3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
8 using C<GMP> or C<imath>.
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
184 =head3 Changes since isl-0.12
188 =item * C<isl_int> has been replaced by C<isl_val>.
189 Some of the old functions are still available in C<isl/deprecated/*.h>
190 but they will be removed in the future.
192 =item * The functions C<isl_pw_qpolynomial_eval>,
193 C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval>
194 and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return
195 an C<isl_val> instead of an C<isl_qpolynomial>.
197 =item * The function C<isl_band_member_is_zero_distance>
198 has been removed. Essentially the same functionality is available
199 through C<isl_band_member_is_coincident>, except that is requires
200 setting up coincidence constraints.
201 The option C<schedule_outer_zero_distance> has accordingly been
202 replaced by the option C<schedule_outer_coincidence>.
204 =item * The function C<isl_vertex_get_expr> has been changed
205 to return an C<isl_multi_aff> instead of a rational C<isl_basic_set>.
206 The function C<isl_vertex_get_domain> has been changed to return
207 a regular basic set, rather than a rational basic set.
213 C<isl> is released under the MIT license.
217 Permission is hereby granted, free of charge, to any person obtaining a copy of
218 this software and associated documentation files (the "Software"), to deal in
219 the Software without restriction, including without limitation the rights to
220 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
221 of the Software, and to permit persons to whom the Software is furnished to do
222 so, subject to the following conditions:
224 The above copyright notice and this permission notice shall be included in all
225 copies or substantial portions of the Software.
227 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
228 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
229 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
230 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
231 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
232 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
237 Note that by default C<isl> requires C<GMP>, which is released
238 under the GNU Lesser General Public License (LGPL). This means
239 that code linked against C<isl> is also linked against LGPL code.
241 When configuring with C<--with-int=imath>, C<isl> will link against C<imath>, a
242 library for exact integer arithmetic released under the MIT license.
246 The source of C<isl> can be obtained either as a tarball
247 or from the git repository. Both are available from
248 L<http://freshmeat.net/projects/isl/>.
249 The installation process depends on how you obtained
252 =head2 Installation from the git repository
256 =item 1 Clone or update the repository
258 The first time the source is obtained, you need to clone
261 git clone git://repo.or.cz/isl.git
263 To obtain updates, you need to pull in the latest changes
267 =item 2 Optionally get C<imath> submodule
269 To build C<isl> with C<imath>, you need to obtain the C<imath>
270 submodule by running in the git source tree of C<isl>
275 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
277 =item 2 Generate C<configure>
283 After performing the above steps, continue
284 with the L<Common installation instructions>.
286 =head2 Common installation instructions
290 =item 1 Obtain C<GMP>
292 By default, building C<isl> requires C<GMP>, including its headers files.
293 Your distribution may not provide these header files by default
294 and you may need to install a package called C<gmp-devel> or something
295 similar. Alternatively, C<GMP> can be built from
296 source, available from L<http://gmplib.org/>.
297 C<GMP> is not needed if you build C<isl> with C<imath>.
301 C<isl> uses the standard C<autoconf> C<configure> script.
306 optionally followed by some configure options.
307 A complete list of options can be obtained by running
311 Below we discuss some of the more common options.
317 Installation prefix for C<isl>
319 =item C<--with-int=[gmp|imath]>
321 Select the integer library to be used by C<isl>, the default is C<gmp>.
322 Note that C<isl> may run significantly slower if you use C<imath>.
324 =item C<--with-gmp-prefix>
326 Installation prefix for C<GMP> (architecture-independent files).
328 =item C<--with-gmp-exec-prefix>
330 Installation prefix for C<GMP> (architecture-dependent files).
338 =item 4 Install (optional)
344 =head1 Integer Set Library
346 =head2 Initialization
348 All manipulations of integer sets and relations occur within
349 the context of an C<isl_ctx>.
350 A given C<isl_ctx> can only be used within a single thread.
351 All arguments of a function are required to have been allocated
352 within the same context.
353 There are currently no functions available for moving an object
354 from one C<isl_ctx> to another C<isl_ctx>. This means that
355 there is currently no way of safely moving an object from one
356 thread to another, unless the whole C<isl_ctx> is moved.
358 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
359 freed using C<isl_ctx_free>.
360 All objects allocated within an C<isl_ctx> should be freed
361 before the C<isl_ctx> itself is freed.
363 isl_ctx *isl_ctx_alloc();
364 void isl_ctx_free(isl_ctx *ctx);
366 The user can impose a bound on the number of low-level I<operations>
367 that can be performed by an C<isl_ctx>. This bound can be set and
368 retrieved using the following functions. A bound of zero means that
369 no bound is imposed. The number of operations performed can be
370 reset using C<isl_ctx_reset_operations>. Note that the number
371 of low-level operations needed to perform a high-level computation
372 may differ significantly across different versions
373 of C<isl>, but it should be the same across different platforms
374 for the same version of C<isl>.
376 Warning: This feature is experimental. C<isl> has good support to abort and
377 bail out during the computation, but this feature may exercise error code paths
378 that are normally not used that much. Consequently, it is not unlikely that
379 hidden bugs will be exposed.
381 void isl_ctx_set_max_operations(isl_ctx *ctx,
382 unsigned long max_operations);
383 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
384 void isl_ctx_reset_operations(isl_ctx *ctx);
386 =head2 Memory Management
388 Since a high-level operation on isl objects usually involves
389 several substeps and since the user is usually not interested in
390 the intermediate results, most functions that return a new object
391 will also release all the objects passed as arguments.
392 If the user still wants to use one or more of these arguments
393 after the function call, she should pass along a copy of the
394 object rather than the object itself.
395 The user is then responsible for making sure that the original
396 object gets used somewhere else or is explicitly freed.
398 The arguments and return values of all documented functions are
399 annotated to make clear which arguments are released and which
400 arguments are preserved. In particular, the following annotations
407 C<__isl_give> means that a new object is returned.
408 The user should make sure that the returned pointer is
409 used exactly once as a value for an C<__isl_take> argument.
410 In between, it can be used as a value for as many
411 C<__isl_keep> arguments as the user likes.
412 There is one exception, and that is the case where the
413 pointer returned is C<NULL>. Is this case, the user
414 is free to use it as an C<__isl_take> argument or not.
418 C<__isl_null> means that a C<NULL> value is returned.
422 C<__isl_take> means that the object the argument points to
423 is taken over by the function and may no longer be used
424 by the user as an argument to any other function.
425 The pointer value must be one returned by a function
426 returning an C<__isl_give> pointer.
427 If the user passes in a C<NULL> value, then this will
428 be treated as an error in the sense that the function will
429 not perform its usual operation. However, it will still
430 make sure that all the other C<__isl_take> arguments
435 C<__isl_keep> means that the function will only use the object
436 temporarily. After the function has finished, the user
437 can still use it as an argument to other functions.
438 A C<NULL> value will be treated in the same way as
439 a C<NULL> value for an C<__isl_take> argument.
445 An C<isl_val> represents an integer value, a rational value
446 or one of three special values, infinity, negative infinity and NaN.
447 Some predefined values can be created using the following functions.
450 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
451 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
452 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
453 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
454 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
455 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
457 Specific integer values can be created using the following functions.
460 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
462 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
464 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
465 size_t n, size_t size, const void *chunks);
467 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
468 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
469 The least significant digit is assumed to be stored first.
471 Value objects can be copied and freed using the following functions.
474 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
475 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
477 They can be inspected using the following functions.
480 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
481 long isl_val_get_num_si(__isl_keep isl_val *v);
482 long isl_val_get_den_si(__isl_keep isl_val *v);
483 double isl_val_get_d(__isl_keep isl_val *v);
484 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
486 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
487 size_t size, void *chunks);
489 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
490 of C<size> bytes needed to store the absolute value of the
492 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
493 which is assumed to have been preallocated by the caller.
494 The least significant digit is stored first.
495 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
496 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
497 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
499 An C<isl_val> can be modified using the following function.
502 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
505 The following unary properties are defined on C<isl_val>s.
508 int isl_val_sgn(__isl_keep isl_val *v);
509 int isl_val_is_zero(__isl_keep isl_val *v);
510 int isl_val_is_one(__isl_keep isl_val *v);
511 int isl_val_is_negone(__isl_keep isl_val *v);
512 int isl_val_is_nonneg(__isl_keep isl_val *v);
513 int isl_val_is_nonpos(__isl_keep isl_val *v);
514 int isl_val_is_pos(__isl_keep isl_val *v);
515 int isl_val_is_neg(__isl_keep isl_val *v);
516 int isl_val_is_int(__isl_keep isl_val *v);
517 int isl_val_is_rat(__isl_keep isl_val *v);
518 int isl_val_is_nan(__isl_keep isl_val *v);
519 int isl_val_is_infty(__isl_keep isl_val *v);
520 int isl_val_is_neginfty(__isl_keep isl_val *v);
522 Note that the sign of NaN is undefined.
524 The following binary properties are defined on pairs of C<isl_val>s.
527 int isl_val_lt(__isl_keep isl_val *v1,
528 __isl_keep isl_val *v2);
529 int isl_val_le(__isl_keep isl_val *v1,
530 __isl_keep isl_val *v2);
531 int isl_val_gt(__isl_keep isl_val *v1,
532 __isl_keep isl_val *v2);
533 int isl_val_ge(__isl_keep isl_val *v1,
534 __isl_keep isl_val *v2);
535 int isl_val_eq(__isl_keep isl_val *v1,
536 __isl_keep isl_val *v2);
537 int isl_val_ne(__isl_keep isl_val *v1,
538 __isl_keep isl_val *v2);
540 For integer C<isl_val>s we additionally have the following binary property.
543 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
544 __isl_keep isl_val *v2);
546 An C<isl_val> can also be compared to an integer using the following
547 function. The result is undefined for NaN.
550 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
552 The following unary operations are available on C<isl_val>s.
555 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
556 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
557 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
558 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
559 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
561 The following binary operations are available on C<isl_val>s.
564 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
565 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
566 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
567 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
568 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
569 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
570 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
571 __isl_take isl_val *v2);
572 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
573 __isl_take isl_val *v2);
574 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
575 __isl_take isl_val *v2);
576 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
578 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
579 __isl_take isl_val *v2);
580 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
582 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
583 __isl_take isl_val *v2);
584 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
586 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
587 __isl_take isl_val *v2);
589 On integer values, we additionally have the following operations.
592 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
593 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
594 __isl_take isl_val *v2);
595 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
596 __isl_take isl_val *v2);
597 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
598 __isl_take isl_val *v2, __isl_give isl_val **x,
599 __isl_give isl_val **y);
601 The function C<isl_val_gcdext> returns the greatest common divisor g
602 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
603 that C<*x> * C<v1> + C<*y> * C<v2> = g.
605 A value can be read from input using
608 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
611 A value can be printed using
614 __isl_give isl_printer *isl_printer_print_val(
615 __isl_take isl_printer *p, __isl_keep isl_val *v);
617 =head3 GMP specific functions
619 These functions are only available if C<isl> has been compiled with C<GMP>
622 Specific integer and rational values can be created from C<GMP> values using
623 the following functions.
625 #include <isl/val_gmp.h>
626 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
628 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
629 const mpz_t n, const mpz_t d);
631 The numerator and denominator of a rational value can be extracted as
632 C<GMP> values using the following functions.
634 #include <isl/val_gmp.h>
635 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
636 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
638 =head2 Sets and Relations
640 C<isl> uses six types of objects for representing sets and relations,
641 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
642 C<isl_union_set> and C<isl_union_map>.
643 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
644 can be described as a conjunction of affine constraints, while
645 C<isl_set> and C<isl_map> represent unions of
646 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
647 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
648 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
649 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
650 where spaces are considered different if they have a different number
651 of dimensions and/or different names (see L<"Spaces">).
652 The difference between sets and relations (maps) is that sets have
653 one set of variables, while relations have two sets of variables,
654 input variables and output variables.
656 =head2 Error Handling
658 C<isl> supports different ways to react in case a runtime error is triggered.
659 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
660 with two maps that have incompatible spaces. There are three possible ways
661 to react on error: to warn, to continue or to abort.
663 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
664 the last error in the corresponding C<isl_ctx> and the function in which the
665 error was triggered returns C<NULL>. An error does not corrupt internal state,
666 such that isl can continue to be used. C<isl> also provides functions to
667 read the last error and to reset the memory that stores the last error. The
668 last error is only stored for information purposes. Its presence does not
669 change the behavior of C<isl>. Hence, resetting an error is not required to
670 continue to use isl, but only to observe new errors.
673 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
674 void isl_ctx_reset_error(isl_ctx *ctx);
676 Another option is to continue on error. This is similar to warn on error mode,
677 except that C<isl> does not print any warning. This allows a program to
678 implement its own error reporting.
680 The last option is to directly abort the execution of the program from within
681 the isl library. This makes it obviously impossible to recover from an error,
682 but it allows to directly spot the error location. By aborting on error,
683 debuggers break at the location the error occurred and can provide a stack
684 trace. Other tools that automatically provide stack traces on abort or that do
685 not want to continue execution after an error was triggered may also prefer to
688 The on error behavior of isl can be specified by calling
689 C<isl_options_set_on_error> or by setting the command line option
690 C<--isl-on-error>. Valid arguments for the function call are
691 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
692 choices for the command line option are C<warn>, C<continue> and C<abort>.
693 It is also possible to query the current error mode.
695 #include <isl/options.h>
696 int isl_options_set_on_error(isl_ctx *ctx, int val);
697 int isl_options_get_on_error(isl_ctx *ctx);
701 Identifiers are used to identify both individual dimensions
702 and tuples of dimensions. They consist of an optional name and an optional
703 user pointer. The name and the user pointer cannot both be C<NULL>, however.
704 Identifiers with the same name but different pointer values
705 are considered to be distinct.
706 Similarly, identifiers with different names but the same pointer value
707 are also considered to be distinct.
708 Equal identifiers are represented using the same object.
709 Pairs of identifiers can therefore be tested for equality using the
711 Identifiers can be constructed, copied, freed, inspected and printed
712 using the following functions.
715 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
716 __isl_keep const char *name, void *user);
717 __isl_give isl_id *isl_id_set_free_user(
718 __isl_take isl_id *id,
719 __isl_give void (*free_user)(void *user));
720 __isl_give isl_id *isl_id_copy(isl_id *id);
721 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
723 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
724 void *isl_id_get_user(__isl_keep isl_id *id);
725 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
727 __isl_give isl_printer *isl_printer_print_id(
728 __isl_take isl_printer *p, __isl_keep isl_id *id);
730 The callback set by C<isl_id_set_free_user> is called on the user
731 pointer when the last reference to the C<isl_id> is freed.
732 Note that C<isl_id_get_name> returns a pointer to some internal
733 data structure, so the result can only be used while the
734 corresponding C<isl_id> is alive.
738 Whenever a new set, relation or similiar object is created from scratch,
739 the space in which it lives needs to be specified using an C<isl_space>.
740 Each space involves zero or more parameters and zero, one or two
741 tuples of set or input/output dimensions. The parameters and dimensions
742 are identified by an C<isl_dim_type> and a position.
743 The type C<isl_dim_param> refers to parameters,
744 the type C<isl_dim_set> refers to set dimensions (for spaces
745 with a single tuple of dimensions) and the types C<isl_dim_in>
746 and C<isl_dim_out> refer to input and output dimensions
747 (for spaces with two tuples of dimensions).
748 Local spaces (see L</"Local Spaces">) also contain dimensions
749 of type C<isl_dim_div>.
750 Note that parameters are only identified by their position within
751 a given object. Across different objects, parameters are (usually)
752 identified by their names or identifiers. Only unnamed parameters
753 are identified by their positions across objects. The use of unnamed
754 parameters is discouraged.
756 #include <isl/space.h>
757 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
758 unsigned nparam, unsigned n_in, unsigned n_out);
759 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
761 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
762 unsigned nparam, unsigned dim);
763 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
764 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
765 unsigned isl_space_dim(__isl_keep isl_space *space,
766 enum isl_dim_type type);
768 The space used for creating a parameter domain
769 needs to be created using C<isl_space_params_alloc>.
770 For other sets, the space
771 needs to be created using C<isl_space_set_alloc>, while
772 for a relation, the space
773 needs to be created using C<isl_space_alloc>.
774 C<isl_space_dim> can be used
775 to find out the number of dimensions of each type in
776 a space, where type may be
777 C<isl_dim_param>, C<isl_dim_in> (only for relations),
778 C<isl_dim_out> (only for relations), C<isl_dim_set>
779 (only for sets) or C<isl_dim_all>.
781 To check whether a given space is that of a set or a map
782 or whether it is a parameter space, use these functions:
784 #include <isl/space.h>
785 int isl_space_is_params(__isl_keep isl_space *space);
786 int isl_space_is_set(__isl_keep isl_space *space);
787 int isl_space_is_map(__isl_keep isl_space *space);
789 Spaces can be compared using the following functions:
791 #include <isl/space.h>
792 int isl_space_is_equal(__isl_keep isl_space *space1,
793 __isl_keep isl_space *space2);
794 int isl_space_is_domain(__isl_keep isl_space *space1,
795 __isl_keep isl_space *space2);
796 int isl_space_is_range(__isl_keep isl_space *space1,
797 __isl_keep isl_space *space2);
799 C<isl_space_is_domain> checks whether the first argument is equal
800 to the domain of the second argument. This requires in particular that
801 the first argument is a set space and that the second argument
804 It is often useful to create objects that live in the
805 same space as some other object. This can be accomplished
806 by creating the new objects
807 (see L</"Creating New Sets and Relations"> or
808 L</"Creating New (Piecewise) Quasipolynomials">) based on the space
809 of the original object.
812 __isl_give isl_space *isl_basic_set_get_space(
813 __isl_keep isl_basic_set *bset);
814 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
816 #include <isl/union_set.h>
817 __isl_give isl_space *isl_union_set_get_space(
818 __isl_keep isl_union_set *uset);
821 __isl_give isl_space *isl_basic_map_get_space(
822 __isl_keep isl_basic_map *bmap);
823 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
825 #include <isl/union_map.h>
826 __isl_give isl_space *isl_union_map_get_space(
827 __isl_keep isl_union_map *umap);
829 #include <isl/constraint.h>
830 __isl_give isl_space *isl_constraint_get_space(
831 __isl_keep isl_constraint *constraint);
833 #include <isl/polynomial.h>
834 __isl_give isl_space *isl_qpolynomial_get_domain_space(
835 __isl_keep isl_qpolynomial *qp);
836 __isl_give isl_space *isl_qpolynomial_get_space(
837 __isl_keep isl_qpolynomial *qp);
838 __isl_give isl_space *isl_qpolynomial_fold_get_space(
839 __isl_keep isl_qpolynomial_fold *fold);
840 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
841 __isl_keep isl_pw_qpolynomial *pwqp);
842 __isl_give isl_space *isl_pw_qpolynomial_get_space(
843 __isl_keep isl_pw_qpolynomial *pwqp);
844 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
845 __isl_keep isl_pw_qpolynomial_fold *pwf);
846 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
847 __isl_keep isl_pw_qpolynomial_fold *pwf);
848 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
849 __isl_keep isl_union_pw_qpolynomial *upwqp);
850 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
851 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
854 __isl_give isl_space *isl_multi_val_get_space(
855 __isl_keep isl_multi_val *mv);
858 __isl_give isl_space *isl_aff_get_domain_space(
859 __isl_keep isl_aff *aff);
860 __isl_give isl_space *isl_aff_get_space(
861 __isl_keep isl_aff *aff);
862 __isl_give isl_space *isl_pw_aff_get_domain_space(
863 __isl_keep isl_pw_aff *pwaff);
864 __isl_give isl_space *isl_pw_aff_get_space(
865 __isl_keep isl_pw_aff *pwaff);
866 __isl_give isl_space *isl_multi_aff_get_domain_space(
867 __isl_keep isl_multi_aff *maff);
868 __isl_give isl_space *isl_multi_aff_get_space(
869 __isl_keep isl_multi_aff *maff);
870 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
871 __isl_keep isl_pw_multi_aff *pma);
872 __isl_give isl_space *isl_pw_multi_aff_get_space(
873 __isl_keep isl_pw_multi_aff *pma);
874 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
875 __isl_keep isl_union_pw_multi_aff *upma);
876 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
877 __isl_keep isl_multi_pw_aff *mpa);
878 __isl_give isl_space *isl_multi_pw_aff_get_space(
879 __isl_keep isl_multi_pw_aff *mpa);
881 #include <isl/point.h>
882 __isl_give isl_space *isl_point_get_space(
883 __isl_keep isl_point *pnt);
885 The identifiers or names of the individual dimensions may be set or read off
886 using the following functions.
888 #include <isl/space.h>
889 __isl_give isl_space *isl_space_set_dim_id(
890 __isl_take isl_space *space,
891 enum isl_dim_type type, unsigned pos,
892 __isl_take isl_id *id);
893 int isl_space_has_dim_id(__isl_keep isl_space *space,
894 enum isl_dim_type type, unsigned pos);
895 __isl_give isl_id *isl_space_get_dim_id(
896 __isl_keep isl_space *space,
897 enum isl_dim_type type, unsigned pos);
898 __isl_give isl_space *isl_space_set_dim_name(
899 __isl_take isl_space *space,
900 enum isl_dim_type type, unsigned pos,
901 __isl_keep const char *name);
902 int isl_space_has_dim_name(__isl_keep isl_space *space,
903 enum isl_dim_type type, unsigned pos);
904 __isl_keep const char *isl_space_get_dim_name(
905 __isl_keep isl_space *space,
906 enum isl_dim_type type, unsigned pos);
908 Note that C<isl_space_get_name> returns a pointer to some internal
909 data structure, so the result can only be used while the
910 corresponding C<isl_space> is alive.
911 Also note that every function that operates on two sets or relations
912 requires that both arguments have the same parameters. This also
913 means that if one of the arguments has named parameters, then the
914 other needs to have named parameters too and the names need to match.
915 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
916 arguments may have different parameters (as long as they are named),
917 in which case the result will have as parameters the union of the parameters of
920 Given the identifier or name of a dimension (typically a parameter),
921 its position can be obtained from the following function.
923 #include <isl/space.h>
924 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
925 enum isl_dim_type type, __isl_keep isl_id *id);
926 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
927 enum isl_dim_type type, const char *name);
929 The identifiers or names of entire spaces may be set or read off
930 using the following functions.
932 #include <isl/space.h>
933 __isl_give isl_space *isl_space_set_tuple_id(
934 __isl_take isl_space *space,
935 enum isl_dim_type type, __isl_take isl_id *id);
936 __isl_give isl_space *isl_space_reset_tuple_id(
937 __isl_take isl_space *space, enum isl_dim_type type);
938 int isl_space_has_tuple_id(__isl_keep isl_space *space,
939 enum isl_dim_type type);
940 __isl_give isl_id *isl_space_get_tuple_id(
941 __isl_keep isl_space *space, enum isl_dim_type type);
942 __isl_give isl_space *isl_space_set_tuple_name(
943 __isl_take isl_space *space,
944 enum isl_dim_type type, const char *s);
945 int isl_space_has_tuple_name(__isl_keep isl_space *space,
946 enum isl_dim_type type);
947 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
948 enum isl_dim_type type);
950 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
951 or C<isl_dim_set>. As with C<isl_space_get_name>,
952 the C<isl_space_get_tuple_name> function returns a pointer to some internal
954 Binary operations require the corresponding spaces of their arguments
955 to have the same name.
957 To keep the names of all parameters and tuples, but reset the user pointers
958 of all the corresponding identifiers, use the following function.
960 __isl_give isl_space *isl_space_reset_user(
961 __isl_take isl_space *space);
963 Spaces can be nested. In particular, the domain of a set or
964 the domain or range of a relation can be a nested relation.
965 This process is also called I<wrapping>.
966 The functions for detecting, constructing and deconstructing
967 such nested spaces can be found in the wrapping properties
968 of L</"Unary Properties">, the wrapping operations
969 of L</"Unary Operations"> and the Cartesian product operations
970 of L</"Basic Operations">.
972 Spaces can be created from other spaces
973 using the following functions.
975 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
976 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
977 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
978 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
979 __isl_give isl_space *isl_space_domain_map(
980 __isl_take isl_space *space);
981 __isl_give isl_space *isl_space_range_map(
982 __isl_take isl_space *space);
983 __isl_give isl_space *isl_space_params(
984 __isl_take isl_space *space);
985 __isl_give isl_space *isl_space_set_from_params(
986 __isl_take isl_space *space);
987 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
988 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
989 __isl_take isl_space *right);
990 __isl_give isl_space *isl_space_align_params(
991 __isl_take isl_space *space1, __isl_take isl_space *space2)
992 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
993 enum isl_dim_type type, unsigned pos, unsigned n);
994 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
995 enum isl_dim_type type, unsigned n);
996 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
997 enum isl_dim_type type, unsigned first, unsigned n);
998 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
999 enum isl_dim_type dst_type, unsigned dst_pos,
1000 enum isl_dim_type src_type, unsigned src_pos,
1002 __isl_give isl_space *isl_space_map_from_set(
1003 __isl_take isl_space *space);
1004 __isl_give isl_space *isl_space_map_from_domain_and_range(
1005 __isl_take isl_space *domain,
1006 __isl_take isl_space *range);
1007 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
1008 __isl_give isl_space *isl_space_curry(
1009 __isl_take isl_space *space);
1010 __isl_give isl_space *isl_space_uncurry(
1011 __isl_take isl_space *space);
1013 Note that if dimensions are added or removed from a space, then
1014 the name and the internal structure are lost.
1018 A local space is essentially a space with
1019 zero or more existentially quantified variables.
1020 The local space of a (constraint of a) basic set or relation can be obtained
1021 using the following functions.
1023 #include <isl/constraint.h>
1024 __isl_give isl_local_space *isl_constraint_get_local_space(
1025 __isl_keep isl_constraint *constraint);
1027 #include <isl/set.h>
1028 __isl_give isl_local_space *isl_basic_set_get_local_space(
1029 __isl_keep isl_basic_set *bset);
1031 #include <isl/map.h>
1032 __isl_give isl_local_space *isl_basic_map_get_local_space(
1033 __isl_keep isl_basic_map *bmap);
1035 A new local space can be created from a space using
1037 #include <isl/local_space.h>
1038 __isl_give isl_local_space *isl_local_space_from_space(
1039 __isl_take isl_space *space);
1041 They can be inspected, modified, copied and freed using the following functions.
1043 #include <isl/local_space.h>
1044 isl_ctx *isl_local_space_get_ctx(
1045 __isl_keep isl_local_space *ls);
1046 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1047 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1048 enum isl_dim_type type);
1049 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1050 __isl_take isl_local_space *ls,
1051 enum isl_dim_type type, __isl_take isl_id *id);
1052 int isl_local_space_has_dim_id(
1053 __isl_keep isl_local_space *ls,
1054 enum isl_dim_type type, unsigned pos);
1055 __isl_give isl_id *isl_local_space_get_dim_id(
1056 __isl_keep isl_local_space *ls,
1057 enum isl_dim_type type, unsigned pos);
1058 int isl_local_space_has_dim_name(
1059 __isl_keep isl_local_space *ls,
1060 enum isl_dim_type type, unsigned pos)
1061 const char *isl_local_space_get_dim_name(
1062 __isl_keep isl_local_space *ls,
1063 enum isl_dim_type type, unsigned pos);
1064 __isl_give isl_local_space *isl_local_space_set_dim_name(
1065 __isl_take isl_local_space *ls,
1066 enum isl_dim_type type, unsigned pos, const char *s);
1067 __isl_give isl_local_space *isl_local_space_set_dim_id(
1068 __isl_take isl_local_space *ls,
1069 enum isl_dim_type type, unsigned pos,
1070 __isl_take isl_id *id);
1071 __isl_give isl_space *isl_local_space_get_space(
1072 __isl_keep isl_local_space *ls);
1073 __isl_give isl_aff *isl_local_space_get_div(
1074 __isl_keep isl_local_space *ls, int pos);
1075 __isl_give isl_local_space *isl_local_space_copy(
1076 __isl_keep isl_local_space *ls);
1077 __isl_null isl_local_space *isl_local_space_free(
1078 __isl_take isl_local_space *ls);
1080 Note that C<isl_local_space_get_div> can only be used on local spaces
1083 Two local spaces can be compared using
1085 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1086 __isl_keep isl_local_space *ls2);
1088 Local spaces can be created from other local spaces
1089 using the functions described in L</"Unary Operations">
1090 and L</"Binary Operations">.
1092 =head2 Input and Output
1094 C<isl> supports its own input/output format, which is similar
1095 to the C<Omega> format, but also supports the C<PolyLib> format
1098 =head3 C<isl> format
1100 The C<isl> format is similar to that of C<Omega>, but has a different
1101 syntax for describing the parameters and allows for the definition
1102 of an existentially quantified variable as the integer division
1103 of an affine expression.
1104 For example, the set of integers C<i> between C<0> and C<n>
1105 such that C<i % 10 <= 6> can be described as
1107 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1110 A set or relation can have several disjuncts, separated
1111 by the keyword C<or>. Each disjunct is either a conjunction
1112 of constraints or a projection (C<exists>) of a conjunction
1113 of constraints. The constraints are separated by the keyword
1116 =head3 C<PolyLib> format
1118 If the represented set is a union, then the first line
1119 contains a single number representing the number of disjuncts.
1120 Otherwise, a line containing the number C<1> is optional.
1122 Each disjunct is represented by a matrix of constraints.
1123 The first line contains two numbers representing
1124 the number of rows and columns,
1125 where the number of rows is equal to the number of constraints
1126 and the number of columns is equal to two plus the number of variables.
1127 The following lines contain the actual rows of the constraint matrix.
1128 In each row, the first column indicates whether the constraint
1129 is an equality (C<0>) or inequality (C<1>). The final column
1130 corresponds to the constant term.
1132 If the set is parametric, then the coefficients of the parameters
1133 appear in the last columns before the constant column.
1134 The coefficients of any existentially quantified variables appear
1135 between those of the set variables and those of the parameters.
1137 =head3 Extended C<PolyLib> format
1139 The extended C<PolyLib> format is nearly identical to the
1140 C<PolyLib> format. The only difference is that the line
1141 containing the number of rows and columns of a constraint matrix
1142 also contains four additional numbers:
1143 the number of output dimensions, the number of input dimensions,
1144 the number of local dimensions (i.e., the number of existentially
1145 quantified variables) and the number of parameters.
1146 For sets, the number of ``output'' dimensions is equal
1147 to the number of set dimensions, while the number of ``input''
1152 #include <isl/set.h>
1153 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1154 isl_ctx *ctx, FILE *input);
1155 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1156 isl_ctx *ctx, const char *str);
1157 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1159 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1162 #include <isl/map.h>
1163 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1164 isl_ctx *ctx, FILE *input);
1165 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1166 isl_ctx *ctx, const char *str);
1167 __isl_give isl_map *isl_map_read_from_file(
1168 isl_ctx *ctx, FILE *input);
1169 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1172 #include <isl/union_set.h>
1173 __isl_give isl_union_set *isl_union_set_read_from_file(
1174 isl_ctx *ctx, FILE *input);
1175 __isl_give isl_union_set *isl_union_set_read_from_str(
1176 isl_ctx *ctx, const char *str);
1178 #include <isl/union_map.h>
1179 __isl_give isl_union_map *isl_union_map_read_from_file(
1180 isl_ctx *ctx, FILE *input);
1181 __isl_give isl_union_map *isl_union_map_read_from_str(
1182 isl_ctx *ctx, const char *str);
1184 The input format is autodetected and may be either the C<PolyLib> format
1185 or the C<isl> format.
1189 Before anything can be printed, an C<isl_printer> needs to
1192 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1194 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1195 __isl_null isl_printer *isl_printer_free(
1196 __isl_take isl_printer *printer);
1197 __isl_give char *isl_printer_get_str(
1198 __isl_keep isl_printer *printer);
1200 The printer can be inspected using the following functions.
1202 FILE *isl_printer_get_file(
1203 __isl_keep isl_printer *printer);
1204 int isl_printer_get_output_format(
1205 __isl_keep isl_printer *p);
1207 The behavior of the printer can be modified in various ways
1209 __isl_give isl_printer *isl_printer_set_output_format(
1210 __isl_take isl_printer *p, int output_format);
1211 __isl_give isl_printer *isl_printer_set_indent(
1212 __isl_take isl_printer *p, int indent);
1213 __isl_give isl_printer *isl_printer_set_indent_prefix(
1214 __isl_take isl_printer *p, const char *prefix);
1215 __isl_give isl_printer *isl_printer_indent(
1216 __isl_take isl_printer *p, int indent);
1217 __isl_give isl_printer *isl_printer_set_prefix(
1218 __isl_take isl_printer *p, const char *prefix);
1219 __isl_give isl_printer *isl_printer_set_suffix(
1220 __isl_take isl_printer *p, const char *suffix);
1222 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1223 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1224 and defaults to C<ISL_FORMAT_ISL>.
1225 Each line in the output is prefixed by C<indent_prefix>,
1226 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
1227 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1228 In the C<PolyLib> format output,
1229 the coefficients of the existentially quantified variables
1230 appear between those of the set variables and those
1232 The function C<isl_printer_indent> increases the indentation
1233 by the specified amount (which may be negative).
1235 To actually print something, use
1237 #include <isl/printer.h>
1238 __isl_give isl_printer *isl_printer_print_double(
1239 __isl_take isl_printer *p, double d);
1241 #include <isl/set.h>
1242 __isl_give isl_printer *isl_printer_print_basic_set(
1243 __isl_take isl_printer *printer,
1244 __isl_keep isl_basic_set *bset);
1245 __isl_give isl_printer *isl_printer_print_set(
1246 __isl_take isl_printer *printer,
1247 __isl_keep isl_set *set);
1249 #include <isl/map.h>
1250 __isl_give isl_printer *isl_printer_print_basic_map(
1251 __isl_take isl_printer *printer,
1252 __isl_keep isl_basic_map *bmap);
1253 __isl_give isl_printer *isl_printer_print_map(
1254 __isl_take isl_printer *printer,
1255 __isl_keep isl_map *map);
1257 #include <isl/union_set.h>
1258 __isl_give isl_printer *isl_printer_print_union_set(
1259 __isl_take isl_printer *p,
1260 __isl_keep isl_union_set *uset);
1262 #include <isl/union_map.h>
1263 __isl_give isl_printer *isl_printer_print_union_map(
1264 __isl_take isl_printer *p,
1265 __isl_keep isl_union_map *umap);
1267 When called on a file printer, the following function flushes
1268 the file. When called on a string printer, the buffer is cleared.
1270 __isl_give isl_printer *isl_printer_flush(
1271 __isl_take isl_printer *p);
1273 =head2 Creating New Sets and Relations
1275 C<isl> has functions for creating some standard sets and relations.
1279 =item * Empty sets and relations
1281 __isl_give isl_basic_set *isl_basic_set_empty(
1282 __isl_take isl_space *space);
1283 __isl_give isl_basic_map *isl_basic_map_empty(
1284 __isl_take isl_space *space);
1285 __isl_give isl_set *isl_set_empty(
1286 __isl_take isl_space *space);
1287 __isl_give isl_map *isl_map_empty(
1288 __isl_take isl_space *space);
1289 __isl_give isl_union_set *isl_union_set_empty(
1290 __isl_take isl_space *space);
1291 __isl_give isl_union_map *isl_union_map_empty(
1292 __isl_take isl_space *space);
1294 For C<isl_union_set>s and C<isl_union_map>s, the space
1295 is only used to specify the parameters.
1297 =item * Universe sets and relations
1299 __isl_give isl_basic_set *isl_basic_set_universe(
1300 __isl_take isl_space *space);
1301 __isl_give isl_basic_map *isl_basic_map_universe(
1302 __isl_take isl_space *space);
1303 __isl_give isl_set *isl_set_universe(
1304 __isl_take isl_space *space);
1305 __isl_give isl_map *isl_map_universe(
1306 __isl_take isl_space *space);
1307 __isl_give isl_union_set *isl_union_set_universe(
1308 __isl_take isl_union_set *uset);
1309 __isl_give isl_union_map *isl_union_map_universe(
1310 __isl_take isl_union_map *umap);
1312 The sets and relations constructed by the functions above
1313 contain all integer values, while those constructed by the
1314 functions below only contain non-negative values.
1316 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1317 __isl_take isl_space *space);
1318 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1319 __isl_take isl_space *space);
1320 __isl_give isl_set *isl_set_nat_universe(
1321 __isl_take isl_space *space);
1322 __isl_give isl_map *isl_map_nat_universe(
1323 __isl_take isl_space *space);
1325 =item * Identity relations
1327 __isl_give isl_basic_map *isl_basic_map_identity(
1328 __isl_take isl_space *space);
1329 __isl_give isl_map *isl_map_identity(
1330 __isl_take isl_space *space);
1332 The number of input and output dimensions in C<space> needs
1335 =item * Lexicographic order
1337 __isl_give isl_map *isl_map_lex_lt(
1338 __isl_take isl_space *set_space);
1339 __isl_give isl_map *isl_map_lex_le(
1340 __isl_take isl_space *set_space);
1341 __isl_give isl_map *isl_map_lex_gt(
1342 __isl_take isl_space *set_space);
1343 __isl_give isl_map *isl_map_lex_ge(
1344 __isl_take isl_space *set_space);
1345 __isl_give isl_map *isl_map_lex_lt_first(
1346 __isl_take isl_space *space, unsigned n);
1347 __isl_give isl_map *isl_map_lex_le_first(
1348 __isl_take isl_space *space, unsigned n);
1349 __isl_give isl_map *isl_map_lex_gt_first(
1350 __isl_take isl_space *space, unsigned n);
1351 __isl_give isl_map *isl_map_lex_ge_first(
1352 __isl_take isl_space *space, unsigned n);
1354 The first four functions take a space for a B<set>
1355 and return relations that express that the elements in the domain
1356 are lexicographically less
1357 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1358 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1359 than the elements in the range.
1360 The last four functions take a space for a map
1361 and return relations that express that the first C<n> dimensions
1362 in the domain are lexicographically less
1363 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1364 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1365 than the first C<n> dimensions in the range.
1369 A basic set or relation can be converted to a set or relation
1370 using the following functions.
1372 __isl_give isl_set *isl_set_from_basic_set(
1373 __isl_take isl_basic_set *bset);
1374 __isl_give isl_map *isl_map_from_basic_map(
1375 __isl_take isl_basic_map *bmap);
1377 Sets and relations can be converted to union sets and relations
1378 using the following functions.
1380 __isl_give isl_union_set *isl_union_set_from_basic_set(
1381 __isl_take isl_basic_set *bset);
1382 __isl_give isl_union_map *isl_union_map_from_basic_map(
1383 __isl_take isl_basic_map *bmap);
1384 __isl_give isl_union_set *isl_union_set_from_set(
1385 __isl_take isl_set *set);
1386 __isl_give isl_union_map *isl_union_map_from_map(
1387 __isl_take isl_map *map);
1389 The inverse conversions below can only be used if the input
1390 union set or relation is known to contain elements in exactly one
1393 __isl_give isl_set *isl_set_from_union_set(
1394 __isl_take isl_union_set *uset);
1395 __isl_give isl_map *isl_map_from_union_map(
1396 __isl_take isl_union_map *umap);
1398 A zero-dimensional (basic) set can be constructed on a given parameter domain
1399 using the following function.
1401 __isl_give isl_basic_set *isl_basic_set_from_params(
1402 __isl_take isl_basic_set *bset);
1403 __isl_give isl_set *isl_set_from_params(
1404 __isl_take isl_set *set);
1406 Sets and relations can be copied and freed again using the following
1409 __isl_give isl_basic_set *isl_basic_set_copy(
1410 __isl_keep isl_basic_set *bset);
1411 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1412 __isl_give isl_union_set *isl_union_set_copy(
1413 __isl_keep isl_union_set *uset);
1414 __isl_give isl_basic_map *isl_basic_map_copy(
1415 __isl_keep isl_basic_map *bmap);
1416 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1417 __isl_give isl_union_map *isl_union_map_copy(
1418 __isl_keep isl_union_map *umap);
1419 __isl_null isl_basic_set *isl_basic_set_free(
1420 __isl_take isl_basic_set *bset);
1421 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1422 __isl_null isl_union_set *isl_union_set_free(
1423 __isl_take isl_union_set *uset);
1424 __isl_null isl_basic_map *isl_basic_map_free(
1425 __isl_take isl_basic_map *bmap);
1426 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1427 __isl_null isl_union_map *isl_union_map_free(
1428 __isl_take isl_union_map *umap);
1430 Other sets and relations can be constructed by starting
1431 from a universe set or relation, adding equality and/or
1432 inequality constraints and then projecting out the
1433 existentially quantified variables, if any.
1434 Constraints can be constructed, manipulated and
1435 added to (or removed from) (basic) sets and relations
1436 using the following functions.
1438 #include <isl/constraint.h>
1439 __isl_give isl_constraint *isl_equality_alloc(
1440 __isl_take isl_local_space *ls);
1441 __isl_give isl_constraint *isl_inequality_alloc(
1442 __isl_take isl_local_space *ls);
1443 __isl_give isl_constraint *isl_constraint_set_constant_si(
1444 __isl_take isl_constraint *constraint, int v);
1445 __isl_give isl_constraint *isl_constraint_set_constant_val(
1446 __isl_take isl_constraint *constraint,
1447 __isl_take isl_val *v);
1448 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1449 __isl_take isl_constraint *constraint,
1450 enum isl_dim_type type, int pos, int v);
1451 __isl_give isl_constraint *
1452 isl_constraint_set_coefficient_val(
1453 __isl_take isl_constraint *constraint,
1454 enum isl_dim_type type, int pos,
1455 __isl_take isl_val *v);
1456 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1457 __isl_take isl_basic_map *bmap,
1458 __isl_take isl_constraint *constraint);
1459 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1460 __isl_take isl_basic_set *bset,
1461 __isl_take isl_constraint *constraint);
1462 __isl_give isl_map *isl_map_add_constraint(
1463 __isl_take isl_map *map,
1464 __isl_take isl_constraint *constraint);
1465 __isl_give isl_set *isl_set_add_constraint(
1466 __isl_take isl_set *set,
1467 __isl_take isl_constraint *constraint);
1468 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1469 __isl_take isl_basic_set *bset,
1470 __isl_take isl_constraint *constraint);
1472 For example, to create a set containing the even integers
1473 between 10 and 42, you would use the following code.
1476 isl_local_space *ls;
1478 isl_basic_set *bset;
1480 space = isl_space_set_alloc(ctx, 0, 2);
1481 bset = isl_basic_set_universe(isl_space_copy(space));
1482 ls = isl_local_space_from_space(space);
1484 c = isl_equality_alloc(isl_local_space_copy(ls));
1485 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1486 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1487 bset = isl_basic_set_add_constraint(bset, c);
1489 c = isl_inequality_alloc(isl_local_space_copy(ls));
1490 c = isl_constraint_set_constant_si(c, -10);
1491 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1492 bset = isl_basic_set_add_constraint(bset, c);
1494 c = isl_inequality_alloc(ls);
1495 c = isl_constraint_set_constant_si(c, 42);
1496 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1497 bset = isl_basic_set_add_constraint(bset, c);
1499 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1503 isl_basic_set *bset;
1504 bset = isl_basic_set_read_from_str(ctx,
1505 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1507 A basic set or relation can also be constructed from two matrices
1508 describing the equalities and the inequalities.
1510 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1511 __isl_take isl_space *space,
1512 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1513 enum isl_dim_type c1,
1514 enum isl_dim_type c2, enum isl_dim_type c3,
1515 enum isl_dim_type c4);
1516 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1517 __isl_take isl_space *space,
1518 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1519 enum isl_dim_type c1,
1520 enum isl_dim_type c2, enum isl_dim_type c3,
1521 enum isl_dim_type c4, enum isl_dim_type c5);
1523 The C<isl_dim_type> arguments indicate the order in which
1524 different kinds of variables appear in the input matrices
1525 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1526 C<isl_dim_set> and C<isl_dim_div> for sets and
1527 of C<isl_dim_cst>, C<isl_dim_param>,
1528 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1530 A (basic or union) set or relation can also be constructed from a
1531 (union) (piecewise) (multiple) affine expression
1532 or a list of affine expressions
1533 (See L<"Piecewise Quasi Affine Expressions"> and
1534 L<"Piecewise Multiple Quasi Affine Expressions">).
1536 __isl_give isl_basic_map *isl_basic_map_from_aff(
1537 __isl_take isl_aff *aff);
1538 __isl_give isl_map *isl_map_from_aff(
1539 __isl_take isl_aff *aff);
1540 __isl_give isl_set *isl_set_from_pw_aff(
1541 __isl_take isl_pw_aff *pwaff);
1542 __isl_give isl_map *isl_map_from_pw_aff(
1543 __isl_take isl_pw_aff *pwaff);
1544 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1545 __isl_take isl_space *domain_space,
1546 __isl_take isl_aff_list *list);
1547 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1548 __isl_take isl_multi_aff *maff)
1549 __isl_give isl_map *isl_map_from_multi_aff(
1550 __isl_take isl_multi_aff *maff)
1551 __isl_give isl_set *isl_set_from_pw_multi_aff(
1552 __isl_take isl_pw_multi_aff *pma);
1553 __isl_give isl_map *isl_map_from_pw_multi_aff(
1554 __isl_take isl_pw_multi_aff *pma);
1555 __isl_give isl_set *isl_set_from_multi_pw_aff(
1556 __isl_take isl_multi_pw_aff *mpa);
1557 __isl_give isl_map *isl_map_from_multi_pw_aff(
1558 __isl_take isl_multi_pw_aff *mpa);
1559 __isl_give isl_union_map *
1560 isl_union_map_from_union_pw_multi_aff(
1561 __isl_take isl_union_pw_multi_aff *upma);
1563 The C<domain_space> argument describes the domain of the resulting
1564 basic relation. It is required because the C<list> may consist
1565 of zero affine expressions.
1567 =head2 Inspecting Sets and Relations
1569 Usually, the user should not have to care about the actual constraints
1570 of the sets and maps, but should instead apply the abstract operations
1571 explained in the following sections.
1572 Occasionally, however, it may be required to inspect the individual
1573 coefficients of the constraints. This section explains how to do so.
1574 In these cases, it may also be useful to have C<isl> compute
1575 an explicit representation of the existentially quantified variables.
1577 __isl_give isl_set *isl_set_compute_divs(
1578 __isl_take isl_set *set);
1579 __isl_give isl_map *isl_map_compute_divs(
1580 __isl_take isl_map *map);
1581 __isl_give isl_union_set *isl_union_set_compute_divs(
1582 __isl_take isl_union_set *uset);
1583 __isl_give isl_union_map *isl_union_map_compute_divs(
1584 __isl_take isl_union_map *umap);
1586 This explicit representation defines the existentially quantified
1587 variables as integer divisions of the other variables, possibly
1588 including earlier existentially quantified variables.
1589 An explicitly represented existentially quantified variable therefore
1590 has a unique value when the values of the other variables are known.
1591 If, furthermore, the same existentials, i.e., existentials
1592 with the same explicit representations, should appear in the
1593 same order in each of the disjuncts of a set or map, then the user should call
1594 either of the following functions.
1596 __isl_give isl_set *isl_set_align_divs(
1597 __isl_take isl_set *set);
1598 __isl_give isl_map *isl_map_align_divs(
1599 __isl_take isl_map *map);
1601 Alternatively, the existentially quantified variables can be removed
1602 using the following functions, which compute an overapproximation.
1604 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1605 __isl_take isl_basic_set *bset);
1606 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1607 __isl_take isl_basic_map *bmap);
1608 __isl_give isl_set *isl_set_remove_divs(
1609 __isl_take isl_set *set);
1610 __isl_give isl_map *isl_map_remove_divs(
1611 __isl_take isl_map *map);
1613 It is also possible to only remove those divs that are defined
1614 in terms of a given range of dimensions or only those for which
1615 no explicit representation is known.
1617 __isl_give isl_basic_set *
1618 isl_basic_set_remove_divs_involving_dims(
1619 __isl_take isl_basic_set *bset,
1620 enum isl_dim_type type,
1621 unsigned first, unsigned n);
1622 __isl_give isl_basic_map *
1623 isl_basic_map_remove_divs_involving_dims(
1624 __isl_take isl_basic_map *bmap,
1625 enum isl_dim_type type,
1626 unsigned first, unsigned n);
1627 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1628 __isl_take isl_set *set, enum isl_dim_type type,
1629 unsigned first, unsigned n);
1630 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1631 __isl_take isl_map *map, enum isl_dim_type type,
1632 unsigned first, unsigned n);
1634 __isl_give isl_basic_set *
1635 isl_basic_set_remove_unknown_divs(
1636 __isl_take isl_basic_set *bset);
1637 __isl_give isl_set *isl_set_remove_unknown_divs(
1638 __isl_take isl_set *set);
1639 __isl_give isl_map *isl_map_remove_unknown_divs(
1640 __isl_take isl_map *map);
1642 To iterate over all the sets or maps in a union set or map, use
1644 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1645 int (*fn)(__isl_take isl_set *set, void *user),
1647 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1648 int (*fn)(__isl_take isl_map *map, void *user),
1651 The number of sets or maps in a union set or map can be obtained
1654 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1655 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1657 To extract the set or map in a given space from a union, use
1659 __isl_give isl_set *isl_union_set_extract_set(
1660 __isl_keep isl_union_set *uset,
1661 __isl_take isl_space *space);
1662 __isl_give isl_map *isl_union_map_extract_map(
1663 __isl_keep isl_union_map *umap,
1664 __isl_take isl_space *space);
1666 To iterate over all the basic sets or maps in a set or map, use
1668 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1669 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1671 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1672 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1675 The callback function C<fn> should return 0 if successful and
1676 -1 if an error occurs. In the latter case, or if any other error
1677 occurs, the above functions will return -1.
1679 It should be noted that C<isl> does not guarantee that
1680 the basic sets or maps passed to C<fn> are disjoint.
1681 If this is required, then the user should call one of
1682 the following functions first.
1684 __isl_give isl_set *isl_set_make_disjoint(
1685 __isl_take isl_set *set);
1686 __isl_give isl_map *isl_map_make_disjoint(
1687 __isl_take isl_map *map);
1689 The number of basic sets in a set can be obtained
1692 int isl_set_n_basic_set(__isl_keep isl_set *set);
1694 To iterate over the constraints of a basic set or map, use
1696 #include <isl/constraint.h>
1698 int isl_basic_set_n_constraint(
1699 __isl_keep isl_basic_set *bset);
1700 int isl_basic_set_foreach_constraint(
1701 __isl_keep isl_basic_set *bset,
1702 int (*fn)(__isl_take isl_constraint *c, void *user),
1704 int isl_basic_map_n_constraint(
1705 __isl_keep isl_basic_map *bmap);
1706 int isl_basic_map_foreach_constraint(
1707 __isl_keep isl_basic_map *bmap,
1708 int (*fn)(__isl_take isl_constraint *c, void *user),
1710 __isl_null isl_constraint *isl_constraint_free(
1711 __isl_take isl_constraint *c);
1713 Again, the callback function C<fn> should return 0 if successful and
1714 -1 if an error occurs. In the latter case, or if any other error
1715 occurs, the above functions will return -1.
1716 The constraint C<c> represents either an equality or an inequality.
1717 Use the following function to find out whether a constraint
1718 represents an equality. If not, it represents an inequality.
1720 int isl_constraint_is_equality(
1721 __isl_keep isl_constraint *constraint);
1723 It is also possible to obtain a list of constraints from a basic
1726 #include <isl/constraint.h>
1727 __isl_give isl_constraint_list *
1728 isl_basic_map_get_constraint_list(
1729 __isl_keep isl_basic_map *bmap);
1730 __isl_give isl_constraint_list *
1731 isl_basic_set_get_constraint_list(
1732 __isl_keep isl_basic_set *bset);
1734 These functions require that all existentially quantified variables
1735 have an explicit representation.
1736 The returned list can be manipulated using the functions in L<"Lists">.
1738 The coefficients of the constraints can be inspected using
1739 the following functions.
1741 int isl_constraint_is_lower_bound(
1742 __isl_keep isl_constraint *constraint,
1743 enum isl_dim_type type, unsigned pos);
1744 int isl_constraint_is_upper_bound(
1745 __isl_keep isl_constraint *constraint,
1746 enum isl_dim_type type, unsigned pos);
1747 __isl_give isl_val *isl_constraint_get_constant_val(
1748 __isl_keep isl_constraint *constraint);
1749 __isl_give isl_val *isl_constraint_get_coefficient_val(
1750 __isl_keep isl_constraint *constraint,
1751 enum isl_dim_type type, int pos);
1752 int isl_constraint_involves_dims(
1753 __isl_keep isl_constraint *constraint,
1754 enum isl_dim_type type, unsigned first, unsigned n);
1756 The explicit representations of the existentially quantified
1757 variables can be inspected using the following function.
1758 Note that the user is only allowed to use this function
1759 if the inspected set or map is the result of a call
1760 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1761 The existentially quantified variable is equal to the floor
1762 of the returned affine expression. The affine expression
1763 itself can be inspected using the functions in
1764 L<"Piecewise Quasi Affine Expressions">.
1766 __isl_give isl_aff *isl_constraint_get_div(
1767 __isl_keep isl_constraint *constraint, int pos);
1769 To obtain the constraints of a basic set or map in matrix
1770 form, use the following functions.
1772 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1773 __isl_keep isl_basic_set *bset,
1774 enum isl_dim_type c1, enum isl_dim_type c2,
1775 enum isl_dim_type c3, enum isl_dim_type c4);
1776 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1777 __isl_keep isl_basic_set *bset,
1778 enum isl_dim_type c1, enum isl_dim_type c2,
1779 enum isl_dim_type c3, enum isl_dim_type c4);
1780 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1781 __isl_keep isl_basic_map *bmap,
1782 enum isl_dim_type c1,
1783 enum isl_dim_type c2, enum isl_dim_type c3,
1784 enum isl_dim_type c4, enum isl_dim_type c5);
1785 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1786 __isl_keep isl_basic_map *bmap,
1787 enum isl_dim_type c1,
1788 enum isl_dim_type c2, enum isl_dim_type c3,
1789 enum isl_dim_type c4, enum isl_dim_type c5);
1791 The C<isl_dim_type> arguments dictate the order in which
1792 different kinds of variables appear in the resulting matrix
1793 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1794 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1796 The number of parameters, input, output or set dimensions can
1797 be obtained using the following functions.
1799 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1800 enum isl_dim_type type);
1801 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1802 enum isl_dim_type type);
1803 unsigned isl_set_dim(__isl_keep isl_set *set,
1804 enum isl_dim_type type);
1805 unsigned isl_map_dim(__isl_keep isl_map *map,
1806 enum isl_dim_type type);
1807 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1808 enum isl_dim_type type);
1810 Note that a C<isl_union_map> only has parameters.
1812 To check whether the description of a set or relation depends
1813 on one or more given dimensions, it is not necessary to iterate over all
1814 constraints. Instead the following functions can be used.
1816 int isl_basic_set_involves_dims(
1817 __isl_keep isl_basic_set *bset,
1818 enum isl_dim_type type, unsigned first, unsigned n);
1819 int isl_set_involves_dims(__isl_keep isl_set *set,
1820 enum isl_dim_type type, unsigned first, unsigned n);
1821 int isl_basic_map_involves_dims(
1822 __isl_keep isl_basic_map *bmap,
1823 enum isl_dim_type type, unsigned first, unsigned n);
1824 int isl_map_involves_dims(__isl_keep isl_map *map,
1825 enum isl_dim_type type, unsigned first, unsigned n);
1827 Similarly, the following functions can be used to check whether
1828 a given dimension is involved in any lower or upper bound.
1830 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1831 enum isl_dim_type type, unsigned pos);
1832 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1833 enum isl_dim_type type, unsigned pos);
1835 Note that these functions return true even if there is a bound on
1836 the dimension on only some of the basic sets of C<set>.
1837 To check if they have a bound for all of the basic sets in C<set>,
1838 use the following functions instead.
1840 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1841 enum isl_dim_type type, unsigned pos);
1842 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1843 enum isl_dim_type type, unsigned pos);
1845 The identifiers or names of the domain and range spaces of a set
1846 or relation can be read off or set using the following functions.
1848 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1849 __isl_take isl_basic_set *bset,
1850 __isl_take isl_id *id);
1851 __isl_give isl_set *isl_set_set_tuple_id(
1852 __isl_take isl_set *set, __isl_take isl_id *id);
1853 __isl_give isl_set *isl_set_reset_tuple_id(
1854 __isl_take isl_set *set);
1855 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1856 __isl_give isl_id *isl_set_get_tuple_id(
1857 __isl_keep isl_set *set);
1858 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1859 __isl_take isl_basic_map *bmap,
1860 enum isl_dim_type type, __isl_take isl_id *id);
1861 __isl_give isl_map *isl_map_set_tuple_id(
1862 __isl_take isl_map *map, enum isl_dim_type type,
1863 __isl_take isl_id *id);
1864 __isl_give isl_map *isl_map_reset_tuple_id(
1865 __isl_take isl_map *map, enum isl_dim_type type);
1866 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1867 enum isl_dim_type type);
1868 __isl_give isl_id *isl_map_get_tuple_id(
1869 __isl_keep isl_map *map, enum isl_dim_type type);
1871 const char *isl_basic_set_get_tuple_name(
1872 __isl_keep isl_basic_set *bset);
1873 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1874 __isl_take isl_basic_set *set, const char *s);
1875 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1876 const char *isl_set_get_tuple_name(
1877 __isl_keep isl_set *set);
1878 __isl_give isl_set *isl_set_set_tuple_name(
1879 __isl_take isl_set *set, const char *s);
1880 const char *isl_basic_map_get_tuple_name(
1881 __isl_keep isl_basic_map *bmap,
1882 enum isl_dim_type type);
1883 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1884 __isl_take isl_basic_map *bmap,
1885 enum isl_dim_type type, const char *s);
1886 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1887 enum isl_dim_type type);
1888 const char *isl_map_get_tuple_name(
1889 __isl_keep isl_map *map,
1890 enum isl_dim_type type);
1891 __isl_give isl_map *isl_map_set_tuple_name(
1892 __isl_take isl_map *map,
1893 enum isl_dim_type type, const char *s);
1895 As with C<isl_space_get_tuple_name>, the value returned points to
1896 an internal data structure.
1897 The identifiers, positions or names of individual dimensions can be
1898 read off using the following functions.
1900 __isl_give isl_id *isl_basic_set_get_dim_id(
1901 __isl_keep isl_basic_set *bset,
1902 enum isl_dim_type type, unsigned pos);
1903 __isl_give isl_set *isl_set_set_dim_id(
1904 __isl_take isl_set *set, enum isl_dim_type type,
1905 unsigned pos, __isl_take isl_id *id);
1906 int isl_set_has_dim_id(__isl_keep isl_set *set,
1907 enum isl_dim_type type, unsigned pos);
1908 __isl_give isl_id *isl_set_get_dim_id(
1909 __isl_keep isl_set *set, enum isl_dim_type type,
1911 int isl_basic_map_has_dim_id(
1912 __isl_keep isl_basic_map *bmap,
1913 enum isl_dim_type type, unsigned pos);
1914 __isl_give isl_map *isl_map_set_dim_id(
1915 __isl_take isl_map *map, enum isl_dim_type type,
1916 unsigned pos, __isl_take isl_id *id);
1917 int isl_map_has_dim_id(__isl_keep isl_map *map,
1918 enum isl_dim_type type, unsigned pos);
1919 __isl_give isl_id *isl_map_get_dim_id(
1920 __isl_keep isl_map *map, enum isl_dim_type type,
1922 __isl_give isl_id *isl_union_map_get_dim_id(
1923 __isl_keep isl_union_map *umap,
1924 enum isl_dim_type type, unsigned pos);
1926 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1927 enum isl_dim_type type, __isl_keep isl_id *id);
1928 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1929 enum isl_dim_type type, __isl_keep isl_id *id);
1930 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1931 enum isl_dim_type type, const char *name);
1932 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1933 enum isl_dim_type type, const char *name);
1935 const char *isl_constraint_get_dim_name(
1936 __isl_keep isl_constraint *constraint,
1937 enum isl_dim_type type, unsigned pos);
1938 const char *isl_basic_set_get_dim_name(
1939 __isl_keep isl_basic_set *bset,
1940 enum isl_dim_type type, unsigned pos);
1941 int isl_set_has_dim_name(__isl_keep isl_set *set,
1942 enum isl_dim_type type, unsigned pos);
1943 const char *isl_set_get_dim_name(
1944 __isl_keep isl_set *set,
1945 enum isl_dim_type type, unsigned pos);
1946 const char *isl_basic_map_get_dim_name(
1947 __isl_keep isl_basic_map *bmap,
1948 enum isl_dim_type type, unsigned pos);
1949 int isl_map_has_dim_name(__isl_keep isl_map *map,
1950 enum isl_dim_type type, unsigned pos);
1951 const char *isl_map_get_dim_name(
1952 __isl_keep isl_map *map,
1953 enum isl_dim_type type, unsigned pos);
1955 These functions are mostly useful to obtain the identifiers, positions
1956 or names of the parameters. Identifiers of individual dimensions are
1957 essentially only useful for printing. They are ignored by all other
1958 operations and may not be preserved across those operations.
1960 The user pointers on all parameters and tuples can be reset
1961 using the following functions.
1963 #include <isl/set.h>
1964 __isl_give isl_set *isl_set_reset_user(
1965 __isl_take isl_set *set);
1966 #include <isl/map.h>
1967 __isl_give isl_map *isl_map_reset_user(
1968 __isl_take isl_map *map);
1969 #include <isl/union_set.h>
1970 __isl_give isl_union_set *isl_union_set_reset_user(
1971 __isl_take isl_union_set *uset);
1972 #include <isl/union_map.h>
1973 __isl_give isl_union_map *isl_union_map_reset_user(
1974 __isl_take isl_union_map *umap);
1978 =head3 Unary Properties
1984 The following functions test whether the given set or relation
1985 contains any integer points. The ``plain'' variants do not perform
1986 any computations, but simply check if the given set or relation
1987 is already known to be empty.
1989 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1990 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1991 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1992 int isl_set_is_empty(__isl_keep isl_set *set);
1993 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1994 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1995 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1996 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1997 int isl_map_is_empty(__isl_keep isl_map *map);
1998 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
2000 =item * Universality
2002 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
2003 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
2004 int isl_set_plain_is_universe(__isl_keep isl_set *set);
2006 =item * Single-valuedness
2008 int isl_basic_map_is_single_valued(
2009 __isl_keep isl_basic_map *bmap);
2010 int isl_map_plain_is_single_valued(
2011 __isl_keep isl_map *map);
2012 int isl_map_is_single_valued(__isl_keep isl_map *map);
2013 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
2017 int isl_map_plain_is_injective(__isl_keep isl_map *map);
2018 int isl_map_is_injective(__isl_keep isl_map *map);
2019 int isl_union_map_plain_is_injective(
2020 __isl_keep isl_union_map *umap);
2021 int isl_union_map_is_injective(
2022 __isl_keep isl_union_map *umap);
2026 int isl_map_is_bijective(__isl_keep isl_map *map);
2027 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
2031 __isl_give isl_val *
2032 isl_basic_map_plain_get_val_if_fixed(
2033 __isl_keep isl_basic_map *bmap,
2034 enum isl_dim_type type, unsigned pos);
2035 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
2036 __isl_keep isl_set *set,
2037 enum isl_dim_type type, unsigned pos);
2038 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
2039 __isl_keep isl_map *map,
2040 enum isl_dim_type type, unsigned pos);
2042 If the set or relation obviously lies on a hyperplane where the given dimension
2043 has a fixed value, then return that value.
2044 Otherwise return NaN.
2048 int isl_set_dim_residue_class_val(
2049 __isl_keep isl_set *set,
2050 int pos, __isl_give isl_val **modulo,
2051 __isl_give isl_val **residue);
2053 Check if the values of the given set dimension are equal to a fixed
2054 value modulo some integer value. If so, assign the modulo to C<*modulo>
2055 and the fixed value to C<*residue>. If the given dimension attains only
2056 a single value, then assign C<0> to C<*modulo> and the fixed value to
2058 If the dimension does not attain only a single value and if no modulo
2059 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
2063 To check whether a set is a parameter domain, use this function:
2065 int isl_set_is_params(__isl_keep isl_set *set);
2066 int isl_union_set_is_params(
2067 __isl_keep isl_union_set *uset);
2071 The following functions check whether the space of the given
2072 (basic) set or relation range is a wrapped relation.
2074 #include <isl/space.h>
2075 int isl_space_is_wrapping(
2076 __isl_keep isl_space *space);
2077 int isl_space_domain_is_wrapping(
2078 __isl_keep isl_space *space);
2079 int isl_space_range_is_wrapping(
2080 __isl_keep isl_space *space);
2082 #include <isl/set.h>
2083 int isl_basic_set_is_wrapping(
2084 __isl_keep isl_basic_set *bset);
2085 int isl_set_is_wrapping(__isl_keep isl_set *set);
2087 #include <isl/map.h>
2088 int isl_map_domain_is_wrapping(
2089 __isl_keep isl_map *map);
2090 int isl_map_range_is_wrapping(
2091 __isl_keep isl_map *map);
2093 The input to C<isl_space_is_wrapping> should
2094 be the space of a set, while that of
2095 C<isl_space_domain_is_wrapping> and
2096 C<isl_space_range_is_wrapping> should be the space of a relation.
2098 =item * Internal Product
2100 int isl_basic_map_can_zip(
2101 __isl_keep isl_basic_map *bmap);
2102 int isl_map_can_zip(__isl_keep isl_map *map);
2104 Check whether the product of domain and range of the given relation
2106 i.e., whether both domain and range are nested relations.
2110 int isl_basic_map_can_curry(
2111 __isl_keep isl_basic_map *bmap);
2112 int isl_map_can_curry(__isl_keep isl_map *map);
2114 Check whether the domain of the (basic) relation is a wrapped relation.
2116 int isl_basic_map_can_uncurry(
2117 __isl_keep isl_basic_map *bmap);
2118 int isl_map_can_uncurry(__isl_keep isl_map *map);
2120 Check whether the range of the (basic) relation is a wrapped relation.
2124 =head3 Binary Properties
2130 int isl_basic_set_plain_is_equal(
2131 __isl_keep isl_basic_set *bset1,
2132 __isl_keep isl_basic_set *bset2);
2133 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2134 __isl_keep isl_set *set2);
2135 int isl_set_is_equal(__isl_keep isl_set *set1,
2136 __isl_keep isl_set *set2);
2137 int isl_union_set_is_equal(
2138 __isl_keep isl_union_set *uset1,
2139 __isl_keep isl_union_set *uset2);
2140 int isl_basic_map_is_equal(
2141 __isl_keep isl_basic_map *bmap1,
2142 __isl_keep isl_basic_map *bmap2);
2143 int isl_map_is_equal(__isl_keep isl_map *map1,
2144 __isl_keep isl_map *map2);
2145 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2146 __isl_keep isl_map *map2);
2147 int isl_union_map_is_equal(
2148 __isl_keep isl_union_map *umap1,
2149 __isl_keep isl_union_map *umap2);
2151 =item * Disjointness
2153 int isl_basic_set_is_disjoint(
2154 __isl_keep isl_basic_set *bset1,
2155 __isl_keep isl_basic_set *bset2);
2156 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2157 __isl_keep isl_set *set2);
2158 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2159 __isl_keep isl_set *set2);
2160 int isl_basic_map_is_disjoint(
2161 __isl_keep isl_basic_map *bmap1,
2162 __isl_keep isl_basic_map *bmap2);
2163 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2164 __isl_keep isl_map *map2);
2168 int isl_basic_set_is_subset(
2169 __isl_keep isl_basic_set *bset1,
2170 __isl_keep isl_basic_set *bset2);
2171 int isl_set_is_subset(__isl_keep isl_set *set1,
2172 __isl_keep isl_set *set2);
2173 int isl_set_is_strict_subset(
2174 __isl_keep isl_set *set1,
2175 __isl_keep isl_set *set2);
2176 int isl_union_set_is_subset(
2177 __isl_keep isl_union_set *uset1,
2178 __isl_keep isl_union_set *uset2);
2179 int isl_union_set_is_strict_subset(
2180 __isl_keep isl_union_set *uset1,
2181 __isl_keep isl_union_set *uset2);
2182 int isl_basic_map_is_subset(
2183 __isl_keep isl_basic_map *bmap1,
2184 __isl_keep isl_basic_map *bmap2);
2185 int isl_basic_map_is_strict_subset(
2186 __isl_keep isl_basic_map *bmap1,
2187 __isl_keep isl_basic_map *bmap2);
2188 int isl_map_is_subset(
2189 __isl_keep isl_map *map1,
2190 __isl_keep isl_map *map2);
2191 int isl_map_is_strict_subset(
2192 __isl_keep isl_map *map1,
2193 __isl_keep isl_map *map2);
2194 int isl_union_map_is_subset(
2195 __isl_keep isl_union_map *umap1,
2196 __isl_keep isl_union_map *umap2);
2197 int isl_union_map_is_strict_subset(
2198 __isl_keep isl_union_map *umap1,
2199 __isl_keep isl_union_map *umap2);
2201 Check whether the first argument is a (strict) subset of the
2206 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2207 __isl_keep isl_set *set2);
2209 This function is useful for sorting C<isl_set>s.
2210 The order depends on the internal representation of the inputs.
2211 The order is fixed over different calls to the function (assuming
2212 the internal representation of the inputs has not changed), but may
2213 change over different versions of C<isl>.
2217 =head2 Unary Operations
2223 __isl_give isl_set *isl_set_complement(
2224 __isl_take isl_set *set);
2225 __isl_give isl_map *isl_map_complement(
2226 __isl_take isl_map *map);
2230 __isl_give isl_basic_map *isl_basic_map_reverse(
2231 __isl_take isl_basic_map *bmap);
2232 __isl_give isl_map *isl_map_reverse(
2233 __isl_take isl_map *map);
2234 __isl_give isl_union_map *isl_union_map_reverse(
2235 __isl_take isl_union_map *umap);
2239 #include <isl/local_space.h>
2240 __isl_give isl_local_space *isl_local_space_domain(
2241 __isl_take isl_local_space *ls);
2242 __isl_give isl_local_space *isl_local_space_range(
2243 __isl_take isl_local_space *ls);
2245 #include <isl/set.h>
2246 __isl_give isl_basic_set *isl_basic_set_project_out(
2247 __isl_take isl_basic_set *bset,
2248 enum isl_dim_type type, unsigned first, unsigned n);
2249 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2250 enum isl_dim_type type, unsigned first, unsigned n);
2251 __isl_give isl_basic_set *isl_basic_set_params(
2252 __isl_take isl_basic_set *bset);
2253 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2255 #include <isl/map.h>
2256 __isl_give isl_basic_map *isl_basic_map_project_out(
2257 __isl_take isl_basic_map *bmap,
2258 enum isl_dim_type type, unsigned first, unsigned n);
2259 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2260 enum isl_dim_type type, unsigned first, unsigned n);
2261 __isl_give isl_basic_set *isl_basic_map_domain(
2262 __isl_take isl_basic_map *bmap);
2263 __isl_give isl_basic_set *isl_basic_map_range(
2264 __isl_take isl_basic_map *bmap);
2265 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2266 __isl_give isl_set *isl_map_domain(
2267 __isl_take isl_map *bmap);
2268 __isl_give isl_set *isl_map_range(
2269 __isl_take isl_map *map);
2271 #include <isl/union_set.h>
2272 __isl_give isl_set *isl_union_set_params(
2273 __isl_take isl_union_set *uset);
2275 #include <isl/union_map.h>
2276 __isl_give isl_union_map *isl_union_map_project_out(
2277 __isl_take isl_union_map *umap,
2278 enum isl_dim_type type, unsigned first, unsigned n);
2279 __isl_give isl_set *isl_union_map_params(
2280 __isl_take isl_union_map *umap);
2281 __isl_give isl_union_set *isl_union_map_domain(
2282 __isl_take isl_union_map *umap);
2283 __isl_give isl_union_set *isl_union_map_range(
2284 __isl_take isl_union_map *umap);
2286 The function C<isl_union_map_project_out> can only project out
2289 #include <isl/map.h>
2290 __isl_give isl_basic_map *isl_basic_map_domain_map(
2291 __isl_take isl_basic_map *bmap);
2292 __isl_give isl_basic_map *isl_basic_map_range_map(
2293 __isl_take isl_basic_map *bmap);
2294 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2295 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2297 #include <isl/union_map.h>
2298 __isl_give isl_union_map *isl_union_map_domain_map(
2299 __isl_take isl_union_map *umap);
2300 __isl_give isl_union_map *isl_union_map_range_map(
2301 __isl_take isl_union_map *umap);
2303 The functions above construct a (basic, regular or union) relation
2304 that maps (a wrapped version of) the input relation to its domain or range.
2308 __isl_give isl_basic_set *isl_basic_set_eliminate(
2309 __isl_take isl_basic_set *bset,
2310 enum isl_dim_type type,
2311 unsigned first, unsigned n);
2312 __isl_give isl_set *isl_set_eliminate(
2313 __isl_take isl_set *set, enum isl_dim_type type,
2314 unsigned first, unsigned n);
2315 __isl_give isl_basic_map *isl_basic_map_eliminate(
2316 __isl_take isl_basic_map *bmap,
2317 enum isl_dim_type type,
2318 unsigned first, unsigned n);
2319 __isl_give isl_map *isl_map_eliminate(
2320 __isl_take isl_map *map, enum isl_dim_type type,
2321 unsigned first, unsigned n);
2323 Eliminate the coefficients for the given dimensions from the constraints,
2324 without removing the dimensions.
2326 =item * Constructing a relation from a set
2328 #include <isl/local_space.h>
2329 __isl_give isl_local_space *isl_local_space_from_domain(
2330 __isl_take isl_local_space *ls);
2332 #include <isl/map.h>
2333 __isl_give isl_map *isl_map_from_domain(
2334 __isl_take isl_set *set);
2335 __isl_give isl_map *isl_map_from_range(
2336 __isl_take isl_set *set);
2338 Create a relation with the given set as domain or range.
2339 The range or domain of the created relation is a zero-dimensional
2340 flat anonymous space.
2344 __isl_give isl_basic_set *isl_basic_set_fix_si(
2345 __isl_take isl_basic_set *bset,
2346 enum isl_dim_type type, unsigned pos, int value);
2347 __isl_give isl_basic_set *isl_basic_set_fix_val(
2348 __isl_take isl_basic_set *bset,
2349 enum isl_dim_type type, unsigned pos,
2350 __isl_take isl_val *v);
2351 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2352 enum isl_dim_type type, unsigned pos, int value);
2353 __isl_give isl_set *isl_set_fix_val(
2354 __isl_take isl_set *set,
2355 enum isl_dim_type type, unsigned pos,
2356 __isl_take isl_val *v);
2357 __isl_give isl_basic_map *isl_basic_map_fix_si(
2358 __isl_take isl_basic_map *bmap,
2359 enum isl_dim_type type, unsigned pos, int value);
2360 __isl_give isl_basic_map *isl_basic_map_fix_val(
2361 __isl_take isl_basic_map *bmap,
2362 enum isl_dim_type type, unsigned pos,
2363 __isl_take isl_val *v);
2364 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2365 enum isl_dim_type type, unsigned pos, int value);
2366 __isl_give isl_map *isl_map_fix_val(
2367 __isl_take isl_map *map,
2368 enum isl_dim_type type, unsigned pos,
2369 __isl_take isl_val *v);
2371 Intersect the set or relation with the hyperplane where the given
2372 dimension has the fixed given value.
2374 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2375 __isl_take isl_basic_map *bmap,
2376 enum isl_dim_type type, unsigned pos, int value);
2377 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2378 __isl_take isl_basic_map *bmap,
2379 enum isl_dim_type type, unsigned pos, int value);
2380 __isl_give isl_set *isl_set_lower_bound_si(
2381 __isl_take isl_set *set,
2382 enum isl_dim_type type, unsigned pos, int value);
2383 __isl_give isl_set *isl_set_lower_bound_val(
2384 __isl_take isl_set *set,
2385 enum isl_dim_type type, unsigned pos,
2386 __isl_take isl_val *value);
2387 __isl_give isl_map *isl_map_lower_bound_si(
2388 __isl_take isl_map *map,
2389 enum isl_dim_type type, unsigned pos, int value);
2390 __isl_give isl_set *isl_set_upper_bound_si(
2391 __isl_take isl_set *set,
2392 enum isl_dim_type type, unsigned pos, int value);
2393 __isl_give isl_set *isl_set_upper_bound_val(
2394 __isl_take isl_set *set,
2395 enum isl_dim_type type, unsigned pos,
2396 __isl_take isl_val *value);
2397 __isl_give isl_map *isl_map_upper_bound_si(
2398 __isl_take isl_map *map,
2399 enum isl_dim_type type, unsigned pos, int value);
2401 Intersect the set or relation with the half-space where the given
2402 dimension has a value bounded by the fixed given integer value.
2404 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2405 enum isl_dim_type type1, int pos1,
2406 enum isl_dim_type type2, int pos2);
2407 __isl_give isl_basic_map *isl_basic_map_equate(
2408 __isl_take isl_basic_map *bmap,
2409 enum isl_dim_type type1, int pos1,
2410 enum isl_dim_type type2, int pos2);
2411 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2412 enum isl_dim_type type1, int pos1,
2413 enum isl_dim_type type2, int pos2);
2415 Intersect the set or relation with the hyperplane where the given
2416 dimensions are equal to each other.
2418 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2419 enum isl_dim_type type1, int pos1,
2420 enum isl_dim_type type2, int pos2);
2422 Intersect the relation with the hyperplane where the given
2423 dimensions have opposite values.
2425 __isl_give isl_map *isl_map_order_le(
2426 __isl_take isl_map *map,
2427 enum isl_dim_type type1, int pos1,
2428 enum isl_dim_type type2, int pos2);
2429 __isl_give isl_basic_map *isl_basic_map_order_ge(
2430 __isl_take isl_basic_map *bmap,
2431 enum isl_dim_type type1, int pos1,
2432 enum isl_dim_type type2, int pos2);
2433 __isl_give isl_map *isl_map_order_ge(
2434 __isl_take isl_map *map,
2435 enum isl_dim_type type1, int pos1,
2436 enum isl_dim_type type2, int pos2);
2437 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2438 enum isl_dim_type type1, int pos1,
2439 enum isl_dim_type type2, int pos2);
2440 __isl_give isl_basic_map *isl_basic_map_order_gt(
2441 __isl_take isl_basic_map *bmap,
2442 enum isl_dim_type type1, int pos1,
2443 enum isl_dim_type type2, int pos2);
2444 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2445 enum isl_dim_type type1, int pos1,
2446 enum isl_dim_type type2, int pos2);
2448 Intersect the relation with the half-space where the given
2449 dimensions satisfy the given ordering.
2453 __isl_give isl_map *isl_set_identity(
2454 __isl_take isl_set *set);
2455 __isl_give isl_union_map *isl_union_set_identity(
2456 __isl_take isl_union_set *uset);
2458 Construct an identity relation on the given (union) set.
2462 __isl_give isl_basic_set *isl_basic_map_deltas(
2463 __isl_take isl_basic_map *bmap);
2464 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2465 __isl_give isl_union_set *isl_union_map_deltas(
2466 __isl_take isl_union_map *umap);
2468 These functions return a (basic) set containing the differences
2469 between image elements and corresponding domain elements in the input.
2471 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2472 __isl_take isl_basic_map *bmap);
2473 __isl_give isl_map *isl_map_deltas_map(
2474 __isl_take isl_map *map);
2475 __isl_give isl_union_map *isl_union_map_deltas_map(
2476 __isl_take isl_union_map *umap);
2478 The functions above construct a (basic, regular or union) relation
2479 that maps (a wrapped version of) the input relation to its delta set.
2483 Simplify the representation of a set or relation by trying
2484 to combine pairs of basic sets or relations into a single
2485 basic set or relation.
2487 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2488 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2489 __isl_give isl_union_set *isl_union_set_coalesce(
2490 __isl_take isl_union_set *uset);
2491 __isl_give isl_union_map *isl_union_map_coalesce(
2492 __isl_take isl_union_map *umap);
2494 One of the methods for combining pairs of basic sets or relations
2495 can result in coefficients that are much larger than those that appear
2496 in the constraints of the input. By default, the coefficients are
2497 not allowed to grow larger, but this can be changed by unsetting
2498 the following option.
2500 int isl_options_set_coalesce_bounded_wrapping(
2501 isl_ctx *ctx, int val);
2502 int isl_options_get_coalesce_bounded_wrapping(
2505 =item * Detecting equalities
2507 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2508 __isl_take isl_basic_set *bset);
2509 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2510 __isl_take isl_basic_map *bmap);
2511 __isl_give isl_set *isl_set_detect_equalities(
2512 __isl_take isl_set *set);
2513 __isl_give isl_map *isl_map_detect_equalities(
2514 __isl_take isl_map *map);
2515 __isl_give isl_union_set *isl_union_set_detect_equalities(
2516 __isl_take isl_union_set *uset);
2517 __isl_give isl_union_map *isl_union_map_detect_equalities(
2518 __isl_take isl_union_map *umap);
2520 Simplify the representation of a set or relation by detecting implicit
2523 =item * Removing redundant constraints
2525 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2526 __isl_take isl_basic_set *bset);
2527 __isl_give isl_set *isl_set_remove_redundancies(
2528 __isl_take isl_set *set);
2529 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2530 __isl_take isl_basic_map *bmap);
2531 __isl_give isl_map *isl_map_remove_redundancies(
2532 __isl_take isl_map *map);
2536 __isl_give isl_basic_set *isl_set_convex_hull(
2537 __isl_take isl_set *set);
2538 __isl_give isl_basic_map *isl_map_convex_hull(
2539 __isl_take isl_map *map);
2541 If the input set or relation has any existentially quantified
2542 variables, then the result of these operations is currently undefined.
2546 __isl_give isl_basic_set *
2547 isl_set_unshifted_simple_hull(
2548 __isl_take isl_set *set);
2549 __isl_give isl_basic_map *
2550 isl_map_unshifted_simple_hull(
2551 __isl_take isl_map *map);
2552 __isl_give isl_basic_set *isl_set_simple_hull(
2553 __isl_take isl_set *set);
2554 __isl_give isl_basic_map *isl_map_simple_hull(
2555 __isl_take isl_map *map);
2556 __isl_give isl_union_map *isl_union_map_simple_hull(
2557 __isl_take isl_union_map *umap);
2559 These functions compute a single basic set or relation
2560 that contains the whole input set or relation.
2561 In particular, the output is described by translates
2562 of the constraints describing the basic sets or relations in the input.
2563 In case of C<isl_set_unshifted_simple_hull>, only the original
2564 constraints are used, without any translation.
2568 (See \autoref{s:simple hull}.)
2574 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2575 __isl_take isl_basic_set *bset);
2576 __isl_give isl_basic_set *isl_set_affine_hull(
2577 __isl_take isl_set *set);
2578 __isl_give isl_union_set *isl_union_set_affine_hull(
2579 __isl_take isl_union_set *uset);
2580 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2581 __isl_take isl_basic_map *bmap);
2582 __isl_give isl_basic_map *isl_map_affine_hull(
2583 __isl_take isl_map *map);
2584 __isl_give isl_union_map *isl_union_map_affine_hull(
2585 __isl_take isl_union_map *umap);
2587 In case of union sets and relations, the affine hull is computed
2590 =item * Polyhedral hull
2592 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2593 __isl_take isl_set *set);
2594 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2595 __isl_take isl_map *map);
2596 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2597 __isl_take isl_union_set *uset);
2598 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2599 __isl_take isl_union_map *umap);
2601 These functions compute a single basic set or relation
2602 not involving any existentially quantified variables
2603 that contains the whole input set or relation.
2604 In case of union sets and relations, the polyhedral hull is computed
2607 =item * Other approximations
2609 __isl_give isl_basic_set *
2610 isl_basic_set_drop_constraints_involving_dims(
2611 __isl_take isl_basic_set *bset,
2612 enum isl_dim_type type,
2613 unsigned first, unsigned n);
2614 __isl_give isl_basic_map *
2615 isl_basic_map_drop_constraints_involving_dims(
2616 __isl_take isl_basic_map *bmap,
2617 enum isl_dim_type type,
2618 unsigned first, unsigned n);
2619 __isl_give isl_basic_set *
2620 isl_basic_set_drop_constraints_not_involving_dims(
2621 __isl_take isl_basic_set *bset,
2622 enum isl_dim_type type,
2623 unsigned first, unsigned n);
2624 __isl_give isl_set *
2625 isl_set_drop_constraints_involving_dims(
2626 __isl_take isl_set *set,
2627 enum isl_dim_type type,
2628 unsigned first, unsigned n);
2629 __isl_give isl_map *
2630 isl_map_drop_constraints_involving_dims(
2631 __isl_take isl_map *map,
2632 enum isl_dim_type type,
2633 unsigned first, unsigned n);
2635 These functions drop any constraints (not) involving the specified dimensions.
2636 Note that the result depends on the representation of the input.
2640 __isl_give isl_basic_set *isl_basic_set_sample(
2641 __isl_take isl_basic_set *bset);
2642 __isl_give isl_basic_set *isl_set_sample(
2643 __isl_take isl_set *set);
2644 __isl_give isl_basic_map *isl_basic_map_sample(
2645 __isl_take isl_basic_map *bmap);
2646 __isl_give isl_basic_map *isl_map_sample(
2647 __isl_take isl_map *map);
2649 If the input (basic) set or relation is non-empty, then return
2650 a singleton subset of the input. Otherwise, return an empty set.
2652 =item * Optimization
2654 #include <isl/ilp.h>
2655 __isl_give isl_val *isl_basic_set_max_val(
2656 __isl_keep isl_basic_set *bset,
2657 __isl_keep isl_aff *obj);
2658 __isl_give isl_val *isl_set_min_val(
2659 __isl_keep isl_set *set,
2660 __isl_keep isl_aff *obj);
2661 __isl_give isl_val *isl_set_max_val(
2662 __isl_keep isl_set *set,
2663 __isl_keep isl_aff *obj);
2665 Compute the minimum or maximum of the integer affine expression C<obj>
2666 over the points in C<set>, returning the result in C<opt>.
2667 The result is C<NULL> in case of an error, the optimal value in case
2668 there is one, negative infinity or infinity if the problem is unbounded and
2669 NaN if the problem is empty.
2671 =item * Parametric optimization
2673 __isl_give isl_pw_aff *isl_set_dim_min(
2674 __isl_take isl_set *set, int pos);
2675 __isl_give isl_pw_aff *isl_set_dim_max(
2676 __isl_take isl_set *set, int pos);
2677 __isl_give isl_pw_aff *isl_map_dim_max(
2678 __isl_take isl_map *map, int pos);
2680 Compute the minimum or maximum of the given set or output dimension
2681 as a function of the parameters (and input dimensions), but independently
2682 of the other set or output dimensions.
2683 For lexicographic optimization, see L<"Lexicographic Optimization">.
2687 The following functions compute either the set of (rational) coefficient
2688 values of valid constraints for the given set or the set of (rational)
2689 values satisfying the constraints with coefficients from the given set.
2690 Internally, these two sets of functions perform essentially the
2691 same operations, except that the set of coefficients is assumed to
2692 be a cone, while the set of values may be any polyhedron.
2693 The current implementation is based on the Farkas lemma and
2694 Fourier-Motzkin elimination, but this may change or be made optional
2695 in future. In particular, future implementations may use different
2696 dualization algorithms or skip the elimination step.
2698 __isl_give isl_basic_set *isl_basic_set_coefficients(
2699 __isl_take isl_basic_set *bset);
2700 __isl_give isl_basic_set *isl_set_coefficients(
2701 __isl_take isl_set *set);
2702 __isl_give isl_union_set *isl_union_set_coefficients(
2703 __isl_take isl_union_set *bset);
2704 __isl_give isl_basic_set *isl_basic_set_solutions(
2705 __isl_take isl_basic_set *bset);
2706 __isl_give isl_basic_set *isl_set_solutions(
2707 __isl_take isl_set *set);
2708 __isl_give isl_union_set *isl_union_set_solutions(
2709 __isl_take isl_union_set *bset);
2713 __isl_give isl_map *isl_map_fixed_power_val(
2714 __isl_take isl_map *map,
2715 __isl_take isl_val *exp);
2716 __isl_give isl_union_map *
2717 isl_union_map_fixed_power_val(
2718 __isl_take isl_union_map *umap,
2719 __isl_take isl_val *exp);
2721 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2722 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2723 of C<map> is computed.
2725 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2727 __isl_give isl_union_map *isl_union_map_power(
2728 __isl_take isl_union_map *umap, int *exact);
2730 Compute a parametric representation for all positive powers I<k> of C<map>.
2731 The result maps I<k> to a nested relation corresponding to the
2732 I<k>th power of C<map>.
2733 The result may be an overapproximation. If the result is known to be exact,
2734 then C<*exact> is set to C<1>.
2736 =item * Transitive closure
2738 __isl_give isl_map *isl_map_transitive_closure(
2739 __isl_take isl_map *map, int *exact);
2740 __isl_give isl_union_map *isl_union_map_transitive_closure(
2741 __isl_take isl_union_map *umap, int *exact);
2743 Compute the transitive closure of C<map>.
2744 The result may be an overapproximation. If the result is known to be exact,
2745 then C<*exact> is set to C<1>.
2747 =item * Reaching path lengths
2749 __isl_give isl_map *isl_map_reaching_path_lengths(
2750 __isl_take isl_map *map, int *exact);
2752 Compute a relation that maps each element in the range of C<map>
2753 to the lengths of all paths composed of edges in C<map> that
2754 end up in the given element.
2755 The result may be an overapproximation. If the result is known to be exact,
2756 then C<*exact> is set to C<1>.
2757 To compute the I<maximal> path length, the resulting relation
2758 should be postprocessed by C<isl_map_lexmax>.
2759 In particular, if the input relation is a dependence relation
2760 (mapping sources to sinks), then the maximal path length corresponds
2761 to the free schedule.
2762 Note, however, that C<isl_map_lexmax> expects the maximum to be
2763 finite, so if the path lengths are unbounded (possibly due to
2764 the overapproximation), then you will get an error message.
2768 #include <isl/space.h>
2769 __isl_give isl_space *isl_space_wrap(
2770 __isl_take isl_space *space);
2771 __isl_give isl_space *isl_space_unwrap(
2772 __isl_take isl_space *space);
2774 #include <isl/set.h>
2775 __isl_give isl_basic_map *isl_basic_set_unwrap(
2776 __isl_take isl_basic_set *bset);
2777 __isl_give isl_map *isl_set_unwrap(
2778 __isl_take isl_set *set);
2780 #include <isl/map.h>
2781 __isl_give isl_basic_set *isl_basic_map_wrap(
2782 __isl_take isl_basic_map *bmap);
2783 __isl_give isl_set *isl_map_wrap(
2784 __isl_take isl_map *map);
2786 #include <isl/union_set.h>
2787 __isl_give isl_union_map *isl_union_set_unwrap(
2788 __isl_take isl_union_set *uset);
2790 #include <isl/union_map.h>
2791 __isl_give isl_union_set *isl_union_map_wrap(
2792 __isl_take isl_union_map *umap);
2794 The input to C<isl_space_unwrap> should
2795 be the space of a set, while that of
2796 C<isl_space_wrap> should be the space of a relation.
2797 Conversely, the output of C<isl_space_unwrap> is the space
2798 of a relation, while that of C<isl_space_wrap> is the space of a set.
2802 Remove any internal structure of domain (and range) of the given
2803 set or relation. If there is any such internal structure in the input,
2804 then the name of the space is also removed.
2806 #include <isl/local_space.h>
2807 __isl_give isl_local_space *
2808 isl_local_space_flatten_domain(
2809 __isl_take isl_local_space *ls);
2810 __isl_give isl_local_space *
2811 isl_local_space_flatten_range(
2812 __isl_take isl_local_space *ls);
2814 #include <isl/set.h>
2815 __isl_give isl_basic_set *isl_basic_set_flatten(
2816 __isl_take isl_basic_set *bset);
2817 __isl_give isl_set *isl_set_flatten(
2818 __isl_take isl_set *set);
2820 #include <isl/map.h>
2821 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2822 __isl_take isl_basic_map *bmap);
2823 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2824 __isl_take isl_basic_map *bmap);
2825 __isl_give isl_map *isl_map_flatten_range(
2826 __isl_take isl_map *map);
2827 __isl_give isl_map *isl_map_flatten_domain(
2828 __isl_take isl_map *map);
2829 __isl_give isl_basic_map *isl_basic_map_flatten(
2830 __isl_take isl_basic_map *bmap);
2831 __isl_give isl_map *isl_map_flatten(
2832 __isl_take isl_map *map);
2834 #include <isl/map.h>
2835 __isl_give isl_map *isl_set_flatten_map(
2836 __isl_take isl_set *set);
2838 The function above constructs a relation
2839 that maps the input set to a flattened version of the set.
2843 Lift the input set to a space with extra dimensions corresponding
2844 to the existentially quantified variables in the input.
2845 In particular, the result lives in a wrapped map where the domain
2846 is the original space and the range corresponds to the original
2847 existentially quantified variables.
2849 __isl_give isl_basic_set *isl_basic_set_lift(
2850 __isl_take isl_basic_set *bset);
2851 __isl_give isl_set *isl_set_lift(
2852 __isl_take isl_set *set);
2853 __isl_give isl_union_set *isl_union_set_lift(
2854 __isl_take isl_union_set *uset);
2856 Given a local space that contains the existentially quantified
2857 variables of a set, a basic relation that, when applied to
2858 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2859 can be constructed using the following function.
2861 #include <isl/local_space.h>
2862 __isl_give isl_basic_map *isl_local_space_lifting(
2863 __isl_take isl_local_space *ls);
2865 =item * Internal Product
2867 __isl_give isl_basic_map *isl_basic_map_zip(
2868 __isl_take isl_basic_map *bmap);
2869 __isl_give isl_map *isl_map_zip(
2870 __isl_take isl_map *map);
2871 __isl_give isl_union_map *isl_union_map_zip(
2872 __isl_take isl_union_map *umap);
2874 Given a relation with nested relations for domain and range,
2875 interchange the range of the domain with the domain of the range.
2879 __isl_give isl_basic_map *isl_basic_map_curry(
2880 __isl_take isl_basic_map *bmap);
2881 __isl_give isl_basic_map *isl_basic_map_uncurry(
2882 __isl_take isl_basic_map *bmap);
2883 __isl_give isl_map *isl_map_curry(
2884 __isl_take isl_map *map);
2885 __isl_give isl_map *isl_map_uncurry(
2886 __isl_take isl_map *map);
2887 __isl_give isl_union_map *isl_union_map_curry(
2888 __isl_take isl_union_map *umap);
2889 __isl_give isl_union_map *isl_union_map_uncurry(
2890 __isl_take isl_union_map *umap);
2892 Given a relation with a nested relation for domain,
2893 the C<curry> functions
2894 move the range of the nested relation out of the domain
2895 and use it as the domain of a nested relation in the range,
2896 with the original range as range of this nested relation.
2897 The C<uncurry> functions perform the inverse operation.
2899 =item * Aligning parameters
2901 __isl_give isl_basic_set *isl_basic_set_align_params(
2902 __isl_take isl_basic_set *bset,
2903 __isl_take isl_space *model);
2904 __isl_give isl_set *isl_set_align_params(
2905 __isl_take isl_set *set,
2906 __isl_take isl_space *model);
2907 __isl_give isl_basic_map *isl_basic_map_align_params(
2908 __isl_take isl_basic_map *bmap,
2909 __isl_take isl_space *model);
2910 __isl_give isl_map *isl_map_align_params(
2911 __isl_take isl_map *map,
2912 __isl_take isl_space *model);
2914 Change the order of the parameters of the given set or relation
2915 such that the first parameters match those of C<model>.
2916 This may involve the introduction of extra parameters.
2917 All parameters need to be named.
2919 =item * Dimension manipulation
2921 #include <isl/local_space.h>
2922 __isl_give isl_local_space *isl_local_space_add_dims(
2923 __isl_take isl_local_space *ls,
2924 enum isl_dim_type type, unsigned n);
2925 __isl_give isl_local_space *isl_local_space_insert_dims(
2926 __isl_take isl_local_space *ls,
2927 enum isl_dim_type type, unsigned first, unsigned n);
2928 __isl_give isl_local_space *isl_local_space_drop_dims(
2929 __isl_take isl_local_space *ls,
2930 enum isl_dim_type type, unsigned first, unsigned n);
2932 #include <isl/set.h>
2933 __isl_give isl_basic_set *isl_basic_set_add_dims(
2934 __isl_take isl_basic_set *bset,
2935 enum isl_dim_type type, unsigned n);
2936 __isl_give isl_set *isl_set_add_dims(
2937 __isl_take isl_set *set,
2938 enum isl_dim_type type, unsigned n);
2939 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2940 __isl_take isl_basic_set *bset,
2941 enum isl_dim_type type, unsigned pos,
2943 __isl_give isl_set *isl_set_insert_dims(
2944 __isl_take isl_set *set,
2945 enum isl_dim_type type, unsigned pos, unsigned n);
2946 __isl_give isl_basic_set *isl_basic_set_move_dims(
2947 __isl_take isl_basic_set *bset,
2948 enum isl_dim_type dst_type, unsigned dst_pos,
2949 enum isl_dim_type src_type, unsigned src_pos,
2951 __isl_give isl_set *isl_set_move_dims(
2952 __isl_take isl_set *set,
2953 enum isl_dim_type dst_type, unsigned dst_pos,
2954 enum isl_dim_type src_type, unsigned src_pos,
2957 #include <isl/map.h>
2958 __isl_give isl_map *isl_map_add_dims(
2959 __isl_take isl_map *map,
2960 enum isl_dim_type type, unsigned n);
2961 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2962 __isl_take isl_basic_map *bmap,
2963 enum isl_dim_type type, unsigned pos,
2965 __isl_give isl_map *isl_map_insert_dims(
2966 __isl_take isl_map *map,
2967 enum isl_dim_type type, unsigned pos, unsigned n);
2968 __isl_give isl_basic_map *isl_basic_map_move_dims(
2969 __isl_take isl_basic_map *bmap,
2970 enum isl_dim_type dst_type, unsigned dst_pos,
2971 enum isl_dim_type src_type, unsigned src_pos,
2973 __isl_give isl_map *isl_map_move_dims(
2974 __isl_take isl_map *map,
2975 enum isl_dim_type dst_type, unsigned dst_pos,
2976 enum isl_dim_type src_type, unsigned src_pos,
2979 It is usually not advisable to directly change the (input or output)
2980 space of a set or a relation as this removes the name and the internal
2981 structure of the space. However, the above functions can be useful
2982 to add new parameters, assuming
2983 C<isl_set_align_params> and C<isl_map_align_params>
2988 =head2 Binary Operations
2990 The two arguments of a binary operation not only need to live
2991 in the same C<isl_ctx>, they currently also need to have
2992 the same (number of) parameters.
2994 =head3 Basic Operations
2998 =item * Intersection
3000 #include <isl/local_space.h>
3001 __isl_give isl_local_space *isl_local_space_intersect(
3002 __isl_take isl_local_space *ls1,
3003 __isl_take isl_local_space *ls2);
3005 #include <isl/set.h>
3006 __isl_give isl_basic_set *isl_basic_set_intersect_params(
3007 __isl_take isl_basic_set *bset1,
3008 __isl_take isl_basic_set *bset2);
3009 __isl_give isl_basic_set *isl_basic_set_intersect(
3010 __isl_take isl_basic_set *bset1,
3011 __isl_take isl_basic_set *bset2);
3012 __isl_give isl_set *isl_set_intersect_params(
3013 __isl_take isl_set *set,
3014 __isl_take isl_set *params);
3015 __isl_give isl_set *isl_set_intersect(
3016 __isl_take isl_set *set1,
3017 __isl_take isl_set *set2);
3019 #include <isl/map.h>
3020 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
3021 __isl_take isl_basic_map *bmap,
3022 __isl_take isl_basic_set *bset);
3023 __isl_give isl_basic_map *isl_basic_map_intersect_range(
3024 __isl_take isl_basic_map *bmap,
3025 __isl_take isl_basic_set *bset);
3026 __isl_give isl_basic_map *isl_basic_map_intersect(
3027 __isl_take isl_basic_map *bmap1,
3028 __isl_take isl_basic_map *bmap2);
3029 __isl_give isl_map *isl_map_intersect_params(
3030 __isl_take isl_map *map,
3031 __isl_take isl_set *params);
3032 __isl_give isl_map *isl_map_intersect_domain(
3033 __isl_take isl_map *map,
3034 __isl_take isl_set *set);
3035 __isl_give isl_map *isl_map_intersect_range(
3036 __isl_take isl_map *map,
3037 __isl_take isl_set *set);
3038 __isl_give isl_map *isl_map_intersect(
3039 __isl_take isl_map *map1,
3040 __isl_take isl_map *map2);
3042 #include <isl/union_set.h>
3043 __isl_give isl_union_set *isl_union_set_intersect_params(
3044 __isl_take isl_union_set *uset,
3045 __isl_take isl_set *set);
3046 __isl_give isl_union_set *isl_union_set_intersect(
3047 __isl_take isl_union_set *uset1,
3048 __isl_take isl_union_set *uset2);
3050 #include <isl/union_map.h>
3051 __isl_give isl_union_map *isl_union_map_intersect_params(
3052 __isl_take isl_union_map *umap,
3053 __isl_take isl_set *set);
3054 __isl_give isl_union_map *isl_union_map_intersect_domain(
3055 __isl_take isl_union_map *umap,
3056 __isl_take isl_union_set *uset);
3057 __isl_give isl_union_map *isl_union_map_intersect_range(
3058 __isl_take isl_union_map *umap,
3059 __isl_take isl_union_set *uset);
3060 __isl_give isl_union_map *isl_union_map_intersect(
3061 __isl_take isl_union_map *umap1,
3062 __isl_take isl_union_map *umap2);
3064 The second argument to the C<_params> functions needs to be
3065 a parametric (basic) set. For the other functions, a parametric set
3066 for either argument is only allowed if the other argument is
3067 a parametric set as well.
3071 __isl_give isl_set *isl_basic_set_union(
3072 __isl_take isl_basic_set *bset1,
3073 __isl_take isl_basic_set *bset2);
3074 __isl_give isl_map *isl_basic_map_union(
3075 __isl_take isl_basic_map *bmap1,
3076 __isl_take isl_basic_map *bmap2);
3077 __isl_give isl_set *isl_set_union(
3078 __isl_take isl_set *set1,
3079 __isl_take isl_set *set2);
3080 __isl_give isl_map *isl_map_union(
3081 __isl_take isl_map *map1,
3082 __isl_take isl_map *map2);
3083 __isl_give isl_union_set *isl_union_set_union(
3084 __isl_take isl_union_set *uset1,
3085 __isl_take isl_union_set *uset2);
3086 __isl_give isl_union_map *isl_union_map_union(
3087 __isl_take isl_union_map *umap1,
3088 __isl_take isl_union_map *umap2);
3090 =item * Set difference
3092 __isl_give isl_set *isl_set_subtract(
3093 __isl_take isl_set *set1,
3094 __isl_take isl_set *set2);
3095 __isl_give isl_map *isl_map_subtract(
3096 __isl_take isl_map *map1,
3097 __isl_take isl_map *map2);
3098 __isl_give isl_map *isl_map_subtract_domain(
3099 __isl_take isl_map *map,
3100 __isl_take isl_set *dom);
3101 __isl_give isl_map *isl_map_subtract_range(
3102 __isl_take isl_map *map,
3103 __isl_take isl_set *dom);
3104 __isl_give isl_union_set *isl_union_set_subtract(
3105 __isl_take isl_union_set *uset1,
3106 __isl_take isl_union_set *uset2);
3107 __isl_give isl_union_map *isl_union_map_subtract(
3108 __isl_take isl_union_map *umap1,
3109 __isl_take isl_union_map *umap2);
3110 __isl_give isl_union_map *isl_union_map_subtract_domain(
3111 __isl_take isl_union_map *umap,
3112 __isl_take isl_union_set *dom);
3113 __isl_give isl_union_map *isl_union_map_subtract_range(
3114 __isl_take isl_union_map *umap,
3115 __isl_take isl_union_set *dom);
3119 __isl_give isl_basic_set *isl_basic_set_apply(
3120 __isl_take isl_basic_set *bset,
3121 __isl_take isl_basic_map *bmap);
3122 __isl_give isl_set *isl_set_apply(
3123 __isl_take isl_set *set,
3124 __isl_take isl_map *map);
3125 __isl_give isl_union_set *isl_union_set_apply(
3126 __isl_take isl_union_set *uset,
3127 __isl_take isl_union_map *umap);
3128 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3129 __isl_take isl_basic_map *bmap1,
3130 __isl_take isl_basic_map *bmap2);
3131 __isl_give isl_basic_map *isl_basic_map_apply_range(
3132 __isl_take isl_basic_map *bmap1,
3133 __isl_take isl_basic_map *bmap2);
3134 __isl_give isl_map *isl_map_apply_domain(
3135 __isl_take isl_map *map1,
3136 __isl_take isl_map *map2);
3137 __isl_give isl_union_map *isl_union_map_apply_domain(
3138 __isl_take isl_union_map *umap1,
3139 __isl_take isl_union_map *umap2);
3140 __isl_give isl_map *isl_map_apply_range(
3141 __isl_take isl_map *map1,
3142 __isl_take isl_map *map2);
3143 __isl_give isl_union_map *isl_union_map_apply_range(
3144 __isl_take isl_union_map *umap1,
3145 __isl_take isl_union_map *umap2);
3149 #include <isl/set.h>
3150 __isl_give isl_basic_set *
3151 isl_basic_set_preimage_multi_aff(
3152 __isl_take isl_basic_set *bset,
3153 __isl_take isl_multi_aff *ma);
3154 __isl_give isl_set *isl_set_preimage_multi_aff(
3155 __isl_take isl_set *set,
3156 __isl_take isl_multi_aff *ma);
3157 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3158 __isl_take isl_set *set,
3159 __isl_take isl_pw_multi_aff *pma);
3160 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
3161 __isl_take isl_set *set,
3162 __isl_take isl_multi_pw_aff *mpa);
3164 #include <isl/union_set.h>
3165 __isl_give isl_union_set *
3166 isl_union_set_preimage_multi_aff(
3167 __isl_take isl_union_set *uset,
3168 __isl_take isl_multi_aff *ma);
3169 __isl_give isl_union_set *
3170 isl_union_set_preimage_pw_multi_aff(
3171 __isl_take isl_union_set *uset,
3172 __isl_take isl_pw_multi_aff *pma);
3173 __isl_give isl_union_set *
3174 isl_union_set_preimage_union_pw_multi_aff(
3175 __isl_take isl_union_set *uset,
3176 __isl_take isl_union_pw_multi_aff *upma);
3178 #include <isl/map.h>
3179 __isl_give isl_basic_map *
3180 isl_basic_map_preimage_domain_multi_aff(
3181 __isl_take isl_basic_map *bmap,
3182 __isl_take isl_multi_aff *ma);
3183 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3184 __isl_take isl_map *map,
3185 __isl_take isl_multi_aff *ma);
3186 __isl_give isl_map *isl_map_preimage_range_multi_aff(
3187 __isl_take isl_map *map,
3188 __isl_take isl_multi_aff *ma);
3189 __isl_give isl_map *
3190 isl_map_preimage_domain_pw_multi_aff(
3191 __isl_take isl_map *map,
3192 __isl_take isl_pw_multi_aff *pma);
3193 __isl_give isl_map *
3194 isl_map_preimage_range_pw_multi_aff(
3195 __isl_take isl_map *map,
3196 __isl_take isl_pw_multi_aff *pma);
3197 __isl_give isl_map *
3198 isl_map_preimage_domain_multi_pw_aff(
3199 __isl_take isl_map *map,
3200 __isl_take isl_multi_pw_aff *mpa);
3201 __isl_give isl_basic_map *
3202 isl_basic_map_preimage_range_multi_aff(
3203 __isl_take isl_basic_map *bmap,
3204 __isl_take isl_multi_aff *ma);
3206 #include <isl/union_map.h>
3207 __isl_give isl_union_map *
3208 isl_union_map_preimage_domain_multi_aff(
3209 __isl_take isl_union_map *umap,
3210 __isl_take isl_multi_aff *ma);
3211 __isl_give isl_union_map *
3212 isl_union_map_preimage_range_multi_aff(
3213 __isl_take isl_union_map *umap,
3214 __isl_take isl_multi_aff *ma);
3215 __isl_give isl_union_map *
3216 isl_union_map_preimage_domain_pw_multi_aff(
3217 __isl_take isl_union_map *umap,
3218 __isl_take isl_pw_multi_aff *pma);
3219 __isl_give isl_union_map *
3220 isl_union_map_preimage_range_pw_multi_aff(
3221 __isl_take isl_union_map *umap,
3222 __isl_take isl_pw_multi_aff *pma);
3223 __isl_give isl_union_map *
3224 isl_union_map_preimage_domain_union_pw_multi_aff(
3225 __isl_take isl_union_map *umap,
3226 __isl_take isl_union_pw_multi_aff *upma);
3227 __isl_give isl_union_map *
3228 isl_union_map_preimage_range_union_pw_multi_aff(
3229 __isl_take isl_union_map *umap,
3230 __isl_take isl_union_pw_multi_aff *upma);
3232 These functions compute the preimage of the given set or map domain/range under
3233 the given function. In other words, the expression is plugged
3234 into the set description or into the domain/range of the map.
3235 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3236 L</"Piecewise Multiple Quasi Affine Expressions">.
3238 =item * Cartesian Product
3240 #include <isl/space.h>
3241 __isl_give isl_space *isl_space_product(
3242 __isl_take isl_space *space1,
3243 __isl_take isl_space *space2);
3244 __isl_give isl_space *isl_space_domain_product(
3245 __isl_take isl_space *space1,
3246 __isl_take isl_space *space2);
3247 __isl_give isl_space *isl_space_range_product(
3248 __isl_take isl_space *space1,
3249 __isl_take isl_space *space2);
3252 C<isl_space_product>, C<isl_space_domain_product>
3253 and C<isl_space_range_product> take pairs or relation spaces and
3254 produce a single relations space, where either the domain, the range
3255 or both domain and range are wrapped spaces of relations between
3256 the domains and/or ranges of the input spaces.
3257 If the product is only constructed over the domain or the range
3258 then the ranges or the domains of the inputs should be the same.
3259 The function C<isl_space_product> also accepts a pair of set spaces,
3260 in which case it returns a wrapped space of a relation between the
3263 #include <isl/set.h>
3264 __isl_give isl_set *isl_set_product(
3265 __isl_take isl_set *set1,
3266 __isl_take isl_set *set2);
3268 #include <isl/map.h>
3269 __isl_give isl_basic_map *isl_basic_map_domain_product(
3270 __isl_take isl_basic_map *bmap1,
3271 __isl_take isl_basic_map *bmap2);
3272 __isl_give isl_basic_map *isl_basic_map_range_product(
3273 __isl_take isl_basic_map *bmap1,
3274 __isl_take isl_basic_map *bmap2);
3275 __isl_give isl_basic_map *isl_basic_map_product(
3276 __isl_take isl_basic_map *bmap1,
3277 __isl_take isl_basic_map *bmap2);
3278 __isl_give isl_map *isl_map_domain_product(
3279 __isl_take isl_map *map1,
3280 __isl_take isl_map *map2);
3281 __isl_give isl_map *isl_map_range_product(
3282 __isl_take isl_map *map1,
3283 __isl_take isl_map *map2);
3284 __isl_give isl_map *isl_map_product(
3285 __isl_take isl_map *map1,
3286 __isl_take isl_map *map2);
3288 #include <isl/union_set.h>
3289 __isl_give isl_union_set *isl_union_set_product(
3290 __isl_take isl_union_set *uset1,
3291 __isl_take isl_union_set *uset2);
3293 #include <isl/union_map.h>
3294 __isl_give isl_union_map *isl_union_map_domain_product(
3295 __isl_take isl_union_map *umap1,
3296 __isl_take isl_union_map *umap2);
3297 __isl_give isl_union_map *isl_union_map_range_product(
3298 __isl_take isl_union_map *umap1,
3299 __isl_take isl_union_map *umap2);
3300 __isl_give isl_union_map *isl_union_map_product(
3301 __isl_take isl_union_map *umap1,
3302 __isl_take isl_union_map *umap2);
3304 The above functions compute the cross product of the given
3305 sets or relations. The domains and ranges of the results
3306 are wrapped maps between domains and ranges of the inputs.
3307 To obtain a ``flat'' product, use the following functions
3310 __isl_give isl_basic_set *isl_basic_set_flat_product(
3311 __isl_take isl_basic_set *bset1,
3312 __isl_take isl_basic_set *bset2);
3313 __isl_give isl_set *isl_set_flat_product(
3314 __isl_take isl_set *set1,
3315 __isl_take isl_set *set2);
3316 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3317 __isl_take isl_basic_map *bmap1,
3318 __isl_take isl_basic_map *bmap2);
3319 __isl_give isl_map *isl_map_flat_domain_product(
3320 __isl_take isl_map *map1,
3321 __isl_take isl_map *map2);
3322 __isl_give isl_map *isl_map_flat_range_product(
3323 __isl_take isl_map *map1,
3324 __isl_take isl_map *map2);
3325 __isl_give isl_union_map *isl_union_map_flat_range_product(
3326 __isl_take isl_union_map *umap1,
3327 __isl_take isl_union_map *umap2);
3328 __isl_give isl_basic_map *isl_basic_map_flat_product(
3329 __isl_take isl_basic_map *bmap1,
3330 __isl_take isl_basic_map *bmap2);
3331 __isl_give isl_map *isl_map_flat_product(
3332 __isl_take isl_map *map1,
3333 __isl_take isl_map *map2);
3335 #include <isl/space.h>
3336 __isl_give isl_space *isl_space_domain_factor_domain(
3337 __isl_take isl_space *space);
3338 __isl_give isl_space *isl_space_range_factor_domain(
3339 __isl_take isl_space *space);
3340 __isl_give isl_space *isl_space_range_factor_range(
3341 __isl_take isl_space *space);
3343 The functions C<isl_space_range_factor_domain> and
3344 C<isl_space_range_factor_range> extract the two arguments from
3345 the result of a call to C<isl_space_range_product>.
3347 The arguments of a call to C<isl_map_range_product> can be extracted
3348 from the result using the following two functions.
3350 #include <isl/map.h>
3351 __isl_give isl_map *isl_map_range_factor_domain(
3352 __isl_take isl_map *map);
3353 __isl_give isl_map *isl_map_range_factor_range(
3354 __isl_take isl_map *map);
3356 =item * Simplification
3358 __isl_give isl_basic_set *isl_basic_set_gist(
3359 __isl_take isl_basic_set *bset,
3360 __isl_take isl_basic_set *context);
3361 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3362 __isl_take isl_set *context);
3363 __isl_give isl_set *isl_set_gist_params(
3364 __isl_take isl_set *set,
3365 __isl_take isl_set *context);
3366 __isl_give isl_union_set *isl_union_set_gist(
3367 __isl_take isl_union_set *uset,
3368 __isl_take isl_union_set *context);
3369 __isl_give isl_union_set *isl_union_set_gist_params(
3370 __isl_take isl_union_set *uset,
3371 __isl_take isl_set *set);
3372 __isl_give isl_basic_map *isl_basic_map_gist(
3373 __isl_take isl_basic_map *bmap,
3374 __isl_take isl_basic_map *context);
3375 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3376 __isl_take isl_map *context);
3377 __isl_give isl_map *isl_map_gist_params(
3378 __isl_take isl_map *map,
3379 __isl_take isl_set *context);
3380 __isl_give isl_map *isl_map_gist_domain(
3381 __isl_take isl_map *map,
3382 __isl_take isl_set *context);
3383 __isl_give isl_map *isl_map_gist_range(
3384 __isl_take isl_map *map,
3385 __isl_take isl_set *context);
3386 __isl_give isl_union_map *isl_union_map_gist(
3387 __isl_take isl_union_map *umap,
3388 __isl_take isl_union_map *context);
3389 __isl_give isl_union_map *isl_union_map_gist_params(
3390 __isl_take isl_union_map *umap,
3391 __isl_take isl_set *set);
3392 __isl_give isl_union_map *isl_union_map_gist_domain(
3393 __isl_take isl_union_map *umap,
3394 __isl_take isl_union_set *uset);
3395 __isl_give isl_union_map *isl_union_map_gist_range(
3396 __isl_take isl_union_map *umap,
3397 __isl_take isl_union_set *uset);
3399 The gist operation returns a set or relation that has the
3400 same intersection with the context as the input set or relation.
3401 Any implicit equality in the intersection is made explicit in the result,
3402 while all inequalities that are redundant with respect to the intersection
3404 In case of union sets and relations, the gist operation is performed
3409 =head3 Lexicographic Optimization
3411 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3412 the following functions
3413 compute a set that contains the lexicographic minimum or maximum
3414 of the elements in C<set> (or C<bset>) for those values of the parameters
3415 that satisfy C<dom>.
3416 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3417 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3419 In other words, the union of the parameter values
3420 for which the result is non-empty and of C<*empty>
3423 __isl_give isl_set *isl_basic_set_partial_lexmin(
3424 __isl_take isl_basic_set *bset,
3425 __isl_take isl_basic_set *dom,
3426 __isl_give isl_set **empty);
3427 __isl_give isl_set *isl_basic_set_partial_lexmax(
3428 __isl_take isl_basic_set *bset,
3429 __isl_take isl_basic_set *dom,
3430 __isl_give isl_set **empty);
3431 __isl_give isl_set *isl_set_partial_lexmin(
3432 __isl_take isl_set *set, __isl_take isl_set *dom,
3433 __isl_give isl_set **empty);
3434 __isl_give isl_set *isl_set_partial_lexmax(
3435 __isl_take isl_set *set, __isl_take isl_set *dom,
3436 __isl_give isl_set **empty);
3438 Given a (basic) set C<set> (or C<bset>), the following functions simply
3439 return a set containing the lexicographic minimum or maximum
3440 of the elements in C<set> (or C<bset>).
3441 In case of union sets, the optimum is computed per space.
3443 __isl_give isl_set *isl_basic_set_lexmin(
3444 __isl_take isl_basic_set *bset);
3445 __isl_give isl_set *isl_basic_set_lexmax(
3446 __isl_take isl_basic_set *bset);
3447 __isl_give isl_set *isl_set_lexmin(
3448 __isl_take isl_set *set);
3449 __isl_give isl_set *isl_set_lexmax(
3450 __isl_take isl_set *set);
3451 __isl_give isl_union_set *isl_union_set_lexmin(
3452 __isl_take isl_union_set *uset);
3453 __isl_give isl_union_set *isl_union_set_lexmax(
3454 __isl_take isl_union_set *uset);
3456 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3457 the following functions
3458 compute a relation that maps each element of C<dom>
3459 to the single lexicographic minimum or maximum
3460 of the elements that are associated to that same
3461 element in C<map> (or C<bmap>).
3462 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3463 that contains the elements in C<dom> that do not map
3464 to any elements in C<map> (or C<bmap>).
3465 In other words, the union of the domain of the result and of C<*empty>
3468 __isl_give isl_map *isl_basic_map_partial_lexmax(
3469 __isl_take isl_basic_map *bmap,
3470 __isl_take isl_basic_set *dom,
3471 __isl_give isl_set **empty);
3472 __isl_give isl_map *isl_basic_map_partial_lexmin(
3473 __isl_take isl_basic_map *bmap,
3474 __isl_take isl_basic_set *dom,
3475 __isl_give isl_set **empty);
3476 __isl_give isl_map *isl_map_partial_lexmax(
3477 __isl_take isl_map *map, __isl_take isl_set *dom,
3478 __isl_give isl_set **empty);
3479 __isl_give isl_map *isl_map_partial_lexmin(
3480 __isl_take isl_map *map, __isl_take isl_set *dom,
3481 __isl_give isl_set **empty);
3483 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3484 return a map mapping each element in the domain of
3485 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3486 of all elements associated to that element.
3487 In case of union relations, the optimum is computed per space.
3489 __isl_give isl_map *isl_basic_map_lexmin(
3490 __isl_take isl_basic_map *bmap);
3491 __isl_give isl_map *isl_basic_map_lexmax(
3492 __isl_take isl_basic_map *bmap);
3493 __isl_give isl_map *isl_map_lexmin(
3494 __isl_take isl_map *map);
3495 __isl_give isl_map *isl_map_lexmax(
3496 __isl_take isl_map *map);
3497 __isl_give isl_union_map *isl_union_map_lexmin(
3498 __isl_take isl_union_map *umap);
3499 __isl_give isl_union_map *isl_union_map_lexmax(
3500 __isl_take isl_union_map *umap);
3502 The following functions return their result in the form of
3503 a piecewise multi-affine expression
3504 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3505 but are otherwise equivalent to the corresponding functions
3506 returning a basic set or relation.
3508 __isl_give isl_pw_multi_aff *
3509 isl_basic_map_lexmin_pw_multi_aff(
3510 __isl_take isl_basic_map *bmap);
3511 __isl_give isl_pw_multi_aff *
3512 isl_basic_set_partial_lexmin_pw_multi_aff(
3513 __isl_take isl_basic_set *bset,
3514 __isl_take isl_basic_set *dom,
3515 __isl_give isl_set **empty);
3516 __isl_give isl_pw_multi_aff *
3517 isl_basic_set_partial_lexmax_pw_multi_aff(
3518 __isl_take isl_basic_set *bset,
3519 __isl_take isl_basic_set *dom,
3520 __isl_give isl_set **empty);
3521 __isl_give isl_pw_multi_aff *
3522 isl_basic_map_partial_lexmin_pw_multi_aff(
3523 __isl_take isl_basic_map *bmap,
3524 __isl_take isl_basic_set *dom,
3525 __isl_give isl_set **empty);
3526 __isl_give isl_pw_multi_aff *
3527 isl_basic_map_partial_lexmax_pw_multi_aff(
3528 __isl_take isl_basic_map *bmap,
3529 __isl_take isl_basic_set *dom,
3530 __isl_give isl_set **empty);
3531 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3532 __isl_take isl_set *set);
3533 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3534 __isl_take isl_set *set);
3535 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3536 __isl_take isl_map *map);
3537 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3538 __isl_take isl_map *map);
3542 Lists are defined over several element types, including
3543 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3544 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3545 Here we take lists of C<isl_set>s as an example.
3546 Lists can be created, copied, modified and freed using the following functions.
3548 #include <isl/list.h>
3549 __isl_give isl_set_list *isl_set_list_from_set(
3550 __isl_take isl_set *el);
3551 __isl_give isl_set_list *isl_set_list_alloc(
3552 isl_ctx *ctx, int n);
3553 __isl_give isl_set_list *isl_set_list_copy(
3554 __isl_keep isl_set_list *list);
3555 __isl_give isl_set_list *isl_set_list_insert(
3556 __isl_take isl_set_list *list, unsigned pos,
3557 __isl_take isl_set *el);
3558 __isl_give isl_set_list *isl_set_list_add(
3559 __isl_take isl_set_list *list,
3560 __isl_take isl_set *el);
3561 __isl_give isl_set_list *isl_set_list_drop(
3562 __isl_take isl_set_list *list,
3563 unsigned first, unsigned n);
3564 __isl_give isl_set_list *isl_set_list_set_set(
3565 __isl_take isl_set_list *list, int index,
3566 __isl_take isl_set *set);
3567 __isl_give isl_set_list *isl_set_list_concat(
3568 __isl_take isl_set_list *list1,
3569 __isl_take isl_set_list *list2);
3570 __isl_give isl_set_list *isl_set_list_sort(
3571 __isl_take isl_set_list *list,
3572 int (*cmp)(__isl_keep isl_set *a,
3573 __isl_keep isl_set *b, void *user),
3575 __isl_null isl_set_list *isl_set_list_free(
3576 __isl_take isl_set_list *list);
3578 C<isl_set_list_alloc> creates an empty list with a capacity for
3579 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3582 Lists can be inspected using the following functions.
3584 #include <isl/list.h>
3585 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3586 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3587 __isl_give isl_set *isl_set_list_get_set(
3588 __isl_keep isl_set_list *list, int index);
3589 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3590 int (*fn)(__isl_take isl_set *el, void *user),
3592 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3593 int (*follows)(__isl_keep isl_set *a,
3594 __isl_keep isl_set *b, void *user),
3596 int (*fn)(__isl_take isl_set *el, void *user),
3599 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3600 strongly connected components of the graph with as vertices the elements
3601 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3602 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3603 should return C<-1> on error.
3605 Lists can be printed using
3607 #include <isl/list.h>
3608 __isl_give isl_printer *isl_printer_print_set_list(
3609 __isl_take isl_printer *p,
3610 __isl_keep isl_set_list *list);
3612 =head2 Associative arrays
3614 Associative arrays map isl objects of a specific type to isl objects
3615 of some (other) specific type. They are defined for several pairs
3616 of types, including (C<isl_map>, C<isl_basic_set>),
3617 (C<isl_id>, C<isl_ast_expr>) and.
3618 (C<isl_id>, C<isl_pw_aff>).
3619 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3622 Associative arrays can be created, copied and freed using
3623 the following functions.
3625 #include <isl/id_to_ast_expr.h>
3626 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3627 isl_ctx *ctx, int min_size);
3628 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3629 __isl_keep id_to_ast_expr *id2expr);
3630 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
3631 __isl_take id_to_ast_expr *id2expr);
3633 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3634 to specify the expected size of the associative array.
3635 The associative array will be grown automatically as needed.
3637 Associative arrays can be inspected using the following functions.
3639 #include <isl/id_to_ast_expr.h>
3640 isl_ctx *isl_id_to_ast_expr_get_ctx(
3641 __isl_keep id_to_ast_expr *id2expr);
3642 int isl_id_to_ast_expr_has(
3643 __isl_keep id_to_ast_expr *id2expr,
3644 __isl_keep isl_id *key);
3645 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3646 __isl_keep id_to_ast_expr *id2expr,
3647 __isl_take isl_id *key);
3648 int isl_id_to_ast_expr_foreach(
3649 __isl_keep id_to_ast_expr *id2expr,
3650 int (*fn)(__isl_take isl_id *key,
3651 __isl_take isl_ast_expr *val, void *user),
3654 They can be modified using the following function.
3656 #include <isl/id_to_ast_expr.h>
3657 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3658 __isl_take id_to_ast_expr *id2expr,
3659 __isl_take isl_id *key,
3660 __isl_take isl_ast_expr *val);
3661 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
3662 __isl_take id_to_ast_expr *id2expr,
3663 __isl_take isl_id *key);
3665 Associative arrays can be printed using the following function.
3667 #include <isl/id_to_ast_expr.h>
3668 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3669 __isl_take isl_printer *p,
3670 __isl_keep id_to_ast_expr *id2expr);
3672 =head2 Multiple Values
3674 An C<isl_multi_val> object represents a sequence of zero or more values,
3675 living in a set space.
3677 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3678 using the following function
3680 #include <isl/val.h>
3681 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3682 __isl_take isl_space *space,
3683 __isl_take isl_val_list *list);
3685 The zero multiple value (with value zero for each set dimension)
3686 can be created using the following function.
3688 #include <isl/val.h>
3689 __isl_give isl_multi_val *isl_multi_val_zero(
3690 __isl_take isl_space *space);
3692 Multiple values can be copied and freed using
3694 #include <isl/val.h>
3695 __isl_give isl_multi_val *isl_multi_val_copy(
3696 __isl_keep isl_multi_val *mv);
3697 __isl_null isl_multi_val *isl_multi_val_free(
3698 __isl_take isl_multi_val *mv);
3700 They can be inspected using
3702 #include <isl/val.h>
3703 isl_ctx *isl_multi_val_get_ctx(
3704 __isl_keep isl_multi_val *mv);
3705 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3706 enum isl_dim_type type);
3707 __isl_give isl_val *isl_multi_val_get_val(
3708 __isl_keep isl_multi_val *mv, int pos);
3709 int isl_multi_val_find_dim_by_id(
3710 __isl_keep isl_multi_val *mv,
3711 enum isl_dim_type type, __isl_keep isl_id *id);
3712 __isl_give isl_id *isl_multi_val_get_dim_id(
3713 __isl_keep isl_multi_val *mv,
3714 enum isl_dim_type type, unsigned pos);
3715 const char *isl_multi_val_get_tuple_name(
3716 __isl_keep isl_multi_val *mv,
3717 enum isl_dim_type type);
3718 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3719 enum isl_dim_type type);
3720 __isl_give isl_id *isl_multi_val_get_tuple_id(
3721 __isl_keep isl_multi_val *mv,
3722 enum isl_dim_type type);
3723 int isl_multi_val_range_is_wrapping(
3724 __isl_keep isl_multi_val *mv);
3726 They can be modified using
3728 #include <isl/val.h>
3729 __isl_give isl_multi_val *isl_multi_val_set_val(
3730 __isl_take isl_multi_val *mv, int pos,
3731 __isl_take isl_val *val);
3732 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3733 __isl_take isl_multi_val *mv,
3734 enum isl_dim_type type, unsigned pos, const char *s);
3735 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3736 __isl_take isl_multi_val *mv,
3737 enum isl_dim_type type, unsigned pos,
3738 __isl_take isl_id *id);
3739 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3740 __isl_take isl_multi_val *mv,
3741 enum isl_dim_type type, const char *s);
3742 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3743 __isl_take isl_multi_val *mv,
3744 enum isl_dim_type type, __isl_take isl_id *id);
3745 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3746 __isl_take isl_multi_val *mv,
3747 enum isl_dim_type type);
3748 __isl_give isl_multi_val *isl_multi_val_reset_user(
3749 __isl_take isl_multi_val *mv);
3751 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3752 __isl_take isl_multi_val *mv,
3753 enum isl_dim_type type, unsigned first, unsigned n);
3754 __isl_give isl_multi_val *isl_multi_val_add_dims(
3755 __isl_take isl_multi_val *mv,
3756 enum isl_dim_type type, unsigned n);
3757 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3758 __isl_take isl_multi_val *mv,
3759 enum isl_dim_type type, unsigned first, unsigned n);
3763 #include <isl/val.h>
3764 __isl_give isl_multi_val *isl_multi_val_align_params(
3765 __isl_take isl_multi_val *mv,
3766 __isl_take isl_space *model);
3767 __isl_give isl_multi_val *isl_multi_val_from_range(
3768 __isl_take isl_multi_val *mv);
3769 __isl_give isl_multi_val *isl_multi_val_range_splice(
3770 __isl_take isl_multi_val *mv1, unsigned pos,
3771 __isl_take isl_multi_val *mv2);
3772 __isl_give isl_multi_val *isl_multi_val_range_product(
3773 __isl_take isl_multi_val *mv1,
3774 __isl_take isl_multi_val *mv2);
3775 __isl_give isl_multi_val *
3776 isl_multi_val_range_factor_domain(
3777 __isl_take isl_multi_val *mv);
3778 __isl_give isl_multi_val *
3779 isl_multi_val_range_factor_range(
3780 __isl_take isl_multi_val *mv);
3781 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3782 __isl_take isl_multi_val *mv1,
3783 __isl_take isl_multi_aff *mv2);
3784 __isl_give isl_multi_val *isl_multi_val_product(
3785 __isl_take isl_multi_val *mv1,
3786 __isl_take isl_multi_val *mv2);
3787 __isl_give isl_multi_val *isl_multi_val_add_val(
3788 __isl_take isl_multi_val *mv,
3789 __isl_take isl_val *v);
3790 __isl_give isl_multi_val *isl_multi_val_mod_val(
3791 __isl_take isl_multi_val *mv,
3792 __isl_take isl_val *v);
3793 __isl_give isl_multi_val *isl_multi_val_scale_val(
3794 __isl_take isl_multi_val *mv,
3795 __isl_take isl_val *v);
3796 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3797 __isl_take isl_multi_val *mv1,
3798 __isl_take isl_multi_val *mv2);
3799 __isl_give isl_multi_val *
3800 isl_multi_val_scale_down_multi_val(
3801 __isl_take isl_multi_val *mv1,
3802 __isl_take isl_multi_val *mv2);
3804 A multiple value can be printed using
3806 __isl_give isl_printer *isl_printer_print_multi_val(
3807 __isl_take isl_printer *p,
3808 __isl_keep isl_multi_val *mv);
3812 Vectors can be created, copied and freed using the following functions.
3814 #include <isl/vec.h>
3815 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3817 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3818 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
3820 Note that the elements of a newly created vector may have arbitrary values.
3821 The elements can be changed and inspected using the following functions.
3823 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3824 int isl_vec_size(__isl_keep isl_vec *vec);
3825 __isl_give isl_val *isl_vec_get_element_val(
3826 __isl_keep isl_vec *vec, int pos);
3827 __isl_give isl_vec *isl_vec_set_element_si(
3828 __isl_take isl_vec *vec, int pos, int v);
3829 __isl_give isl_vec *isl_vec_set_element_val(
3830 __isl_take isl_vec *vec, int pos,
3831 __isl_take isl_val *v);
3832 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3834 __isl_give isl_vec *isl_vec_set_val(
3835 __isl_take isl_vec *vec, __isl_take isl_val *v);
3836 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3837 __isl_keep isl_vec *vec2, int pos);
3839 C<isl_vec_get_element> will return a negative value if anything went wrong.
3840 In that case, the value of C<*v> is undefined.
3842 The following function can be used to concatenate two vectors.
3844 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3845 __isl_take isl_vec *vec2);
3849 Matrices can be created, copied and freed using the following functions.
3851 #include <isl/mat.h>
3852 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3853 unsigned n_row, unsigned n_col);
3854 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3855 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
3857 Note that the elements of a newly created matrix may have arbitrary values.
3858 The elements can be changed and inspected using the following functions.
3860 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3861 int isl_mat_rows(__isl_keep isl_mat *mat);
3862 int isl_mat_cols(__isl_keep isl_mat *mat);
3863 __isl_give isl_val *isl_mat_get_element_val(
3864 __isl_keep isl_mat *mat, int row, int col);
3865 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3866 int row, int col, int v);
3867 __isl_give isl_mat *isl_mat_set_element_val(
3868 __isl_take isl_mat *mat, int row, int col,
3869 __isl_take isl_val *v);
3871 C<isl_mat_get_element> will return a negative value if anything went wrong.
3872 In that case, the value of C<*v> is undefined.
3874 The following function can be used to compute the (right) inverse
3875 of a matrix, i.e., a matrix such that the product of the original
3876 and the inverse (in that order) is a multiple of the identity matrix.
3877 The input matrix is assumed to be of full row-rank.
3879 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3881 The following function can be used to compute the (right) kernel
3882 (or null space) of a matrix, i.e., a matrix such that the product of
3883 the original and the kernel (in that order) is the zero matrix.
3885 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3887 =head2 Piecewise Quasi Affine Expressions
3889 The zero quasi affine expression or the quasi affine expression
3890 that is equal to a given value or
3891 a specified dimension on a given domain can be created using
3893 __isl_give isl_aff *isl_aff_zero_on_domain(
3894 __isl_take isl_local_space *ls);
3895 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3896 __isl_take isl_local_space *ls);
3897 __isl_give isl_aff *isl_aff_val_on_domain(
3898 __isl_take isl_local_space *ls,
3899 __isl_take isl_val *val);
3900 __isl_give isl_aff *isl_aff_var_on_domain(
3901 __isl_take isl_local_space *ls,
3902 enum isl_dim_type type, unsigned pos);
3903 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3904 __isl_take isl_local_space *ls,
3905 enum isl_dim_type type, unsigned pos);
3906 __isl_give isl_aff *isl_aff_nan_on_domain(
3907 __isl_take isl_local_space *ls);
3908 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3909 __isl_take isl_local_space *ls);
3911 Note that the space in which the resulting objects live is a map space
3912 with the given space as domain and a one-dimensional range.
3914 An empty piecewise quasi affine expression (one with no cells)
3915 or a piecewise quasi affine expression with a single cell can
3916 be created using the following functions.
3918 #include <isl/aff.h>
3919 __isl_give isl_pw_aff *isl_pw_aff_empty(
3920 __isl_take isl_space *space);
3921 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3922 __isl_take isl_set *set, __isl_take isl_aff *aff);
3923 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3924 __isl_take isl_aff *aff);
3926 A piecewise quasi affine expression that is equal to 1 on a set
3927 and 0 outside the set can be created using the following function.
3929 #include <isl/aff.h>
3930 __isl_give isl_pw_aff *isl_set_indicator_function(
3931 __isl_take isl_set *set);
3933 Quasi affine expressions can be copied and freed using
3935 #include <isl/aff.h>
3936 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3937 __isl_null isl_aff *isl_aff_free(__isl_take isl_aff *aff);
3939 __isl_give isl_pw_aff *isl_pw_aff_copy(
3940 __isl_keep isl_pw_aff *pwaff);
3941 __isl_null isl_pw_aff *isl_pw_aff_free(
3942 __isl_take isl_pw_aff *pwaff);
3944 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3945 using the following function. The constraint is required to have
3946 a non-zero coefficient for the specified dimension.
3948 #include <isl/constraint.h>
3949 __isl_give isl_aff *isl_constraint_get_bound(
3950 __isl_keep isl_constraint *constraint,
3951 enum isl_dim_type type, int pos);
3953 The entire affine expression of the constraint can also be extracted
3954 using the following function.
3956 #include <isl/constraint.h>
3957 __isl_give isl_aff *isl_constraint_get_aff(
3958 __isl_keep isl_constraint *constraint);
3960 Conversely, an equality constraint equating
3961 the affine expression to zero or an inequality constraint enforcing
3962 the affine expression to be non-negative, can be constructed using
3964 __isl_give isl_constraint *isl_equality_from_aff(
3965 __isl_take isl_aff *aff);
3966 __isl_give isl_constraint *isl_inequality_from_aff(
3967 __isl_take isl_aff *aff);
3969 The expression can be inspected using
3971 #include <isl/aff.h>
3972 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3973 int isl_aff_dim(__isl_keep isl_aff *aff,
3974 enum isl_dim_type type);
3975 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3976 __isl_keep isl_aff *aff);
3977 __isl_give isl_local_space *isl_aff_get_local_space(
3978 __isl_keep isl_aff *aff);
3979 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3980 enum isl_dim_type type, unsigned pos);
3981 const char *isl_pw_aff_get_dim_name(
3982 __isl_keep isl_pw_aff *pa,
3983 enum isl_dim_type type, unsigned pos);
3984 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3985 enum isl_dim_type type, unsigned pos);
3986 __isl_give isl_id *isl_pw_aff_get_dim_id(
3987 __isl_keep isl_pw_aff *pa,
3988 enum isl_dim_type type, unsigned pos);
3989 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
3990 enum isl_dim_type type);
3991 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3992 __isl_keep isl_pw_aff *pa,
3993 enum isl_dim_type type);
3994 __isl_give isl_val *isl_aff_get_constant_val(
3995 __isl_keep isl_aff *aff);
3996 __isl_give isl_val *isl_aff_get_coefficient_val(
3997 __isl_keep isl_aff *aff,
3998 enum isl_dim_type type, int pos);
3999 __isl_give isl_val *isl_aff_get_denominator_val(
4000 __isl_keep isl_aff *aff);
4001 __isl_give isl_aff *isl_aff_get_div(
4002 __isl_keep isl_aff *aff, int pos);
4004 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
4005 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
4006 int (*fn)(__isl_take isl_set *set,
4007 __isl_take isl_aff *aff,
4008 void *user), void *user);
4010 int isl_aff_is_cst(__isl_keep isl_aff *aff);
4011 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4013 int isl_aff_is_nan(__isl_keep isl_aff *aff);
4014 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
4016 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
4017 enum isl_dim_type type, unsigned first, unsigned n);
4018 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
4019 enum isl_dim_type type, unsigned first, unsigned n);
4021 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
4022 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
4023 enum isl_dim_type type);
4024 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
4026 It can be modified using
4028 #include <isl/aff.h>
4029 __isl_give isl_aff *isl_aff_set_tuple_id(
4030 __isl_take isl_aff *aff,
4031 enum isl_dim_type type, __isl_take isl_id *id);
4032 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
4033 __isl_take isl_pw_aff *pwaff,
4034 enum isl_dim_type type, __isl_take isl_id *id);
4035 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
4036 __isl_take isl_pw_aff *pa,
4037 enum isl_dim_type type);
4038 __isl_give isl_aff *isl_aff_set_dim_name(
4039 __isl_take isl_aff *aff, enum isl_dim_type type,
4040 unsigned pos, const char *s);
4041 __isl_give isl_aff *isl_aff_set_dim_id(
4042 __isl_take isl_aff *aff, enum isl_dim_type type,
4043 unsigned pos, __isl_take isl_id *id);
4044 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
4045 __isl_take isl_pw_aff *pma,
4046 enum isl_dim_type type, unsigned pos,
4047 __isl_take isl_id *id);
4048 __isl_give isl_aff *isl_aff_set_constant_si(
4049 __isl_take isl_aff *aff, int v);
4050 __isl_give isl_aff *isl_aff_set_constant_val(
4051 __isl_take isl_aff *aff, __isl_take isl_val *v);
4052 __isl_give isl_aff *isl_aff_set_coefficient_si(
4053 __isl_take isl_aff *aff,
4054 enum isl_dim_type type, int pos, int v);
4055 __isl_give isl_aff *isl_aff_set_coefficient_val(
4056 __isl_take isl_aff *aff,
4057 enum isl_dim_type type, int pos,
4058 __isl_take isl_val *v);
4060 __isl_give isl_aff *isl_aff_add_constant_si(
4061 __isl_take isl_aff *aff, int v);
4062 __isl_give isl_aff *isl_aff_add_constant_val(
4063 __isl_take isl_aff *aff, __isl_take isl_val *v);
4064 __isl_give isl_aff *isl_aff_add_constant_num_si(
4065 __isl_take isl_aff *aff, int v);
4066 __isl_give isl_aff *isl_aff_add_coefficient_si(
4067 __isl_take isl_aff *aff,
4068 enum isl_dim_type type, int pos, int v);
4069 __isl_give isl_aff *isl_aff_add_coefficient_val(
4070 __isl_take isl_aff *aff,
4071 enum isl_dim_type type, int pos,
4072 __isl_take isl_val *v);
4074 __isl_give isl_aff *isl_aff_insert_dims(
4075 __isl_take isl_aff *aff,
4076 enum isl_dim_type type, unsigned first, unsigned n);
4077 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
4078 __isl_take isl_pw_aff *pwaff,
4079 enum isl_dim_type type, unsigned first, unsigned n);
4080 __isl_give isl_aff *isl_aff_add_dims(
4081 __isl_take isl_aff *aff,
4082 enum isl_dim_type type, unsigned n);
4083 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
4084 __isl_take isl_pw_aff *pwaff,
4085 enum isl_dim_type type, unsigned n);
4086 __isl_give isl_aff *isl_aff_drop_dims(
4087 __isl_take isl_aff *aff,
4088 enum isl_dim_type type, unsigned first, unsigned n);
4089 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
4090 __isl_take isl_pw_aff *pwaff,
4091 enum isl_dim_type type, unsigned first, unsigned n);
4092 __isl_give isl_aff *isl_aff_move_dims(
4093 __isl_take isl_aff *aff,
4094 enum isl_dim_type dst_type, unsigned dst_pos,
4095 enum isl_dim_type src_type, unsigned src_pos,
4097 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
4098 __isl_take isl_pw_aff *pa,
4099 enum isl_dim_type dst_type, unsigned dst_pos,
4100 enum isl_dim_type src_type, unsigned src_pos,
4103 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
4104 set the I<numerator> of the constant or coefficient, while
4105 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
4106 the constant or coefficient as a whole.
4107 The C<add_constant> and C<add_coefficient> functions add an integer
4108 or rational value to
4109 the possibly rational constant or coefficient.
4110 The C<add_constant_num> functions add an integer value to
4113 To check whether an affine expressions is obviously zero
4114 or (obviously) equal to some other affine expression, use
4116 #include <isl/aff.h>
4117 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
4118 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
4119 __isl_keep isl_aff *aff2);
4120 int isl_pw_aff_plain_is_equal(
4121 __isl_keep isl_pw_aff *pwaff1,
4122 __isl_keep isl_pw_aff *pwaff2);
4123 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
4124 __isl_keep isl_pw_aff *pa2);
4125 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4126 __isl_keep isl_pw_aff *pa2);
4128 The function C<isl_pw_aff_plain_cmp> can be used to sort
4129 C<isl_pw_aff>s. The order is not strictly defined.
4130 The current order sorts expressions that only involve
4131 earlier dimensions before those that involve later dimensions.
4135 #include <isl/aff.h>
4136 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
4137 __isl_take isl_aff *aff2);
4138 __isl_give isl_pw_aff *isl_pw_aff_add(
4139 __isl_take isl_pw_aff *pwaff1,
4140 __isl_take isl_pw_aff *pwaff2);
4141 __isl_give isl_pw_aff *isl_pw_aff_min(
4142 __isl_take isl_pw_aff *pwaff1,
4143 __isl_take isl_pw_aff *pwaff2);
4144 __isl_give isl_pw_aff *isl_pw_aff_max(
4145 __isl_take isl_pw_aff *pwaff1,
4146 __isl_take isl_pw_aff *pwaff2);
4147 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
4148 __isl_take isl_aff *aff2);
4149 __isl_give isl_pw_aff *isl_pw_aff_sub(
4150 __isl_take isl_pw_aff *pwaff1,
4151 __isl_take isl_pw_aff *pwaff2);
4152 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
4153 __isl_give isl_pw_aff *isl_pw_aff_neg(
4154 __isl_take isl_pw_aff *pwaff);
4155 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
4156 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4157 __isl_take isl_pw_aff *pwaff);
4158 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
4159 __isl_give isl_pw_aff *isl_pw_aff_floor(
4160 __isl_take isl_pw_aff *pwaff);
4161 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
4162 __isl_take isl_val *mod);
4163 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
4164 __isl_take isl_pw_aff *pa,
4165 __isl_take isl_val *mod);
4166 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
4167 __isl_take isl_val *v);
4168 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
4169 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
4170 __isl_give isl_aff *isl_aff_scale_down_ui(
4171 __isl_take isl_aff *aff, unsigned f);
4172 __isl_give isl_aff *isl_aff_scale_down_val(
4173 __isl_take isl_aff *aff, __isl_take isl_val *v);
4174 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
4175 __isl_take isl_pw_aff *pa,
4176 __isl_take isl_val *f);
4178 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4179 __isl_take isl_pw_aff_list *list);
4180 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4181 __isl_take isl_pw_aff_list *list);
4183 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4184 __isl_take isl_pw_aff *pwqp);
4186 __isl_give isl_aff *isl_aff_align_params(
4187 __isl_take isl_aff *aff,
4188 __isl_take isl_space *model);
4189 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4190 __isl_take isl_pw_aff *pwaff,
4191 __isl_take isl_space *model);
4193 __isl_give isl_aff *isl_aff_project_domain_on_params(
4194 __isl_take isl_aff *aff);
4195 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4196 __isl_take isl_pw_aff *pwa);
4198 __isl_give isl_aff *isl_aff_gist_params(
4199 __isl_take isl_aff *aff,
4200 __isl_take isl_set *context);
4201 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
4202 __isl_take isl_set *context);
4203 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
4204 __isl_take isl_pw_aff *pwaff,
4205 __isl_take isl_set *context);
4206 __isl_give isl_pw_aff *isl_pw_aff_gist(
4207 __isl_take isl_pw_aff *pwaff,
4208 __isl_take isl_set *context);
4210 __isl_give isl_set *isl_pw_aff_domain(
4211 __isl_take isl_pw_aff *pwaff);
4212 __isl_give isl_set *isl_pw_aff_params(
4213 __isl_take isl_pw_aff *pwa);
4214 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4215 __isl_take isl_pw_aff *pa,
4216 __isl_take isl_set *set);
4217 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4218 __isl_take isl_pw_aff *pa,
4219 __isl_take isl_set *set);
4221 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
4222 __isl_take isl_aff *aff2);
4223 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
4224 __isl_take isl_aff *aff2);
4225 __isl_give isl_pw_aff *isl_pw_aff_mul(
4226 __isl_take isl_pw_aff *pwaff1,
4227 __isl_take isl_pw_aff *pwaff2);
4228 __isl_give isl_pw_aff *isl_pw_aff_div(
4229 __isl_take isl_pw_aff *pa1,
4230 __isl_take isl_pw_aff *pa2);
4231 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
4232 __isl_take isl_pw_aff *pa1,
4233 __isl_take isl_pw_aff *pa2);
4234 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
4235 __isl_take isl_pw_aff *pa1,
4236 __isl_take isl_pw_aff *pa2);
4238 When multiplying two affine expressions, at least one of the two needs
4239 to be a constant. Similarly, when dividing an affine expression by another,
4240 the second expression needs to be a constant.
4241 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
4242 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
4245 #include <isl/aff.h>
4246 __isl_give isl_aff *isl_aff_pullback_aff(
4247 __isl_take isl_aff *aff1,
4248 __isl_take isl_aff *aff2);
4249 __isl_give isl_aff *isl_aff_pullback_multi_aff(
4250 __isl_take isl_aff *aff,
4251 __isl_take isl_multi_aff *ma);
4252 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
4253 __isl_take isl_pw_aff *pa,
4254 __isl_take isl_multi_aff *ma);
4255 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
4256 __isl_take isl_pw_aff *pa,
4257 __isl_take isl_pw_multi_aff *pma);
4258 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
4259 __isl_take isl_pw_aff *pa,
4260 __isl_take isl_multi_pw_aff *mpa);
4262 These functions precompose the input expression by the given
4263 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
4264 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
4265 into the (piecewise) affine expression.
4266 Objects of type C<isl_multi_aff> are described in
4267 L</"Piecewise Multiple Quasi Affine Expressions">.
4269 #include <isl/aff.h>
4270 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4271 __isl_take isl_aff *aff);
4272 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4273 __isl_take isl_aff *aff);
4274 __isl_give isl_basic_set *isl_aff_le_basic_set(
4275 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4276 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4277 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4278 __isl_give isl_set *isl_pw_aff_eq_set(
4279 __isl_take isl_pw_aff *pwaff1,
4280 __isl_take isl_pw_aff *pwaff2);
4281 __isl_give isl_set *isl_pw_aff_ne_set(
4282 __isl_take isl_pw_aff *pwaff1,
4283 __isl_take isl_pw_aff *pwaff2);
4284 __isl_give isl_set *isl_pw_aff_le_set(
4285 __isl_take isl_pw_aff *pwaff1,
4286 __isl_take isl_pw_aff *pwaff2);
4287 __isl_give isl_set *isl_pw_aff_lt_set(
4288 __isl_take isl_pw_aff *pwaff1,
4289 __isl_take isl_pw_aff *pwaff2);
4290 __isl_give isl_set *isl_pw_aff_ge_set(
4291 __isl_take isl_pw_aff *pwaff1,
4292 __isl_take isl_pw_aff *pwaff2);
4293 __isl_give isl_set *isl_pw_aff_gt_set(
4294 __isl_take isl_pw_aff *pwaff1,
4295 __isl_take isl_pw_aff *pwaff2);
4297 __isl_give isl_set *isl_pw_aff_list_eq_set(
4298 __isl_take isl_pw_aff_list *list1,
4299 __isl_take isl_pw_aff_list *list2);
4300 __isl_give isl_set *isl_pw_aff_list_ne_set(
4301 __isl_take isl_pw_aff_list *list1,
4302 __isl_take isl_pw_aff_list *list2);
4303 __isl_give isl_set *isl_pw_aff_list_le_set(
4304 __isl_take isl_pw_aff_list *list1,
4305 __isl_take isl_pw_aff_list *list2);
4306 __isl_give isl_set *isl_pw_aff_list_lt_set(
4307 __isl_take isl_pw_aff_list *list1,
4308 __isl_take isl_pw_aff_list *list2);
4309 __isl_give isl_set *isl_pw_aff_list_ge_set(
4310 __isl_take isl_pw_aff_list *list1,
4311 __isl_take isl_pw_aff_list *list2);
4312 __isl_give isl_set *isl_pw_aff_list_gt_set(
4313 __isl_take isl_pw_aff_list *list1,
4314 __isl_take isl_pw_aff_list *list2);
4316 The function C<isl_aff_neg_basic_set> returns a basic set
4317 containing those elements in the domain space
4318 of C<aff> where C<aff> is negative.
4319 The function C<isl_aff_ge_basic_set> returns a basic set
4320 containing those elements in the shared space
4321 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4322 The function C<isl_pw_aff_ge_set> returns a set
4323 containing those elements in the shared domain
4324 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4325 The functions operating on C<isl_pw_aff_list> apply the corresponding
4326 C<isl_pw_aff> function to each pair of elements in the two lists.
4328 #include <isl/aff.h>
4329 __isl_give isl_set *isl_pw_aff_nonneg_set(
4330 __isl_take isl_pw_aff *pwaff);
4331 __isl_give isl_set *isl_pw_aff_zero_set(
4332 __isl_take isl_pw_aff *pwaff);
4333 __isl_give isl_set *isl_pw_aff_non_zero_set(
4334 __isl_take isl_pw_aff *pwaff);
4336 The function C<isl_pw_aff_nonneg_set> returns a set
4337 containing those elements in the domain
4338 of C<pwaff> where C<pwaff> is non-negative.
4340 #include <isl/aff.h>
4341 __isl_give isl_pw_aff *isl_pw_aff_cond(
4342 __isl_take isl_pw_aff *cond,
4343 __isl_take isl_pw_aff *pwaff_true,
4344 __isl_take isl_pw_aff *pwaff_false);
4346 The function C<isl_pw_aff_cond> performs a conditional operator
4347 and returns an expression that is equal to C<pwaff_true>
4348 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4349 where C<cond> is zero.
4351 #include <isl/aff.h>
4352 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4353 __isl_take isl_pw_aff *pwaff1,
4354 __isl_take isl_pw_aff *pwaff2);
4355 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4356 __isl_take isl_pw_aff *pwaff1,
4357 __isl_take isl_pw_aff *pwaff2);
4358 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4359 __isl_take isl_pw_aff *pwaff1,
4360 __isl_take isl_pw_aff *pwaff2);
4362 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4363 expression with a domain that is the union of those of C<pwaff1> and
4364 C<pwaff2> and such that on each cell, the quasi-affine expression is
4365 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4366 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4367 associated expression is the defined one.
4369 An expression can be read from input using
4371 #include <isl/aff.h>
4372 __isl_give isl_aff *isl_aff_read_from_str(
4373 isl_ctx *ctx, const char *str);
4374 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4375 isl_ctx *ctx, const char *str);
4377 An expression can be printed using
4379 #include <isl/aff.h>
4380 __isl_give isl_printer *isl_printer_print_aff(
4381 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4383 __isl_give isl_printer *isl_printer_print_pw_aff(
4384 __isl_take isl_printer *p,
4385 __isl_keep isl_pw_aff *pwaff);
4387 =head2 Piecewise Multiple Quasi Affine Expressions
4389 An C<isl_multi_aff> object represents a sequence of
4390 zero or more affine expressions, all defined on the same domain space.
4391 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4392 zero or more piecewise affine expressions.
4394 An C<isl_multi_aff> can be constructed from a single
4395 C<isl_aff> or an C<isl_aff_list> using the
4396 following functions. Similarly for C<isl_multi_pw_aff>
4397 and C<isl_pw_multi_aff>.
4399 #include <isl/aff.h>
4400 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4401 __isl_take isl_aff *aff);
4402 __isl_give isl_multi_pw_aff *
4403 isl_multi_pw_aff_from_multi_aff(
4404 __isl_take isl_multi_aff *ma);
4405 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4406 __isl_take isl_pw_aff *pa);
4407 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4408 __isl_take isl_pw_aff *pa);
4409 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4410 __isl_take isl_space *space,
4411 __isl_take isl_aff_list *list);
4413 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4414 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4415 Note however that the domain
4416 of the result is the intersection of the domains of the input.
4417 The reverse conversion is exact.
4419 #include <isl/aff.h>
4420 __isl_give isl_pw_multi_aff *
4421 isl_pw_multi_aff_from_multi_pw_aff(
4422 __isl_take isl_multi_pw_aff *mpa);
4423 __isl_give isl_multi_pw_aff *
4424 isl_multi_pw_aff_from_pw_multi_aff(
4425 __isl_take isl_pw_multi_aff *pma);
4427 An empty piecewise multiple quasi affine expression (one with no cells),
4428 the zero piecewise multiple quasi affine expression (with value zero
4429 for each output dimension),
4430 a piecewise multiple quasi affine expression with a single cell (with
4431 either a universe or a specified domain) or
4432 a zero-dimensional piecewise multiple quasi affine expression
4434 can be created using the following functions.
4436 #include <isl/aff.h>
4437 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4438 __isl_take isl_space *space);
4439 __isl_give isl_multi_aff *isl_multi_aff_zero(
4440 __isl_take isl_space *space);
4441 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4442 __isl_take isl_space *space);
4443 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4444 __isl_take isl_space *space);
4445 __isl_give isl_multi_aff *isl_multi_aff_identity(
4446 __isl_take isl_space *space);
4447 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4448 __isl_take isl_space *space);
4449 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4450 __isl_take isl_space *space);
4451 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4452 __isl_take isl_space *space);
4453 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4454 __isl_take isl_space *space);
4455 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4456 __isl_take isl_space *space,
4457 enum isl_dim_type type,
4458 unsigned first, unsigned n);
4459 __isl_give isl_pw_multi_aff *
4460 isl_pw_multi_aff_project_out_map(
4461 __isl_take isl_space *space,
4462 enum isl_dim_type type,
4463 unsigned first, unsigned n);
4464 __isl_give isl_pw_multi_aff *
4465 isl_pw_multi_aff_from_multi_aff(
4466 __isl_take isl_multi_aff *ma);
4467 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4468 __isl_take isl_set *set,
4469 __isl_take isl_multi_aff *maff);
4470 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4471 __isl_take isl_set *set);
4473 __isl_give isl_union_pw_multi_aff *
4474 isl_union_pw_multi_aff_empty(
4475 __isl_take isl_space *space);
4476 __isl_give isl_union_pw_multi_aff *
4477 isl_union_pw_multi_aff_add_pw_multi_aff(
4478 __isl_take isl_union_pw_multi_aff *upma,
4479 __isl_take isl_pw_multi_aff *pma);
4480 __isl_give isl_union_pw_multi_aff *
4481 isl_union_pw_multi_aff_from_domain(
4482 __isl_take isl_union_set *uset);
4484 A piecewise multiple quasi affine expression can also be initialized
4485 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4486 and the C<isl_map> is single-valued.
4487 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4488 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4490 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4491 __isl_take isl_set *set);
4492 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4493 __isl_take isl_map *map);
4495 __isl_give isl_union_pw_multi_aff *
4496 isl_union_pw_multi_aff_from_union_set(
4497 __isl_take isl_union_set *uset);
4498 __isl_give isl_union_pw_multi_aff *
4499 isl_union_pw_multi_aff_from_union_map(
4500 __isl_take isl_union_map *umap);
4502 Multiple quasi affine expressions can be copied and freed using
4504 #include <isl/aff.h>
4505 __isl_give isl_multi_aff *isl_multi_aff_copy(
4506 __isl_keep isl_multi_aff *maff);
4507 __isl_null isl_multi_aff *isl_multi_aff_free(
4508 __isl_take isl_multi_aff *maff);
4510 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4511 __isl_keep isl_pw_multi_aff *pma);
4512 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
4513 __isl_take isl_pw_multi_aff *pma);
4515 __isl_give isl_union_pw_multi_aff *
4516 isl_union_pw_multi_aff_copy(
4517 __isl_keep isl_union_pw_multi_aff *upma);
4518 __isl_null isl_union_pw_multi_aff *
4519 isl_union_pw_multi_aff_free(
4520 __isl_take isl_union_pw_multi_aff *upma);
4522 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4523 __isl_keep isl_multi_pw_aff *mpa);
4524 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
4525 __isl_take isl_multi_pw_aff *mpa);
4527 The expression can be inspected using
4529 #include <isl/aff.h>
4530 isl_ctx *isl_multi_aff_get_ctx(
4531 __isl_keep isl_multi_aff *maff);
4532 isl_ctx *isl_pw_multi_aff_get_ctx(
4533 __isl_keep isl_pw_multi_aff *pma);
4534 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4535 __isl_keep isl_union_pw_multi_aff *upma);
4536 isl_ctx *isl_multi_pw_aff_get_ctx(
4537 __isl_keep isl_multi_pw_aff *mpa);
4539 int isl_multi_aff_involves_dims(
4540 __isl_keep isl_multi_aff *ma,
4541 enum isl_dim_type type, unsigned first, unsigned n);
4542 int isl_multi_pw_aff_involves_dims(
4543 __isl_keep isl_multi_pw_aff *mpa,
4544 enum isl_dim_type type, unsigned first, unsigned n);
4546 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4547 enum isl_dim_type type);
4548 unsigned isl_pw_multi_aff_dim(
4549 __isl_keep isl_pw_multi_aff *pma,
4550 enum isl_dim_type type);
4551 unsigned isl_multi_pw_aff_dim(
4552 __isl_keep isl_multi_pw_aff *mpa,
4553 enum isl_dim_type type);
4554 __isl_give isl_aff *isl_multi_aff_get_aff(
4555 __isl_keep isl_multi_aff *multi, int pos);
4556 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4557 __isl_keep isl_pw_multi_aff *pma, int pos);
4558 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4559 __isl_keep isl_multi_pw_aff *mpa, int pos);
4560 int isl_multi_aff_find_dim_by_id(
4561 __isl_keep isl_multi_aff *ma,
4562 enum isl_dim_type type, __isl_keep isl_id *id);
4563 int isl_multi_pw_aff_find_dim_by_id(
4564 __isl_keep isl_multi_pw_aff *mpa,
4565 enum isl_dim_type type, __isl_keep isl_id *id);
4566 const char *isl_pw_multi_aff_get_dim_name(
4567 __isl_keep isl_pw_multi_aff *pma,
4568 enum isl_dim_type type, unsigned pos);
4569 __isl_give isl_id *isl_multi_aff_get_dim_id(
4570 __isl_keep isl_multi_aff *ma,
4571 enum isl_dim_type type, unsigned pos);
4572 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4573 __isl_keep isl_pw_multi_aff *pma,
4574 enum isl_dim_type type, unsigned pos);
4575 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4576 __isl_keep isl_multi_pw_aff *mpa,
4577 enum isl_dim_type type, unsigned pos);
4578 const char *isl_multi_aff_get_tuple_name(
4579 __isl_keep isl_multi_aff *multi,
4580 enum isl_dim_type type);
4581 int isl_pw_multi_aff_has_tuple_name(
4582 __isl_keep isl_pw_multi_aff *pma,
4583 enum isl_dim_type type);
4584 const char *isl_pw_multi_aff_get_tuple_name(
4585 __isl_keep isl_pw_multi_aff *pma,
4586 enum isl_dim_type type);
4587 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4588 enum isl_dim_type type);
4589 int isl_pw_multi_aff_has_tuple_id(
4590 __isl_keep isl_pw_multi_aff *pma,
4591 enum isl_dim_type type);
4592 int isl_multi_pw_aff_has_tuple_id(
4593 __isl_keep isl_multi_pw_aff *mpa,
4594 enum isl_dim_type type);
4595 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4596 __isl_keep isl_multi_aff *ma,
4597 enum isl_dim_type type);
4598 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4599 __isl_keep isl_pw_multi_aff *pma,
4600 enum isl_dim_type type);
4601 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4602 __isl_keep isl_multi_pw_aff *mpa,
4603 enum isl_dim_type type);
4604 int isl_multi_aff_range_is_wrapping(
4605 __isl_keep isl_multi_aff *ma);
4606 int isl_multi_pw_aff_range_is_wrapping(
4607 __isl_keep isl_multi_pw_aff *mpa);
4609 int isl_pw_multi_aff_foreach_piece(
4610 __isl_keep isl_pw_multi_aff *pma,
4611 int (*fn)(__isl_take isl_set *set,
4612 __isl_take isl_multi_aff *maff,
4613 void *user), void *user);
4615 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4616 __isl_keep isl_union_pw_multi_aff *upma,
4617 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4618 void *user), void *user);
4620 It can be modified using
4622 #include <isl/aff.h>
4623 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4624 __isl_take isl_multi_aff *multi, int pos,
4625 __isl_take isl_aff *aff);
4626 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4627 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4628 __isl_take isl_pw_aff *pa);
4629 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4630 __isl_take isl_multi_aff *maff,
4631 enum isl_dim_type type, unsigned pos, const char *s);
4632 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4633 __isl_take isl_multi_aff *maff,
4634 enum isl_dim_type type, unsigned pos,
4635 __isl_take isl_id *id);
4636 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4637 __isl_take isl_multi_aff *maff,
4638 enum isl_dim_type type, const char *s);
4639 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4640 __isl_take isl_multi_aff *maff,
4641 enum isl_dim_type type, __isl_take isl_id *id);
4642 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4643 __isl_take isl_pw_multi_aff *pma,
4644 enum isl_dim_type type, __isl_take isl_id *id);
4645 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4646 __isl_take isl_multi_aff *ma,
4647 enum isl_dim_type type);
4648 __isl_give isl_multi_pw_aff *
4649 isl_multi_pw_aff_reset_tuple_id(
4650 __isl_take isl_multi_pw_aff *mpa,
4651 enum isl_dim_type type);
4652 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4653 __isl_take isl_multi_aff *ma);
4654 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4655 __isl_take isl_multi_pw_aff *mpa);
4657 __isl_give isl_multi_pw_aff *
4658 isl_multi_pw_aff_set_dim_name(
4659 __isl_take isl_multi_pw_aff *mpa,
4660 enum isl_dim_type type, unsigned pos, const char *s);
4661 __isl_give isl_multi_pw_aff *
4662 isl_multi_pw_aff_set_dim_id(
4663 __isl_take isl_multi_pw_aff *mpa,
4664 enum isl_dim_type type, unsigned pos,
4665 __isl_take isl_id *id);
4666 __isl_give isl_multi_pw_aff *
4667 isl_multi_pw_aff_set_tuple_name(
4668 __isl_take isl_multi_pw_aff *mpa,
4669 enum isl_dim_type type, const char *s);
4671 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4672 __isl_take isl_multi_aff *ma);
4674 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4675 __isl_take isl_multi_aff *ma,
4676 enum isl_dim_type type, unsigned first, unsigned n);
4677 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4678 __isl_take isl_multi_aff *ma,
4679 enum isl_dim_type type, unsigned n);
4680 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4681 __isl_take isl_multi_aff *maff,
4682 enum isl_dim_type type, unsigned first, unsigned n);
4683 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4684 __isl_take isl_pw_multi_aff *pma,
4685 enum isl_dim_type type, unsigned first, unsigned n);
4687 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4688 __isl_take isl_multi_pw_aff *mpa,
4689 enum isl_dim_type type, unsigned first, unsigned n);
4690 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4691 __isl_take isl_multi_pw_aff *mpa,
4692 enum isl_dim_type type, unsigned n);
4693 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4694 __isl_take isl_multi_pw_aff *pma,
4695 enum isl_dim_type dst_type, unsigned dst_pos,
4696 enum isl_dim_type src_type, unsigned src_pos,
4699 To check whether two multiple affine expressions are
4700 (obviously) equal to each other, use
4702 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4703 __isl_keep isl_multi_aff *maff2);
4704 int isl_pw_multi_aff_plain_is_equal(
4705 __isl_keep isl_pw_multi_aff *pma1,
4706 __isl_keep isl_pw_multi_aff *pma2);
4707 int isl_multi_pw_aff_plain_is_equal(
4708 __isl_keep isl_multi_pw_aff *mpa1,
4709 __isl_keep isl_multi_pw_aff *mpa2);
4710 int isl_multi_pw_aff_is_equal(
4711 __isl_keep isl_multi_pw_aff *mpa1,
4712 __isl_keep isl_multi_pw_aff *mpa2);
4716 #include <isl/aff.h>
4717 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4718 __isl_take isl_pw_multi_aff *pma1,
4719 __isl_take isl_pw_multi_aff *pma2);
4720 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4721 __isl_take isl_pw_multi_aff *pma1,
4722 __isl_take isl_pw_multi_aff *pma2);
4723 __isl_give isl_multi_aff *isl_multi_aff_floor(
4724 __isl_take isl_multi_aff *ma);
4725 __isl_give isl_multi_aff *isl_multi_aff_add(
4726 __isl_take isl_multi_aff *maff1,
4727 __isl_take isl_multi_aff *maff2);
4728 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4729 __isl_take isl_pw_multi_aff *pma1,
4730 __isl_take isl_pw_multi_aff *pma2);
4731 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4732 __isl_take isl_union_pw_multi_aff *upma1,
4733 __isl_take isl_union_pw_multi_aff *upma2);
4734 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4735 __isl_take isl_pw_multi_aff *pma1,
4736 __isl_take isl_pw_multi_aff *pma2);
4737 __isl_give isl_multi_aff *isl_multi_aff_sub(
4738 __isl_take isl_multi_aff *ma1,
4739 __isl_take isl_multi_aff *ma2);
4740 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4741 __isl_take isl_pw_multi_aff *pma1,
4742 __isl_take isl_pw_multi_aff *pma2);
4743 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4744 __isl_take isl_union_pw_multi_aff *upma1,
4745 __isl_take isl_union_pw_multi_aff *upma2);
4747 C<isl_multi_aff_sub> subtracts the second argument from the first.
4749 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4750 __isl_take isl_multi_aff *ma,
4751 __isl_take isl_val *v);
4752 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4753 __isl_take isl_pw_multi_aff *pma,
4754 __isl_take isl_val *v);
4755 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4756 __isl_take isl_multi_pw_aff *mpa,
4757 __isl_take isl_val *v);
4758 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4759 __isl_take isl_multi_aff *ma,
4760 __isl_take isl_multi_val *mv);
4761 __isl_give isl_pw_multi_aff *
4762 isl_pw_multi_aff_scale_multi_val(
4763 __isl_take isl_pw_multi_aff *pma,
4764 __isl_take isl_multi_val *mv);
4765 __isl_give isl_multi_pw_aff *
4766 isl_multi_pw_aff_scale_multi_val(
4767 __isl_take isl_multi_pw_aff *mpa,
4768 __isl_take isl_multi_val *mv);
4769 __isl_give isl_union_pw_multi_aff *
4770 isl_union_pw_multi_aff_scale_multi_val(
4771 __isl_take isl_union_pw_multi_aff *upma,
4772 __isl_take isl_multi_val *mv);
4773 __isl_give isl_multi_aff *
4774 isl_multi_aff_scale_down_multi_val(
4775 __isl_take isl_multi_aff *ma,
4776 __isl_take isl_multi_val *mv);
4777 __isl_give isl_multi_pw_aff *
4778 isl_multi_pw_aff_scale_down_multi_val(
4779 __isl_take isl_multi_pw_aff *mpa,
4780 __isl_take isl_multi_val *mv);
4782 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4783 by the corresponding elements of C<mv>.
4785 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4786 __isl_take isl_pw_multi_aff *pma,
4787 enum isl_dim_type type, unsigned pos, int value);
4788 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4789 __isl_take isl_pw_multi_aff *pma,
4790 __isl_take isl_set *set);
4791 __isl_give isl_set *isl_multi_pw_aff_domain(
4792 __isl_take isl_multi_pw_aff *mpa);
4793 __isl_give isl_multi_pw_aff *
4794 isl_multi_pw_aff_intersect_params(
4795 __isl_take isl_multi_pw_aff *mpa,
4796 __isl_take isl_set *set);
4797 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4798 __isl_take isl_pw_multi_aff *pma,
4799 __isl_take isl_set *set);
4800 __isl_give isl_multi_pw_aff *
4801 isl_multi_pw_aff_intersect_domain(
4802 __isl_take isl_multi_pw_aff *mpa,
4803 __isl_take isl_set *domain);
4804 __isl_give isl_union_pw_multi_aff *
4805 isl_union_pw_multi_aff_intersect_domain(
4806 __isl_take isl_union_pw_multi_aff *upma,
4807 __isl_take isl_union_set *uset);
4808 __isl_give isl_multi_aff *isl_multi_aff_lift(
4809 __isl_take isl_multi_aff *maff,
4810 __isl_give isl_local_space **ls);
4811 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4812 __isl_take isl_pw_multi_aff *pma);
4813 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4814 __isl_take isl_multi_pw_aff *mpa);
4815 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4816 __isl_take isl_multi_aff *multi,
4817 __isl_take isl_space *model);
4818 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4819 __isl_take isl_pw_multi_aff *pma,
4820 __isl_take isl_space *model);
4821 __isl_give isl_union_pw_multi_aff *
4822 isl_union_pw_multi_aff_align_params(
4823 __isl_take isl_union_pw_multi_aff *upma,
4824 __isl_take isl_space *model);
4825 __isl_give isl_pw_multi_aff *
4826 isl_pw_multi_aff_project_domain_on_params(
4827 __isl_take isl_pw_multi_aff *pma);
4828 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4829 __isl_take isl_multi_aff *maff,
4830 __isl_take isl_set *context);
4831 __isl_give isl_multi_aff *isl_multi_aff_gist(
4832 __isl_take isl_multi_aff *maff,
4833 __isl_take isl_set *context);
4834 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4835 __isl_take isl_pw_multi_aff *pma,
4836 __isl_take isl_set *set);
4837 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4838 __isl_take isl_pw_multi_aff *pma,
4839 __isl_take isl_set *set);
4840 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4841 __isl_take isl_multi_pw_aff *mpa,
4842 __isl_take isl_set *set);
4843 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4844 __isl_take isl_multi_pw_aff *mpa,
4845 __isl_take isl_set *set);
4846 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4847 __isl_take isl_multi_aff *ma);
4848 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4849 __isl_take isl_multi_pw_aff *mpa);
4850 __isl_give isl_set *isl_pw_multi_aff_domain(
4851 __isl_take isl_pw_multi_aff *pma);
4852 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4853 __isl_take isl_union_pw_multi_aff *upma);
4854 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4855 __isl_take isl_multi_aff *ma1, unsigned pos,
4856 __isl_take isl_multi_aff *ma2);
4857 __isl_give isl_multi_aff *isl_multi_aff_splice(
4858 __isl_take isl_multi_aff *ma1,
4859 unsigned in_pos, unsigned out_pos,
4860 __isl_take isl_multi_aff *ma2);
4861 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4862 __isl_take isl_multi_aff *ma1,
4863 __isl_take isl_multi_aff *ma2);
4864 __isl_give isl_multi_aff *
4865 isl_multi_aff_range_factor_domain(
4866 __isl_take isl_multi_aff *ma);
4867 __isl_give isl_multi_aff *
4868 isl_multi_aff_range_factor_range(
4869 __isl_take isl_multi_aff *ma);
4870 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4871 __isl_take isl_multi_aff *ma1,
4872 __isl_take isl_multi_aff *ma2);
4873 __isl_give isl_multi_aff *isl_multi_aff_product(
4874 __isl_take isl_multi_aff *ma1,
4875 __isl_take isl_multi_aff *ma2);
4876 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4877 __isl_take isl_multi_pw_aff *mpa1,
4878 __isl_take isl_multi_pw_aff *mpa2);
4879 __isl_give isl_pw_multi_aff *
4880 isl_pw_multi_aff_range_product(
4881 __isl_take isl_pw_multi_aff *pma1,
4882 __isl_take isl_pw_multi_aff *pma2);
4883 __isl_give isl_multi_pw_aff *
4884 isl_multi_pw_aff_range_factor_domain(
4885 __isl_take isl_multi_pw_aff *mpa);
4886 __isl_give isl_multi_pw_aff *
4887 isl_multi_pw_aff_range_factor_range(
4888 __isl_take isl_multi_pw_aff *mpa);
4889 __isl_give isl_pw_multi_aff *
4890 isl_pw_multi_aff_flat_range_product(
4891 __isl_take isl_pw_multi_aff *pma1,
4892 __isl_take isl_pw_multi_aff *pma2);
4893 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4894 __isl_take isl_pw_multi_aff *pma1,
4895 __isl_take isl_pw_multi_aff *pma2);
4896 __isl_give isl_union_pw_multi_aff *
4897 isl_union_pw_multi_aff_flat_range_product(
4898 __isl_take isl_union_pw_multi_aff *upma1,
4899 __isl_take isl_union_pw_multi_aff *upma2);
4900 __isl_give isl_multi_pw_aff *
4901 isl_multi_pw_aff_range_splice(
4902 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4903 __isl_take isl_multi_pw_aff *mpa2);
4904 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4905 __isl_take isl_multi_pw_aff *mpa1,
4906 unsigned in_pos, unsigned out_pos,
4907 __isl_take isl_multi_pw_aff *mpa2);
4908 __isl_give isl_multi_pw_aff *
4909 isl_multi_pw_aff_range_product(
4910 __isl_take isl_multi_pw_aff *mpa1,
4911 __isl_take isl_multi_pw_aff *mpa2);
4912 __isl_give isl_multi_pw_aff *
4913 isl_multi_pw_aff_flat_range_product(
4914 __isl_take isl_multi_pw_aff *mpa1,
4915 __isl_take isl_multi_pw_aff *mpa2);
4917 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4918 then it is assigned the local space that lies at the basis of
4919 the lifting applied.
4921 #include <isl/aff.h>
4922 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4923 __isl_take isl_multi_aff *ma1,
4924 __isl_take isl_multi_aff *ma2);
4925 __isl_give isl_pw_multi_aff *
4926 isl_pw_multi_aff_pullback_multi_aff(
4927 __isl_take isl_pw_multi_aff *pma,
4928 __isl_take isl_multi_aff *ma);
4929 __isl_give isl_multi_pw_aff *
4930 isl_multi_pw_aff_pullback_multi_aff(
4931 __isl_take isl_multi_pw_aff *mpa,
4932 __isl_take isl_multi_aff *ma);
4933 __isl_give isl_pw_multi_aff *
4934 isl_pw_multi_aff_pullback_pw_multi_aff(
4935 __isl_take isl_pw_multi_aff *pma1,
4936 __isl_take isl_pw_multi_aff *pma2);
4937 __isl_give isl_multi_pw_aff *
4938 isl_multi_pw_aff_pullback_pw_multi_aff(
4939 __isl_take isl_multi_pw_aff *mpa,
4940 __isl_take isl_pw_multi_aff *pma);
4941 __isl_give isl_multi_pw_aff *
4942 isl_multi_pw_aff_pullback_multi_pw_aff(
4943 __isl_take isl_multi_pw_aff *mpa1,
4944 __isl_take isl_multi_pw_aff *mpa2);
4946 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4947 In other words, C<ma2> is plugged
4950 __isl_give isl_set *isl_multi_aff_lex_le_set(
4951 __isl_take isl_multi_aff *ma1,
4952 __isl_take isl_multi_aff *ma2);
4953 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4954 __isl_take isl_multi_aff *ma1,
4955 __isl_take isl_multi_aff *ma2);
4957 The function C<isl_multi_aff_lex_le_set> returns a set
4958 containing those elements in the shared domain space
4959 where C<ma1> is lexicographically smaller than or
4962 An expression can be read from input using
4964 #include <isl/aff.h>
4965 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4966 isl_ctx *ctx, const char *str);
4967 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4968 isl_ctx *ctx, const char *str);
4969 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4970 isl_ctx *ctx, const char *str);
4971 __isl_give isl_union_pw_multi_aff *
4972 isl_union_pw_multi_aff_read_from_str(
4973 isl_ctx *ctx, const char *str);
4975 An expression can be printed using
4977 #include <isl/aff.h>
4978 __isl_give isl_printer *isl_printer_print_multi_aff(
4979 __isl_take isl_printer *p,
4980 __isl_keep isl_multi_aff *maff);
4981 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4982 __isl_take isl_printer *p,
4983 __isl_keep isl_pw_multi_aff *pma);
4984 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4985 __isl_take isl_printer *p,
4986 __isl_keep isl_union_pw_multi_aff *upma);
4987 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4988 __isl_take isl_printer *p,
4989 __isl_keep isl_multi_pw_aff *mpa);
4993 Points are elements of a set. They can be used to construct
4994 simple sets (boxes) or they can be used to represent the
4995 individual elements of a set.
4996 The zero point (the origin) can be created using
4998 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
5000 The coordinates of a point can be inspected, set and changed
5003 __isl_give isl_val *isl_point_get_coordinate_val(
5004 __isl_keep isl_point *pnt,
5005 enum isl_dim_type type, int pos);
5006 __isl_give isl_point *isl_point_set_coordinate_val(
5007 __isl_take isl_point *pnt,
5008 enum isl_dim_type type, int pos,
5009 __isl_take isl_val *v);
5011 __isl_give isl_point *isl_point_add_ui(
5012 __isl_take isl_point *pnt,
5013 enum isl_dim_type type, int pos, unsigned val);
5014 __isl_give isl_point *isl_point_sub_ui(
5015 __isl_take isl_point *pnt,
5016 enum isl_dim_type type, int pos, unsigned val);
5018 Other properties can be obtained using
5020 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
5022 Points can be copied or freed using
5024 __isl_give isl_point *isl_point_copy(
5025 __isl_keep isl_point *pnt);
5026 void isl_point_free(__isl_take isl_point *pnt);
5028 A singleton set can be created from a point using
5030 __isl_give isl_basic_set *isl_basic_set_from_point(
5031 __isl_take isl_point *pnt);
5032 __isl_give isl_set *isl_set_from_point(
5033 __isl_take isl_point *pnt);
5035 and a box can be created from two opposite extremal points using
5037 __isl_give isl_basic_set *isl_basic_set_box_from_points(
5038 __isl_take isl_point *pnt1,
5039 __isl_take isl_point *pnt2);
5040 __isl_give isl_set *isl_set_box_from_points(
5041 __isl_take isl_point *pnt1,
5042 __isl_take isl_point *pnt2);
5044 All elements of a B<bounded> (union) set can be enumerated using
5045 the following functions.
5047 int isl_set_foreach_point(__isl_keep isl_set *set,
5048 int (*fn)(__isl_take isl_point *pnt, void *user),
5050 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
5051 int (*fn)(__isl_take isl_point *pnt, void *user),
5054 The function C<fn> is called for each integer point in
5055 C<set> with as second argument the last argument of
5056 the C<isl_set_foreach_point> call. The function C<fn>
5057 should return C<0> on success and C<-1> on failure.
5058 In the latter case, C<isl_set_foreach_point> will stop
5059 enumerating and return C<-1> as well.
5060 If the enumeration is performed successfully and to completion,
5061 then C<isl_set_foreach_point> returns C<0>.
5063 To obtain a single point of a (basic) set, use
5065 __isl_give isl_point *isl_basic_set_sample_point(
5066 __isl_take isl_basic_set *bset);
5067 __isl_give isl_point *isl_set_sample_point(
5068 __isl_take isl_set *set);
5070 If C<set> does not contain any (integer) points, then the
5071 resulting point will be ``void'', a property that can be
5074 int isl_point_is_void(__isl_keep isl_point *pnt);
5076 =head2 Piecewise Quasipolynomials
5078 A piecewise quasipolynomial is a particular kind of function that maps
5079 a parametric point to a rational value.
5080 More specifically, a quasipolynomial is a polynomial expression in greatest
5081 integer parts of affine expressions of parameters and variables.
5082 A piecewise quasipolynomial is a subdivision of a given parametric
5083 domain into disjoint cells with a quasipolynomial associated to
5084 each cell. The value of the piecewise quasipolynomial at a given
5085 point is the value of the quasipolynomial associated to the cell
5086 that contains the point. Outside of the union of cells,
5087 the value is assumed to be zero.
5088 For example, the piecewise quasipolynomial
5090 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
5092 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
5093 A given piecewise quasipolynomial has a fixed domain dimension.
5094 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
5095 defined over different domains.
5096 Piecewise quasipolynomials are mainly used by the C<barvinok>
5097 library for representing the number of elements in a parametric set or map.
5098 For example, the piecewise quasipolynomial above represents
5099 the number of points in the map
5101 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
5103 =head3 Input and Output
5105 Piecewise quasipolynomials can be read from input using
5107 __isl_give isl_union_pw_qpolynomial *
5108 isl_union_pw_qpolynomial_read_from_str(
5109 isl_ctx *ctx, const char *str);
5111 Quasipolynomials and piecewise quasipolynomials can be printed
5112 using the following functions.
5114 __isl_give isl_printer *isl_printer_print_qpolynomial(
5115 __isl_take isl_printer *p,
5116 __isl_keep isl_qpolynomial *qp);
5118 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
5119 __isl_take isl_printer *p,
5120 __isl_keep isl_pw_qpolynomial *pwqp);
5122 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
5123 __isl_take isl_printer *p,
5124 __isl_keep isl_union_pw_qpolynomial *upwqp);
5126 The output format of the printer
5127 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5128 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
5130 In case of printing in C<ISL_FORMAT_C>, the user may want
5131 to set the names of all dimensions
5133 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
5134 __isl_take isl_qpolynomial *qp,
5135 enum isl_dim_type type, unsigned pos,
5137 __isl_give isl_pw_qpolynomial *
5138 isl_pw_qpolynomial_set_dim_name(
5139 __isl_take isl_pw_qpolynomial *pwqp,
5140 enum isl_dim_type type, unsigned pos,
5143 =head3 Creating New (Piecewise) Quasipolynomials
5145 Some simple quasipolynomials can be created using the following functions.
5146 More complicated quasipolynomials can be created by applying
5147 operations such as addition and multiplication
5148 on the resulting quasipolynomials
5150 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
5151 __isl_take isl_space *domain);
5152 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
5153 __isl_take isl_space *domain);
5154 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
5155 __isl_take isl_space *domain);
5156 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
5157 __isl_take isl_space *domain);
5158 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
5159 __isl_take isl_space *domain);
5160 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
5161 __isl_take isl_space *domain,
5162 __isl_take isl_val *val);
5163 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
5164 __isl_take isl_space *domain,
5165 enum isl_dim_type type, unsigned pos);
5166 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
5167 __isl_take isl_aff *aff);
5169 Note that the space in which a quasipolynomial lives is a map space
5170 with a one-dimensional range. The C<domain> argument in some of
5171 the functions above corresponds to the domain of this map space.
5173 The zero piecewise quasipolynomial or a piecewise quasipolynomial
5174 with a single cell can be created using the following functions.
5175 Multiple of these single cell piecewise quasipolynomials can
5176 be combined to create more complicated piecewise quasipolynomials.
5178 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
5179 __isl_take isl_space *space);
5180 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
5181 __isl_take isl_set *set,
5182 __isl_take isl_qpolynomial *qp);
5183 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
5184 __isl_take isl_qpolynomial *qp);
5185 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
5186 __isl_take isl_pw_aff *pwaff);
5188 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
5189 __isl_take isl_space *space);
5190 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
5191 __isl_take isl_pw_qpolynomial *pwqp);
5192 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
5193 __isl_take isl_union_pw_qpolynomial *upwqp,
5194 __isl_take isl_pw_qpolynomial *pwqp);
5196 Quasipolynomials can be copied and freed again using the following
5199 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
5200 __isl_keep isl_qpolynomial *qp);
5201 __isl_null isl_qpolynomial *isl_qpolynomial_free(
5202 __isl_take isl_qpolynomial *qp);
5204 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
5205 __isl_keep isl_pw_qpolynomial *pwqp);
5206 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
5207 __isl_take isl_pw_qpolynomial *pwqp);
5209 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
5210 __isl_keep isl_union_pw_qpolynomial *upwqp);
5211 __isl_null isl_union_pw_qpolynomial *
5212 isl_union_pw_qpolynomial_free(
5213 __isl_take isl_union_pw_qpolynomial *upwqp);
5215 =head3 Inspecting (Piecewise) Quasipolynomials
5217 To iterate over all piecewise quasipolynomials in a union
5218 piecewise quasipolynomial, use the following function
5220 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
5221 __isl_keep isl_union_pw_qpolynomial *upwqp,
5222 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
5225 To extract the piecewise quasipolynomial in a given space from a union, use
5227 __isl_give isl_pw_qpolynomial *
5228 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
5229 __isl_keep isl_union_pw_qpolynomial *upwqp,
5230 __isl_take isl_space *space);
5232 To iterate over the cells in a piecewise quasipolynomial,
5233 use either of the following two functions
5235 int isl_pw_qpolynomial_foreach_piece(
5236 __isl_keep isl_pw_qpolynomial *pwqp,
5237 int (*fn)(__isl_take isl_set *set,
5238 __isl_take isl_qpolynomial *qp,
5239 void *user), void *user);
5240 int isl_pw_qpolynomial_foreach_lifted_piece(
5241 __isl_keep isl_pw_qpolynomial *pwqp,
5242 int (*fn)(__isl_take isl_set *set,
5243 __isl_take isl_qpolynomial *qp,
5244 void *user), void *user);
5246 As usual, the function C<fn> should return C<0> on success
5247 and C<-1> on failure. The difference between
5248 C<isl_pw_qpolynomial_foreach_piece> and
5249 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
5250 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
5251 compute unique representations for all existentially quantified
5252 variables and then turn these existentially quantified variables
5253 into extra set variables, adapting the associated quasipolynomial
5254 accordingly. This means that the C<set> passed to C<fn>
5255 will not have any existentially quantified variables, but that
5256 the dimensions of the sets may be different for different
5257 invocations of C<fn>.
5259 The constant term of a quasipolynomial can be extracted using
5261 __isl_give isl_val *isl_qpolynomial_get_constant_val(
5262 __isl_keep isl_qpolynomial *qp);
5264 To iterate over all terms in a quasipolynomial,
5267 int isl_qpolynomial_foreach_term(
5268 __isl_keep isl_qpolynomial *qp,
5269 int (*fn)(__isl_take isl_term *term,
5270 void *user), void *user);
5272 The terms themselves can be inspected and freed using
5275 unsigned isl_term_dim(__isl_keep isl_term *term,
5276 enum isl_dim_type type);
5277 __isl_give isl_val *isl_term_get_coefficient_val(
5278 __isl_keep isl_term *term);
5279 int isl_term_get_exp(__isl_keep isl_term *term,
5280 enum isl_dim_type type, unsigned pos);
5281 __isl_give isl_aff *isl_term_get_div(
5282 __isl_keep isl_term *term, unsigned pos);
5283 void isl_term_free(__isl_take isl_term *term);
5285 Each term is a product of parameters, set variables and
5286 integer divisions. The function C<isl_term_get_exp>
5287 returns the exponent of a given dimensions in the given term.
5289 =head3 Properties of (Piecewise) Quasipolynomials
5291 To check whether two union piecewise quasipolynomials are
5292 obviously equal, use
5294 int isl_union_pw_qpolynomial_plain_is_equal(
5295 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5296 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5298 =head3 Operations on (Piecewise) Quasipolynomials
5300 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5301 __isl_take isl_qpolynomial *qp,
5302 __isl_take isl_val *v);
5303 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5304 __isl_take isl_qpolynomial *qp);
5305 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5306 __isl_take isl_qpolynomial *qp1,
5307 __isl_take isl_qpolynomial *qp2);
5308 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5309 __isl_take isl_qpolynomial *qp1,
5310 __isl_take isl_qpolynomial *qp2);
5311 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5312 __isl_take isl_qpolynomial *qp1,
5313 __isl_take isl_qpolynomial *qp2);
5314 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5315 __isl_take isl_qpolynomial *qp, unsigned exponent);
5317 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5318 __isl_take isl_pw_qpolynomial *pwqp,
5319 enum isl_dim_type type, unsigned n,
5320 __isl_take isl_val *v);
5321 __isl_give isl_pw_qpolynomial *
5322 isl_pw_qpolynomial_scale_val(
5323 __isl_take isl_pw_qpolynomial *pwqp,
5324 __isl_take isl_val *v);
5325 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5326 __isl_take isl_pw_qpolynomial *pwqp1,
5327 __isl_take isl_pw_qpolynomial *pwqp2);
5328 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5329 __isl_take isl_pw_qpolynomial *pwqp1,
5330 __isl_take isl_pw_qpolynomial *pwqp2);
5331 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5332 __isl_take isl_pw_qpolynomial *pwqp1,
5333 __isl_take isl_pw_qpolynomial *pwqp2);
5334 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5335 __isl_take isl_pw_qpolynomial *pwqp);
5336 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5337 __isl_take isl_pw_qpolynomial *pwqp1,
5338 __isl_take isl_pw_qpolynomial *pwqp2);
5339 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5340 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5342 __isl_give isl_union_pw_qpolynomial *
5343 isl_union_pw_qpolynomial_scale_val(
5344 __isl_take isl_union_pw_qpolynomial *upwqp,
5345 __isl_take isl_val *v);
5346 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5347 __isl_take isl_union_pw_qpolynomial *upwqp1,
5348 __isl_take isl_union_pw_qpolynomial *upwqp2);
5349 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5350 __isl_take isl_union_pw_qpolynomial *upwqp1,
5351 __isl_take isl_union_pw_qpolynomial *upwqp2);
5352 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5353 __isl_take isl_union_pw_qpolynomial *upwqp1,
5354 __isl_take isl_union_pw_qpolynomial *upwqp2);
5356 __isl_give isl_val *isl_pw_qpolynomial_eval(
5357 __isl_take isl_pw_qpolynomial *pwqp,
5358 __isl_take isl_point *pnt);
5360 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5361 __isl_take isl_union_pw_qpolynomial *upwqp,
5362 __isl_take isl_point *pnt);
5364 __isl_give isl_set *isl_pw_qpolynomial_domain(
5365 __isl_take isl_pw_qpolynomial *pwqp);
5366 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5367 __isl_take isl_pw_qpolynomial *pwpq,
5368 __isl_take isl_set *set);
5369 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5370 __isl_take isl_pw_qpolynomial *pwpq,
5371 __isl_take isl_set *set);
5373 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5374 __isl_take isl_union_pw_qpolynomial *upwqp);
5375 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5376 __isl_take isl_union_pw_qpolynomial *upwpq,
5377 __isl_take isl_union_set *uset);
5378 __isl_give isl_union_pw_qpolynomial *
5379 isl_union_pw_qpolynomial_intersect_params(
5380 __isl_take isl_union_pw_qpolynomial *upwpq,
5381 __isl_take isl_set *set);
5383 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5384 __isl_take isl_qpolynomial *qp,
5385 __isl_take isl_space *model);
5387 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5388 __isl_take isl_qpolynomial *qp);
5389 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5390 __isl_take isl_pw_qpolynomial *pwqp);
5392 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5393 __isl_take isl_union_pw_qpolynomial *upwqp);
5395 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5396 __isl_take isl_qpolynomial *qp,
5397 __isl_take isl_set *context);
5398 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5399 __isl_take isl_qpolynomial *qp,
5400 __isl_take isl_set *context);
5402 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5403 __isl_take isl_pw_qpolynomial *pwqp,
5404 __isl_take isl_set *context);
5405 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5406 __isl_take isl_pw_qpolynomial *pwqp,
5407 __isl_take isl_set *context);
5409 __isl_give isl_union_pw_qpolynomial *
5410 isl_union_pw_qpolynomial_gist_params(
5411 __isl_take isl_union_pw_qpolynomial *upwqp,
5412 __isl_take isl_set *context);
5413 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5414 __isl_take isl_union_pw_qpolynomial *upwqp,
5415 __isl_take isl_union_set *context);
5417 The gist operation applies the gist operation to each of
5418 the cells in the domain of the input piecewise quasipolynomial.
5419 The context is also exploited
5420 to simplify the quasipolynomials associated to each cell.
5422 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5423 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5424 __isl_give isl_union_pw_qpolynomial *
5425 isl_union_pw_qpolynomial_to_polynomial(
5426 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5428 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5429 the polynomial will be an overapproximation. If C<sign> is negative,
5430 it will be an underapproximation. If C<sign> is zero, the approximation
5431 will lie somewhere in between.
5433 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5435 A piecewise quasipolynomial reduction is a piecewise
5436 reduction (or fold) of quasipolynomials.
5437 In particular, the reduction can be maximum or a minimum.
5438 The objects are mainly used to represent the result of
5439 an upper or lower bound on a quasipolynomial over its domain,
5440 i.e., as the result of the following function.
5442 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5443 __isl_take isl_pw_qpolynomial *pwqp,
5444 enum isl_fold type, int *tight);
5446 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5447 __isl_take isl_union_pw_qpolynomial *upwqp,
5448 enum isl_fold type, int *tight);
5450 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5451 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5452 is the returned bound is known be tight, i.e., for each value
5453 of the parameters there is at least
5454 one element in the domain that reaches the bound.
5455 If the domain of C<pwqp> is not wrapping, then the bound is computed
5456 over all elements in that domain and the result has a purely parametric
5457 domain. If the domain of C<pwqp> is wrapping, then the bound is
5458 computed over the range of the wrapped relation. The domain of the
5459 wrapped relation becomes the domain of the result.
5461 A (piecewise) quasipolynomial reduction can be copied or freed using the
5462 following functions.
5464 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5465 __isl_keep isl_qpolynomial_fold *fold);
5466 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5467 __isl_keep isl_pw_qpolynomial_fold *pwf);
5468 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5469 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5470 void isl_qpolynomial_fold_free(
5471 __isl_take isl_qpolynomial_fold *fold);
5472 __isl_null isl_pw_qpolynomial_fold *
5473 isl_pw_qpolynomial_fold_free(
5474 __isl_take isl_pw_qpolynomial_fold *pwf);
5475 __isl_null isl_union_pw_qpolynomial_fold *
5476 isl_union_pw_qpolynomial_fold_free(
5477 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5479 =head3 Printing Piecewise Quasipolynomial Reductions
5481 Piecewise quasipolynomial reductions can be printed
5482 using the following function.
5484 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5485 __isl_take isl_printer *p,
5486 __isl_keep isl_pw_qpolynomial_fold *pwf);
5487 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5488 __isl_take isl_printer *p,
5489 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5491 For C<isl_printer_print_pw_qpolynomial_fold>,
5492 output format of the printer
5493 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5494 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5495 output format of the printer
5496 needs to be set to C<ISL_FORMAT_ISL>.
5497 In case of printing in C<ISL_FORMAT_C>, the user may want
5498 to set the names of all dimensions
5500 __isl_give isl_pw_qpolynomial_fold *
5501 isl_pw_qpolynomial_fold_set_dim_name(
5502 __isl_take isl_pw_qpolynomial_fold *pwf,
5503 enum isl_dim_type type, unsigned pos,
5506 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5508 To iterate over all piecewise quasipolynomial reductions in a union
5509 piecewise quasipolynomial reduction, use the following function
5511 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5512 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5513 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5514 void *user), void *user);
5516 To iterate over the cells in a piecewise quasipolynomial reduction,
5517 use either of the following two functions
5519 int isl_pw_qpolynomial_fold_foreach_piece(
5520 __isl_keep isl_pw_qpolynomial_fold *pwf,
5521 int (*fn)(__isl_take isl_set *set,
5522 __isl_take isl_qpolynomial_fold *fold,
5523 void *user), void *user);
5524 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5525 __isl_keep isl_pw_qpolynomial_fold *pwf,
5526 int (*fn)(__isl_take isl_set *set,
5527 __isl_take isl_qpolynomial_fold *fold,
5528 void *user), void *user);
5530 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5531 of the difference between these two functions.
5533 To iterate over all quasipolynomials in a reduction, use
5535 int isl_qpolynomial_fold_foreach_qpolynomial(
5536 __isl_keep isl_qpolynomial_fold *fold,
5537 int (*fn)(__isl_take isl_qpolynomial *qp,
5538 void *user), void *user);
5540 =head3 Properties of Piecewise Quasipolynomial Reductions
5542 To check whether two union piecewise quasipolynomial reductions are
5543 obviously equal, use
5545 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5546 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5547 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5549 =head3 Operations on Piecewise Quasipolynomial Reductions
5551 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5552 __isl_take isl_qpolynomial_fold *fold,
5553 __isl_take isl_val *v);
5554 __isl_give isl_pw_qpolynomial_fold *
5555 isl_pw_qpolynomial_fold_scale_val(
5556 __isl_take isl_pw_qpolynomial_fold *pwf,
5557 __isl_take isl_val *v);
5558 __isl_give isl_union_pw_qpolynomial_fold *
5559 isl_union_pw_qpolynomial_fold_scale_val(
5560 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5561 __isl_take isl_val *v);
5563 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5564 __isl_take isl_pw_qpolynomial_fold *pwf1,
5565 __isl_take isl_pw_qpolynomial_fold *pwf2);
5567 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5568 __isl_take isl_pw_qpolynomial_fold *pwf1,
5569 __isl_take isl_pw_qpolynomial_fold *pwf2);
5571 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5572 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5573 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5575 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5576 __isl_take isl_pw_qpolynomial_fold *pwf,
5577 __isl_take isl_point *pnt);
5579 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5580 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5581 __isl_take isl_point *pnt);
5583 __isl_give isl_pw_qpolynomial_fold *
5584 isl_pw_qpolynomial_fold_intersect_params(
5585 __isl_take isl_pw_qpolynomial_fold *pwf,
5586 __isl_take isl_set *set);
5588 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5589 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5590 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5591 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5592 __isl_take isl_union_set *uset);
5593 __isl_give isl_union_pw_qpolynomial_fold *
5594 isl_union_pw_qpolynomial_fold_intersect_params(
5595 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5596 __isl_take isl_set *set);
5598 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5599 __isl_take isl_pw_qpolynomial_fold *pwf);
5601 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5602 __isl_take isl_pw_qpolynomial_fold *pwf);
5604 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5605 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5607 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5608 __isl_take isl_qpolynomial_fold *fold,
5609 __isl_take isl_set *context);
5610 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5611 __isl_take isl_qpolynomial_fold *fold,
5612 __isl_take isl_set *context);
5614 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5615 __isl_take isl_pw_qpolynomial_fold *pwf,
5616 __isl_take isl_set *context);
5617 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5618 __isl_take isl_pw_qpolynomial_fold *pwf,
5619 __isl_take isl_set *context);
5621 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5622 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5623 __isl_take isl_union_set *context);
5624 __isl_give isl_union_pw_qpolynomial_fold *
5625 isl_union_pw_qpolynomial_fold_gist_params(
5626 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5627 __isl_take isl_set *context);
5629 The gist operation applies the gist operation to each of
5630 the cells in the domain of the input piecewise quasipolynomial reduction.
5631 In future, the operation will also exploit the context
5632 to simplify the quasipolynomial reductions associated to each cell.
5634 __isl_give isl_pw_qpolynomial_fold *
5635 isl_set_apply_pw_qpolynomial_fold(
5636 __isl_take isl_set *set,
5637 __isl_take isl_pw_qpolynomial_fold *pwf,
5639 __isl_give isl_pw_qpolynomial_fold *
5640 isl_map_apply_pw_qpolynomial_fold(
5641 __isl_take isl_map *map,
5642 __isl_take isl_pw_qpolynomial_fold *pwf,
5644 __isl_give isl_union_pw_qpolynomial_fold *
5645 isl_union_set_apply_union_pw_qpolynomial_fold(
5646 __isl_take isl_union_set *uset,
5647 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5649 __isl_give isl_union_pw_qpolynomial_fold *
5650 isl_union_map_apply_union_pw_qpolynomial_fold(
5651 __isl_take isl_union_map *umap,
5652 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5655 The functions taking a map
5656 compose the given map with the given piecewise quasipolynomial reduction.
5657 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5658 over all elements in the intersection of the range of the map
5659 and the domain of the piecewise quasipolynomial reduction
5660 as a function of an element in the domain of the map.
5661 The functions taking a set compute a bound over all elements in the
5662 intersection of the set and the domain of the
5663 piecewise quasipolynomial reduction.
5665 =head2 Parametric Vertex Enumeration
5667 The parametric vertex enumeration described in this section
5668 is mainly intended to be used internally and by the C<barvinok>
5671 #include <isl/vertices.h>
5672 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5673 __isl_keep isl_basic_set *bset);
5675 The function C<isl_basic_set_compute_vertices> performs the
5676 actual computation of the parametric vertices and the chamber
5677 decomposition and store the result in an C<isl_vertices> object.
5678 This information can be queried by either iterating over all
5679 the vertices or iterating over all the chambers or cells
5680 and then iterating over all vertices that are active on the chamber.
5682 int isl_vertices_foreach_vertex(
5683 __isl_keep isl_vertices *vertices,
5684 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5687 int isl_vertices_foreach_cell(
5688 __isl_keep isl_vertices *vertices,
5689 int (*fn)(__isl_take isl_cell *cell, void *user),
5691 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5692 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5695 Other operations that can be performed on an C<isl_vertices> object are
5698 isl_ctx *isl_vertices_get_ctx(
5699 __isl_keep isl_vertices *vertices);
5700 int isl_vertices_get_n_vertices(
5701 __isl_keep isl_vertices *vertices);
5702 void isl_vertices_free(__isl_take isl_vertices *vertices);
5704 Vertices can be inspected and destroyed using the following functions.
5706 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5707 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5708 __isl_give isl_basic_set *isl_vertex_get_domain(
5709 __isl_keep isl_vertex *vertex);
5710 __isl_give isl_multi_aff *isl_vertex_get_expr(
5711 __isl_keep isl_vertex *vertex);
5712 void isl_vertex_free(__isl_take isl_vertex *vertex);
5714 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
5715 describing the vertex in terms of the parameters,
5716 while C<isl_vertex_get_domain> returns the activity domain
5719 Chambers can be inspected and destroyed using the following functions.
5721 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5722 __isl_give isl_basic_set *isl_cell_get_domain(
5723 __isl_keep isl_cell *cell);
5724 void isl_cell_free(__isl_take isl_cell *cell);
5726 =head1 Polyhedral Compilation Library
5728 This section collects functionality in C<isl> that has been specifically
5729 designed for use during polyhedral compilation.
5731 =head2 Dependence Analysis
5733 C<isl> contains specialized functionality for performing
5734 array dataflow analysis. That is, given a I<sink> access relation
5735 and a collection of possible I<source> access relations,
5736 C<isl> can compute relations that describe
5737 for each iteration of the sink access, which iteration
5738 of which of the source access relations was the last
5739 to access the same data element before the given iteration
5741 The resulting dependence relations map source iterations
5742 to the corresponding sink iterations.
5743 To compute standard flow dependences, the sink should be
5744 a read, while the sources should be writes.
5745 If any of the source accesses are marked as being I<may>
5746 accesses, then there will be a dependence from the last
5747 I<must> access B<and> from any I<may> access that follows
5748 this last I<must> access.
5749 In particular, if I<all> sources are I<may> accesses,
5750 then memory based dependence analysis is performed.
5751 If, on the other hand, all sources are I<must> accesses,
5752 then value based dependence analysis is performed.
5754 #include <isl/flow.h>
5756 typedef int (*isl_access_level_before)(void *first, void *second);
5758 __isl_give isl_access_info *isl_access_info_alloc(
5759 __isl_take isl_map *sink,
5760 void *sink_user, isl_access_level_before fn,
5762 __isl_give isl_access_info *isl_access_info_add_source(
5763 __isl_take isl_access_info *acc,
5764 __isl_take isl_map *source, int must,
5766 __isl_null isl_access_info *isl_access_info_free(
5767 __isl_take isl_access_info *acc);
5769 __isl_give isl_flow *isl_access_info_compute_flow(
5770 __isl_take isl_access_info *acc);
5772 int isl_flow_foreach(__isl_keep isl_flow *deps,
5773 int (*fn)(__isl_take isl_map *dep, int must,
5774 void *dep_user, void *user),
5776 __isl_give isl_map *isl_flow_get_no_source(
5777 __isl_keep isl_flow *deps, int must);
5778 void isl_flow_free(__isl_take isl_flow *deps);
5780 The function C<isl_access_info_compute_flow> performs the actual
5781 dependence analysis. The other functions are used to construct
5782 the input for this function or to read off the output.
5784 The input is collected in an C<isl_access_info>, which can
5785 be created through a call to C<isl_access_info_alloc>.
5786 The arguments to this functions are the sink access relation
5787 C<sink>, a token C<sink_user> used to identify the sink
5788 access to the user, a callback function for specifying the
5789 relative order of source and sink accesses, and the number
5790 of source access relations that will be added.
5791 The callback function has type C<int (*)(void *first, void *second)>.
5792 The function is called with two user supplied tokens identifying
5793 either a source or the sink and it should return the shared nesting
5794 level and the relative order of the two accesses.
5795 In particular, let I<n> be the number of loops shared by
5796 the two accesses. If C<first> precedes C<second> textually,
5797 then the function should return I<2 * n + 1>; otherwise,
5798 it should return I<2 * n>.
5799 The sources can be added to the C<isl_access_info> by performing
5800 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5801 C<must> indicates whether the source is a I<must> access
5802 or a I<may> access. Note that a multi-valued access relation
5803 should only be marked I<must> if every iteration in the domain
5804 of the relation accesses I<all> elements in its image.
5805 The C<source_user> token is again used to identify
5806 the source access. The range of the source access relation
5807 C<source> should have the same dimension as the range
5808 of the sink access relation.
5809 The C<isl_access_info_free> function should usually not be
5810 called explicitly, because it is called implicitly by
5811 C<isl_access_info_compute_flow>.
5813 The result of the dependence analysis is collected in an
5814 C<isl_flow>. There may be elements of
5815 the sink access for which no preceding source access could be
5816 found or for which all preceding sources are I<may> accesses.
5817 The relations containing these elements can be obtained through
5818 calls to C<isl_flow_get_no_source>, the first with C<must> set
5819 and the second with C<must> unset.
5820 In the case of standard flow dependence analysis,
5821 with the sink a read and the sources I<must> writes,
5822 the first relation corresponds to the reads from uninitialized
5823 array elements and the second relation is empty.
5824 The actual flow dependences can be extracted using
5825 C<isl_flow_foreach>. This function will call the user-specified
5826 callback function C<fn> for each B<non-empty> dependence between
5827 a source and the sink. The callback function is called
5828 with four arguments, the actual flow dependence relation
5829 mapping source iterations to sink iterations, a boolean that
5830 indicates whether it is a I<must> or I<may> dependence, a token
5831 identifying the source and an additional C<void *> with value
5832 equal to the third argument of the C<isl_flow_foreach> call.
5833 A dependence is marked I<must> if it originates from a I<must>
5834 source and if it is not followed by any I<may> sources.
5836 After finishing with an C<isl_flow>, the user should call
5837 C<isl_flow_free> to free all associated memory.
5839 A higher-level interface to dependence analysis is provided
5840 by the following function.
5842 #include <isl/flow.h>
5844 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5845 __isl_take isl_union_map *must_source,
5846 __isl_take isl_union_map *may_source,
5847 __isl_take isl_union_map *schedule,
5848 __isl_give isl_union_map **must_dep,
5849 __isl_give isl_union_map **may_dep,
5850 __isl_give isl_union_map **must_no_source,
5851 __isl_give isl_union_map **may_no_source);
5853 The arrays are identified by the tuple names of the ranges
5854 of the accesses. The iteration domains by the tuple names
5855 of the domains of the accesses and of the schedule.
5856 The relative order of the iteration domains is given by the
5857 schedule. The relations returned through C<must_no_source>
5858 and C<may_no_source> are subsets of C<sink>.
5859 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5860 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5861 any of the other arguments is treated as an error.
5863 =head3 Interaction with Dependence Analysis
5865 During the dependence analysis, we frequently need to perform
5866 the following operation. Given a relation between sink iterations
5867 and potential source iterations from a particular source domain,
5868 what is the last potential source iteration corresponding to each
5869 sink iteration. It can sometimes be convenient to adjust
5870 the set of potential source iterations before or after each such operation.
5871 The prototypical example is fuzzy array dataflow analysis,
5872 where we need to analyze if, based on data-dependent constraints,
5873 the sink iteration can ever be executed without one or more of
5874 the corresponding potential source iterations being executed.
5875 If so, we can introduce extra parameters and select an unknown
5876 but fixed source iteration from the potential source iterations.
5877 To be able to perform such manipulations, C<isl> provides the following
5880 #include <isl/flow.h>
5882 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5883 __isl_keep isl_map *source_map,
5884 __isl_keep isl_set *sink, void *source_user,
5886 __isl_give isl_access_info *isl_access_info_set_restrict(
5887 __isl_take isl_access_info *acc,
5888 isl_access_restrict fn, void *user);
5890 The function C<isl_access_info_set_restrict> should be called
5891 before calling C<isl_access_info_compute_flow> and registers a callback function
5892 that will be called any time C<isl> is about to compute the last
5893 potential source. The first argument is the (reverse) proto-dependence,
5894 mapping sink iterations to potential source iterations.
5895 The second argument represents the sink iterations for which
5896 we want to compute the last source iteration.
5897 The third argument is the token corresponding to the source
5898 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5899 The callback is expected to return a restriction on either the input or
5900 the output of the operation computing the last potential source.
5901 If the input needs to be restricted then restrictions are needed
5902 for both the source and the sink iterations. The sink iterations
5903 and the potential source iterations will be intersected with these sets.
5904 If the output needs to be restricted then only a restriction on the source
5905 iterations is required.
5906 If any error occurs, the callback should return C<NULL>.
5907 An C<isl_restriction> object can be created, freed and inspected
5908 using the following functions.
5910 #include <isl/flow.h>
5912 __isl_give isl_restriction *isl_restriction_input(
5913 __isl_take isl_set *source_restr,
5914 __isl_take isl_set *sink_restr);
5915 __isl_give isl_restriction *isl_restriction_output(
5916 __isl_take isl_set *source_restr);
5917 __isl_give isl_restriction *isl_restriction_none(
5918 __isl_take isl_map *source_map);
5919 __isl_give isl_restriction *isl_restriction_empty(
5920 __isl_take isl_map *source_map);
5921 __isl_null isl_restriction *isl_restriction_free(
5922 __isl_take isl_restriction *restr);
5923 isl_ctx *isl_restriction_get_ctx(
5924 __isl_keep isl_restriction *restr);
5926 C<isl_restriction_none> and C<isl_restriction_empty> are special
5927 cases of C<isl_restriction_input>. C<isl_restriction_none>
5928 is essentially equivalent to
5930 isl_restriction_input(isl_set_universe(
5931 isl_space_range(isl_map_get_space(source_map))),
5933 isl_space_domain(isl_map_get_space(source_map))));
5935 whereas C<isl_restriction_empty> is essentially equivalent to
5937 isl_restriction_input(isl_set_empty(
5938 isl_space_range(isl_map_get_space(source_map))),
5940 isl_space_domain(isl_map_get_space(source_map))));
5944 B<The functionality described in this section is fairly new
5945 and may be subject to change.>
5947 #include <isl/schedule.h>
5948 __isl_give isl_schedule *
5949 isl_schedule_constraints_compute_schedule(
5950 __isl_take isl_schedule_constraints *sc);
5951 __isl_null isl_schedule *isl_schedule_free(
5952 __isl_take isl_schedule *sched);
5954 The function C<isl_schedule_constraints_compute_schedule> can be
5955 used to compute a schedule that satisfy the given schedule constraints.
5956 These schedule constraints include the iteration domain for which
5957 a schedule should be computed and dependences between pairs of
5958 iterations. In particular, these dependences include
5959 I<validity> dependences and I<proximity> dependences.
5960 By default, the algorithm used to construct the schedule is similar
5961 to that of C<Pluto>.
5962 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5964 The generated schedule respects all validity dependences.
5965 That is, all dependence distances over these dependences in the
5966 scheduled space are lexicographically positive.
5967 The default algorithm tries to ensure that the dependence distances
5968 over coincidence constraints are zero and to minimize the
5969 dependence distances over proximity dependences.
5970 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5971 for groups of domains where the dependence distances over validity
5972 dependences have only non-negative values.
5973 When using Feautrier's algorithm, the coincidence and proximity constraints
5974 are only taken into account during the extension to a
5975 full-dimensional schedule.
5977 An C<isl_schedule_constraints> object can be constructed
5978 and manipulated using the following functions.
5980 #include <isl/schedule.h>
5981 __isl_give isl_schedule_constraints *
5982 isl_schedule_constraints_copy(
5983 __isl_keep isl_schedule_constraints *sc);
5984 __isl_give isl_schedule_constraints *
5985 isl_schedule_constraints_on_domain(
5986 __isl_take isl_union_set *domain);
5987 isl_ctx *isl_schedule_constraints_get_ctx(
5988 __isl_keep isl_schedule_constraints *sc);
5989 __isl_give isl_schedule_constraints *
5990 isl_schedule_constraints_set_validity(
5991 __isl_take isl_schedule_constraints *sc,
5992 __isl_take isl_union_map *validity);
5993 __isl_give isl_schedule_constraints *
5994 isl_schedule_constraints_set_coincidence(
5995 __isl_take isl_schedule_constraints *sc,
5996 __isl_take isl_union_map *coincidence);
5997 __isl_give isl_schedule_constraints *
5998 isl_schedule_constraints_set_proximity(
5999 __isl_take isl_schedule_constraints *sc,
6000 __isl_take isl_union_map *proximity);
6001 __isl_give isl_schedule_constraints *
6002 isl_schedule_constraints_set_conditional_validity(
6003 __isl_take isl_schedule_constraints *sc,
6004 __isl_take isl_union_map *condition,
6005 __isl_take isl_union_map *validity);
6006 __isl_null isl_schedule_constraints *
6007 isl_schedule_constraints_free(
6008 __isl_take isl_schedule_constraints *sc);
6010 The initial C<isl_schedule_constraints> object created by
6011 C<isl_schedule_constraints_on_domain> does not impose any constraints.
6012 That is, it has an empty set of dependences.
6013 The function C<isl_schedule_constraints_set_validity> replaces the
6014 validity dependences, mapping domain elements I<i> to domain
6015 elements that should be scheduled after I<i>.
6016 The function C<isl_schedule_constraints_set_coincidence> replaces the
6017 coincidence dependences, mapping domain elements I<i> to domain
6018 elements that should be scheduled together with I<I>, if possible.
6019 The function C<isl_schedule_constraints_set_proximity> replaces the
6020 proximity dependences, mapping domain elements I<i> to domain
6021 elements that should be scheduled either before I<I>
6022 or as early as possible after I<i>.
6024 The function C<isl_schedule_constraints_set_conditional_validity>
6025 replaces the conditional validity constraints.
6026 A conditional validity constraint is only imposed when any of the corresponding
6027 conditions is satisfied, i.e., when any of them is non-zero.
6028 That is, the scheduler ensures that within each band if the dependence
6029 distances over the condition constraints are not all zero
6030 then all corresponding conditional validity constraints are respected.
6031 A conditional validity constraint corresponds to a condition
6032 if the two are adjacent, i.e., if the domain of one relation intersect
6033 the range of the other relation.
6034 The typical use case of conditional validity constraints is
6035 to allow order constraints between live ranges to be violated
6036 as long as the live ranges themselves are local to the band.
6037 To allow more fine-grained control over which conditions correspond
6038 to which conditional validity constraints, the domains and ranges
6039 of these relations may include I<tags>. That is, the domains and
6040 ranges of those relation may themselves be wrapped relations
6041 where the iteration domain appears in the domain of those wrapped relations
6042 and the range of the wrapped relations can be arbitrarily chosen
6043 by the user. Conditions and conditional validity constraints are only
6044 considere adjacent to each other if the entire wrapped relation matches.
6045 In particular, a relation with a tag will never be considered adjacent
6046 to a relation without a tag.
6048 The following function computes a schedule directly from
6049 an iteration domain and validity and proximity dependences
6050 and is implemented in terms of the functions described above.
6051 The use of C<isl_union_set_compute_schedule> is discouraged.
6053 #include <isl/schedule.h>
6054 __isl_give isl_schedule *isl_union_set_compute_schedule(
6055 __isl_take isl_union_set *domain,
6056 __isl_take isl_union_map *validity,
6057 __isl_take isl_union_map *proximity);
6059 A mapping from the domains to the scheduled space can be obtained
6060 from an C<isl_schedule> using the following function.
6062 __isl_give isl_union_map *isl_schedule_get_map(
6063 __isl_keep isl_schedule *sched);
6065 A representation of the schedule can be printed using
6067 __isl_give isl_printer *isl_printer_print_schedule(
6068 __isl_take isl_printer *p,
6069 __isl_keep isl_schedule *schedule);
6071 A representation of the schedule as a forest of bands can be obtained
6072 using the following function.
6074 __isl_give isl_band_list *isl_schedule_get_band_forest(
6075 __isl_keep isl_schedule *schedule);
6077 The individual bands can be visited in depth-first post-order
6078 using the following function.
6080 #include <isl/schedule.h>
6081 int isl_schedule_foreach_band(
6082 __isl_keep isl_schedule *sched,
6083 int (*fn)(__isl_keep isl_band *band, void *user),
6086 The list can be manipulated as explained in L<"Lists">.
6087 The bands inside the list can be copied and freed using the following
6090 #include <isl/band.h>
6091 __isl_give isl_band *isl_band_copy(
6092 __isl_keep isl_band *band);
6093 __isl_null isl_band *isl_band_free(
6094 __isl_take isl_band *band);
6096 Each band contains zero or more scheduling dimensions.
6097 These are referred to as the members of the band.
6098 The section of the schedule that corresponds to the band is
6099 referred to as the partial schedule of the band.
6100 For those nodes that participate in a band, the outer scheduling
6101 dimensions form the prefix schedule, while the inner scheduling
6102 dimensions form the suffix schedule.
6103 That is, if we take a cut of the band forest, then the union of
6104 the concatenations of the prefix, partial and suffix schedules of
6105 each band in the cut is equal to the entire schedule (modulo
6106 some possible padding at the end with zero scheduling dimensions).
6107 The properties of a band can be inspected using the following functions.
6109 #include <isl/band.h>
6110 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
6112 int isl_band_has_children(__isl_keep isl_band *band);
6113 __isl_give isl_band_list *isl_band_get_children(
6114 __isl_keep isl_band *band);
6116 __isl_give isl_union_map *isl_band_get_prefix_schedule(
6117 __isl_keep isl_band *band);
6118 __isl_give isl_union_map *isl_band_get_partial_schedule(
6119 __isl_keep isl_band *band);
6120 __isl_give isl_union_map *isl_band_get_suffix_schedule(
6121 __isl_keep isl_band *band);
6123 int isl_band_n_member(__isl_keep isl_band *band);
6124 int isl_band_member_is_coincident(
6125 __isl_keep isl_band *band, int pos);
6127 int isl_band_list_foreach_band(
6128 __isl_keep isl_band_list *list,
6129 int (*fn)(__isl_keep isl_band *band, void *user),
6132 Note that a scheduling dimension is considered to be ``coincident''
6133 if it satisfies the coincidence constraints within its band.
6134 That is, if the dependence distances of the coincidence
6135 constraints are all zero in that direction (for fixed
6136 iterations of outer bands).
6137 Like C<isl_schedule_foreach_band>,
6138 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
6139 in depth-first post-order.
6141 A band can be tiled using the following function.
6143 #include <isl/band.h>
6144 int isl_band_tile(__isl_keep isl_band *band,
6145 __isl_take isl_vec *sizes);
6147 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
6149 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
6150 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
6152 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
6154 The C<isl_band_tile> function tiles the band using the given tile sizes
6155 inside its schedule.
6156 A new child band is created to represent the point loops and it is
6157 inserted between the modified band and its children.
6158 The C<tile_scale_tile_loops> option specifies whether the tile
6159 loops iterators should be scaled by the tile sizes.
6160 If the C<tile_shift_point_loops> option is set, then the point loops
6161 are shifted to start at zero.
6163 A band can be split into two nested bands using the following function.
6165 int isl_band_split(__isl_keep isl_band *band, int pos);
6167 The resulting outer band contains the first C<pos> dimensions of C<band>
6168 while the inner band contains the remaining dimensions.
6170 A representation of the band can be printed using
6172 #include <isl/band.h>
6173 __isl_give isl_printer *isl_printer_print_band(
6174 __isl_take isl_printer *p,
6175 __isl_keep isl_band *band);
6179 #include <isl/schedule.h>
6180 int isl_options_set_schedule_max_coefficient(
6181 isl_ctx *ctx, int val);
6182 int isl_options_get_schedule_max_coefficient(
6184 int isl_options_set_schedule_max_constant_term(
6185 isl_ctx *ctx, int val);
6186 int isl_options_get_schedule_max_constant_term(
6188 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
6189 int isl_options_get_schedule_fuse(isl_ctx *ctx);
6190 int isl_options_set_schedule_maximize_band_depth(
6191 isl_ctx *ctx, int val);
6192 int isl_options_get_schedule_maximize_band_depth(
6194 int isl_options_set_schedule_outer_coincidence(
6195 isl_ctx *ctx, int val);
6196 int isl_options_get_schedule_outer_coincidence(
6198 int isl_options_set_schedule_split_scaled(
6199 isl_ctx *ctx, int val);
6200 int isl_options_get_schedule_split_scaled(
6202 int isl_options_set_schedule_algorithm(
6203 isl_ctx *ctx, int val);
6204 int isl_options_get_schedule_algorithm(
6206 int isl_options_set_schedule_separate_components(
6207 isl_ctx *ctx, int val);
6208 int isl_options_get_schedule_separate_components(
6213 =item * schedule_max_coefficient
6215 This option enforces that the coefficients for variable and parameter
6216 dimensions in the calculated schedule are not larger than the specified value.
6217 This option can significantly increase the speed of the scheduling calculation
6218 and may also prevent fusing of unrelated dimensions. A value of -1 means that
6219 this option does not introduce bounds on the variable or parameter
6222 =item * schedule_max_constant_term
6224 This option enforces that the constant coefficients in the calculated schedule
6225 are not larger than the maximal constant term. This option can significantly
6226 increase the speed of the scheduling calculation and may also prevent fusing of
6227 unrelated dimensions. A value of -1 means that this option does not introduce
6228 bounds on the constant coefficients.
6230 =item * schedule_fuse
6232 This option controls the level of fusion.
6233 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6234 resulting schedule will be distributed as much as possible.
6235 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6236 try to fuse loops in the resulting schedule.
6238 =item * schedule_maximize_band_depth
6240 If this option is set, we do not split bands at the point
6241 where we detect splitting is necessary. Instead, we
6242 backtrack and split bands as early as possible. This
6243 reduces the number of splits and maximizes the width of
6244 the bands. Wider bands give more possibilities for tiling.
6245 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6246 then bands will be split as early as possible, even if there is no need.
6247 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6249 =item * schedule_outer_coincidence
6251 If this option is set, then we try to construct schedules
6252 where the outermost scheduling dimension in each band
6253 satisfies the coincidence constraints.
6255 =item * schedule_split_scaled
6257 If this option is set, then we try to construct schedules in which the
6258 constant term is split off from the linear part if the linear parts of
6259 the scheduling rows for all nodes in the graphs have a common non-trivial
6261 The constant term is then placed in a separate band and the linear
6264 =item * schedule_algorithm
6266 Selects the scheduling algorithm to be used.
6267 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6268 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6270 =item * schedule_separate_components
6272 If at any point the dependence graph contains any (weakly connected) components,
6273 then these components are scheduled separately.
6274 If this option is not set, then some iterations of the domains
6275 in these components may be scheduled together.
6276 If this option is set, then the components are given consecutive
6281 =head2 AST Generation
6283 This section describes the C<isl> functionality for generating
6284 ASTs that visit all the elements
6285 in a domain in an order specified by a schedule.
6286 In particular, given a C<isl_union_map>, an AST is generated
6287 that visits all the elements in the domain of the C<isl_union_map>
6288 according to the lexicographic order of the corresponding image
6289 element(s). If the range of the C<isl_union_map> consists of
6290 elements in more than one space, then each of these spaces is handled
6291 separately in an arbitrary order.
6292 It should be noted that the image elements only specify the I<order>
6293 in which the corresponding domain elements should be visited.
6294 No direct relation between the image elements and the loop iterators
6295 in the generated AST should be assumed.
6297 Each AST is generated within a build. The initial build
6298 simply specifies the constraints on the parameters (if any)
6299 and can be created, inspected, copied and freed using the following functions.
6301 #include <isl/ast_build.h>
6302 __isl_give isl_ast_build *isl_ast_build_from_context(
6303 __isl_take isl_set *set);
6304 isl_ctx *isl_ast_build_get_ctx(
6305 __isl_keep isl_ast_build *build);
6306 __isl_give isl_ast_build *isl_ast_build_copy(
6307 __isl_keep isl_ast_build *build);
6308 __isl_null isl_ast_build *isl_ast_build_free(
6309 __isl_take isl_ast_build *build);
6311 The C<set> argument is usually a parameter set with zero or more parameters.
6312 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6313 and L</"Fine-grained Control over AST Generation">.
6314 Finally, the AST itself can be constructed using the following
6317 #include <isl/ast_build.h>
6318 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6319 __isl_keep isl_ast_build *build,
6320 __isl_take isl_union_map *schedule);
6322 =head3 Inspecting the AST
6324 The basic properties of an AST node can be obtained as follows.
6326 #include <isl/ast.h>
6327 isl_ctx *isl_ast_node_get_ctx(
6328 __isl_keep isl_ast_node *node);
6329 enum isl_ast_node_type isl_ast_node_get_type(
6330 __isl_keep isl_ast_node *node);
6332 The type of an AST node is one of
6333 C<isl_ast_node_for>,
6335 C<isl_ast_node_block> or
6336 C<isl_ast_node_user>.
6337 An C<isl_ast_node_for> represents a for node.
6338 An C<isl_ast_node_if> represents an if node.
6339 An C<isl_ast_node_block> represents a compound node.
6340 An C<isl_ast_node_user> represents an expression statement.
6341 An expression statement typically corresponds to a domain element, i.e.,
6342 one of the elements that is visited by the AST.
6344 Each type of node has its own additional properties.
6346 #include <isl/ast.h>
6347 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6348 __isl_keep isl_ast_node *node);
6349 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6350 __isl_keep isl_ast_node *node);
6351 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6352 __isl_keep isl_ast_node *node);
6353 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6354 __isl_keep isl_ast_node *node);
6355 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6356 __isl_keep isl_ast_node *node);
6357 int isl_ast_node_for_is_degenerate(
6358 __isl_keep isl_ast_node *node);
6360 An C<isl_ast_for> is considered degenerate if it is known to execute
6363 #include <isl/ast.h>
6364 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6365 __isl_keep isl_ast_node *node);
6366 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6367 __isl_keep isl_ast_node *node);
6368 int isl_ast_node_if_has_else(
6369 __isl_keep isl_ast_node *node);
6370 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6371 __isl_keep isl_ast_node *node);
6373 __isl_give isl_ast_node_list *
6374 isl_ast_node_block_get_children(
6375 __isl_keep isl_ast_node *node);
6377 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6378 __isl_keep isl_ast_node *node);
6380 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6381 the following functions.
6383 #include <isl/ast.h>
6384 isl_ctx *isl_ast_expr_get_ctx(
6385 __isl_keep isl_ast_expr *expr);
6386 enum isl_ast_expr_type isl_ast_expr_get_type(
6387 __isl_keep isl_ast_expr *expr);
6389 The type of an AST expression is one of
6391 C<isl_ast_expr_id> or
6392 C<isl_ast_expr_int>.
6393 An C<isl_ast_expr_op> represents the result of an operation.
6394 An C<isl_ast_expr_id> represents an identifier.
6395 An C<isl_ast_expr_int> represents an integer value.
6397 Each type of expression has its own additional properties.
6399 #include <isl/ast.h>
6400 enum isl_ast_op_type isl_ast_expr_get_op_type(
6401 __isl_keep isl_ast_expr *expr);
6402 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6403 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6404 __isl_keep isl_ast_expr *expr, int pos);
6405 int isl_ast_node_foreach_ast_op_type(
6406 __isl_keep isl_ast_node *node,
6407 int (*fn)(enum isl_ast_op_type type, void *user),
6410 C<isl_ast_expr_get_op_type> returns the type of the operation
6411 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6412 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6414 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6415 C<isl_ast_op_type> that appears in C<node>.
6416 The operation type is one of the following.
6420 =item C<isl_ast_op_and>
6422 Logical I<and> of two arguments.
6423 Both arguments can be evaluated.
6425 =item C<isl_ast_op_and_then>
6427 Logical I<and> of two arguments.
6428 The second argument can only be evaluated if the first evaluates to true.
6430 =item C<isl_ast_op_or>
6432 Logical I<or> of two arguments.
6433 Both arguments can be evaluated.
6435 =item C<isl_ast_op_or_else>
6437 Logical I<or> of two arguments.
6438 The second argument can only be evaluated if the first evaluates to false.
6440 =item C<isl_ast_op_max>
6442 Maximum of two or more arguments.
6444 =item C<isl_ast_op_min>
6446 Minimum of two or more arguments.
6448 =item C<isl_ast_op_minus>
6452 =item C<isl_ast_op_add>
6454 Sum of two arguments.
6456 =item C<isl_ast_op_sub>
6458 Difference of two arguments.
6460 =item C<isl_ast_op_mul>
6462 Product of two arguments.
6464 =item C<isl_ast_op_div>
6466 Exact division. That is, the result is known to be an integer.
6468 =item C<isl_ast_op_fdiv_q>
6470 Result of integer division, rounded towards negative
6473 =item C<isl_ast_op_pdiv_q>
6475 Result of integer division, where dividend is known to be non-negative.
6477 =item C<isl_ast_op_pdiv_r>
6479 Remainder of integer division, where dividend is known to be non-negative.
6481 =item C<isl_ast_op_cond>
6483 Conditional operator defined on three arguments.
6484 If the first argument evaluates to true, then the result
6485 is equal to the second argument. Otherwise, the result
6486 is equal to the third argument.
6487 The second and third argument may only be evaluated if
6488 the first argument evaluates to true and false, respectively.
6489 Corresponds to C<a ? b : c> in C.
6491 =item C<isl_ast_op_select>
6493 Conditional operator defined on three arguments.
6494 If the first argument evaluates to true, then the result
6495 is equal to the second argument. Otherwise, the result
6496 is equal to the third argument.
6497 The second and third argument may be evaluated independently
6498 of the value of the first argument.
6499 Corresponds to C<a * b + (1 - a) * c> in C.
6501 =item C<isl_ast_op_eq>
6505 =item C<isl_ast_op_le>
6507 Less than or equal relation.
6509 =item C<isl_ast_op_lt>
6513 =item C<isl_ast_op_ge>
6515 Greater than or equal relation.
6517 =item C<isl_ast_op_gt>
6519 Greater than relation.
6521 =item C<isl_ast_op_call>
6524 The number of arguments of the C<isl_ast_expr> is one more than
6525 the number of arguments in the function call, the first argument
6526 representing the function being called.
6528 =item C<isl_ast_op_access>
6531 The number of arguments of the C<isl_ast_expr> is one more than
6532 the number of index expressions in the array access, the first argument
6533 representing the array being accessed.
6535 =item C<isl_ast_op_member>
6538 This operation has two arguments, a structure and the name of
6539 the member of the structure being accessed.
6543 #include <isl/ast.h>
6544 __isl_give isl_id *isl_ast_expr_get_id(
6545 __isl_keep isl_ast_expr *expr);
6547 Return the identifier represented by the AST expression.
6549 #include <isl/ast.h>
6550 __isl_give isl_val *isl_ast_expr_get_val(
6551 __isl_keep isl_ast_expr *expr);
6553 Return the integer represented by the AST expression.
6555 =head3 Properties of ASTs
6557 #include <isl/ast.h>
6558 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6559 __isl_keep isl_ast_expr *expr2);
6561 Check if two C<isl_ast_expr>s are equal to each other.
6563 =head3 Manipulating and printing the AST
6565 AST nodes can be copied and freed using the following functions.
6567 #include <isl/ast.h>
6568 __isl_give isl_ast_node *isl_ast_node_copy(
6569 __isl_keep isl_ast_node *node);
6570 __isl_null isl_ast_node *isl_ast_node_free(
6571 __isl_take isl_ast_node *node);
6573 AST expressions can be copied and freed using the following functions.
6575 #include <isl/ast.h>
6576 __isl_give isl_ast_expr *isl_ast_expr_copy(
6577 __isl_keep isl_ast_expr *expr);
6578 __isl_null isl_ast_expr *isl_ast_expr_free(
6579 __isl_take isl_ast_expr *expr);
6581 New AST expressions can be created either directly or within
6582 the context of an C<isl_ast_build>.
6584 #include <isl/ast.h>
6585 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6586 __isl_take isl_val *v);
6587 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6588 __isl_take isl_id *id);
6589 __isl_give isl_ast_expr *isl_ast_expr_neg(
6590 __isl_take isl_ast_expr *expr);
6591 __isl_give isl_ast_expr *isl_ast_expr_add(
6592 __isl_take isl_ast_expr *expr1,
6593 __isl_take isl_ast_expr *expr2);
6594 __isl_give isl_ast_expr *isl_ast_expr_sub(
6595 __isl_take isl_ast_expr *expr1,
6596 __isl_take isl_ast_expr *expr2);
6597 __isl_give isl_ast_expr *isl_ast_expr_mul(
6598 __isl_take isl_ast_expr *expr1,
6599 __isl_take isl_ast_expr *expr2);
6600 __isl_give isl_ast_expr *isl_ast_expr_div(
6601 __isl_take isl_ast_expr *expr1,
6602 __isl_take isl_ast_expr *expr2);
6603 __isl_give isl_ast_expr *isl_ast_expr_and(
6604 __isl_take isl_ast_expr *expr1,
6605 __isl_take isl_ast_expr *expr2)
6606 __isl_give isl_ast_expr *isl_ast_expr_or(
6607 __isl_take isl_ast_expr *expr1,
6608 __isl_take isl_ast_expr *expr2)
6609 __isl_give isl_ast_expr *isl_ast_expr_access(
6610 __isl_take isl_ast_expr *array,
6611 __isl_take isl_ast_expr_list *indices);
6613 #include <isl/ast_build.h>
6614 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6615 __isl_keep isl_ast_build *build,
6616 __isl_take isl_pw_aff *pa);
6617 __isl_give isl_ast_expr *
6618 isl_ast_build_access_from_pw_multi_aff(
6619 __isl_keep isl_ast_build *build,
6620 __isl_take isl_pw_multi_aff *pma);
6621 __isl_give isl_ast_expr *
6622 isl_ast_build_access_from_multi_pw_aff(
6623 __isl_keep isl_ast_build *build,
6624 __isl_take isl_multi_pw_aff *mpa);
6625 __isl_give isl_ast_expr *
6626 isl_ast_build_call_from_pw_multi_aff(
6627 __isl_keep isl_ast_build *build,
6628 __isl_take isl_pw_multi_aff *pma);
6629 __isl_give isl_ast_expr *
6630 isl_ast_build_call_from_multi_pw_aff(
6631 __isl_keep isl_ast_build *build,
6632 __isl_take isl_multi_pw_aff *mpa);
6634 The domains of C<pa>, C<mpa> and C<pma> should correspond
6635 to the schedule space of C<build>.
6636 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6637 the function being called.
6638 If the accessed space is a nested relation, then it is taken
6639 to represent an access of the member specified by the range
6640 of this nested relation of the structure specified by the domain
6641 of the nested relation.
6643 The following functions can be used to modify an C<isl_ast_expr>.
6645 #include <isl/ast.h>
6646 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6647 __isl_take isl_ast_expr *expr, int pos,
6648 __isl_take isl_ast_expr *arg);
6650 Replace the argument of C<expr> at position C<pos> by C<arg>.
6652 #include <isl/ast.h>
6653 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6654 __isl_take isl_ast_expr *expr,
6655 __isl_take isl_id_to_ast_expr *id2expr);
6657 The function C<isl_ast_expr_substitute_ids> replaces the
6658 subexpressions of C<expr> of type C<isl_ast_expr_id>
6659 by the corresponding expression in C<id2expr>, if there is any.
6662 User specified data can be attached to an C<isl_ast_node> and obtained
6663 from the same C<isl_ast_node> using the following functions.
6665 #include <isl/ast.h>
6666 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6667 __isl_take isl_ast_node *node,
6668 __isl_take isl_id *annotation);
6669 __isl_give isl_id *isl_ast_node_get_annotation(
6670 __isl_keep isl_ast_node *node);
6672 Basic printing can be performed using the following functions.
6674 #include <isl/ast.h>
6675 __isl_give isl_printer *isl_printer_print_ast_expr(
6676 __isl_take isl_printer *p,
6677 __isl_keep isl_ast_expr *expr);
6678 __isl_give isl_printer *isl_printer_print_ast_node(
6679 __isl_take isl_printer *p,
6680 __isl_keep isl_ast_node *node);
6682 More advanced printing can be performed using the following functions.
6684 #include <isl/ast.h>
6685 __isl_give isl_printer *isl_ast_op_type_print_macro(
6686 enum isl_ast_op_type type,
6687 __isl_take isl_printer *p);
6688 __isl_give isl_printer *isl_ast_node_print_macros(
6689 __isl_keep isl_ast_node *node,
6690 __isl_take isl_printer *p);
6691 __isl_give isl_printer *isl_ast_node_print(
6692 __isl_keep isl_ast_node *node,
6693 __isl_take isl_printer *p,
6694 __isl_take isl_ast_print_options *options);
6695 __isl_give isl_printer *isl_ast_node_for_print(
6696 __isl_keep isl_ast_node *node,
6697 __isl_take isl_printer *p,
6698 __isl_take isl_ast_print_options *options);
6699 __isl_give isl_printer *isl_ast_node_if_print(
6700 __isl_keep isl_ast_node *node,
6701 __isl_take isl_printer *p,
6702 __isl_take isl_ast_print_options *options);
6704 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6705 C<isl> may print out an AST that makes use of macros such
6706 as C<floord>, C<min> and C<max>.
6707 C<isl_ast_op_type_print_macro> prints out the macro
6708 corresponding to a specific C<isl_ast_op_type>.
6709 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6710 for expressions where these macros would be used and prints
6711 out the required macro definitions.
6712 Essentially, C<isl_ast_node_print_macros> calls
6713 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6714 as function argument.
6715 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6716 C<isl_ast_node_if_print> print an C<isl_ast_node>
6717 in C<ISL_FORMAT_C>, but allow for some extra control
6718 through an C<isl_ast_print_options> object.
6719 This object can be created using the following functions.
6721 #include <isl/ast.h>
6722 __isl_give isl_ast_print_options *
6723 isl_ast_print_options_alloc(isl_ctx *ctx);
6724 __isl_give isl_ast_print_options *
6725 isl_ast_print_options_copy(
6726 __isl_keep isl_ast_print_options *options);
6727 __isl_null isl_ast_print_options *
6728 isl_ast_print_options_free(
6729 __isl_take isl_ast_print_options *options);
6731 __isl_give isl_ast_print_options *
6732 isl_ast_print_options_set_print_user(
6733 __isl_take isl_ast_print_options *options,
6734 __isl_give isl_printer *(*print_user)(
6735 __isl_take isl_printer *p,
6736 __isl_take isl_ast_print_options *options,
6737 __isl_keep isl_ast_node *node, void *user),
6739 __isl_give isl_ast_print_options *
6740 isl_ast_print_options_set_print_for(
6741 __isl_take isl_ast_print_options *options,
6742 __isl_give isl_printer *(*print_for)(
6743 __isl_take isl_printer *p,
6744 __isl_take isl_ast_print_options *options,
6745 __isl_keep isl_ast_node *node, void *user),
6748 The callback set by C<isl_ast_print_options_set_print_user>
6749 is called whenever a node of type C<isl_ast_node_user> needs to
6751 The callback set by C<isl_ast_print_options_set_print_for>
6752 is called whenever a node of type C<isl_ast_node_for> needs to
6754 Note that C<isl_ast_node_for_print> will I<not> call the
6755 callback set by C<isl_ast_print_options_set_print_for> on the node
6756 on which C<isl_ast_node_for_print> is called, but only on nested
6757 nodes of type C<isl_ast_node_for>. It is therefore safe to
6758 call C<isl_ast_node_for_print> from within the callback set by
6759 C<isl_ast_print_options_set_print_for>.
6761 The following option determines the type to be used for iterators
6762 while printing the AST.
6764 int isl_options_set_ast_iterator_type(
6765 isl_ctx *ctx, const char *val);
6766 const char *isl_options_get_ast_iterator_type(
6771 #include <isl/ast_build.h>
6772 int isl_options_set_ast_build_atomic_upper_bound(
6773 isl_ctx *ctx, int val);
6774 int isl_options_get_ast_build_atomic_upper_bound(
6776 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6778 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6779 int isl_options_set_ast_build_exploit_nested_bounds(
6780 isl_ctx *ctx, int val);
6781 int isl_options_get_ast_build_exploit_nested_bounds(
6783 int isl_options_set_ast_build_group_coscheduled(
6784 isl_ctx *ctx, int val);
6785 int isl_options_get_ast_build_group_coscheduled(
6787 int isl_options_set_ast_build_scale_strides(
6788 isl_ctx *ctx, int val);
6789 int isl_options_get_ast_build_scale_strides(
6791 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6793 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6794 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6796 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6800 =item * ast_build_atomic_upper_bound
6802 Generate loop upper bounds that consist of the current loop iterator,
6803 an operator and an expression not involving the iterator.
6804 If this option is not set, then the current loop iterator may appear
6805 several times in the upper bound.
6806 For example, when this option is turned off, AST generation
6809 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6813 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6816 When the option is turned on, the following AST is generated
6818 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6821 =item * ast_build_prefer_pdiv
6823 If this option is turned off, then the AST generation will
6824 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6825 operators, but no C<isl_ast_op_pdiv_q> or
6826 C<isl_ast_op_pdiv_r> operators.
6827 If this options is turned on, then C<isl> will try to convert
6828 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6829 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6831 =item * ast_build_exploit_nested_bounds
6833 Simplify conditions based on bounds of nested for loops.
6834 In particular, remove conditions that are implied by the fact
6835 that one or more nested loops have at least one iteration,
6836 meaning that the upper bound is at least as large as the lower bound.
6837 For example, when this option is turned off, AST generation
6840 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6846 for (int c0 = 0; c0 <= N; c0 += 1)
6847 for (int c1 = 0; c1 <= M; c1 += 1)
6850 When the option is turned on, the following AST is generated
6852 for (int c0 = 0; c0 <= N; c0 += 1)
6853 for (int c1 = 0; c1 <= M; c1 += 1)
6856 =item * ast_build_group_coscheduled
6858 If two domain elements are assigned the same schedule point, then
6859 they may be executed in any order and they may even appear in different
6860 loops. If this options is set, then the AST generator will make
6861 sure that coscheduled domain elements do not appear in separate parts
6862 of the AST. This is useful in case of nested AST generation
6863 if the outer AST generation is given only part of a schedule
6864 and the inner AST generation should handle the domains that are
6865 coscheduled by this initial part of the schedule together.
6866 For example if an AST is generated for a schedule
6868 { A[i] -> [0]; B[i] -> [0] }
6870 then the C<isl_ast_build_set_create_leaf> callback described
6871 below may get called twice, once for each domain.
6872 Setting this option ensures that the callback is only called once
6873 on both domains together.
6875 =item * ast_build_separation_bounds
6877 This option specifies which bounds to use during separation.
6878 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6879 then all (possibly implicit) bounds on the current dimension will
6880 be used during separation.
6881 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6882 then only those bounds that are explicitly available will
6883 be used during separation.
6885 =item * ast_build_scale_strides
6887 This option specifies whether the AST generator is allowed
6888 to scale down iterators of strided loops.
6890 =item * ast_build_allow_else
6892 This option specifies whether the AST generator is allowed
6893 to construct if statements with else branches.
6895 =item * ast_build_allow_or
6897 This option specifies whether the AST generator is allowed
6898 to construct if conditions with disjunctions.
6902 =head3 Fine-grained Control over AST Generation
6904 Besides specifying the constraints on the parameters,
6905 an C<isl_ast_build> object can be used to control
6906 various aspects of the AST generation process.
6907 The most prominent way of control is through ``options'',
6908 which can be set using the following function.
6910 #include <isl/ast_build.h>
6911 __isl_give isl_ast_build *
6912 isl_ast_build_set_options(
6913 __isl_take isl_ast_build *control,
6914 __isl_take isl_union_map *options);
6916 The options are encoded in an <isl_union_map>.
6917 The domain of this union relation refers to the schedule domain,
6918 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6919 In the case of nested AST generation (see L</"Nested AST Generation">),
6920 the domain of C<options> should refer to the extra piece of the schedule.
6921 That is, it should be equal to the range of the wrapped relation in the
6922 range of the schedule.
6923 The range of the options can consist of elements in one or more spaces,
6924 the names of which determine the effect of the option.
6925 The values of the range typically also refer to the schedule dimension
6926 to which the option applies. In case of nested AST generation
6927 (see L</"Nested AST Generation">), these values refer to the position
6928 of the schedule dimension within the innermost AST generation.
6929 The constraints on the domain elements of
6930 the option should only refer to this dimension and earlier dimensions.
6931 We consider the following spaces.
6935 =item C<separation_class>
6937 This space is a wrapped relation between two one dimensional spaces.
6938 The input space represents the schedule dimension to which the option
6939 applies and the output space represents the separation class.
6940 While constructing a loop corresponding to the specified schedule
6941 dimension(s), the AST generator will try to generate separate loops
6942 for domain elements that are assigned different classes.
6943 If only some of the elements are assigned a class, then those elements
6944 that are not assigned any class will be treated as belonging to a class
6945 that is separate from the explicitly assigned classes.
6946 The typical use case for this option is to separate full tiles from
6948 The other options, described below, are applied after the separation
6951 As an example, consider the separation into full and partial tiles
6952 of a tiling of a triangular domain.
6953 Take, for example, the domain
6955 { A[i,j] : 0 <= i,j and i + j <= 100 }
6957 and a tiling into tiles of 10 by 10. The input to the AST generator
6958 is then the schedule
6960 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6963 Without any options, the following AST is generated
6965 for (int c0 = 0; c0 <= 10; c0 += 1)
6966 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6967 for (int c2 = 10 * c0;
6968 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6970 for (int c3 = 10 * c1;
6971 c3 <= min(10 * c1 + 9, -c2 + 100);
6975 Separation into full and partial tiles can be obtained by assigning
6976 a class, say C<0>, to the full tiles. The full tiles are represented by those
6977 values of the first and second schedule dimensions for which there are
6978 values of the third and fourth dimensions to cover an entire tile.
6979 That is, we need to specify the following option
6981 { [a,b,c,d] -> separation_class[[0]->[0]] :
6982 exists b': 0 <= 10a,10b' and
6983 10a+9+10b'+9 <= 100;
6984 [a,b,c,d] -> separation_class[[1]->[0]] :
6985 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6989 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6990 a >= 0 and b >= 0 and b <= 8 - a;
6991 [a, b, c, d] -> separation_class[[0] -> [0]] :
6994 With this option, the generated AST is as follows
6997 for (int c0 = 0; c0 <= 8; c0 += 1) {
6998 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6999 for (int c2 = 10 * c0;
7000 c2 <= 10 * c0 + 9; c2 += 1)
7001 for (int c3 = 10 * c1;
7002 c3 <= 10 * c1 + 9; c3 += 1)
7004 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
7005 for (int c2 = 10 * c0;
7006 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7008 for (int c3 = 10 * c1;
7009 c3 <= min(-c2 + 100, 10 * c1 + 9);
7013 for (int c0 = 9; c0 <= 10; c0 += 1)
7014 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
7015 for (int c2 = 10 * c0;
7016 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7018 for (int c3 = 10 * c1;
7019 c3 <= min(10 * c1 + 9, -c2 + 100);
7026 This is a single-dimensional space representing the schedule dimension(s)
7027 to which ``separation'' should be applied. Separation tries to split
7028 a loop into several pieces if this can avoid the generation of guards
7030 See also the C<atomic> option.
7034 This is a single-dimensional space representing the schedule dimension(s)
7035 for which the domains should be considered ``atomic''. That is, the
7036 AST generator will make sure that any given domain space will only appear
7037 in a single loop at the specified level.
7039 Consider the following schedule
7041 { a[i] -> [i] : 0 <= i < 10;
7042 b[i] -> [i+1] : 0 <= i < 10 }
7044 If the following option is specified
7046 { [i] -> separate[x] }
7048 then the following AST will be generated
7052 for (int c0 = 1; c0 <= 9; c0 += 1) {
7059 If, on the other hand, the following option is specified
7061 { [i] -> atomic[x] }
7063 then the following AST will be generated
7065 for (int c0 = 0; c0 <= 10; c0 += 1) {
7072 If neither C<atomic> nor C<separate> is specified, then the AST generator
7073 may produce either of these two results or some intermediate form.
7077 This is a single-dimensional space representing the schedule dimension(s)
7078 that should be I<completely> unrolled.
7079 To obtain a partial unrolling, the user should apply an additional
7080 strip-mining to the schedule and fully unroll the inner loop.
7084 Additional control is available through the following functions.
7086 #include <isl/ast_build.h>
7087 __isl_give isl_ast_build *
7088 isl_ast_build_set_iterators(
7089 __isl_take isl_ast_build *control,
7090 __isl_take isl_id_list *iterators);
7092 The function C<isl_ast_build_set_iterators> allows the user to
7093 specify a list of iterator C<isl_id>s to be used as iterators.
7094 If the input schedule is injective, then
7095 the number of elements in this list should be as large as the dimension
7096 of the schedule space, but no direct correspondence should be assumed
7097 between dimensions and elements.
7098 If the input schedule is not injective, then an additional number
7099 of C<isl_id>s equal to the largest dimension of the input domains
7101 If the number of provided C<isl_id>s is insufficient, then additional
7102 names are automatically generated.
7104 #include <isl/ast_build.h>
7105 __isl_give isl_ast_build *
7106 isl_ast_build_set_create_leaf(
7107 __isl_take isl_ast_build *control,
7108 __isl_give isl_ast_node *(*fn)(
7109 __isl_take isl_ast_build *build,
7110 void *user), void *user);
7113 C<isl_ast_build_set_create_leaf> function allows for the
7114 specification of a callback that should be called whenever the AST
7115 generator arrives at an element of the schedule domain.
7116 The callback should return an AST node that should be inserted
7117 at the corresponding position of the AST. The default action (when
7118 the callback is not set) is to continue generating parts of the AST to scan
7119 all the domain elements associated to the schedule domain element
7120 and to insert user nodes, ``calling'' the domain element, for each of them.
7121 The C<build> argument contains the current state of the C<isl_ast_build>.
7122 To ease nested AST generation (see L</"Nested AST Generation">),
7123 all control information that is
7124 specific to the current AST generation such as the options and
7125 the callbacks has been removed from this C<isl_ast_build>.
7126 The callback would typically return the result of a nested
7128 user defined node created using the following function.
7130 #include <isl/ast.h>
7131 __isl_give isl_ast_node *isl_ast_node_alloc_user(
7132 __isl_take isl_ast_expr *expr);
7134 #include <isl/ast_build.h>
7135 __isl_give isl_ast_build *
7136 isl_ast_build_set_at_each_domain(
7137 __isl_take isl_ast_build *build,
7138 __isl_give isl_ast_node *(*fn)(
7139 __isl_take isl_ast_node *node,
7140 __isl_keep isl_ast_build *build,
7141 void *user), void *user);
7142 __isl_give isl_ast_build *
7143 isl_ast_build_set_before_each_for(
7144 __isl_take isl_ast_build *build,
7145 __isl_give isl_id *(*fn)(
7146 __isl_keep isl_ast_build *build,
7147 void *user), void *user);
7148 __isl_give isl_ast_build *
7149 isl_ast_build_set_after_each_for(
7150 __isl_take isl_ast_build *build,
7151 __isl_give isl_ast_node *(*fn)(
7152 __isl_take isl_ast_node *node,
7153 __isl_keep isl_ast_build *build,
7154 void *user), void *user);
7156 The callback set by C<isl_ast_build_set_at_each_domain> will
7157 be called for each domain AST node.
7158 The callbacks set by C<isl_ast_build_set_before_each_for>
7159 and C<isl_ast_build_set_after_each_for> will be called
7160 for each for AST node. The first will be called in depth-first
7161 pre-order, while the second will be called in depth-first post-order.
7162 Since C<isl_ast_build_set_before_each_for> is called before the for
7163 node is actually constructed, it is only passed an C<isl_ast_build>.
7164 The returned C<isl_id> will be added as an annotation (using
7165 C<isl_ast_node_set_annotation>) to the constructed for node.
7166 In particular, if the user has also specified an C<after_each_for>
7167 callback, then the annotation can be retrieved from the node passed to
7168 that callback using C<isl_ast_node_get_annotation>.
7169 All callbacks should C<NULL> on failure.
7170 The given C<isl_ast_build> can be used to create new
7171 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
7172 or C<isl_ast_build_call_from_pw_multi_aff>.
7174 =head3 Nested AST Generation
7176 C<isl> allows the user to create an AST within the context
7177 of another AST. These nested ASTs are created using the
7178 same C<isl_ast_build_ast_from_schedule> function that is used to create the
7179 outer AST. The C<build> argument should be an C<isl_ast_build>
7180 passed to a callback set by
7181 C<isl_ast_build_set_create_leaf>.
7182 The space of the range of the C<schedule> argument should refer
7183 to this build. In particular, the space should be a wrapped
7184 relation and the domain of this wrapped relation should be the
7185 same as that of the range of the schedule returned by
7186 C<isl_ast_build_get_schedule> below.
7187 In practice, the new schedule is typically
7188 created by calling C<isl_union_map_range_product> on the old schedule
7189 and some extra piece of the schedule.
7190 The space of the schedule domain is also available from
7191 the C<isl_ast_build>.
7193 #include <isl/ast_build.h>
7194 __isl_give isl_union_map *isl_ast_build_get_schedule(
7195 __isl_keep isl_ast_build *build);
7196 __isl_give isl_space *isl_ast_build_get_schedule_space(
7197 __isl_keep isl_ast_build *build);
7198 __isl_give isl_ast_build *isl_ast_build_restrict(
7199 __isl_take isl_ast_build *build,
7200 __isl_take isl_set *set);
7202 The C<isl_ast_build_get_schedule> function returns a (partial)
7203 schedule for the domains elements for which part of the AST still needs to
7204 be generated in the current build.
7205 In particular, the domain elements are mapped to those iterations of the loops
7206 enclosing the current point of the AST generation inside which
7207 the domain elements are executed.
7208 No direct correspondence between
7209 the input schedule and this schedule should be assumed.
7210 The space obtained from C<isl_ast_build_get_schedule_space> can be used
7211 to create a set for C<isl_ast_build_restrict> to intersect
7212 with the current build. In particular, the set passed to
7213 C<isl_ast_build_restrict> can have additional parameters.
7214 The ids of the set dimensions in the space returned by
7215 C<isl_ast_build_get_schedule_space> correspond to the
7216 iterators of the already generated loops.
7217 The user should not rely on the ids of the output dimensions
7218 of the relations in the union relation returned by
7219 C<isl_ast_build_get_schedule> having any particular value.
7223 Although C<isl> is mainly meant to be used as a library,
7224 it also contains some basic applications that use some
7225 of the functionality of C<isl>.
7226 The input may be specified in either the L<isl format>
7227 or the L<PolyLib format>.
7229 =head2 C<isl_polyhedron_sample>
7231 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7232 an integer element of the polyhedron, if there is any.
7233 The first column in the output is the denominator and is always
7234 equal to 1. If the polyhedron contains no integer points,
7235 then a vector of length zero is printed.
7239 C<isl_pip> takes the same input as the C<example> program
7240 from the C<piplib> distribution, i.e., a set of constraints
7241 on the parameters, a line containing only -1 and finally a set
7242 of constraints on a parametric polyhedron.
7243 The coefficients of the parameters appear in the last columns
7244 (but before the final constant column).
7245 The output is the lexicographic minimum of the parametric polyhedron.
7246 As C<isl> currently does not have its own output format, the output
7247 is just a dump of the internal state.
7249 =head2 C<isl_polyhedron_minimize>
7251 C<isl_polyhedron_minimize> computes the minimum of some linear
7252 or affine objective function over the integer points in a polyhedron.
7253 If an affine objective function
7254 is given, then the constant should appear in the last column.
7256 =head2 C<isl_polytope_scan>
7258 Given a polytope, C<isl_polytope_scan> prints
7259 all integer points in the polytope.
7261 =head2 C<isl_codegen>
7263 Given a schedule, a context set and an options relation,
7264 C<isl_codegen> prints out an AST that scans the domain elements
7265 of the schedule in the order of their image(s) taking into account
7266 the constraints in the context set.