue to use isl, but only to observe new errors.
673 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
674 void isl_ctx_reset_error(isl_ctx *ctx);
676 Another option is to continue on error. This is similar to warn on error mode,
677 except that C<isl> does not print any warning. This allows a program to
678 implement its own error reporting.
680 The last option is to directly abort the execution of the program from within
681 the isl library. This makes it obviously impossible to recover from an error,
682 but it allows to directly spot the error location. By aborting on error,
683 debuggers break at the location the error occurred and can provide a stack
684 trace. Other tools that automatically provide stack traces on abort or that do
685 not want to continue execution after an error was triggered may also prefer to
688 The on error behavior of isl can be specified by calling
689 C<isl_options_set_on_error> or by setting the command line option
690 C<--isl-on-error>. Valid arguments for the function call are
691 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
692 choices for the command line option are C<warn>, C<continue> and C<abort>.
693 It is also possible to query the current error mode.
695 #include <isl/options.h>
696 int isl_options_set_on_error(isl_ctx *ctx, int val);
697 int isl_options_get_on_error(isl_ctx *ctx);
701 Identifiers are used to identify both individual dimensions
702 and tuples of dimensions. They consist of an optional name and an optional
703 user pointer. The name and the user pointer cannot both be C<NULL>, however.
704 Identifiers with the same name but different pointer values
705 are considered to be distinct.
706 Similarly, identifiers with different names but the same pointer value
707 are also considered to be distinct.
708 Equal identifiers are represented using the same object.
709 Pairs of identifiers can therefore be tested for equality using the
711 Identifiers can be constructed, copied, freed, inspected and printed
712 using the following functions.
715 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
716 __isl_keep const char *name, void *user);
717 __isl_give isl_id *isl_id_set_free_user(
718 __isl_take isl_id *id,
719 __isl_give void (*free_user)(void *user));
720 __isl_give isl_id *isl_id_copy(isl_id *id);
721 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
723 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
724 void *isl_id_get_user(__isl_keep isl_id *id);
725 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
727 __isl_give isl_printer *isl_printer_print_id(
728 __isl_take isl_printer *p, __isl_keep isl_id *id);
730 The callback set by C<isl_id_set_free_user> is called on the user
731 pointer when the last reference to the C<isl_id> is freed.
732 Note that C<isl_id_get_name> returns a pointer to some internal
733 data structure, so the result can only be used while the
734 corresponding C<isl_id> is alive.
738 Whenever a new set, relation or similiar object is created from scratch,
739 the space in which it lives needs to be specified using an C<isl_space>.
740 Each space involves zero or more parameters and zero, one or two
741 tuples of set or input/output dimensions. The parameters and dimensions
742 are identified by an C<isl_dim_type> and a position.
743 The type C<isl_dim_param> refers to parameters,
744 the type C<isl_dim_set> refers to set dimensions (for spaces
745 with a single tuple of dimensions) and the types C<isl_dim_in>
746 and C<isl_dim_out> refer to input and output dimensions
747 (for spaces with two tuples of dimensions).
748 Local spaces (see L</"Local Spaces">) also contain dimensions
749 of type C<isl_dim_div>.
750 Note that parameters are only identified by their position within
751 a given object. Across different objects, parameters are (usually)
752 identified by their names or identifiers. Only unnamed parameters
753 are identified by their positions across objects. The use of unnamed
754 parameters is discouraged.
756 #include <isl/space.h>
757 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
758 unsigned nparam, unsigned n_in, unsigned n_out);
759 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
761 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
762 unsigned nparam, unsigned dim);
763 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
764 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
765 unsigned isl_space_dim(__isl_keep isl_space *space,
766 enum isl_dim_type type);
768 The space used for creating a parameter domain
769 needs to be created using C<isl_space_params_alloc>.
770 For other sets, the space
771 needs to be created using C<isl_space_set_alloc>, while
772 for a relation, the space
773 needs to be created using C<isl_space_alloc>.
774 C<isl_space_dim> can be used
775 to find out the number of dimensions of each type in
776 a space, where type may be
777 C<isl_dim_param>, C<isl_dim_in> (only for relations),
778 C<isl_dim_out> (only for relations), C<isl_dim_set>
779 (only for sets) or C<isl_dim_all>.
781 To check whether a given space is that of a set or a map
782 or whether it is a parameter space, use these functions:
784 #include <isl/space.h>
785 int isl_space_is_params(__isl_keep isl_space *space);
786 int isl_space_is_set(__isl_keep isl_space *space);
787 int isl_space_is_map(__isl_keep isl_space *space);
789 Spaces can be compared using the following functions:
791 #include <isl/space.h>
792 int isl_space_is_equal(__isl_keep isl_space *space1,
793 __isl_keep isl_space *space2);
794 int isl_space_is_domain(__isl_keep isl_space *space1,
795 __isl_keep isl_space *space2);
796 int isl_space_is_range(__isl_keep isl_space *space1,
797 __isl_keep isl_space *space2);
799 C<isl_space_is_domain> checks whether the first argument is equal
800 to the domain of the second argument. This requires in particular that
801 the first argument is a set space and that the second argument
804 It is often useful to create objects that live in the
805 same space as some other object. This can be accomplished
806 by creating the new objects
807 (see L</"Creating New Sets and Relations"> or
808 L</"Creating New (Piecewise) Quasipolynomials">) based on the space
809 of the original object.
812 __isl_give isl_space *isl_basic_set_get_space(
813 __isl_keep isl_basic_set *bset);
814 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
816 #include <isl/union_set.h>
817 __isl_give isl_space *isl_union_set_get_space(
818 __isl_keep isl_union_set *uset);
821 __isl_give isl_space *isl_basic_map_get_space(
822 __isl_keep isl_basic_map *bmap);
823 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
825 #include <isl/union_map.h>
826 __isl_give isl_space *isl_union_map_get_space(
827 __isl_keep isl_union_map *umap);
829 #include <isl/constraint.h>
830 __isl_give isl_space *isl_constraint_get_space(
831 __isl_keep isl_constraint *constraint);
833 #include <isl/polynomial.h>
834 __isl_give isl_space *isl_qpolynomial_get_domain_space(
835 __isl_keep isl_qpolynomial *qp);
836 __isl_give isl_space *isl_qpolynomial_get_space(
837 __isl_keep isl_qpolynomial *qp);
838 __isl_give isl_space *isl_qpolynomial_fold_get_space(
839 __isl_keep isl_qpolynomial_fold *fold);
840 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
841 __isl_keep isl_pw_qpolynomial *pwqp);
842 __isl_give isl_space *isl_pw_qpolynomial_get_space(
843 __isl_keep isl_pw_qpolynomial *pwqp);
844 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
845 __isl_keep isl_pw_qpolynomial_fold *pwf);
846 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
847 __isl_keep isl_pw_qpolynomial_fold *pwf);
848 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
849 __isl_keep isl_union_pw_qpolynomial *upwqp);
850 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
851 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
854 __isl_give isl_space *isl_multi_val_get_space(
855 __isl_keep isl_multi_val *mv);
858 __isl_give isl_space *isl_aff_get_domain_space(
859 __isl_keep isl_aff *aff);
860 __isl_give isl_space *isl_aff_get_space(
861 __isl_keep isl_aff *aff);
862 __isl_give isl_space *isl_pw_aff_get_domain_space(
863 __isl_keep isl_pw_aff *pwaff);
864 __isl_give isl_space *isl_pw_aff_get_space(
865 __isl_keep isl_pw_aff *pwaff);
866 __isl_give isl_space *isl_multi_aff_get_domain_space(
867 __isl_keep isl_multi_aff *maff);
868 __isl_give isl_space *isl_multi_aff_get_space(
869 __isl_keep isl_multi_aff *maff);
870 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
871 __isl_keep isl_pw_multi_aff *pma);
872 __isl_give isl_space *isl_pw_multi_aff_get_space(
873 __isl_keep isl_pw_multi_aff *pma);
874 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
875 __isl_keep isl_union_pw_multi_aff *upma);
876 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
877 __isl_keep isl_multi_pw_aff *mpa);
878 __isl_give isl_space *isl_multi_pw_aff_get_space(
879 __isl_keep isl_multi_pw_aff *mpa);
881 #include <isl/point.h>
882 __isl_give isl_space *isl_point_get_space(
883 __isl_keep isl_point *pnt);
885 The identifiers or names of the individual dimensions may be set or read off
886 using the following functions.
888 #include <isl/space.h>
889 __isl_give isl_space *isl_space_set_dim_id(
890 __isl_take isl_space *space,
891 enum isl_dim_type type, unsigned pos,
892 __isl_take isl_id *id);
893 int isl_space_has_dim_id(__isl_keep isl_space *space,
894 enum isl_dim_type type, unsigned pos);
895 __isl_give isl_id *isl_space_get_dim_id(
896 __isl_keep isl_space *space,
897 enum isl_dim_type type, unsigned pos);
898 __isl_give isl_space *isl_space_set_dim_name(
899 __isl_take isl_space *space,
900 enum isl_dim_type type, unsigned pos,
901 __isl_keep const char *name);
902 int isl_space_has_dim_name(__isl_keep isl_space *space,
903 enum isl_dim_type type, unsigned pos);
904 __isl_keep const char *isl_space_get_dim_name(
905 __isl_keep isl_space *space,
906 enum isl_dim_type type, unsigned pos);
908 Note that C<isl_space_get_name> returns a pointer to some internal
909 data structure, so the result can only be used while the
910 corresponding C<isl_space> is alive.
911 Also note that every function that operates on two sets or relations
912 requires that both arguments have the same parameters. This also
913 means that if one of the arguments has named parameters, then the
914 other needs to have named parameters too and the names need to match.
915 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
916 arguments may have different parameters (as long as they are named),
917 in which case the result will have as parameters the union of the parameters of
920 Given the identifier or name of a dimension (typically a parameter),
921 its position can be obtained from the following function.
923 #include <isl/space.h>
924 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
925 enum isl_dim_type type, __isl_keep isl_id *id);
926 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
927 enum isl_dim_type type, const char *name);
929 The identifiers or names of entire spaces may be set or read off
930 using the following functions.
932 #include <isl/space.h>
933 __isl_give isl_space *isl_space_set_tuple_id(
934 __isl_take isl_space *space,
935 enum isl_dim_type type, __isl_take isl_id *id);
936 __isl_give isl_space *isl_space_reset_tuple_id(
937 __isl_take isl_space *space, enum isl_dim_type type);
938 int isl_space_has_tuple_id(__isl_keep isl_space *space,
939 enum isl_dim_type type);
940 __isl_give isl_id *isl_space_get_tuple_id(
941 __isl_keep isl_space *space, enum isl_dim_type type);
942 __isl_give isl_space *isl_space_set_tuple_name(
943 __isl_take isl_space *space,
944 enum isl_dim_type type, const char *s);
945 int isl_space_has_tuple_name(__isl_keep isl_space *space,
946 enum isl_dim_type type);
947 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
948 enum isl_dim_type type);
950 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
951 or C<isl_dim_set>. As with C<isl_space_get_name>,
952 the C<isl_space_get_tuple_name> function returns a pointer to some internal
954 Binary operations require the corresponding spaces of their arguments
955 to have the same name.
957 To keep the names of all parameters and tuples, but reset the user pointers
958 of all the corresponding identifiers, use the following function.
960 __isl_give isl_space *isl_space_reset_user(
961 __isl_take isl_space *space);
963 Spaces can be nested. In particular, the domain of a set or
964 the domain or range of a relation can be a nested relation.
965 This process is also called I<wrapping>.
966 The functions for detecting, constructing and deconstructing
967 such nested spaces can be found in the wrapping properties
968 of L</"Unary Properties">, the wrapping operations
969 of L</"Unary Operations"> and the Cartesian product operations
970 of L</"Basic Operations">.
972 Spaces can be created from other spaces
973 using the following functions.
975 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
976 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
977 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
978 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
979 __isl_give isl_space *isl_space_domain_map(
980 __isl_take isl_space *space);
981 __isl_give isl_space *isl_space_range_map(
982 __isl_take isl_space *space);
983 __isl_give isl_space *isl_space_params(
984 __isl_take isl_space *space);
985 __isl_give isl_space *isl_space_set_from_params(
986 __isl_take isl_space *space);
987 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
988 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
989 __isl_take isl_space *right);
990 __isl_give isl_space *isl_space_align_params(
991 __isl_take isl_space *space1, __isl_take isl_space *space2)
992 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
993 enum isl_dim_type type, unsigned pos, unsigned n);
994 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
995 enum isl_dim_type type, unsigned n);
996 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
997 enum isl_dim_type type, unsigned first, unsigned n);
998 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
999 enum isl_dim_type dst_type, unsigned dst_pos,
1000 enum isl_dim_type src_type, unsigned src_pos,
1002 __isl_give isl_space *isl_space_map_from_set(
1003 __isl_take isl_space *space);
1004 __isl_give isl_space *isl_space_map_from_domain_and_range(
1005 __isl_take isl_space *domain,
1006 __isl_take isl_space *range);
1007 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
1008 __isl_give isl_space *isl_space_curry(
1009 __isl_take isl_space *space);
1010 __isl_give isl_space *isl_space_uncurry(
1011 __isl_take isl_space *space);
1013 Note that if dimensions are added or removed from a space, then
1014 the name and the internal structure are lost.
1018 A local space is essentially a space with
1019 zero or more existentially quantified variables.
1020 The local space of a (constraint of a) basic set or relation can be obtained
1021 using the following functions.
1023 #include <isl/constraint.h>
1024 __isl_give isl_local_space *isl_constraint_get_local_space(
1025 __isl_keep isl_constraint *constraint);
1027 #include <isl/set.h>
1028 __isl_give isl_local_space *isl_basic_set_get_local_space(
1029 __isl_keep isl_basic_set *bset);
1031 #include <isl/map.h>
1032 __isl_give isl_local_space *isl_basic_map_get_local_space(
1033 __isl_keep isl_basic_map *bmap);
1035 A new local space can be created from a space using
1037 #include <isl/local_space.h>
1038 __isl_give isl_local_space *isl_local_space_from_space(
1039 __isl_take isl_space *space);
1041 They can be inspected, modified, copied and freed using the following functions.
1043 #include <isl/local_space.h>
1044 isl_ctx *isl_local_space_get_ctx(
1045 __isl_keep isl_local_space *ls);
1046 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1047 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1048 enum isl_dim_type type);
1049 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1050 __isl_take isl_local_space *ls,
1051 enum isl_dim_type type, __isl_take isl_id *id);
1052 int isl_local_space_has_dim_id(
1053 __isl_keep isl_local_space *ls,
1054 enum isl_dim_type type, unsigned pos);
1055 __isl_give isl_id *isl_local_space_get_dim_id(
1056 __isl_keep isl_local_space *ls,
1057 enum isl_dim_type type, unsigned pos);
1058 int isl_local_space_has_dim_name(
1059 __isl_keep isl_local_space *ls,
1060 enum isl_dim_type type, unsigned pos)
1061 const char *isl_local_space_get_dim_name(
1062 __isl_keep isl_local_space *ls,
1063 enum isl_dim_type type, unsigned pos);
1064 __isl_give isl_local_space *isl_local_space_set_dim_name(
1065 __isl_take isl_local_space *ls,
1066 enum isl_dim_type type, unsigned pos, const char *s);
1067 __isl_give isl_local_space *isl_local_space_set_dim_id(
1068 __isl_take isl_local_space *ls,
1069 enum isl_dim_type type, unsigned pos,
1070 __isl_take isl_id *id);
1071 __isl_give isl_space *isl_local_space_get_space(
1072 __isl_keep isl_local_space *ls);
1073 __isl_give isl_aff *isl_local_space_get_div(
1074 __isl_keep isl_local_space *ls, int pos);
1075 __isl_give isl_local_space *isl_local_space_copy(
1076 __isl_keep isl_local_space *ls);
1077 __isl_null isl_local_space *isl_local_space_free(
1078 __isl_take isl_local_space *ls);
1080 Note that C<isl_local_space_get_div> can only be used on local spaces
1083 Two local spaces can be compared using
1085 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1086 __isl_keep isl_local_space *ls2);
1088 Local spaces can be created from other local spaces
1089 using the functions described in L</"Unary Operations">
1090 and L</"Binary Operations">.
1092 =head2 Input and Output
1094 C<isl> supports its own input/output format, which is similar
1095 to the C<Omega> format, but also supports the C<PolyLib> format
1098 =head3 C<isl> format
1100 The C<isl> format is similar to that of C<Omega>, but has a different
1101 syntax for describing the parameters and allows for the definition
1102 of an existentially quantified variable as the integer division
1103 of an affine expression.
1104 For example, the set of integers C<i> between C<0> and C<n>
1105 such that C<i % 10 <= 6> can be described as
1107 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1110 A set or relation can have several disjuncts, separated
1111 by the keyword C<or>. Each disjunct is either a conjunction
1112 of constraints or a projection (C<exists>) of a conjunction
1113 of constraints. The constraints are separated by the keyword
1116 =head3 C<PolyLib> format
1118 If the represented set is a union, then the first line
1119 contains a single number representing the number of disjuncts.
1120 Otherwise, a line containing the number C<1> is optional.
1122 Each disjunct is represented by a matrix of constraints.
1123 The first line contains two numbers representing
1124 the number of rows and columns,
1125 where the number of rows is equal to the number of constraints
1126 and the number of columns is equal to two plus the number of variables.
1127 The following lines contain the actual rows of the constraint matrix.
1128 In each row, the first column indicates whether the constraint
1129 is an equality (C<0>) or inequality (C<1>). The final column
1130 corresponds to the constant term.
1132 If the set is parametric, then the coefficients of the parameters
1133 appear in the last columns before the constant column.
1134 The coefficients of any existentially quantified variables appear
1135 between those of the set variables and those of the parameters.
1137 =head3 Extended C<PolyLib> format
1139 The extended C<PolyLib> format is nearly identical to the
1140 C<PolyLib> format. The only difference is that the line
1141 containing the number of rows and columns of a constraint matrix
1142 also contains four additional numbers:
1143 the number of output dimensions, the number of input dimensions,
1144 the number of local dimensions (i.e., the number of existentially
1145 quantified variables) and the number of parameters.
1146 For sets, the number of ``output'' dimensions is equal
1147 to the number of set dimensions, while the number of ``input''
1152 #include <isl/set.h>
1153 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1154 isl_ctx *ctx, FILE *input);
1155 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1156 isl_ctx *ctx, const char *str);
1157 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1159 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1162 #include <isl/map.h>
1163 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1164 isl_ctx *ctx, FILE *input);
1165 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1166 isl_ctx *ctx, const char *str);
1167 __isl_give isl_map *isl_map_read_from_file(
1168 isl_ctx *ctx, FILE *input);
1169 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1172 #include <isl/union_set.h>
1173 __isl_give isl_union_set *isl_union_set_read_from_file(
1174 isl_ctx *ctx, FILE *input);
1175 __isl_give isl_union_set *isl_union_set_read_from_str(
1176 isl_ctx *ctx, const char *str);
1178 #include <isl/union_map.h>
1179 __isl_give isl_union_map *isl_union_map_read_from_file(
1180 isl_ctx *ctx, FILE *input);
1181 __isl_give isl_union_map *isl_union_map_read_from_str(
1182 isl_ctx *ctx, const char *str);
1184 The input format is autodetected and may be either the C<PolyLib> format
1185 or the C<isl> format.
1189 Before anything can be printed, an C<isl_printer> needs to
1192 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1194 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1195 __isl_null isl_printer *isl_printer_free(
1196 __isl_take isl_printer *printer);
1197 __isl_give char *isl_printer_get_str(
1198 __isl_keep isl_printer *printer);
1200 The printer can be inspected using the following functions.
1202 FILE *isl_printer_get_file(
1203 __isl_keep isl_printer *printer);
1204 int isl_printer_get_output_format(
1205 __isl_keep isl_printer *p);
1207 The behavior of the printer can be modified in various ways
1209 __isl_give isl_printer *isl_printer_set_output_format(
1210 __isl_take isl_printer *p, int output_format);
1211 __isl_give isl_printer *isl_printer_set_indent(
1212 __isl_take isl_printer *p, int indent);
1213 __isl_give isl_printer *isl_printer_set_indent_prefix(
1214 __isl_take isl_printer *p, const char *prefix);
1215 __isl_give isl_printer *isl_printer_indent(
1216 __isl_take isl_printer *p, int indent);
1217 __isl_give isl_printer *isl_printer_set_prefix(
1218 __isl_take isl_printer *p, const char *prefix);
1219 __isl_give isl_printer *isl_printer_set_suffix(
1220 __isl_take isl_printer *p, const char *suffix);
1222 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1223 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1224 and defaults to C<ISL_FORMAT_ISL>.
1225 Each line in the output is prefixed by C<indent_prefix>,
1226 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
1227 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1228 In the C<PolyLib> format output,
1229 the coefficients of the existentially quantified variables
1230 appear between those of the set variables and those
1232 The function C<isl_printer_indent> increases the indentation
1233 by the specified amount (which may be negative).
1235 To actually print something, use
1237 #include <isl/printer.h>
1238 __isl_give isl_printer *isl_printer_print_double(
1239 __isl_take isl_printer *p, double d);
1241 #include <isl/set.h>
1242 __isl_give isl_printer *isl_printer_print_basic_set(
1243 __isl_take isl_printer *printer,
1244 __isl_keep isl_basic_set *bset);
1245 __isl_give isl_printer *isl_printer_print_set(
1246 __isl_take isl_printer *printer,
1247 __isl_keep isl_set *set);
1249 #include <isl/map.h>
1250 __isl_give isl_printer *isl_printer_print_basic_map(
1251 __isl_take isl_printer *printer,
1252 __isl_keep isl_basic_map *bmap);
1253 __isl_give isl_printer *isl_printer_print_map(
1254 __isl_take isl_printer *printer,
1255 __isl_keep isl_map *map);
1257 #include <isl/union_set.h>
1258 __isl_give isl_printer *isl_printer_print_union_set(
1259 __isl_take isl_printer *p,
1260 __isl_keep isl_union_set *uset);
1262 #include <isl/union_map.h>
1263 __isl_give isl_printer *isl_printer_print_union_map(
1264 __isl_take isl_printer *p,
1265 __isl_keep isl_union_map *umap);
1267 When called on a file printer, the following function flushes
1268 the file. When called on a string printer, the buffer is cleared.
1270 __isl_give isl_printer *isl_printer_flush(
1271 __isl_take isl_printer *p);
1273 =head2 Creating New Sets and Relations
1275 C<isl> has functions for creating some standard sets and relations.
1279 =item * Empty sets and relations
1281 __isl_give isl_basic_set *isl_basic_set_empty(
1282 __isl_take isl_space *space);
1283 __isl_give isl_basic_map *isl_basic_map_empty(
1284 __isl_take isl_space *space);
1285 __isl_give isl_set *isl_set_empty(
1286 __isl_take isl_space *space);
1287 __isl_give isl_map *isl_map_empty(
1288 __isl_take isl_space *space);
1289 __isl_give isl_union_set *isl_union_set_empty(
1290 __isl_take isl_space *space);
1291 __isl_give isl_union_map *isl_union_map_empty(
1292 __isl_take isl_space *space);
1294 For C<isl_union_set>s and C<isl_union_map>s, the space
1295 is only used to specify the parameters.
1297 =item * Universe sets and relations
1299 __isl_give isl_basic_set *isl_basic_set_universe(
1300 __isl_take isl_space *space);
1301 __isl_give isl_basic_map *isl_basic_map_universe(
1302 __isl_take isl_space *space);
1303 __isl_give isl_set *isl_set_universe(
1304 __isl_take isl_space *space);
1305 __isl_give isl_map *isl_map_universe(
1306 __isl_take isl_space *space);
1307 __isl_give isl_union_set *isl_union_set_universe(
1308 __isl_take isl_union_set *uset);
1309 __isl_give isl_union_map *isl_union_map_universe(
1310 __isl_take isl_union_map *umap);
1312 The sets and relations constructed by the functions above
1313 contain all integer values, while those constructed by the
1314 functions below only contain non-negative values.
1316 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1317 __isl_take isl_space *space);
1318 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1319 __isl_take isl_space *space);
1320 __isl_give isl_set *isl_set_nat_universe(
1321 __isl_take isl_space *space);
1322 __isl_give isl_map *isl_map_nat_universe(
1323 __isl_take isl_space *space);
1325 =item * Identity relations
1327 __isl_give isl_basic_map *isl_basic_map_identity(
1328 __isl_take isl_space *space);
1329 __isl_give isl_map *isl_map_identity(
1330 __isl_take isl_space *space);
1332 The number of input and output dimensions in C<space> needs
1335 =item * Lexicographic order
1337 __isl_give isl_map *isl_map_lex_lt(
1338 __isl_take isl_space *set_space);
1339 __isl_give isl_map *isl_map_lex_le(
1340 __isl_take isl_space *set_space);
1341 __isl_give isl_map *isl_map_lex_gt(
1342 __isl_take isl_space *set_space);
1343 __isl_give isl_map *isl_map_lex_ge(
1344 __isl_take isl_space *set_space);
1345 __isl_give isl_map *isl_map_lex_lt_first(
1346 __isl_take isl_space *space, unsigned n);
1347 __isl_give isl_map *isl_map_lex_le_first(
1348 __isl_take isl_space *space, unsigned n);
1349 __isl_give isl_map *isl_map_lex_gt_first(
1350 __isl_take isl_space *space, unsigned n);
1351 __isl_give isl_map *isl_map_lex_ge_first(
1352 __isl_take isl_space *space, unsigned n);
1354 The first four functions take a space for a B<set>
1355 and return relations that express that the elements in the domain
1356 are lexicographically less
1357 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1358 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1359 than the elements in the range.
1360 The last four functions take a space for a map
1361 and return relations that express that the first C<n> dimensions
1362 in the domain are lexicographically less
1363 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1364 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1365 than the first C<n> dimensions in the range.
1369 A basic set or relation can be converted to a set or relation
1370 using the following functions.
1372 __isl_give isl_set *isl_set_from_basic_set(
1373 __isl_take isl_basic_set *bset);
1374 __isl_give isl_map *isl_map_from_basic_map(
1375 __isl_take isl_basic_map *bmap);
1377 Sets and relations can be converted to union sets and relations
1378 using the following functions.
1380 __isl_give isl_union_set *isl_union_set_from_basic_set(
1381 __isl_take isl_basic_set *bset);
1382 __isl_give isl_union_map *isl_union_map_from_basic_map(
1383 __isl_take isl_basic_map *bmap);
1384 __isl_give isl_union_set *isl_union_set_from_set(
1385 __isl_take isl_set *set);
1386 __isl_give isl_union_map *isl_union_map_from_map(
1387 __isl_take isl_map *map);
1389 The inverse conversions below can only be used if the input
1390 union set or relation is known to contain elements in exactly one
1393 __isl_give isl_set *isl_set_from_union_set(
1394 __isl_take isl_union_set *uset);
1395 __isl_give isl_map *isl_map_from_union_map(
1396 __isl_take isl_union_map *umap);
1398 A zero-dimensional (basic) set can be constructed on a given parameter domain
1399 using the following function.
1401 __isl_give isl_basic_set *isl_basic_set_from_params(
1402 __isl_take isl_basic_set *bset);
1403 __isl_give isl_set *isl_set_from_params(
1404 __isl_take isl_set *set);
1406 Sets and relations can be copied and freed again using the following
1409 __isl_give isl_basic_set *isl_basic_set_copy(
1410 __isl_keep isl_basic_set *bset);
1411 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1412 __isl_give isl_union_set *isl_union_set_copy(
1413 __isl_keep isl_union_set *uset);
1414 __isl_give isl_basic_map *isl_basic_map_copy(
1415 __isl_keep isl_basic_map *bmap);
1416 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1417 __isl_give isl_union_map *isl_union_map_copy(
1418 __isl_keep isl_union_map *umap);
1419 __isl_null isl_basic_set *isl_basic_set_free(
1420 __isl_take isl_basic_set *bset);
1421 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1422 __isl_null isl_union_set *isl_union_set_free(
1423 __isl_take isl_union_set *uset);
1424 __isl_null isl_basic_map *isl_basic_map_free(
1425 __isl_take isl_basic_map *bmap);
1426 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1427 __isl_null isl_union_map *isl_union_map_free(
1428 __isl_take isl_union_map *umap);
1430 Other sets and relations can be constructed by starting
1431 from a universe set or relation, adding equality and/or
1432 inequality constraints and then projecting out the
1433 existentially quantified variables, if any.
1434 Constraints can be constructed, manipulated and
1435 added to (or removed from) (basic) sets and relations
1436 using the following functions.
1438 #include <isl/constraint.h>
1439 __isl_give isl_constraint *isl_equality_alloc(
1440 __isl_take isl_local_space *ls);
1441 __isl_give isl_constraint *isl_inequality_alloc(
1442 __isl_take isl_local_space *ls);
1443 __isl_give isl_constraint *isl_constraint_set_constant_si(
1444 __isl_take isl_constraint *constraint, int v);
1445 __isl_give isl_constraint *isl_constraint_set_constant_val(
1446 __isl_take isl_constraint *constraint,
1447 __isl_take isl_val *v);
1448 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1449 __isl_take isl_constraint *constraint,
1450 enum isl_dim_type type, int pos, int v);
1451 __isl_give isl_constraint *
1452 isl_constraint_set_coefficient_val(
1453 __isl_take isl_constraint *constraint,
1454 enum isl_dim_type type, int pos,
1455 __isl_take isl_val *v);
1456 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1457 __isl_take isl_basic_map *bmap,
1458 __isl_take isl_constraint *constraint);
1459 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1460 __isl_take isl_basic_set *bset,
1461 __isl_take isl_constraint *constraint);
1462 __isl_give isl_map *isl_map_add_constraint(
1463 __isl_take isl_map *map,
1464 __isl_take isl_constraint *constraint);
1465 __isl_give isl_set *isl_set_add_constraint(
1466 __isl_take isl_set *set,
1467 __isl_take isl_constraint *constraint);
1468 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1469 __isl_take isl_basic_set *bset,
1470 __isl_take isl_constraint *constraint);
1472 For example, to create a set containing the even integers
1473 between 10 and 42, you would use the following code.
1476 isl_local_space *ls;
1478 isl_basic_set *bset;
1480 space = isl_space_set_alloc(ctx, 0, 2);
1481 bset = isl_basic_set_universe(isl_space_copy(space));
1482 ls = isl_local_space_from_space(space);
1484 c = isl_equality_alloc(isl_local_space_copy(ls));
1485 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1486 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1487 bset = isl_basic_set_add_constraint(bset, c);
1489 c = isl_inequality_alloc(isl_local_space_copy(ls));
1490 c = isl_constraint_set_constant_si(c, -10);
1491 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1492 bset = isl_basic_set_add_constraint(bset, c);
1494 c = isl_inequality_alloc(ls);
1495 c = isl_constraint_set_constant_si(c, 42);
1496 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1497 bset = isl_basic_set_add_constraint(bset, c);
1499 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1503 isl_basic_set *bset;
1504 bset = isl_basic_set_read_from_str(ctx,
1505 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1507 A basic set or relation can also be constructed from two matrices
1508 describing the equalities and the inequalities.
1510 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1511 __isl_take isl_space *space,
1512 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1513 enum isl_dim_type c1,
1514 enum isl_dim_type c2, enum isl_dim_type c3,
1515 enum isl_dim_type c4);
1516 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1517 __isl_take isl_space *space,
1518 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1519 enum isl_dim_type c1,
1520 enum isl_dim_type c2, enum isl_dim_type c3,
1521 enum isl_dim_type c4, enum isl_dim_type c5);
1523 The C<isl_dim_type> arguments indicate the order in which
1524 different kinds of variables appear in the input matrices
1525 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1526 C<isl_dim_set> and C<isl_dim_div> for sets and
1527 of C<isl_dim_cst>, C<isl_dim_param>,
1528 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1530 A (basic or union) set or relation can also be constructed from a
1531 (union) (piecewise) (multiple) affine expression
1532 or a list of affine expressions
1533 (See L<"Piecewise Quasi Affine Expressions"> and
1534 L<"Piecewise Multiple Quasi Affine Expressions">).
1536 __isl_give isl_basic_map *isl_basic_map_from_aff(
1537 __isl_take isl_aff *aff);
1538 __isl_give isl_map *isl_map_from_aff(
1539 __isl_take isl_aff *aff);
1540 __isl_give isl_set *isl_set_from_pw_aff(
1541 __isl_take isl_pw_aff *pwaff);
1542 __isl_give isl_map *isl_map_from_pw_aff(
1543 __isl_take isl_pw_aff *pwaff);
1544 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1545 __isl_take isl_space *domain_space,
1546 __isl_take isl_aff_list *list);
1547 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1548 __isl_take isl_multi_aff *maff)
1549 __isl_give isl_map *isl_map_from_multi_aff(
1550 __isl_take isl_multi_aff *maff)
1551 __isl_give isl_set *isl_set_from_pw_multi_aff(
1552 __isl_take isl_pw_multi_aff *pma);
1553 __isl_give isl_map *isl_map_from_pw_multi_aff(
1554 __isl_take isl_pw_multi_aff *pma);
1555 __isl_give isl_set *isl_set_from_multi_pw_aff(
1556 __isl_take isl_multi_pw_aff *mpa);
1557 __isl_give isl_map *isl_map_from_multi_pw_aff(
1558 __isl_take isl_multi_pw_aff *mpa);
1559 __isl_give isl_union_map *
1560 isl_union_map_from_union_pw_multi_aff(
1561 __isl_take isl_union_pw_multi_aff *upma);
1563 The C<domain_space> argument describes the domain of the resulting
1564 basic relation. It is required because the C<list> may consist
1565 of zero affine expressions.
1567 =head2 Inspecting Sets and Relations
1569 Usually, the user should not have to care about the actual constraints
1570 of the sets and maps, but should instead apply the abstract operations
1571 explained in the following sections.
1572 Occasionally, however, it may be required to inspect the individual
1573 coefficients of the constraints. This section explains how to do so.
1574 In these cases, it may also be useful to have C<isl> compute
1575 an explicit representation of the existentially quantified variables.
1577 __isl_give isl_set *isl_set_compute_divs(
1578 __isl_take isl_set *set);
1579 __isl_give isl_map *isl_map_compute_divs(
1580 __isl_take isl_map *map);
1581 __isl_give isl_union_set *isl_union_set_compute_divs(
1582 __isl_take isl_union_set *uset);
1583 __isl_give isl_union_map *isl_union_map_compute_divs(
1584 __isl_take isl_union_map *umap);
1586 This explicit representation defines the existentially quantified
1587 variables as integer divisions of the other variables, possibly
1588 including earlier existentially quantified variables.
1589 An explicitly represented existentially quantified variable therefore
1590 has a unique value when the values of the other variables are known.
1591 If, furthermore, the same existentials, i.e., existentials
1592 with the same explicit representations, should appear in the
1593 same order in each of the disjuncts of a set or map, then the user should call
1594 either of the following functions.
1596 __isl_give isl_set *isl_set_align_divs(
1597 __isl_take isl_set *set);
1598 __isl_give isl_map *isl_map_align_divs(
1599 __isl_take isl_map *map);
1601 Alternatively, the existentially quantified variables can be removed
1602 using the following functions, which compute an overapproximation.
1604 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1605 __isl_take isl_basic_set *bset);
1606 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1607 __isl_take isl_basic_map *bmap);
1608 __isl_give isl_set *isl_set_remove_divs(
1609 __isl_take isl_set *set);
1610 __isl_give isl_map *isl_map_remove_divs(
1611 __isl_take isl_map *map);
1613 It is also possible to only remove those divs that are defined
1614 in terms of a given range of dimensions or only those for which
1615 no explicit representation is known.
1617 __isl_give isl_basic_set *
1618 isl_basic_set_remove_divs_involving_dims(
1619 __isl_take isl_basic_set *bset,
1620 enum isl_dim_type type,
1621 unsigned first, unsigned n);
1622 __isl_give isl_basic_map *
1623 isl_basic_map_remove_divs_involving_dims(
1624 __isl_take isl_basic_map *bmap,
1625 enum isl_dim_type type,
1626 unsigned first, unsigned n);
1627 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1628 __isl_take isl_set *set, enum isl_dim_type type,
1629 unsigned first, unsigned n);
1630 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1631 __isl_take isl_map *map, enum isl_dim_type type,
1632 unsigned first, unsigned n);
1634 __isl_give isl_basic_set *
1635 isl_basic_set_remove_unknown_divs(
1636 __isl_take isl_basic_set *bset);
1637 __isl_give isl_set *isl_set_remove_unknown_divs(
1638 __isl_take isl_set *set);
1639 __isl_give isl_map *isl_map_remove_unknown_divs(
1640 __isl_take isl_map *map);
1642 To iterate over all the sets or maps in a union set or map, use
1644 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1645 int (*fn)(__isl_take isl_set *set, void *user),
1647 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1648 int (*fn)(__isl_take isl_map *map, void *user),
1651 The number of sets or maps in a union set or map can be obtained
1654 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1655 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1657 To extract the set or map in a given space from a union, use
1659 __isl_give isl_set *isl_union_set_extract_set(
1660 __isl_keep isl_union_set *uset,
1661 __isl_take isl_space *space);
1662 __isl_give isl_map *isl_union_map_extract_map(
1663 __isl_keep isl_union_map *umap,
1664 __isl_take isl_space *space);
1666 To iterate over all the basic sets or maps in a set or map, use
1668 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1669 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1671 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1672 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1675 The callback function C<fn> should return 0 if successful and
1676 -1 if an error occurs. In the latter case, or if any other error
1677 occurs, the above functions will return -1.
1679 It should be noted that C<isl> does not guarantee that
1680 the basic sets or maps passed to C<fn> are disjoint.
1681 If this is required, then the user should call one of
1682 the following functions first.
1684 __isl_give isl_set *isl_set_make_disjoint(
1685 __isl_take isl_set *set);
1686 __isl_give isl_map *isl_map_make_disjoint(
1687 __isl_take isl_map *map);
1689 The number of basic sets in a set can be obtained
1692 int isl_set_n_basic_set(__isl_keep isl_set *set);
1694 To iterate over the constraints of a basic set or map, use
1696 #include <isl/constraint.h>
1698 int isl_basic_set_n_constraint(
1699 __isl_keep isl_basic_set *bset);
1700 int isl_basic_set_foreach_constraint(
1701 __isl_keep isl_basic_set *bset,
1702 int (*fn)(__isl_take isl_constraint *c, void *user),
1704 int isl_basic_map_n_constraint(
1705 __isl_keep isl_basic_map *bmap);
1706 int isl_basic_map_foreach_constraint(
1707 __isl_keep isl_basic_map *bmap,
1708 int (*fn)(__isl_take isl_constraint *c, void *user),
1710 __isl_null isl_constraint *isl_constraint_free(
1711 __isl_take isl_constraint *c);
1713 Again, the callback function C<fn> should return 0 if successful and
1714 -1 if an error occurs. In the latter case, or if any other error
1715 occurs, the above functions will return -1.
1716 The constraint C<c> represents either an equality or an inequality.
1717 Use the following function to find out whether a constraint
1718 represents an equality. If not, it represents an inequality.
1720 int isl_constraint_is_equality(
1721 __isl_keep isl_constraint *constraint);
1723 The coefficients of the constraints can be inspected using
1724 the following functions.
1726 int isl_constraint_is_lower_bound(
1727 __isl_keep isl_constraint *constraint,
1728 enum isl_dim_type type, unsigned pos);
1729 int isl_constraint_is_upper_bound(
1730 __isl_keep isl_constraint *constraint,
1731 enum isl_dim_type type, unsigned pos);
1732 __isl_give isl_val *isl_constraint_get_constant_val(
1733 __isl_keep isl_constraint *constraint);
1734 __isl_give isl_val *isl_constraint_get_coefficient_val(
1735 __isl_keep isl_constraint *constraint,
1736 enum isl_dim_type type, int pos);
1737 int isl_constraint_involves_dims(
1738 __isl_keep isl_constraint *constraint,
1739 enum isl_dim_type type, unsigned first, unsigned n);
1741 The explicit representations of the existentially quantified
1742 variables can be inspected using the following function.
1743 Note that the user is only allowed to use this function
1744 if the inspected set or map is the result of a call
1745 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1746 The existentially quantified variable is equal to the floor
1747 of the returned affine expression. The affine expression
1748 itself can be inspected using the functions in
1749 L<"Piecewise Quasi Affine Expressions">.
1751 __isl_give isl_aff *isl_constraint_get_div(
1752 __isl_keep isl_constraint *constraint, int pos);
1754 To obtain the constraints of a basic set or map in matrix
1755 form, use the following functions.
1757 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1758 __isl_keep isl_basic_set *bset,
1759 enum isl_dim_type c1, enum isl_dim_type c2,
1760 enum isl_dim_type c3, enum isl_dim_type c4);
1761 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1762 __isl_keep isl_basic_set *bset,
1763 enum isl_dim_type c1, enum isl_dim_type c2,
1764 enum isl_dim_type c3, enum isl_dim_type c4);
1765 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1766 __isl_keep isl_basic_map *bmap,
1767 enum isl_dim_type c1,
1768 enum isl_dim_type c2, enum isl_dim_type c3,
1769 enum isl_dim_type c4, enum isl_dim_type c5);
1770 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1771 __isl_keep isl_basic_map *bmap,
1772 enum isl_dim_type c1,
1773 enum isl_dim_type c2, enum isl_dim_type c3,
1774 enum isl_dim_type c4, enum isl_dim_type c5);
1776 The C<isl_dim_type> arguments dictate the order in which
1777 different kinds of variables appear in the resulting matrix
1778 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1779 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1781 The number of parameters, input, output or set dimensions can
1782 be obtained using the following functions.
1784 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1785 enum isl_dim_type type);
1786 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1787 enum isl_dim_type type);
1788 unsigned isl_set_dim(__isl_keep isl_set *set,
1789 enum isl_dim_type type);
1790 unsigned isl_map_dim(__isl_keep isl_map *map,
1791 enum isl_dim_type type);
1792 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1793 enum isl_dim_type type);
1795 Note that a C<isl_union_map> only has parameters.
1797 To check whether the description of a set or relation depends
1798 on one or more given dimensions, it is not necessary to iterate over all
1799 constraints. Instead the following functions can be used.
1801 int isl_basic_set_involves_dims(
1802 __isl_keep isl_basic_set *bset,
1803 enum isl_dim_type type, unsigned first, unsigned n);
1804 int isl_set_involves_dims(__isl_keep isl_set *set,
1805 enum isl_dim_type type, unsigned first, unsigned n);
1806 int isl_basic_map_involves_dims(
1807 __isl_keep isl_basic_map *bmap,
1808 enum isl_dim_type type, unsigned first, unsigned n);
1809 int isl_map_involves_dims(__isl_keep isl_map *map,
1810 enum isl_dim_type type, unsigned first, unsigned n);
1812 Similarly, the following functions can be used to check whether
1813 a given dimension is involved in any lower or upper bound.
1815 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1816 enum isl_dim_type type, unsigned pos);
1817 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1818 enum isl_dim_type type, unsigned pos);
1820 Note that these functions return true even if there is a bound on
1821 the dimension on only some of the basic sets of C<set>.
1822 To check if they have a bound for all of the basic sets in C<set>,
1823 use the following functions instead.
1825 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1826 enum isl_dim_type type, unsigned pos);
1827 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1828 enum isl_dim_type type, unsigned pos);
1830 The identifiers or names of the domain and range spaces of a set
1831 or relation can be read off or set using the following functions.
1833 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1834 __isl_take isl_basic_set *bset,
1835 __isl_take isl_id *id);
1836 __isl_give isl_set *isl_set_set_tuple_id(
1837 __isl_take isl_set *set, __isl_take isl_id *id);
1838 __isl_give isl_set *isl_set_reset_tuple_id(
1839 __isl_take isl_set *set);
1840 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1841 __isl_give isl_id *isl_set_get_tuple_id(
1842 __isl_keep isl_set *set);
1843 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1844 __isl_take isl_basic_map *bmap,
1845 enum isl_dim_type type, __isl_take isl_id *id);
1846 __isl_give isl_map *isl_map_set_tuple_id(
1847 __isl_take isl_map *map, enum isl_dim_type type,
1848 __isl_take isl_id *id);
1849 __isl_give isl_map *isl_map_reset_tuple_id(
1850 __isl_take isl_map *map, enum isl_dim_type type);
1851 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1852 enum isl_dim_type type);
1853 __isl_give isl_id *isl_map_get_tuple_id(
1854 __isl_keep isl_map *map, enum isl_dim_type type);
1856 const char *isl_basic_set_get_tuple_name(
1857 __isl_keep isl_basic_set *bset);
1858 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1859 __isl_take isl_basic_set *set, const char *s);
1860 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1861 const char *isl_set_get_tuple_name(
1862 __isl_keep isl_set *set);
1863 __isl_give isl_set *isl_set_set_tuple_name(
1864 __isl_take isl_set *set, const char *s);
1865 const char *isl_basic_map_get_tuple_name(
1866 __isl_keep isl_basic_map *bmap,
1867 enum isl_dim_type type);
1868 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1869 __isl_take isl_basic_map *bmap,
1870 enum isl_dim_type type, const char *s);
1871 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1872 enum isl_dim_type type);
1873 const char *isl_map_get_tuple_name(
1874 __isl_keep isl_map *map,
1875 enum isl_dim_type type);
1876 __isl_give isl_map *isl_map_set_tuple_name(
1877 __isl_take isl_map *map,
1878 enum isl_dim_type type, const char *s);
1880 As with C<isl_space_get_tuple_name>, the value returned points to
1881 an internal data structure.
1882 The identifiers, positions or names of individual dimensions can be
1883 read off using the following functions.
1885 __isl_give isl_id *isl_basic_set_get_dim_id(
1886 __isl_keep isl_basic_set *bset,
1887 enum isl_dim_type type, unsigned pos);
1888 __isl_give isl_set *isl_set_set_dim_id(
1889 __isl_take isl_set *set, enum isl_dim_type type,
1890 unsigned pos, __isl_take isl_id *id);
1891 int isl_set_has_dim_id(__isl_keep isl_set *set,
1892 enum isl_dim_type type, unsigned pos);
1893 __isl_give isl_id *isl_set_get_dim_id(
1894 __isl_keep isl_set *set, enum isl_dim_type type,
1896 int isl_basic_map_has_dim_id(
1897 __isl_keep isl_basic_map *bmap,
1898 enum isl_dim_type type, unsigned pos);
1899 __isl_give isl_map *isl_map_set_dim_id(
1900 __isl_take isl_map *map, enum isl_dim_type type,
1901 unsigned pos, __isl_take isl_id *id);
1902 int isl_map_has_dim_id(__isl_keep isl_map *map,
1903 enum isl_dim_type type, unsigned pos);
1904 __isl_give isl_id *isl_map_get_dim_id(
1905 __isl_keep isl_map *map, enum isl_dim_type type,
1907 __isl_give isl_id *isl_union_map_get_dim_id(
1908 __isl_keep isl_union_map *umap,
1909 enum isl_dim_type type, unsigned pos);
1911 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1912 enum isl_dim_type type, __isl_keep isl_id *id);
1913 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1914 enum isl_dim_type type, __isl_keep isl_id *id);
1915 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1916 enum isl_dim_type type, const char *name);
1917 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1918 enum isl_dim_type type, const char *name);
1920 const char *isl_constraint_get_dim_name(
1921 __isl_keep isl_constraint *constraint,
1922 enum isl_dim_type type, unsigned pos);
1923 const char *isl_basic_set_get_dim_name(
1924 __isl_keep isl_basic_set *bset,
1925 enum isl_dim_type type, unsigned pos);
1926 int isl_set_has_dim_name(__isl_keep isl_set *set,
1927 enum isl_dim_type type, unsigned pos);
1928 const char *isl_set_get_dim_name(
1929 __isl_keep isl_set *set,
1930 enum isl_dim_type type, unsigned pos);
1931 const char *isl_basic_map_get_dim_name(
1932 __isl_keep isl_basic_map *bmap,
1933 enum isl_dim_type type, unsigned pos);
1934 int isl_map_has_dim_name(__isl_keep isl_map *map,
1935 enum isl_dim_type type, unsigned pos);
1936 const char *isl_map_get_dim_name(
1937 __isl_keep isl_map *map,
1938 enum isl_dim_type type, unsigned pos);
1940 These functions are mostly useful to obtain the identifiers, positions
1941 or names of the parameters. Identifiers of individual dimensions are
1942 essentially only useful for printing. They are ignored by all other
1943 operations and may not be preserved across those operations.
1945 The user pointers on all parameters and tuples can be reset
1946 using the following functions.
1948 #include <isl/set.h>
1949 __isl_give isl_set *isl_set_reset_user(
1950 __isl_take isl_set *set);
1951 #include <isl/map.h>
1952 __isl_give isl_map *isl_map_reset_user(
1953 __isl_take isl_map *map);
1954 #include <isl/union_set.h>
1955 __isl_give isl_union_set *isl_union_set_reset_user(
1956 __isl_take isl_union_set *uset);
1957 #include <isl/union_map.h>
1958 __isl_give isl_union_map *isl_union_map_reset_user(
1959 __isl_take isl_union_map *umap);
1963 =head3 Unary Properties
1969 The following functions test whether the given set or relation
1970 contains any integer points. The ``plain'' variants do not perform
1971 any computations, but simply check if the given set or relation
1972 is already known to be empty.
1974 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1975 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1976 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1977 int isl_set_is_empty(__isl_keep isl_set *set);
1978 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1979 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1980 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1981 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1982 int isl_map_is_empty(__isl_keep isl_map *map);
1983 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1985 =item * Universality
1987 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1988 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1989 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1991 =item * Single-valuedness
1993 int isl_basic_map_is_single_valued(
1994 __isl_keep isl_basic_map *bmap);
1995 int isl_map_plain_is_single_valued(
1996 __isl_keep isl_map *map);
1997 int isl_map_is_single_valued(__isl_keep isl_map *map);
1998 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
2002 int isl_map_plain_is_injective(__isl_keep isl_map *map);
2003 int isl_map_is_injective(__isl_keep isl_map *map);
2004 int isl_union_map_plain_is_injective(
2005 __isl_keep isl_union_map *umap);
2006 int isl_union_map_is_injective(
2007 __isl_keep isl_union_map *umap);
2011 int isl_map_is_bijective(__isl_keep isl_map *map);
2012 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
2016 __isl_give isl_val *
2017 isl_basic_map_plain_get_val_if_fixed(
2018 __isl_keep isl_basic_map *bmap,
2019 enum isl_dim_type type, unsigned pos);
2020 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
2021 __isl_keep isl_set *set,
2022 enum isl_dim_type type, unsigned pos);
2023 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
2024 __isl_keep isl_map *map,
2025 enum isl_dim_type type, unsigned pos);
2027 If the set or relation obviously lies on a hyperplane where the given dimension
2028 has a fixed value, then return that value.
2029 Otherwise return NaN.
2033 int isl_set_dim_residue_class_val(
2034 __isl_keep isl_set *set,
2035 int pos, __isl_give isl_val **modulo,
2036 __isl_give isl_val **residue);
2038 Check if the values of the given set dimension are equal to a fixed
2039 value modulo some integer value. If so, assign the modulo to C<*modulo>
2040 and the fixed value to C<*residue>. If the given dimension attains only
2041 a single value, then assign C<0> to C<*modulo> and the fixed value to
2043 If the dimension does not attain only a single value and if no modulo
2044 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
2048 To check whether a set is a parameter domain, use this function:
2050 int isl_set_is_params(__isl_keep isl_set *set);
2051 int isl_union_set_is_params(
2052 __isl_keep isl_union_set *uset);
2056 The following functions check whether the space of the given
2057 (basic) set or relation range is a wrapped relation.
2059 #include <isl/space.h>
2060 int isl_space_is_wrapping(
2061 __isl_keep isl_space *space);
2062 int isl_space_domain_is_wrapping(
2063 __isl_keep isl_space *space);
2064 int isl_space_range_is_wrapping(
2065 __isl_keep isl_space *space);
2067 #include <isl/set.h>
2068 int isl_basic_set_is_wrapping(
2069 __isl_keep isl_basic_set *bset);
2070 int isl_set_is_wrapping(__isl_keep isl_set *set);
2072 #include <isl/map.h>
2073 int isl_map_domain_is_wrapping(
2074 __isl_keep isl_map *map);
2075 int isl_map_range_is_wrapping(
2076 __isl_keep isl_map *map);
2078 The input to C<isl_space_is_wrapping> should
2079 be the space of a set, while that of
2080 C<isl_space_domain_is_wrapping> and
2081 C<isl_space_range_is_wrapping> should be the space of a relation.
2083 =item * Internal Product
2085 int isl_basic_map_can_zip(
2086 __isl_keep isl_basic_map *bmap);
2087 int isl_map_can_zip(__isl_keep isl_map *map);
2089 Check whether the product of domain and range of the given relation
2091 i.e., whether both domain and range are nested relations.
2095 int isl_basic_map_can_curry(
2096 __isl_keep isl_basic_map *bmap);
2097 int isl_map_can_curry(__isl_keep isl_map *map);
2099 Check whether the domain of the (basic) relation is a wrapped relation.
2101 int isl_basic_map_can_uncurry(
2102 __isl_keep isl_basic_map *bmap);
2103 int isl_map_can_uncurry(__isl_keep isl_map *map);
2105 Check whether the range of the (basic) relation is a wrapped relation.
2109 =head3 Binary Properties
2115 int isl_basic_set_plain_is_equal(
2116 __isl_keep isl_basic_set *bset1,
2117 __isl_keep isl_basic_set *bset2);
2118 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2119 __isl_keep isl_set *set2);
2120 int isl_set_is_equal(__isl_keep isl_set *set1,
2121 __isl_keep isl_set *set2);
2122 int isl_union_set_is_equal(
2123 __isl_keep isl_union_set *uset1,
2124 __isl_keep isl_union_set *uset2);
2125 int isl_basic_map_is_equal(
2126 __isl_keep isl_basic_map *bmap1,
2127 __isl_keep isl_basic_map *bmap2);
2128 int isl_map_is_equal(__isl_keep isl_map *map1,
2129 __isl_keep isl_map *map2);
2130 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2131 __isl_keep isl_map *map2);
2132 int isl_union_map_is_equal(
2133 __isl_keep isl_union_map *umap1,
2134 __isl_keep isl_union_map *umap2);
2136 =item * Disjointness
2138 int isl_basic_set_is_disjoint(
2139 __isl_keep isl_basic_set *bset1,
2140 __isl_keep isl_basic_set *bset2);
2141 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2142 __isl_keep isl_set *set2);
2143 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2144 __isl_keep isl_set *set2);
2145 int isl_basic_map_is_disjoint(
2146 __isl_keep isl_basic_map *bmap1,
2147 __isl_keep isl_basic_map *bmap2);
2148 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2149 __isl_keep isl_map *map2);
2153 int isl_basic_set_is_subset(
2154 __isl_keep isl_basic_set *bset1,
2155 __isl_keep isl_basic_set *bset2);
2156 int isl_set_is_subset(__isl_keep isl_set *set1,
2157 __isl_keep isl_set *set2);
2158 int isl_set_is_strict_subset(
2159 __isl_keep isl_set *set1,
2160 __isl_keep isl_set *set2);
2161 int isl_union_set_is_subset(
2162 __isl_keep isl_union_set *uset1,
2163 __isl_keep isl_union_set *uset2);
2164 int isl_union_set_is_strict_subset(
2165 __isl_keep isl_union_set *uset1,
2166 __isl_keep isl_union_set *uset2);
2167 int isl_basic_map_is_subset(
2168 __isl_keep isl_basic_map *bmap1,
2169 __isl_keep isl_basic_map *bmap2);
2170 int isl_basic_map_is_strict_subset(
2171 __isl_keep isl_basic_map *bmap1,
2172 __isl_keep isl_basic_map *bmap2);
2173 int isl_map_is_subset(
2174 __isl_keep isl_map *map1,
2175 __isl_keep isl_map *map2);
2176 int isl_map_is_strict_subset(
2177 __isl_keep isl_map *map1,
2178 __isl_keep isl_map *map2);
2179 int isl_union_map_is_subset(
2180 __isl_keep isl_union_map *umap1,
2181 __isl_keep isl_union_map *umap2);
2182 int isl_union_map_is_strict_subset(
2183 __isl_keep isl_union_map *umap1,
2184 __isl_keep isl_union_map *umap2);
2186 Check whether the first argument is a (strict) subset of the
2191 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2192 __isl_keep isl_set *set2);
2194 This function is useful for sorting C<isl_set>s.
2195 The order depends on the internal representation of the inputs.
2196 The order is fixed over different calls to the function (assuming
2197 the internal representation of the inputs has not changed), but may
2198 change over different versions of C<isl>.
2202 =head2 Unary Operations
2208 __isl_give isl_set *isl_set_complement(
2209 __isl_take isl_set *set);
2210 __isl_give isl_map *isl_map_complement(
2211 __isl_take isl_map *map);
2215 __isl_give isl_basic_map *isl_basic_map_reverse(
2216 __isl_take isl_basic_map *bmap);
2217 __isl_give isl_map *isl_map_reverse(
2218 __isl_take isl_map *map);
2219 __isl_give isl_union_map *isl_union_map_reverse(
2220 __isl_take isl_union_map *umap);
2224 #include <isl/local_space.h>
2225 __isl_give isl_local_space *isl_local_space_domain(
2226 __isl_take isl_local_space *ls);
2227 __isl_give isl_local_space *isl_local_space_range(
2228 __isl_take isl_local_space *ls);
2230 #include <isl/set.h>
2231 __isl_give isl_basic_set *isl_basic_set_project_out(
2232 __isl_take isl_basic_set *bset,
2233 enum isl_dim_type type, unsigned first, unsigned n);
2234 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2235 enum isl_dim_type type, unsigned first, unsigned n);
2236 __isl_give isl_basic_set *isl_basic_set_params(
2237 __isl_take isl_basic_set *bset);
2238 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2240 #include <isl/map.h>
2241 __isl_give isl_basic_map *isl_basic_map_project_out(
2242 __isl_take isl_basic_map *bmap,
2243 enum isl_dim_type type, unsigned first, unsigned n);
2244 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2245 enum isl_dim_type type, unsigned first, unsigned n);
2246 __isl_give isl_basic_set *isl_basic_map_domain(
2247 __isl_take isl_basic_map *bmap);
2248 __isl_give isl_basic_set *isl_basic_map_range(
2249 __isl_take isl_basic_map *bmap);
2250 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2251 __isl_give isl_set *isl_map_domain(
2252 __isl_take isl_map *bmap);
2253 __isl_give isl_set *isl_map_range(
2254 __isl_take isl_map *map);
2256 #include <isl/union_set.h>
2257 __isl_give isl_set *isl_union_set_params(
2258 __isl_take isl_union_set *uset);
2260 #include <isl/union_map.h>
2261 __isl_give isl_union_map *isl_union_map_project_out(
2262 __isl_take isl_union_map *umap,
2263 enum isl_dim_type type, unsigned first, unsigned n);
2264 __isl_give isl_set *isl_union_map_params(
2265 __isl_take isl_union_map *umap);
2266 __isl_give isl_union_set *isl_union_map_domain(
2267 __isl_take isl_union_map *umap);
2268 __isl_give isl_union_set *isl_union_map_range(
2269 __isl_take isl_union_map *umap);
2271 The function C<isl_union_map_project_out> can only project out
2274 #include <isl/map.h>
2275 __isl_give isl_basic_map *isl_basic_map_domain_map(
2276 __isl_take isl_basic_map *bmap);
2277 __isl_give isl_basic_map *isl_basic_map_range_map(
2278 __isl_take isl_basic_map *bmap);
2279 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2280 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2282 #include <isl/union_map.h>
2283 __isl_give isl_union_map *isl_union_map_domain_map(
2284 __isl_take isl_union_map *umap);
2285 __isl_give isl_union_map *isl_union_map_range_map(
2286 __isl_take isl_union_map *umap);
2288 The functions above construct a (basic, regular or union) relation
2289 that maps (a wrapped version of) the input relation to its domain or range.
2293 __isl_give isl_basic_set *isl_basic_set_eliminate(
2294 __isl_take isl_basic_set *bset,
2295 enum isl_dim_type type,
2296 unsigned first, unsigned n);
2297 __isl_give isl_set *isl_set_eliminate(
2298 __isl_take isl_set *set, enum isl_dim_type type,
2299 unsigned first, unsigned n);
2300 __isl_give isl_basic_map *isl_basic_map_eliminate(
2301 __isl_take isl_basic_map *bmap,
2302 enum isl_dim_type type,
2303 unsigned first, unsigned n);
2304 __isl_give isl_map *isl_map_eliminate(
2305 __isl_take isl_map *map, enum isl_dim_type type,
2306 unsigned first, unsigned n);
2308 Eliminate the coefficients for the given dimensions from the constraints,
2309 without removing the dimensions.
2311 =item * Constructing a relation from a set
2313 #include <isl/local_space.h>
2314 __isl_give isl_local_space *isl_local_space_from_domain(
2315 __isl_take isl_local_space *ls);
2317 #include <isl/map.h>
2318 __isl_give isl_map *isl_map_from_domain(
2319 __isl_take isl_set *set);
2320 __isl_give isl_map *isl_map_from_range(
2321 __isl_take isl_set *set);
2323 Create a relation with the given set as domain or range.
2324 The range or domain of the created relation is a zero-dimensional
2325 flat anonymous space.
2329 __isl_give isl_basic_set *isl_basic_set_fix_si(
2330 __isl_take isl_basic_set *bset,
2331 enum isl_dim_type type, unsigned pos, int value);
2332 __isl_give isl_basic_set *isl_basic_set_fix_val(
2333 __isl_take isl_basic_set *bset,
2334 enum isl_dim_type type, unsigned pos,
2335 __isl_take isl_val *v);
2336 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2337 enum isl_dim_type type, unsigned pos, int value);
2338 __isl_give isl_set *isl_set_fix_val(
2339 __isl_take isl_set *set,
2340 enum isl_dim_type type, unsigned pos,
2341 __isl_take isl_val *v);
2342 __isl_give isl_basic_map *isl_basic_map_fix_si(
2343 __isl_take isl_basic_map *bmap,
2344 enum isl_dim_type type, unsigned pos, int value);
2345 __isl_give isl_basic_map *isl_basic_map_fix_val(
2346 __isl_take isl_basic_map *bmap,
2347 enum isl_dim_type type, unsigned pos,
2348 __isl_take isl_val *v);
2349 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2350 enum isl_dim_type type, unsigned pos, int value);
2351 __isl_give isl_map *isl_map_fix_val(
2352 __isl_take isl_map *map,
2353 enum isl_dim_type type, unsigned pos,
2354 __isl_take isl_val *v);
2356 Intersect the set or relation with the hyperplane where the given
2357 dimension has the fixed given value.
2359 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2360 __isl_take isl_basic_map *bmap,
2361 enum isl_dim_type type, unsigned pos, int value);
2362 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2363 __isl_take isl_basic_map *bmap,
2364 enum isl_dim_type type, unsigned pos, int value);
2365 __isl_give isl_set *isl_set_lower_bound_si(
2366 __isl_take isl_set *set,
2367 enum isl_dim_type type, unsigned pos, int value);
2368 __isl_give isl_set *isl_set_lower_bound_val(
2369 __isl_take isl_set *set,
2370 enum isl_dim_type type, unsigned pos,
2371 __isl_take isl_val *value);
2372 __isl_give isl_map *isl_map_lower_bound_si(
2373 __isl_take isl_map *map,
2374 enum isl_dim_type type, unsigned pos, int value);
2375 __isl_give isl_set *isl_set_upper_bound_si(
2376 __isl_take isl_set *set,
2377 enum isl_dim_type type, unsigned pos, int value);
2378 __isl_give isl_set *isl_set_upper_bound_val(
2379 __isl_take isl_set *set,
2380 enum isl_dim_type type, unsigned pos,
2381 __isl_take isl_val *value);
2382 __isl_give isl_map *isl_map_upper_bound_si(
2383 __isl_take isl_map *map,
2384 enum isl_dim_type type, unsigned pos, int value);
2386 Intersect the set or relation with the half-space where the given
2387 dimension has a value bounded by the fixed given integer value.
2389 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2390 enum isl_dim_type type1, int pos1,
2391 enum isl_dim_type type2, int pos2);
2392 __isl_give isl_basic_map *isl_basic_map_equate(
2393 __isl_take isl_basic_map *bmap,
2394 enum isl_dim_type type1, int pos1,
2395 enum isl_dim_type type2, int pos2);
2396 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2397 enum isl_dim_type type1, int pos1,
2398 enum isl_dim_type type2, int pos2);
2400 Intersect the set or relation with the hyperplane where the given
2401 dimensions are equal to each other.
2403 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2404 enum isl_dim_type type1, int pos1,
2405 enum isl_dim_type type2, int pos2);
2407 Intersect the relation with the hyperplane where the given
2408 dimensions have opposite values.
2410 __isl_give isl_map *isl_map_order_le(
2411 __isl_take isl_map *map,
2412 enum isl_dim_type type1, int pos1,
2413 enum isl_dim_type type2, int pos2);
2414 __isl_give isl_basic_map *isl_basic_map_order_ge(
2415 __isl_take isl_basic_map *bmap,
2416 enum isl_dim_type type1, int pos1,
2417 enum isl_dim_type type2, int pos2);
2418 __isl_give isl_map *isl_map_order_ge(
2419 __isl_take isl_map *map,
2420 enum isl_dim_type type1, int pos1,
2421 enum isl_dim_type type2, int pos2);
2422 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2423 enum isl_dim_type type1, int pos1,
2424 enum isl_dim_type type2, int pos2);
2425 __isl_give isl_basic_map *isl_basic_map_order_gt(
2426 __isl_take isl_basic_map *bmap,
2427 enum isl_dim_type type1, int pos1,
2428 enum isl_dim_type type2, int pos2);
2429 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2430 enum isl_dim_type type1, int pos1,
2431 enum isl_dim_type type2, int pos2);
2433 Intersect the relation with the half-space where the given
2434 dimensions satisfy the given ordering.
2438 __isl_give isl_map *isl_set_identity(
2439 __isl_take isl_set *set);
2440 __isl_give isl_union_map *isl_union_set_identity(
2441 __isl_take isl_union_set *uset);
2443 Construct an identity relation on the given (union) set.
2447 __isl_give isl_basic_set *isl_basic_map_deltas(
2448 __isl_take isl_basic_map *bmap);
2449 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2450 __isl_give isl_union_set *isl_union_map_deltas(
2451 __isl_take isl_union_map *umap);
2453 These functions return a (basic) set containing the differences
2454 between image elements and corresponding domain elements in the input.
2456 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2457 __isl_take isl_basic_map *bmap);
2458 __isl_give isl_map *isl_map_deltas_map(
2459 __isl_take isl_map *map);
2460 __isl_give isl_union_map *isl_union_map_deltas_map(
2461 __isl_take isl_union_map *umap);
2463 The functions above construct a (basic, regular or union) relation
2464 that maps (a wrapped version of) the input relation to its delta set.
2468 Simplify the representation of a set or relation by trying
2469 to combine pairs of basic sets or relations into a single
2470 basic set or relation.
2472 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2473 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2474 __isl_give isl_union_set *isl_union_set_coalesce(
2475 __isl_take isl_union_set *uset);
2476 __isl_give isl_union_map *isl_union_map_coalesce(
2477 __isl_take isl_union_map *umap);
2479 One of the methods for combining pairs of basic sets or relations
2480 can result in coefficients that are much larger than those that appear
2481 in the constraints of the input. By default, the coefficients are
2482 not allowed to grow larger, but this can be changed by unsetting
2483 the following option.
2485 int isl_options_set_coalesce_bounded_wrapping(
2486 isl_ctx *ctx, int val);
2487 int isl_options_get_coalesce_bounded_wrapping(
2490 =item * Detecting equalities
2492 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2493 __isl_take isl_basic_set *bset);
2494 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2495 __isl_take isl_basic_map *bmap);
2496 __isl_give isl_set *isl_set_detect_equalities(
2497 __isl_take isl_set *set);
2498 __isl_give isl_map *isl_map_detect_equalities(
2499 __isl_take isl_map *map);
2500 __isl_give isl_union_set *isl_union_set_detect_equalities(
2501 __isl_take isl_union_set *uset);
2502 __isl_give isl_union_map *isl_union_map_detect_equalities(
2503 __isl_take isl_union_map *umap);
2505 Simplify the representation of a set or relation by detecting implicit
2508 =item * Removing redundant constraints
2510 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2511 __isl_take isl_basic_set *bset);
2512 __isl_give isl_set *isl_set_remove_redundancies(
2513 __isl_take isl_set *set);
2514 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2515 __isl_take isl_basic_map *bmap);
2516 __isl_give isl_map *isl_map_remove_redundancies(
2517 __isl_take isl_map *map);
2521 __isl_give isl_basic_set *isl_set_convex_hull(
2522 __isl_take isl_set *set);
2523 __isl_give isl_basic_map *isl_map_convex_hull(
2524 __isl_take isl_map *map);
2526 If the input set or relation has any existentially quantified
2527 variables, then the result of these operations is currently undefined.
2531 __isl_give isl_basic_set *
2532 isl_set_unshifted_simple_hull(
2533 __isl_take isl_set *set);
2534 __isl_give isl_basic_map *
2535 isl_map_unshifted_simple_hull(
2536 __isl_take isl_map *map);
2537 __isl_give isl_basic_set *isl_set_simple_hull(
2538 __isl_take isl_set *set);
2539 __isl_give isl_basic_map *isl_map_simple_hull(
2540 __isl_take isl_map *map);
2541 __isl_give isl_union_map *isl_union_map_simple_hull(
2542 __isl_take isl_union_map *umap);
2544 These functions compute a single basic set or relation
2545 that contains the whole input set or relation.
2546 In particular, the output is described by translates
2547 of the constraints describing the basic sets or relations in the input.
2548 In case of C<isl_set_unshifted_simple_hull>, only the original
2549 constraints are used, without any translation.
2553 (See \autoref{s:simple hull}.)
2559 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2560 __isl_take isl_basic_set *bset);
2561 __isl_give isl_basic_set *isl_set_affine_hull(
2562 __isl_take isl_set *set);
2563 __isl_give isl_union_set *isl_union_set_affine_hull(
2564 __isl_take isl_union_set *uset);
2565 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2566 __isl_take isl_basic_map *bmap);
2567 __isl_give isl_basic_map *isl_map_affine_hull(
2568 __isl_take isl_map *map);
2569 __isl_give isl_union_map *isl_union_map_affine_hull(
2570 __isl_take isl_union_map *umap);
2572 In case of union sets and relations, the affine hull is computed
2575 =item * Polyhedral hull
2577 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2578 __isl_take isl_set *set);
2579 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2580 __isl_take isl_map *map);
2581 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2582 __isl_take isl_union_set *uset);
2583 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2584 __isl_take isl_union_map *umap);
2586 These functions compute a single basic set or relation
2587 not involving any existentially quantified variables
2588 that contains the whole input set or relation.
2589 In case of union sets and relations, the polyhedral hull is computed
2592 =item * Other approximations
2594 __isl_give isl_basic_set *
2595 isl_basic_set_drop_constraints_involving_dims(
2596 __isl_take isl_basic_set *bset,
2597 enum isl_dim_type type,
2598 unsigned first, unsigned n);
2599 __isl_give isl_basic_map *
2600 isl_basic_map_drop_constraints_involving_dims(
2601 __isl_take isl_basic_map *bmap,
2602 enum isl_dim_type type,
2603 unsigned first, unsigned n);
2604 __isl_give isl_basic_set *
2605 isl_basic_set_drop_constraints_not_involving_dims(
2606 __isl_take isl_basic_set *bset,
2607 enum isl_dim_type type,
2608 unsigned first, unsigned n);
2609 __isl_give isl_set *
2610 isl_set_drop_constraints_involving_dims(
2611 __isl_take isl_set *set,
2612 enum isl_dim_type type,
2613 unsigned first, unsigned n);
2614 __isl_give isl_map *
2615 isl_map_drop_constraints_involving_dims(
2616 __isl_take isl_map *map,
2617 enum isl_dim_type type,
2618 unsigned first, unsigned n);
2620 These functions drop any constraints (not) involving the specified dimensions.
2621 Note that the result depends on the representation of the input.
2625 __isl_give isl_basic_set *isl_basic_set_sample(
2626 __isl_take isl_basic_set *bset);
2627 __isl_give isl_basic_set *isl_set_sample(
2628 __isl_take isl_set *set);
2629 __isl_give isl_basic_map *isl_basic_map_sample(
2630 __isl_take isl_basic_map *bmap);
2631 __isl_give isl_basic_map *isl_map_sample(
2632 __isl_take isl_map *map);
2634 If the input (basic) set or relation is non-empty, then return
2635 a singleton subset of the input. Otherwise, return an empty set.
2637 =item * Optimization
2639 #include <isl/ilp.h>
2640 __isl_give isl_val *isl_basic_set_max_val(
2641 __isl_keep isl_basic_set *bset,
2642 __isl_keep isl_aff *obj);
2643 __isl_give isl_val *isl_set_min_val(
2644 __isl_keep isl_set *set,
2645 __isl_keep isl_aff *obj);
2646 __isl_give isl_val *isl_set_max_val(
2647 __isl_keep isl_set *set,
2648 __isl_keep isl_aff *obj);
2650 Compute the minimum or maximum of the integer affine expression C<obj>
2651 over the points in C<set>, returning the result in C<opt>.
2652 The result is C<NULL> in case of an error, the optimal value in case
2653 there is one, negative infinity or infinity if the problem is unbounded and
2654 NaN if the problem is empty.
2656 =item * Parametric optimization
2658 __isl_give isl_pw_aff *isl_set_dim_min(
2659 __isl_take isl_set *set, int pos);
2660 __isl_give isl_pw_aff *isl_set_dim_max(
2661 __isl_take isl_set *set, int pos);
2662 __isl_give isl_pw_aff *isl_map_dim_max(
2663 __isl_take isl_map *map, int pos);
2665 Compute the minimum or maximum of the given set or output dimension
2666 as a function of the parameters (and input dimensions), but independently
2667 of the other set or output dimensions.
2668 For lexicographic optimization, see L<"Lexicographic Optimization">.
2672 The following functions compute either the set of (rational) coefficient
2673 values of valid constraints for the given set or the set of (rational)
2674 values satisfying the constraints with coefficients from the given set.
2675 Internally, these two sets of functions perform essentially the
2676 same operations, except that the set of coefficients is assumed to
2677 be a cone, while the set of values may be any polyhedron.
2678 The current implementation is based on the Farkas lemma and
2679 Fourier-Motzkin elimination, but this may change or be made optional
2680 in future. In particular, future implementations may use different
2681 dualization algorithms or skip the elimination step.
2683 __isl_give isl_basic_set *isl_basic_set_coefficients(
2684 __isl_take isl_basic_set *bset);
2685 __isl_give isl_basic_set *isl_set_coefficients(
2686 __isl_take isl_set *set);
2687 __isl_give isl_union_set *isl_union_set_coefficients(
2688 __isl_take isl_union_set *bset);
2689 __isl_give isl_basic_set *isl_basic_set_solutions(
2690 __isl_take isl_basic_set *bset);
2691 __isl_give isl_basic_set *isl_set_solutions(
2692 __isl_take isl_set *set);
2693 __isl_give isl_union_set *isl_union_set_solutions(
2694 __isl_take isl_union_set *bset);
2698 __isl_give isl_map *isl_map_fixed_power_val(
2699 __isl_take isl_map *map,
2700 __isl_take isl_val *exp);
2701 __isl_give isl_union_map *
2702 isl_union_map_fixed_power_val(
2703 __isl_take isl_union_map *umap,
2704 __isl_take isl_val *exp);
2706 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2707 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2708 of C<map> is computed.
2710 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2712 __isl_give isl_union_map *isl_union_map_power(
2713 __isl_take isl_union_map *umap, int *exact);
2715 Compute a parametric representation for all positive powers I<k> of C<map>.
2716 The result maps I<k> to a nested relation corresponding to the
2717 I<k>th power of C<map>.
2718 The result may be an overapproximation. If the result is known to be exact,
2719 then C<*exact> is set to C<1>.
2721 =item * Transitive closure
2723 __isl_give isl_map *isl_map_transitive_closure(
2724 __isl_take isl_map *map, int *exact);
2725 __isl_give isl_union_map *isl_union_map_transitive_closure(
2726 __isl_take isl_union_map *umap, int *exact);
2728 Compute the transitive closure of C<map>.
2729 The result may be an overapproximation. If the result is known to be exact,
2730 then C<*exact> is set to C<1>.
2732 =item * Reaching path lengths
2734 __isl_give isl_map *isl_map_reaching_path_lengths(
2735 __isl_take isl_map *map, int *exact);
2737 Compute a relation that maps each element in the range of C<map>
2738 to the lengths of all paths composed of edges in C<map> that
2739 end up in the given element.
2740 The result may be an overapproximation. If the result is known to be exact,
2741 then C<*exact> is set to C<1>.
2742 To compute the I<maximal> path length, the resulting relation
2743 should be postprocessed by C<isl_map_lexmax>.
2744 In particular, if the input relation is a dependence relation
2745 (mapping sources to sinks), then the maximal path length corresponds
2746 to the free schedule.
2747 Note, however, that C<isl_map_lexmax> expects the maximum to be
2748 finite, so if the path lengths are unbounded (possibly due to
2749 the overapproximation), then you will get an error message.
2753 #include <isl/space.h>
2754 __isl_give isl_space *isl_space_wrap(
2755 __isl_take isl_space *space);
2756 __isl_give isl_space *isl_space_unwrap(
2757 __isl_take isl_space *space);
2759 #include <isl/set.h>
2760 __isl_give isl_basic_map *isl_basic_set_unwrap(
2761 __isl_take isl_basic_set *bset);
2762 __isl_give isl_map *isl_set_unwrap(
2763 __isl_take isl_set *set);
2765 #include <isl/map.h>
2766 __isl_give isl_basic_set *isl_basic_map_wrap(
2767 __isl_take isl_basic_map *bmap);
2768 __isl_give isl_set *isl_map_wrap(
2769 __isl_take isl_map *map);
2771 #include <isl/union_set.h>
2772 __isl_give isl_union_map *isl_union_set_unwrap(
2773 __isl_take isl_union_set *uset);
2775 #include <isl/union_map.h>
2776 __isl_give isl_union_set *isl_union_map_wrap(
2777 __isl_take isl_union_map *umap);
2779 The input to C<isl_space_unwrap> should
2780 be the space of a set, while that of
2781 C<isl_space_wrap> should be the space of a relation.
2782 Conversely, the output of C<isl_space_unwrap> is the space
2783 of a relation, while that of C<isl_space_wrap> is the space of a set.
2787 Remove any internal structure of domain (and range) of the given
2788 set or relation. If there is any such internal structure in the input,
2789 then the name of the space is also removed.
2791 #include <isl/local_space.h>
2792 __isl_give isl_local_space *
2793 isl_local_space_flatten_domain(
2794 __isl_take isl_local_space *ls);
2795 __isl_give isl_local_space *
2796 isl_local_space_flatten_range(
2797 __isl_take isl_local_space *ls);
2799 #include <isl/set.h>
2800 __isl_give isl_basic_set *isl_basic_set_flatten(
2801 __isl_take isl_basic_set *bset);
2802 __isl_give isl_set *isl_set_flatten(
2803 __isl_take isl_set *set);
2805 #include <isl/map.h>
2806 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2807 __isl_take isl_basic_map *bmap);
2808 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2809 __isl_take isl_basic_map *bmap);
2810 __isl_give isl_map *isl_map_flatten_range(
2811 __isl_take isl_map *map);
2812 __isl_give isl_map *isl_map_flatten_domain(
2813 __isl_take isl_map *map);
2814 __isl_give isl_basic_map *isl_basic_map_flatten(
2815 __isl_take isl_basic_map *bmap);
2816 __isl_give isl_map *isl_map_flatten(
2817 __isl_take isl_map *map);
2819 #include <isl/map.h>
2820 __isl_give isl_map *isl_set_flatten_map(
2821 __isl_take isl_set *set);
2823 The function above constructs a relation
2824 that maps the input set to a flattened version of the set.
2828 Lift the input set to a space with extra dimensions corresponding
2829 to the existentially quantified variables in the input.
2830 In particular, the result lives in a wrapped map where the domain
2831 is the original space and the range corresponds to the original
2832 existentially quantified variables.
2834 __isl_give isl_basic_set *isl_basic_set_lift(
2835 __isl_take isl_basic_set *bset);
2836 __isl_give isl_set *isl_set_lift(
2837 __isl_take isl_set *set);
2838 __isl_give isl_union_set *isl_union_set_lift(
2839 __isl_take isl_union_set *uset);
2841 Given a local space that contains the existentially quantified
2842 variables of a set, a basic relation that, when applied to
2843 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2844 can be constructed using the following function.
2846 #include <isl/local_space.h>
2847 __isl_give isl_basic_map *isl_local_space_lifting(
2848 __isl_take isl_local_space *ls);
2850 =item * Internal Product
2852 __isl_give isl_basic_map *isl_basic_map_zip(
2853 __isl_take isl_basic_map *bmap);
2854 __isl_give isl_map *isl_map_zip(
2855 __isl_take isl_map *map);
2856 __isl_give isl_union_map *isl_union_map_zip(
2857 __isl_take isl_union_map *umap);
2859 Given a relation with nested relations for domain and range,
2860 interchange the range of the domain with the domain of the range.
2864 __isl_give isl_basic_map *isl_basic_map_curry(
2865 __isl_take isl_basic_map *bmap);
2866 __isl_give isl_basic_map *isl_basic_map_uncurry(
2867 __isl_take isl_basic_map *bmap);
2868 __isl_give isl_map *isl_map_curry(
2869 __isl_take isl_map *map);
2870 __isl_give isl_map *isl_map_uncurry(
2871 __isl_take isl_map *map);
2872 __isl_give isl_union_map *isl_union_map_curry(
2873 __isl_take isl_union_map *umap);
2874 __isl_give isl_union_map *isl_union_map_uncurry(
2875 __isl_take isl_union_map *umap);
2877 Given a relation with a nested relation for domain,
2878 the C<curry> functions
2879 move the range of the nested relation out of the domain
2880 and use it as the domain of a nested relation in the range,
2881 with the original range as range of this nested relation.
2882 The C<uncurry> functions perform the inverse operation.
2884 =item * Aligning parameters
2886 __isl_give isl_basic_set *isl_basic_set_align_params(
2887 __isl_take isl_basic_set *bset,
2888 __isl_take isl_space *model);
2889 __isl_give isl_set *isl_set_align_params(
2890 __isl_take isl_set *set,
2891 __isl_take isl_space *model);
2892 __isl_give isl_basic_map *isl_basic_map_align_params(
2893 __isl_take isl_basic_map *bmap,
2894 __isl_take isl_space *model);
2895 __isl_give isl_map *isl_map_align_params(
2896 __isl_take isl_map *map,
2897 __isl_take isl_space *model);
2899 Change the order of the parameters of the given set or relation
2900 such that the first parameters match those of C<model>.
2901 This may involve the introduction of extra parameters.
2902 All parameters need to be named.
2904 =item * Dimension manipulation
2906 #include <isl/local_space.h>
2907 __isl_give isl_local_space *isl_local_space_add_dims(
2908 __isl_take isl_local_space *ls,
2909 enum isl_dim_type type, unsigned n);
2910 __isl_give isl_local_space *isl_local_space_insert_dims(
2911 __isl_take isl_local_space *ls,
2912 enum isl_dim_type type, unsigned first, unsigned n);
2913 __isl_give isl_local_space *isl_local_space_drop_dims(
2914 __isl_take isl_local_space *ls,
2915 enum isl_dim_type type, unsigned first, unsigned n);
2917 #include <isl/set.h>
2918 __isl_give isl_basic_set *isl_basic_set_add_dims(
2919 __isl_take isl_basic_set *bset,
2920 enum isl_dim_type type, unsigned n);
2921 __isl_give isl_set *isl_set_add_dims(
2922 __isl_take isl_set *set,
2923 enum isl_dim_type type, unsigned n);
2924 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2925 __isl_take isl_basic_set *bset,
2926 enum isl_dim_type type, unsigned pos,
2928 __isl_give isl_set *isl_set_insert_dims(
2929 __isl_take isl_set *set,
2930 enum isl_dim_type type, unsigned pos, unsigned n);
2931 __isl_give isl_basic_set *isl_basic_set_move_dims(
2932 __isl_take isl_basic_set *bset,
2933 enum isl_dim_type dst_type, unsigned dst_pos,
2934 enum isl_dim_type src_type, unsigned src_pos,
2936 __isl_give isl_set *isl_set_move_dims(
2937 __isl_take isl_set *set,
2938 enum isl_dim_type dst_type, unsigned dst_pos,
2939 enum isl_dim_type src_type, unsigned src_pos,
2942 #include <isl/map.h>
2943 __isl_give isl_map *isl_map_add_dims(
2944 __isl_take isl_map *map,
2945 enum isl_dim_type type, unsigned n);
2946 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2947 __isl_take isl_basic_map *bmap,
2948 enum isl_dim_type type, unsigned pos,
2950 __isl_give isl_map *isl_map_insert_dims(
2951 __isl_take isl_map *map,
2952 enum isl_dim_type type, unsigned pos, unsigned n);
2953 __isl_give isl_basic_map *isl_basic_map_move_dims(
2954 __isl_take isl_basic_map *bmap,
2955 enum isl_dim_type dst_type, unsigned dst_pos,
2956 enum isl_dim_type src_type, unsigned src_pos,
2958 __isl_give isl_map *isl_map_move_dims(
2959 __isl_take isl_map *map,
2960 enum isl_dim_type dst_type, unsigned dst_pos,
2961 enum isl_dim_type src_type, unsigned src_pos,
2964 It is usually not advisable to directly change the (input or output)
2965 space of a set or a relation as this removes the name and the internal
2966 structure of the space. However, the above functions can be useful
2967 to add new parameters, assuming
2968 C<isl_set_align_params> and C<isl_map_align_params>
2973 =head2 Binary Operations
2975 The two arguments of a binary operation not only need to live
2976 in the same C<isl_ctx>, they currently also need to have
2977 the same (number of) parameters.
2979 =head3 Basic Operations
2983 =item * Intersection
2985 #include <isl/local_space.h>
2986 __isl_give isl_local_space *isl_local_space_intersect(
2987 __isl_take isl_local_space *ls1,
2988 __isl_take isl_local_space *ls2);
2990 #include <isl/set.h>
2991 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2992 __isl_take isl_basic_set *bset1,
2993 __isl_take isl_basic_set *bset2);
2994 __isl_give isl_basic_set *isl_basic_set_intersect(
2995 __isl_take isl_basic_set *bset1,
2996 __isl_take isl_basic_set *bset2);
2997 __isl_give isl_set *isl_set_intersect_params(
2998 __isl_take isl_set *set,
2999 __isl_take isl_set *params);
3000 __isl_give isl_set *isl_set_intersect(
3001 __isl_take isl_set *set1,
3002 __isl_take isl_set *set2);
3004 #include <isl/map.h>
3005 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
3006 __isl_take isl_basic_map *bmap,
3007 __isl_take isl_basic_set *bset);
3008 __isl_give isl_basic_map *isl_basic_map_intersect_range(
3009 __isl_take isl_basic_map *bmap,
3010 __isl_take isl_basic_set *bset);
3011 __isl_give isl_basic_map *isl_basic_map_intersect(
3012 __isl_take isl_basic_map *bmap1,
3013 __isl_take isl_basic_map *bmap2);
3014 __isl_give isl_map *isl_map_intersect_params(
3015 __isl_take isl_map *map,
3016 __isl_take isl_set *params);
3017 __isl_give isl_map *isl_map_intersect_domain(
3018 __isl_take isl_map *map,
3019 __isl_take isl_set *set);
3020 __isl_give isl_map *isl_map_intersect_range(
3021 __isl_take isl_map *map,
3022 __isl_take isl_set *set);
3023 __isl_give isl_map *isl_map_intersect(
3024 __isl_take isl_map *map1,
3025 __isl_take isl_map *map2);
3027 #include <isl/union_set.h>
3028 __isl_give isl_union_set *isl_union_set_intersect_params(
3029 __isl_take isl_union_set *uset,
3030 __isl_take isl_set *set);
3031 __isl_give isl_union_set *isl_union_set_intersect(
3032 __isl_take isl_union_set *uset1,
3033 __isl_take isl_union_set *uset2);
3035 #include <isl/union_map.h>
3036 __isl_give isl_union_map *isl_union_map_intersect_params(
3037 __isl_take isl_union_map *umap,
3038 __isl_take isl_set *set);
3039 __isl_give isl_union_map *isl_union_map_intersect_domain(
3040 __isl_take isl_union_map *umap,
3041 __isl_take isl_union_set *uset);
3042 __isl_give isl_union_map *isl_union_map_intersect_range(
3043 __isl_take isl_union_map *umap,
3044 __isl_take isl_union_set *uset);
3045 __isl_give isl_union_map *isl_union_map_intersect(
3046 __isl_take isl_union_map *umap1,
3047 __isl_take isl_union_map *umap2);
3049 The second argument to the C<_params> functions needs to be
3050 a parametric (basic) set. For the other functions, a parametric set
3051 for either argument is only allowed if the other argument is
3052 a parametric set as well.
3056 __isl_give isl_set *isl_basic_set_union(
3057 __isl_take isl_basic_set *bset1,
3058 __isl_take isl_basic_set *bset2);
3059 __isl_give isl_map *isl_basic_map_union(
3060 __isl_take isl_basic_map *bmap1,
3061 __isl_take isl_basic_map *bmap2);
3062 __isl_give isl_set *isl_set_union(
3063 __isl_take isl_set *set1,
3064 __isl_take isl_set *set2);
3065 __isl_give isl_map *isl_map_union(
3066 __isl_take isl_map *map1,
3067 __isl_take isl_map *map2);
3068 __isl_give isl_union_set *isl_union_set_union(
3069 __isl_take isl_union_set *uset1,
3070 __isl_take isl_union_set *uset2);
3071 __isl_give isl_union_map *isl_union_map_union(
3072 __isl_take isl_union_map *umap1,
3073 __isl_take isl_union_map *umap2);
3075 =item * Set difference
3077 __isl_give isl_set *isl_set_subtract(
3078 __isl_take isl_set *set1,
3079 __isl_take isl_set *set2);
3080 __isl_give isl_map *isl_map_subtract(
3081 __isl_take isl_map *map1,
3082 __isl_take isl_map *map2);
3083 __isl_give isl_map *isl_map_subtract_domain(
3084 __isl_take isl_map *map,
3085 __isl_take isl_set *dom);
3086 __isl_give isl_map *isl_map_subtract_range(
3087 __isl_take isl_map *map,
3088 __isl_take isl_set *dom);
3089 __isl_give isl_union_set *isl_union_set_subtract(
3090 __isl_take isl_union_set *uset1,
3091 __isl_take isl_union_set *uset2);
3092 __isl_give isl_union_map *isl_union_map_subtract(
3093 __isl_take isl_union_map *umap1,
3094 __isl_take isl_union_map *umap2);
3095 __isl_give isl_union_map *isl_union_map_subtract_domain(
3096 __isl_take isl_union_map *umap,
3097 __isl_take isl_union_set *dom);
3098 __isl_give isl_union_map *isl_union_map_subtract_range(
3099 __isl_take isl_union_map *umap,
3100 __isl_take isl_union_set *dom);
3104 __isl_give isl_basic_set *isl_basic_set_apply(
3105 __isl_take isl_basic_set *bset,
3106 __isl_take isl_basic_map *bmap);
3107 __isl_give isl_set *isl_set_apply(
3108 __isl_take isl_set *set,
3109 __isl_take isl_map *map);
3110 __isl_give isl_union_set *isl_union_set_apply(
3111 __isl_take isl_union_set *uset,
3112 __isl_take isl_union_map *umap);
3113 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3114 __isl_take isl_basic_map *bmap1,
3115 __isl_take isl_basic_map *bmap2);
3116 __isl_give isl_basic_map *isl_basic_map_apply_range(
3117 __isl_take isl_basic_map *bmap1,
3118 __isl_take isl_basic_map *bmap2);
3119 __isl_give isl_map *isl_map_apply_domain(
3120 __isl_take isl_map *map1,
3121 __isl_take isl_map *map2);
3122 __isl_give isl_union_map *isl_union_map_apply_domain(
3123 __isl_take isl_union_map *umap1,
3124 __isl_take isl_union_map *umap2);
3125 __isl_give isl_map *isl_map_apply_range(
3126 __isl_take isl_map *map1,
3127 __isl_take isl_map *map2);
3128 __isl_give isl_union_map *isl_union_map_apply_range(
3129 __isl_take isl_union_map *umap1,
3130 __isl_take isl_union_map *umap2);
3134 #include <isl/set.h>
3135 __isl_give isl_basic_set *
3136 isl_basic_set_preimage_multi_aff(
3137 __isl_take isl_basic_set *bset,
3138 __isl_take isl_multi_aff *ma);
3139 __isl_give isl_set *isl_set_preimage_multi_aff(
3140 __isl_take isl_set *set,
3141 __isl_take isl_multi_aff *ma);
3142 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3143 __isl_take isl_set *set,
3144 __isl_take isl_pw_multi_aff *pma);
3145 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
3146 __isl_take isl_set *set,
3147 __isl_take isl_multi_pw_aff *mpa);
3149 #include <isl/union_set.h>
3150 __isl_give isl_union_set *
3151 isl_union_set_preimage_multi_aff(
3152 __isl_take isl_union_set *uset,
3153 __isl_take isl_multi_aff *ma);
3154 __isl_give isl_union_set *
3155 isl_union_set_preimage_pw_multi_aff(
3156 __isl_take isl_union_set *uset,
3157 __isl_take isl_pw_multi_aff *pma);
3158 __isl_give isl_union_set *
3159 isl_union_set_preimage_union_pw_multi_aff(
3160 __isl_take isl_union_set *uset,
3161 __isl_take isl_union_pw_multi_aff *upma);
3163 #include <isl/map.h>
3164 __isl_give isl_basic_map *
3165 isl_basic_map_preimage_domain_multi_aff(
3166 __isl_take isl_basic_map *bmap,
3167 __isl_take isl_multi_aff *ma);
3168 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3169 __isl_take isl_map *map,
3170 __isl_take isl_multi_aff *ma);
3171 __isl_give isl_map *isl_map_preimage_range_multi_aff(
3172 __isl_take isl_map *map,
3173 __isl_take isl_multi_aff *ma);
3174 __isl_give isl_map *
3175 isl_map_preimage_domain_pw_multi_aff(
3176 __isl_take isl_map *map,
3177 __isl_take isl_pw_multi_aff *pma);
3178 __isl_give isl_map *
3179 isl_map_preimage_range_pw_multi_aff(
3180 __isl_take isl_map *map,
3181 __isl_take isl_pw_multi_aff *pma);
3182 __isl_give isl_map *
3183 isl_map_preimage_domain_multi_pw_aff(
3184 __isl_take isl_map *map,
3185 __isl_take isl_multi_pw_aff *mpa);
3186 __isl_give isl_basic_map *
3187 isl_basic_map_preimage_range_multi_aff(
3188 __isl_take isl_basic_map *bmap,
3189 __isl_take isl_multi_aff *ma);
3191 #include <isl/union_map.h>
3192 __isl_give isl_union_map *
3193 isl_union_map_preimage_domain_multi_aff(
3194 __isl_take isl_union_map *umap,
3195 __isl_take isl_multi_aff *ma);
3196 __isl_give isl_union_map *
3197 isl_union_map_preimage_range_multi_aff(
3198 __isl_take isl_union_map *umap,
3199 __isl_take isl_multi_aff *ma);
3200 __isl_give isl_union_map *
3201 isl_union_map_preimage_domain_pw_multi_aff(
3202 __isl_take isl_union_map *umap,
3203 __isl_take isl_pw_multi_aff *pma);
3204 __isl_give isl_union_map *
3205 isl_union_map_preimage_range_pw_multi_aff(
3206 __isl_take isl_union_map *umap,
3207 __isl_take isl_pw_multi_aff *pma);
3208 __isl_give isl_union_map *
3209 isl_union_map_preimage_domain_union_pw_multi_aff(
3210 __isl_take isl_union_map *umap,
3211 __isl_take isl_union_pw_multi_aff *upma);
3212 __isl_give isl_union_map *
3213 isl_union_map_preimage_range_union_pw_multi_aff(
3214 __isl_take isl_union_map *umap,
3215 __isl_take isl_union_pw_multi_aff *upma);
3217 These functions compute the preimage of the given set or map domain/range under
3218 the given function. In other words, the expression is plugged
3219 into the set description or into the domain/range of the map.
3220 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3221 L</"Piecewise Multiple Quasi Affine Expressions">.
3223 =item * Cartesian Product
3225 #include <isl/space.h>
3226 __isl_give isl_space *isl_space_product(
3227 __isl_take isl_space *space1,
3228 __isl_take isl_space *space2);
3229 __isl_give isl_space *isl_space_domain_product(
3230 __isl_take isl_space *space1,
3231 __isl_take isl_space *space2);
3232 __isl_give isl_space *isl_space_range_product(
3233 __isl_take isl_space *space1,
3234 __isl_take isl_space *space2);
3237 C<isl_space_product>, C<isl_space_domain_product>
3238 and C<isl_space_range_product> take pairs or relation spaces and
3239 produce a single relations space, where either the domain, the range
3240 or both domain and range are wrapped spaces of relations between
3241 the domains and/or ranges of the input spaces.
3242 If the product is only constructed over the domain or the range
3243 then the ranges or the domains of the inputs should be the same.
3244 The function C<isl_space_product> also accepts a pair of set spaces,
3245 in which case it returns a wrapped space of a relation between the
3248 #include <isl/set.h>
3249 __isl_give isl_set *isl_set_product(
3250 __isl_take isl_set *set1,
3251 __isl_take isl_set *set2);
3253 #include <isl/map.h>
3254 __isl_give isl_basic_map *isl_basic_map_domain_product(
3255 __isl_take isl_basic_map *bmap1,
3256 __isl_take isl_basic_map *bmap2);
3257 __isl_give isl_basic_map *isl_basic_map_range_product(
3258 __isl_take isl_basic_map *bmap1,
3259 __isl_take isl_basic_map *bmap2);
3260 __isl_give isl_basic_map *isl_basic_map_product(
3261 __isl_take isl_basic_map *bmap1,
3262 __isl_take isl_basic_map *bmap2);
3263 __isl_give isl_map *isl_map_domain_product(
3264 __isl_take isl_map *map1,
3265 __isl_take isl_map *map2);
3266 __isl_give isl_map *isl_map_range_product(
3267 __isl_take isl_map *map1,
3268 __isl_take isl_map *map2);
3269 __isl_give isl_map *isl_map_product(
3270 __isl_take isl_map *map1,
3271 __isl_take isl_map *map2);
3273 #include <isl/union_set.h>
3274 __isl_give isl_union_set *isl_union_set_product(
3275 __isl_take isl_union_set *uset1,
3276 __isl_take isl_union_set *uset2);
3278 #include <isl/union_map.h>
3279 __isl_give isl_union_map *isl_union_map_domain_product(
3280 __isl_take isl_union_map *umap1,
3281 __isl_take isl_union_map *umap2);
3282 __isl_give isl_union_map *isl_union_map_range_product(
3283 __isl_take isl_union_map *umap1,
3284 __isl_take isl_union_map *umap2);
3285 __isl_give isl_union_map *isl_union_map_product(
3286 __isl_take isl_union_map *umap1,
3287 __isl_take isl_union_map *umap2);
3289 The above functions compute the cross product of the given
3290 sets or relations. The domains and ranges of the results
3291 are wrapped maps between domains and ranges of the inputs.
3292 To obtain a ``flat'' product, use the following functions
3295 __isl_give isl_basic_set *isl_basic_set_flat_product(
3296 __isl_take isl_basic_set *bset1,
3297 __isl_take isl_basic_set *bset2);
3298 __isl_give isl_set *isl_set_flat_product(
3299 __isl_take isl_set *set1,
3300 __isl_take isl_set *set2);
3301 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3302 __isl_take isl_basic_map *bmap1,
3303 __isl_take isl_basic_map *bmap2);
3304 __isl_give isl_map *isl_map_flat_domain_product(
3305 __isl_take isl_map *map1,
3306 __isl_take isl_map *map2);
3307 __isl_give isl_map *isl_map_flat_range_product(
3308 __isl_take isl_map *map1,
3309 __isl_take isl_map *map2);
3310 __isl_give isl_union_map *isl_union_map_flat_range_product(
3311 __isl_take isl_union_map *umap1,
3312 __isl_take isl_union_map *umap2);
3313 __isl_give isl_basic_map *isl_basic_map_flat_product(
3314 __isl_take isl_basic_map *bmap1,
3315 __isl_take isl_basic_map *bmap2);
3316 __isl_give isl_map *isl_map_flat_product(
3317 __isl_take isl_map *map1,
3318 __isl_take isl_map *map2);
3320 #include <isl/space.h>
3321 __isl_give isl_space *isl_space_domain_factor_domain(
3322 __isl_take isl_space *space);
3323 __isl_give isl_space *isl_space_range_factor_domain(
3324 __isl_take isl_space *space);
3325 __isl_give isl_space *isl_space_range_factor_range(
3326 __isl_take isl_space *space);
3328 The functions C<isl_space_range_factor_domain> and
3329 C<isl_space_range_factor_range> extract the two arguments from
3330 the result of a call to C<isl_space_range_product>.
3332 The arguments of a call to C<isl_map_range_product> can be extracted
3333 from the result using the following two functions.
3335 #include <isl/map.h>
3336 __isl_give isl_map *isl_map_range_factor_domain(
3337 __isl_take isl_map *map);
3338 __isl_give isl_map *isl_map_range_factor_range(
3339 __isl_take isl_map *map);
3341 =item * Simplification
3343 __isl_give isl_basic_set *isl_basic_set_gist(
3344 __isl_take isl_basic_set *bset,
3345 __isl_take isl_basic_set *context);
3346 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3347 __isl_take isl_set *context);
3348 __isl_give isl_set *isl_set_gist_params(
3349 __isl_take isl_set *set,
3350 __isl_take isl_set *context);
3351 __isl_give isl_union_set *isl_union_set_gist(
3352 __isl_take isl_union_set *uset,
3353 __isl_take isl_union_set *context);
3354 __isl_give isl_union_set *isl_union_set_gist_params(
3355 __isl_take isl_union_set *uset,
3356 __isl_take isl_set *set);
3357 __isl_give isl_basic_map *isl_basic_map_gist(
3358 __isl_take isl_basic_map *bmap,
3359 __isl_take isl_basic_map *context);
3360 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3361 __isl_take isl_map *context);
3362 __isl_give isl_map *isl_map_gist_params(
3363 __isl_take isl_map *map,
3364 __isl_take isl_set *context);
3365 __isl_give isl_map *isl_map_gist_domain(
3366 __isl_take isl_map *map,
3367 __isl_take isl_set *context);
3368 __isl_give isl_map *isl_map_gist_range(
3369 __isl_take isl_map *map,
3370 __isl_take isl_set *context);
3371 __isl_give isl_union_map *isl_union_map_gist(
3372 __isl_take isl_union_map *umap,
3373 __isl_take isl_union_map *context);
3374 __isl_give isl_union_map *isl_union_map_gist_params(
3375 __isl_take isl_union_map *umap,
3376 __isl_take isl_set *set);
3377 __isl_give isl_union_map *isl_union_map_gist_domain(
3378 __isl_take isl_union_map *umap,
3379 __isl_take isl_union_set *uset);
3380 __isl_give isl_union_map *isl_union_map_gist_range(
3381 __isl_take isl_union_map *umap,
3382 __isl_take isl_union_set *uset);
3384 The gist operation returns a set or relation that has the
3385 same intersection with the context as the input set or relation.
3386 Any implicit equality in the intersection is made explicit in the result,
3387 while all inequalities that are redundant with respect to the intersection
3389 In case of union sets and relations, the gist operation is performed
3394 =head3 Lexicographic Optimization
3396 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3397 the following functions
3398 compute a set that contains the lexicographic minimum or maximum
3399 of the elements in C<set> (or C<bset>) for those values of the parameters
3400 that satisfy C<dom>.
3401 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3402 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3404 In other words, the union of the parameter values
3405 for which the result is non-empty and of C<*empty>
3408 __isl_give isl_set *isl_basic_set_partial_lexmin(
3409 __isl_take isl_basic_set *bset,
3410 __isl_take isl_basic_set *dom,
3411 __isl_give isl_set **empty);
3412 __isl_give isl_set *isl_basic_set_partial_lexmax(
3413 __isl_take isl_basic_set *bset,
3414 __isl_take isl_basic_set *dom,
3415 __isl_give isl_set **empty);
3416 __isl_give isl_set *isl_set_partial_lexmin(
3417 __isl_take isl_set *set, __isl_take isl_set *dom,
3418 __isl_give isl_set **empty);
3419 __isl_give isl_set *isl_set_partial_lexmax(
3420 __isl_take isl_set *set, __isl_take isl_set *dom,
3421 __isl_give isl_set **empty);
3423 Given a (basic) set C<set> (or C<bset>), the following functions simply
3424 return a set containing the lexicographic minimum or maximum
3425 of the elements in C<set> (or C<bset>).
3426 In case of union sets, the optimum is computed per space.
3428 __isl_give isl_set *isl_basic_set_lexmin(
3429 __isl_take isl_basic_set *bset);
3430 __isl_give isl_set *isl_basic_set_lexmax(
3431 __isl_take isl_basic_set *bset);
3432 __isl_give isl_set *isl_set_lexmin(
3433 __isl_take isl_set *set);
3434 __isl_give isl_set *isl_set_lexmax(
3435 __isl_take isl_set *set);
3436 __isl_give isl_union_set *isl_union_set_lexmin(
3437 __isl_take isl_union_set *uset);
3438 __isl_give isl_union_set *isl_union_set_lexmax(
3439 __isl_take isl_union_set *uset);
3441 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3442 the following functions
3443 compute a relation that maps each element of C<dom>
3444 to the single lexicographic minimum or maximum
3445 of the elements that are associated to that same
3446 element in C<map> (or C<bmap>).
3447 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3448 that contains the elements in C<dom> that do not map
3449 to any elements in C<map> (or C<bmap>).
3450 In other words, the union of the domain of the result and of C<*empty>
3453 __isl_give isl_map *isl_basic_map_partial_lexmax(
3454 __isl_take isl_basic_map *bmap,
3455 __isl_take isl_basic_set *dom,
3456 __isl_give isl_set **empty);
3457 __isl_give isl_map *isl_basic_map_partial_lexmin(
3458 __isl_take isl_basic_map *bmap,
3459 __isl_take isl_basic_set *dom,
3460 __isl_give isl_set **empty);
3461 __isl_give isl_map *isl_map_partial_lexmax(
3462 __isl_take isl_map *map, __isl_take isl_set *dom,
3463 __isl_give isl_set **empty);
3464 __isl_give isl_map *isl_map_partial_lexmin(
3465 __isl_take isl_map *map, __isl_take isl_set *dom,
3466 __isl_give isl_set **empty);
3468 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3469 return a map mapping each element in the domain of
3470 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3471 of all elements associated to that element.
3472 In case of union relations, the optimum is computed per space.
3474 __isl_give isl_map *isl_basic_map_lexmin(
3475 __isl_take isl_basic_map *bmap);
3476 __isl_give isl_map *isl_basic_map_lexmax(
3477 __isl_take isl_basic_map *bmap);
3478 __isl_give isl_map *isl_map_lexmin(
3479 __isl_take isl_map *map);
3480 __isl_give isl_map *isl_map_lexmax(
3481 __isl_take isl_map *map);
3482 __isl_give isl_union_map *isl_union_map_lexmin(
3483 __isl_take isl_union_map *umap);
3484 __isl_give isl_union_map *isl_union_map_lexmax(
3485 __isl_take isl_union_map *umap);
3487 The following functions return their result in the form of
3488 a piecewise multi-affine expression
3489 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3490 but are otherwise equivalent to the corresponding functions
3491 returning a basic set or relation.
3493 __isl_give isl_pw_multi_aff *
3494 isl_basic_map_lexmin_pw_multi_aff(
3495 __isl_take isl_basic_map *bmap);
3496 __isl_give isl_pw_multi_aff *
3497 isl_basic_set_partial_lexmin_pw_multi_aff(
3498 __isl_take isl_basic_set *bset,
3499 __isl_take isl_basic_set *dom,
3500 __isl_give isl_set **empty);
3501 __isl_give isl_pw_multi_aff *
3502 isl_basic_set_partial_lexmax_pw_multi_aff(
3503 __isl_take isl_basic_set *bset,
3504 __isl_take isl_basic_set *dom,
3505 __isl_give isl_set **empty);
3506 __isl_give isl_pw_multi_aff *
3507 isl_basic_map_partial_lexmin_pw_multi_aff(
3508 __isl_take isl_basic_map *bmap,
3509 __isl_take isl_basic_set *dom,
3510 __isl_give isl_set **empty);
3511 __isl_give isl_pw_multi_aff *
3512 isl_basic_map_partial_lexmax_pw_multi_aff(
3513 __isl_take isl_basic_map *bmap,
3514 __isl_take isl_basic_set *dom,
3515 __isl_give isl_set **empty);
3516 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3517 __isl_take isl_set *set);
3518 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3519 __isl_take isl_set *set);
3520 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3521 __isl_take isl_map *map);
3522 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3523 __isl_take isl_map *map);
3527 Lists are defined over several element types, including
3528 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3529 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3530 Here we take lists of C<isl_set>s as an example.
3531 Lists can be created, copied, modified and freed using the following functions.
3533 #include <isl/list.h>
3534 __isl_give isl_set_list *isl_set_list_from_set(
3535 __isl_take isl_set *el);
3536 __isl_give isl_set_list *isl_set_list_alloc(
3537 isl_ctx *ctx, int n);
3538 __isl_give isl_set_list *isl_set_list_copy(
3539 __isl_keep isl_set_list *list);
3540 __isl_give isl_set_list *isl_set_list_insert(
3541 __isl_take isl_set_list *list, unsigned pos,
3542 __isl_take isl_set *el);
3543 __isl_give isl_set_list *isl_set_list_add(
3544 __isl_take isl_set_list *list,
3545 __isl_take isl_set *el);
3546 __isl_give isl_set_list *isl_set_list_drop(
3547 __isl_take isl_set_list *list,
3548 unsigned first, unsigned n);
3549 __isl_give isl_set_list *isl_set_list_set_set(
3550 __isl_take isl_set_list *list, int index,
3551 __isl_take isl_set *set);
3552 __isl_give isl_set_list *isl_set_list_concat(
3553 __isl_take isl_set_list *list1,
3554 __isl_take isl_set_list *list2);
3555 __isl_give isl_set_list *isl_set_list_sort(
3556 __isl_take isl_set_list *list,
3557 int (*cmp)(__isl_keep isl_set *a,
3558 __isl_keep isl_set *b, void *user),
3560 __isl_null isl_set_list *isl_set_list_free(
3561 __isl_take isl_set_list *list);
3563 C<isl_set_list_alloc> creates an empty list with a capacity for
3564 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3567 Lists can be inspected using the following functions.
3569 #include <isl/list.h>
3570 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3571 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3572 __isl_give isl_set *isl_set_list_get_set(
3573 __isl_keep isl_set_list *list, int index);
3574 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3575 int (*fn)(__isl_take isl_set *el, void *user),
3577 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3578 int (*follows)(__isl_keep isl_set *a,
3579 __isl_keep isl_set *b, void *user),
3581 int (*fn)(__isl_take isl_set *el, void *user),
3584 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3585 strongly connected components of the graph with as vertices the elements
3586 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3587 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3588 should return C<-1> on error.
3590 Lists can be printed using
3592 #include <isl/list.h>
3593 __isl_give isl_printer *isl_printer_print_set_list(
3594 __isl_take isl_printer *p,
3595 __isl_keep isl_set_list *list);
3597 =head2 Associative arrays
3599 Associative arrays map isl objects of a specific type to isl objects
3600 of some (other) specific type. They are defined for several pairs
3601 of types, including (C<isl_map>, C<isl_basic_set>),
3602 (C<isl_id>, C<isl_ast_expr>) and.
3603 (C<isl_id>, C<isl_pw_aff>).
3604 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3607 Associative arrays can be created, copied and freed using
3608 the following functions.
3610 #include <isl/id_to_ast_expr.h>
3611 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3612 isl_ctx *ctx, int min_size);
3613 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3614 __isl_keep id_to_ast_expr *id2expr);
3615 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
3616 __isl_take id_to_ast_expr *id2expr);
3618 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3619 to specify the expected size of the associative array.
3620 The associative array will be grown automatically as needed.
3622 Associative arrays can be inspected using the following functions.
3624 #include <isl/id_to_ast_expr.h>
3625 isl_ctx *isl_id_to_ast_expr_get_ctx(
3626 __isl_keep id_to_ast_expr *id2expr);
3627 int isl_id_to_ast_expr_has(
3628 __isl_keep id_to_ast_expr *id2expr,
3629 __isl_keep isl_id *key);
3630 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3631 __isl_keep id_to_ast_expr *id2expr,
3632 __isl_take isl_id *key);
3633 int isl_id_to_ast_expr_foreach(
3634 __isl_keep id_to_ast_expr *id2expr,
3635 int (*fn)(__isl_take isl_id *key,
3636 __isl_take isl_ast_expr *val, void *user),
3639 They can be modified using the following function.
3641 #include <isl/id_to_ast_expr.h>
3642 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3643 __isl_take id_to_ast_expr *id2expr,
3644 __isl_take isl_id *key,
3645 __isl_take isl_ast_expr *val);
3646 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
3647 __isl_take id_to_ast_expr *id2expr,
3648 __isl_take isl_id *key);
3650 Associative arrays can be printed using the following function.
3652 #include <isl/id_to_ast_expr.h>
3653 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3654 __isl_take isl_printer *p,
3655 __isl_keep id_to_ast_expr *id2expr);
3657 =head2 Multiple Values
3659 An C<isl_multi_val> object represents a sequence of zero or more values,
3660 living in a set space.
3662 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3663 using the following function
3665 #include <isl/val.h>
3666 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3667 __isl_take isl_space *space,
3668 __isl_take isl_val_list *list);
3670 The zero multiple value (with value zero for each set dimension)
3671 can be created using the following function.
3673 #include <isl/val.h>
3674 __isl_give isl_multi_val *isl_multi_val_zero(
3675 __isl_take isl_space *space);
3677 Multiple values can be copied and freed using
3679 #include <isl/val.h>
3680 __isl_give isl_multi_val *isl_multi_val_copy(
3681 __isl_keep isl_multi_val *mv);
3682 __isl_null isl_multi_val *isl_multi_val_free(
3683 __isl_take isl_multi_val *mv);
3685 They can be inspected using
3687 #include <isl/val.h>
3688 isl_ctx *isl_multi_val_get_ctx(
3689 __isl_keep isl_multi_val *mv);
3690 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3691 enum isl_dim_type type);
3692 __isl_give isl_val *isl_multi_val_get_val(
3693 __isl_keep isl_multi_val *mv, int pos);
3694 int isl_multi_val_find_dim_by_id(
3695 __isl_keep isl_multi_val *mv,
3696 enum isl_dim_type type, __isl_keep isl_id *id);
3697 __isl_give isl_id *isl_multi_val_get_dim_id(
3698 __isl_keep isl_multi_val *mv,
3699 enum isl_dim_type type, unsigned pos);
3700 const char *isl_multi_val_get_tuple_name(
3701 __isl_keep isl_multi_val *mv,
3702 enum isl_dim_type type);
3703 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3704 enum isl_dim_type type);
3705 __isl_give isl_id *isl_multi_val_get_tuple_id(
3706 __isl_keep isl_multi_val *mv,
3707 enum isl_dim_type type);
3708 int isl_multi_val_range_is_wrapping(
3709 __isl_keep isl_multi_val *mv);
3711 They can be modified using
3713 #include <isl/val.h>
3714 __isl_give isl_multi_val *isl_multi_val_set_val(
3715 __isl_take isl_multi_val *mv, int pos,
3716 __isl_take isl_val *val);
3717 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3718 __isl_take isl_multi_val *mv,
3719 enum isl_dim_type type, unsigned pos, const char *s);
3720 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3721 __isl_take isl_multi_val *mv,
3722 enum isl_dim_type type, unsigned pos,
3723 __isl_take isl_id *id);
3724 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3725 __isl_take isl_multi_val *mv,
3726 enum isl_dim_type type, const char *s);
3727 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3728 __isl_take isl_multi_val *mv,
3729 enum isl_dim_type type, __isl_take isl_id *id);
3730 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3731 __isl_take isl_multi_val *mv,
3732 enum isl_dim_type type);
3733 __isl_give isl_multi_val *isl_multi_val_reset_user(
3734 __isl_take isl_multi_val *mv);
3736 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3737 __isl_take isl_multi_val *mv,
3738 enum isl_dim_type type, unsigned first, unsigned n);
3739 __isl_give isl_multi_val *isl_multi_val_add_dims(
3740 __isl_take isl_multi_val *mv,
3741 enum isl_dim_type type, unsigned n);
3742 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3743 __isl_take isl_multi_val *mv,
3744 enum isl_dim_type type, unsigned first, unsigned n);
3748 #include <isl/val.h>
3749 __isl_give isl_multi_val *isl_multi_val_align_params(
3750 __isl_take isl_multi_val *mv,
3751 __isl_take isl_space *model);
3752 __isl_give isl_multi_val *isl_multi_val_from_range(
3753 __isl_take isl_multi_val *mv);
3754 __isl_give isl_multi_val *isl_multi_val_range_splice(
3755 __isl_take isl_multi_val *mv1, unsigned pos,
3756 __isl_take isl_multi_val *mv2);
3757 __isl_give isl_multi_val *isl_multi_val_range_product(
3758 __isl_take isl_multi_val *mv1,
3759 __isl_take isl_multi_val *mv2);
3760 __isl_give isl_multi_val *
3761 isl_multi_val_range_factor_domain(
3762 __isl_take isl_multi_val *mv);
3763 __isl_give isl_multi_val *
3764 isl_multi_val_range_factor_range(
3765 __isl_take isl_multi_val *mv);
3766 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3767 __isl_take isl_multi_val *mv1,
3768 __isl_take isl_multi_aff *mv2);
3769 __isl_give isl_multi_val *isl_multi_val_product(
3770 __isl_take isl_multi_val *mv1,
3771 __isl_take isl_multi_val *mv2);
3772 __isl_give isl_multi_val *isl_multi_val_add_val(
3773 __isl_take isl_multi_val *mv,
3774 __isl_take isl_val *v);
3775 __isl_give isl_multi_val *isl_multi_val_mod_val(
3776 __isl_take isl_multi_val *mv,
3777 __isl_take isl_val *v);
3778 __isl_give isl_multi_val *isl_multi_val_scale_val(
3779 __isl_take isl_multi_val *mv,
3780 __isl_take isl_val *v);
3781 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3782 __isl_take isl_multi_val *mv1,
3783 __isl_take isl_multi_val *mv2);
3784 __isl_give isl_multi_val *
3785 isl_multi_val_scale_down_multi_val(
3786 __isl_take isl_multi_val *mv1,
3787 __isl_take isl_multi_val *mv2);
3789 A multiple value can be printed using
3791 __isl_give isl_printer *isl_printer_print_multi_val(
3792 __isl_take isl_printer *p,
3793 __isl_keep isl_multi_val *mv);
3797 Vectors can be created, copied and freed using the following functions.
3799 #include <isl/vec.h>
3800 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3802 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3803 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
3805 Note that the elements of a newly created vector may have arbitrary values.
3806 The elements can be changed and inspected using the following functions.
3808 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3809 int isl_vec_size(__isl_keep isl_vec *vec);
3810 __isl_give isl_val *isl_vec_get_element_val(
3811 __isl_keep isl_vec *vec, int pos);
3812 __isl_give isl_vec *isl_vec_set_element_si(
3813 __isl_take isl_vec *vec, int pos, int v);
3814 __isl_give isl_vec *isl_vec_set_element_val(
3815 __isl_take isl_vec *vec, int pos,
3816 __isl_take isl_val *v);
3817 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3819 __isl_give isl_vec *isl_vec_set_val(
3820 __isl_take isl_vec *vec, __isl_take isl_val *v);
3821 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3822 __isl_keep isl_vec *vec2, int pos);
3824 C<isl_vec_get_element> will return a negative value if anything went wrong.
3825 In that case, the value of C<*v> is undefined.
3827 The following function can be used to concatenate two vectors.
3829 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3830 __isl_take isl_vec *vec2);
3834 Matrices can be created, copied and freed using the following functions.
3836 #include <isl/mat.h>
3837 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3838 unsigned n_row, unsigned n_col);
3839 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3840 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
3842 Note that the elements of a newly created matrix may have arbitrary values.
3843 The elements can be changed and inspected using the following functions.
3845 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3846 int isl_mat_rows(__isl_keep isl_mat *mat);
3847 int isl_mat_cols(__isl_keep isl_mat *mat);
3848 __isl_give isl_val *isl_mat_get_element_val(
3849 __isl_keep isl_mat *mat, int row, int col);
3850 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3851 int row, int col, int v);
3852 __isl_give isl_mat *isl_mat_set_element_val(
3853 __isl_take isl_mat *mat, int row, int col,
3854 __isl_take isl_val *v);
3856 C<isl_mat_get_element> will return a negative value if anything went wrong.
3857 In that case, the value of C<*v> is undefined.
3859 The following function can be used to compute the (right) inverse
3860 of a matrix, i.e., a matrix such that the product of the original
3861 and the inverse (in that order) is a multiple of the identity matrix.
3862 The input matrix is assumed to be of full row-rank.
3864 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3866 The following function can be used to compute the (right) kernel
3867 (or null space) of a matrix, i.e., a matrix such that the product of
3868 the original and the kernel (in that order) is the zero matrix.
3870 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3872 =head2 Piecewise Quasi Affine Expressions
3874 The zero quasi affine expression or the quasi affine expression
3875 that is equal to a given value or
3876 a specified dimension on a given domain can be created using
3878 __isl_give isl_aff *isl_aff_zero_on_domain(
3879 __isl_take isl_local_space *ls);
3880 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3881 __isl_take isl_local_space *ls);
3882 __isl_give isl_aff *isl_aff_val_on_domain(
3883 __isl_take isl_local_space *ls,
3884 __isl_take isl_val *val);
3885 __isl_give isl_aff *isl_aff_var_on_domain(
3886 __isl_take isl_local_space *ls,
3887 enum isl_dim_type type, unsigned pos);
3888 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3889 __isl_take isl_local_space *ls,
3890 enum isl_dim_type type, unsigned pos);
3891 __isl_give isl_aff *isl_aff_nan_on_domain(
3892 __isl_take isl_local_space *ls);
3893 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3894 __isl_take isl_local_space *ls);
3896 Note that the space in which the resulting objects live is a map space
3897 with the given space as domain and a one-dimensional range.
3899 An empty piecewise quasi affine expression (one with no cells)
3900 or a piecewise quasi affine expression with a single cell can
3901 be created using the following functions.
3903 #include <isl/aff.h>
3904 __isl_give isl_pw_aff *isl_pw_aff_empty(
3905 __isl_take isl_space *space);
3906 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3907 __isl_take isl_set *set, __isl_take isl_aff *aff);
3908 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3909 __isl_take isl_aff *aff);
3911 A piecewise quasi affine expression that is equal to 1 on a set
3912 and 0 outside the set can be created using the following function.
3914 #include <isl/aff.h>
3915 __isl_give isl_pw_aff *isl_set_indicator_function(
3916 __isl_take isl_set *set);
3918 Quasi affine expressions can be copied and freed using
3920 #include <isl/aff.h>
3921 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3922 __isl_null isl_aff *isl_aff_free(__isl_take isl_aff *aff);
3924 __isl_give isl_pw_aff *isl_pw_aff_copy(
3925 __isl_keep isl_pw_aff *pwaff);
3926 __isl_null isl_pw_aff *isl_pw_aff_free(
3927 __isl_take isl_pw_aff *pwaff);
3929 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3930 using the following function. The constraint is required to have
3931 a non-zero coefficient for the specified dimension.
3933 #include <isl/constraint.h>
3934 __isl_give isl_aff *isl_constraint_get_bound(
3935 __isl_keep isl_constraint *constraint,
3936 enum isl_dim_type type, int pos);
3938 The entire affine expression of the constraint can also be extracted
3939 using the following function.
3941 #include <isl/constraint.h>
3942 __isl_give isl_aff *isl_constraint_get_aff(
3943 __isl_keep isl_constraint *constraint);
3945 Conversely, an equality constraint equating
3946 the affine expression to zero or an inequality constraint enforcing
3947 the affine expression to be non-negative, can be constructed using
3949 __isl_give isl_constraint *isl_equality_from_aff(
3950 __isl_take isl_aff *aff);
3951 __isl_give isl_constraint *isl_inequality_from_aff(
3952 __isl_take isl_aff *aff);
3954 The expression can be inspected using
3956 #include <isl/aff.h>
3957 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3958 int isl_aff_dim(__isl_keep isl_aff *aff,
3959 enum isl_dim_type type);
3960 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3961 __isl_keep isl_aff *aff);
3962 __isl_give isl_local_space *isl_aff_get_local_space(
3963 __isl_keep isl_aff *aff);
3964 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3965 enum isl_dim_type type, unsigned pos);
3966 const char *isl_pw_aff_get_dim_name(
3967 __isl_keep isl_pw_aff *pa,
3968 enum isl_dim_type type, unsigned pos);
3969 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3970 enum isl_dim_type type, unsigned pos);
3971 __isl_give isl_id *isl_pw_aff_get_dim_id(
3972 __isl_keep isl_pw_aff *pa,
3973 enum isl_dim_type type, unsigned pos);
3974 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
3975 enum isl_dim_type type);
3976 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3977 __isl_keep isl_pw_aff *pa,
3978 enum isl_dim_type type);
3979 __isl_give isl_val *isl_aff_get_constant_val(
3980 __isl_keep isl_aff *aff);
3981 __isl_give isl_val *isl_aff_get_coefficient_val(
3982 __isl_keep isl_aff *aff,
3983 enum isl_dim_type type, int pos);
3984 __isl_give isl_val *isl_aff_get_denominator_val(
3985 __isl_keep isl_aff *aff);
3986 __isl_give isl_aff *isl_aff_get_div(
3987 __isl_keep isl_aff *aff, int pos);
3989 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3990 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3991 int (*fn)(__isl_take isl_set *set,
3992 __isl_take isl_aff *aff,
3993 void *user), void *user);
3995 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3996 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3998 int isl_aff_is_nan(__isl_keep isl_aff *aff);
3999 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
4001 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
4002 enum isl_dim_type type, unsigned first, unsigned n);
4003 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
4004 enum isl_dim_type type, unsigned first, unsigned n);
4006 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
4007 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
4008 enum isl_dim_type type);
4009 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
4011 It can be modified using
4013 #include <isl/aff.h>
4014 __isl_give isl_aff *isl_aff_set_tuple_id(
4015 __isl_take isl_aff *aff,
4016 enum isl_dim_type type, __isl_take isl_id *id);
4017 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
4018 __isl_take isl_pw_aff *pwaff,
4019 enum isl_dim_type type, __isl_take isl_id *id);
4020 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
4021 __isl_take isl_pw_aff *pa,
4022 enum isl_dim_type type);
4023 __isl_give isl_aff *isl_aff_set_dim_name(
4024 __isl_take isl_aff *aff, enum isl_dim_type type,
4025 unsigned pos, const char *s);
4026 __isl_give isl_aff *isl_aff_set_dim_id(
4027 __isl_take isl_aff *aff, enum isl_dim_type type,
4028 unsigned pos, __isl_take isl_id *id);
4029 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
4030 __isl_take isl_pw_aff *pma,
4031 enum isl_dim_type type, unsigned pos,
4032 __isl_take isl_id *id);
4033 __isl_give isl_aff *isl_aff_set_constant_si(
4034 __isl_take isl_aff *aff, int v);
4035 __isl_give isl_aff *isl_aff_set_constant_val(
4036 __isl_take isl_aff *aff, __isl_take isl_val *v);
4037 __isl_give isl_aff *isl_aff_set_coefficient_si(
4038 __isl_take isl_aff *aff,
4039 enum isl_dim_type type, int pos, int v);
4040 __isl_give isl_aff *isl_aff_set_coefficient_val(
4041 __isl_take isl_aff *aff,
4042 enum isl_dim_type type, int pos,
4043 __isl_take isl_val *v);
4045 __isl_give isl_aff *isl_aff_add_constant_si(
4046 __isl_take isl_aff *aff, int v);
4047 __isl_give isl_aff *isl_aff_add_constant_val(
4048 __isl_take isl_aff *aff, __isl_take isl_val *v);
4049 __isl_give isl_aff *isl_aff_add_constant_num_si(
4050 __isl_take isl_aff *aff, int v);
4051 __isl_give isl_aff *isl_aff_add_coefficient_si(
4052 __isl_take isl_aff *aff,
4053 enum isl_dim_type type, int pos, int v);
4054 __isl_give isl_aff *isl_aff_add_coefficient_val(
4055 __isl_take isl_aff *aff,
4056 enum isl_dim_type type, int pos,
4057 __isl_take isl_val *v);
4059 __isl_give isl_aff *isl_aff_insert_dims(
4060 __isl_take isl_aff *aff,
4061 enum isl_dim_type type, unsigned first, unsigned n);
4062 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
4063 __isl_take isl_pw_aff *pwaff,
4064 enum isl_dim_type type, unsigned first, unsigned n);
4065 __isl_give isl_aff *isl_aff_add_dims(
4066 __isl_take isl_aff *aff,
4067 enum isl_dim_type type, unsigned n);
4068 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
4069 __isl_take isl_pw_aff *pwaff,
4070 enum isl_dim_type type, unsigned n);
4071 __isl_give isl_aff *isl_aff_drop_dims(
4072 __isl_take isl_aff *aff,
4073 enum isl_dim_type type, unsigned first, unsigned n);
4074 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
4075 __isl_take isl_pw_aff *pwaff,
4076 enum isl_dim_type type, unsigned first, unsigned n);
4077 __isl_give isl_aff *isl_aff_move_dims(
4078 __isl_take isl_aff *aff,
4079 enum isl_dim_type dst_type, unsigned dst_pos,
4080 enum isl_dim_type src_type, unsigned src_pos,
4082 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
4083 __isl_take isl_pw_aff *pa,
4084 enum isl_dim_type dst_type, unsigned dst_pos,
4085 enum isl_dim_type src_type, unsigned src_pos,
4088 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
4089 set the I<numerator> of the constant or coefficient, while
4090 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
4091 the constant or coefficient as a whole.
4092 The C<add_constant> and C<add_coefficient> functions add an integer
4093 or rational value to
4094 the possibly rational constant or coefficient.
4095 The C<add_constant_num> functions add an integer value to
4098 To check whether an affine expressions is obviously zero
4099 or (obviously) equal to some other affine expression, use
4101 #include <isl/aff.h>
4102 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
4103 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
4104 __isl_keep isl_aff *aff2);
4105 int isl_pw_aff_plain_is_equal(
4106 __isl_keep isl_pw_aff *pwaff1,
4107 __isl_keep isl_pw_aff *pwaff2);
4108 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
4109 __isl_keep isl_pw_aff *pa2);
4110 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4111 __isl_keep isl_pw_aff *pa2);
4113 The function C<isl_pw_aff_plain_cmp> can be used to sort
4114 C<isl_pw_aff>s. The order is not strictly defined.
4115 The current order sorts expressions that only involve
4116 earlier dimensions before those that involve later dimensions.
4120 #include <isl/aff.h>
4121 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
4122 __isl_take isl_aff *aff2);
4123 __isl_give isl_pw_aff *isl_pw_aff_add(
4124 __isl_take isl_pw_aff *pwaff1,
4125 __isl_take isl_pw_aff *pwaff2);
4126 __isl_give isl_pw_aff *isl_pw_aff_min(
4127 __isl_take isl_pw_aff *pwaff1,
4128 __isl_take isl_pw_aff *pwaff2);
4129 __isl_give isl_pw_aff *isl_pw_aff_max(
4130 __isl_take isl_pw_aff *pwaff1,
4131 __isl_take isl_pw_aff *pwaff2);
4132 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
4133 __isl_take isl_aff *aff2);
4134 __isl_give isl_pw_aff *isl_pw_aff_sub(
4135 __isl_take isl_pw_aff *pwaff1,
4136 __isl_take isl_pw_aff *pwaff2);
4137 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
4138 __isl_give isl_pw_aff *isl_pw_aff_neg(
4139 __isl_take isl_pw_aff *pwaff);
4140 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
4141 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4142 __isl_take isl_pw_aff *pwaff);
4143 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
4144 __isl_give isl_pw_aff *isl_pw_aff_floor(
4145 __isl_take isl_pw_aff *pwaff);
4146 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
4147 __isl_take isl_val *mod);
4148 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
4149 __isl_take isl_pw_aff *pa,
4150 __isl_take isl_val *mod);
4151 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
4152 __isl_take isl_val *v);
4153 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
4154 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
4155 __isl_give isl_aff *isl_aff_scale_down_ui(
4156 __isl_take isl_aff *aff, unsigned f);
4157 __isl_give isl_aff *isl_aff_scale_down_val(
4158 __isl_take isl_aff *aff, __isl_take isl_val *v);
4159 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
4160 __isl_take isl_pw_aff *pa,
4161 __isl_take isl_val *f);
4163 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4164 __isl_take isl_pw_aff_list *list);
4165 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4166 __isl_take isl_pw_aff_list *list);
4168 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4169 __isl_take isl_pw_aff *pwqp);
4171 __isl_give isl_aff *isl_aff_align_params(
4172 __isl_take isl_aff *aff,
4173 __isl_take isl_space *model);
4174 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4175 __isl_take isl_pw_aff *pwaff,
4176 __isl_take isl_space *model);
4178 __isl_give isl_aff *isl_aff_project_domain_on_params(
4179 __isl_take isl_aff *aff);
4180 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4181 __isl_take isl_pw_aff *pwa);
4183 __isl_give isl_aff *isl_aff_gist_params(
4184 __isl_take isl_aff *aff,
4185 __isl_take isl_set *context);
4186 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
4187 __isl_take isl_set *context);
4188 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
4189 __isl_take isl_pw_aff *pwaff,
4190 __isl_take isl_set *context);
4191 __isl_give isl_pw_aff *isl_pw_aff_gist(
4192 __isl_take isl_pw_aff *pwaff,
4193 __isl_take isl_set *context);
4195 __isl_give isl_set *isl_pw_aff_domain(
4196 __isl_take isl_pw_aff *pwaff);
4197 __isl_give isl_set *isl_pw_aff_params(
4198 __isl_take isl_pw_aff *pwa);
4199 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4200 __isl_take isl_pw_aff *pa,
4201 __isl_take isl_set *set);
4202 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4203 __isl_take isl_pw_aff *pa,
4204 __isl_take isl_set *set);
4206 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
4207 __isl_take isl_aff *aff2);
4208 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
4209 __isl_take isl_aff *aff2);
4210 __isl_give isl_pw_aff *isl_pw_aff_mul(
4211 __isl_take isl_pw_aff *pwaff1,
4212 __isl_take isl_pw_aff *pwaff2);
4213 __isl_give isl_pw_aff *isl_pw_aff_div(
4214 __isl_take isl_pw_aff *pa1,
4215 __isl_take isl_pw_aff *pa2);
4216 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
4217 __isl_take isl_pw_aff *pa1,
4218 __isl_take isl_pw_aff *pa2);
4219 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
4220 __isl_take isl_pw_aff *pa1,
4221 __isl_take isl_pw_aff *pa2);
4223 When multiplying two affine expressions, at least one of the two needs
4224 to be a constant. Similarly, when dividing an affine expression by another,
4225 the second expression needs to be a constant.
4226 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
4227 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
4230 #include <isl/aff.h>
4231 __isl_give isl_aff *isl_aff_pullback_aff(
4232 __isl_take isl_aff *aff1,
4233 __isl_take isl_aff *aff2);
4234 __isl_give isl_aff *isl_aff_pullback_multi_aff(
4235 __isl_take isl_aff *aff,
4236 __isl_take isl_multi_aff *ma);
4237 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
4238 __isl_take isl_pw_aff *pa,
4239 __isl_take isl_multi_aff *ma);
4240 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
4241 __isl_take isl_pw_aff *pa,
4242 __isl_take isl_pw_multi_aff *pma);
4243 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
4244 __isl_take isl_pw_aff *pa,
4245 __isl_take isl_multi_pw_aff *mpa);
4247 These functions precompose the input expression by the given
4248 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
4249 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
4250 into the (piecewise) affine expression.
4251 Objects of type C<isl_multi_aff> are described in
4252 L</"Piecewise Multiple Quasi Affine Expressions">.
4254 #include <isl/aff.h>
4255 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4256 __isl_take isl_aff *aff);
4257 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4258 __isl_take isl_aff *aff);
4259 __isl_give isl_basic_set *isl_aff_le_basic_set(
4260 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4261 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4262 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4263 __isl_give isl_set *isl_pw_aff_eq_set(
4264 __isl_take isl_pw_aff *pwaff1,
4265 __isl_take isl_pw_aff *pwaff2);
4266 __isl_give isl_set *isl_pw_aff_ne_set(
4267 __isl_take isl_pw_aff *pwaff1,
4268 __isl_take isl_pw_aff *pwaff2);
4269 __isl_give isl_set *isl_pw_aff_le_set(
4270 __isl_take isl_pw_aff *pwaff1,
4271 __isl_take isl_pw_aff *pwaff2);
4272 __isl_give isl_set *isl_pw_aff_lt_set(
4273 __isl_take isl_pw_aff *pwaff1,
4274 __isl_take isl_pw_aff *pwaff2);
4275 __isl_give isl_set *isl_pw_aff_ge_set(
4276 __isl_take isl_pw_aff *pwaff1,
4277 __isl_take isl_pw_aff *pwaff2);
4278 __isl_give isl_set *isl_pw_aff_gt_set(
4279 __isl_take isl_pw_aff *pwaff1,
4280 __isl_take isl_pw_aff *pwaff2);
4282 __isl_give isl_set *isl_pw_aff_list_eq_set(
4283 __isl_take isl_pw_aff_list *list1,
4284 __isl_take isl_pw_aff_list *list2);
4285 __isl_give isl_set *isl_pw_aff_list_ne_set(
4286 __isl_take isl_pw_aff_list *list1,
4287 __isl_take isl_pw_aff_list *list2);
4288 __isl_give isl_set *isl_pw_aff_list_le_set(
4289 __isl_take isl_pw_aff_list *list1,
4290 __isl_take isl_pw_aff_list *list2);
4291 __isl_give isl_set *isl_pw_aff_list_lt_set(
4292 __isl_take isl_pw_aff_list *list1,
4293 __isl_take isl_pw_aff_list *list2);
4294 __isl_give isl_set *isl_pw_aff_list_ge_set(
4295 __isl_take isl_pw_aff_list *list1,
4296 __isl_take isl_pw_aff_list *list2);
4297 __isl_give isl_set *isl_pw_aff_list_gt_set(
4298 __isl_take isl_pw_aff_list *list1,
4299 __isl_take isl_pw_aff_list *list2);
4301 The function C<isl_aff_neg_basic_set> returns a basic set
4302 containing those elements in the domain space
4303 of C<aff> where C<aff> is negative.
4304 The function C<isl_aff_ge_basic_set> returns a basic set
4305 containing those elements in the shared space
4306 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4307 The function C<isl_pw_aff_ge_set> returns a set
4308 containing those elements in the shared domain
4309 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4310 The functions operating on C<isl_pw_aff_list> apply the corresponding
4311 C<isl_pw_aff> function to each pair of elements in the two lists.
4313 #include <isl/aff.h>
4314 __isl_give isl_set *isl_pw_aff_nonneg_set(
4315 __isl_take isl_pw_aff *pwaff);
4316 __isl_give isl_set *isl_pw_aff_zero_set(
4317 __isl_take isl_pw_aff *pwaff);
4318 __isl_give isl_set *isl_pw_aff_non_zero_set(
4319 __isl_take isl_pw_aff *pwaff);
4321 The function C<isl_pw_aff_nonneg_set> returns a set
4322 containing those elements in the domain
4323 of C<pwaff> where C<pwaff> is non-negative.
4325 #include <isl/aff.h>
4326 __isl_give isl_pw_aff *isl_pw_aff_cond(
4327 __isl_take isl_pw_aff *cond,
4328 __isl_take isl_pw_aff *pwaff_true,
4329 __isl_take isl_pw_aff *pwaff_false);
4331 The function C<isl_pw_aff_cond> performs a conditional operator
4332 and returns an expression that is equal to C<pwaff_true>
4333 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4334 where C<cond> is zero.
4336 #include <isl/aff.h>
4337 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4338 __isl_take isl_pw_aff *pwaff1,
4339 __isl_take isl_pw_aff *pwaff2);
4340 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4341 __isl_take isl_pw_aff *pwaff1,
4342 __isl_take isl_pw_aff *pwaff2);
4343 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4344 __isl_take isl_pw_aff *pwaff1,
4345 __isl_take isl_pw_aff *pwaff2);
4347 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4348 expression with a domain that is the union of those of C<pwaff1> and
4349 C<pwaff2> and such that on each cell, the quasi-affine expression is
4350 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4351 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4352 associated expression is the defined one.
4354 An expression can be read from input using
4356 #include <isl/aff.h>
4357 __isl_give isl_aff *isl_aff_read_from_str(
4358 isl_ctx *ctx, const char *str);
4359 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4360 isl_ctx *ctx, const char *str);
4362 An expression can be printed using
4364 #include <isl/aff.h>
4365 __isl_give isl_printer *isl_printer_print_aff(
4366 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4368 __isl_give isl_printer *isl_printer_print_pw_aff(
4369 __isl_take isl_printer *p,
4370 __isl_keep isl_pw_aff *pwaff);
4372 =head2 Piecewise Multiple Quasi Affine Expressions
4374 An C<isl_multi_aff> object represents a sequence of
4375 zero or more affine expressions, all defined on the same domain space.
4376 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4377 zero or more piecewise affine expressions.
4379 An C<isl_multi_aff> can be constructed from a single
4380 C<isl_aff> or an C<isl_aff_list> using the
4381 following functions. Similarly for C<isl_multi_pw_aff>
4382 and C<isl_pw_multi_aff>.
4384 #include <isl/aff.h>
4385 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4386 __isl_take isl_aff *aff);
4387 __isl_give isl_multi_pw_aff *
4388 isl_multi_pw_aff_from_multi_aff(
4389 __isl_take isl_multi_aff *ma);
4390 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4391 __isl_take isl_pw_aff *pa);
4392 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4393 __isl_take isl_pw_aff *pa);
4394 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4395 __isl_take isl_space *space,
4396 __isl_take isl_aff_list *list);
4398 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4399 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4400 Note however that the domain
4401 of the result is the intersection of the domains of the input.
4402 The reverse conversion is exact.
4404 #include <isl/aff.h>
4405 __isl_give isl_pw_multi_aff *
4406 isl_pw_multi_aff_from_multi_pw_aff(
4407 __isl_take isl_multi_pw_aff *mpa);
4408 __isl_give isl_multi_pw_aff *
4409 isl_multi_pw_aff_from_pw_multi_aff(
4410 __isl_take isl_pw_multi_aff *pma);
4412 An empty piecewise multiple quasi affine expression (one with no cells),
4413 the zero piecewise multiple quasi affine expression (with value zero
4414 for each output dimension),
4415 a piecewise multiple quasi affine expression with a single cell (with
4416 either a universe or a specified domain) or
4417 a zero-dimensional piecewise multiple quasi affine expression
4419 can be created using the following functions.
4421 #include <isl/aff.h>
4422 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4423 __isl_take isl_space *space);
4424 __isl_give isl_multi_aff *isl_multi_aff_zero(
4425 __isl_take isl_space *space);
4426 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4427 __isl_take isl_space *space);
4428 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4429 __isl_take isl_space *space);
4430 __isl_give isl_multi_aff *isl_multi_aff_identity(
4431 __isl_take isl_space *space);
4432 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4433 __isl_take isl_space *space);
4434 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4435 __isl_take isl_space *space);
4436 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4437 __isl_take isl_space *space);
4438 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4439 __isl_take isl_space *space);
4440 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4441 __isl_take isl_space *space,
4442 enum isl_dim_type type,
4443 unsigned first, unsigned n);
4444 __isl_give isl_pw_multi_aff *
4445 isl_pw_multi_aff_project_out_map(
4446 __isl_take isl_space *space,
4447 enum isl_dim_type type,
4448 unsigned first, unsigned n);
4449 __isl_give isl_pw_multi_aff *
4450 isl_pw_multi_aff_from_multi_aff(
4451 __isl_take isl_multi_aff *ma);
4452 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4453 __isl_take isl_set *set,
4454 __isl_take isl_multi_aff *maff);
4455 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4456 __isl_take isl_set *set);
4458 __isl_give isl_union_pw_multi_aff *
4459 isl_union_pw_multi_aff_empty(
4460 __isl_take isl_space *space);
4461 __isl_give isl_union_pw_multi_aff *
4462 isl_union_pw_multi_aff_add_pw_multi_aff(
4463 __isl_take isl_union_pw_multi_aff *upma,
4464 __isl_take isl_pw_multi_aff *pma);
4465 __isl_give isl_union_pw_multi_aff *
4466 isl_union_pw_multi_aff_from_domain(
4467 __isl_take isl_union_set *uset);
4469 A piecewise multiple quasi affine expression can also be initialized
4470 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4471 and the C<isl_map> is single-valued.
4472 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4473 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4475 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4476 __isl_take isl_set *set);
4477 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4478 __isl_take isl_map *map);
4480 __isl_give isl_union_pw_multi_aff *
4481 isl_union_pw_multi_aff_from_union_set(
4482 __isl_take isl_union_set *uset);
4483 __isl_give isl_union_pw_multi_aff *
4484 isl_union_pw_multi_aff_from_union_map(
4485 __isl_take isl_union_map *umap);
4487 Multiple quasi affine expressions can be copied and freed using
4489 #include <isl/aff.h>
4490 __isl_give isl_multi_aff *isl_multi_aff_copy(
4491 __isl_keep isl_multi_aff *maff);
4492 __isl_null isl_multi_aff *isl_multi_aff_free(
4493 __isl_take isl_multi_aff *maff);
4495 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4496 __isl_keep isl_pw_multi_aff *pma);
4497 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
4498 __isl_take isl_pw_multi_aff *pma);
4500 __isl_give isl_union_pw_multi_aff *
4501 isl_union_pw_multi_aff_copy(
4502 __isl_keep isl_union_pw_multi_aff *upma);
4503 __isl_null isl_union_pw_multi_aff *
4504 isl_union_pw_multi_aff_free(
4505 __isl_take isl_union_pw_multi_aff *upma);
4507 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4508 __isl_keep isl_multi_pw_aff *mpa);
4509 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
4510 __isl_take isl_multi_pw_aff *mpa);
4512 The expression can be inspected using
4514 #include <isl/aff.h>
4515 isl_ctx *isl_multi_aff_get_ctx(
4516 __isl_keep isl_multi_aff *maff);
4517 isl_ctx *isl_pw_multi_aff_get_ctx(
4518 __isl_keep isl_pw_multi_aff *pma);
4519 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4520 __isl_keep isl_union_pw_multi_aff *upma);
4521 isl_ctx *isl_multi_pw_aff_get_ctx(
4522 __isl_keep isl_multi_pw_aff *mpa);
4524 int isl_multi_aff_involves_dims(
4525 __isl_keep isl_multi_aff *ma,
4526 enum isl_dim_type type, unsigned first, unsigned n);
4527 int isl_multi_pw_aff_involves_dims(
4528 __isl_keep isl_multi_pw_aff *mpa,
4529 enum isl_dim_type type, unsigned first, unsigned n);
4531 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4532 enum isl_dim_type type);
4533 unsigned isl_pw_multi_aff_dim(
4534 __isl_keep isl_pw_multi_aff *pma,
4535 enum isl_dim_type type);
4536 unsigned isl_multi_pw_aff_dim(
4537 __isl_keep isl_multi_pw_aff *mpa,
4538 enum isl_dim_type type);
4539 __isl_give isl_aff *isl_multi_aff_get_aff(
4540 __isl_keep isl_multi_aff *multi, int pos);
4541 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4542 __isl_keep isl_pw_multi_aff *pma, int pos);
4543 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4544 __isl_keep isl_multi_pw_aff *mpa, int pos);
4545 int isl_multi_aff_find_dim_by_id(
4546 __isl_keep isl_multi_aff *ma,
4547 enum isl_dim_type type, __isl_keep isl_id *id);
4548 int isl_multi_pw_aff_find_dim_by_id(
4549 __isl_keep isl_multi_pw_aff *mpa,
4550 enum isl_dim_type type, __isl_keep isl_id *id);
4551 const char *isl_pw_multi_aff_get_dim_name(
4552 __isl_keep isl_pw_multi_aff *pma,
4553 enum isl_dim_type type, unsigned pos);
4554 __isl_give isl_id *isl_multi_aff_get_dim_id(
4555 __isl_keep isl_multi_aff *ma,
4556 enum isl_dim_type type, unsigned pos);
4557 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4558 __isl_keep isl_pw_multi_aff *pma,
4559 enum isl_dim_type type, unsigned pos);
4560 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4561 __isl_keep isl_multi_pw_aff *mpa,
4562 enum isl_dim_type type, unsigned pos);
4563 const char *isl_multi_aff_get_tuple_name(
4564 __isl_keep isl_multi_aff *multi,
4565 enum isl_dim_type type);
4566 int isl_pw_multi_aff_has_tuple_name(
4567 __isl_keep isl_pw_multi_aff *pma,
4568 enum isl_dim_type type);
4569 const char *isl_pw_multi_aff_get_tuple_name(
4570 __isl_keep isl_pw_multi_aff *pma,
4571 enum isl_dim_type type);
4572 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4573 enum isl_dim_type type);
4574 int isl_pw_multi_aff_has_tuple_id(
4575 __isl_keep isl_pw_multi_aff *pma,
4576 enum isl_dim_type type);
4577 int isl_multi_pw_aff_has_tuple_id(
4578 __isl_keep isl_multi_pw_aff *mpa,
4579 enum isl_dim_type type);
4580 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4581 __isl_keep isl_multi_aff *ma,
4582 enum isl_dim_type type);
4583 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4584 __isl_keep isl_pw_multi_aff *pma,
4585 enum isl_dim_type type);
4586 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4587 __isl_keep isl_multi_pw_aff *mpa,
4588 enum isl_dim_type type);
4589 int isl_multi_aff_range_is_wrapping(
4590 __isl_keep isl_multi_aff *ma);
4591 int isl_multi_pw_aff_range_is_wrapping(
4592 __isl_keep isl_multi_pw_aff *mpa);
4594 int isl_pw_multi_aff_foreach_piece(
4595 __isl_keep isl_pw_multi_aff *pma,
4596 int (*fn)(__isl_take isl_set *set,
4597 __isl_take isl_multi_aff *maff,
4598 void *user), void *user);
4600 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4601 __isl_keep isl_union_pw_multi_aff *upma,
4602 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4603 void *user), void *user);
4605 It can be modified using
4607 #include <isl/aff.h>
4608 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4609 __isl_take isl_multi_aff *multi, int pos,
4610 __isl_take isl_aff *aff);
4611 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4612 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4613 __isl_take isl_pw_aff *pa);
4614 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4615 __isl_take isl_multi_aff *maff,
4616 enum isl_dim_type type, unsigned pos, const char *s);
4617 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4618 __isl_take isl_multi_aff *maff,
4619 enum isl_dim_type type, unsigned pos,
4620 __isl_take isl_id *id);
4621 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4622 __isl_take isl_multi_aff *maff,
4623 enum isl_dim_type type, const char *s);
4624 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4625 __isl_take isl_multi_aff *maff,
4626 enum isl_dim_type type, __isl_take isl_id *id);
4627 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4628 __isl_take isl_pw_multi_aff *pma,
4629 enum isl_dim_type type, __isl_take isl_id *id);
4630 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4631 __isl_take isl_multi_aff *ma,
4632 enum isl_dim_type type);
4633 __isl_give isl_multi_pw_aff *
4634 isl_multi_pw_aff_reset_tuple_id(
4635 __isl_take isl_multi_pw_aff *mpa,
4636 enum isl_dim_type type);
4637 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4638 __isl_take isl_multi_aff *ma);
4639 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4640 __isl_take isl_multi_pw_aff *mpa);
4642 __isl_give isl_multi_pw_aff *
4643 isl_multi_pw_aff_set_dim_name(
4644 __isl_take isl_multi_pw_aff *mpa,
4645 enum isl_dim_type type, unsigned pos, const char *s);
4646 __isl_give isl_multi_pw_aff *
4647 isl_multi_pw_aff_set_dim_id(
4648 __isl_take isl_multi_pw_aff *mpa,
4649 enum isl_dim_type type, unsigned pos,
4650 __isl_take isl_id *id);
4651 __isl_give isl_multi_pw_aff *
4652 isl_multi_pw_aff_set_tuple_name(
4653 __isl_take isl_multi_pw_aff *mpa,
4654 enum isl_dim_type type, const char *s);
4656 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4657 __isl_take isl_multi_aff *ma);
4659 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4660 __isl_take isl_multi_aff *ma,
4661 enum isl_dim_type type, unsigned first, unsigned n);
4662 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4663 __isl_take isl_multi_aff *ma,
4664 enum isl_dim_type type, unsigned n);
4665 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4666 __isl_take isl_multi_aff *maff,
4667 enum isl_dim_type type, unsigned first, unsigned n);
4668 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4669 __isl_take isl_pw_multi_aff *pma,
4670 enum isl_dim_type type, unsigned first, unsigned n);
4672 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4673 __isl_take isl_multi_pw_aff *mpa,
4674 enum isl_dim_type type, unsigned first, unsigned n);
4675 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4676 __isl_take isl_multi_pw_aff *mpa,
4677 enum isl_dim_type type, unsigned n);
4678 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4679 __isl_take isl_multi_pw_aff *pma,
4680 enum isl_dim_type dst_type, unsigned dst_pos,
4681 enum isl_dim_type src_type, unsigned src_pos,
4684 To check whether two multiple affine expressions are
4685 (obviously) equal to each other, use
4687 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4688 __isl_keep isl_multi_aff *maff2);
4689 int isl_pw_multi_aff_plain_is_equal(
4690 __isl_keep isl_pw_multi_aff *pma1,
4691 __isl_keep isl_pw_multi_aff *pma2);
4692 int isl_multi_pw_aff_plain_is_equal(
4693 __isl_keep isl_multi_pw_aff *mpa1,
4694 __isl_keep isl_multi_pw_aff *mpa2);
4695 int isl_multi_pw_aff_is_equal(
4696 __isl_keep isl_multi_pw_aff *mpa1,
4697 __isl_keep isl_multi_pw_aff *mpa2);
4701 #include <isl/aff.h>
4702 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4703 __isl_take isl_pw_multi_aff *pma1,
4704 __isl_take isl_pw_multi_aff *pma2);
4705 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4706 __isl_take isl_pw_multi_aff *pma1,
4707 __isl_take isl_pw_multi_aff *pma2);
4708 __isl_give isl_multi_aff *isl_multi_aff_floor(
4709 __isl_take isl_multi_aff *ma);
4710 __isl_give isl_multi_aff *isl_multi_aff_add(
4711 __isl_take isl_multi_aff *maff1,
4712 __isl_take isl_multi_aff *maff2);
4713 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4714 __isl_take isl_pw_multi_aff *pma1,
4715 __isl_take isl_pw_multi_aff *pma2);
4716 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4717 __isl_take isl_union_pw_multi_aff *upma1,
4718 __isl_take isl_union_pw_multi_aff *upma2);
4719 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4720 __isl_take isl_pw_multi_aff *pma1,
4721 __isl_take isl_pw_multi_aff *pma2);
4722 __isl_give isl_multi_aff *isl_multi_aff_sub(
4723 __isl_take isl_multi_aff *ma1,
4724 __isl_take isl_multi_aff *ma2);
4725 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4726 __isl_take isl_pw_multi_aff *pma1,
4727 __isl_take isl_pw_multi_aff *pma2);
4728 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4729 __isl_take isl_union_pw_multi_aff *upma1,
4730 __isl_take isl_union_pw_multi_aff *upma2);
4732 C<isl_multi_aff_sub> subtracts the second argument from the first.
4734 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4735 __isl_take isl_multi_aff *ma,
4736 __isl_take isl_val *v);
4737 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4738 __isl_take isl_pw_multi_aff *pma,
4739 __isl_take isl_val *v);
4740 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4741 __isl_take isl_multi_pw_aff *mpa,
4742 __isl_take isl_val *v);
4743 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4744 __isl_take isl_multi_aff *ma,
4745 __isl_take isl_multi_val *mv);
4746 __isl_give isl_pw_multi_aff *
4747 isl_pw_multi_aff_scale_multi_val(
4748 __isl_take isl_pw_multi_aff *pma,
4749 __isl_take isl_multi_val *mv);
4750 __isl_give isl_multi_pw_aff *
4751 isl_multi_pw_aff_scale_multi_val(
4752 __isl_take isl_multi_pw_aff *mpa,
4753 __isl_take isl_multi_val *mv);
4754 __isl_give isl_union_pw_multi_aff *
4755 isl_union_pw_multi_aff_scale_multi_val(
4756 __isl_take isl_union_pw_multi_aff *upma,
4757 __isl_take isl_multi_val *mv);
4758 __isl_give isl_multi_aff *
4759 isl_multi_aff_scale_down_multi_val(
4760 __isl_take isl_multi_aff *ma,
4761 __isl_take isl_multi_val *mv);
4762 __isl_give isl_multi_pw_aff *
4763 isl_multi_pw_aff_scale_down_multi_val(
4764 __isl_take isl_multi_pw_aff *mpa,
4765 __isl_take isl_multi_val *mv);
4767 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4768 by the corresponding elements of C<mv>.
4770 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4771 __isl_take isl_pw_multi_aff *pma,
4772 enum isl_dim_type type, unsigned pos, int value);
4773 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4774 __isl_take isl_pw_multi_aff *pma,
4775 __isl_take isl_set *set);
4776 __isl_give isl_set *isl_multi_pw_aff_domain(
4777 __isl_take isl_multi_pw_aff *mpa);
4778 __isl_give isl_multi_pw_aff *
4779 isl_multi_pw_aff_intersect_params(
4780 __isl_take isl_multi_pw_aff *mpa,
4781 __isl_take isl_set *set);
4782 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4783 __isl_take isl_pw_multi_aff *pma,
4784 __isl_take isl_set *set);
4785 __isl_give isl_multi_pw_aff *
4786 isl_multi_pw_aff_intersect_domain(
4787 __isl_take isl_multi_pw_aff *mpa,
4788 __isl_take isl_set *domain);
4789 __isl_give isl_union_pw_multi_aff *
4790 isl_union_pw_multi_aff_intersect_domain(
4791 __isl_take isl_union_pw_multi_aff *upma,
4792 __isl_take isl_union_set *uset);
4793 __isl_give isl_multi_aff *isl_multi_aff_lift(
4794 __isl_take isl_multi_aff *maff,
4795 __isl_give isl_local_space **ls);
4796 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4797 __isl_take isl_pw_multi_aff *pma);
4798 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4799 __isl_take isl_multi_pw_aff *mpa);
4800 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4801 __isl_take isl_multi_aff *multi,
4802 __isl_take isl_space *model);
4803 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4804 __isl_take isl_pw_multi_aff *pma,
4805 __isl_take isl_space *model);
4806 __isl_give isl_union_pw_multi_aff *
4807 isl_union_pw_multi_aff_align_params(
4808 __isl_take isl_union_pw_multi_aff *upma,
4809 __isl_take isl_space *model);
4810 __isl_give isl_pw_multi_aff *
4811 isl_pw_multi_aff_project_domain_on_params(
4812 __isl_take isl_pw_multi_aff *pma);
4813 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4814 __isl_take isl_multi_aff *maff,
4815 __isl_take isl_set *context);
4816 __isl_give isl_multi_aff *isl_multi_aff_gist(
4817 __isl_take isl_multi_aff *maff,
4818 __isl_take isl_set *context);
4819 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4820 __isl_take isl_pw_multi_aff *pma,
4821 __isl_take isl_set *set);
4822 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4823 __isl_take isl_pw_multi_aff *pma,
4824 __isl_take isl_set *set);
4825 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4826 __isl_take isl_multi_pw_aff *mpa,
4827 __isl_take isl_set *set);
4828 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4829 __isl_take isl_multi_pw_aff *mpa,
4830 __isl_take isl_set *set);
4831 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4832 __isl_take isl_multi_aff *ma);
4833 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4834 __isl_take isl_multi_pw_aff *mpa);
4835 __isl_give isl_set *isl_pw_multi_aff_domain(
4836 __isl_take isl_pw_multi_aff *pma);
4837 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4838 __isl_take isl_union_pw_multi_aff *upma);
4839 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4840 __isl_take isl_multi_aff *ma1, unsigned pos,
4841 __isl_take isl_multi_aff *ma2);
4842 __isl_give isl_multi_aff *isl_multi_aff_splice(
4843 __isl_take isl_multi_aff *ma1,
4844 unsigned in_pos, unsigned out_pos,
4845 __isl_take isl_multi_aff *ma2);
4846 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4847 __isl_take isl_multi_aff *ma1,
4848 __isl_take isl_multi_aff *ma2);
4849 __isl_give isl_multi_aff *
4850 isl_multi_aff_range_factor_domain(
4851 __isl_take isl_multi_aff *ma);
4852 __isl_give isl_multi_aff *
4853 isl_multi_aff_range_factor_range(
4854 __isl_take isl_multi_aff *ma);
4855 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4856 __isl_take isl_multi_aff *ma1,
4857 __isl_take isl_multi_aff *ma2);
4858 __isl_give isl_multi_aff *isl_multi_aff_product(
4859 __isl_take isl_multi_aff *ma1,
4860 __isl_take isl_multi_aff *ma2);
4861 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4862 __isl_take isl_multi_pw_aff *mpa1,
4863 __isl_take isl_multi_pw_aff *mpa2);
4864 __isl_give isl_pw_multi_aff *
4865 isl_pw_multi_aff_range_product(
4866 __isl_take isl_pw_multi_aff *pma1,
4867 __isl_take isl_pw_multi_aff *pma2);
4868 __isl_give isl_multi_pw_aff *
4869 isl_multi_pw_aff_range_factor_domain(
4870 __isl_take isl_multi_pw_aff *mpa);
4871 __isl_give isl_multi_pw_aff *
4872 isl_multi_pw_aff_range_factor_range(
4873 __isl_take isl_multi_pw_aff *mpa);
4874 __isl_give isl_pw_multi_aff *
4875 isl_pw_multi_aff_flat_range_product(
4876 __isl_take isl_pw_multi_aff *pma1,
4877 __isl_take isl_pw_multi_aff *pma2);
4878 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4879 __isl_take isl_pw_multi_aff *pma1,
4880 __isl_take isl_pw_multi_aff *pma2);
4881 __isl_give isl_union_pw_multi_aff *
4882 isl_union_pw_multi_aff_flat_range_product(
4883 __isl_take isl_union_pw_multi_aff *upma1,
4884 __isl_take isl_union_pw_multi_aff *upma2);
4885 __isl_give isl_multi_pw_aff *
4886 isl_multi_pw_aff_range_splice(
4887 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4888 __isl_take isl_multi_pw_aff *mpa2);
4889 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4890 __isl_take isl_multi_pw_aff *mpa1,
4891 unsigned in_pos, unsigned out_pos,
4892 __isl_take isl_multi_pw_aff *mpa2);
4893 __isl_give isl_multi_pw_aff *
4894 isl_multi_pw_aff_range_product(
4895 __isl_take isl_multi_pw_aff *mpa1,
4896 __isl_take isl_multi_pw_aff *mpa2);
4897 __isl_give isl_multi_pw_aff *
4898 isl_multi_pw_aff_flat_range_product(
4899 __isl_take isl_multi_pw_aff *mpa1,
4900 __isl_take isl_multi_pw_aff *mpa2);
4902 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4903 then it is assigned the local space that lies at the basis of
4904 the lifting applied.
4906 #include <isl/aff.h>
4907 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4908 __isl_take isl_multi_aff *ma1,
4909 __isl_take isl_multi_aff *ma2);
4910 __isl_give isl_pw_multi_aff *
4911 isl_pw_multi_aff_pullback_multi_aff(
4912 __isl_take isl_pw_multi_aff *pma,
4913 __isl_take isl_multi_aff *ma);
4914 __isl_give isl_multi_pw_aff *
4915 isl_multi_pw_aff_pullback_multi_aff(
4916 __isl_take isl_multi_pw_aff *mpa,
4917 __isl_take isl_multi_aff *ma);
4918 __isl_give isl_pw_multi_aff *
4919 isl_pw_multi_aff_pullback_pw_multi_aff(
4920 __isl_take isl_pw_multi_aff *pma1,
4921 __isl_take isl_pw_multi_aff *pma2);
4922 __isl_give isl_multi_pw_aff *
4923 isl_multi_pw_aff_pullback_pw_multi_aff(
4924 __isl_take isl_multi_pw_aff *mpa,
4925 __isl_take isl_pw_multi_aff *pma);
4926 __isl_give isl_multi_pw_aff *
4927 isl_multi_pw_aff_pullback_multi_pw_aff(
4928 __isl_take isl_multi_pw_aff *mpa1,
4929 __isl_take isl_multi_pw_aff *mpa2);
4931 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4932 In other words, C<ma2> is plugged
4935 __isl_give isl_set *isl_multi_aff_lex_le_set(
4936 __isl_take isl_multi_aff *ma1,
4937 __isl_take isl_multi_aff *ma2);
4938 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4939 __isl_take isl_multi_aff *ma1,
4940 __isl_take isl_multi_aff *ma2);
4942 The function C<isl_multi_aff_lex_le_set> returns a set
4943 containing those elements in the shared domain space
4944 where C<ma1> is lexicographically smaller than or
4947 An expression can be read from input using
4949 #include <isl/aff.h>
4950 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4951 isl_ctx *ctx, const char *str);
4952 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4953 isl_ctx *ctx, const char *str);
4954 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4955 isl_ctx *ctx, const char *str);
4956 __isl_give isl_union_pw_multi_aff *
4957 isl_union_pw_multi_aff_read_from_str(
4958 isl_ctx *ctx, const char *str);
4960 An expression can be printed using
4962 #include <isl/aff.h>
4963 __isl_give isl_printer *isl_printer_print_multi_aff(
4964 __isl_take isl_printer *p,
4965 __isl_keep isl_multi_aff *maff);
4966 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4967 __isl_take isl_printer *p,
4968 __isl_keep isl_pw_multi_aff *pma);
4969 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4970 __isl_take isl_printer *p,
4971 __isl_keep isl_union_pw_multi_aff *upma);
4972 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4973 __isl_take isl_printer *p,
4974 __isl_keep isl_multi_pw_aff *mpa);
4978 Points are elements of a set. They can be used to construct
4979 simple sets (boxes) or they can be used to represent the
4980 individual elements of a set.
4981 The zero point (the origin) can be created using
4983 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4985 The coordinates of a point can be inspected, set and changed
4988 __isl_give isl_val *isl_point_get_coordinate_val(
4989 __isl_keep isl_point *pnt,
4990 enum isl_dim_type type, int pos);
4991 __isl_give isl_point *isl_point_set_coordinate_val(
4992 __isl_take isl_point *pnt,
4993 enum isl_dim_type type, int pos,
4994 __isl_take isl_val *v);
4996 __isl_give isl_point *isl_point_add_ui(
4997 __isl_take isl_point *pnt,
4998 enum isl_dim_type type, int pos, unsigned val);
4999 __isl_give isl_point *isl_point_sub_ui(
5000 __isl_take isl_point *pnt,
5001 enum isl_dim_type type, int pos, unsigned val);
5003 Other properties can be obtained using
5005 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
5007 Points can be copied or freed using
5009 __isl_give isl_point *isl_point_copy(
5010 __isl_keep isl_point *pnt);
5011 void isl_point_free(__isl_take isl_point *pnt);
5013 A singleton set can be created from a point using
5015 __isl_give isl_basic_set *isl_basic_set_from_point(
5016 __isl_take isl_point *pnt);
5017 __isl_give isl_set *isl_set_from_point(
5018 __isl_take isl_point *pnt);
5020 and a box can be created from two opposite extremal points using
5022 __isl_give isl_basic_set *isl_basic_set_box_from_points(
5023 __isl_take isl_point *pnt1,
5024 __isl_take isl_point *pnt2);
5025 __isl_give isl_set *isl_set_box_from_points(
5026 __isl_take isl_point *pnt1,
5027 __isl_take isl_point *pnt2);
5029 All elements of a B<bounded> (union) set can be enumerated using
5030 the following functions.
5032 int isl_set_foreach_point(__isl_keep isl_set *set,
5033 int (*fn)(__isl_take isl_point *pnt, void *user),
5035 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
5036 int (*fn)(__isl_take isl_point *pnt, void *user),
5039 The function C<fn> is called for each integer point in
5040 C<set> with as second argument the last argument of
5041 the C<isl_set_foreach_point> call. The function C<fn>
5042 should return C<0> on success and C<-1> on failure.
5043 In the latter case, C<isl_set_foreach_point> will stop
5044 enumerating and return C<-1> as well.
5045 If the enumeration is performed successfully and to completion,
5046 then C<isl_set_foreach_point> returns C<0>.
5048 To obtain a single point of a (basic) set, use
5050 __isl_give isl_point *isl_basic_set_sample_point(
5051 __isl_take isl_basic_set *bset);
5052 __isl_give isl_point *isl_set_sample_point(
5053 __isl_take isl_set *set);
5055 If C<set> does not contain any (integer) points, then the
5056 resulting point will be ``void'', a property that can be
5059 int isl_point_is_void(__isl_keep isl_point *pnt);
5061 =head2 Piecewise Quasipolynomials
5063 A piecewise quasipolynomial is a particular kind of function that maps
5064 a parametric point to a rational value.
5065 More specifically, a quasipolynomial is a polynomial expression in greatest
5066 integer parts of affine expressions of parameters and variables.
5067 A piecewise quasipolynomial is a subdivision of a given parametric
5068 domain into disjoint cells with a quasipolynomial associated to
5069 each cell. The value of the piecewise quasipolynomial at a given
5070 point is the value of the quasipolynomial associated to the cell
5071 that contains the point. Outside of the union of cells,
5072 the value is assumed to be zero.
5073 For example, the piecewise quasipolynomial
5075 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
5077 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
5078 A given piecewise quasipolynomial has a fixed domain dimension.
5079 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
5080 defined over different domains.
5081 Piecewise quasipolynomials are mainly used by the C<barvinok>
5082 library for representing the number of elements in a parametric set or map.
5083 For example, the piecewise quasipolynomial above represents
5084 the number of points in the map
5086 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
5088 =head3 Input and Output
5090 Piecewise quasipolynomials can be read from input using
5092 __isl_give isl_union_pw_qpolynomial *
5093 isl_union_pw_qpolynomial_read_from_str(
5094 isl_ctx *ctx, const char *str);
5096 Quasipolynomials and piecewise quasipolynomials can be printed
5097 using the following functions.
5099 __isl_give isl_printer *isl_printer_print_qpolynomial(
5100 __isl_take isl_printer *p,
5101 __isl_keep isl_qpolynomial *qp);
5103 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
5104 __isl_take isl_printer *p,
5105 __isl_keep isl_pw_qpolynomial *pwqp);
5107 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
5108 __isl_take isl_printer *p,
5109 __isl_keep isl_union_pw_qpolynomial *upwqp);
5111 The output format of the printer
5112 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5113 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
5115 In case of printing in C<ISL_FORMAT_C>, the user may want
5116 to set the names of all dimensions
5118 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
5119 __isl_take isl_qpolynomial *qp,
5120 enum isl_dim_type type, unsigned pos,
5122 __isl_give isl_pw_qpolynomial *
5123 isl_pw_qpolynomial_set_dim_name(
5124 __isl_take isl_pw_qpolynomial *pwqp,
5125 enum isl_dim_type type, unsigned pos,
5128 =head3 Creating New (Piecewise) Quasipolynomials
5130 Some simple quasipolynomials can be created using the following functions.
5131 More complicated quasipolynomials can be created by applying
5132 operations such as addition and multiplication
5133 on the resulting quasipolynomials
5135 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
5136 __isl_take isl_space *domain);
5137 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
5138 __isl_take isl_space *domain);
5139 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
5140 __isl_take isl_space *domain);
5141 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
5142 __isl_take isl_space *domain);
5143 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
5144 __isl_take isl_space *domain);
5145 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
5146 __isl_take isl_space *domain,
5147 __isl_take isl_val *val);
5148 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
5149 __isl_take isl_space *domain,
5150 enum isl_dim_type type, unsigned pos);
5151 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
5152 __isl_take isl_aff *aff);
5154 Note that the space in which a quasipolynomial lives is a map space
5155 with a one-dimensional range. The C<domain> argument in some of
5156 the functions above corresponds to the domain of this map space.
5158 The zero piecewise quasipolynomial or a piecewise quasipolynomial
5159 with a single cell can be created using the following functions.
5160 Multiple of these single cell piecewise quasipolynomials can
5161 be combined to create more complicated piecewise quasipolynomials.
5163 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
5164 __isl_take isl_space *space);
5165 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
5166 __isl_take isl_set *set,
5167 __isl_take isl_qpolynomial *qp);
5168 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
5169 __isl_take isl_qpolynomial *qp);
5170 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
5171 __isl_take isl_pw_aff *pwaff);
5173 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
5174 __isl_take isl_space *space);
5175 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
5176 __isl_take isl_pw_qpolynomial *pwqp);
5177 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
5178 __isl_take isl_union_pw_qpolynomial *upwqp,
5179 __isl_take isl_pw_qpolynomial *pwqp);
5181 Quasipolynomials can be copied and freed again using the following
5184 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
5185 __isl_keep isl_qpolynomial *qp);
5186 __isl_null isl_qpolynomial *isl_qpolynomial_free(
5187 __isl_take isl_qpolynomial *qp);
5189 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
5190 __isl_keep isl_pw_qpolynomial *pwqp);
5191 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
5192 __isl_take isl_pw_qpolynomial *pwqp);
5194 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
5195 __isl_keep isl_union_pw_qpolynomial *upwqp);
5196 __isl_null isl_union_pw_qpolynomial *
5197 isl_union_pw_qpolynomial_free(
5198 __isl_take isl_union_pw_qpolynomial *upwqp);
5200 =head3 Inspecting (Piecewise) Quasipolynomials
5202 To iterate over all piecewise quasipolynomials in a union
5203 piecewise quasipolynomial, use the following function
5205 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
5206 __isl_keep isl_union_pw_qpolynomial *upwqp,
5207 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
5210 To extract the piecewise quasipolynomial in a given space from a union, use
5212 __isl_give isl_pw_qpolynomial *
5213 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
5214 __isl_keep isl_union_pw_qpolynomial *upwqp,
5215 __isl_take isl_space *space);
5217 To iterate over the cells in a piecewise quasipolynomial,
5218 use either of the following two functions
5220 int isl_pw_qpolynomial_foreach_piece(
5221 __isl_keep isl_pw_qpolynomial *pwqp,
5222 int (*fn)(__isl_take isl_set *set,
5223 __isl_take isl_qpolynomial *qp,
5224 void *user), void *user);
5225 int isl_pw_qpolynomial_foreach_lifted_piece(
5226 __isl_keep isl_pw_qpolynomial *pwqp,
5227 int (*fn)(__isl_take isl_set *set,
5228 __isl_take isl_qpolynomial *qp,
5229 void *user), void *user);
5231 As usual, the function C<fn> should return C<0> on success
5232 and C<-1> on failure. The difference between
5233 C<isl_pw_qpolynomial_foreach_piece> and
5234 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
5235 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
5236 compute unique representations for all existentially quantified
5237 variables and then turn these existentially quantified variables
5238 into extra set variables, adapting the associated quasipolynomial
5239 accordingly. This means that the C<set> passed to C<fn>
5240 will not have any existentially quantified variables, but that
5241 the dimensions of the sets may be different for different
5242 invocations of C<fn>.
5244 The constant term of a quasipolynomial can be extracted using
5246 __isl_give isl_val *isl_qpolynomial_get_constant_val(
5247 __isl_keep isl_qpolynomial *qp);
5249 To iterate over all terms in a quasipolynomial,
5252 int isl_qpolynomial_foreach_term(
5253 __isl_keep isl_qpolynomial *qp,
5254 int (*fn)(__isl_take isl_term *term,
5255 void *user), void *user);
5257 The terms themselves can be inspected and freed using
5260 unsigned isl_term_dim(__isl_keep isl_term *term,
5261 enum isl_dim_type type);
5262 __isl_give isl_val *isl_term_get_coefficient_val(
5263 __isl_keep isl_term *term);
5264 int isl_term_get_exp(__isl_keep isl_term *term,
5265 enum isl_dim_type type, unsigned pos);
5266 __isl_give isl_aff *isl_term_get_div(
5267 __isl_keep isl_term *term, unsigned pos);
5268 void isl_term_free(__isl_take isl_term *term);
5270 Each term is a product of parameters, set variables and
5271 integer divisions. The function C<isl_term_get_exp>
5272 returns the exponent of a given dimensions in the given term.
5274 =head3 Properties of (Piecewise) Quasipolynomials
5276 To check whether two union piecewise quasipolynomials are
5277 obviously equal, use
5279 int isl_union_pw_qpolynomial_plain_is_equal(
5280 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5281 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5283 =head3 Operations on (Piecewise) Quasipolynomials
5285 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5286 __isl_take isl_qpolynomial *qp,
5287 __isl_take isl_val *v);
5288 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5289 __isl_take isl_qpolynomial *qp);
5290 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5291 __isl_take isl_qpolynomial *qp1,
5292 __isl_take isl_qpolynomial *qp2);
5293 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5294 __isl_take isl_qpolynomial *qp1,
5295 __isl_take isl_qpolynomial *qp2);
5296 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5297 __isl_take isl_qpolynomial *qp1,
5298 __isl_take isl_qpolynomial *qp2);
5299 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5300 __isl_take isl_qpolynomial *qp, unsigned exponent);
5302 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5303 __isl_take isl_pw_qpolynomial *pwqp,
5304 enum isl_dim_type type, unsigned n,
5305 __isl_take isl_val *v);
5306 __isl_give isl_pw_qpolynomial *
5307 isl_pw_qpolynomial_scale_val(
5308 __isl_take isl_pw_qpolynomial *pwqp,
5309 __isl_take isl_val *v);
5310 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5311 __isl_take isl_pw_qpolynomial *pwqp1,
5312 __isl_take isl_pw_qpolynomial *pwqp2);
5313 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5314 __isl_take isl_pw_qpolynomial *pwqp1,
5315 __isl_take isl_pw_qpolynomial *pwqp2);
5316 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5317 __isl_take isl_pw_qpolynomial *pwqp1,
5318 __isl_take isl_pw_qpolynomial *pwqp2);
5319 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5320 __isl_take isl_pw_qpolynomial *pwqp);
5321 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5322 __isl_take isl_pw_qpolynomial *pwqp1,
5323 __isl_take isl_pw_qpolynomial *pwqp2);
5324 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5325 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5327 __isl_give isl_union_pw_qpolynomial *
5328 isl_union_pw_qpolynomial_scale_val(
5329 __isl_take isl_union_pw_qpolynomial *upwqp,
5330 __isl_take isl_val *v);
5331 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5332 __isl_take isl_union_pw_qpolynomial *upwqp1,
5333 __isl_take isl_union_pw_qpolynomial *upwqp2);
5334 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5335 __isl_take isl_union_pw_qpolynomial *upwqp1,
5336 __isl_take isl_union_pw_qpolynomial *upwqp2);
5337 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5338 __isl_take isl_union_pw_qpolynomial *upwqp1,
5339 __isl_take isl_union_pw_qpolynomial *upwqp2);
5341 __isl_give isl_val *isl_pw_qpolynomial_eval(
5342 __isl_take isl_pw_qpolynomial *pwqp,
5343 __isl_take isl_point *pnt);
5345 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5346 __isl_take isl_union_pw_qpolynomial *upwqp,
5347 __isl_take isl_point *pnt);
5349 __isl_give isl_set *isl_pw_qpolynomial_domain(
5350 __isl_take isl_pw_qpolynomial *pwqp);
5351 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5352 __isl_take isl_pw_qpolynomial *pwpq,
5353 __isl_take isl_set *set);
5354 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5355 __isl_take isl_pw_qpolynomial *pwpq,
5356 __isl_take isl_set *set);
5358 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5359 __isl_take isl_union_pw_qpolynomial *upwqp);
5360 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5361 __isl_take isl_union_pw_qpolynomial *upwpq,
5362 __isl_take isl_union_set *uset);
5363 __isl_give isl_union_pw_qpolynomial *
5364 isl_union_pw_qpolynomial_intersect_params(
5365 __isl_take isl_union_pw_qpolynomial *upwpq,
5366 __isl_take isl_set *set);
5368 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5369 __isl_take isl_qpolynomial *qp,
5370 __isl_take isl_space *model);
5372 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5373 __isl_take isl_qpolynomial *qp);
5374 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5375 __isl_take isl_pw_qpolynomial *pwqp);
5377 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5378 __isl_take isl_union_pw_qpolynomial *upwqp);
5380 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5381 __isl_take isl_qpolynomial *qp,
5382 __isl_take isl_set *context);
5383 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5384 __isl_take isl_qpolynomial *qp,
5385 __isl_take isl_set *context);
5387 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5388 __isl_take isl_pw_qpolynomial *pwqp,
5389 __isl_take isl_set *context);
5390 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5391 __isl_take isl_pw_qpolynomial *pwqp,
5392 __isl_take isl_set *context);
5394 __isl_give isl_union_pw_qpolynomial *
5395 isl_union_pw_qpolynomial_gist_params(
5396 __isl_take isl_union_pw_qpolynomial *upwqp,
5397 __isl_take isl_set *context);
5398 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5399 __isl_take isl_union_pw_qpolynomial *upwqp,
5400 __isl_take isl_union_set *context);
5402 The gist operation applies the gist operation to each of
5403 the cells in the domain of the input piecewise quasipolynomial.
5404 The context is also exploited
5405 to simplify the quasipolynomials associated to each cell.
5407 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5408 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5409 __isl_give isl_union_pw_qpolynomial *
5410 isl_union_pw_qpolynomial_to_polynomial(
5411 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5413 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5414 the polynomial will be an overapproximation. If C<sign> is negative,
5415 it will be an underapproximation. If C<sign> is zero, the approximation
5416 will lie somewhere in between.
5418 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5420 A piecewise quasipolynomial reduction is a piecewise
5421 reduction (or fold) of quasipolynomials.
5422 In particular, the reduction can be maximum or a minimum.
5423 The objects are mainly used to represent the result of
5424 an upper or lower bound on a quasipolynomial over its domain,
5425 i.e., as the result of the following function.
5427 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5428 __isl_take isl_pw_qpolynomial *pwqp,
5429 enum isl_fold type, int *tight);
5431 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5432 __isl_take isl_union_pw_qpolynomial *upwqp,
5433 enum isl_fold type, int *tight);
5435 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5436 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5437 is the returned bound is known be tight, i.e., for each value
5438 of the parameters there is at least
5439 one element in the domain that reaches the bound.
5440 If the domain of C<pwqp> is not wrapping, then the bound is computed
5441 over all elements in that domain and the result has a purely parametric
5442 domain. If the domain of C<pwqp> is wrapping, then the bound is
5443 computed over the range of the wrapped relation. The domain of the
5444 wrapped relation becomes the domain of the result.
5446 A (piecewise) quasipolynomial reduction can be copied or freed using the
5447 following functions.
5449 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5450 __isl_keep isl_qpolynomial_fold *fold);
5451 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5452 __isl_keep isl_pw_qpolynomial_fold *pwf);
5453 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5454 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5455 void isl_qpolynomial_fold_free(
5456 __isl_take isl_qpolynomial_fold *fold);
5457 __isl_null isl_pw_qpolynomial_fold *
5458 isl_pw_qpolynomial_fold_free(
5459 __isl_take isl_pw_qpolynomial_fold *pwf);
5460 __isl_null isl_union_pw_qpolynomial_fold *
5461 isl_union_pw_qpolynomial_fold_free(
5462 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5464 =head3 Printing Piecewise Quasipolynomial Reductions
5466 Piecewise quasipolynomial reductions can be printed
5467 using the following function.
5469 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5470 __isl_take isl_printer *p,
5471 __isl_keep isl_pw_qpolynomial_fold *pwf);
5472 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5473 __isl_take isl_printer *p,
5474 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5476 For C<isl_printer_print_pw_qpolynomial_fold>,
5477 output format of the printer
5478 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5479 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5480 output format of the printer
5481 needs to be set to C<ISL_FORMAT_ISL>.
5482 In case of printing in C<ISL_FORMAT_C>, the user may want
5483 to set the names of all dimensions
5485 __isl_give isl_pw_qpolynomial_fold *
5486 isl_pw_qpolynomial_fold_set_dim_name(
5487 __isl_take isl_pw_qpolynomial_fold *pwf,
5488 enum isl_dim_type type, unsigned pos,
5491 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5493 To iterate over all piecewise quasipolynomial reductions in a union
5494 piecewise quasipolynomial reduction, use the following function
5496 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5497 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5498 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5499 void *user), void *user);
5501 To iterate over the cells in a piecewise quasipolynomial reduction,
5502 use either of the following two functions
5504 int isl_pw_qpolynomial_fold_foreach_piece(
5505 __isl_keep isl_pw_qpolynomial_fold *pwf,
5506 int (*fn)(__isl_take isl_set *set,
5507 __isl_take isl_qpolynomial_fold *fold,
5508 void *user), void *user);
5509 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5510 __isl_keep isl_pw_qpolynomial_fold *pwf,
5511 int (*fn)(__isl_take isl_set *set,
5512 __isl_take isl_qpolynomial_fold *fold,
5513 void *user), void *user);
5515 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5516 of the difference between these two functions.
5518 To iterate over all quasipolynomials in a reduction, use
5520 int isl_qpolynomial_fold_foreach_qpolynomial(
5521 __isl_keep isl_qpolynomial_fold *fold,
5522 int (*fn)(__isl_take isl_qpolynomial *qp,
5523 void *user), void *user);
5525 =head3 Properties of Piecewise Quasipolynomial Reductions
5527 To check whether two union piecewise quasipolynomial reductions are
5528 obviously equal, use
5530 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5531 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5532 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5534 =head3 Operations on Piecewise Quasipolynomial Reductions
5536 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5537 __isl_take isl_qpolynomial_fold *fold,
5538 __isl_take isl_val *v);
5539 __isl_give isl_pw_qpolynomial_fold *
5540 isl_pw_qpolynomial_fold_scale_val(
5541 __isl_take isl_pw_qpolynomial_fold *pwf,
5542 __isl_take isl_val *v);
5543 __isl_give isl_union_pw_qpolynomial_fold *
5544 isl_union_pw_qpolynomial_fold_scale_val(
5545 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5546 __isl_take isl_val *v);
5548 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5549 __isl_take isl_pw_qpolynomial_fold *pwf1,
5550 __isl_take isl_pw_qpolynomial_fold *pwf2);
5552 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5553 __isl_take isl_pw_qpolynomial_fold *pwf1,
5554 __isl_take isl_pw_qpolynomial_fold *pwf2);
5556 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5557 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5558 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5560 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5561 __isl_take isl_pw_qpolynomial_fold *pwf,
5562 __isl_take isl_point *pnt);
5564 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5565 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5566 __isl_take isl_point *pnt);
5568 __isl_give isl_pw_qpolynomial_fold *
5569 isl_pw_qpolynomial_fold_intersect_params(
5570 __isl_take isl_pw_qpolynomial_fold *pwf,
5571 __isl_take isl_set *set);
5573 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5574 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5575 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5576 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5577 __isl_take isl_union_set *uset);
5578 __isl_give isl_union_pw_qpolynomial_fold *
5579 isl_union_pw_qpolynomial_fold_intersect_params(
5580 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5581 __isl_take isl_set *set);
5583 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5584 __isl_take isl_pw_qpolynomial_fold *pwf);
5586 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5587 __isl_take isl_pw_qpolynomial_fold *pwf);
5589 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5590 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5592 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5593 __isl_take isl_qpolynomial_fold *fold,
5594 __isl_take isl_set *context);
5595 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5596 __isl_take isl_qpolynomial_fold *fold,
5597 __isl_take isl_set *context);
5599 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5600 __isl_take isl_pw_qpolynomial_fold *pwf,
5601 __isl_take isl_set *context);
5602 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5603 __isl_take isl_pw_qpolynomial_fold *pwf,
5604 __isl_take isl_set *context);
5606 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5607 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5608 __isl_take isl_union_set *context);
5609 __isl_give isl_union_pw_qpolynomial_fold *
5610 isl_union_pw_qpolynomial_fold_gist_params(
5611 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5612 __isl_take isl_set *context);
5614 The gist operation applies the gist operation to each of
5615 the cells in the domain of the input piecewise quasipolynomial reduction.
5616 In future, the operation will also exploit the context
5617 to simplify the quasipolynomial reductions associated to each cell.
5619 __isl_give isl_pw_qpolynomial_fold *
5620 isl_set_apply_pw_qpolynomial_fold(
5621 __isl_take isl_set *set,
5622 __isl_take isl_pw_qpolynomial_fold *pwf,
5624 __isl_give isl_pw_qpolynomial_fold *
5625 isl_map_apply_pw_qpolynomial_fold(
5626 __isl_take isl_map *map,
5627 __isl_take isl_pw_qpolynomial_fold *pwf,
5629 __isl_give isl_union_pw_qpolynomial_fold *
5630 isl_union_set_apply_union_pw_qpolynomial_fold(
5631 __isl_take isl_union_set *uset,
5632 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5634 __isl_give isl_union_pw_qpolynomial_fold *
5635 isl_union_map_apply_union_pw_qpolynomial_fold(
5636 __isl_take isl_union_map *umap,
5637 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5640 The functions taking a map
5641 compose the given map with the given piecewise quasipolynomial reduction.
5642 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5643 over all elements in the intersection of the range of the map
5644 and the domain of the piecewise quasipolynomial reduction
5645 as a function of an element in the domain of the map.
5646 The functions taking a set compute a bound over all elements in the
5647 intersection of the set and the domain of the
5648 piecewise quasipolynomial reduction.
5650 =head2 Parametric Vertex Enumeration
5652 The parametric vertex enumeration described in this section
5653 is mainly intended to be used internally and by the C<barvinok>
5656 #include <isl/vertices.h>
5657 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5658 __isl_keep isl_basic_set *bset);
5660 The function C<isl_basic_set_compute_vertices> performs the
5661 actual computation of the parametric vertices and the chamber
5662 decomposition and store the result in an C<isl_vertices> object.
5663 This information can be queried by either iterating over all
5664 the vertices or iterating over all the chambers or cells
5665 and then iterating over all vertices that are active on the chamber.
5667 int isl_vertices_foreach_vertex(
5668 __isl_keep isl_vertices *vertices,
5669 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5672 int isl_vertices_foreach_cell(
5673 __isl_keep isl_vertices *vertices,
5674 int (*fn)(__isl_take isl_cell *cell, void *user),
5676 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5677 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5680 Other operations that can be performed on an C<isl_vertices> object are
5683 isl_ctx *isl_vertices_get_ctx(
5684 __isl_keep isl_vertices *vertices);
5685 int isl_vertices_get_n_vertices(
5686 __isl_keep isl_vertices *vertices);
5687 void isl_vertices_free(__isl_take isl_vertices *vertices);
5689 Vertices can be inspected and destroyed using the following functions.
5691 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5692 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5693 __isl_give isl_basic_set *isl_vertex_get_domain(
5694 __isl_keep isl_vertex *vertex);
5695 __isl_give isl_multi_aff *isl_vertex_get_expr(
5696 __isl_keep isl_vertex *vertex);
5697 void isl_vertex_free(__isl_take isl_vertex *vertex);
5699 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
5700 describing the vertex in terms of the parameters,
5701 while C<isl_vertex_get_domain> returns the activity domain
5704 Chambers can be inspected and destroyed using the following functions.
5706 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5707 __isl_give isl_basic_set *isl_cell_get_domain(
5708 __isl_keep isl_cell *cell);
5709 void isl_cell_free(__isl_take isl_cell *cell);
5711 =head1 Polyhedral Compilation Library
5713 This section collects functionality in C<isl> that has been specifically
5714 designed for use during polyhedral compilation.
5716 =head2 Dependence Analysis
5718 C<isl> contains specialized functionality for performing
5719 array dataflow analysis. That is, given a I<sink> access relation
5720 and a collection of possible I<source> access relations,
5721 C<isl> can compute relations that describe
5722 for each iteration of the sink access, which iteration
5723 of which of the source access relations was the last
5724 to access the same data element before the given iteration
5726 The resulting dependence relations map source iterations
5727 to the corresponding sink iterations.
5728 To compute standard flow dependences, the sink should be
5729 a read, while the sources should be writes.
5730 If any of the source accesses are marked as being I<may>
5731 accesses, then there will be a dependence from the last
5732 I<must> access B<and> from any I<may> access that follows
5733 this last I<must> access.
5734 In particular, if I<all> sources are I<may> accesses,
5735 then memory based dependence analysis is performed.
5736 If, on the other hand, all sources are I<must> accesses,
5737 then value based dependence analysis is performed.
5739 #include <isl/flow.h>
5741 typedef int (*isl_access_level_before)(void *first, void *second);
5743 __isl_give isl_access_info *isl_access_info_alloc(
5744 __isl_take isl_map *sink,
5745 void *sink_user, isl_access_level_before fn,
5747 __isl_give isl_access_info *isl_access_info_add_source(
5748 __isl_take isl_access_info *acc,
5749 __isl_take isl_map *source, int must,
5751 __isl_null isl_access_info *isl_access_info_free(
5752 __isl_take isl_access_info *acc);
5754 __isl_give isl_flow *isl_access_info_compute_flow(
5755 __isl_take isl_access_info *acc);
5757 int isl_flow_foreach(__isl_keep isl_flow *deps,
5758 int (*fn)(__isl_take isl_map *dep, int must,
5759 void *dep_user, void *user),
5761 __isl_give isl_map *isl_flow_get_no_source(
5762 __isl_keep isl_flow *deps, int must);
5763 void isl_flow_free(__isl_take isl_flow *deps);
5765 The function C<isl_access_info_compute_flow> performs the actual
5766 dependence analysis. The other functions are used to construct
5767 the input for this function or to read off the output.
5769 The input is collected in an C<isl_access_info>, which can
5770 be created through a call to C<isl_access_info_alloc>.
5771 The arguments to this functions are the sink access relation
5772 C<sink>, a token C<sink_user> used to identify the sink
5773 access to the user, a callback function for specifying the
5774 relative order of source and sink accesses, and the number
5775 of source access relations that will be added.
5776 The callback function has type C<int (*)(void *first, void *second)>.
5777 The function is called with two user supplied tokens identifying
5778 either a source or the sink and it should return the shared nesting
5779 level and the relative order of the two accesses.
5780 In particular, let I<n> be the number of loops shared by
5781 the two accesses. If C<first> precedes C<second> textually,
5782 then the function should return I<2 * n + 1>; otherwise,
5783 it should return I<2 * n>.
5784 The sources can be added to the C<isl_access_info> by performing
5785 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5786 C<must> indicates whether the source is a I<must> access
5787 or a I<may> access. Note that a multi-valued access relation
5788 should only be marked I<must> if every iteration in the domain
5789 of the relation accesses I<all> elements in its image.
5790 The C<source_user> token is again used to identify
5791 the source access. The range of the source access relation
5792 C<source> should have the same dimension as the range
5793 of the sink access relation.
5794 The C<isl_access_info_free> function should usually not be
5795 called explicitly, because it is called implicitly by
5796 C<isl_access_info_compute_flow>.
5798 The result of the dependence analysis is collected in an
5799 C<isl_flow>. There may be elements of
5800 the sink access for which no preceding source access could be
5801 found or for which all preceding sources are I<may> accesses.
5802 The relations containing these elements can be obtained through
5803 calls to C<isl_flow_get_no_source>, the first with C<must> set
5804 and the second with C<must> unset.
5805 In the case of standard flow dependence analysis,
5806 with the sink a read and the sources I<must> writes,
5807 the first relation corresponds to the reads from uninitialized
5808 array elements and the second relation is empty.
5809 The actual flow dependences can be extracted using
5810 C<isl_flow_foreach>. This function will call the user-specified
5811 callback function C<fn> for each B<non-empty> dependence between
5812 a source and the sink. The callback function is called
5813 with four arguments, the actual flow dependence relation
5814 mapping source iterations to sink iterations, a boolean that
5815 indicates whether it is a I<must> or I<may> dependence, a token
5816 identifying the source and an additional C<void *> with value
5817 equal to the third argument of the C<isl_flow_foreach> call.
5818 A dependence is marked I<must> if it originates from a I<must>
5819 source and if it is not followed by any I<may> sources.
5821 After finishing with an C<isl_flow>, the user should call
5822 C<isl_flow_free> to free all associated memory.
5824 A higher-level interface to dependence analysis is provided
5825 by the following function.
5827 #include <isl/flow.h>
5829 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5830 __isl_take isl_union_map *must_source,
5831 __isl_take isl_union_map *may_source,
5832 __isl_take isl_union_map *schedule,
5833 __isl_give isl_union_map **must_dep,
5834 __isl_give isl_union_map **may_dep,
5835 __isl_give isl_union_map **must_no_source,
5836 __isl_give isl_union_map **may_no_source);
5838 The arrays are identified by the tuple names of the ranges
5839 of the accesses. The iteration domains by the tuple names
5840 of the domains of the accesses and of the schedule.
5841 The relative order of the iteration domains is given by the
5842 schedule. The relations returned through C<must_no_source>
5843 and C<may_no_source> are subsets of C<sink>.
5844 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5845 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5846 any of the other arguments is treated as an error.
5848 =head3 Interaction with Dependence Analysis
5850 During the dependence analysis, we frequently need to perform
5851 the following operation. Given a relation between sink iterations
5852 and potential source iterations from a particular source domain,
5853 what is the last potential source iteration corresponding to each
5854 sink iteration. It can sometimes be convenient to adjust
5855 the set of potential source iterations before or after each such operation.
5856 The prototypical example is fuzzy array dataflow analysis,
5857 where we need to analyze if, based on data-dependent constraints,
5858 the sink iteration can ever be executed without one or more of
5859 the corresponding potential source iterations being executed.
5860 If so, we can introduce extra parameters and select an unknown
5861 but fixed source iteration from the potential source iterations.
5862 To be able to perform such manipulations, C<isl> provides the following
5865 #include <isl/flow.h>
5867 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5868 __isl_keep isl_map *source_map,
5869 __isl_keep isl_set *sink, void *source_user,
5871 __isl_give isl_access_info *isl_access_info_set_restrict(
5872 __isl_take isl_access_info *acc,
5873 isl_access_restrict fn, void *user);
5875 The function C<isl_access_info_set_restrict> should be called
5876 before calling C<isl_access_info_compute_flow> and registers a callback function
5877 that will be called any time C<isl> is about to compute the last
5878 potential source. The first argument is the (reverse) proto-dependence,
5879 mapping sink iterations to potential source iterations.
5880 The second argument represents the sink iterations for which
5881 we want to compute the last source iteration.
5882 The third argument is the token corresponding to the source
5883 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5884 The callback is expected to return a restriction on either the input or
5885 the output of the operation computing the last potential source.
5886 If the input needs to be restricted then restrictions are needed
5887 for both the source and the sink iterations. The sink iterations
5888 and the potential source iterations will be intersected with these sets.
5889 If the output needs to be restricted then only a restriction on the source
5890 iterations is required.
5891 If any error occurs, the callback should return C<NULL>.
5892 An C<isl_restriction> object can be created, freed and inspected
5893 using the following functions.
5895 #include <isl/flow.h>
5897 __isl_give isl_restriction *isl_restriction_input(
5898 __isl_take isl_set *source_restr,
5899 __isl_take isl_set *sink_restr);
5900 __isl_give isl_restriction *isl_restriction_output(
5901 __isl_take isl_set *source_restr);
5902 __isl_give isl_restriction *isl_restriction_none(
5903 __isl_take isl_map *source_map);
5904 __isl_give isl_restriction *isl_restriction_empty(
5905 __isl_take isl_map *source_map);
5906 __isl_null isl_restriction *isl_restriction_free(
5907 __isl_take isl_restriction *restr);
5908 isl_ctx *isl_restriction_get_ctx(
5909 __isl_keep isl_restriction *restr);
5911 C<isl_restriction_none> and C<isl_restriction_empty> are special
5912 cases of C<isl_restriction_input>. C<isl_restriction_none>
5913 is essentially equivalent to
5915 isl_restriction_input(isl_set_universe(
5916 isl_space_range(isl_map_get_space(source_map))),
5918 isl_space_domain(isl_map_get_space(source_map))));
5920 whereas C<isl_restriction_empty> is essentially equivalent to
5922 isl_restriction_input(isl_set_empty(
5923 isl_space_range(isl_map_get_space(source_map))),
5925 isl_space_domain(isl_map_get_space(source_map))));
5929 B<The functionality described in this section is fairly new
5930 and may be subject to change.>
5932 #include <isl/schedule.h>
5933 __isl_give isl_schedule *
5934 isl_schedule_constraints_compute_schedule(
5935 __isl_take isl_schedule_constraints *sc);
5936 __isl_null isl_schedule *isl_schedule_free(
5937 __isl_take isl_schedule *sched);
5939 The function C<isl_schedule_constraints_compute_schedule> can be
5940 used to compute a schedule that satisfy the given schedule constraints.
5941 These schedule constraints include the iteration domain for which
5942 a schedule should be computed and dependences between pairs of
5943 iterations. In particular, these dependences include
5944 I<validity> dependences and I<proximity> dependences.
5945 By default, the algorithm used to construct the schedule is similar
5946 to that of C<Pluto>.
5947 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5949 The generated schedule respects all validity dependences.
5950 That is, all dependence distances over these dependences in the
5951 scheduled space are lexicographically positive.
5952 The default algorithm tries to ensure that the dependence distances
5953 over coincidence constraints are zero and to minimize the
5954 dependence distances over proximity dependences.
5955 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5956 for groups of domains where the dependence distances over validity
5957 dependences have only non-negative values.
5958 When using Feautrier's algorithm, the coincidence and proximity constraints
5959 are only taken into account during the extension to a
5960 full-dimensional schedule.
5962 An C<isl_schedule_constraints> object can be constructed
5963 and manipulated using the following functions.
5965 #include <isl/schedule.h>
5966 __isl_give isl_schedule_constraints *
5967 isl_schedule_constraints_copy(
5968 __isl_keep isl_schedule_constraints *sc);
5969 __isl_give isl_schedule_constraints *
5970 isl_schedule_constraints_on_domain(
5971 __isl_take isl_union_set *domain);
5972 isl_ctx *isl_schedule_constraints_get_ctx(
5973 __isl_keep isl_schedule_constraints *sc);
5974 __isl_give isl_schedule_constraints *
5975 isl_schedule_constraints_set_validity(
5976 __isl_take isl_schedule_constraints *sc,
5977 __isl_take isl_union_map *validity);
5978 __isl_give isl_schedule_constraints *
5979 isl_schedule_constraints_set_coincidence(
5980 __isl_take isl_schedule_constraints *sc,
5981 __isl_take isl_union_map *coincidence);
5982 __isl_give isl_schedule_constraints *
5983 isl_schedule_constraints_set_proximity(
5984 __isl_take isl_schedule_constraints *sc,
5985 __isl_take isl_union_map *proximity);
5986 __isl_give isl_schedule_constraints *
5987 isl_schedule_constraints_set_conditional_validity(
5988 __isl_take isl_schedule_constraints *sc,
5989 __isl_take isl_union_map *condition,
5990 __isl_take isl_union_map *validity);
5991 __isl_null isl_schedule_constraints *
5992 isl_schedule_constraints_free(
5993 __isl_take isl_schedule_constraints *sc);
5995 The initial C<isl_schedule_constraints> object created by
5996 C<isl_schedule_constraints_on_domain> does not impose any constraints.
5997 That is, it has an empty set of dependences.
5998 The function C<isl_schedule_constraints_set_validity> replaces the
5999 validity dependences, mapping domain elements I<i> to domain
6000 elements that should be scheduled after I<i>.
6001 The function C<isl_schedule_constraints_set_coincidence> replaces the
6002 coincidence dependences, mapping domain elements I<i> to domain
6003 elements that should be scheduled together with I<I>, if possible.
6004 The function C<isl_schedule_constraints_set_proximity> replaces the
6005 proximity dependences, mapping domain elements I<i> to domain
6006 elements that should be scheduled either before I<I>
6007 or as early as possible after I<i>.
6009 The function C<isl_schedule_constraints_set_conditional_validity>
6010 replaces the conditional validity constraints.
6011 A conditional validity constraint is only imposed when any of the corresponding
6012 conditions is satisfied, i.e., when any of them is non-zero.
6013 That is, the scheduler ensures that within each band if the dependence
6014 distances over the condition constraints are not all zero
6015 then all corresponding conditional validity constraints are respected.
6016 A conditional validity constraint corresponds to a condition
6017 if the two are adjacent, i.e., if the domain of one relation intersect
6018 the range of the other relation.
6019 The typical use case of conditional validity constraints is
6020 to allow order constraints between live ranges to be violated
6021 as long as the live ranges themselves are local to the band.
6022 To allow more fine-grained control over which conditions correspond
6023 to which conditional validity constraints, the domains and ranges
6024 of these relations may include I<tags>. That is, the domains and
6025 ranges of those relation may themselves be wrapped relations
6026 where the iteration domain appears in the domain of those wrapped relations
6027 and the range of the wrapped relations can be arbitrarily chosen
6028 by the user. Conditions and conditional validity constraints are only
6029 considere adjacent to each other if the entire wrapped relation matches.
6030 In particular, a relation with a tag will never be considered adjacent
6031 to a relation without a tag.
6033 The following function computes a schedule directly from
6034 an iteration domain and validity and proximity dependences
6035 and is implemented in terms of the functions described above.
6036 The use of C<isl_union_set_compute_schedule> is discouraged.
6038 #include <isl/schedule.h>
6039 __isl_give isl_schedule *isl_union_set_compute_schedule(
6040 __isl_take isl_union_set *domain,
6041 __isl_take isl_union_map *validity,
6042 __isl_take isl_union_map *proximity);
6044 A mapping from the domains to the scheduled space can be obtained
6045 from an C<isl_schedule> using the following function.
6047 __isl_give isl_union_map *isl_schedule_get_map(
6048 __isl_keep isl_schedule *sched);
6050 A representation of the schedule can be printed using
6052 __isl_give isl_printer *isl_printer_print_schedule(
6053 __isl_take isl_printer *p,
6054 __isl_keep isl_schedule *schedule);
6056 A representation of the schedule as a forest of bands can be obtained
6057 using the following function.
6059 __isl_give isl_band_list *isl_schedule_get_band_forest(
6060 __isl_keep isl_schedule *schedule);
6062 The individual bands can be visited in depth-first post-order
6063 using the following function.
6065 #include <isl/schedule.h>
6066 int isl_schedule_foreach_band(
6067 __isl_keep isl_schedule *sched,
6068 int (*fn)(__isl_keep isl_band *band, void *user),
6071 The list can be manipulated as explained in L<"Lists">.
6072 The bands inside the list can be copied and freed using the following
6075 #include <isl/band.h>
6076 __isl_give isl_band *isl_band_copy(
6077 __isl_keep isl_band *band);
6078 __isl_null isl_band *isl_band_free(
6079 __isl_take isl_band *band);
6081 Each band contains zero or more scheduling dimensions.
6082 These are referred to as the members of the band.
6083 The section of the schedule that corresponds to the band is
6084 referred to as the partial schedule of the band.
6085 For those nodes that participate in a band, the outer scheduling
6086 dimensions form the prefix schedule, while the inner scheduling
6087 dimensions form the suffix schedule.
6088 That is, if we take a cut of the band forest, then the union of
6089 the concatenations of the prefix, partial and suffix schedules of
6090 each band in the cut is equal to the entire schedule (modulo
6091 some possible padding at the end with zero scheduling dimensions).
6092 The properties of a band can be inspected using the following functions.
6094 #include <isl/band.h>
6095 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
6097 int isl_band_has_children(__isl_keep isl_band *band);
6098 __isl_give isl_band_list *isl_band_get_children(
6099 __isl_keep isl_band *band);
6101 __isl_give isl_union_map *isl_band_get_prefix_schedule(
6102 __isl_keep isl_band *band);
6103 __isl_give isl_union_map *isl_band_get_partial_schedule(
6104 __isl_keep isl_band *band);
6105 __isl_give isl_union_map *isl_band_get_suffix_schedule(
6106 __isl_keep isl_band *band);
6108 int isl_band_n_member(__isl_keep isl_band *band);
6109 int isl_band_member_is_coincident(
6110 __isl_keep isl_band *band, int pos);
6112 int isl_band_list_foreach_band(
6113 __isl_keep isl_band_list *list,
6114 int (*fn)(__isl_keep isl_band *band, void *user),
6117 Note that a scheduling dimension is considered to be ``coincident''
6118 if it satisfies the coincidence constraints within its band.
6119 That is, if the dependence distances of the coincidence
6120 constraints are all zero in that direction (for fixed
6121 iterations of outer bands).
6122 Like C<isl_schedule_foreach_band>,
6123 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
6124 in depth-first post-order.
6126 A band can be tiled using the following function.
6128 #include <isl/band.h>
6129 int isl_band_tile(__isl_keep isl_band *band,
6130 __isl_take isl_vec *sizes);
6132 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
6134 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
6135 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
6137 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
6139 The C<isl_band_tile> function tiles the band using the given tile sizes
6140 inside its schedule.
6141 A new child band is created to represent the point loops and it is
6142 inserted between the modified band and its children.
6143 The C<tile_scale_tile_loops> option specifies whether the tile
6144 loops iterators should be scaled by the tile sizes.
6145 If the C<tile_shift_point_loops> option is set, then the point loops
6146 are shifted to start at zero.
6148 A band can be split into two nested bands using the following function.
6150 int isl_band_split(__isl_keep isl_band *band, int pos);
6152 The resulting outer band contains the first C<pos> dimensions of C<band>
6153 while the inner band contains the remaining dimensions.
6155 A representation of the band can be printed using
6157 #include <isl/band.h>
6158 __isl_give isl_printer *isl_printer_print_band(
6159 __isl_take isl_printer *p,
6160 __isl_keep isl_band *band);
6164 #include <isl/schedule.h>
6165 int isl_options_set_schedule_max_coefficient(
6166 isl_ctx *ctx, int val);
6167 int isl_options_get_schedule_max_coefficient(
6169 int isl_options_set_schedule_max_constant_term(
6170 isl_ctx *ctx, int val);
6171 int isl_options_get_schedule_max_constant_term(
6173 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
6174 int isl_options_get_schedule_fuse(isl_ctx *ctx);
6175 int isl_options_set_schedule_maximize_band_depth(
6176 isl_ctx *ctx, int val);
6177 int isl_options_get_schedule_maximize_band_depth(
6179 int isl_options_set_schedule_outer_coincidence(
6180 isl_ctx *ctx, int val);
6181 int isl_options_get_schedule_outer_coincidence(
6183 int isl_options_set_schedule_split_scaled(
6184 isl_ctx *ctx, int val);
6185 int isl_options_get_schedule_split_scaled(
6187 int isl_options_set_schedule_algorithm(
6188 isl_ctx *ctx, int val);
6189 int isl_options_get_schedule_algorithm(
6191 int isl_options_set_schedule_separate_components(
6192 isl_ctx *ctx, int val);
6193 int isl_options_get_schedule_separate_components(
6198 =item * schedule_max_coefficient
6200 This option enforces that the coefficients for variable and parameter
6201 dimensions in the calculated schedule are not larger than the specified value.
6202 This option can significantly increase the speed of the scheduling calculation
6203 and may also prevent fusing of unrelated dimensions. A value of -1 means that
6204 this option does not introduce bounds on the variable or parameter
6207 =item * schedule_max_constant_term
6209 This option enforces that the constant coefficients in the calculated schedule
6210 are not larger than the maximal constant term. This option can significantly
6211 increase the speed of the scheduling calculation and may also prevent fusing of
6212 unrelated dimensions. A value of -1 means that this option does not introduce
6213 bounds on the constant coefficients.
6215 =item * schedule_fuse
6217 This option controls the level of fusion.
6218 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6219 resulting schedule will be distributed as much as possible.
6220 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6221 try to fuse loops in the resulting schedule.
6223 =item * schedule_maximize_band_depth
6225 If this option is set, we do not split bands at the point
6226 where we detect splitting is necessary. Instead, we
6227 backtrack and split bands as early as possible. This
6228 reduces the number of splits and maximizes the width of
6229 the bands. Wider bands give more possibilities for tiling.
6230 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6231 then bands will be split as early as possible, even if there is no need.
6232 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6234 =item * schedule_outer_coincidence
6236 If this option is set, then we try to construct schedules
6237 where the outermost scheduling dimension in each band
6238 satisfies the coincidence constraints.
6240 =item * schedule_split_scaled
6242 If this option is set, then we try to construct schedules in which the
6243 constant term is split off from the linear part if the linear parts of
6244 the scheduling rows for all nodes in the graphs have a common non-trivial
6246 The constant term is then placed in a separate band and the linear
6249 =item * schedule_algorithm
6251 Selects the scheduling algorithm to be used.
6252 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6253 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6255 =item * schedule_separate_components
6257 If at any point the dependence graph contains any (weakly connected) components,
6258 then these components are scheduled separately.
6259 If this option is not set, then some iterations of the domains
6260 in these components may be scheduled together.
6261 If this option is set, then the components are given consecutive
6266 =head2 AST Generation
6268 This section describes the C<isl> functionality for generating
6269 ASTs that visit all the elements
6270 in a domain in an order specified by a schedule.
6271 In particular, given a C<isl_union_map>, an AST is generated
6272 that visits all the elements in the domain of the C<isl_union_map>
6273 according to the lexicographic order of the corresponding image
6274 element(s). If the range of the C<isl_union_map> consists of
6275 elements in more than one space, then each of these spaces is handled
6276 separately in an arbitrary order.
6277 It should be noted that the image elements only specify the I<order>
6278 in which the corresponding domain elements should be visited.
6279 No direct relation between the image elements and the loop iterators
6280 in the generated AST should be assumed.
6282 Each AST is generated within a build. The initial build
6283 simply specifies the constraints on the parameters (if any)
6284 and can be created, inspected, copied and freed using the following functions.
6286 #include <isl/ast_build.h>
6287 __isl_give isl_ast_build *isl_ast_build_from_context(
6288 __isl_take isl_set *set);
6289 isl_ctx *isl_ast_build_get_ctx(
6290 __isl_keep isl_ast_build *build);
6291 __isl_give isl_ast_build *isl_ast_build_copy(
6292 __isl_keep isl_ast_build *build);
6293 __isl_null isl_ast_build *isl_ast_build_free(
6294 __isl_take isl_ast_build *build);
6296 The C<set> argument is usually a parameter set with zero or more parameters.
6297 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6298 and L</"Fine-grained Control over AST Generation">.
6299 Finally, the AST itself can be constructed using the following
6302 #include <isl/ast_build.h>
6303 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6304 __isl_keep isl_ast_build *build,
6305 __isl_take isl_union_map *schedule);
6307 =head3 Inspecting the AST
6309 The basic properties of an AST node can be obtained as follows.
6311 #include <isl/ast.h>
6312 isl_ctx *isl_ast_node_get_ctx(
6313 __isl_keep isl_ast_node *node);
6314 enum isl_ast_node_type isl_ast_node_get_type(
6315 __isl_keep isl_ast_node *node);
6317 The type of an AST node is one of
6318 C<isl_ast_node_for>,
6320 C<isl_ast_node_block> or
6321 C<isl_ast_node_user>.
6322 An C<isl_ast_node_for> represents a for node.
6323 An C<isl_ast_node_if> represents an if node.
6324 An C<isl_ast_node_block> represents a compound node.
6325 An C<isl_ast_node_user> represents an expression statement.
6326 An expression statement typically corresponds to a domain element, i.e.,
6327 one of the elements that is visited by the AST.
6329 Each type of node has its own additional properties.
6331 #include <isl/ast.h>
6332 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6333 __isl_keep isl_ast_node *node);
6334 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6335 __isl_keep isl_ast_node *node);
6336 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6337 __isl_keep isl_ast_node *node);
6338 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6339 __isl_keep isl_ast_node *node);
6340 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6341 __isl_keep isl_ast_node *node);
6342 int isl_ast_node_for_is_degenerate(
6343 __isl_keep isl_ast_node *node);
6345 An C<isl_ast_for> is considered degenerate if it is known to execute
6348 #include <isl/ast.h>
6349 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6350 __isl_keep isl_ast_node *node);
6351 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6352 __isl_keep isl_ast_node *node);
6353 int isl_ast_node_if_has_else(
6354 __isl_keep isl_ast_node *node);
6355 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6356 __isl_keep isl_ast_node *node);
6358 __isl_give isl_ast_node_list *
6359 isl_ast_node_block_get_children(
6360 __isl_keep isl_ast_node *node);
6362 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6363 __isl_keep isl_ast_node *node);
6365 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6366 the following functions.
6368 #include <isl/ast.h>
6369 isl_ctx *isl_ast_expr_get_ctx(
6370 __isl_keep isl_ast_expr *expr);
6371 enum isl_ast_expr_type isl_ast_expr_get_type(
6372 __isl_keep isl_ast_expr *expr);
6374 The type of an AST expression is one of
6376 C<isl_ast_expr_id> or
6377 C<isl_ast_expr_int>.
6378 An C<isl_ast_expr_op> represents the result of an operation.
6379 An C<isl_ast_expr_id> represents an identifier.
6380 An C<isl_ast_expr_int> represents an integer value.
6382 Each type of expression has its own additional properties.
6384 #include <isl/ast.h>
6385 enum isl_ast_op_type isl_ast_expr_get_op_type(
6386 __isl_keep isl_ast_expr *expr);
6387 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6388 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6389 __isl_keep isl_ast_expr *expr, int pos);
6390 int isl_ast_node_foreach_ast_op_type(
6391 __isl_keep isl_ast_node *node,
6392 int (*fn)(enum isl_ast_op_type type, void *user),
6395 C<isl_ast_expr_get_op_type> returns the type of the operation
6396 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6397 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6399 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6400 C<isl_ast_op_type> that appears in C<node>.
6401 The operation type is one of the following.
6405 =item C<isl_ast_op_and>
6407 Logical I<and> of two arguments.
6408 Both arguments can be evaluated.
6410 =item C<isl_ast_op_and_then>
6412 Logical I<and> of two arguments.
6413 The second argument can only be evaluated if the first evaluates to true.
6415 =item C<isl_ast_op_or>
6417 Logical I<or> of two arguments.
6418 Both arguments can be evaluated.
6420 =item C<isl_ast_op_or_else>
6422 Logical I<or> of two arguments.
6423 The second argument can only be evaluated if the first evaluates to false.
6425 =item C<isl_ast_op_max>
6427 Maximum of two or more arguments.
6429 =item C<isl_ast_op_min>
6431 Minimum of two or more arguments.
6433 =item C<isl_ast_op_minus>
6437 =item C<isl_ast_op_add>
6439 Sum of two arguments.
6441 =item C<isl_ast_op_sub>
6443 Difference of two arguments.
6445 =item C<isl_ast_op_mul>
6447 Product of two arguments.
6449 =item C<isl_ast_op_div>
6451 Exact division. That is, the result is known to be an integer.
6453 =item C<isl_ast_op_fdiv_q>
6455 Result of integer division, rounded towards negative
6458 =item C<isl_ast_op_pdiv_q>
6460 Result of integer division, where dividend is known to be non-negative.
6462 =item C<isl_ast_op_pdiv_r>
6464 Remainder of integer division, where dividend is known to be non-negative.
6466 =item C<isl_ast_op_cond>
6468 Conditional operator defined on three arguments.
6469 If the first argument evaluates to true, then the result
6470 is equal to the second argument. Otherwise, the result
6471 is equal to the third argument.
6472 The second and third argument may only be evaluated if
6473 the first argument evaluates to true and false, respectively.
6474 Corresponds to C<a ? b : c> in C.
6476 =item C<isl_ast_op_select>
6478 Conditional operator defined on three arguments.
6479 If the first argument evaluates to true, then the result
6480 is equal to the second argument. Otherwise, the result
6481 is equal to the third argument.
6482 The second and third argument may be evaluated independently
6483 of the value of the first argument.
6484 Corresponds to C<a * b + (1 - a) * c> in C.
6486 =item C<isl_ast_op_eq>
6490 =item C<isl_ast_op_le>
6492 Less than or equal relation.
6494 =item C<isl_ast_op_lt>
6498 =item C<isl_ast_op_ge>
6500 Greater than or equal relation.
6502 =item C<isl_ast_op_gt>
6504 Greater than relation.
6506 =item C<isl_ast_op_call>
6509 The number of arguments of the C<isl_ast_expr> is one more than
6510 the number of arguments in the function call, the first argument
6511 representing the function being called.
6513 =item C<isl_ast_op_access>
6516 The number of arguments of the C<isl_ast_expr> is one more than
6517 the number of index expressions in the array access, the first argument
6518 representing the array being accessed.
6520 =item C<isl_ast_op_member>
6523 This operation has two arguments, a structure and the name of
6524 the member of the structure being accessed.
6528 #include <isl/ast.h>
6529 __isl_give isl_id *isl_ast_expr_get_id(
6530 __isl_keep isl_ast_expr *expr);
6532 Return the identifier represented by the AST expression.
6534 #include <isl/ast.h>
6535 __isl_give isl_val *isl_ast_expr_get_val(
6536 __isl_keep isl_ast_expr *expr);
6538 Return the integer represented by the AST expression.
6540 =head3 Properties of ASTs
6542 #include <isl/ast.h>
6543 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6544 __isl_keep isl_ast_expr *expr2);
6546 Check if two C<isl_ast_expr>s are equal to each other.
6548 =head3 Manipulating and printing the AST
6550 AST nodes can be copied and freed using the following functions.
6552 #include <isl/ast.h>
6553 __isl_give isl_ast_node *isl_ast_node_copy(
6554 __isl_keep isl_ast_node *node);
6555 __isl_null isl_ast_node *isl_ast_node_free(
6556 __isl_take isl_ast_node *node);
6558 AST expressions can be copied and freed using the following functions.
6560 #include <isl/ast.h>
6561 __isl_give isl_ast_expr *isl_ast_expr_copy(
6562 __isl_keep isl_ast_expr *expr);
6563 __isl_null isl_ast_expr *isl_ast_expr_free(
6564 __isl_take isl_ast_expr *expr);
6566 New AST expressions can be created either directly or within
6567 the context of an C<isl_ast_build>.
6569 #include <isl/ast.h>
6570 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6571 __isl_take isl_val *v);
6572 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6573 __isl_take isl_id *id);
6574 __isl_give isl_ast_expr *isl_ast_expr_neg(
6575 __isl_take isl_ast_expr *expr);
6576 __isl_give isl_ast_expr *isl_ast_expr_add(
6577 __isl_take isl_ast_expr *expr1,
6578 __isl_take isl_ast_expr *expr2);
6579 __isl_give isl_ast_expr *isl_ast_expr_sub(
6580 __isl_take isl_ast_expr *expr1,
6581 __isl_take isl_ast_expr *expr2);
6582 __isl_give isl_ast_expr *isl_ast_expr_mul(
6583 __isl_take isl_ast_expr *expr1,
6584 __isl_take isl_ast_expr *expr2);
6585 __isl_give isl_ast_expr *isl_ast_expr_div(
6586 __isl_take isl_ast_expr *expr1,
6587 __isl_take isl_ast_expr *expr2);
6588 __isl_give isl_ast_expr *isl_ast_expr_and(
6589 __isl_take isl_ast_expr *expr1,
6590 __isl_take isl_ast_expr *expr2)
6591 __isl_give isl_ast_expr *isl_ast_expr_or(
6592 __isl_take isl_ast_expr *expr1,
6593 __isl_take isl_ast_expr *expr2)
6594 __isl_give isl_ast_expr *isl_ast_expr_access(
6595 __isl_take isl_ast_expr *array,
6596 __isl_take isl_ast_expr_list *indices);
6598 #include <isl/ast_build.h>
6599 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6600 __isl_keep isl_ast_build *build,
6601 __isl_take isl_pw_aff *pa);
6602 __isl_give isl_ast_expr *
6603 isl_ast_build_access_from_pw_multi_aff(
6604 __isl_keep isl_ast_build *build,
6605 __isl_take isl_pw_multi_aff *pma);
6606 __isl_give isl_ast_expr *
6607 isl_ast_build_access_from_multi_pw_aff(
6608 __isl_keep isl_ast_build *build,
6609 __isl_take isl_multi_pw_aff *mpa);
6610 __isl_give isl_ast_expr *
6611 isl_ast_build_call_from_pw_multi_aff(
6612 __isl_keep isl_ast_build *build,
6613 __isl_take isl_pw_multi_aff *pma);
6614 __isl_give isl_ast_expr *
6615 isl_ast_build_call_from_multi_pw_aff(
6616 __isl_keep isl_ast_build *build,
6617 __isl_take isl_multi_pw_aff *mpa);
6619 The domains of C<pa>, C<mpa> and C<pma> should correspond
6620 to the schedule space of C<build>.
6621 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6622 the function being called.
6623 If the accessed space is a nested relation, then it is taken
6624 to represent an access of the member specified by the range
6625 of this nested relation of the structure specified by the domain
6626 of the nested relation.
6628 The following functions can be used to modify an C<isl_ast_expr>.
6630 #include <isl/ast.h>
6631 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6632 __isl_take isl_ast_expr *expr, int pos,
6633 __isl_take isl_ast_expr *arg);
6635 Replace the argument of C<expr> at position C<pos> by C<arg>.
6637 #include <isl/ast.h>
6638 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6639 __isl_take isl_ast_expr *expr,
6640 __isl_take isl_id_to_ast_expr *id2expr);
6642 The function C<isl_ast_expr_substitute_ids> replaces the
6643 subexpressions of C<expr> of type C<isl_ast_expr_id>
6644 by the corresponding expression in C<id2expr>, if there is any.
6647 User specified data can be attached to an C<isl_ast_node> and obtained
6648 from the same C<isl_ast_node> using the following functions.
6650 #include <isl/ast.h>
6651 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6652 __isl_take isl_ast_node *node,
6653 __isl_take isl_id *annotation);
6654 __isl_give isl_id *isl_ast_node_get_annotation(
6655 __isl_keep isl_ast_node *node);
6657 Basic printing can be performed using the following functions.
6659 #include <isl/ast.h>
6660 __isl_give isl_printer *isl_printer_print_ast_expr(
6661 __isl_take isl_printer *p,
6662 __isl_keep isl_ast_expr *expr);
6663 __isl_give isl_printer *isl_printer_print_ast_node(
6664 __isl_take isl_printer *p,
6665 __isl_keep isl_ast_node *node);
6667 More advanced printing can be performed using the following functions.
6669 #include <isl/ast.h>
6670 __isl_give isl_printer *isl_ast_op_type_print_macro(
6671 enum isl_ast_op_type type,
6672 __isl_take isl_printer *p);
6673 __isl_give isl_printer *isl_ast_node_print_macros(
6674 __isl_keep isl_ast_node *node,
6675 __isl_take isl_printer *p);
6676 __isl_give isl_printer *isl_ast_node_print(
6677 __isl_keep isl_ast_node *node,
6678 __isl_take isl_printer *p,
6679 __isl_take isl_ast_print_options *options);
6680 __isl_give isl_printer *isl_ast_node_for_print(
6681 __isl_keep isl_ast_node *node,
6682 __isl_take isl_printer *p,
6683 __isl_take isl_ast_print_options *options);
6684 __isl_give isl_printer *isl_ast_node_if_print(
6685 __isl_keep isl_ast_node *node,
6686 __isl_take isl_printer *p,
6687 __isl_take isl_ast_print_options *options);
6689 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6690 C<isl> may print out an AST that makes use of macros such
6691 as C<floord>, C<min> and C<max>.
6692 C<isl_ast_op_type_print_macro> prints out the macro
6693 corresponding to a specific C<isl_ast_op_type>.
6694 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6695 for expressions where these macros would be used and prints
6696 out the required macro definitions.
6697 Essentially, C<isl_ast_node_print_macros> calls
6698 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6699 as function argument.
6700 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6701 C<isl_ast_node_if_print> print an C<isl_ast_node>
6702 in C<ISL_FORMAT_C>, but allow for some extra control
6703 through an C<isl_ast_print_options> object.
6704 This object can be created using the following functions.
6706 #include <isl/ast.h>
6707 __isl_give isl_ast_print_options *
6708 isl_ast_print_options_alloc(isl_ctx *ctx);
6709 __isl_give isl_ast_print_options *
6710 isl_ast_print_options_copy(
6711 __isl_keep isl_ast_print_options *options);
6712 __isl_null isl_ast_print_options *
6713 isl_ast_print_options_free(
6714 __isl_take isl_ast_print_options *options);
6716 __isl_give isl_ast_print_options *
6717 isl_ast_print_options_set_print_user(
6718 __isl_take isl_ast_print_options *options,
6719 __isl_give isl_printer *(*print_user)(
6720 __isl_take isl_printer *p,
6721 __isl_take isl_ast_print_options *options,
6722 __isl_keep isl_ast_node *node, void *user),
6724 __isl_give isl_ast_print_options *
6725 isl_ast_print_options_set_print_for(
6726 __isl_take isl_ast_print_options *options,
6727 __isl_give isl_printer *(*print_for)(
6728 __isl_take isl_printer *p,
6729 __isl_take isl_ast_print_options *options,
6730 __isl_keep isl_ast_node *node, void *user),
6733 The callback set by C<isl_ast_print_options_set_print_user>
6734 is called whenever a node of type C<isl_ast_node_user> needs to
6736 The callback set by C<isl_ast_print_options_set_print_for>
6737 is called whenever a node of type C<isl_ast_node_for> needs to
6739 Note that C<isl_ast_node_for_print> will I<not> call the
6740 callback set by C<isl_ast_print_options_set_print_for> on the node
6741 on which C<isl_ast_node_for_print> is called, but only on nested
6742 nodes of type C<isl_ast_node_for>. It is therefore safe to
6743 call C<isl_ast_node_for_print> from within the callback set by
6744 C<isl_ast_print_options_set_print_for>.
6746 The following option determines the type to be used for iterators
6747 while printing the AST.
6749 int isl_options_set_ast_iterator_type(
6750 isl_ctx *ctx, const char *val);
6751 const char *isl_options_get_ast_iterator_type(
6756 #include <isl/ast_build.h>
6757 int isl_options_set_ast_build_atomic_upper_bound(
6758 isl_ctx *ctx, int val);
6759 int isl_options_get_ast_build_atomic_upper_bound(
6761 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6763 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6764 int isl_options_set_ast_build_exploit_nested_bounds(
6765 isl_ctx *ctx, int val);
6766 int isl_options_get_ast_build_exploit_nested_bounds(
6768 int isl_options_set_ast_build_group_coscheduled(
6769 isl_ctx *ctx, int val);
6770 int isl_options_get_ast_build_group_coscheduled(
6772 int isl_options_set_ast_build_scale_strides(
6773 isl_ctx *ctx, int val);
6774 int isl_options_get_ast_build_scale_strides(
6776 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6778 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6779 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6781 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6785 =item * ast_build_atomic_upper_bound
6787 Generate loop upper bounds that consist of the current loop iterator,
6788 an operator and an expression not involving the iterator.
6789 If this option is not set, then the current loop iterator may appear
6790 several times in the upper bound.
6791 For example, when this option is turned off, AST generation
6794 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6798 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6801 When the option is turned on, the following AST is generated
6803 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6806 =item * ast_build_prefer_pdiv
6808 If this option is turned off, then the AST generation will
6809 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6810 operators, but no C<isl_ast_op_pdiv_q> or
6811 C<isl_ast_op_pdiv_r> operators.
6812 If this options is turned on, then C<isl> will try to convert
6813 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6814 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6816 =item * ast_build_exploit_nested_bounds
6818 Simplify conditions based on bounds of nested for loops.
6819 In particular, remove conditions that are implied by the fact
6820 that one or more nested loops have at least one iteration,
6821 meaning that the upper bound is at least as large as the lower bound.
6822 For example, when this option is turned off, AST generation
6825 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6831 for (int c0 = 0; c0 <= N; c0 += 1)
6832 for (int c1 = 0; c1 <= M; c1 += 1)
6835 When the option is turned on, the following AST is generated
6837 for (int c0 = 0; c0 <= N; c0 += 1)
6838 for (int c1 = 0; c1 <= M; c1 += 1)
6841 =item * ast_build_group_coscheduled
6843 If two domain elements are assigned the same schedule point, then
6844 they may be executed in any order and they may even appear in different
6845 loops. If this options is set, then the AST generator will make
6846 sure that coscheduled domain elements do not appear in separate parts
6847 of the AST. This is useful in case of nested AST generation
6848 if the outer AST generation is given only part of a schedule
6849 and the inner AST generation should handle the domains that are
6850 coscheduled by this initial part of the schedule together.
6851 For example if an AST is generated for a schedule
6853 { A[i] -> [0]; B[i] -> [0] }
6855 then the C<isl_ast_build_set_create_leaf> callback described
6856 below may get called twice, once for each domain.
6857 Setting this option ensures that the callback is only called once
6858 on both domains together.
6860 =item * ast_build_separation_bounds
6862 This option specifies which bounds to use during separation.
6863 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6864 then all (possibly implicit) bounds on the current dimension will
6865 be used during separation.
6866 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6867 then only those bounds that are explicitly available will
6868 be used during separation.
6870 =item * ast_build_scale_strides
6872 This option specifies whether the AST generator is allowed
6873 to scale down iterators of strided loops.
6875 =item * ast_build_allow_else
6877 This option specifies whether the AST generator is allowed
6878 to construct if statements with else branches.
6880 =item * ast_build_allow_or
6882 This option specifies whether the AST generator is allowed
6883 to construct if conditions with disjunctions.
6887 =head3 Fine-grained Control over AST Generation
6889 Besides specifying the constraints on the parameters,
6890 an C<isl_ast_build> object can be used to control
6891 various aspects of the AST generation process.
6892 The most prominent way of control is through ``options'',
6893 which can be set using the following function.
6895 #include <isl/ast_build.h>
6896 __isl_give isl_ast_build *
6897 isl_ast_build_set_options(
6898 __isl_take isl_ast_build *control,
6899 __isl_take isl_union_map *options);
6901 The options are encoded in an <isl_union_map>.
6902 The domain of this union relation refers to the schedule domain,
6903 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6904 In the case of nested AST generation (see L</"Nested AST Generation">),
6905 the domain of C<options> should refer to the extra piece of the schedule.
6906 That is, it should be equal to the range of the wrapped relation in the
6907 range of the schedule.
6908 The range of the options can consist of elements in one or more spaces,
6909 the names of which determine the effect of the option.
6910 The values of the range typically also refer to the schedule dimension
6911 to which the option applies. In case of nested AST generation
6912 (see L</"Nested AST Generation">), these values refer to the position
6913 of the schedule dimension within the innermost AST generation.
6914 The constraints on the domain elements of
6915 the option should only refer to this dimension and earlier dimensions.
6916 We consider the following spaces.
6920 =item C<separation_class>
6922 This space is a wrapped relation between two one dimensional spaces.
6923 The input space represents the schedule dimension to which the option
6924 applies and the output space represents the separation class.
6925 While constructing a loop corresponding to the specified schedule
6926 dimension(s), the AST generator will try to generate separate loops
6927 for domain elements that are assigned different classes.
6928 If only some of the elements are assigned a class, then those elements
6929 that are not assigned any class will be treated as belonging to a class
6930 that is separate from the explicitly assigned classes.
6931 The typical use case for this option is to separate full tiles from
6933 The other options, described below, are applied after the separation
6936 As an example, consider the separation into full and partial tiles
6937 of a tiling of a triangular domain.
6938 Take, for example, the domain
6940 { A[i,j] : 0 <= i,j and i + j <= 100 }
6942 and a tiling into tiles of 10 by 10. The input to the AST generator
6943 is then the schedule
6945 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6948 Without any options, the following AST is generated
6950 for (int c0 = 0; c0 <= 10; c0 += 1)
6951 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6952 for (int c2 = 10 * c0;
6953 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6955 for (int c3 = 10 * c1;
6956 c3 <= min(10 * c1 + 9, -c2 + 100);
6960 Separation into full and partial tiles can be obtained by assigning
6961 a class, say C<0>, to the full tiles. The full tiles are represented by those
6962 values of the first and second schedule dimensions for which there are
6963 values of the third and fourth dimensions to cover an entire tile.
6964 That is, we need to specify the following option
6966 { [a,b,c,d] -> separation_class[[0]->[0]] :
6967 exists b': 0 <= 10a,10b' and
6968 10a+9+10b'+9 <= 100;
6969 [a,b,c,d] -> separation_class[[1]->[0]] :
6970 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6974 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6975 a >= 0 and b >= 0 and b <= 8 - a;
6976 [a, b, c, d] -> separation_class[[0] -> [0]] :
6979 With this option, the generated AST is as follows
6982 for (int c0 = 0; c0 <= 8; c0 += 1) {
6983 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6984 for (int c2 = 10 * c0;
6985 c2 <= 10 * c0 + 9; c2 += 1)
6986 for (int c3 = 10 * c1;
6987 c3 <= 10 * c1 + 9; c3 += 1)
6989 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6990 for (int c2 = 10 * c0;
6991 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6993 for (int c3 = 10 * c1;
6994 c3 <= min(-c2 + 100, 10 * c1 + 9);
6998 for (int c0 = 9; c0 <= 10; c0 += 1)
6999 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
7000 for (int c2 = 10 * c0;
7001 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7003 for (int c3 = 10 * c1;
7004 c3 <= min(10 * c1 + 9, -c2 + 100);
7011 This is a single-dimensional space representing the schedule dimension(s)
7012 to which ``separation'' should be applied. Separation tries to split
7013 a loop into several pieces if this can avoid the generation of guards
7015 See also the C<atomic> option.
7019 This is a single-dimensional space representing the schedule dimension(s)
7020 for which the domains should be considered ``atomic''. That is, the
7021 AST generator will make sure that any given domain space will only appear
7022 in a single loop at the specified level.
7024 Consider the following schedule
7026 { a[i] -> [i] : 0 <= i < 10;
7027 b[i] -> [i+1] : 0 <= i < 10 }
7029 If the following option is specified
7031 { [i] -> separate[x] }
7033 then the following AST will be generated
7037 for (int c0 = 1; c0 <= 9; c0 += 1) {
7044 If, on the other hand, the following option is specified
7046 { [i] -> atomic[x] }
7048 then the following AST will be generated
7050 for (int c0 = 0; c0 <= 10; c0 += 1) {
7057 If neither C<atomic> nor C<separate> is specified, then the AST generator
7058 may produce either of these two results or some intermediate form.
7062 This is a single-dimensional space representing the schedule dimension(s)
7063 that should be I<completely> unrolled.
7064 To obtain a partial unrolling, the user should apply an additional
7065 strip-mining to the schedule and fully unroll the inner loop.
7069 Additional control is available through the following functions.
7071 #include <isl/ast_build.h>
7072 __isl_give isl_ast_build *
7073 isl_ast_build_set_iterators(
7074 __isl_take isl_ast_build *control,
7075 __isl_take isl_id_list *iterators);
7077 The function C<isl_ast_build_set_iterators> allows the user to
7078 specify a list of iterator C<isl_id>s to be used as iterators.
7079 If the input schedule is injective, then
7080 the number of elements in this list should be as large as the dimension
7081 of the schedule space, but no direct correspondence should be assumed
7082 between dimensions and elements.
7083 If the input schedule is not injective, then an additional number
7084 of C<isl_id>s equal to the largest dimension of the input domains
7086 If the number of provided C<isl_id>s is insufficient, then additional
7087 names are automatically generated.
7089 #include <isl/ast_build.h>
7090 __isl_give isl_ast_build *
7091 isl_ast_build_set_create_leaf(
7092 __isl_take isl_ast_build *control,
7093 __isl_give isl_ast_node *(*fn)(
7094 __isl_take isl_ast_build *build,
7095 void *user), void *user);
7098 C<isl_ast_build_set_create_leaf> function allows for the
7099 specification of a callback that should be called whenever the AST
7100 generator arrives at an element of the schedule domain.
7101 The callback should return an AST node that should be inserted
7102 at the corresponding position of the AST. The default action (when
7103 the callback is not set) is to continue generating parts of the AST to scan
7104 all the domain elements associated to the schedule domain element
7105 and to insert user nodes, ``calling'' the domain element, for each of them.
7106 The C<build> argument contains the current state of the C<isl_ast_build>.
7107 To ease nested AST generation (see L</"Nested AST Generation">),
7108 all control information that is
7109 specific to the current AST generation such as the options and
7110 the callbacks has been removed from this C<isl_ast_build>.
7111 The callback would typically return the result of a nested
7113 user defined node created using the following function.
7115 #include <isl/ast.h>
7116 __isl_give isl_ast_node *isl_ast_node_alloc_user(
7117 __isl_take isl_ast_expr *expr);
7119 #include <isl/ast_build.h>
7120 __isl_give isl_ast_build *
7121 isl_ast_build_set_at_each_domain(
7122 __isl_take isl_ast_build *build,
7123 __isl_give isl_ast_node *(*fn)(
7124 __isl_take isl_ast_node *node,
7125 __isl_keep isl_ast_build *build,
7126 void *user), void *user);
7127 __isl_give isl_ast_build *
7128 isl_ast_build_set_before_each_for(
7129 __isl_take isl_ast_build *build,
7130 __isl_give isl_id *(*fn)(
7131 __isl_keep isl_ast_build *build,
7132 void *user), void *user);
7133 __isl_give isl_ast_build *
7134 isl_ast_build_set_after_each_for(
7135 __isl_take isl_ast_build *build,
7136 __isl_give isl_ast_node *(*fn)(
7137 __isl_take isl_ast_node *node,
7138 __isl_keep isl_ast_build *build,
7139 void *user), void *user);
7141 The callback set by C<isl_ast_build_set_at_each_domain> will
7142 be called for each domain AST node.
7143 The callbacks set by C<isl_ast_build_set_before_each_for>
7144 and C<isl_ast_build_set_after_each_for> will be called
7145 for each for AST node. The first will be called in depth-first
7146 pre-order, while the second will be called in depth-first post-order.
7147 Since C<isl_ast_build_set_before_each_for> is called before the for
7148 node is actually constructed, it is only passed an C<isl_ast_build>.
7149 The returned C<isl_id> will be added as an annotation (using
7150 C<isl_ast_node_set_annotation>) to the constructed for node.
7151 In particular, if the user has also specified an C<after_each_for>
7152 callback, then the annotation can be retrieved from the node passed to
7153 that callback using C<isl_ast_node_get_annotation>.
7154 All callbacks should C<NULL> on failure.
7155 The given C<isl_ast_build> can be used to create new
7156 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
7157 or C<isl_ast_build_call_from_pw_multi_aff>.
7159 =head3 Nested AST Generation
7161 C<isl> allows the user to create an AST within the context
7162 of another AST. These nested ASTs are created using the
7163 same C<isl_ast_build_ast_from_schedule> function that is used to create the
7164 outer AST. The C<build> argument should be an C<isl_ast_build>
7165 passed to a callback set by
7166 C<isl_ast_build_set_create_leaf>.
7167 The space of the range of the C<schedule> argument should refer
7168 to this build. In particular, the space should be a wrapped
7169 relation and the domain of this wrapped relation should be the
7170 same as that of the range of the schedule returned by
7171 C<isl_ast_build_get_schedule> below.
7172 In practice, the new schedule is typically
7173 created by calling C<isl_union_map_range_product> on the old schedule
7174 and some extra piece of the schedule.
7175 The space of the schedule domain is also available from
7176 the C<isl_ast_build>.
7178 #include <isl/ast_build.h>
7179 __isl_give isl_union_map *isl_ast_build_get_schedule(
7180 __isl_keep isl_ast_build *build);
7181 __isl_give isl_space *isl_ast_build_get_schedule_space(
7182 __isl_keep isl_ast_build *build);
7183 __isl_give isl_ast_build *isl_ast_build_restrict(
7184 __isl_take isl_ast_build *build,
7185 __isl_take isl_set *set);
7187 The C<isl_ast_build_get_schedule> function returns a (partial)
7188 schedule for the domains elements for which part of the AST still needs to
7189 be generated in the current build.
7190 In particular, the domain elements are mapped to those iterations of the loops
7191 enclosing the current point of the AST generation inside which
7192 the domain elements are executed.
7193 No direct correspondence between
7194 the input schedule and this schedule should be assumed.
7195 The space obtained from C<isl_ast_build_get_schedule_space> can be used
7196 to create a set for C<isl_ast_build_restrict> to intersect
7197 with the current build. In particular, the set passed to
7198 C<isl_ast_build_restrict> can have additional parameters.
7199 The ids of the set dimensions in the space returned by
7200 C<isl_ast_build_get_schedule_space> correspond to the
7201 iterators of the already generated loops.
7202 The user should not rely on the ids of the output dimensions
7203 of the relations in the union relation returned by
7204 C<isl_ast_build_get_schedule> having any particular value.
7208 Although C<isl> is mainly meant to be used as a library,
7209 it also contains some basic applications that use some
7210 of the functionality of C<isl>.
7211 The input may be specified in either the L<isl format>
7212 or the L<PolyLib format>.
7214 =head2 C<isl_polyhedron_sample>
7216 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7217 an integer element of the polyhedron, if there is any.
7218 The first column in the output is the denominator and is always
7219 equal to 1. If the polyhedron contains no integer points,
7220 then a vector of length zero is printed.
7224 C<isl_pip> takes the same input as the C<example> program
7225 from the C<piplib> distribution, i.e., a set of constraints
7226 on the parameters, a line containing only -1 and finally a set
7227 of constraints on a parametric polyhedron.
7228 The coefficients of the parameters appear in the last columns
7229 (but before the final constant column).
7230 The output is the lexicographic minimum of the parametric polyhedron.
7231 As C<isl> currently does not have its own output format, the output
7232 is just a dump of the internal state.
7234 =head2 C<isl_polyhedron_minimize>
7236 C<isl_polyhedron_minimize> computes the minimum of some linear
7237 or affine objective function over the integer points in a polyhedron.
7238 If an affine objective function
7239 is given, then the constant should appear in the last column.
7241 =head2 C<isl_polytope_scan>
7243 Given a polytope, C<isl_polytope_scan> prints
7244 all integer points in the polytope.
7246 =head2 C<isl_codegen>
7248 Given a schedule, a context set and an options relation,
7249 C<isl_codegen> prints out an AST that scans the domain elements
7250 of the schedule in the order of their image(s) taking into account
7251 the constraints in the context set.