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);
560 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
562 The following binary operations are available on C<isl_val>s.
565 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
566 __isl_take isl_val *v2);
567 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
568 __isl_take isl_val *v2);
569 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
570 __isl_take isl_val *v2);
571 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
573 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
574 __isl_take isl_val *v2);
575 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
577 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
578 __isl_take isl_val *v2);
579 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
581 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
582 __isl_take isl_val *v2);
584 On integer values, we additionally have the following operations.
587 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
588 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
589 __isl_take isl_val *v2);
590 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
591 __isl_take isl_val *v2);
592 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
593 __isl_take isl_val *v2, __isl_give isl_val **x,
594 __isl_give isl_val **y);
596 The function C<isl_val_gcdext> returns the greatest common divisor g
597 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
598 that C<*x> * C<v1> + C<*y> * C<v2> = g.
600 A value can be read from input using
603 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
606 A value can be printed using
609 __isl_give isl_printer *isl_printer_print_val(
610 __isl_take isl_printer *p, __isl_keep isl_val *v);
612 =head3 GMP specific functions
614 These functions are only available if C<isl> has been compiled with C<GMP>
617 Specific integer and rational values can be created from C<GMP> values using
618 the following functions.
620 #include <isl/val_gmp.h>
621 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
623 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
624 const mpz_t n, const mpz_t d);
626 The numerator and denominator of a rational value can be extracted as
627 C<GMP> values using the following functions.
629 #include <isl/val_gmp.h>
630 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
631 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
633 =head2 Sets and Relations
635 C<isl> uses six types of objects for representing sets and relations,
636 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
637 C<isl_union_set> and C<isl_union_map>.
638 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
639 can be described as a conjunction of affine constraints, while
640 C<isl_set> and C<isl_map> represent unions of
641 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
642 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
643 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
644 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
645 where spaces are considered different if they have a different number
646 of dimensions and/or different names (see L<"Spaces">).
647 The difference between sets and relations (maps) is that sets have
648 one set of variables, while relations have two sets of variables,
649 input variables and output variables.
651 =head2 Error Handling
653 C<isl> supports different ways to react in case a runtime error is triggered.
654 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
655 with two maps that have incompatible spaces. There are three possible ways
656 to react on error: to warn, to continue or to abort.
658 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
659 the last error in the corresponding C<isl_ctx> and the function in which the
660 error was triggered returns C<NULL>. An error does not corrupt internal state,
661 such that isl can continue to be used. C<isl> also provides functions to
662 read the last error and to reset the memory that stores the last error. The
663 last error is only stored for information purposes. Its presence does not
664 change the behavior of C<isl>. Hence, resetting an error is not required to
665 continue to use isl, but only to observe new errors.
668 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
669 void isl_ctx_reset_error(isl_ctx *ctx);
671 Another option is to continue on error. This is similar to warn on error mode,
672 except that C<isl> does not print any warning. This allows a program to
673 implement its own error reporting.
675 The last option is to directly abort the execution of the program from within
676 the isl library. This makes it obviously impossible to recover from an error,
677 but it allows to directly spot the error location. By aborting on error,
678 debuggers break at the location the error occurred and can provide a stack
679 trace. Other tools that automatically provide stack traces on abort or that do
680 not want to continue execution after an error was triggered may also prefer to
683 The on error behavior of isl can be specified by calling
684 C<isl_options_set_on_error> or by setting the command line option
685 C<--isl-on-error>. Valid arguments for the function call are
686 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
687 choices for the command line option are C<warn>, C<continue> and C<abort>.
688 It is also possible to query the current error mode.
690 #include <isl/options.h>
691 int isl_options_set_on_error(isl_ctx *ctx, int val);
692 int isl_options_get_on_error(isl_ctx *ctx);
696 Identifiers are used to identify both individual dimensions
697 and tuples of dimensions. They consist of an optional name and an optional
698 user pointer. The name and the user pointer cannot both be C<NULL>, however.
699 Identifiers with the same name but different pointer values
700 are considered to be distinct.
701 Similarly, identifiers with different names but the same pointer value
702 are also considered to be distinct.
703 Equal identifiers are represented using the same object.
704 Pairs of identifiers can therefore be tested for equality using the
706 Identifiers can be constructed, copied, freed, inspected and printed
707 using the following functions.
710 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
711 __isl_keep const char *name, void *user);
712 __isl_give isl_id *isl_id_set_free_user(
713 __isl_take isl_id *id,
714 __isl_give void (*free_user)(void *user));
715 __isl_give isl_id *isl_id_copy(isl_id *id);
716 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
718 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
719 void *isl_id_get_user(__isl_keep isl_id *id);
720 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
722 __isl_give isl_printer *isl_printer_print_id(
723 __isl_take isl_printer *p, __isl_keep isl_id *id);
725 The callback set by C<isl_id_set_free_user> is called on the user
726 pointer when the last reference to the C<isl_id> is freed.
727 Note that C<isl_id_get_name> returns a pointer to some internal
728 data structure, so the result can only be used while the
729 corresponding C<isl_id> is alive.
733 Whenever a new set, relation or similiar object is created from scratch,
734 the space in which it lives needs to be specified using an C<isl_space>.
735 Each space involves zero or more parameters and zero, one or two
736 tuples of set or input/output dimensions. The parameters and dimensions
737 are identified by an C<isl_dim_type> and a position.
738 The type C<isl_dim_param> refers to parameters,
739 the type C<isl_dim_set> refers to set dimensions (for spaces
740 with a single tuple of dimensions) and the types C<isl_dim_in>
741 and C<isl_dim_out> refer to input and output dimensions
742 (for spaces with two tuples of dimensions).
743 Local spaces (see L</"Local Spaces">) also contain dimensions
744 of type C<isl_dim_div>.
745 Note that parameters are only identified by their position within
746 a given object. Across different objects, parameters are (usually)
747 identified by their names or identifiers. Only unnamed parameters
748 are identified by their positions across objects. The use of unnamed
749 parameters is discouraged.
751 #include <isl/space.h>
752 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
753 unsigned nparam, unsigned n_in, unsigned n_out);
754 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
756 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
757 unsigned nparam, unsigned dim);
758 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
759 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
760 unsigned isl_space_dim(__isl_keep isl_space *space,
761 enum isl_dim_type type);
763 The space used for creating a parameter domain
764 needs to be created using C<isl_space_params_alloc>.
765 For other sets, the space
766 needs to be created using C<isl_space_set_alloc>, while
767 for a relation, the space
768 needs to be created using C<isl_space_alloc>.
769 C<isl_space_dim> can be used
770 to find out the number of dimensions of each type in
771 a space, where type may be
772 C<isl_dim_param>, C<isl_dim_in> (only for relations),
773 C<isl_dim_out> (only for relations), C<isl_dim_set>
774 (only for sets) or C<isl_dim_all>.
776 To check whether a given space is that of a set or a map
777 or whether it is a parameter space, use these functions:
779 #include <isl/space.h>
780 int isl_space_is_params(__isl_keep isl_space *space);
781 int isl_space_is_set(__isl_keep isl_space *space);
782 int isl_space_is_map(__isl_keep isl_space *space);
784 Spaces can be compared using the following functions:
786 #include <isl/space.h>
787 int isl_space_is_equal(__isl_keep isl_space *space1,
788 __isl_keep isl_space *space2);
789 int isl_space_is_domain(__isl_keep isl_space *space1,
790 __isl_keep isl_space *space2);
791 int isl_space_is_range(__isl_keep isl_space *space1,
792 __isl_keep isl_space *space2);
793 int isl_space_tuple_is_equal(
794 __isl_keep isl_space *space1,
795 enum isl_dim_type type1,
796 __isl_keep isl_space *space2,
797 enum isl_dim_type type2);
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
802 is a map space. C<isl_space_tuple_is_equal> checks whether the given
803 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
804 spaces are the same. That is, it checks if they have the same
805 identifier (if any), the same dimension and the same internal structure
808 It is often useful to create objects that live in the
809 same space as some other object. This can be accomplished
810 by creating the new objects
811 (see L</"Creating New Sets and Relations"> or
812 L</"Creating New (Piecewise) Quasipolynomials">) based on the space
813 of the original object.
816 __isl_give isl_space *isl_basic_set_get_space(
817 __isl_keep isl_basic_set *bset);
818 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
820 #include <isl/union_set.h>
821 __isl_give isl_space *isl_union_set_get_space(
822 __isl_keep isl_union_set *uset);
825 __isl_give isl_space *isl_basic_map_get_space(
826 __isl_keep isl_basic_map *bmap);
827 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
829 #include <isl/union_map.h>
830 __isl_give isl_space *isl_union_map_get_space(
831 __isl_keep isl_union_map *umap);
833 #include <isl/constraint.h>
834 __isl_give isl_space *isl_constraint_get_space(
835 __isl_keep isl_constraint *constraint);
837 #include <isl/polynomial.h>
838 __isl_give isl_space *isl_qpolynomial_get_domain_space(
839 __isl_keep isl_qpolynomial *qp);
840 __isl_give isl_space *isl_qpolynomial_get_space(
841 __isl_keep isl_qpolynomial *qp);
842 __isl_give isl_space *isl_qpolynomial_fold_get_space(
843 __isl_keep isl_qpolynomial_fold *fold);
844 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
845 __isl_keep isl_pw_qpolynomial *pwqp);
846 __isl_give isl_space *isl_pw_qpolynomial_get_space(
847 __isl_keep isl_pw_qpolynomial *pwqp);
848 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
849 __isl_keep isl_pw_qpolynomial_fold *pwf);
850 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
851 __isl_keep isl_pw_qpolynomial_fold *pwf);
852 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
853 __isl_keep isl_union_pw_qpolynomial *upwqp);
854 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
855 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
858 __isl_give isl_space *isl_multi_val_get_space(
859 __isl_keep isl_multi_val *mv);
862 __isl_give isl_space *isl_aff_get_domain_space(
863 __isl_keep isl_aff *aff);
864 __isl_give isl_space *isl_aff_get_space(
865 __isl_keep isl_aff *aff);
866 __isl_give isl_space *isl_pw_aff_get_domain_space(
867 __isl_keep isl_pw_aff *pwaff);
868 __isl_give isl_space *isl_pw_aff_get_space(
869 __isl_keep isl_pw_aff *pwaff);
870 __isl_give isl_space *isl_multi_aff_get_domain_space(
871 __isl_keep isl_multi_aff *maff);
872 __isl_give isl_space *isl_multi_aff_get_space(
873 __isl_keep isl_multi_aff *maff);
874 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
875 __isl_keep isl_pw_multi_aff *pma);
876 __isl_give isl_space *isl_pw_multi_aff_get_space(
877 __isl_keep isl_pw_multi_aff *pma);
878 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
879 __isl_keep isl_union_pw_multi_aff *upma);
880 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
881 __isl_keep isl_multi_pw_aff *mpa);
882 __isl_give isl_space *isl_multi_pw_aff_get_space(
883 __isl_keep isl_multi_pw_aff *mpa);
885 #include <isl/point.h>
886 __isl_give isl_space *isl_point_get_space(
887 __isl_keep isl_point *pnt);
889 The identifiers or names of the individual dimensions may be set or read off
890 using the following functions.
892 #include <isl/space.h>
893 __isl_give isl_space *isl_space_set_dim_id(
894 __isl_take isl_space *space,
895 enum isl_dim_type type, unsigned pos,
896 __isl_take isl_id *id);
897 int isl_space_has_dim_id(__isl_keep isl_space *space,
898 enum isl_dim_type type, unsigned pos);
899 __isl_give isl_id *isl_space_get_dim_id(
900 __isl_keep isl_space *space,
901 enum isl_dim_type type, unsigned pos);
902 __isl_give isl_space *isl_space_set_dim_name(
903 __isl_take isl_space *space,
904 enum isl_dim_type type, unsigned pos,
905 __isl_keep const char *name);
906 int isl_space_has_dim_name(__isl_keep isl_space *space,
907 enum isl_dim_type type, unsigned pos);
908 __isl_keep const char *isl_space_get_dim_name(
909 __isl_keep isl_space *space,
910 enum isl_dim_type type, unsigned pos);
912 Note that C<isl_space_get_name> returns a pointer to some internal
913 data structure, so the result can only be used while the
914 corresponding C<isl_space> is alive.
915 Also note that every function that operates on two sets or relations
916 requires that both arguments have the same parameters. This also
917 means that if one of the arguments has named parameters, then the
918 other needs to have named parameters too and the names need to match.
919 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
920 arguments may have different parameters (as long as they are named),
921 in which case the result will have as parameters the union of the parameters of
924 Given the identifier or name of a dimension (typically a parameter),
925 its position can be obtained from the following function.
927 #include <isl/space.h>
928 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
929 enum isl_dim_type type, __isl_keep isl_id *id);
930 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
931 enum isl_dim_type type, const char *name);
933 The identifiers or names of entire spaces may be set or read off
934 using the following functions.
936 #include <isl/space.h>
937 __isl_give isl_space *isl_space_set_tuple_id(
938 __isl_take isl_space *space,
939 enum isl_dim_type type, __isl_take isl_id *id);
940 __isl_give isl_space *isl_space_reset_tuple_id(
941 __isl_take isl_space *space, enum isl_dim_type type);
942 int isl_space_has_tuple_id(__isl_keep isl_space *space,
943 enum isl_dim_type type);
944 __isl_give isl_id *isl_space_get_tuple_id(
945 __isl_keep isl_space *space, enum isl_dim_type type);
946 __isl_give isl_space *isl_space_set_tuple_name(
947 __isl_take isl_space *space,
948 enum isl_dim_type type, const char *s);
949 int isl_space_has_tuple_name(__isl_keep isl_space *space,
950 enum isl_dim_type type);
951 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
952 enum isl_dim_type type);
954 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
955 or C<isl_dim_set>. As with C<isl_space_get_name>,
956 the C<isl_space_get_tuple_name> function returns a pointer to some internal
958 Binary operations require the corresponding spaces of their arguments
959 to have the same name.
961 To keep the names of all parameters and tuples, but reset the user pointers
962 of all the corresponding identifiers, use the following function.
964 __isl_give isl_space *isl_space_reset_user(
965 __isl_take isl_space *space);
967 Spaces can be nested. In particular, the domain of a set or
968 the domain or range of a relation can be a nested relation.
969 This process is also called I<wrapping>.
970 The functions for detecting, constructing and deconstructing
971 such nested spaces can be found in the wrapping properties
972 of L</"Unary Properties">, the wrapping operations
973 of L</"Unary Operations"> and the Cartesian product operations
974 of L</"Basic Operations">.
976 Spaces can be created from other spaces
977 using the following functions.
979 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
980 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
981 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
982 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
983 __isl_give isl_space *isl_space_domain_map(
984 __isl_take isl_space *space);
985 __isl_give isl_space *isl_space_range_map(
986 __isl_take isl_space *space);
987 __isl_give isl_space *isl_space_params(
988 __isl_take isl_space *space);
989 __isl_give isl_space *isl_space_set_from_params(
990 __isl_take isl_space *space);
991 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
992 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
993 __isl_take isl_space *right);
994 __isl_give isl_space *isl_space_align_params(
995 __isl_take isl_space *space1, __isl_take isl_space *space2)
996 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
997 enum isl_dim_type type, unsigned pos, unsigned n);
998 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
999 enum isl_dim_type type, unsigned n);
1000 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
1001 enum isl_dim_type type, unsigned first, unsigned n);
1002 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
1003 enum isl_dim_type dst_type, unsigned dst_pos,
1004 enum isl_dim_type src_type, unsigned src_pos,
1006 __isl_give isl_space *isl_space_map_from_set(
1007 __isl_take isl_space *space);
1008 __isl_give isl_space *isl_space_map_from_domain_and_range(
1009 __isl_take isl_space *domain,
1010 __isl_take isl_space *range);
1011 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
1012 __isl_give isl_space *isl_space_curry(
1013 __isl_take isl_space *space);
1014 __isl_give isl_space *isl_space_uncurry(
1015 __isl_take isl_space *space);
1017 Note that if dimensions are added or removed from a space, then
1018 the name and the internal structure are lost.
1022 A local space is essentially a space with
1023 zero or more existentially quantified variables.
1024 The local space of a (constraint of a) basic set or relation can be obtained
1025 using the following functions.
1027 #include <isl/constraint.h>
1028 __isl_give isl_local_space *isl_constraint_get_local_space(
1029 __isl_keep isl_constraint *constraint);
1031 #include <isl/set.h>
1032 __isl_give isl_local_space *isl_basic_set_get_local_space(
1033 __isl_keep isl_basic_set *bset);
1035 #include <isl/map.h>
1036 __isl_give isl_local_space *isl_basic_map_get_local_space(
1037 __isl_keep isl_basic_map *bmap);
1039 A new local space can be created from a space using
1041 #include <isl/local_space.h>
1042 __isl_give isl_local_space *isl_local_space_from_space(
1043 __isl_take isl_space *space);
1045 They can be inspected, modified, copied and freed using the following functions.
1047 #include <isl/local_space.h>
1048 isl_ctx *isl_local_space_get_ctx(
1049 __isl_keep isl_local_space *ls);
1050 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1051 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1052 enum isl_dim_type type);
1053 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1054 __isl_take isl_local_space *ls,
1055 enum isl_dim_type type, __isl_take isl_id *id);
1056 int isl_local_space_has_dim_id(
1057 __isl_keep isl_local_space *ls,
1058 enum isl_dim_type type, unsigned pos);
1059 __isl_give isl_id *isl_local_space_get_dim_id(
1060 __isl_keep isl_local_space *ls,
1061 enum isl_dim_type type, unsigned pos);
1062 int isl_local_space_has_dim_name(
1063 __isl_keep isl_local_space *ls,
1064 enum isl_dim_type type, unsigned pos)
1065 const char *isl_local_space_get_dim_name(
1066 __isl_keep isl_local_space *ls,
1067 enum isl_dim_type type, unsigned pos);
1068 __isl_give isl_local_space *isl_local_space_set_dim_name(
1069 __isl_take isl_local_space *ls,
1070 enum isl_dim_type type, unsigned pos, const char *s);
1071 __isl_give isl_local_space *isl_local_space_set_dim_id(
1072 __isl_take isl_local_space *ls,
1073 enum isl_dim_type type, unsigned pos,
1074 __isl_take isl_id *id);
1075 __isl_give isl_space *isl_local_space_get_space(
1076 __isl_keep isl_local_space *ls);
1077 __isl_give isl_aff *isl_local_space_get_div(
1078 __isl_keep isl_local_space *ls, int pos);
1079 __isl_give isl_local_space *isl_local_space_copy(
1080 __isl_keep isl_local_space *ls);
1081 __isl_null isl_local_space *isl_local_space_free(
1082 __isl_take isl_local_space *ls);
1084 Note that C<isl_local_space_get_div> can only be used on local spaces
1087 Two local spaces can be compared using
1089 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1090 __isl_keep isl_local_space *ls2);
1092 Local spaces can be created from other local spaces
1093 using the functions described in L</"Unary Operations">
1094 and L</"Binary Operations">.
1096 =head2 Input and Output
1098 C<isl> supports its own input/output format, which is similar
1099 to the C<Omega> format, but also supports the C<PolyLib> format
1102 =head3 C<isl> format
1104 The C<isl> format is similar to that of C<Omega>, but has a different
1105 syntax for describing the parameters and allows for the definition
1106 of an existentially quantified variable as the integer division
1107 of an affine expression.
1108 For example, the set of integers C<i> between C<0> and C<n>
1109 such that C<i % 10 <= 6> can be described as
1111 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1114 A set or relation can have several disjuncts, separated
1115 by the keyword C<or>. Each disjunct is either a conjunction
1116 of constraints or a projection (C<exists>) of a conjunction
1117 of constraints. The constraints are separated by the keyword
1120 =head3 C<PolyLib> format
1122 If the represented set is a union, then the first line
1123 contains a single number representing the number of disjuncts.
1124 Otherwise, a line containing the number C<1> is optional.
1126 Each disjunct is represented by a matrix of constraints.
1127 The first line contains two numbers representing
1128 the number of rows and columns,
1129 where the number of rows is equal to the number of constraints
1130 and the number of columns is equal to two plus the number of variables.
1131 The following lines contain the actual rows of the constraint matrix.
1132 In each row, the first column indicates whether the constraint
1133 is an equality (C<0>) or inequality (C<1>). The final column
1134 corresponds to the constant term.
1136 If the set is parametric, then the coefficients of the parameters
1137 appear in the last columns before the constant column.
1138 The coefficients of any existentially quantified variables appear
1139 between those of the set variables and those of the parameters.
1141 =head3 Extended C<PolyLib> format
1143 The extended C<PolyLib> format is nearly identical to the
1144 C<PolyLib> format. The only difference is that the line
1145 containing the number of rows and columns of a constraint matrix
1146 also contains four additional numbers:
1147 the number of output dimensions, the number of input dimensions,
1148 the number of local dimensions (i.e., the number of existentially
1149 quantified variables) and the number of parameters.
1150 For sets, the number of ``output'' dimensions is equal
1151 to the number of set dimensions, while the number of ``input''
1156 #include <isl/set.h>
1157 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1158 isl_ctx *ctx, FILE *input);
1159 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1160 isl_ctx *ctx, const char *str);
1161 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1163 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1166 #include <isl/map.h>
1167 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1168 isl_ctx *ctx, FILE *input);
1169 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1170 isl_ctx *ctx, const char *str);
1171 __isl_give isl_map *isl_map_read_from_file(
1172 isl_ctx *ctx, FILE *input);
1173 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1176 #include <isl/union_set.h>
1177 __isl_give isl_union_set *isl_union_set_read_from_file(
1178 isl_ctx *ctx, FILE *input);
1179 __isl_give isl_union_set *isl_union_set_read_from_str(
1180 isl_ctx *ctx, const char *str);
1182 #include <isl/union_map.h>
1183 __isl_give isl_union_map *isl_union_map_read_from_file(
1184 isl_ctx *ctx, FILE *input);
1185 __isl_give isl_union_map *isl_union_map_read_from_str(
1186 isl_ctx *ctx, const char *str);
1188 The input format is autodetected and may be either the C<PolyLib> format
1189 or the C<isl> format.
1193 Before anything can be printed, an C<isl_printer> needs to
1196 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1198 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1199 __isl_null isl_printer *isl_printer_free(
1200 __isl_take isl_printer *printer);
1201 __isl_give char *isl_printer_get_str(
1202 __isl_keep isl_printer *printer);
1204 The printer can be inspected using the following functions.
1206 FILE *isl_printer_get_file(
1207 __isl_keep isl_printer *printer);
1208 int isl_printer_get_output_format(
1209 __isl_keep isl_printer *p);
1211 The behavior of the printer can be modified in various ways
1213 __isl_give isl_printer *isl_printer_set_output_format(
1214 __isl_take isl_printer *p, int output_format);
1215 __isl_give isl_printer *isl_printer_set_indent(
1216 __isl_take isl_printer *p, int indent);
1217 __isl_give isl_printer *isl_printer_set_indent_prefix(
1218 __isl_take isl_printer *p, const char *prefix);
1219 __isl_give isl_printer *isl_printer_indent(
1220 __isl_take isl_printer *p, int indent);
1221 __isl_give isl_printer *isl_printer_set_prefix(
1222 __isl_take isl_printer *p, const char *prefix);
1223 __isl_give isl_printer *isl_printer_set_suffix(
1224 __isl_take isl_printer *p, const char *suffix);
1226 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1227 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1228 and defaults to C<ISL_FORMAT_ISL>.
1229 Each line in the output is prefixed by C<indent_prefix>,
1230 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
1231 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1232 In the C<PolyLib> format output,
1233 the coefficients of the existentially quantified variables
1234 appear between those of the set variables and those
1236 The function C<isl_printer_indent> increases the indentation
1237 by the specified amount (which may be negative).
1239 To actually print something, use
1241 #include <isl/printer.h>
1242 __isl_give isl_printer *isl_printer_print_double(
1243 __isl_take isl_printer *p, double d);
1245 #include <isl/set.h>
1246 __isl_give isl_printer *isl_printer_print_basic_set(
1247 __isl_take isl_printer *printer,
1248 __isl_keep isl_basic_set *bset);
1249 __isl_give isl_printer *isl_printer_print_set(
1250 __isl_take isl_printer *printer,
1251 __isl_keep isl_set *set);
1253 #include <isl/map.h>
1254 __isl_give isl_printer *isl_printer_print_basic_map(
1255 __isl_take isl_printer *printer,
1256 __isl_keep isl_basic_map *bmap);
1257 __isl_give isl_printer *isl_printer_print_map(
1258 __isl_take isl_printer *printer,
1259 __isl_keep isl_map *map);
1261 #include <isl/union_set.h>
1262 __isl_give isl_printer *isl_printer_print_union_set(
1263 __isl_take isl_printer *p,
1264 __isl_keep isl_union_set *uset);
1266 #include <isl/union_map.h>
1267 __isl_give isl_printer *isl_printer_print_union_map(
1268 __isl_take isl_printer *p,
1269 __isl_keep isl_union_map *umap);
1271 When called on a file printer, the following function flushes
1272 the file. When called on a string printer, the buffer is cleared.
1274 __isl_give isl_printer *isl_printer_flush(
1275 __isl_take isl_printer *p);
1277 =head2 Creating New Sets and Relations
1279 C<isl> has functions for creating some standard sets and relations.
1283 =item * Empty sets and relations
1285 __isl_give isl_basic_set *isl_basic_set_empty(
1286 __isl_take isl_space *space);
1287 __isl_give isl_basic_map *isl_basic_map_empty(
1288 __isl_take isl_space *space);
1289 __isl_give isl_set *isl_set_empty(
1290 __isl_take isl_space *space);
1291 __isl_give isl_map *isl_map_empty(
1292 __isl_take isl_space *space);
1293 __isl_give isl_union_set *isl_union_set_empty(
1294 __isl_take isl_space *space);
1295 __isl_give isl_union_map *isl_union_map_empty(
1296 __isl_take isl_space *space);
1298 For C<isl_union_set>s and C<isl_union_map>s, the space
1299 is only used to specify the parameters.
1301 =item * Universe sets and relations
1303 __isl_give isl_basic_set *isl_basic_set_universe(
1304 __isl_take isl_space *space);
1305 __isl_give isl_basic_map *isl_basic_map_universe(
1306 __isl_take isl_space *space);
1307 __isl_give isl_set *isl_set_universe(
1308 __isl_take isl_space *space);
1309 __isl_give isl_map *isl_map_universe(
1310 __isl_take isl_space *space);
1311 __isl_give isl_union_set *isl_union_set_universe(
1312 __isl_take isl_union_set *uset);
1313 __isl_give isl_union_map *isl_union_map_universe(
1314 __isl_take isl_union_map *umap);
1316 The sets and relations constructed by the functions above
1317 contain all integer values, while those constructed by the
1318 functions below only contain non-negative values.
1320 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1321 __isl_take isl_space *space);
1322 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1323 __isl_take isl_space *space);
1324 __isl_give isl_set *isl_set_nat_universe(
1325 __isl_take isl_space *space);
1326 __isl_give isl_map *isl_map_nat_universe(
1327 __isl_take isl_space *space);
1329 =item * Identity relations
1331 __isl_give isl_basic_map *isl_basic_map_identity(
1332 __isl_take isl_space *space);
1333 __isl_give isl_map *isl_map_identity(
1334 __isl_take isl_space *space);
1336 The number of input and output dimensions in C<space> needs
1339 =item * Lexicographic order
1341 __isl_give isl_map *isl_map_lex_lt(
1342 __isl_take isl_space *set_space);
1343 __isl_give isl_map *isl_map_lex_le(
1344 __isl_take isl_space *set_space);
1345 __isl_give isl_map *isl_map_lex_gt(
1346 __isl_take isl_space *set_space);
1347 __isl_give isl_map *isl_map_lex_ge(
1348 __isl_take isl_space *set_space);
1349 __isl_give isl_map *isl_map_lex_lt_first(
1350 __isl_take isl_space *space, unsigned n);
1351 __isl_give isl_map *isl_map_lex_le_first(
1352 __isl_take isl_space *space, unsigned n);
1353 __isl_give isl_map *isl_map_lex_gt_first(
1354 __isl_take isl_space *space, unsigned n);
1355 __isl_give isl_map *isl_map_lex_ge_first(
1356 __isl_take isl_space *space, unsigned n);
1358 The first four functions take a space for a B<set>
1359 and return relations that express that the elements in the domain
1360 are lexicographically less
1361 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1362 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1363 than the elements in the range.
1364 The last four functions take a space for a map
1365 and return relations that express that the first C<n> dimensions
1366 in the domain are lexicographically less
1367 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1368 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1369 than the first C<n> dimensions in the range.
1373 A basic set or relation can be converted to a set or relation
1374 using the following functions.
1376 __isl_give isl_set *isl_set_from_basic_set(
1377 __isl_take isl_basic_set *bset);
1378 __isl_give isl_map *isl_map_from_basic_map(
1379 __isl_take isl_basic_map *bmap);
1381 Sets and relations can be converted to union sets and relations
1382 using the following functions.
1384 __isl_give isl_union_set *isl_union_set_from_basic_set(
1385 __isl_take isl_basic_set *bset);
1386 __isl_give isl_union_map *isl_union_map_from_basic_map(
1387 __isl_take isl_basic_map *bmap);
1388 __isl_give isl_union_set *isl_union_set_from_set(
1389 __isl_take isl_set *set);
1390 __isl_give isl_union_map *isl_union_map_from_map(
1391 __isl_take isl_map *map);
1393 The inverse conversions below can only be used if the input
1394 union set or relation is known to contain elements in exactly one
1397 __isl_give isl_set *isl_set_from_union_set(
1398 __isl_take isl_union_set *uset);
1399 __isl_give isl_map *isl_map_from_union_map(
1400 __isl_take isl_union_map *umap);
1402 A zero-dimensional (basic) set can be constructed on a given parameter domain
1403 using the following function.
1405 __isl_give isl_basic_set *isl_basic_set_from_params(
1406 __isl_take isl_basic_set *bset);
1407 __isl_give isl_set *isl_set_from_params(
1408 __isl_take isl_set *set);
1410 Sets and relations can be copied and freed again using the following
1413 __isl_give isl_basic_set *isl_basic_set_copy(
1414 __isl_keep isl_basic_set *bset);
1415 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1416 __isl_give isl_union_set *isl_union_set_copy(
1417 __isl_keep isl_union_set *uset);
1418 __isl_give isl_basic_map *isl_basic_map_copy(
1419 __isl_keep isl_basic_map *bmap);
1420 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1421 __isl_give isl_union_map *isl_union_map_copy(
1422 __isl_keep isl_union_map *umap);
1423 __isl_null isl_basic_set *isl_basic_set_free(
1424 __isl_take isl_basic_set *bset);
1425 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1426 __isl_null isl_union_set *isl_union_set_free(
1427 __isl_take isl_union_set *uset);
1428 __isl_null isl_basic_map *isl_basic_map_free(
1429 __isl_take isl_basic_map *bmap);
1430 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1431 __isl_null isl_union_map *isl_union_map_free(
1432 __isl_take isl_union_map *umap);
1434 Other sets and relations can be constructed by starting
1435 from a universe set or relation, adding equality and/or
1436 inequality constraints and then projecting out the
1437 existentially quantified variables, if any.
1438 Constraints can be constructed, manipulated and
1439 added to (or removed from) (basic) sets and relations
1440 using the following functions.
1442 #include <isl/constraint.h>
1443 __isl_give isl_constraint *isl_equality_alloc(
1444 __isl_take isl_local_space *ls);
1445 __isl_give isl_constraint *isl_inequality_alloc(
1446 __isl_take isl_local_space *ls);
1447 __isl_give isl_constraint *isl_constraint_set_constant_si(
1448 __isl_take isl_constraint *constraint, int v);
1449 __isl_give isl_constraint *isl_constraint_set_constant_val(
1450 __isl_take isl_constraint *constraint,
1451 __isl_take isl_val *v);
1452 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1453 __isl_take isl_constraint *constraint,
1454 enum isl_dim_type type, int pos, int v);
1455 __isl_give isl_constraint *
1456 isl_constraint_set_coefficient_val(
1457 __isl_take isl_constraint *constraint,
1458 enum isl_dim_type type, int pos,
1459 __isl_take isl_val *v);
1460 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1461 __isl_take isl_basic_map *bmap,
1462 __isl_take isl_constraint *constraint);
1463 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1464 __isl_take isl_basic_set *bset,
1465 __isl_take isl_constraint *constraint);
1466 __isl_give isl_map *isl_map_add_constraint(
1467 __isl_take isl_map *map,
1468 __isl_take isl_constraint *constraint);
1469 __isl_give isl_set *isl_set_add_constraint(
1470 __isl_take isl_set *set,
1471 __isl_take isl_constraint *constraint);
1472 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1473 __isl_take isl_basic_set *bset,
1474 __isl_take isl_constraint *constraint);
1476 For example, to create a set containing the even integers
1477 between 10 and 42, you would use the following code.
1480 isl_local_space *ls;
1482 isl_basic_set *bset;
1484 space = isl_space_set_alloc(ctx, 0, 2);
1485 bset = isl_basic_set_universe(isl_space_copy(space));
1486 ls = isl_local_space_from_space(space);
1488 c = isl_equality_alloc(isl_local_space_copy(ls));
1489 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1490 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1491 bset = isl_basic_set_add_constraint(bset, c);
1493 c = isl_inequality_alloc(isl_local_space_copy(ls));
1494 c = isl_constraint_set_constant_si(c, -10);
1495 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1496 bset = isl_basic_set_add_constraint(bset, c);
1498 c = isl_inequality_alloc(ls);
1499 c = isl_constraint_set_constant_si(c, 42);
1500 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1501 bset = isl_basic_set_add_constraint(bset, c);
1503 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1507 isl_basic_set *bset;
1508 bset = isl_basic_set_read_from_str(ctx,
1509 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1511 A basic set or relation can also be constructed from two matrices
1512 describing the equalities and the inequalities.
1514 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1515 __isl_take isl_space *space,
1516 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1517 enum isl_dim_type c1,
1518 enum isl_dim_type c2, enum isl_dim_type c3,
1519 enum isl_dim_type c4);
1520 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1521 __isl_take isl_space *space,
1522 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1523 enum isl_dim_type c1,
1524 enum isl_dim_type c2, enum isl_dim_type c3,
1525 enum isl_dim_type c4, enum isl_dim_type c5);
1527 The C<isl_dim_type> arguments indicate the order in which
1528 different kinds of variables appear in the input matrices
1529 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1530 C<isl_dim_set> and C<isl_dim_div> for sets and
1531 of C<isl_dim_cst>, C<isl_dim_param>,
1532 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1534 A (basic or union) set or relation can also be constructed from a
1535 (union) (piecewise) (multiple) affine expression
1536 or a list of affine expressions
1537 (See L<"Piecewise Quasi Affine Expressions"> and
1538 L<"Piecewise Multiple Quasi Affine Expressions">).
1540 __isl_give isl_basic_map *isl_basic_map_from_aff(
1541 __isl_take isl_aff *aff);
1542 __isl_give isl_map *isl_map_from_aff(
1543 __isl_take isl_aff *aff);
1544 __isl_give isl_set *isl_set_from_pw_aff(
1545 __isl_take isl_pw_aff *pwaff);
1546 __isl_give isl_map *isl_map_from_pw_aff(
1547 __isl_take isl_pw_aff *pwaff);
1548 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1549 __isl_take isl_space *domain_space,
1550 __isl_take isl_aff_list *list);
1551 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1552 __isl_take isl_multi_aff *maff)
1553 __isl_give isl_map *isl_map_from_multi_aff(
1554 __isl_take isl_multi_aff *maff)
1555 __isl_give isl_set *isl_set_from_pw_multi_aff(
1556 __isl_take isl_pw_multi_aff *pma);
1557 __isl_give isl_map *isl_map_from_pw_multi_aff(
1558 __isl_take isl_pw_multi_aff *pma);
1559 __isl_give isl_set *isl_set_from_multi_pw_aff(
1560 __isl_take isl_multi_pw_aff *mpa);
1561 __isl_give isl_map *isl_map_from_multi_pw_aff(
1562 __isl_take isl_multi_pw_aff *mpa);
1563 __isl_give isl_union_map *
1564 isl_union_map_from_union_pw_multi_aff(
1565 __isl_take isl_union_pw_multi_aff *upma);
1567 The C<domain_space> argument describes the domain of the resulting
1568 basic relation. It is required because the C<list> may consist
1569 of zero affine expressions.
1571 =head2 Inspecting Sets and Relations
1573 Usually, the user should not have to care about the actual constraints
1574 of the sets and maps, but should instead apply the abstract operations
1575 explained in the following sections.
1576 Occasionally, however, it may be required to inspect the individual
1577 coefficients of the constraints. This section explains how to do so.
1578 In these cases, it may also be useful to have C<isl> compute
1579 an explicit representation of the existentially quantified variables.
1581 __isl_give isl_set *isl_set_compute_divs(
1582 __isl_take isl_set *set);
1583 __isl_give isl_map *isl_map_compute_divs(
1584 __isl_take isl_map *map);
1585 __isl_give isl_union_set *isl_union_set_compute_divs(
1586 __isl_take isl_union_set *uset);
1587 __isl_give isl_union_map *isl_union_map_compute_divs(
1588 __isl_take isl_union_map *umap);
1590 This explicit representation defines the existentially quantified
1591 variables as integer divisions of the other variables, possibly
1592 including earlier existentially quantified variables.
1593 An explicitly represented existentially quantified variable therefore
1594 has a unique value when the values of the other variables are known.
1595 If, furthermore, the same existentials, i.e., existentials
1596 with the same explicit representations, should appear in the
1597 same order in each of the disjuncts of a set or map, then the user should call
1598 either of the following functions.
1600 __isl_give isl_set *isl_set_align_divs(
1601 __isl_take isl_set *set);
1602 __isl_give isl_map *isl_map_align_divs(
1603 __isl_take isl_map *map);
1605 Alternatively, the existentially quantified variables can be removed
1606 using the following functions, which compute an overapproximation.
1608 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1609 __isl_take isl_basic_set *bset);
1610 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1611 __isl_take isl_basic_map *bmap);
1612 __isl_give isl_set *isl_set_remove_divs(
1613 __isl_take isl_set *set);
1614 __isl_give isl_map *isl_map_remove_divs(
1615 __isl_take isl_map *map);
1617 It is also possible to only remove those divs that are defined
1618 in terms of a given range of dimensions or only those for which
1619 no explicit representation is known.
1621 __isl_give isl_basic_set *
1622 isl_basic_set_remove_divs_involving_dims(
1623 __isl_take isl_basic_set *bset,
1624 enum isl_dim_type type,
1625 unsigned first, unsigned n);
1626 __isl_give isl_basic_map *
1627 isl_basic_map_remove_divs_involving_dims(
1628 __isl_take isl_basic_map *bmap,
1629 enum isl_dim_type type,
1630 unsigned first, unsigned n);
1631 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1632 __isl_take isl_set *set, enum isl_dim_type type,
1633 unsigned first, unsigned n);
1634 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1635 __isl_take isl_map *map, enum isl_dim_type type,
1636 unsigned first, unsigned n);
1638 __isl_give isl_basic_set *
1639 isl_basic_set_remove_unknown_divs(
1640 __isl_take isl_basic_set *bset);
1641 __isl_give isl_set *isl_set_remove_unknown_divs(
1642 __isl_take isl_set *set);
1643 __isl_give isl_map *isl_map_remove_unknown_divs(
1644 __isl_take isl_map *map);
1646 To iterate over all the sets or maps in a union set or map, use
1648 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1649 int (*fn)(__isl_take isl_set *set, void *user),
1651 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1652 int (*fn)(__isl_take isl_map *map, void *user),
1655 The number of sets or maps in a union set or map can be obtained
1658 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1659 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1661 To extract the set or map in a given space from a union, use
1663 __isl_give isl_set *isl_union_set_extract_set(
1664 __isl_keep isl_union_set *uset,
1665 __isl_take isl_space *space);
1666 __isl_give isl_map *isl_union_map_extract_map(
1667 __isl_keep isl_union_map *umap,
1668 __isl_take isl_space *space);
1670 To iterate over all the basic sets or maps in a set or map, use
1672 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1673 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1675 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1676 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1679 The callback function C<fn> should return 0 if successful and
1680 -1 if an error occurs. In the latter case, or if any other error
1681 occurs, the above functions will return -1.
1683 It should be noted that C<isl> does not guarantee that
1684 the basic sets or maps passed to C<fn> are disjoint.
1685 If this is required, then the user should call one of
1686 the following functions first.
1688 __isl_give isl_set *isl_set_make_disjoint(
1689 __isl_take isl_set *set);
1690 __isl_give isl_map *isl_map_make_disjoint(
1691 __isl_take isl_map *map);
1693 The number of basic sets in a set can be obtained
1696 int isl_set_n_basic_set(__isl_keep isl_set *set);
1698 To iterate over the constraints of a basic set or map, use
1700 #include <isl/constraint.h>
1702 int isl_basic_set_n_constraint(
1703 __isl_keep isl_basic_set *bset);
1704 int isl_basic_set_foreach_constraint(
1705 __isl_keep isl_basic_set *bset,
1706 int (*fn)(__isl_take isl_constraint *c, void *user),
1708 int isl_basic_map_n_constraint(
1709 __isl_keep isl_basic_map *bmap);
1710 int isl_basic_map_foreach_constraint(
1711 __isl_keep isl_basic_map *bmap,
1712 int (*fn)(__isl_take isl_constraint *c, void *user),
1714 __isl_null isl_constraint *isl_constraint_free(
1715 __isl_take isl_constraint *c);
1717 Again, the callback function C<fn> should return 0 if successful and
1718 -1 if an error occurs. In the latter case, or if any other error
1719 occurs, the above functions will return -1.
1720 The constraint C<c> represents either an equality or an inequality.
1721 Use the following function to find out whether a constraint
1722 represents an equality. If not, it represents an inequality.
1724 int isl_constraint_is_equality(
1725 __isl_keep isl_constraint *constraint);
1727 It is also possible to obtain a list of constraints from a basic
1730 #include <isl/constraint.h>
1731 __isl_give isl_constraint_list *
1732 isl_basic_map_get_constraint_list(
1733 __isl_keep isl_basic_map *bmap);
1734 __isl_give isl_constraint_list *
1735 isl_basic_set_get_constraint_list(
1736 __isl_keep isl_basic_set *bset);
1738 These functions require that all existentially quantified variables
1739 have an explicit representation.
1740 The returned list can be manipulated using the functions in L<"Lists">.
1742 The coefficients of the constraints can be inspected using
1743 the following functions.
1745 int isl_constraint_is_lower_bound(
1746 __isl_keep isl_constraint *constraint,
1747 enum isl_dim_type type, unsigned pos);
1748 int isl_constraint_is_upper_bound(
1749 __isl_keep isl_constraint *constraint,
1750 enum isl_dim_type type, unsigned pos);
1751 __isl_give isl_val *isl_constraint_get_constant_val(
1752 __isl_keep isl_constraint *constraint);
1753 __isl_give isl_val *isl_constraint_get_coefficient_val(
1754 __isl_keep isl_constraint *constraint,
1755 enum isl_dim_type type, int pos);
1756 int isl_constraint_involves_dims(
1757 __isl_keep isl_constraint *constraint,
1758 enum isl_dim_type type, unsigned first, unsigned n);
1760 The explicit representations of the existentially quantified
1761 variables can be inspected using the following function.
1762 Note that the user is only allowed to use this function
1763 if the inspected set or map is the result of a call
1764 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1765 The existentially quantified variable is equal to the floor
1766 of the returned affine expression. The affine expression
1767 itself can be inspected using the functions in
1768 L<"Piecewise Quasi Affine Expressions">.
1770 __isl_give isl_aff *isl_constraint_get_div(
1771 __isl_keep isl_constraint *constraint, int pos);
1773 To obtain the constraints of a basic set or map in matrix
1774 form, use the following functions.
1776 __isl_give isl_mat *isl_basic_set_equalities_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_set_inequalities_matrix(
1781 __isl_keep isl_basic_set *bset,
1782 enum isl_dim_type c1, enum isl_dim_type c2,
1783 enum isl_dim_type c3, enum isl_dim_type c4);
1784 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1785 __isl_keep isl_basic_map *bmap,
1786 enum isl_dim_type c1,
1787 enum isl_dim_type c2, enum isl_dim_type c3,
1788 enum isl_dim_type c4, enum isl_dim_type c5);
1789 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1790 __isl_keep isl_basic_map *bmap,
1791 enum isl_dim_type c1,
1792 enum isl_dim_type c2, enum isl_dim_type c3,
1793 enum isl_dim_type c4, enum isl_dim_type c5);
1795 The C<isl_dim_type> arguments dictate the order in which
1796 different kinds of variables appear in the resulting matrix.
1797 For set inputs, they should be a permutation of
1798 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
1799 For map inputs, they should be a permutation of
1800 C<isl_dim_cst>, C<isl_dim_param>,
1801 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1803 The number of parameters, input, output or set dimensions can
1804 be obtained using the following functions.
1806 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1807 enum isl_dim_type type);
1808 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1809 enum isl_dim_type type);
1810 unsigned isl_set_dim(__isl_keep isl_set *set,
1811 enum isl_dim_type type);
1812 unsigned isl_map_dim(__isl_keep isl_map *map,
1813 enum isl_dim_type type);
1814 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1815 enum isl_dim_type type);
1817 Note that a C<isl_union_map> only has parameters.
1819 To check whether the description of a set or relation depends
1820 on one or more given dimensions, it is not necessary to iterate over all
1821 constraints. Instead the following functions can be used.
1823 int isl_basic_set_involves_dims(
1824 __isl_keep isl_basic_set *bset,
1825 enum isl_dim_type type, unsigned first, unsigned n);
1826 int isl_set_involves_dims(__isl_keep isl_set *set,
1827 enum isl_dim_type type, unsigned first, unsigned n);
1828 int isl_basic_map_involves_dims(
1829 __isl_keep isl_basic_map *bmap,
1830 enum isl_dim_type type, unsigned first, unsigned n);
1831 int isl_map_involves_dims(__isl_keep isl_map *map,
1832 enum isl_dim_type type, unsigned first, unsigned n);
1834 Similarly, the following functions can be used to check whether
1835 a given dimension is involved in any lower or upper bound.
1837 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1838 enum isl_dim_type type, unsigned pos);
1839 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1840 enum isl_dim_type type, unsigned pos);
1842 Note that these functions return true even if there is a bound on
1843 the dimension on only some of the basic sets of C<set>.
1844 To check if they have a bound for all of the basic sets in C<set>,
1845 use the following functions instead.
1847 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1848 enum isl_dim_type type, unsigned pos);
1849 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1850 enum isl_dim_type type, unsigned pos);
1852 The identifiers or names of the domain and range spaces of a set
1853 or relation can be read off or set using the following functions.
1855 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1856 __isl_take isl_basic_set *bset,
1857 __isl_take isl_id *id);
1858 __isl_give isl_set *isl_set_set_tuple_id(
1859 __isl_take isl_set *set, __isl_take isl_id *id);
1860 __isl_give isl_set *isl_set_reset_tuple_id(
1861 __isl_take isl_set *set);
1862 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1863 __isl_give isl_id *isl_set_get_tuple_id(
1864 __isl_keep isl_set *set);
1865 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1866 __isl_take isl_basic_map *bmap,
1867 enum isl_dim_type type, __isl_take isl_id *id);
1868 __isl_give isl_map *isl_map_set_tuple_id(
1869 __isl_take isl_map *map, enum isl_dim_type type,
1870 __isl_take isl_id *id);
1871 __isl_give isl_map *isl_map_reset_tuple_id(
1872 __isl_take isl_map *map, enum isl_dim_type type);
1873 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1874 enum isl_dim_type type);
1875 __isl_give isl_id *isl_map_get_tuple_id(
1876 __isl_keep isl_map *map, enum isl_dim_type type);
1878 const char *isl_basic_set_get_tuple_name(
1879 __isl_keep isl_basic_set *bset);
1880 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1881 __isl_take isl_basic_set *set, const char *s);
1882 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1883 const char *isl_set_get_tuple_name(
1884 __isl_keep isl_set *set);
1885 __isl_give isl_set *isl_set_set_tuple_name(
1886 __isl_take isl_set *set, const char *s);
1887 const char *isl_basic_map_get_tuple_name(
1888 __isl_keep isl_basic_map *bmap,
1889 enum isl_dim_type type);
1890 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1891 __isl_take isl_basic_map *bmap,
1892 enum isl_dim_type type, const char *s);
1893 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1894 enum isl_dim_type type);
1895 const char *isl_map_get_tuple_name(
1896 __isl_keep isl_map *map,
1897 enum isl_dim_type type);
1898 __isl_give isl_map *isl_map_set_tuple_name(
1899 __isl_take isl_map *map,
1900 enum isl_dim_type type, const char *s);
1902 As with C<isl_space_get_tuple_name>, the value returned points to
1903 an internal data structure.
1904 The identifiers, positions or names of individual dimensions can be
1905 read off using the following functions.
1907 __isl_give isl_id *isl_basic_set_get_dim_id(
1908 __isl_keep isl_basic_set *bset,
1909 enum isl_dim_type type, unsigned pos);
1910 __isl_give isl_set *isl_set_set_dim_id(
1911 __isl_take isl_set *set, enum isl_dim_type type,
1912 unsigned pos, __isl_take isl_id *id);
1913 int isl_set_has_dim_id(__isl_keep isl_set *set,
1914 enum isl_dim_type type, unsigned pos);
1915 __isl_give isl_id *isl_set_get_dim_id(
1916 __isl_keep isl_set *set, enum isl_dim_type type,
1918 int isl_basic_map_has_dim_id(
1919 __isl_keep isl_basic_map *bmap,
1920 enum isl_dim_type type, unsigned pos);
1921 __isl_give isl_map *isl_map_set_dim_id(
1922 __isl_take isl_map *map, enum isl_dim_type type,
1923 unsigned pos, __isl_take isl_id *id);
1924 int isl_map_has_dim_id(__isl_keep isl_map *map,
1925 enum isl_dim_type type, unsigned pos);
1926 __isl_give isl_id *isl_map_get_dim_id(
1927 __isl_keep isl_map *map, enum isl_dim_type type,
1929 __isl_give isl_id *isl_union_map_get_dim_id(
1930 __isl_keep isl_union_map *umap,
1931 enum isl_dim_type type, unsigned pos);
1933 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1934 enum isl_dim_type type, __isl_keep isl_id *id);
1935 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1936 enum isl_dim_type type, __isl_keep isl_id *id);
1937 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1938 enum isl_dim_type type, const char *name);
1939 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1940 enum isl_dim_type type, const char *name);
1942 const char *isl_constraint_get_dim_name(
1943 __isl_keep isl_constraint *constraint,
1944 enum isl_dim_type type, unsigned pos);
1945 const char *isl_basic_set_get_dim_name(
1946 __isl_keep isl_basic_set *bset,
1947 enum isl_dim_type type, unsigned pos);
1948 int isl_set_has_dim_name(__isl_keep isl_set *set,
1949 enum isl_dim_type type, unsigned pos);
1950 const char *isl_set_get_dim_name(
1951 __isl_keep isl_set *set,
1952 enum isl_dim_type type, unsigned pos);
1953 const char *isl_basic_map_get_dim_name(
1954 __isl_keep isl_basic_map *bmap,
1955 enum isl_dim_type type, unsigned pos);
1956 int isl_map_has_dim_name(__isl_keep isl_map *map,
1957 enum isl_dim_type type, unsigned pos);
1958 const char *isl_map_get_dim_name(
1959 __isl_keep isl_map *map,
1960 enum isl_dim_type type, unsigned pos);
1962 These functions are mostly useful to obtain the identifiers, positions
1963 or names of the parameters. Identifiers of individual dimensions are
1964 essentially only useful for printing. They are ignored by all other
1965 operations and may not be preserved across those operations.
1967 The user pointers on all parameters and tuples can be reset
1968 using the following functions.
1970 #include <isl/set.h>
1971 __isl_give isl_set *isl_set_reset_user(
1972 __isl_take isl_set *set);
1973 #include <isl/map.h>
1974 __isl_give isl_map *isl_map_reset_user(
1975 __isl_take isl_map *map);
1976 #include <isl/union_set.h>
1977 __isl_give isl_union_set *isl_union_set_reset_user(
1978 __isl_take isl_union_set *uset);
1979 #include <isl/union_map.h>
1980 __isl_give isl_union_map *isl_union_map_reset_user(
1981 __isl_take isl_union_map *umap);
1985 =head3 Unary Properties
1991 The following functions test whether the given set or relation
1992 contains any integer points. The ``plain'' variants do not perform
1993 any computations, but simply check if the given set or relation
1994 is already known to be empty.
1996 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1997 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1998 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1999 int isl_set_is_empty(__isl_keep isl_set *set);
2000 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
2001 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
2002 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
2003 int isl_map_plain_is_empty(__isl_keep isl_map *map);
2004 int isl_map_is_empty(__isl_keep isl_map *map);
2005 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
2007 =item * Universality
2009 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
2010 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
2011 int isl_set_plain_is_universe(__isl_keep isl_set *set);
2013 =item * Single-valuedness
2015 int isl_basic_map_is_single_valued(
2016 __isl_keep isl_basic_map *bmap);
2017 int isl_map_plain_is_single_valued(
2018 __isl_keep isl_map *map);
2019 int isl_map_is_single_valued(__isl_keep isl_map *map);
2020 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
2024 int isl_map_plain_is_injective(__isl_keep isl_map *map);
2025 int isl_map_is_injective(__isl_keep isl_map *map);
2026 int isl_union_map_plain_is_injective(
2027 __isl_keep isl_union_map *umap);
2028 int isl_union_map_is_injective(
2029 __isl_keep isl_union_map *umap);
2033 int isl_map_is_bijective(__isl_keep isl_map *map);
2034 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
2038 __isl_give isl_val *
2039 isl_basic_map_plain_get_val_if_fixed(
2040 __isl_keep isl_basic_map *bmap,
2041 enum isl_dim_type type, unsigned pos);
2042 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
2043 __isl_keep isl_set *set,
2044 enum isl_dim_type type, unsigned pos);
2045 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
2046 __isl_keep isl_map *map,
2047 enum isl_dim_type type, unsigned pos);
2049 If the set or relation obviously lies on a hyperplane where the given dimension
2050 has a fixed value, then return that value.
2051 Otherwise return NaN.
2055 int isl_set_dim_residue_class_val(
2056 __isl_keep isl_set *set,
2057 int pos, __isl_give isl_val **modulo,
2058 __isl_give isl_val **residue);
2060 Check if the values of the given set dimension are equal to a fixed
2061 value modulo some integer value. If so, assign the modulo to C<*modulo>
2062 and the fixed value to C<*residue>. If the given dimension attains only
2063 a single value, then assign C<0> to C<*modulo> and the fixed value to
2065 If the dimension does not attain only a single value and if no modulo
2066 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
2070 To check whether a set is a parameter domain, use this function:
2072 int isl_set_is_params(__isl_keep isl_set *set);
2073 int isl_union_set_is_params(
2074 __isl_keep isl_union_set *uset);
2078 The following functions check whether the space of the given
2079 (basic) set or relation range is a wrapped relation.
2081 #include <isl/space.h>
2082 int isl_space_is_wrapping(
2083 __isl_keep isl_space *space);
2084 int isl_space_domain_is_wrapping(
2085 __isl_keep isl_space *space);
2086 int isl_space_range_is_wrapping(
2087 __isl_keep isl_space *space);
2089 #include <isl/set.h>
2090 int isl_basic_set_is_wrapping(
2091 __isl_keep isl_basic_set *bset);
2092 int isl_set_is_wrapping(__isl_keep isl_set *set);
2094 #include <isl/map.h>
2095 int isl_map_domain_is_wrapping(
2096 __isl_keep isl_map *map);
2097 int isl_map_range_is_wrapping(
2098 __isl_keep isl_map *map);
2100 The input to C<isl_space_is_wrapping> should
2101 be the space of a set, while that of
2102 C<isl_space_domain_is_wrapping> and
2103 C<isl_space_range_is_wrapping> should be the space of a relation.
2105 =item * Internal Product
2107 int isl_basic_map_can_zip(
2108 __isl_keep isl_basic_map *bmap);
2109 int isl_map_can_zip(__isl_keep isl_map *map);
2111 Check whether the product of domain and range of the given relation
2113 i.e., whether both domain and range are nested relations.
2117 int isl_basic_map_can_curry(
2118 __isl_keep isl_basic_map *bmap);
2119 int isl_map_can_curry(__isl_keep isl_map *map);
2121 Check whether the domain of the (basic) relation is a wrapped relation.
2123 int isl_basic_map_can_uncurry(
2124 __isl_keep isl_basic_map *bmap);
2125 int isl_map_can_uncurry(__isl_keep isl_map *map);
2127 Check whether the range of the (basic) relation is a wrapped relation.
2131 =head3 Binary Properties
2137 int isl_basic_set_plain_is_equal(
2138 __isl_keep isl_basic_set *bset1,
2139 __isl_keep isl_basic_set *bset2);
2140 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2141 __isl_keep isl_set *set2);
2142 int isl_set_is_equal(__isl_keep isl_set *set1,
2143 __isl_keep isl_set *set2);
2144 int isl_union_set_is_equal(
2145 __isl_keep isl_union_set *uset1,
2146 __isl_keep isl_union_set *uset2);
2147 int isl_basic_map_is_equal(
2148 __isl_keep isl_basic_map *bmap1,
2149 __isl_keep isl_basic_map *bmap2);
2150 int isl_map_is_equal(__isl_keep isl_map *map1,
2151 __isl_keep isl_map *map2);
2152 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2153 __isl_keep isl_map *map2);
2154 int isl_union_map_is_equal(
2155 __isl_keep isl_union_map *umap1,
2156 __isl_keep isl_union_map *umap2);
2158 =item * Disjointness
2160 int isl_basic_set_is_disjoint(
2161 __isl_keep isl_basic_set *bset1,
2162 __isl_keep isl_basic_set *bset2);
2163 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2164 __isl_keep isl_set *set2);
2165 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2166 __isl_keep isl_set *set2);
2167 int isl_basic_map_is_disjoint(
2168 __isl_keep isl_basic_map *bmap1,
2169 __isl_keep isl_basic_map *bmap2);
2170 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2171 __isl_keep isl_map *map2);
2175 int isl_basic_set_is_subset(
2176 __isl_keep isl_basic_set *bset1,
2177 __isl_keep isl_basic_set *bset2);
2178 int isl_set_is_subset(__isl_keep isl_set *set1,
2179 __isl_keep isl_set *set2);
2180 int isl_set_is_strict_subset(
2181 __isl_keep isl_set *set1,
2182 __isl_keep isl_set *set2);
2183 int isl_union_set_is_subset(
2184 __isl_keep isl_union_set *uset1,
2185 __isl_keep isl_union_set *uset2);
2186 int isl_union_set_is_strict_subset(
2187 __isl_keep isl_union_set *uset1,
2188 __isl_keep isl_union_set *uset2);
2189 int isl_basic_map_is_subset(
2190 __isl_keep isl_basic_map *bmap1,
2191 __isl_keep isl_basic_map *bmap2);
2192 int isl_basic_map_is_strict_subset(
2193 __isl_keep isl_basic_map *bmap1,
2194 __isl_keep isl_basic_map *bmap2);
2195 int isl_map_is_subset(
2196 __isl_keep isl_map *map1,
2197 __isl_keep isl_map *map2);
2198 int isl_map_is_strict_subset(
2199 __isl_keep isl_map *map1,
2200 __isl_keep isl_map *map2);
2201 int isl_union_map_is_subset(
2202 __isl_keep isl_union_map *umap1,
2203 __isl_keep isl_union_map *umap2);
2204 int isl_union_map_is_strict_subset(
2205 __isl_keep isl_union_map *umap1,
2206 __isl_keep isl_union_map *umap2);
2208 Check whether the first argument is a (strict) subset of the
2213 Every comparison function returns a negative value if the first
2214 argument is considered smaller than the second, a positive value
2215 if the first argument is considered greater and zero if the two
2216 constraints are considered the same by the comparison criterion.
2218 #include <isl/constraint.h>
2219 int isl_constraint_plain_cmp(
2220 __isl_keep isl_constraint *c1,
2221 __isl_keep isl_constraint *c2);
2223 This function is useful for sorting C<isl_constraint>s.
2224 The order depends on the internal representation of the inputs.
2225 The order is fixed over different calls to the function (assuming
2226 the internal representation of the inputs has not changed), but may
2227 change over different versions of C<isl>.
2229 #include <isl/constraint.h>
2230 int isl_constraint_cmp_last_non_zero(
2231 __isl_keep isl_constraint *c1,
2232 __isl_keep isl_constraint *c2);
2234 This function can be used to sort constraints that live in the same
2235 local space. Constraints that involve ``earlier'' dimensions or
2236 that have a smaller coefficient for the shared latest dimension
2237 are considered smaller than other constraints.
2238 This function only defines a B<partial> order.
2240 #include <isl/set.h>
2241 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2242 __isl_keep isl_set *set2);
2244 This function is useful for sorting C<isl_set>s.
2245 The order depends on the internal representation of the inputs.
2246 The order is fixed over different calls to the function (assuming
2247 the internal representation of the inputs has not changed), but may
2248 change over different versions of C<isl>.
2252 =head2 Unary Operations
2258 __isl_give isl_set *isl_set_complement(
2259 __isl_take isl_set *set);
2260 __isl_give isl_map *isl_map_complement(
2261 __isl_take isl_map *map);
2265 __isl_give isl_basic_map *isl_basic_map_reverse(
2266 __isl_take isl_basic_map *bmap);
2267 __isl_give isl_map *isl_map_reverse(
2268 __isl_take isl_map *map);
2269 __isl_give isl_union_map *isl_union_map_reverse(
2270 __isl_take isl_union_map *umap);
2274 #include <isl/local_space.h>
2275 __isl_give isl_local_space *isl_local_space_domain(
2276 __isl_take isl_local_space *ls);
2277 __isl_give isl_local_space *isl_local_space_range(
2278 __isl_take isl_local_space *ls);
2280 #include <isl/set.h>
2281 __isl_give isl_basic_set *isl_basic_set_project_out(
2282 __isl_take isl_basic_set *bset,
2283 enum isl_dim_type type, unsigned first, unsigned n);
2284 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2285 enum isl_dim_type type, unsigned first, unsigned n);
2286 __isl_give isl_basic_set *isl_basic_set_params(
2287 __isl_take isl_basic_set *bset);
2288 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2290 #include <isl/map.h>
2291 __isl_give isl_basic_map *isl_basic_map_project_out(
2292 __isl_take isl_basic_map *bmap,
2293 enum isl_dim_type type, unsigned first, unsigned n);
2294 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2295 enum isl_dim_type type, unsigned first, unsigned n);
2296 __isl_give isl_basic_set *isl_basic_map_domain(
2297 __isl_take isl_basic_map *bmap);
2298 __isl_give isl_basic_set *isl_basic_map_range(
2299 __isl_take isl_basic_map *bmap);
2300 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2301 __isl_give isl_set *isl_map_domain(
2302 __isl_take isl_map *bmap);
2303 __isl_give isl_set *isl_map_range(
2304 __isl_take isl_map *map);
2306 #include <isl/union_set.h>
2307 __isl_give isl_set *isl_union_set_params(
2308 __isl_take isl_union_set *uset);
2310 #include <isl/union_map.h>
2311 __isl_give isl_union_map *isl_union_map_project_out(
2312 __isl_take isl_union_map *umap,
2313 enum isl_dim_type type, unsigned first, unsigned n);
2314 __isl_give isl_set *isl_union_map_params(
2315 __isl_take isl_union_map *umap);
2316 __isl_give isl_union_set *isl_union_map_domain(
2317 __isl_take isl_union_map *umap);
2318 __isl_give isl_union_set *isl_union_map_range(
2319 __isl_take isl_union_map *umap);
2321 The function C<isl_union_map_project_out> can only project out
2324 #include <isl/map.h>
2325 __isl_give isl_basic_map *isl_basic_map_domain_map(
2326 __isl_take isl_basic_map *bmap);
2327 __isl_give isl_basic_map *isl_basic_map_range_map(
2328 __isl_take isl_basic_map *bmap);
2329 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2330 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2332 #include <isl/union_map.h>
2333 __isl_give isl_union_map *isl_union_map_domain_map(
2334 __isl_take isl_union_map *umap);
2335 __isl_give isl_union_map *isl_union_map_range_map(
2336 __isl_take isl_union_map *umap);
2338 The functions above construct a (basic, regular or union) relation
2339 that maps (a wrapped version of) the input relation to its domain or range.
2343 __isl_give isl_basic_set *isl_basic_set_eliminate(
2344 __isl_take isl_basic_set *bset,
2345 enum isl_dim_type type,
2346 unsigned first, unsigned n);
2347 __isl_give isl_set *isl_set_eliminate(
2348 __isl_take isl_set *set, enum isl_dim_type type,
2349 unsigned first, unsigned n);
2350 __isl_give isl_basic_map *isl_basic_map_eliminate(
2351 __isl_take isl_basic_map *bmap,
2352 enum isl_dim_type type,
2353 unsigned first, unsigned n);
2354 __isl_give isl_map *isl_map_eliminate(
2355 __isl_take isl_map *map, enum isl_dim_type type,
2356 unsigned first, unsigned n);
2358 Eliminate the coefficients for the given dimensions from the constraints,
2359 without removing the dimensions.
2361 =item * Constructing a relation from a set
2363 #include <isl/local_space.h>
2364 __isl_give isl_local_space *isl_local_space_from_domain(
2365 __isl_take isl_local_space *ls);
2367 #include <isl/map.h>
2368 __isl_give isl_map *isl_map_from_domain(
2369 __isl_take isl_set *set);
2370 __isl_give isl_map *isl_map_from_range(
2371 __isl_take isl_set *set);
2373 Create a relation with the given set as domain or range.
2374 The range or domain of the created relation is a zero-dimensional
2375 flat anonymous space.
2379 __isl_give isl_basic_set *isl_basic_set_fix_si(
2380 __isl_take isl_basic_set *bset,
2381 enum isl_dim_type type, unsigned pos, int value);
2382 __isl_give isl_basic_set *isl_basic_set_fix_val(
2383 __isl_take isl_basic_set *bset,
2384 enum isl_dim_type type, unsigned pos,
2385 __isl_take isl_val *v);
2386 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2387 enum isl_dim_type type, unsigned pos, int value);
2388 __isl_give isl_set *isl_set_fix_val(
2389 __isl_take isl_set *set,
2390 enum isl_dim_type type, unsigned pos,
2391 __isl_take isl_val *v);
2392 __isl_give isl_basic_map *isl_basic_map_fix_si(
2393 __isl_take isl_basic_map *bmap,
2394 enum isl_dim_type type, unsigned pos, int value);
2395 __isl_give isl_basic_map *isl_basic_map_fix_val(
2396 __isl_take isl_basic_map *bmap,
2397 enum isl_dim_type type, unsigned pos,
2398 __isl_take isl_val *v);
2399 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2400 enum isl_dim_type type, unsigned pos, int value);
2401 __isl_give isl_map *isl_map_fix_val(
2402 __isl_take isl_map *map,
2403 enum isl_dim_type type, unsigned pos,
2404 __isl_take isl_val *v);
2406 Intersect the set or relation with the hyperplane where the given
2407 dimension has the fixed given value.
2409 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2410 __isl_take isl_basic_map *bmap,
2411 enum isl_dim_type type, unsigned pos, int value);
2412 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2413 __isl_take isl_basic_map *bmap,
2414 enum isl_dim_type type, unsigned pos, int value);
2415 __isl_give isl_set *isl_set_lower_bound_si(
2416 __isl_take isl_set *set,
2417 enum isl_dim_type type, unsigned pos, int value);
2418 __isl_give isl_set *isl_set_lower_bound_val(
2419 __isl_take isl_set *set,
2420 enum isl_dim_type type, unsigned pos,
2421 __isl_take isl_val *value);
2422 __isl_give isl_map *isl_map_lower_bound_si(
2423 __isl_take isl_map *map,
2424 enum isl_dim_type type, unsigned pos, int value);
2425 __isl_give isl_set *isl_set_upper_bound_si(
2426 __isl_take isl_set *set,
2427 enum isl_dim_type type, unsigned pos, int value);
2428 __isl_give isl_set *isl_set_upper_bound_val(
2429 __isl_take isl_set *set,
2430 enum isl_dim_type type, unsigned pos,
2431 __isl_take isl_val *value);
2432 __isl_give isl_map *isl_map_upper_bound_si(
2433 __isl_take isl_map *map,
2434 enum isl_dim_type type, unsigned pos, int value);
2436 Intersect the set or relation with the half-space where the given
2437 dimension has a value bounded by the fixed given integer value.
2439 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2440 enum isl_dim_type type1, int pos1,
2441 enum isl_dim_type type2, int pos2);
2442 __isl_give isl_basic_map *isl_basic_map_equate(
2443 __isl_take isl_basic_map *bmap,
2444 enum isl_dim_type type1, int pos1,
2445 enum isl_dim_type type2, int pos2);
2446 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2447 enum isl_dim_type type1, int pos1,
2448 enum isl_dim_type type2, int pos2);
2450 Intersect the set or relation with the hyperplane where the given
2451 dimensions are equal to each other.
2453 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2454 enum isl_dim_type type1, int pos1,
2455 enum isl_dim_type type2, int pos2);
2457 Intersect the relation with the hyperplane where the given
2458 dimensions have opposite values.
2460 __isl_give isl_map *isl_map_order_le(
2461 __isl_take isl_map *map,
2462 enum isl_dim_type type1, int pos1,
2463 enum isl_dim_type type2, int pos2);
2464 __isl_give isl_basic_map *isl_basic_map_order_ge(
2465 __isl_take isl_basic_map *bmap,
2466 enum isl_dim_type type1, int pos1,
2467 enum isl_dim_type type2, int pos2);
2468 __isl_give isl_map *isl_map_order_ge(
2469 __isl_take isl_map *map,
2470 enum isl_dim_type type1, int pos1,
2471 enum isl_dim_type type2, int pos2);
2472 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2473 enum isl_dim_type type1, int pos1,
2474 enum isl_dim_type type2, int pos2);
2475 __isl_give isl_basic_map *isl_basic_map_order_gt(
2476 __isl_take isl_basic_map *bmap,
2477 enum isl_dim_type type1, int pos1,
2478 enum isl_dim_type type2, int pos2);
2479 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2480 enum isl_dim_type type1, int pos1,
2481 enum isl_dim_type type2, int pos2);
2483 Intersect the relation with the half-space where the given
2484 dimensions satisfy the given ordering.
2488 __isl_give isl_map *isl_set_identity(
2489 __isl_take isl_set *set);
2490 __isl_give isl_union_map *isl_union_set_identity(
2491 __isl_take isl_union_set *uset);
2493 Construct an identity relation on the given (union) set.
2497 __isl_give isl_basic_set *isl_basic_map_deltas(
2498 __isl_take isl_basic_map *bmap);
2499 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2500 __isl_give isl_union_set *isl_union_map_deltas(
2501 __isl_take isl_union_map *umap);
2503 These functions return a (basic) set containing the differences
2504 between image elements and corresponding domain elements in the input.
2506 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2507 __isl_take isl_basic_map *bmap);
2508 __isl_give isl_map *isl_map_deltas_map(
2509 __isl_take isl_map *map);
2510 __isl_give isl_union_map *isl_union_map_deltas_map(
2511 __isl_take isl_union_map *umap);
2513 The functions above construct a (basic, regular or union) relation
2514 that maps (a wrapped version of) the input relation to its delta set.
2518 Simplify the representation of a set or relation by trying
2519 to combine pairs of basic sets or relations into a single
2520 basic set or relation.
2522 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2523 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2524 __isl_give isl_union_set *isl_union_set_coalesce(
2525 __isl_take isl_union_set *uset);
2526 __isl_give isl_union_map *isl_union_map_coalesce(
2527 __isl_take isl_union_map *umap);
2529 One of the methods for combining pairs of basic sets or relations
2530 can result in coefficients that are much larger than those that appear
2531 in the constraints of the input. By default, the coefficients are
2532 not allowed to grow larger, but this can be changed by unsetting
2533 the following option.
2535 int isl_options_set_coalesce_bounded_wrapping(
2536 isl_ctx *ctx, int val);
2537 int isl_options_get_coalesce_bounded_wrapping(
2540 =item * Detecting equalities
2542 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2543 __isl_take isl_basic_set *bset);
2544 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2545 __isl_take isl_basic_map *bmap);
2546 __isl_give isl_set *isl_set_detect_equalities(
2547 __isl_take isl_set *set);
2548 __isl_give isl_map *isl_map_detect_equalities(
2549 __isl_take isl_map *map);
2550 __isl_give isl_union_set *isl_union_set_detect_equalities(
2551 __isl_take isl_union_set *uset);
2552 __isl_give isl_union_map *isl_union_map_detect_equalities(
2553 __isl_take isl_union_map *umap);
2555 Simplify the representation of a set or relation by detecting implicit
2558 =item * Removing redundant constraints
2560 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2561 __isl_take isl_basic_set *bset);
2562 __isl_give isl_set *isl_set_remove_redundancies(
2563 __isl_take isl_set *set);
2564 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2565 __isl_take isl_basic_map *bmap);
2566 __isl_give isl_map *isl_map_remove_redundancies(
2567 __isl_take isl_map *map);
2571 __isl_give isl_basic_set *isl_set_convex_hull(
2572 __isl_take isl_set *set);
2573 __isl_give isl_basic_map *isl_map_convex_hull(
2574 __isl_take isl_map *map);
2576 If the input set or relation has any existentially quantified
2577 variables, then the result of these operations is currently undefined.
2581 #include <isl/set.h>
2582 __isl_give isl_basic_set *
2583 isl_set_unshifted_simple_hull(
2584 __isl_take isl_set *set);
2585 __isl_give isl_basic_set *isl_set_simple_hull(
2586 __isl_take isl_set *set);
2587 __isl_give isl_basic_set *
2588 isl_set_unshifted_simple_hull_from_set_list(
2589 __isl_take isl_set *set,
2590 __isl_take isl_set_list *list);
2592 #include <isl/map.h>
2593 __isl_give isl_basic_map *
2594 isl_map_unshifted_simple_hull(
2595 __isl_take isl_map *map);
2596 __isl_give isl_basic_map *isl_map_simple_hull(
2597 __isl_take isl_map *map);
2599 #include <isl/union_map.h>
2600 __isl_give isl_union_map *isl_union_map_simple_hull(
2601 __isl_take isl_union_map *umap);
2603 These functions compute a single basic set or relation
2604 that contains the whole input set or relation.
2605 In particular, the output is described by translates
2606 of the constraints describing the basic sets or relations in the input.
2607 In case of C<isl_set_unshifted_simple_hull>, only the original
2608 constraints are used, without any translation.
2609 In case of C<isl_set_unshifted_simple_hull_from_set_list>, the
2610 constraints are taken from the elements of the second argument.
2614 (See \autoref{s:simple hull}.)
2620 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2621 __isl_take isl_basic_set *bset);
2622 __isl_give isl_basic_set *isl_set_affine_hull(
2623 __isl_take isl_set *set);
2624 __isl_give isl_union_set *isl_union_set_affine_hull(
2625 __isl_take isl_union_set *uset);
2626 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2627 __isl_take isl_basic_map *bmap);
2628 __isl_give isl_basic_map *isl_map_affine_hull(
2629 __isl_take isl_map *map);
2630 __isl_give isl_union_map *isl_union_map_affine_hull(
2631 __isl_take isl_union_map *umap);
2633 In case of union sets and relations, the affine hull is computed
2636 =item * Polyhedral hull
2638 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2639 __isl_take isl_set *set);
2640 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2641 __isl_take isl_map *map);
2642 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2643 __isl_take isl_union_set *uset);
2644 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2645 __isl_take isl_union_map *umap);
2647 These functions compute a single basic set or relation
2648 not involving any existentially quantified variables
2649 that contains the whole input set or relation.
2650 In case of union sets and relations, the polyhedral hull is computed
2653 =item * Other approximations
2655 __isl_give isl_basic_set *
2656 isl_basic_set_drop_constraints_involving_dims(
2657 __isl_take isl_basic_set *bset,
2658 enum isl_dim_type type,
2659 unsigned first, unsigned n);
2660 __isl_give isl_basic_map *
2661 isl_basic_map_drop_constraints_involving_dims(
2662 __isl_take isl_basic_map *bmap,
2663 enum isl_dim_type type,
2664 unsigned first, unsigned n);
2665 __isl_give isl_basic_set *
2666 isl_basic_set_drop_constraints_not_involving_dims(
2667 __isl_take isl_basic_set *bset,
2668 enum isl_dim_type type,
2669 unsigned first, unsigned n);
2670 __isl_give isl_set *
2671 isl_set_drop_constraints_involving_dims(
2672 __isl_take isl_set *set,
2673 enum isl_dim_type type,
2674 unsigned first, unsigned n);
2675 __isl_give isl_map *
2676 isl_map_drop_constraints_involving_dims(
2677 __isl_take isl_map *map,
2678 enum isl_dim_type type,
2679 unsigned first, unsigned n);
2681 These functions drop any constraints (not) involving the specified dimensions.
2682 Note that the result depends on the representation of the input.
2686 __isl_give isl_basic_set *isl_basic_set_sample(
2687 __isl_take isl_basic_set *bset);
2688 __isl_give isl_basic_set *isl_set_sample(
2689 __isl_take isl_set *set);
2690 __isl_give isl_basic_map *isl_basic_map_sample(
2691 __isl_take isl_basic_map *bmap);
2692 __isl_give isl_basic_map *isl_map_sample(
2693 __isl_take isl_map *map);
2695 If the input (basic) set or relation is non-empty, then return
2696 a singleton subset of the input. Otherwise, return an empty set.
2698 =item * Optimization
2700 #include <isl/ilp.h>
2701 __isl_give isl_val *isl_basic_set_max_val(
2702 __isl_keep isl_basic_set *bset,
2703 __isl_keep isl_aff *obj);
2704 __isl_give isl_val *isl_set_min_val(
2705 __isl_keep isl_set *set,
2706 __isl_keep isl_aff *obj);
2707 __isl_give isl_val *isl_set_max_val(
2708 __isl_keep isl_set *set,
2709 __isl_keep isl_aff *obj);
2711 Compute the minimum or maximum of the integer affine expression C<obj>
2712 over the points in C<set>, returning the result in C<opt>.
2713 The result is C<NULL> in case of an error, the optimal value in case
2714 there is one, negative infinity or infinity if the problem is unbounded and
2715 NaN if the problem is empty.
2717 =item * Parametric optimization
2719 __isl_give isl_pw_aff *isl_set_dim_min(
2720 __isl_take isl_set *set, int pos);
2721 __isl_give isl_pw_aff *isl_set_dim_max(
2722 __isl_take isl_set *set, int pos);
2723 __isl_give isl_pw_aff *isl_map_dim_max(
2724 __isl_take isl_map *map, int pos);
2726 Compute the minimum or maximum of the given set or output dimension
2727 as a function of the parameters (and input dimensions), but independently
2728 of the other set or output dimensions.
2729 For lexicographic optimization, see L<"Lexicographic Optimization">.
2733 The following functions compute either the set of (rational) coefficient
2734 values of valid constraints for the given set or the set of (rational)
2735 values satisfying the constraints with coefficients from the given set.
2736 Internally, these two sets of functions perform essentially the
2737 same operations, except that the set of coefficients is assumed to
2738 be a cone, while the set of values may be any polyhedron.
2739 The current implementation is based on the Farkas lemma and
2740 Fourier-Motzkin elimination, but this may change or be made optional
2741 in future. In particular, future implementations may use different
2742 dualization algorithms or skip the elimination step.
2744 __isl_give isl_basic_set *isl_basic_set_coefficients(
2745 __isl_take isl_basic_set *bset);
2746 __isl_give isl_basic_set *isl_set_coefficients(
2747 __isl_take isl_set *set);
2748 __isl_give isl_union_set *isl_union_set_coefficients(
2749 __isl_take isl_union_set *bset);
2750 __isl_give isl_basic_set *isl_basic_set_solutions(
2751 __isl_take isl_basic_set *bset);
2752 __isl_give isl_basic_set *isl_set_solutions(
2753 __isl_take isl_set *set);
2754 __isl_give isl_union_set *isl_union_set_solutions(
2755 __isl_take isl_union_set *bset);
2759 __isl_give isl_map *isl_map_fixed_power_val(
2760 __isl_take isl_map *map,
2761 __isl_take isl_val *exp);
2762 __isl_give isl_union_map *
2763 isl_union_map_fixed_power_val(
2764 __isl_take isl_union_map *umap,
2765 __isl_take isl_val *exp);
2767 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2768 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2769 of C<map> is computed.
2771 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2773 __isl_give isl_union_map *isl_union_map_power(
2774 __isl_take isl_union_map *umap, int *exact);
2776 Compute a parametric representation for all positive powers I<k> of C<map>.
2777 The result maps I<k> to a nested relation corresponding to the
2778 I<k>th power of C<map>.
2779 The result may be an overapproximation. If the result is known to be exact,
2780 then C<*exact> is set to C<1>.
2782 =item * Transitive closure
2784 __isl_give isl_map *isl_map_transitive_closure(
2785 __isl_take isl_map *map, int *exact);
2786 __isl_give isl_union_map *isl_union_map_transitive_closure(
2787 __isl_take isl_union_map *umap, int *exact);
2789 Compute the transitive closure of C<map>.
2790 The result may be an overapproximation. If the result is known to be exact,
2791 then C<*exact> is set to C<1>.
2793 =item * Reaching path lengths
2795 __isl_give isl_map *isl_map_reaching_path_lengths(
2796 __isl_take isl_map *map, int *exact);
2798 Compute a relation that maps each element in the range of C<map>
2799 to the lengths of all paths composed of edges in C<map> that
2800 end up in the given element.
2801 The result may be an overapproximation. If the result is known to be exact,
2802 then C<*exact> is set to C<1>.
2803 To compute the I<maximal> path length, the resulting relation
2804 should be postprocessed by C<isl_map_lexmax>.
2805 In particular, if the input relation is a dependence relation
2806 (mapping sources to sinks), then the maximal path length corresponds
2807 to the free schedule.
2808 Note, however, that C<isl_map_lexmax> expects the maximum to be
2809 finite, so if the path lengths are unbounded (possibly due to
2810 the overapproximation), then you will get an error message.
2814 #include <isl/space.h>
2815 __isl_give isl_space *isl_space_wrap(
2816 __isl_take isl_space *space);
2817 __isl_give isl_space *isl_space_unwrap(
2818 __isl_take isl_space *space);
2820 #include <isl/set.h>
2821 __isl_give isl_basic_map *isl_basic_set_unwrap(
2822 __isl_take isl_basic_set *bset);
2823 __isl_give isl_map *isl_set_unwrap(
2824 __isl_take isl_set *set);
2826 #include <isl/map.h>
2827 __isl_give isl_basic_set *isl_basic_map_wrap(
2828 __isl_take isl_basic_map *bmap);
2829 __isl_give isl_set *isl_map_wrap(
2830 __isl_take isl_map *map);
2832 #include <isl/union_set.h>
2833 __isl_give isl_union_map *isl_union_set_unwrap(
2834 __isl_take isl_union_set *uset);
2836 #include <isl/union_map.h>
2837 __isl_give isl_union_set *isl_union_map_wrap(
2838 __isl_take isl_union_map *umap);
2840 The input to C<isl_space_unwrap> should
2841 be the space of a set, while that of
2842 C<isl_space_wrap> should be the space of a relation.
2843 Conversely, the output of C<isl_space_unwrap> is the space
2844 of a relation, while that of C<isl_space_wrap> is the space of a set.
2848 Remove any internal structure of domain (and range) of the given
2849 set or relation. If there is any such internal structure in the input,
2850 then the name of the space is also removed.
2852 #include <isl/local_space.h>
2853 __isl_give isl_local_space *
2854 isl_local_space_flatten_domain(
2855 __isl_take isl_local_space *ls);
2856 __isl_give isl_local_space *
2857 isl_local_space_flatten_range(
2858 __isl_take isl_local_space *ls);
2860 #include <isl/set.h>
2861 __isl_give isl_basic_set *isl_basic_set_flatten(
2862 __isl_take isl_basic_set *bset);
2863 __isl_give isl_set *isl_set_flatten(
2864 __isl_take isl_set *set);
2866 #include <isl/map.h>
2867 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2868 __isl_take isl_basic_map *bmap);
2869 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2870 __isl_take isl_basic_map *bmap);
2871 __isl_give isl_map *isl_map_flatten_range(
2872 __isl_take isl_map *map);
2873 __isl_give isl_map *isl_map_flatten_domain(
2874 __isl_take isl_map *map);
2875 __isl_give isl_basic_map *isl_basic_map_flatten(
2876 __isl_take isl_basic_map *bmap);
2877 __isl_give isl_map *isl_map_flatten(
2878 __isl_take isl_map *map);
2880 #include <isl/map.h>
2881 __isl_give isl_map *isl_set_flatten_map(
2882 __isl_take isl_set *set);
2884 The function above constructs a relation
2885 that maps the input set to a flattened version of the set.
2889 Lift the input set to a space with extra dimensions corresponding
2890 to the existentially quantified variables in the input.
2891 In particular, the result lives in a wrapped map where the domain
2892 is the original space and the range corresponds to the original
2893 existentially quantified variables.
2895 __isl_give isl_basic_set *isl_basic_set_lift(
2896 __isl_take isl_basic_set *bset);
2897 __isl_give isl_set *isl_set_lift(
2898 __isl_take isl_set *set);
2899 __isl_give isl_union_set *isl_union_set_lift(
2900 __isl_take isl_union_set *uset);
2902 Given a local space that contains the existentially quantified
2903 variables of a set, a basic relation that, when applied to
2904 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2905 can be constructed using the following function.
2907 #include <isl/local_space.h>
2908 __isl_give isl_basic_map *isl_local_space_lifting(
2909 __isl_take isl_local_space *ls);
2911 =item * Internal Product
2913 __isl_give isl_basic_map *isl_basic_map_zip(
2914 __isl_take isl_basic_map *bmap);
2915 __isl_give isl_map *isl_map_zip(
2916 __isl_take isl_map *map);
2917 __isl_give isl_union_map *isl_union_map_zip(
2918 __isl_take isl_union_map *umap);
2920 Given a relation with nested relations for domain and range,
2921 interchange the range of the domain with the domain of the range.
2925 __isl_give isl_basic_map *isl_basic_map_curry(
2926 __isl_take isl_basic_map *bmap);
2927 __isl_give isl_basic_map *isl_basic_map_uncurry(
2928 __isl_take isl_basic_map *bmap);
2929 __isl_give isl_map *isl_map_curry(
2930 __isl_take isl_map *map);
2931 __isl_give isl_map *isl_map_uncurry(
2932 __isl_take isl_map *map);
2933 __isl_give isl_union_map *isl_union_map_curry(
2934 __isl_take isl_union_map *umap);
2935 __isl_give isl_union_map *isl_union_map_uncurry(
2936 __isl_take isl_union_map *umap);
2938 Given a relation with a nested relation for domain,
2939 the C<curry> functions
2940 move the range of the nested relation out of the domain
2941 and use it as the domain of a nested relation in the range,
2942 with the original range as range of this nested relation.
2943 The C<uncurry> functions perform the inverse operation.
2945 =item * Aligning parameters
2947 __isl_give isl_basic_set *isl_basic_set_align_params(
2948 __isl_take isl_basic_set *bset,
2949 __isl_take isl_space *model);
2950 __isl_give isl_set *isl_set_align_params(
2951 __isl_take isl_set *set,
2952 __isl_take isl_space *model);
2953 __isl_give isl_basic_map *isl_basic_map_align_params(
2954 __isl_take isl_basic_map *bmap,
2955 __isl_take isl_space *model);
2956 __isl_give isl_map *isl_map_align_params(
2957 __isl_take isl_map *map,
2958 __isl_take isl_space *model);
2960 Change the order of the parameters of the given set or relation
2961 such that the first parameters match those of C<model>.
2962 This may involve the introduction of extra parameters.
2963 All parameters need to be named.
2965 =item * Dimension manipulation
2967 #include <isl/local_space.h>
2968 __isl_give isl_local_space *isl_local_space_add_dims(
2969 __isl_take isl_local_space *ls,
2970 enum isl_dim_type type, unsigned n);
2971 __isl_give isl_local_space *isl_local_space_insert_dims(
2972 __isl_take isl_local_space *ls,
2973 enum isl_dim_type type, unsigned first, unsigned n);
2974 __isl_give isl_local_space *isl_local_space_drop_dims(
2975 __isl_take isl_local_space *ls,
2976 enum isl_dim_type type, unsigned first, unsigned n);
2978 #include <isl/set.h>
2979 __isl_give isl_basic_set *isl_basic_set_add_dims(
2980 __isl_take isl_basic_set *bset,
2981 enum isl_dim_type type, unsigned n);
2982 __isl_give isl_set *isl_set_add_dims(
2983 __isl_take isl_set *set,
2984 enum isl_dim_type type, unsigned n);
2985 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2986 __isl_take isl_basic_set *bset,
2987 enum isl_dim_type type, unsigned pos,
2989 __isl_give isl_set *isl_set_insert_dims(
2990 __isl_take isl_set *set,
2991 enum isl_dim_type type, unsigned pos, unsigned n);
2992 __isl_give isl_basic_set *isl_basic_set_move_dims(
2993 __isl_take isl_basic_set *bset,
2994 enum isl_dim_type dst_type, unsigned dst_pos,
2995 enum isl_dim_type src_type, unsigned src_pos,
2997 __isl_give isl_set *isl_set_move_dims(
2998 __isl_take isl_set *set,
2999 enum isl_dim_type dst_type, unsigned dst_pos,
3000 enum isl_dim_type src_type, unsigned src_pos,
3003 #include <isl/map.h>
3004 __isl_give isl_map *isl_map_add_dims(
3005 __isl_take isl_map *map,
3006 enum isl_dim_type type, unsigned n);
3007 __isl_give isl_basic_map *isl_basic_map_insert_dims(
3008 __isl_take isl_basic_map *bmap,
3009 enum isl_dim_type type, unsigned pos,
3011 __isl_give isl_map *isl_map_insert_dims(
3012 __isl_take isl_map *map,
3013 enum isl_dim_type type, unsigned pos, unsigned n);
3014 __isl_give isl_basic_map *isl_basic_map_move_dims(
3015 __isl_take isl_basic_map *bmap,
3016 enum isl_dim_type dst_type, unsigned dst_pos,
3017 enum isl_dim_type src_type, unsigned src_pos,
3019 __isl_give isl_map *isl_map_move_dims(
3020 __isl_take isl_map *map,
3021 enum isl_dim_type dst_type, unsigned dst_pos,
3022 enum isl_dim_type src_type, unsigned src_pos,
3025 It is usually not advisable to directly change the (input or output)
3026 space of a set or a relation as this removes the name and the internal
3027 structure of the space. However, the above functions can be useful
3028 to add new parameters, assuming
3029 C<isl_set_align_params> and C<isl_map_align_params>
3034 =head2 Binary Operations
3036 The two arguments of a binary operation not only need to live
3037 in the same C<isl_ctx>, they currently also need to have
3038 the same (number of) parameters.
3040 =head3 Basic Operations
3044 =item * Intersection
3046 #include <isl/local_space.h>
3047 __isl_give isl_local_space *isl_local_space_intersect(
3048 __isl_take isl_local_space *ls1,
3049 __isl_take isl_local_space *ls2);
3051 #include <isl/set.h>
3052 __isl_give isl_basic_set *isl_basic_set_intersect_params(
3053 __isl_take isl_basic_set *bset1,
3054 __isl_take isl_basic_set *bset2);
3055 __isl_give isl_basic_set *isl_basic_set_intersect(
3056 __isl_take isl_basic_set *bset1,
3057 __isl_take isl_basic_set *bset2);
3058 __isl_give isl_basic_set *isl_basic_set_list_intersect(
3059 __isl_take struct isl_basic_set_list *list);
3060 __isl_give isl_set *isl_set_intersect_params(
3061 __isl_take isl_set *set,
3062 __isl_take isl_set *params);
3063 __isl_give isl_set *isl_set_intersect(
3064 __isl_take isl_set *set1,
3065 __isl_take isl_set *set2);
3067 #include <isl/map.h>
3068 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
3069 __isl_take isl_basic_map *bmap,
3070 __isl_take isl_basic_set *bset);
3071 __isl_give isl_basic_map *isl_basic_map_intersect_range(
3072 __isl_take isl_basic_map *bmap,
3073 __isl_take isl_basic_set *bset);
3074 __isl_give isl_basic_map *isl_basic_map_intersect(
3075 __isl_take isl_basic_map *bmap1,
3076 __isl_take isl_basic_map *bmap2);
3077 __isl_give isl_map *isl_map_intersect_params(
3078 __isl_take isl_map *map,
3079 __isl_take isl_set *params);
3080 __isl_give isl_map *isl_map_intersect_domain(
3081 __isl_take isl_map *map,
3082 __isl_take isl_set *set);
3083 __isl_give isl_map *isl_map_intersect_range(
3084 __isl_take isl_map *map,
3085 __isl_take isl_set *set);
3086 __isl_give isl_map *isl_map_intersect(
3087 __isl_take isl_map *map1,
3088 __isl_take isl_map *map2);
3090 #include <isl/union_set.h>
3091 __isl_give isl_union_set *isl_union_set_intersect_params(
3092 __isl_take isl_union_set *uset,
3093 __isl_take isl_set *set);
3094 __isl_give isl_union_set *isl_union_set_intersect(
3095 __isl_take isl_union_set *uset1,
3096 __isl_take isl_union_set *uset2);
3098 #include <isl/union_map.h>
3099 __isl_give isl_union_map *isl_union_map_intersect_params(
3100 __isl_take isl_union_map *umap,
3101 __isl_take isl_set *set);
3102 __isl_give isl_union_map *isl_union_map_intersect_domain(
3103 __isl_take isl_union_map *umap,
3104 __isl_take isl_union_set *uset);
3105 __isl_give isl_union_map *isl_union_map_intersect_range(
3106 __isl_take isl_union_map *umap,
3107 __isl_take isl_union_set *uset);
3108 __isl_give isl_union_map *isl_union_map_intersect(
3109 __isl_take isl_union_map *umap1,
3110 __isl_take isl_union_map *umap2);
3112 The second argument to the C<_params> functions needs to be
3113 a parametric (basic) set. For the other functions, a parametric set
3114 for either argument is only allowed if the other argument is
3115 a parametric set as well.
3116 The list passed to C<isl_basic_set_list_intersect> needs to have
3117 at least one element and all elements need to live in the same space.
3121 __isl_give isl_set *isl_basic_set_union(
3122 __isl_take isl_basic_set *bset1,
3123 __isl_take isl_basic_set *bset2);
3124 __isl_give isl_map *isl_basic_map_union(
3125 __isl_take isl_basic_map *bmap1,
3126 __isl_take isl_basic_map *bmap2);
3127 __isl_give isl_set *isl_set_union(
3128 __isl_take isl_set *set1,
3129 __isl_take isl_set *set2);
3130 __isl_give isl_map *isl_map_union(
3131 __isl_take isl_map *map1,
3132 __isl_take isl_map *map2);
3133 __isl_give isl_union_set *isl_union_set_union(
3134 __isl_take isl_union_set *uset1,
3135 __isl_take isl_union_set *uset2);
3136 __isl_give isl_union_map *isl_union_map_union(
3137 __isl_take isl_union_map *umap1,
3138 __isl_take isl_union_map *umap2);
3140 =item * Set difference
3142 __isl_give isl_set *isl_set_subtract(
3143 __isl_take isl_set *set1,
3144 __isl_take isl_set *set2);
3145 __isl_give isl_map *isl_map_subtract(
3146 __isl_take isl_map *map1,
3147 __isl_take isl_map *map2);
3148 __isl_give isl_map *isl_map_subtract_domain(
3149 __isl_take isl_map *map,
3150 __isl_take isl_set *dom);
3151 __isl_give isl_map *isl_map_subtract_range(
3152 __isl_take isl_map *map,
3153 __isl_take isl_set *dom);
3154 __isl_give isl_union_set *isl_union_set_subtract(
3155 __isl_take isl_union_set *uset1,
3156 __isl_take isl_union_set *uset2);
3157 __isl_give isl_union_map *isl_union_map_subtract(
3158 __isl_take isl_union_map *umap1,
3159 __isl_take isl_union_map *umap2);
3160 __isl_give isl_union_map *isl_union_map_subtract_domain(
3161 __isl_take isl_union_map *umap,
3162 __isl_take isl_union_set *dom);
3163 __isl_give isl_union_map *isl_union_map_subtract_range(
3164 __isl_take isl_union_map *umap,
3165 __isl_take isl_union_set *dom);
3169 __isl_give isl_basic_set *isl_basic_set_apply(
3170 __isl_take isl_basic_set *bset,
3171 __isl_take isl_basic_map *bmap);
3172 __isl_give isl_set *isl_set_apply(
3173 __isl_take isl_set *set,
3174 __isl_take isl_map *map);
3175 __isl_give isl_union_set *isl_union_set_apply(
3176 __isl_take isl_union_set *uset,
3177 __isl_take isl_union_map *umap);
3178 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3179 __isl_take isl_basic_map *bmap1,
3180 __isl_take isl_basic_map *bmap2);
3181 __isl_give isl_basic_map *isl_basic_map_apply_range(
3182 __isl_take isl_basic_map *bmap1,
3183 __isl_take isl_basic_map *bmap2);
3184 __isl_give isl_map *isl_map_apply_domain(
3185 __isl_take isl_map *map1,
3186 __isl_take isl_map *map2);
3187 __isl_give isl_union_map *isl_union_map_apply_domain(
3188 __isl_take isl_union_map *umap1,
3189 __isl_take isl_union_map *umap2);
3190 __isl_give isl_map *isl_map_apply_range(
3191 __isl_take isl_map *map1,
3192 __isl_take isl_map *map2);
3193 __isl_give isl_union_map *isl_union_map_apply_range(
3194 __isl_take isl_union_map *umap1,
3195 __isl_take isl_union_map *umap2);
3199 #include <isl/set.h>
3200 __isl_give isl_basic_set *
3201 isl_basic_set_preimage_multi_aff(
3202 __isl_take isl_basic_set *bset,
3203 __isl_take isl_multi_aff *ma);
3204 __isl_give isl_set *isl_set_preimage_multi_aff(
3205 __isl_take isl_set *set,
3206 __isl_take isl_multi_aff *ma);
3207 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3208 __isl_take isl_set *set,
3209 __isl_take isl_pw_multi_aff *pma);
3210 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
3211 __isl_take isl_set *set,
3212 __isl_take isl_multi_pw_aff *mpa);
3214 #include <isl/union_set.h>
3215 __isl_give isl_union_set *
3216 isl_union_set_preimage_multi_aff(
3217 __isl_take isl_union_set *uset,
3218 __isl_take isl_multi_aff *ma);
3219 __isl_give isl_union_set *
3220 isl_union_set_preimage_pw_multi_aff(
3221 __isl_take isl_union_set *uset,
3222 __isl_take isl_pw_multi_aff *pma);
3223 __isl_give isl_union_set *
3224 isl_union_set_preimage_union_pw_multi_aff(
3225 __isl_take isl_union_set *uset,
3226 __isl_take isl_union_pw_multi_aff *upma);
3228 #include <isl/map.h>
3229 __isl_give isl_basic_map *
3230 isl_basic_map_preimage_domain_multi_aff(
3231 __isl_take isl_basic_map *bmap,
3232 __isl_take isl_multi_aff *ma);
3233 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3234 __isl_take isl_map *map,
3235 __isl_take isl_multi_aff *ma);
3236 __isl_give isl_map *isl_map_preimage_range_multi_aff(
3237 __isl_take isl_map *map,
3238 __isl_take isl_multi_aff *ma);
3239 __isl_give isl_map *
3240 isl_map_preimage_domain_pw_multi_aff(
3241 __isl_take isl_map *map,
3242 __isl_take isl_pw_multi_aff *pma);
3243 __isl_give isl_map *
3244 isl_map_preimage_range_pw_multi_aff(
3245 __isl_take isl_map *map,
3246 __isl_take isl_pw_multi_aff *pma);
3247 __isl_give isl_map *
3248 isl_map_preimage_domain_multi_pw_aff(
3249 __isl_take isl_map *map,
3250 __isl_take isl_multi_pw_aff *mpa);
3251 __isl_give isl_basic_map *
3252 isl_basic_map_preimage_range_multi_aff(
3253 __isl_take isl_basic_map *bmap,
3254 __isl_take isl_multi_aff *ma);
3256 #include <isl/union_map.h>
3257 __isl_give isl_union_map *
3258 isl_union_map_preimage_domain_multi_aff(
3259 __isl_take isl_union_map *umap,
3260 __isl_take isl_multi_aff *ma);
3261 __isl_give isl_union_map *
3262 isl_union_map_preimage_range_multi_aff(
3263 __isl_take isl_union_map *umap,
3264 __isl_take isl_multi_aff *ma);
3265 __isl_give isl_union_map *
3266 isl_union_map_preimage_domain_pw_multi_aff(
3267 __isl_take isl_union_map *umap,
3268 __isl_take isl_pw_multi_aff *pma);
3269 __isl_give isl_union_map *
3270 isl_union_map_preimage_range_pw_multi_aff(
3271 __isl_take isl_union_map *umap,
3272 __isl_take isl_pw_multi_aff *pma);
3273 __isl_give isl_union_map *
3274 isl_union_map_preimage_domain_union_pw_multi_aff(
3275 __isl_take isl_union_map *umap,
3276 __isl_take isl_union_pw_multi_aff *upma);
3277 __isl_give isl_union_map *
3278 isl_union_map_preimage_range_union_pw_multi_aff(
3279 __isl_take isl_union_map *umap,
3280 __isl_take isl_union_pw_multi_aff *upma);
3282 These functions compute the preimage of the given set or map domain/range under
3283 the given function. In other words, the expression is plugged
3284 into the set description or into the domain/range of the map.
3285 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3286 L</"Piecewise Multiple Quasi Affine Expressions">.
3288 =item * Cartesian Product
3290 #include <isl/space.h>
3291 __isl_give isl_space *isl_space_product(
3292 __isl_take isl_space *space1,
3293 __isl_take isl_space *space2);
3294 __isl_give isl_space *isl_space_domain_product(
3295 __isl_take isl_space *space1,
3296 __isl_take isl_space *space2);
3297 __isl_give isl_space *isl_space_range_product(
3298 __isl_take isl_space *space1,
3299 __isl_take isl_space *space2);
3302 C<isl_space_product>, C<isl_space_domain_product>
3303 and C<isl_space_range_product> take pairs or relation spaces and
3304 produce a single relations space, where either the domain, the range
3305 or both domain and range are wrapped spaces of relations between
3306 the domains and/or ranges of the input spaces.
3307 If the product is only constructed over the domain or the range
3308 then the ranges or the domains of the inputs should be the same.
3309 The function C<isl_space_product> also accepts a pair of set spaces,
3310 in which case it returns a wrapped space of a relation between the
3313 #include <isl/set.h>
3314 __isl_give isl_set *isl_set_product(
3315 __isl_take isl_set *set1,
3316 __isl_take isl_set *set2);
3318 #include <isl/map.h>
3319 __isl_give isl_basic_map *isl_basic_map_domain_product(
3320 __isl_take isl_basic_map *bmap1,
3321 __isl_take isl_basic_map *bmap2);
3322 __isl_give isl_basic_map *isl_basic_map_range_product(
3323 __isl_take isl_basic_map *bmap1,
3324 __isl_take isl_basic_map *bmap2);
3325 __isl_give isl_basic_map *isl_basic_map_product(
3326 __isl_take isl_basic_map *bmap1,
3327 __isl_take isl_basic_map *bmap2);
3328 __isl_give isl_map *isl_map_domain_product(
3329 __isl_take isl_map *map1,
3330 __isl_take isl_map *map2);
3331 __isl_give isl_map *isl_map_range_product(
3332 __isl_take isl_map *map1,
3333 __isl_take isl_map *map2);
3334 __isl_give isl_map *isl_map_product(
3335 __isl_take isl_map *map1,
3336 __isl_take isl_map *map2);
3338 #include <isl/union_set.h>
3339 __isl_give isl_union_set *isl_union_set_product(
3340 __isl_take isl_union_set *uset1,
3341 __isl_take isl_union_set *uset2);
3343 #include <isl/union_map.h>
3344 __isl_give isl_union_map *isl_union_map_domain_product(
3345 __isl_take isl_union_map *umap1,
3346 __isl_take isl_union_map *umap2);
3347 __isl_give isl_union_map *isl_union_map_range_product(
3348 __isl_take isl_union_map *umap1,
3349 __isl_take isl_union_map *umap2);
3350 __isl_give isl_union_map *isl_union_map_product(
3351 __isl_take isl_union_map *umap1,
3352 __isl_take isl_union_map *umap2);
3354 The above functions compute the cross product of the given
3355 sets or relations. The domains and ranges of the results
3356 are wrapped maps between domains and ranges of the inputs.
3357 To obtain a ``flat'' product, use the following functions
3360 __isl_give isl_basic_set *isl_basic_set_flat_product(
3361 __isl_take isl_basic_set *bset1,
3362 __isl_take isl_basic_set *bset2);
3363 __isl_give isl_set *isl_set_flat_product(
3364 __isl_take isl_set *set1,
3365 __isl_take isl_set *set2);
3366 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3367 __isl_take isl_basic_map *bmap1,
3368 __isl_take isl_basic_map *bmap2);
3369 __isl_give isl_map *isl_map_flat_domain_product(
3370 __isl_take isl_map *map1,
3371 __isl_take isl_map *map2);
3372 __isl_give isl_map *isl_map_flat_range_product(
3373 __isl_take isl_map *map1,
3374 __isl_take isl_map *map2);
3375 __isl_give isl_union_map *isl_union_map_flat_range_product(
3376 __isl_take isl_union_map *umap1,
3377 __isl_take isl_union_map *umap2);
3378 __isl_give isl_basic_map *isl_basic_map_flat_product(
3379 __isl_take isl_basic_map *bmap1,
3380 __isl_take isl_basic_map *bmap2);
3381 __isl_give isl_map *isl_map_flat_product(
3382 __isl_take isl_map *map1,
3383 __isl_take isl_map *map2);
3385 #include <isl/space.h>
3386 __isl_give isl_space *isl_space_domain_factor_domain(
3387 __isl_take isl_space *space);
3388 __isl_give isl_space *isl_space_range_factor_domain(
3389 __isl_take isl_space *space);
3390 __isl_give isl_space *isl_space_range_factor_range(
3391 __isl_take isl_space *space);
3393 The functions C<isl_space_range_factor_domain> and
3394 C<isl_space_range_factor_range> extract the two arguments from
3395 the result of a call to C<isl_space_range_product>.
3397 The arguments of a call to C<isl_map_range_product> can be extracted
3398 from the result using the following two functions.
3400 #include <isl/map.h>
3401 __isl_give isl_map *isl_map_range_factor_domain(
3402 __isl_take isl_map *map);
3403 __isl_give isl_map *isl_map_range_factor_range(
3404 __isl_take isl_map *map);
3406 =item * Simplification
3408 __isl_give isl_basic_set *isl_basic_set_gist(
3409 __isl_take isl_basic_set *bset,
3410 __isl_take isl_basic_set *context);
3411 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3412 __isl_take isl_set *context);
3413 __isl_give isl_set *isl_set_gist_params(
3414 __isl_take isl_set *set,
3415 __isl_take isl_set *context);
3416 __isl_give isl_union_set *isl_union_set_gist(
3417 __isl_take isl_union_set *uset,
3418 __isl_take isl_union_set *context);
3419 __isl_give isl_union_set *isl_union_set_gist_params(
3420 __isl_take isl_union_set *uset,
3421 __isl_take isl_set *set);
3422 __isl_give isl_basic_map *isl_basic_map_gist(
3423 __isl_take isl_basic_map *bmap,
3424 __isl_take isl_basic_map *context);
3425 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3426 __isl_take isl_map *context);
3427 __isl_give isl_map *isl_map_gist_params(
3428 __isl_take isl_map *map,
3429 __isl_take isl_set *context);
3430 __isl_give isl_map *isl_map_gist_domain(
3431 __isl_take isl_map *map,
3432 __isl_take isl_set *context);
3433 __isl_give isl_map *isl_map_gist_range(
3434 __isl_take isl_map *map,
3435 __isl_take isl_set *context);
3436 __isl_give isl_union_map *isl_union_map_gist(
3437 __isl_take isl_union_map *umap,
3438 __isl_take isl_union_map *context);
3439 __isl_give isl_union_map *isl_union_map_gist_params(
3440 __isl_take isl_union_map *umap,
3441 __isl_take isl_set *set);
3442 __isl_give isl_union_map *isl_union_map_gist_domain(
3443 __isl_take isl_union_map *umap,
3444 __isl_take isl_union_set *uset);
3445 __isl_give isl_union_map *isl_union_map_gist_range(
3446 __isl_take isl_union_map *umap,
3447 __isl_take isl_union_set *uset);
3449 The gist operation returns a set or relation that has the
3450 same intersection with the context as the input set or relation.
3451 Any implicit equality in the intersection is made explicit in the result,
3452 while all inequalities that are redundant with respect to the intersection
3454 In case of union sets and relations, the gist operation is performed
3459 =head3 Lexicographic Optimization
3461 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3462 the following functions
3463 compute a set that contains the lexicographic minimum or maximum
3464 of the elements in C<set> (or C<bset>) for those values of the parameters
3465 that satisfy C<dom>.
3466 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3467 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3469 In other words, the union of the parameter values
3470 for which the result is non-empty and of C<*empty>
3473 __isl_give isl_set *isl_basic_set_partial_lexmin(
3474 __isl_take isl_basic_set *bset,
3475 __isl_take isl_basic_set *dom,
3476 __isl_give isl_set **empty);
3477 __isl_give isl_set *isl_basic_set_partial_lexmax(
3478 __isl_take isl_basic_set *bset,
3479 __isl_take isl_basic_set *dom,
3480 __isl_give isl_set **empty);
3481 __isl_give isl_set *isl_set_partial_lexmin(
3482 __isl_take isl_set *set, __isl_take isl_set *dom,
3483 __isl_give isl_set **empty);
3484 __isl_give isl_set *isl_set_partial_lexmax(
3485 __isl_take isl_set *set, __isl_take isl_set *dom,
3486 __isl_give isl_set **empty);
3488 Given a (basic) set C<set> (or C<bset>), the following functions simply
3489 return a set containing the lexicographic minimum or maximum
3490 of the elements in C<set> (or C<bset>).
3491 In case of union sets, the optimum is computed per space.
3493 __isl_give isl_set *isl_basic_set_lexmin(
3494 __isl_take isl_basic_set *bset);
3495 __isl_give isl_set *isl_basic_set_lexmax(
3496 __isl_take isl_basic_set *bset);
3497 __isl_give isl_set *isl_set_lexmin(
3498 __isl_take isl_set *set);
3499 __isl_give isl_set *isl_set_lexmax(
3500 __isl_take isl_set *set);
3501 __isl_give isl_union_set *isl_union_set_lexmin(
3502 __isl_take isl_union_set *uset);
3503 __isl_give isl_union_set *isl_union_set_lexmax(
3504 __isl_take isl_union_set *uset);
3506 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3507 the following functions
3508 compute a relation that maps each element of C<dom>
3509 to the single lexicographic minimum or maximum
3510 of the elements that are associated to that same
3511 element in C<map> (or C<bmap>).
3512 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3513 that contains the elements in C<dom> that do not map
3514 to any elements in C<map> (or C<bmap>).
3515 In other words, the union of the domain of the result and of C<*empty>
3518 __isl_give isl_map *isl_basic_map_partial_lexmax(
3519 __isl_take isl_basic_map *bmap,
3520 __isl_take isl_basic_set *dom,
3521 __isl_give isl_set **empty);
3522 __isl_give isl_map *isl_basic_map_partial_lexmin(
3523 __isl_take isl_basic_map *bmap,
3524 __isl_take isl_basic_set *dom,
3525 __isl_give isl_set **empty);
3526 __isl_give isl_map *isl_map_partial_lexmax(
3527 __isl_take isl_map *map, __isl_take isl_set *dom,
3528 __isl_give isl_set **empty);
3529 __isl_give isl_map *isl_map_partial_lexmin(
3530 __isl_take isl_map *map, __isl_take isl_set *dom,
3531 __isl_give isl_set **empty);
3533 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3534 return a map mapping each element in the domain of
3535 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3536 of all elements associated to that element.
3537 In case of union relations, the optimum is computed per space.
3539 __isl_give isl_map *isl_basic_map_lexmin(
3540 __isl_take isl_basic_map *bmap);
3541 __isl_give isl_map *isl_basic_map_lexmax(
3542 __isl_take isl_basic_map *bmap);
3543 __isl_give isl_map *isl_map_lexmin(
3544 __isl_take isl_map *map);
3545 __isl_give isl_map *isl_map_lexmax(
3546 __isl_take isl_map *map);
3547 __isl_give isl_union_map *isl_union_map_lexmin(
3548 __isl_take isl_union_map *umap);
3549 __isl_give isl_union_map *isl_union_map_lexmax(
3550 __isl_take isl_union_map *umap);
3552 The following functions return their result in the form of
3553 a piecewise multi-affine expression
3554 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3555 but are otherwise equivalent to the corresponding functions
3556 returning a basic set or relation.
3558 __isl_give isl_pw_multi_aff *
3559 isl_basic_map_lexmin_pw_multi_aff(
3560 __isl_take isl_basic_map *bmap);
3561 __isl_give isl_pw_multi_aff *
3562 isl_basic_set_partial_lexmin_pw_multi_aff(
3563 __isl_take isl_basic_set *bset,
3564 __isl_take isl_basic_set *dom,
3565 __isl_give isl_set **empty);
3566 __isl_give isl_pw_multi_aff *
3567 isl_basic_set_partial_lexmax_pw_multi_aff(
3568 __isl_take isl_basic_set *bset,
3569 __isl_take isl_basic_set *dom,
3570 __isl_give isl_set **empty);
3571 __isl_give isl_pw_multi_aff *
3572 isl_basic_map_partial_lexmin_pw_multi_aff(
3573 __isl_take isl_basic_map *bmap,
3574 __isl_take isl_basic_set *dom,
3575 __isl_give isl_set **empty);
3576 __isl_give isl_pw_multi_aff *
3577 isl_basic_map_partial_lexmax_pw_multi_aff(
3578 __isl_take isl_basic_map *bmap,
3579 __isl_take isl_basic_set *dom,
3580 __isl_give isl_set **empty);
3581 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3582 __isl_take isl_set *set);
3583 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3584 __isl_take isl_set *set);
3585 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3586 __isl_take isl_map *map);
3587 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3588 __isl_take isl_map *map);
3592 Lists are defined over several element types, including
3593 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3594 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3595 Here we take lists of C<isl_set>s as an example.
3596 Lists can be created, copied, modified and freed using the following functions.
3598 #include <isl/list.h>
3599 __isl_give isl_set_list *isl_set_list_from_set(
3600 __isl_take isl_set *el);
3601 __isl_give isl_set_list *isl_set_list_alloc(
3602 isl_ctx *ctx, int n);
3603 __isl_give isl_set_list *isl_set_list_copy(
3604 __isl_keep isl_set_list *list);
3605 __isl_give isl_set_list *isl_set_list_insert(
3606 __isl_take isl_set_list *list, unsigned pos,
3607 __isl_take isl_set *el);
3608 __isl_give isl_set_list *isl_set_list_add(
3609 __isl_take isl_set_list *list,
3610 __isl_take isl_set *el);
3611 __isl_give isl_set_list *isl_set_list_drop(
3612 __isl_take isl_set_list *list,
3613 unsigned first, unsigned n);
3614 __isl_give isl_set_list *isl_set_list_set_set(
3615 __isl_take isl_set_list *list, int index,
3616 __isl_take isl_set *set);
3617 __isl_give isl_set_list *isl_set_list_concat(
3618 __isl_take isl_set_list *list1,
3619 __isl_take isl_set_list *list2);
3620 __isl_give isl_set_list *isl_set_list_sort(
3621 __isl_take isl_set_list *list,
3622 int (*cmp)(__isl_keep isl_set *a,
3623 __isl_keep isl_set *b, void *user),
3625 __isl_null isl_set_list *isl_set_list_free(
3626 __isl_take isl_set_list *list);
3628 C<isl_set_list_alloc> creates an empty list with a capacity for
3629 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3632 Lists can be inspected using the following functions.
3634 #include <isl/list.h>
3635 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3636 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3637 __isl_give isl_set *isl_set_list_get_set(
3638 __isl_keep isl_set_list *list, int index);
3639 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3640 int (*fn)(__isl_take isl_set *el, void *user),
3642 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3643 int (*follows)(__isl_keep isl_set *a,
3644 __isl_keep isl_set *b, void *user),
3646 int (*fn)(__isl_take isl_set *el, void *user),
3649 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3650 strongly connected components of the graph with as vertices the elements
3651 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3652 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3653 should return C<-1> on error.
3655 Lists can be printed using
3657 #include <isl/list.h>
3658 __isl_give isl_printer *isl_printer_print_set_list(
3659 __isl_take isl_printer *p,
3660 __isl_keep isl_set_list *list);
3662 =head2 Associative arrays
3664 Associative arrays map isl objects of a specific type to isl objects
3665 of some (other) specific type. They are defined for several pairs
3666 of types, including (C<isl_map>, C<isl_basic_set>),
3667 (C<isl_id>, C<isl_ast_expr>) and.
3668 (C<isl_id>, C<isl_pw_aff>).
3669 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3672 Associative arrays can be created, copied and freed using
3673 the following functions.
3675 #include <isl/id_to_ast_expr.h>
3676 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3677 isl_ctx *ctx, int min_size);
3678 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3679 __isl_keep id_to_ast_expr *id2expr);
3680 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
3681 __isl_take id_to_ast_expr *id2expr);
3683 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3684 to specify the expected size of the associative array.
3685 The associative array will be grown automatically as needed.
3687 Associative arrays can be inspected using the following functions.
3689 #include <isl/id_to_ast_expr.h>
3690 isl_ctx *isl_id_to_ast_expr_get_ctx(
3691 __isl_keep id_to_ast_expr *id2expr);
3692 int isl_id_to_ast_expr_has(
3693 __isl_keep id_to_ast_expr *id2expr,
3694 __isl_keep isl_id *key);
3695 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3696 __isl_keep id_to_ast_expr *id2expr,
3697 __isl_take isl_id *key);
3698 int isl_id_to_ast_expr_foreach(
3699 __isl_keep id_to_ast_expr *id2expr,
3700 int (*fn)(__isl_take isl_id *key,
3701 __isl_take isl_ast_expr *val, void *user),
3704 They can be modified using the following function.
3706 #include <isl/id_to_ast_expr.h>
3707 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3708 __isl_take id_to_ast_expr *id2expr,
3709 __isl_take isl_id *key,
3710 __isl_take isl_ast_expr *val);
3711 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
3712 __isl_take id_to_ast_expr *id2expr,
3713 __isl_take isl_id *key);
3715 Associative arrays can be printed using the following function.
3717 #include <isl/id_to_ast_expr.h>
3718 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3719 __isl_take isl_printer *p,
3720 __isl_keep id_to_ast_expr *id2expr);
3722 =head2 Multiple Values
3724 An C<isl_multi_val> object represents a sequence of zero or more values,
3725 living in a set space.
3727 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3728 using the following function
3730 #include <isl/val.h>
3731 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3732 __isl_take isl_space *space,
3733 __isl_take isl_val_list *list);
3735 The zero multiple value (with value zero for each set dimension)
3736 can be created using the following function.
3738 #include <isl/val.h>
3739 __isl_give isl_multi_val *isl_multi_val_zero(
3740 __isl_take isl_space *space);
3742 Multiple values can be copied and freed using
3744 #include <isl/val.h>
3745 __isl_give isl_multi_val *isl_multi_val_copy(
3746 __isl_keep isl_multi_val *mv);
3747 __isl_null isl_multi_val *isl_multi_val_free(
3748 __isl_take isl_multi_val *mv);
3750 They can be inspected using
3752 #include <isl/val.h>
3753 isl_ctx *isl_multi_val_get_ctx(
3754 __isl_keep isl_multi_val *mv);
3755 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3756 enum isl_dim_type type);
3757 __isl_give isl_val *isl_multi_val_get_val(
3758 __isl_keep isl_multi_val *mv, int pos);
3759 int isl_multi_val_find_dim_by_id(
3760 __isl_keep isl_multi_val *mv,
3761 enum isl_dim_type type, __isl_keep isl_id *id);
3762 __isl_give isl_id *isl_multi_val_get_dim_id(
3763 __isl_keep isl_multi_val *mv,
3764 enum isl_dim_type type, unsigned pos);
3765 const char *isl_multi_val_get_tuple_name(
3766 __isl_keep isl_multi_val *mv,
3767 enum isl_dim_type type);
3768 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3769 enum isl_dim_type type);
3770 __isl_give isl_id *isl_multi_val_get_tuple_id(
3771 __isl_keep isl_multi_val *mv,
3772 enum isl_dim_type type);
3773 int isl_multi_val_range_is_wrapping(
3774 __isl_keep isl_multi_val *mv);
3776 They can be modified using
3778 #include <isl/val.h>
3779 __isl_give isl_multi_val *isl_multi_val_set_val(
3780 __isl_take isl_multi_val *mv, int pos,
3781 __isl_take isl_val *val);
3782 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3783 __isl_take isl_multi_val *mv,
3784 enum isl_dim_type type, unsigned pos, const char *s);
3785 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3786 __isl_take isl_multi_val *mv,
3787 enum isl_dim_type type, unsigned pos,
3788 __isl_take isl_id *id);
3789 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3790 __isl_take isl_multi_val *mv,
3791 enum isl_dim_type type, const char *s);
3792 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3793 __isl_take isl_multi_val *mv,
3794 enum isl_dim_type type, __isl_take isl_id *id);
3795 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3796 __isl_take isl_multi_val *mv,
3797 enum isl_dim_type type);
3798 __isl_give isl_multi_val *isl_multi_val_reset_user(
3799 __isl_take isl_multi_val *mv);
3801 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3802 __isl_take isl_multi_val *mv,
3803 enum isl_dim_type type, unsigned first, unsigned n);
3804 __isl_give isl_multi_val *isl_multi_val_add_dims(
3805 __isl_take isl_multi_val *mv,
3806 enum isl_dim_type type, unsigned n);
3807 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3808 __isl_take isl_multi_val *mv,
3809 enum isl_dim_type type, unsigned first, unsigned n);
3813 #include <isl/val.h>
3814 __isl_give isl_multi_val *isl_multi_val_align_params(
3815 __isl_take isl_multi_val *mv,
3816 __isl_take isl_space *model);
3817 __isl_give isl_multi_val *isl_multi_val_from_range(
3818 __isl_take isl_multi_val *mv);
3819 __isl_give isl_multi_val *isl_multi_val_range_splice(
3820 __isl_take isl_multi_val *mv1, unsigned pos,
3821 __isl_take isl_multi_val *mv2);
3822 __isl_give isl_multi_val *isl_multi_val_range_product(
3823 __isl_take isl_multi_val *mv1,
3824 __isl_take isl_multi_val *mv2);
3825 __isl_give isl_multi_val *
3826 isl_multi_val_range_factor_domain(
3827 __isl_take isl_multi_val *mv);
3828 __isl_give isl_multi_val *
3829 isl_multi_val_range_factor_range(
3830 __isl_take isl_multi_val *mv);
3831 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3832 __isl_take isl_multi_val *mv1,
3833 __isl_take isl_multi_aff *mv2);
3834 __isl_give isl_multi_val *isl_multi_val_product(
3835 __isl_take isl_multi_val *mv1,
3836 __isl_take isl_multi_val *mv2);
3837 __isl_give isl_multi_val *isl_multi_val_add_val(
3838 __isl_take isl_multi_val *mv,
3839 __isl_take isl_val *v);
3840 __isl_give isl_multi_val *isl_multi_val_mod_val(
3841 __isl_take isl_multi_val *mv,
3842 __isl_take isl_val *v);
3843 __isl_give isl_multi_val *isl_multi_val_scale_val(
3844 __isl_take isl_multi_val *mv,
3845 __isl_take isl_val *v);
3846 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3847 __isl_take isl_multi_val *mv1,
3848 __isl_take isl_multi_val *mv2);
3849 __isl_give isl_multi_val *
3850 isl_multi_val_scale_down_multi_val(
3851 __isl_take isl_multi_val *mv1,
3852 __isl_take isl_multi_val *mv2);
3854 A multiple value can be printed using
3856 __isl_give isl_printer *isl_printer_print_multi_val(
3857 __isl_take isl_printer *p,
3858 __isl_keep isl_multi_val *mv);
3862 Vectors can be created, copied and freed using the following functions.
3864 #include <isl/vec.h>
3865 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3867 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3868 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
3870 Note that the elements of a newly created vector may have arbitrary values.
3871 The elements can be changed and inspected using the following functions.
3873 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3874 int isl_vec_size(__isl_keep isl_vec *vec);
3875 __isl_give isl_val *isl_vec_get_element_val(
3876 __isl_keep isl_vec *vec, int pos);
3877 __isl_give isl_vec *isl_vec_set_element_si(
3878 __isl_take isl_vec *vec, int pos, int v);
3879 __isl_give isl_vec *isl_vec_set_element_val(
3880 __isl_take isl_vec *vec, int pos,
3881 __isl_take isl_val *v);
3882 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3884 __isl_give isl_vec *isl_vec_set_val(
3885 __isl_take isl_vec *vec, __isl_take isl_val *v);
3886 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3887 __isl_keep isl_vec *vec2, int pos);
3889 C<isl_vec_get_element> will return a negative value if anything went wrong.
3890 In that case, the value of C<*v> is undefined.
3892 The following function can be used to concatenate two vectors.
3894 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3895 __isl_take isl_vec *vec2);
3899 Matrices can be created, copied and freed using the following functions.
3901 #include <isl/mat.h>
3902 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3903 unsigned n_row, unsigned n_col);
3904 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3905 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
3907 Note that the elements of a newly created matrix may have arbitrary values.
3908 The elements can be changed and inspected using the following functions.
3910 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3911 int isl_mat_rows(__isl_keep isl_mat *mat);
3912 int isl_mat_cols(__isl_keep isl_mat *mat);
3913 __isl_give isl_val *isl_mat_get_element_val(
3914 __isl_keep isl_mat *mat, int row, int col);
3915 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3916 int row, int col, int v);
3917 __isl_give isl_mat *isl_mat_set_element_val(
3918 __isl_take isl_mat *mat, int row, int col,
3919 __isl_take isl_val *v);
3921 C<isl_mat_get_element> will return a negative value if anything went wrong.
3922 In that case, the value of C<*v> is undefined.
3924 The following function can be used to compute the (right) inverse
3925 of a matrix, i.e., a matrix such that the product of the original
3926 and the inverse (in that order) is a multiple of the identity matrix.
3927 The input matrix is assumed to be of full row-rank.
3929 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3931 The following function can be used to compute the (right) kernel
3932 (or null space) of a matrix, i.e., a matrix such that the product of
3933 the original and the kernel (in that order) is the zero matrix.
3935 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3937 =head2 Piecewise Quasi Affine Expressions
3939 The zero quasi affine expression or the quasi affine expression
3940 that is equal to a given value or
3941 a specified dimension on a given domain can be created using
3943 __isl_give isl_aff *isl_aff_zero_on_domain(
3944 __isl_take isl_local_space *ls);
3945 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3946 __isl_take isl_local_space *ls);
3947 __isl_give isl_aff *isl_aff_val_on_domain(
3948 __isl_take isl_local_space *ls,
3949 __isl_take isl_val *val);
3950 __isl_give isl_aff *isl_aff_var_on_domain(
3951 __isl_take isl_local_space *ls,
3952 enum isl_dim_type type, unsigned pos);
3953 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3954 __isl_take isl_local_space *ls,
3955 enum isl_dim_type type, unsigned pos);
3956 __isl_give isl_aff *isl_aff_nan_on_domain(
3957 __isl_take isl_local_space *ls);
3958 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3959 __isl_take isl_local_space *ls);
3961 Note that the space in which the resulting objects live is a map space
3962 with the given space as domain and a one-dimensional range.
3964 An empty piecewise quasi affine expression (one with no cells)
3965 or a piecewise quasi affine expression with a single cell can
3966 be created using the following functions.
3968 #include <isl/aff.h>
3969 __isl_give isl_pw_aff *isl_pw_aff_empty(
3970 __isl_take isl_space *space);
3971 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3972 __isl_take isl_set *set, __isl_take isl_aff *aff);
3973 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3974 __isl_take isl_aff *aff);
3976 A piecewise quasi affine expression that is equal to 1 on a set
3977 and 0 outside the set can be created using the following function.
3979 #include <isl/aff.h>
3980 __isl_give isl_pw_aff *isl_set_indicator_function(
3981 __isl_take isl_set *set);
3983 Quasi affine expressions can be copied and freed using
3985 #include <isl/aff.h>
3986 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3987 __isl_null isl_aff *isl_aff_free(__isl_take isl_aff *aff);
3989 __isl_give isl_pw_aff *isl_pw_aff_copy(
3990 __isl_keep isl_pw_aff *pwaff);
3991 __isl_null isl_pw_aff *isl_pw_aff_free(
3992 __isl_take isl_pw_aff *pwaff);
3994 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3995 using the following function. The constraint is required to have
3996 a non-zero coefficient for the specified dimension.
3998 #include <isl/constraint.h>
3999 __isl_give isl_aff *isl_constraint_get_bound(
4000 __isl_keep isl_constraint *constraint,
4001 enum isl_dim_type type, int pos);
4003 The entire affine expression of the constraint can also be extracted
4004 using the following function.
4006 #include <isl/constraint.h>
4007 __isl_give isl_aff *isl_constraint_get_aff(
4008 __isl_keep isl_constraint *constraint);
4010 Conversely, an equality constraint equating
4011 the affine expression to zero or an inequality constraint enforcing
4012 the affine expression to be non-negative, can be constructed using
4014 __isl_give isl_constraint *isl_equality_from_aff(
4015 __isl_take isl_aff *aff);
4016 __isl_give isl_constraint *isl_inequality_from_aff(
4017 __isl_take isl_aff *aff);
4019 The expression can be inspected using
4021 #include <isl/aff.h>
4022 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
4023 int isl_aff_dim(__isl_keep isl_aff *aff,
4024 enum isl_dim_type type);
4025 __isl_give isl_local_space *isl_aff_get_domain_local_space(
4026 __isl_keep isl_aff *aff);
4027 __isl_give isl_local_space *isl_aff_get_local_space(
4028 __isl_keep isl_aff *aff);
4029 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
4030 enum isl_dim_type type, unsigned pos);
4031 const char *isl_pw_aff_get_dim_name(
4032 __isl_keep isl_pw_aff *pa,
4033 enum isl_dim_type type, unsigned pos);
4034 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
4035 enum isl_dim_type type, unsigned pos);
4036 __isl_give isl_id *isl_pw_aff_get_dim_id(
4037 __isl_keep isl_pw_aff *pa,
4038 enum isl_dim_type type, unsigned pos);
4039 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
4040 enum isl_dim_type type);
4041 __isl_give isl_id *isl_pw_aff_get_tuple_id(
4042 __isl_keep isl_pw_aff *pa,
4043 enum isl_dim_type type);
4044 __isl_give isl_val *isl_aff_get_constant_val(
4045 __isl_keep isl_aff *aff);
4046 __isl_give isl_val *isl_aff_get_coefficient_val(
4047 __isl_keep isl_aff *aff,
4048 enum isl_dim_type type, int pos);
4049 __isl_give isl_val *isl_aff_get_denominator_val(
4050 __isl_keep isl_aff *aff);
4051 __isl_give isl_aff *isl_aff_get_div(
4052 __isl_keep isl_aff *aff, int pos);
4054 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
4055 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
4056 int (*fn)(__isl_take isl_set *set,
4057 __isl_take isl_aff *aff,
4058 void *user), void *user);
4060 int isl_aff_is_cst(__isl_keep isl_aff *aff);
4061 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4063 int isl_aff_is_nan(__isl_keep isl_aff *aff);
4064 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
4066 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
4067 enum isl_dim_type type, unsigned first, unsigned n);
4068 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
4069 enum isl_dim_type type, unsigned first, unsigned n);
4071 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
4072 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
4073 enum isl_dim_type type);
4074 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
4076 It can be modified using
4078 #include <isl/aff.h>
4079 __isl_give isl_aff *isl_aff_set_tuple_id(
4080 __isl_take isl_aff *aff,
4081 enum isl_dim_type type, __isl_take isl_id *id);
4082 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
4083 __isl_take isl_pw_aff *pwaff,
4084 enum isl_dim_type type, __isl_take isl_id *id);
4085 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
4086 __isl_take isl_pw_aff *pa,
4087 enum isl_dim_type type);
4088 __isl_give isl_aff *isl_aff_set_dim_name(
4089 __isl_take isl_aff *aff, enum isl_dim_type type,
4090 unsigned pos, const char *s);
4091 __isl_give isl_aff *isl_aff_set_dim_id(
4092 __isl_take isl_aff *aff, enum isl_dim_type type,
4093 unsigned pos, __isl_take isl_id *id);
4094 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
4095 __isl_take isl_pw_aff *pma,
4096 enum isl_dim_type type, unsigned pos,
4097 __isl_take isl_id *id);
4098 __isl_give isl_aff *isl_aff_set_constant_si(
4099 __isl_take isl_aff *aff, int v);
4100 __isl_give isl_aff *isl_aff_set_constant_val(
4101 __isl_take isl_aff *aff, __isl_take isl_val *v);
4102 __isl_give isl_aff *isl_aff_set_coefficient_si(
4103 __isl_take isl_aff *aff,
4104 enum isl_dim_type type, int pos, int v);
4105 __isl_give isl_aff *isl_aff_set_coefficient_val(
4106 __isl_take isl_aff *aff,
4107 enum isl_dim_type type, int pos,
4108 __isl_take isl_val *v);
4110 __isl_give isl_aff *isl_aff_add_constant_si(
4111 __isl_take isl_aff *aff, int v);
4112 __isl_give isl_aff *isl_aff_add_constant_val(
4113 __isl_take isl_aff *aff, __isl_take isl_val *v);
4114 __isl_give isl_aff *isl_aff_add_constant_num_si(
4115 __isl_take isl_aff *aff, int v);
4116 __isl_give isl_aff *isl_aff_add_coefficient_si(
4117 __isl_take isl_aff *aff,
4118 enum isl_dim_type type, int pos, int v);
4119 __isl_give isl_aff *isl_aff_add_coefficient_val(
4120 __isl_take isl_aff *aff,
4121 enum isl_dim_type type, int pos,
4122 __isl_take isl_val *v);
4124 __isl_give isl_aff *isl_aff_insert_dims(
4125 __isl_take isl_aff *aff,
4126 enum isl_dim_type type, unsigned first, unsigned n);
4127 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
4128 __isl_take isl_pw_aff *pwaff,
4129 enum isl_dim_type type, unsigned first, unsigned n);
4130 __isl_give isl_aff *isl_aff_add_dims(
4131 __isl_take isl_aff *aff,
4132 enum isl_dim_type type, unsigned n);
4133 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
4134 __isl_take isl_pw_aff *pwaff,
4135 enum isl_dim_type type, unsigned n);
4136 __isl_give isl_aff *isl_aff_drop_dims(
4137 __isl_take isl_aff *aff,
4138 enum isl_dim_type type, unsigned first, unsigned n);
4139 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
4140 __isl_take isl_pw_aff *pwaff,
4141 enum isl_dim_type type, unsigned first, unsigned n);
4142 __isl_give isl_aff *isl_aff_move_dims(
4143 __isl_take isl_aff *aff,
4144 enum isl_dim_type dst_type, unsigned dst_pos,
4145 enum isl_dim_type src_type, unsigned src_pos,
4147 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
4148 __isl_take isl_pw_aff *pa,
4149 enum isl_dim_type dst_type, unsigned dst_pos,
4150 enum isl_dim_type src_type, unsigned src_pos,
4153 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
4154 set the I<numerator> of the constant or coefficient, while
4155 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
4156 the constant or coefficient as a whole.
4157 The C<add_constant> and C<add_coefficient> functions add an integer
4158 or rational value to
4159 the possibly rational constant or coefficient.
4160 The C<add_constant_num> functions add an integer value to
4163 To check whether an affine expressions is obviously zero
4164 or (obviously) equal to some other affine expression, use
4166 #include <isl/aff.h>
4167 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
4168 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
4169 __isl_keep isl_aff *aff2);
4170 int isl_pw_aff_plain_is_equal(
4171 __isl_keep isl_pw_aff *pwaff1,
4172 __isl_keep isl_pw_aff *pwaff2);
4173 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
4174 __isl_keep isl_pw_aff *pa2);
4175 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4176 __isl_keep isl_pw_aff *pa2);
4178 The function C<isl_pw_aff_plain_cmp> can be used to sort
4179 C<isl_pw_aff>s. The order is not strictly defined.
4180 The current order sorts expressions that only involve
4181 earlier dimensions before those that involve later dimensions.
4185 #include <isl/aff.h>
4186 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
4187 __isl_take isl_aff *aff2);
4188 __isl_give isl_pw_aff *isl_pw_aff_add(
4189 __isl_take isl_pw_aff *pwaff1,
4190 __isl_take isl_pw_aff *pwaff2);
4191 __isl_give isl_pw_aff *isl_pw_aff_min(
4192 __isl_take isl_pw_aff *pwaff1,
4193 __isl_take isl_pw_aff *pwaff2);
4194 __isl_give isl_pw_aff *isl_pw_aff_max(
4195 __isl_take isl_pw_aff *pwaff1,
4196 __isl_take isl_pw_aff *pwaff2);
4197 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
4198 __isl_take isl_aff *aff2);
4199 __isl_give isl_pw_aff *isl_pw_aff_sub(
4200 __isl_take isl_pw_aff *pwaff1,
4201 __isl_take isl_pw_aff *pwaff2);
4202 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
4203 __isl_give isl_pw_aff *isl_pw_aff_neg(
4204 __isl_take isl_pw_aff *pwaff);
4205 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
4206 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4207 __isl_take isl_pw_aff *pwaff);
4208 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
4209 __isl_give isl_pw_aff *isl_pw_aff_floor(
4210 __isl_take isl_pw_aff *pwaff);
4211 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
4212 __isl_take isl_val *mod);
4213 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
4214 __isl_take isl_pw_aff *pa,
4215 __isl_take isl_val *mod);
4216 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
4217 __isl_take isl_val *v);
4218 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
4219 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
4220 __isl_give isl_aff *isl_aff_scale_down_ui(
4221 __isl_take isl_aff *aff, unsigned f);
4222 __isl_give isl_aff *isl_aff_scale_down_val(
4223 __isl_take isl_aff *aff, __isl_take isl_val *v);
4224 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
4225 __isl_take isl_pw_aff *pa,
4226 __isl_take isl_val *f);
4228 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4229 __isl_take isl_pw_aff_list *list);
4230 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4231 __isl_take isl_pw_aff_list *list);
4233 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4234 __isl_take isl_pw_aff *pwqp);
4236 __isl_give isl_aff *isl_aff_align_params(
4237 __isl_take isl_aff *aff,
4238 __isl_take isl_space *model);
4239 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4240 __isl_take isl_pw_aff *pwaff,
4241 __isl_take isl_space *model);
4243 __isl_give isl_aff *isl_aff_project_domain_on_params(
4244 __isl_take isl_aff *aff);
4245 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4246 __isl_take isl_pw_aff *pwa);
4248 __isl_give isl_aff *isl_aff_gist_params(
4249 __isl_take isl_aff *aff,
4250 __isl_take isl_set *context);
4251 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
4252 __isl_take isl_set *context);
4253 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
4254 __isl_take isl_pw_aff *pwaff,
4255 __isl_take isl_set *context);
4256 __isl_give isl_pw_aff *isl_pw_aff_gist(
4257 __isl_take isl_pw_aff *pwaff,
4258 __isl_take isl_set *context);
4260 __isl_give isl_set *isl_pw_aff_domain(
4261 __isl_take isl_pw_aff *pwaff);
4262 __isl_give isl_set *isl_pw_aff_params(
4263 __isl_take isl_pw_aff *pwa);
4264 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4265 __isl_take isl_pw_aff *pa,
4266 __isl_take isl_set *set);
4267 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4268 __isl_take isl_pw_aff *pa,
4269 __isl_take isl_set *set);
4271 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
4272 __isl_take isl_aff *aff2);
4273 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
4274 __isl_take isl_aff *aff2);
4275 __isl_give isl_pw_aff *isl_pw_aff_mul(
4276 __isl_take isl_pw_aff *pwaff1,
4277 __isl_take isl_pw_aff *pwaff2);
4278 __isl_give isl_pw_aff *isl_pw_aff_div(
4279 __isl_take isl_pw_aff *pa1,
4280 __isl_take isl_pw_aff *pa2);
4281 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
4282 __isl_take isl_pw_aff *pa1,
4283 __isl_take isl_pw_aff *pa2);
4284 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
4285 __isl_take isl_pw_aff *pa1,
4286 __isl_take isl_pw_aff *pa2);
4288 When multiplying two affine expressions, at least one of the two needs
4289 to be a constant. Similarly, when dividing an affine expression by another,
4290 the second expression needs to be a constant.
4291 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
4292 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
4295 #include <isl/aff.h>
4296 __isl_give isl_aff *isl_aff_pullback_aff(
4297 __isl_take isl_aff *aff1,
4298 __isl_take isl_aff *aff2);
4299 __isl_give isl_aff *isl_aff_pullback_multi_aff(
4300 __isl_take isl_aff *aff,
4301 __isl_take isl_multi_aff *ma);
4302 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
4303 __isl_take isl_pw_aff *pa,
4304 __isl_take isl_multi_aff *ma);
4305 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
4306 __isl_take isl_pw_aff *pa,
4307 __isl_take isl_pw_multi_aff *pma);
4308 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
4309 __isl_take isl_pw_aff *pa,
4310 __isl_take isl_multi_pw_aff *mpa);
4312 These functions precompose the input expression by the given
4313 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
4314 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
4315 into the (piecewise) affine expression.
4316 Objects of type C<isl_multi_aff> are described in
4317 L</"Piecewise Multiple Quasi Affine Expressions">.
4319 #include <isl/aff.h>
4320 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4321 __isl_take isl_aff *aff);
4322 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4323 __isl_take isl_aff *aff);
4324 __isl_give isl_basic_set *isl_aff_le_basic_set(
4325 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4326 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4327 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4328 __isl_give isl_set *isl_pw_aff_eq_set(
4329 __isl_take isl_pw_aff *pwaff1,
4330 __isl_take isl_pw_aff *pwaff2);
4331 __isl_give isl_set *isl_pw_aff_ne_set(
4332 __isl_take isl_pw_aff *pwaff1,
4333 __isl_take isl_pw_aff *pwaff2);
4334 __isl_give isl_set *isl_pw_aff_le_set(
4335 __isl_take isl_pw_aff *pwaff1,
4336 __isl_take isl_pw_aff *pwaff2);
4337 __isl_give isl_set *isl_pw_aff_lt_set(
4338 __isl_take isl_pw_aff *pwaff1,
4339 __isl_take isl_pw_aff *pwaff2);
4340 __isl_give isl_set *isl_pw_aff_ge_set(
4341 __isl_take isl_pw_aff *pwaff1,
4342 __isl_take isl_pw_aff *pwaff2);
4343 __isl_give isl_set *isl_pw_aff_gt_set(
4344 __isl_take isl_pw_aff *pwaff1,
4345 __isl_take isl_pw_aff *pwaff2);
4347 __isl_give isl_set *isl_pw_aff_list_eq_set(
4348 __isl_take isl_pw_aff_list *list1,
4349 __isl_take isl_pw_aff_list *list2);
4350 __isl_give isl_set *isl_pw_aff_list_ne_set(
4351 __isl_take isl_pw_aff_list *list1,
4352 __isl_take isl_pw_aff_list *list2);
4353 __isl_give isl_set *isl_pw_aff_list_le_set(
4354 __isl_take isl_pw_aff_list *list1,
4355 __isl_take isl_pw_aff_list *list2);
4356 __isl_give isl_set *isl_pw_aff_list_lt_set(
4357 __isl_take isl_pw_aff_list *list1,
4358 __isl_take isl_pw_aff_list *list2);
4359 __isl_give isl_set *isl_pw_aff_list_ge_set(
4360 __isl_take isl_pw_aff_list *list1,
4361 __isl_take isl_pw_aff_list *list2);
4362 __isl_give isl_set *isl_pw_aff_list_gt_set(
4363 __isl_take isl_pw_aff_list *list1,
4364 __isl_take isl_pw_aff_list *list2);
4366 The function C<isl_aff_neg_basic_set> returns a basic set
4367 containing those elements in the domain space
4368 of C<aff> where C<aff> is negative.
4369 The function C<isl_aff_ge_basic_set> returns a basic set
4370 containing those elements in the shared space
4371 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4372 The function C<isl_pw_aff_ge_set> returns a set
4373 containing those elements in the shared domain
4374 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4375 The functions operating on C<isl_pw_aff_list> apply the corresponding
4376 C<isl_pw_aff> function to each pair of elements in the two lists.
4378 #include <isl/aff.h>
4379 __isl_give isl_set *isl_pw_aff_nonneg_set(
4380 __isl_take isl_pw_aff *pwaff);
4381 __isl_give isl_set *isl_pw_aff_zero_set(
4382 __isl_take isl_pw_aff *pwaff);
4383 __isl_give isl_set *isl_pw_aff_non_zero_set(
4384 __isl_take isl_pw_aff *pwaff);
4386 The function C<isl_pw_aff_nonneg_set> returns a set
4387 containing those elements in the domain
4388 of C<pwaff> where C<pwaff> is non-negative.
4390 #include <isl/aff.h>
4391 __isl_give isl_pw_aff *isl_pw_aff_cond(
4392 __isl_take isl_pw_aff *cond,
4393 __isl_take isl_pw_aff *pwaff_true,
4394 __isl_take isl_pw_aff *pwaff_false);
4396 The function C<isl_pw_aff_cond> performs a conditional operator
4397 and returns an expression that is equal to C<pwaff_true>
4398 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4399 where C<cond> is zero.
4401 #include <isl/aff.h>
4402 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4403 __isl_take isl_pw_aff *pwaff1,
4404 __isl_take isl_pw_aff *pwaff2);
4405 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4406 __isl_take isl_pw_aff *pwaff1,
4407 __isl_take isl_pw_aff *pwaff2);
4408 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4409 __isl_take isl_pw_aff *pwaff1,
4410 __isl_take isl_pw_aff *pwaff2);
4412 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4413 expression with a domain that is the union of those of C<pwaff1> and
4414 C<pwaff2> and such that on each cell, the quasi-affine expression is
4415 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4416 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4417 associated expression is the defined one.
4419 An expression can be read from input using
4421 #include <isl/aff.h>
4422 __isl_give isl_aff *isl_aff_read_from_str(
4423 isl_ctx *ctx, const char *str);
4424 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4425 isl_ctx *ctx, const char *str);
4427 An expression can be printed using
4429 #include <isl/aff.h>
4430 __isl_give isl_printer *isl_printer_print_aff(
4431 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4433 __isl_give isl_printer *isl_printer_print_pw_aff(
4434 __isl_take isl_printer *p,
4435 __isl_keep isl_pw_aff *pwaff);
4437 =head2 Piecewise Multiple Quasi Affine Expressions
4439 An C<isl_multi_aff> object represents a sequence of
4440 zero or more affine expressions, all defined on the same domain space.
4441 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4442 zero or more piecewise affine expressions.
4444 An C<isl_multi_aff> can be constructed from a single
4445 C<isl_aff> or an C<isl_aff_list> using the
4446 following functions. Similarly for C<isl_multi_pw_aff>
4447 and C<isl_pw_multi_aff>.
4449 #include <isl/aff.h>
4450 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4451 __isl_take isl_aff *aff);
4452 __isl_give isl_multi_pw_aff *
4453 isl_multi_pw_aff_from_multi_aff(
4454 __isl_take isl_multi_aff *ma);
4455 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4456 __isl_take isl_pw_aff *pa);
4457 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4458 __isl_take isl_pw_aff *pa);
4459 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4460 __isl_take isl_space *space,
4461 __isl_take isl_aff_list *list);
4463 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4464 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4465 Note however that the domain
4466 of the result is the intersection of the domains of the input.
4467 The reverse conversion is exact.
4469 #include <isl/aff.h>
4470 __isl_give isl_pw_multi_aff *
4471 isl_pw_multi_aff_from_multi_pw_aff(
4472 __isl_take isl_multi_pw_aff *mpa);
4473 __isl_give isl_multi_pw_aff *
4474 isl_multi_pw_aff_from_pw_multi_aff(
4475 __isl_take isl_pw_multi_aff *pma);
4477 An empty piecewise multiple quasi affine expression (one with no cells),
4478 the zero piecewise multiple quasi affine expression (with value zero
4479 for each output dimension),
4480 a piecewise multiple quasi affine expression with a single cell (with
4481 either a universe or a specified domain) or
4482 a zero-dimensional piecewise multiple quasi affine expression
4484 can be created using the following functions.
4486 #include <isl/aff.h>
4487 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4488 __isl_take isl_space *space);
4489 __isl_give isl_multi_aff *isl_multi_aff_zero(
4490 __isl_take isl_space *space);
4491 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4492 __isl_take isl_space *space);
4493 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4494 __isl_take isl_space *space);
4495 __isl_give isl_multi_aff *isl_multi_aff_identity(
4496 __isl_take isl_space *space);
4497 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4498 __isl_take isl_space *space);
4499 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4500 __isl_take isl_space *space);
4501 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4502 __isl_take isl_space *space);
4503 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4504 __isl_take isl_space *space);
4505 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4506 __isl_take isl_space *space,
4507 enum isl_dim_type type,
4508 unsigned first, unsigned n);
4509 __isl_give isl_pw_multi_aff *
4510 isl_pw_multi_aff_project_out_map(
4511 __isl_take isl_space *space,
4512 enum isl_dim_type type,
4513 unsigned first, unsigned n);
4514 __isl_give isl_pw_multi_aff *
4515 isl_pw_multi_aff_from_multi_aff(
4516 __isl_take isl_multi_aff *ma);
4517 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4518 __isl_take isl_set *set,
4519 __isl_take isl_multi_aff *maff);
4520 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4521 __isl_take isl_set *set);
4523 __isl_give isl_union_pw_multi_aff *
4524 isl_union_pw_multi_aff_empty(
4525 __isl_take isl_space *space);
4526 __isl_give isl_union_pw_multi_aff *
4527 isl_union_pw_multi_aff_add_pw_multi_aff(
4528 __isl_take isl_union_pw_multi_aff *upma,
4529 __isl_take isl_pw_multi_aff *pma);
4530 __isl_give isl_union_pw_multi_aff *
4531 isl_union_pw_multi_aff_from_domain(
4532 __isl_take isl_union_set *uset);
4534 A piecewise multiple quasi affine expression can also be initialized
4535 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4536 and the C<isl_map> is single-valued.
4537 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4538 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4540 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4541 __isl_take isl_set *set);
4542 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4543 __isl_take isl_map *map);
4545 __isl_give isl_union_pw_multi_aff *
4546 isl_union_pw_multi_aff_from_union_set(
4547 __isl_take isl_union_set *uset);
4548 __isl_give isl_union_pw_multi_aff *
4549 isl_union_pw_multi_aff_from_union_map(
4550 __isl_take isl_union_map *umap);
4552 Multiple quasi affine expressions can be copied and freed using
4554 #include <isl/aff.h>
4555 __isl_give isl_multi_aff *isl_multi_aff_copy(
4556 __isl_keep isl_multi_aff *maff);
4557 __isl_null isl_multi_aff *isl_multi_aff_free(
4558 __isl_take isl_multi_aff *maff);
4560 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4561 __isl_keep isl_pw_multi_aff *pma);
4562 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
4563 __isl_take isl_pw_multi_aff *pma);
4565 __isl_give isl_union_pw_multi_aff *
4566 isl_union_pw_multi_aff_copy(
4567 __isl_keep isl_union_pw_multi_aff *upma);
4568 __isl_null isl_union_pw_multi_aff *
4569 isl_union_pw_multi_aff_free(
4570 __isl_take isl_union_pw_multi_aff *upma);
4572 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4573 __isl_keep isl_multi_pw_aff *mpa);
4574 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
4575 __isl_take isl_multi_pw_aff *mpa);
4577 The expression can be inspected using
4579 #include <isl/aff.h>
4580 isl_ctx *isl_multi_aff_get_ctx(
4581 __isl_keep isl_multi_aff *maff);
4582 isl_ctx *isl_pw_multi_aff_get_ctx(
4583 __isl_keep isl_pw_multi_aff *pma);
4584 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4585 __isl_keep isl_union_pw_multi_aff *upma);
4586 isl_ctx *isl_multi_pw_aff_get_ctx(
4587 __isl_keep isl_multi_pw_aff *mpa);
4589 int isl_multi_aff_involves_dims(
4590 __isl_keep isl_multi_aff *ma,
4591 enum isl_dim_type type, unsigned first, unsigned n);
4592 int isl_multi_pw_aff_involves_dims(
4593 __isl_keep isl_multi_pw_aff *mpa,
4594 enum isl_dim_type type, unsigned first, unsigned n);
4596 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4597 enum isl_dim_type type);
4598 unsigned isl_pw_multi_aff_dim(
4599 __isl_keep isl_pw_multi_aff *pma,
4600 enum isl_dim_type type);
4601 unsigned isl_multi_pw_aff_dim(
4602 __isl_keep isl_multi_pw_aff *mpa,
4603 enum isl_dim_type type);
4604 __isl_give isl_aff *isl_multi_aff_get_aff(
4605 __isl_keep isl_multi_aff *multi, int pos);
4606 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4607 __isl_keep isl_pw_multi_aff *pma, int pos);
4608 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4609 __isl_keep isl_multi_pw_aff *mpa, int pos);
4610 int isl_multi_aff_find_dim_by_id(
4611 __isl_keep isl_multi_aff *ma,
4612 enum isl_dim_type type, __isl_keep isl_id *id);
4613 int isl_multi_pw_aff_find_dim_by_id(
4614 __isl_keep isl_multi_pw_aff *mpa,
4615 enum isl_dim_type type, __isl_keep isl_id *id);
4616 const char *isl_pw_multi_aff_get_dim_name(
4617 __isl_keep isl_pw_multi_aff *pma,
4618 enum isl_dim_type type, unsigned pos);
4619 __isl_give isl_id *isl_multi_aff_get_dim_id(
4620 __isl_keep isl_multi_aff *ma,
4621 enum isl_dim_type type, unsigned pos);
4622 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4623 __isl_keep isl_pw_multi_aff *pma,
4624 enum isl_dim_type type, unsigned pos);
4625 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4626 __isl_keep isl_multi_pw_aff *mpa,
4627 enum isl_dim_type type, unsigned pos);
4628 const char *isl_multi_aff_get_tuple_name(
4629 __isl_keep isl_multi_aff *multi,
4630 enum isl_dim_type type);
4631 int isl_pw_multi_aff_has_tuple_name(
4632 __isl_keep isl_pw_multi_aff *pma,
4633 enum isl_dim_type type);
4634 const char *isl_pw_multi_aff_get_tuple_name(
4635 __isl_keep isl_pw_multi_aff *pma,
4636 enum isl_dim_type type);
4637 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4638 enum isl_dim_type type);
4639 int isl_pw_multi_aff_has_tuple_id(
4640 __isl_keep isl_pw_multi_aff *pma,
4641 enum isl_dim_type type);
4642 int isl_multi_pw_aff_has_tuple_id(
4643 __isl_keep isl_multi_pw_aff *mpa,
4644 enum isl_dim_type type);
4645 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4646 __isl_keep isl_multi_aff *ma,
4647 enum isl_dim_type type);
4648 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4649 __isl_keep isl_pw_multi_aff *pma,
4650 enum isl_dim_type type);
4651 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4652 __isl_keep isl_multi_pw_aff *mpa,
4653 enum isl_dim_type type);
4654 int isl_multi_aff_range_is_wrapping(
4655 __isl_keep isl_multi_aff *ma);
4656 int isl_multi_pw_aff_range_is_wrapping(
4657 __isl_keep isl_multi_pw_aff *mpa);
4659 int isl_pw_multi_aff_foreach_piece(
4660 __isl_keep isl_pw_multi_aff *pma,
4661 int (*fn)(__isl_take isl_set *set,
4662 __isl_take isl_multi_aff *maff,
4663 void *user), void *user);
4665 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4666 __isl_keep isl_union_pw_multi_aff *upma,
4667 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4668 void *user), void *user);
4670 It can be modified using
4672 #include <isl/aff.h>
4673 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4674 __isl_take isl_multi_aff *multi, int pos,
4675 __isl_take isl_aff *aff);
4676 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4677 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4678 __isl_take isl_pw_aff *pa);
4679 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4680 __isl_take isl_multi_aff *maff,
4681 enum isl_dim_type type, unsigned pos, const char *s);
4682 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4683 __isl_take isl_multi_aff *maff,
4684 enum isl_dim_type type, unsigned pos,
4685 __isl_take isl_id *id);
4686 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4687 __isl_take isl_multi_aff *maff,
4688 enum isl_dim_type type, const char *s);
4689 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4690 __isl_take isl_multi_aff *maff,
4691 enum isl_dim_type type, __isl_take isl_id *id);
4692 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4693 __isl_take isl_pw_multi_aff *pma,
4694 enum isl_dim_type type, __isl_take isl_id *id);
4695 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4696 __isl_take isl_multi_aff *ma,
4697 enum isl_dim_type type);
4698 __isl_give isl_multi_pw_aff *
4699 isl_multi_pw_aff_reset_tuple_id(
4700 __isl_take isl_multi_pw_aff *mpa,
4701 enum isl_dim_type type);
4702 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4703 __isl_take isl_multi_aff *ma);
4704 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4705 __isl_take isl_multi_pw_aff *mpa);
4707 __isl_give isl_multi_pw_aff *
4708 isl_multi_pw_aff_set_dim_name(
4709 __isl_take isl_multi_pw_aff *mpa,
4710 enum isl_dim_type type, unsigned pos, const char *s);
4711 __isl_give isl_multi_pw_aff *
4712 isl_multi_pw_aff_set_dim_id(
4713 __isl_take isl_multi_pw_aff *mpa,
4714 enum isl_dim_type type, unsigned pos,
4715 __isl_take isl_id *id);
4716 __isl_give isl_multi_pw_aff *
4717 isl_multi_pw_aff_set_tuple_name(
4718 __isl_take isl_multi_pw_aff *mpa,
4719 enum isl_dim_type type, const char *s);
4721 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4722 __isl_take isl_multi_aff *ma);
4724 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4725 __isl_take isl_multi_aff *ma,
4726 enum isl_dim_type type, unsigned first, unsigned n);
4727 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4728 __isl_take isl_multi_aff *ma,
4729 enum isl_dim_type type, unsigned n);
4730 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4731 __isl_take isl_multi_aff *maff,
4732 enum isl_dim_type type, unsigned first, unsigned n);
4733 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4734 __isl_take isl_pw_multi_aff *pma,
4735 enum isl_dim_type type, unsigned first, unsigned n);
4737 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4738 __isl_take isl_multi_pw_aff *mpa,
4739 enum isl_dim_type type, unsigned first, unsigned n);
4740 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4741 __isl_take isl_multi_pw_aff *mpa,
4742 enum isl_dim_type type, unsigned n);
4743 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4744 __isl_take isl_multi_pw_aff *pma,
4745 enum isl_dim_type dst_type, unsigned dst_pos,
4746 enum isl_dim_type src_type, unsigned src_pos,
4749 To check whether two multiple affine expressions are
4750 (obviously) equal to each other, use
4752 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4753 __isl_keep isl_multi_aff *maff2);
4754 int isl_pw_multi_aff_plain_is_equal(
4755 __isl_keep isl_pw_multi_aff *pma1,
4756 __isl_keep isl_pw_multi_aff *pma2);
4757 int isl_multi_pw_aff_plain_is_equal(
4758 __isl_keep isl_multi_pw_aff *mpa1,
4759 __isl_keep isl_multi_pw_aff *mpa2);
4760 int isl_multi_pw_aff_is_equal(
4761 __isl_keep isl_multi_pw_aff *mpa1,
4762 __isl_keep isl_multi_pw_aff *mpa2);
4766 #include <isl/aff.h>
4767 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4768 __isl_take isl_pw_multi_aff *pma1,
4769 __isl_take isl_pw_multi_aff *pma2);
4770 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4771 __isl_take isl_pw_multi_aff *pma1,
4772 __isl_take isl_pw_multi_aff *pma2);
4773 __isl_give isl_multi_aff *isl_multi_aff_floor(
4774 __isl_take isl_multi_aff *ma);
4775 __isl_give isl_multi_aff *isl_multi_aff_add(
4776 __isl_take isl_multi_aff *maff1,
4777 __isl_take isl_multi_aff *maff2);
4778 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4779 __isl_take isl_pw_multi_aff *pma1,
4780 __isl_take isl_pw_multi_aff *pma2);
4781 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4782 __isl_take isl_union_pw_multi_aff *upma1,
4783 __isl_take isl_union_pw_multi_aff *upma2);
4784 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4785 __isl_take isl_pw_multi_aff *pma1,
4786 __isl_take isl_pw_multi_aff *pma2);
4787 __isl_give isl_multi_aff *isl_multi_aff_sub(
4788 __isl_take isl_multi_aff *ma1,
4789 __isl_take isl_multi_aff *ma2);
4790 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4791 __isl_take isl_pw_multi_aff *pma1,
4792 __isl_take isl_pw_multi_aff *pma2);
4793 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4794 __isl_take isl_union_pw_multi_aff *upma1,
4795 __isl_take isl_union_pw_multi_aff *upma2);
4797 C<isl_multi_aff_sub> subtracts the second argument from the first.
4799 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4800 __isl_take isl_multi_aff *ma,
4801 __isl_take isl_val *v);
4802 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4803 __isl_take isl_pw_multi_aff *pma,
4804 __isl_take isl_val *v);
4805 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4806 __isl_take isl_multi_pw_aff *mpa,
4807 __isl_take isl_val *v);
4808 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4809 __isl_take isl_multi_aff *ma,
4810 __isl_take isl_multi_val *mv);
4811 __isl_give isl_pw_multi_aff *
4812 isl_pw_multi_aff_scale_multi_val(
4813 __isl_take isl_pw_multi_aff *pma,
4814 __isl_take isl_multi_val *mv);
4815 __isl_give isl_multi_pw_aff *
4816 isl_multi_pw_aff_scale_multi_val(
4817 __isl_take isl_multi_pw_aff *mpa,
4818 __isl_take isl_multi_val *mv);
4819 __isl_give isl_union_pw_multi_aff *
4820 isl_union_pw_multi_aff_scale_multi_val(
4821 __isl_take isl_union_pw_multi_aff *upma,
4822 __isl_take isl_multi_val *mv);
4823 __isl_give isl_multi_aff *
4824 isl_multi_aff_scale_down_multi_val(
4825 __isl_take isl_multi_aff *ma,
4826 __isl_take isl_multi_val *mv);
4827 __isl_give isl_multi_pw_aff *
4828 isl_multi_pw_aff_scale_down_multi_val(
4829 __isl_take isl_multi_pw_aff *mpa,
4830 __isl_take isl_multi_val *mv);
4832 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4833 by the corresponding elements of C<mv>.
4835 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4836 __isl_take isl_pw_multi_aff *pma,
4837 enum isl_dim_type type, unsigned pos, int value);
4838 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4839 __isl_take isl_pw_multi_aff *pma,
4840 __isl_take isl_set *set);
4841 __isl_give isl_set *isl_multi_pw_aff_domain(
4842 __isl_take isl_multi_pw_aff *mpa);
4843 __isl_give isl_multi_pw_aff *
4844 isl_multi_pw_aff_intersect_params(
4845 __isl_take isl_multi_pw_aff *mpa,
4846 __isl_take isl_set *set);
4847 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4848 __isl_take isl_pw_multi_aff *pma,
4849 __isl_take isl_set *set);
4850 __isl_give isl_multi_pw_aff *
4851 isl_multi_pw_aff_intersect_domain(
4852 __isl_take isl_multi_pw_aff *mpa,
4853 __isl_take isl_set *domain);
4854 __isl_give isl_union_pw_multi_aff *
4855 isl_union_pw_multi_aff_intersect_domain(
4856 __isl_take isl_union_pw_multi_aff *upma,
4857 __isl_take isl_union_set *uset);
4858 __isl_give isl_multi_aff *isl_multi_aff_lift(
4859 __isl_take isl_multi_aff *maff,
4860 __isl_give isl_local_space **ls);
4861 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4862 __isl_take isl_pw_multi_aff *pma);
4863 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4864 __isl_take isl_multi_pw_aff *mpa);
4865 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4866 __isl_take isl_multi_aff *multi,
4867 __isl_take isl_space *model);
4868 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4869 __isl_take isl_pw_multi_aff *pma,
4870 __isl_take isl_space *model);
4871 __isl_give isl_union_pw_multi_aff *
4872 isl_union_pw_multi_aff_align_params(
4873 __isl_take isl_union_pw_multi_aff *upma,
4874 __isl_take isl_space *model);
4875 __isl_give isl_pw_multi_aff *
4876 isl_pw_multi_aff_project_domain_on_params(
4877 __isl_take isl_pw_multi_aff *pma);
4878 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4879 __isl_take isl_multi_aff *maff,
4880 __isl_take isl_set *context);
4881 __isl_give isl_multi_aff *isl_multi_aff_gist(
4882 __isl_take isl_multi_aff *maff,
4883 __isl_take isl_set *context);
4884 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4885 __isl_take isl_pw_multi_aff *pma,
4886 __isl_take isl_set *set);
4887 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4888 __isl_take isl_pw_multi_aff *pma,
4889 __isl_take isl_set *set);
4890 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4891 __isl_take isl_multi_pw_aff *mpa,
4892 __isl_take isl_set *set);
4893 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4894 __isl_take isl_multi_pw_aff *mpa,
4895 __isl_take isl_set *set);
4896 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4897 __isl_take isl_multi_aff *ma);
4898 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4899 __isl_take isl_multi_pw_aff *mpa);
4900 __isl_give isl_set *isl_pw_multi_aff_domain(
4901 __isl_take isl_pw_multi_aff *pma);
4902 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4903 __isl_take isl_union_pw_multi_aff *upma);
4904 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4905 __isl_take isl_multi_aff *ma1, unsigned pos,
4906 __isl_take isl_multi_aff *ma2);
4907 __isl_give isl_multi_aff *isl_multi_aff_splice(
4908 __isl_take isl_multi_aff *ma1,
4909 unsigned in_pos, unsigned out_pos,
4910 __isl_take isl_multi_aff *ma2);
4911 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4912 __isl_take isl_multi_aff *ma1,
4913 __isl_take isl_multi_aff *ma2);
4914 __isl_give isl_multi_aff *
4915 isl_multi_aff_range_factor_domain(
4916 __isl_take isl_multi_aff *ma);
4917 __isl_give isl_multi_aff *
4918 isl_multi_aff_range_factor_range(
4919 __isl_take isl_multi_aff *ma);
4920 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4921 __isl_take isl_multi_aff *ma1,
4922 __isl_take isl_multi_aff *ma2);
4923 __isl_give isl_multi_aff *isl_multi_aff_product(
4924 __isl_take isl_multi_aff *ma1,
4925 __isl_take isl_multi_aff *ma2);
4926 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4927 __isl_take isl_multi_pw_aff *mpa1,
4928 __isl_take isl_multi_pw_aff *mpa2);
4929 __isl_give isl_pw_multi_aff *
4930 isl_pw_multi_aff_range_product(
4931 __isl_take isl_pw_multi_aff *pma1,
4932 __isl_take isl_pw_multi_aff *pma2);
4933 __isl_give isl_multi_pw_aff *
4934 isl_multi_pw_aff_range_factor_domain(
4935 __isl_take isl_multi_pw_aff *mpa);
4936 __isl_give isl_multi_pw_aff *
4937 isl_multi_pw_aff_range_factor_range(
4938 __isl_take isl_multi_pw_aff *mpa);
4939 __isl_give isl_pw_multi_aff *
4940 isl_pw_multi_aff_flat_range_product(
4941 __isl_take isl_pw_multi_aff *pma1,
4942 __isl_take isl_pw_multi_aff *pma2);
4943 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4944 __isl_take isl_pw_multi_aff *pma1,
4945 __isl_take isl_pw_multi_aff *pma2);
4946 __isl_give isl_union_pw_multi_aff *
4947 isl_union_pw_multi_aff_flat_range_product(
4948 __isl_take isl_union_pw_multi_aff *upma1,
4949 __isl_take isl_union_pw_multi_aff *upma2);
4950 __isl_give isl_multi_pw_aff *
4951 isl_multi_pw_aff_range_splice(
4952 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4953 __isl_take isl_multi_pw_aff *mpa2);
4954 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4955 __isl_take isl_multi_pw_aff *mpa1,
4956 unsigned in_pos, unsigned out_pos,
4957 __isl_take isl_multi_pw_aff *mpa2);
4958 __isl_give isl_multi_pw_aff *
4959 isl_multi_pw_aff_range_product(
4960 __isl_take isl_multi_pw_aff *mpa1,
4961 __isl_take isl_multi_pw_aff *mpa2);
4962 __isl_give isl_multi_pw_aff *
4963 isl_multi_pw_aff_flat_range_product(
4964 __isl_take isl_multi_pw_aff *mpa1,
4965 __isl_take isl_multi_pw_aff *mpa2);
4967 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4968 then it is assigned the local space that lies at the basis of
4969 the lifting applied.
4971 #include <isl/aff.h>
4972 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4973 __isl_take isl_multi_aff *ma1,
4974 __isl_take isl_multi_aff *ma2);
4975 __isl_give isl_pw_multi_aff *
4976 isl_pw_multi_aff_pullback_multi_aff(
4977 __isl_take isl_pw_multi_aff *pma,
4978 __isl_take isl_multi_aff *ma);
4979 __isl_give isl_multi_pw_aff *
4980 isl_multi_pw_aff_pullback_multi_aff(
4981 __isl_take isl_multi_pw_aff *mpa,
4982 __isl_take isl_multi_aff *ma);
4983 __isl_give isl_pw_multi_aff *
4984 isl_pw_multi_aff_pullback_pw_multi_aff(
4985 __isl_take isl_pw_multi_aff *pma1,
4986 __isl_take isl_pw_multi_aff *pma2);
4987 __isl_give isl_multi_pw_aff *
4988 isl_multi_pw_aff_pullback_pw_multi_aff(
4989 __isl_take isl_multi_pw_aff *mpa,
4990 __isl_take isl_pw_multi_aff *pma);
4991 __isl_give isl_multi_pw_aff *
4992 isl_multi_pw_aff_pullback_multi_pw_aff(
4993 __isl_take isl_multi_pw_aff *mpa1,
4994 __isl_take isl_multi_pw_aff *mpa2);
4996 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4997 In other words, C<ma2> is plugged
5000 __isl_give isl_set *isl_multi_aff_lex_le_set(
5001 __isl_take isl_multi_aff *ma1,
5002 __isl_take isl_multi_aff *ma2);
5003 __isl_give isl_set *isl_multi_aff_lex_ge_set(
5004 __isl_take isl_multi_aff *ma1,
5005 __isl_take isl_multi_aff *ma2);
5007 The function C<isl_multi_aff_lex_le_set> returns a set
5008 containing those elements in the shared domain space
5009 where C<ma1> is lexicographically smaller than or
5012 An expression can be read from input using
5014 #include <isl/aff.h>
5015 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
5016 isl_ctx *ctx, const char *str);
5017 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
5018 isl_ctx *ctx, const char *str);
5019 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
5020 isl_ctx *ctx, const char *str);
5021 __isl_give isl_union_pw_multi_aff *
5022 isl_union_pw_multi_aff_read_from_str(
5023 isl_ctx *ctx, const char *str);
5025 An expression can be printed using
5027 #include <isl/aff.h>
5028 __isl_give isl_printer *isl_printer_print_multi_aff(
5029 __isl_take isl_printer *p,
5030 __isl_keep isl_multi_aff *maff);
5031 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
5032 __isl_take isl_printer *p,
5033 __isl_keep isl_pw_multi_aff *pma);
5034 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
5035 __isl_take isl_printer *p,
5036 __isl_keep isl_union_pw_multi_aff *upma);
5037 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
5038 __isl_take isl_printer *p,
5039 __isl_keep isl_multi_pw_aff *mpa);
5043 Points are elements of a set. They can be used to construct
5044 simple sets (boxes) or they can be used to represent the
5045 individual elements of a set.
5046 The zero point (the origin) can be created using
5048 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
5050 The coordinates of a point can be inspected, set and changed
5053 __isl_give isl_val *isl_point_get_coordinate_val(
5054 __isl_keep isl_point *pnt,
5055 enum isl_dim_type type, int pos);
5056 __isl_give isl_point *isl_point_set_coordinate_val(
5057 __isl_take isl_point *pnt,
5058 enum isl_dim_type type, int pos,
5059 __isl_take isl_val *v);
5061 __isl_give isl_point *isl_point_add_ui(
5062 __isl_take isl_point *pnt,
5063 enum isl_dim_type type, int pos, unsigned val);
5064 __isl_give isl_point *isl_point_sub_ui(
5065 __isl_take isl_point *pnt,
5066 enum isl_dim_type type, int pos, unsigned val);
5068 Other properties can be obtained using
5070 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
5072 Points can be copied or freed using
5074 __isl_give isl_point *isl_point_copy(
5075 __isl_keep isl_point *pnt);
5076 void isl_point_free(__isl_take isl_point *pnt);
5078 A singleton set can be created from a point using
5080 __isl_give isl_basic_set *isl_basic_set_from_point(
5081 __isl_take isl_point *pnt);
5082 __isl_give isl_set *isl_set_from_point(
5083 __isl_take isl_point *pnt);
5085 and a box can be created from two opposite extremal points using
5087 __isl_give isl_basic_set *isl_basic_set_box_from_points(
5088 __isl_take isl_point *pnt1,
5089 __isl_take isl_point *pnt2);
5090 __isl_give isl_set *isl_set_box_from_points(
5091 __isl_take isl_point *pnt1,
5092 __isl_take isl_point *pnt2);
5094 All elements of a B<bounded> (union) set can be enumerated using
5095 the following functions.
5097 int isl_set_foreach_point(__isl_keep isl_set *set,
5098 int (*fn)(__isl_take isl_point *pnt, void *user),
5100 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
5101 int (*fn)(__isl_take isl_point *pnt, void *user),
5104 The function C<fn> is called for each integer point in
5105 C<set> with as second argument the last argument of
5106 the C<isl_set_foreach_point> call. The function C<fn>
5107 should return C<0> on success and C<-1> on failure.
5108 In the latter case, C<isl_set_foreach_point> will stop
5109 enumerating and return C<-1> as well.
5110 If the enumeration is performed successfully and to completion,
5111 then C<isl_set_foreach_point> returns C<0>.
5113 To obtain a single point of a (basic) set, use
5115 __isl_give isl_point *isl_basic_set_sample_point(
5116 __isl_take isl_basic_set *bset);
5117 __isl_give isl_point *isl_set_sample_point(
5118 __isl_take isl_set *set);
5120 If C<set> does not contain any (integer) points, then the
5121 resulting point will be ``void'', a property that can be
5124 int isl_point_is_void(__isl_keep isl_point *pnt);
5126 =head2 Piecewise Quasipolynomials
5128 A piecewise quasipolynomial is a particular kind of function that maps
5129 a parametric point to a rational value.
5130 More specifically, a quasipolynomial is a polynomial expression in greatest
5131 integer parts of affine expressions of parameters and variables.
5132 A piecewise quasipolynomial is a subdivision of a given parametric
5133 domain into disjoint cells with a quasipolynomial associated to
5134 each cell. The value of the piecewise quasipolynomial at a given
5135 point is the value of the quasipolynomial associated to the cell
5136 that contains the point. Outside of the union of cells,
5137 the value is assumed to be zero.
5138 For example, the piecewise quasipolynomial
5140 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
5142 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
5143 A given piecewise quasipolynomial has a fixed domain dimension.
5144 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
5145 defined over different domains.
5146 Piecewise quasipolynomials are mainly used by the C<barvinok>
5147 library for representing the number of elements in a parametric set or map.
5148 For example, the piecewise quasipolynomial above represents
5149 the number of points in the map
5151 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
5153 =head3 Input and Output
5155 Piecewise quasipolynomials can be read from input using
5157 __isl_give isl_union_pw_qpolynomial *
5158 isl_union_pw_qpolynomial_read_from_str(
5159 isl_ctx *ctx, const char *str);
5161 Quasipolynomials and piecewise quasipolynomials can be printed
5162 using the following functions.
5164 __isl_give isl_printer *isl_printer_print_qpolynomial(
5165 __isl_take isl_printer *p,
5166 __isl_keep isl_qpolynomial *qp);
5168 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
5169 __isl_take isl_printer *p,
5170 __isl_keep isl_pw_qpolynomial *pwqp);
5172 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
5173 __isl_take isl_printer *p,
5174 __isl_keep isl_union_pw_qpolynomial *upwqp);
5176 The output format of the printer
5177 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5178 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
5180 In case of printing in C<ISL_FORMAT_C>, the user may want
5181 to set the names of all dimensions
5183 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
5184 __isl_take isl_qpolynomial *qp,
5185 enum isl_dim_type type, unsigned pos,
5187 __isl_give isl_pw_qpolynomial *
5188 isl_pw_qpolynomial_set_dim_name(
5189 __isl_take isl_pw_qpolynomial *pwqp,
5190 enum isl_dim_type type, unsigned pos,
5193 =head3 Creating New (Piecewise) Quasipolynomials
5195 Some simple quasipolynomials can be created using the following functions.
5196 More complicated quasipolynomials can be created by applying
5197 operations such as addition and multiplication
5198 on the resulting quasipolynomials
5200 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
5201 __isl_take isl_space *domain);
5202 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
5203 __isl_take isl_space *domain);
5204 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
5205 __isl_take isl_space *domain);
5206 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
5207 __isl_take isl_space *domain);
5208 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
5209 __isl_take isl_space *domain);
5210 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
5211 __isl_take isl_space *domain,
5212 __isl_take isl_val *val);
5213 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
5214 __isl_take isl_space *domain,
5215 enum isl_dim_type type, unsigned pos);
5216 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
5217 __isl_take isl_aff *aff);
5219 Note that the space in which a quasipolynomial lives is a map space
5220 with a one-dimensional range. The C<domain> argument in some of
5221 the functions above corresponds to the domain of this map space.
5223 The zero piecewise quasipolynomial or a piecewise quasipolynomial
5224 with a single cell can be created using the following functions.
5225 Multiple of these single cell piecewise quasipolynomials can
5226 be combined to create more complicated piecewise quasipolynomials.
5228 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
5229 __isl_take isl_space *space);
5230 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
5231 __isl_take isl_set *set,
5232 __isl_take isl_qpolynomial *qp);
5233 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
5234 __isl_take isl_qpolynomial *qp);
5235 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
5236 __isl_take isl_pw_aff *pwaff);
5238 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
5239 __isl_take isl_space *space);
5240 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
5241 __isl_take isl_pw_qpolynomial *pwqp);
5242 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
5243 __isl_take isl_union_pw_qpolynomial *upwqp,
5244 __isl_take isl_pw_qpolynomial *pwqp);
5246 Quasipolynomials can be copied and freed again using the following
5249 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
5250 __isl_keep isl_qpolynomial *qp);
5251 __isl_null isl_qpolynomial *isl_qpolynomial_free(
5252 __isl_take isl_qpolynomial *qp);
5254 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
5255 __isl_keep isl_pw_qpolynomial *pwqp);
5256 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
5257 __isl_take isl_pw_qpolynomial *pwqp);
5259 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
5260 __isl_keep isl_union_pw_qpolynomial *upwqp);
5261 __isl_null isl_union_pw_qpolynomial *
5262 isl_union_pw_qpolynomial_free(
5263 __isl_take isl_union_pw_qpolynomial *upwqp);
5265 =head3 Inspecting (Piecewise) Quasipolynomials
5267 To iterate over all piecewise quasipolynomials in a union
5268 piecewise quasipolynomial, use the following function
5270 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
5271 __isl_keep isl_union_pw_qpolynomial *upwqp,
5272 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
5275 To extract the piecewise quasipolynomial in a given space from a union, use
5277 __isl_give isl_pw_qpolynomial *
5278 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
5279 __isl_keep isl_union_pw_qpolynomial *upwqp,
5280 __isl_take isl_space *space);
5282 To iterate over the cells in a piecewise quasipolynomial,
5283 use either of the following two functions
5285 int isl_pw_qpolynomial_foreach_piece(
5286 __isl_keep isl_pw_qpolynomial *pwqp,
5287 int (*fn)(__isl_take isl_set *set,
5288 __isl_take isl_qpolynomial *qp,
5289 void *user), void *user);
5290 int isl_pw_qpolynomial_foreach_lifted_piece(
5291 __isl_keep isl_pw_qpolynomial *pwqp,
5292 int (*fn)(__isl_take isl_set *set,
5293 __isl_take isl_qpolynomial *qp,
5294 void *user), void *user);
5296 As usual, the function C<fn> should return C<0> on success
5297 and C<-1> on failure. The difference between
5298 C<isl_pw_qpolynomial_foreach_piece> and
5299 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
5300 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
5301 compute unique representations for all existentially quantified
5302 variables and then turn these existentially quantified variables
5303 into extra set variables, adapting the associated quasipolynomial
5304 accordingly. This means that the C<set> passed to C<fn>
5305 will not have any existentially quantified variables, but that
5306 the dimensions of the sets may be different for different
5307 invocations of C<fn>.
5309 The constant term of a quasipolynomial can be extracted using
5311 __isl_give isl_val *isl_qpolynomial_get_constant_val(
5312 __isl_keep isl_qpolynomial *qp);
5314 To iterate over all terms in a quasipolynomial,
5317 int isl_qpolynomial_foreach_term(
5318 __isl_keep isl_qpolynomial *qp,
5319 int (*fn)(__isl_take isl_term *term,
5320 void *user), void *user);
5322 The terms themselves can be inspected and freed using
5325 unsigned isl_term_dim(__isl_keep isl_term *term,
5326 enum isl_dim_type type);
5327 __isl_give isl_val *isl_term_get_coefficient_val(
5328 __isl_keep isl_term *term);
5329 int isl_term_get_exp(__isl_keep isl_term *term,
5330 enum isl_dim_type type, unsigned pos);
5331 __isl_give isl_aff *isl_term_get_div(
5332 __isl_keep isl_term *term, unsigned pos);
5333 void isl_term_free(__isl_take isl_term *term);
5335 Each term is a product of parameters, set variables and
5336 integer divisions. The function C<isl_term_get_exp>
5337 returns the exponent of a given dimensions in the given term.
5339 =head3 Properties of (Piecewise) Quasipolynomials
5341 To check whether two union piecewise quasipolynomials are
5342 obviously equal, use
5344 int isl_union_pw_qpolynomial_plain_is_equal(
5345 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5346 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5348 =head3 Operations on (Piecewise) Quasipolynomials
5350 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5351 __isl_take isl_qpolynomial *qp,
5352 __isl_take isl_val *v);
5353 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5354 __isl_take isl_qpolynomial *qp);
5355 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5356 __isl_take isl_qpolynomial *qp1,
5357 __isl_take isl_qpolynomial *qp2);
5358 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5359 __isl_take isl_qpolynomial *qp1,
5360 __isl_take isl_qpolynomial *qp2);
5361 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5362 __isl_take isl_qpolynomial *qp1,
5363 __isl_take isl_qpolynomial *qp2);
5364 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5365 __isl_take isl_qpolynomial *qp, unsigned exponent);
5367 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5368 __isl_take isl_pw_qpolynomial *pwqp,
5369 enum isl_dim_type type, unsigned n,
5370 __isl_take isl_val *v);
5371 __isl_give isl_pw_qpolynomial *
5372 isl_pw_qpolynomial_scale_val(
5373 __isl_take isl_pw_qpolynomial *pwqp,
5374 __isl_take isl_val *v);
5375 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5376 __isl_take isl_pw_qpolynomial *pwqp1,
5377 __isl_take isl_pw_qpolynomial *pwqp2);
5378 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5379 __isl_take isl_pw_qpolynomial *pwqp1,
5380 __isl_take isl_pw_qpolynomial *pwqp2);
5381 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5382 __isl_take isl_pw_qpolynomial *pwqp1,
5383 __isl_take isl_pw_qpolynomial *pwqp2);
5384 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5385 __isl_take isl_pw_qpolynomial *pwqp);
5386 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5387 __isl_take isl_pw_qpolynomial *pwqp1,
5388 __isl_take isl_pw_qpolynomial *pwqp2);
5389 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5390 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5392 __isl_give isl_union_pw_qpolynomial *
5393 isl_union_pw_qpolynomial_scale_val(
5394 __isl_take isl_union_pw_qpolynomial *upwqp,
5395 __isl_take isl_val *v);
5396 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5397 __isl_take isl_union_pw_qpolynomial *upwqp1,
5398 __isl_take isl_union_pw_qpolynomial *upwqp2);
5399 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5400 __isl_take isl_union_pw_qpolynomial *upwqp1,
5401 __isl_take isl_union_pw_qpolynomial *upwqp2);
5402 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5403 __isl_take isl_union_pw_qpolynomial *upwqp1,
5404 __isl_take isl_union_pw_qpolynomial *upwqp2);
5406 __isl_give isl_val *isl_pw_qpolynomial_eval(
5407 __isl_take isl_pw_qpolynomial *pwqp,
5408 __isl_take isl_point *pnt);
5410 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5411 __isl_take isl_union_pw_qpolynomial *upwqp,
5412 __isl_take isl_point *pnt);
5414 __isl_give isl_set *isl_pw_qpolynomial_domain(
5415 __isl_take isl_pw_qpolynomial *pwqp);
5416 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5417 __isl_take isl_pw_qpolynomial *pwpq,
5418 __isl_take isl_set *set);
5419 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5420 __isl_take isl_pw_qpolynomial *pwpq,
5421 __isl_take isl_set *set);
5423 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5424 __isl_take isl_union_pw_qpolynomial *upwqp);
5425 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5426 __isl_take isl_union_pw_qpolynomial *upwpq,
5427 __isl_take isl_union_set *uset);
5428 __isl_give isl_union_pw_qpolynomial *
5429 isl_union_pw_qpolynomial_intersect_params(
5430 __isl_take isl_union_pw_qpolynomial *upwpq,
5431 __isl_take isl_set *set);
5433 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5434 __isl_take isl_qpolynomial *qp,
5435 __isl_take isl_space *model);
5437 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5438 __isl_take isl_qpolynomial *qp);
5439 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5440 __isl_take isl_pw_qpolynomial *pwqp);
5442 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5443 __isl_take isl_union_pw_qpolynomial *upwqp);
5445 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5446 __isl_take isl_qpolynomial *qp,
5447 __isl_take isl_set *context);
5448 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5449 __isl_take isl_qpolynomial *qp,
5450 __isl_take isl_set *context);
5452 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5453 __isl_take isl_pw_qpolynomial *pwqp,
5454 __isl_take isl_set *context);
5455 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5456 __isl_take isl_pw_qpolynomial *pwqp,
5457 __isl_take isl_set *context);
5459 __isl_give isl_union_pw_qpolynomial *
5460 isl_union_pw_qpolynomial_gist_params(
5461 __isl_take isl_union_pw_qpolynomial *upwqp,
5462 __isl_take isl_set *context);
5463 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5464 __isl_take isl_union_pw_qpolynomial *upwqp,
5465 __isl_take isl_union_set *context);
5467 The gist operation applies the gist operation to each of
5468 the cells in the domain of the input piecewise quasipolynomial.
5469 The context is also exploited
5470 to simplify the quasipolynomials associated to each cell.
5472 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5473 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5474 __isl_give isl_union_pw_qpolynomial *
5475 isl_union_pw_qpolynomial_to_polynomial(
5476 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5478 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5479 the polynomial will be an overapproximation. If C<sign> is negative,
5480 it will be an underapproximation. If C<sign> is zero, the approximation
5481 will lie somewhere in between.
5483 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5485 A piecewise quasipolynomial reduction is a piecewise
5486 reduction (or fold) of quasipolynomials.
5487 In particular, the reduction can be maximum or a minimum.
5488 The objects are mainly used to represent the result of
5489 an upper or lower bound on a quasipolynomial over its domain,
5490 i.e., as the result of the following function.
5492 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5493 __isl_take isl_pw_qpolynomial *pwqp,
5494 enum isl_fold type, int *tight);
5496 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5497 __isl_take isl_union_pw_qpolynomial *upwqp,
5498 enum isl_fold type, int *tight);
5500 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5501 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5502 is the returned bound is known be tight, i.e., for each value
5503 of the parameters there is at least
5504 one element in the domain that reaches the bound.
5505 If the domain of C<pwqp> is not wrapping, then the bound is computed
5506 over all elements in that domain and the result has a purely parametric
5507 domain. If the domain of C<pwqp> is wrapping, then the bound is
5508 computed over the range of the wrapped relation. The domain of the
5509 wrapped relation becomes the domain of the result.
5511 A (piecewise) quasipolynomial reduction can be copied or freed using the
5512 following functions.
5514 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5515 __isl_keep isl_qpolynomial_fold *fold);
5516 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5517 __isl_keep isl_pw_qpolynomial_fold *pwf);
5518 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5519 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5520 void isl_qpolynomial_fold_free(
5521 __isl_take isl_qpolynomial_fold *fold);
5522 __isl_null isl_pw_qpolynomial_fold *
5523 isl_pw_qpolynomial_fold_free(
5524 __isl_take isl_pw_qpolynomial_fold *pwf);
5525 __isl_null isl_union_pw_qpolynomial_fold *
5526 isl_union_pw_qpolynomial_fold_free(
5527 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5529 =head3 Printing Piecewise Quasipolynomial Reductions
5531 Piecewise quasipolynomial reductions can be printed
5532 using the following function.
5534 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5535 __isl_take isl_printer *p,
5536 __isl_keep isl_pw_qpolynomial_fold *pwf);
5537 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5538 __isl_take isl_printer *p,
5539 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5541 For C<isl_printer_print_pw_qpolynomial_fold>,
5542 output format of the printer
5543 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5544 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5545 output format of the printer
5546 needs to be set to C<ISL_FORMAT_ISL>.
5547 In case of printing in C<ISL_FORMAT_C>, the user may want
5548 to set the names of all dimensions
5550 __isl_give isl_pw_qpolynomial_fold *
5551 isl_pw_qpolynomial_fold_set_dim_name(
5552 __isl_take isl_pw_qpolynomial_fold *pwf,
5553 enum isl_dim_type type, unsigned pos,
5556 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5558 To iterate over all piecewise quasipolynomial reductions in a union
5559 piecewise quasipolynomial reduction, use the following function
5561 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5562 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5563 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5564 void *user), void *user);
5566 To iterate over the cells in a piecewise quasipolynomial reduction,
5567 use either of the following two functions
5569 int isl_pw_qpolynomial_fold_foreach_piece(
5570 __isl_keep isl_pw_qpolynomial_fold *pwf,
5571 int (*fn)(__isl_take isl_set *set,
5572 __isl_take isl_qpolynomial_fold *fold,
5573 void *user), void *user);
5574 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5575 __isl_keep isl_pw_qpolynomial_fold *pwf,
5576 int (*fn)(__isl_take isl_set *set,
5577 __isl_take isl_qpolynomial_fold *fold,
5578 void *user), void *user);
5580 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5581 of the difference between these two functions.
5583 To iterate over all quasipolynomials in a reduction, use
5585 int isl_qpolynomial_fold_foreach_qpolynomial(
5586 __isl_keep isl_qpolynomial_fold *fold,
5587 int (*fn)(__isl_take isl_qpolynomial *qp,
5588 void *user), void *user);
5590 =head3 Properties of Piecewise Quasipolynomial Reductions
5592 To check whether two union piecewise quasipolynomial reductions are
5593 obviously equal, use
5595 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5596 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5597 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5599 =head3 Operations on Piecewise Quasipolynomial Reductions
5601 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5602 __isl_take isl_qpolynomial_fold *fold,
5603 __isl_take isl_val *v);
5604 __isl_give isl_pw_qpolynomial_fold *
5605 isl_pw_qpolynomial_fold_scale_val(
5606 __isl_take isl_pw_qpolynomial_fold *pwf,
5607 __isl_take isl_val *v);
5608 __isl_give isl_union_pw_qpolynomial_fold *
5609 isl_union_pw_qpolynomial_fold_scale_val(
5610 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5611 __isl_take isl_val *v);
5613 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5614 __isl_take isl_pw_qpolynomial_fold *pwf1,
5615 __isl_take isl_pw_qpolynomial_fold *pwf2);
5617 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5618 __isl_take isl_pw_qpolynomial_fold *pwf1,
5619 __isl_take isl_pw_qpolynomial_fold *pwf2);
5621 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5622 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5623 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5625 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5626 __isl_take isl_pw_qpolynomial_fold *pwf,
5627 __isl_take isl_point *pnt);
5629 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5630 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5631 __isl_take isl_point *pnt);
5633 __isl_give isl_pw_qpolynomial_fold *
5634 isl_pw_qpolynomial_fold_intersect_params(
5635 __isl_take isl_pw_qpolynomial_fold *pwf,
5636 __isl_take isl_set *set);
5638 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5639 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5640 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5641 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5642 __isl_take isl_union_set *uset);
5643 __isl_give isl_union_pw_qpolynomial_fold *
5644 isl_union_pw_qpolynomial_fold_intersect_params(
5645 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5646 __isl_take isl_set *set);
5648 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5649 __isl_take isl_pw_qpolynomial_fold *pwf);
5651 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5652 __isl_take isl_pw_qpolynomial_fold *pwf);
5654 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5655 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5657 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5658 __isl_take isl_qpolynomial_fold *fold,
5659 __isl_take isl_set *context);
5660 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5661 __isl_take isl_qpolynomial_fold *fold,
5662 __isl_take isl_set *context);
5664 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5665 __isl_take isl_pw_qpolynomial_fold *pwf,
5666 __isl_take isl_set *context);
5667 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5668 __isl_take isl_pw_qpolynomial_fold *pwf,
5669 __isl_take isl_set *context);
5671 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5672 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5673 __isl_take isl_union_set *context);
5674 __isl_give isl_union_pw_qpolynomial_fold *
5675 isl_union_pw_qpolynomial_fold_gist_params(
5676 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5677 __isl_take isl_set *context);
5679 The gist operation applies the gist operation to each of
5680 the cells in the domain of the input piecewise quasipolynomial reduction.
5681 In future, the operation will also exploit the context
5682 to simplify the quasipolynomial reductions associated to each cell.
5684 __isl_give isl_pw_qpolynomial_fold *
5685 isl_set_apply_pw_qpolynomial_fold(
5686 __isl_take isl_set *set,
5687 __isl_take isl_pw_qpolynomial_fold *pwf,
5689 __isl_give isl_pw_qpolynomial_fold *
5690 isl_map_apply_pw_qpolynomial_fold(
5691 __isl_take isl_map *map,
5692 __isl_take isl_pw_qpolynomial_fold *pwf,
5694 __isl_give isl_union_pw_qpolynomial_fold *
5695 isl_union_set_apply_union_pw_qpolynomial_fold(
5696 __isl_take isl_union_set *uset,
5697 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5699 __isl_give isl_union_pw_qpolynomial_fold *
5700 isl_union_map_apply_union_pw_qpolynomial_fold(
5701 __isl_take isl_union_map *umap,
5702 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5705 The functions taking a map
5706 compose the given map with the given piecewise quasipolynomial reduction.
5707 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5708 over all elements in the intersection of the range of the map
5709 and the domain of the piecewise quasipolynomial reduction
5710 as a function of an element in the domain of the map.
5711 The functions taking a set compute a bound over all elements in the
5712 intersection of the set and the domain of the
5713 piecewise quasipolynomial reduction.
5715 =head2 Parametric Vertex Enumeration
5717 The parametric vertex enumeration described in this section
5718 is mainly intended to be used internally and by the C<barvinok>
5721 #include <isl/vertices.h>
5722 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5723 __isl_keep isl_basic_set *bset);
5725 The function C<isl_basic_set_compute_vertices> performs the
5726 actual computation of the parametric vertices and the chamber
5727 decomposition and store the result in an C<isl_vertices> object.
5728 This information can be queried by either iterating over all
5729 the vertices or iterating over all the chambers or cells
5730 and then iterating over all vertices that are active on the chamber.
5732 int isl_vertices_foreach_vertex(
5733 __isl_keep isl_vertices *vertices,
5734 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5737 int isl_vertices_foreach_cell(
5738 __isl_keep isl_vertices *vertices,
5739 int (*fn)(__isl_take isl_cell *cell, void *user),
5741 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5742 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5745 Other operations that can be performed on an C<isl_vertices> object are
5748 isl_ctx *isl_vertices_get_ctx(
5749 __isl_keep isl_vertices *vertices);
5750 int isl_vertices_get_n_vertices(
5751 __isl_keep isl_vertices *vertices);
5752 void isl_vertices_free(__isl_take isl_vertices *vertices);
5754 Vertices can be inspected and destroyed using the following functions.
5756 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5757 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5758 __isl_give isl_basic_set *isl_vertex_get_domain(
5759 __isl_keep isl_vertex *vertex);
5760 __isl_give isl_multi_aff *isl_vertex_get_expr(
5761 __isl_keep isl_vertex *vertex);
5762 void isl_vertex_free(__isl_take isl_vertex *vertex);
5764 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
5765 describing the vertex in terms of the parameters,
5766 while C<isl_vertex_get_domain> returns the activity domain
5769 Chambers can be inspected and destroyed using the following functions.
5771 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5772 __isl_give isl_basic_set *isl_cell_get_domain(
5773 __isl_keep isl_cell *cell);
5774 void isl_cell_free(__isl_take isl_cell *cell);
5776 =head1 Polyhedral Compilation Library
5778 This section collects functionality in C<isl> that has been specifically
5779 designed for use during polyhedral compilation.
5781 =head2 Dependence Analysis
5783 C<isl> contains specialized functionality for performing
5784 array dataflow analysis. That is, given a I<sink> access relation
5785 and a collection of possible I<source> access relations,
5786 C<isl> can compute relations that describe
5787 for each iteration of the sink access, which iteration
5788 of which of the source access relations was the last
5789 to access the same data element before the given iteration
5791 The resulting dependence relations map source iterations
5792 to the corresponding sink iterations.
5793 To compute standard flow dependences, the sink should be
5794 a read, while the sources should be writes.
5795 If any of the source accesses are marked as being I<may>
5796 accesses, then there will be a dependence from the last
5797 I<must> access B<and> from any I<may> access that follows
5798 this last I<must> access.
5799 In particular, if I<all> sources are I<may> accesses,
5800 then memory based dependence analysis is performed.
5801 If, on the other hand, all sources are I<must> accesses,
5802 then value based dependence analysis is performed.
5804 #include <isl/flow.h>
5806 typedef int (*isl_access_level_before)(void *first, void *second);
5808 __isl_give isl_access_info *isl_access_info_alloc(
5809 __isl_take isl_map *sink,
5810 void *sink_user, isl_access_level_before fn,
5812 __isl_give isl_access_info *isl_access_info_add_source(
5813 __isl_take isl_access_info *acc,
5814 __isl_take isl_map *source, int must,
5816 __isl_null isl_access_info *isl_access_info_free(
5817 __isl_take isl_access_info *acc);
5819 __isl_give isl_flow *isl_access_info_compute_flow(
5820 __isl_take isl_access_info *acc);
5822 int isl_flow_foreach(__isl_keep isl_flow *deps,
5823 int (*fn)(__isl_take isl_map *dep, int must,
5824 void *dep_user, void *user),
5826 __isl_give isl_map *isl_flow_get_no_source(
5827 __isl_keep isl_flow *deps, int must);
5828 void isl_flow_free(__isl_take isl_flow *deps);
5830 The function C<isl_access_info_compute_flow> performs the actual
5831 dependence analysis. The other functions are used to construct
5832 the input for this function or to read off the output.
5834 The input is collected in an C<isl_access_info>, which can
5835 be created through a call to C<isl_access_info_alloc>.
5836 The arguments to this functions are the sink access relation
5837 C<sink>, a token C<sink_user> used to identify the sink
5838 access to the user, a callback function for specifying the
5839 relative order of source and sink accesses, and the number
5840 of source access relations that will be added.
5841 The callback function has type C<int (*)(void *first, void *second)>.
5842 The function is called with two user supplied tokens identifying
5843 either a source or the sink and it should return the shared nesting
5844 level and the relative order of the two accesses.
5845 In particular, let I<n> be the number of loops shared by
5846 the two accesses. If C<first> precedes C<second> textually,
5847 then the function should return I<2 * n + 1>; otherwise,
5848 it should return I<2 * n>.
5849 The sources can be added to the C<isl_access_info> by performing
5850 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5851 C<must> indicates whether the source is a I<must> access
5852 or a I<may> access. Note that a multi-valued access relation
5853 should only be marked I<must> if every iteration in the domain
5854 of the relation accesses I<all> elements in its image.
5855 The C<source_user> token is again used to identify
5856 the source access. The range of the source access relation
5857 C<source> should have the same dimension as the range
5858 of the sink access relation.
5859 The C<isl_access_info_free> function should usually not be
5860 called explicitly, because it is called implicitly by
5861 C<isl_access_info_compute_flow>.
5863 The result of the dependence analysis is collected in an
5864 C<isl_flow>. There may be elements of
5865 the sink access for which no preceding source access could be
5866 found or for which all preceding sources are I<may> accesses.
5867 The relations containing these elements can be obtained through
5868 calls to C<isl_flow_get_no_source>, the first with C<must> set
5869 and the second with C<must> unset.
5870 In the case of standard flow dependence analysis,
5871 with the sink a read and the sources I<must> writes,
5872 the first relation corresponds to the reads from uninitialized
5873 array elements and the second relation is empty.
5874 The actual flow dependences can be extracted using
5875 C<isl_flow_foreach>. This function will call the user-specified
5876 callback function C<fn> for each B<non-empty> dependence between
5877 a source and the sink. The callback function is called
5878 with four arguments, the actual flow dependence relation
5879 mapping source iterations to sink iterations, a boolean that
5880 indicates whether it is a I<must> or I<may> dependence, a token
5881 identifying the source and an additional C<void *> with value
5882 equal to the third argument of the C<isl_flow_foreach> call.
5883 A dependence is marked I<must> if it originates from a I<must>
5884 source and if it is not followed by any I<may> sources.
5886 After finishing with an C<isl_flow>, the user should call
5887 C<isl_flow_free> to free all associated memory.
5889 A higher-level interface to dependence analysis is provided
5890 by the following function.
5892 #include <isl/flow.h>
5894 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5895 __isl_take isl_union_map *must_source,
5896 __isl_take isl_union_map *may_source,
5897 __isl_take isl_union_map *schedule,
5898 __isl_give isl_union_map **must_dep,
5899 __isl_give isl_union_map **may_dep,
5900 __isl_give isl_union_map **must_no_source,
5901 __isl_give isl_union_map **may_no_source);
5903 The arrays are identified by the tuple names of the ranges
5904 of the accesses. The iteration domains by the tuple names
5905 of the domains of the accesses and of the schedule.
5906 The relative order of the iteration domains is given by the
5907 schedule. The relations returned through C<must_no_source>
5908 and C<may_no_source> are subsets of C<sink>.
5909 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5910 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5911 any of the other arguments is treated as an error.
5913 =head3 Interaction with Dependence Analysis
5915 During the dependence analysis, we frequently need to perform
5916 the following operation. Given a relation between sink iterations
5917 and potential source iterations from a particular source domain,
5918 what is the last potential source iteration corresponding to each
5919 sink iteration. It can sometimes be convenient to adjust
5920 the set of potential source iterations before or after each such operation.
5921 The prototypical example is fuzzy array dataflow analysis,
5922 where we need to analyze if, based on data-dependent constraints,
5923 the sink iteration can ever be executed without one or more of
5924 the corresponding potential source iterations being executed.
5925 If so, we can introduce extra parameters and select an unknown
5926 but fixed source iteration from the potential source iterations.
5927 To be able to perform such manipulations, C<isl> provides the following
5930 #include <isl/flow.h>
5932 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5933 __isl_keep isl_map *source_map,
5934 __isl_keep isl_set *sink, void *source_user,
5936 __isl_give isl_access_info *isl_access_info_set_restrict(
5937 __isl_take isl_access_info *acc,
5938 isl_access_restrict fn, void *user);
5940 The function C<isl_access_info_set_restrict> should be called
5941 before calling C<isl_access_info_compute_flow> and registers a callback function
5942 that will be called any time C<isl> is about to compute the last
5943 potential source. The first argument is the (reverse) proto-dependence,
5944 mapping sink iterations to potential source iterations.
5945 The second argument represents the sink iterations for which
5946 we want to compute the last source iteration.
5947 The third argument is the token corresponding to the source
5948 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5949 The callback is expected to return a restriction on either the input or
5950 the output of the operation computing the last potential source.
5951 If the input needs to be restricted then restrictions are needed
5952 for both the source and the sink iterations. The sink iterations
5953 and the potential source iterations will be intersected with these sets.
5954 If the output needs to be restricted then only a restriction on the source
5955 iterations is required.
5956 If any error occurs, the callback should return C<NULL>.
5957 An C<isl_restriction> object can be created, freed and inspected
5958 using the following functions.
5960 #include <isl/flow.h>
5962 __isl_give isl_restriction *isl_restriction_input(
5963 __isl_take isl_set *source_restr,
5964 __isl_take isl_set *sink_restr);
5965 __isl_give isl_restriction *isl_restriction_output(
5966 __isl_take isl_set *source_restr);
5967 __isl_give isl_restriction *isl_restriction_none(
5968 __isl_take isl_map *source_map);
5969 __isl_give isl_restriction *isl_restriction_empty(
5970 __isl_take isl_map *source_map);
5971 __isl_null isl_restriction *isl_restriction_free(
5972 __isl_take isl_restriction *restr);
5973 isl_ctx *isl_restriction_get_ctx(
5974 __isl_keep isl_restriction *restr);
5976 C<isl_restriction_none> and C<isl_restriction_empty> are special
5977 cases of C<isl_restriction_input>. C<isl_restriction_none>
5978 is essentially equivalent to
5980 isl_restriction_input(isl_set_universe(
5981 isl_space_range(isl_map_get_space(source_map))),
5983 isl_space_domain(isl_map_get_space(source_map))));
5985 whereas C<isl_restriction_empty> is essentially equivalent to
5987 isl_restriction_input(isl_set_empty(
5988 isl_space_range(isl_map_get_space(source_map))),
5990 isl_space_domain(isl_map_get_space(source_map))));
5994 B<The functionality described in this section is fairly new
5995 and may be subject to change.>
5997 #include <isl/schedule.h>
5998 __isl_give isl_schedule *
5999 isl_schedule_constraints_compute_schedule(
6000 __isl_take isl_schedule_constraints *sc);
6001 __isl_null isl_schedule *isl_schedule_free(
6002 __isl_take isl_schedule *sched);
6004 The function C<isl_schedule_constraints_compute_schedule> can be
6005 used to compute a schedule that satisfy the given schedule constraints.
6006 These schedule constraints include the iteration domain for which
6007 a schedule should be computed and dependences between pairs of
6008 iterations. In particular, these dependences include
6009 I<validity> dependences and I<proximity> dependences.
6010 By default, the algorithm used to construct the schedule is similar
6011 to that of C<Pluto>.
6012 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
6014 The generated schedule respects all validity dependences.
6015 That is, all dependence distances over these dependences in the
6016 scheduled space are lexicographically positive.
6017 The default algorithm tries to ensure that the dependence distances
6018 over coincidence constraints are zero and to minimize the
6019 dependence distances over proximity dependences.
6020 Moreover, it tries to obtain sequences (bands) of schedule dimensions
6021 for groups of domains where the dependence distances over validity
6022 dependences have only non-negative values.
6023 When using Feautrier's algorithm, the coincidence and proximity constraints
6024 are only taken into account during the extension to a
6025 full-dimensional schedule.
6027 An C<isl_schedule_constraints> object can be constructed
6028 and manipulated using the following functions.
6030 #include <isl/schedule.h>
6031 __isl_give isl_schedule_constraints *
6032 isl_schedule_constraints_copy(
6033 __isl_keep isl_schedule_constraints *sc);
6034 __isl_give isl_schedule_constraints *
6035 isl_schedule_constraints_on_domain(
6036 __isl_take isl_union_set *domain);
6037 isl_ctx *isl_schedule_constraints_get_ctx(
6038 __isl_keep isl_schedule_constraints *sc);
6039 __isl_give isl_schedule_constraints *
6040 isl_schedule_constraints_set_validity(
6041 __isl_take isl_schedule_constraints *sc,
6042 __isl_take isl_union_map *validity);
6043 __isl_give isl_schedule_constraints *
6044 isl_schedule_constraints_set_coincidence(
6045 __isl_take isl_schedule_constraints *sc,
6046 __isl_take isl_union_map *coincidence);
6047 __isl_give isl_schedule_constraints *
6048 isl_schedule_constraints_set_proximity(
6049 __isl_take isl_schedule_constraints *sc,
6050 __isl_take isl_union_map *proximity);
6051 __isl_give isl_schedule_constraints *
6052 isl_schedule_constraints_set_conditional_validity(
6053 __isl_take isl_schedule_constraints *sc,
6054 __isl_take isl_union_map *condition,
6055 __isl_take isl_union_map *validity);
6056 __isl_null isl_schedule_constraints *
6057 isl_schedule_constraints_free(
6058 __isl_take isl_schedule_constraints *sc);
6060 The initial C<isl_schedule_constraints> object created by
6061 C<isl_schedule_constraints_on_domain> does not impose any constraints.
6062 That is, it has an empty set of dependences.
6063 The function C<isl_schedule_constraints_set_validity> replaces the
6064 validity dependences, mapping domain elements I<i> to domain
6065 elements that should be scheduled after I<i>.
6066 The function C<isl_schedule_constraints_set_coincidence> replaces the
6067 coincidence dependences, mapping domain elements I<i> to domain
6068 elements that should be scheduled together with I<I>, if possible.
6069 The function C<isl_schedule_constraints_set_proximity> replaces the
6070 proximity dependences, mapping domain elements I<i> to domain
6071 elements that should be scheduled either before I<I>
6072 or as early as possible after I<i>.
6074 The function C<isl_schedule_constraints_set_conditional_validity>
6075 replaces the conditional validity constraints.
6076 A conditional validity constraint is only imposed when any of the corresponding
6077 conditions is satisfied, i.e., when any of them is non-zero.
6078 That is, the scheduler ensures that within each band if the dependence
6079 distances over the condition constraints are not all zero
6080 then all corresponding conditional validity constraints are respected.
6081 A conditional validity constraint corresponds to a condition
6082 if the two are adjacent, i.e., if the domain of one relation intersect
6083 the range of the other relation.
6084 The typical use case of conditional validity constraints is
6085 to allow order constraints between live ranges to be violated
6086 as long as the live ranges themselves are local to the band.
6087 To allow more fine-grained control over which conditions correspond
6088 to which conditional validity constraints, the domains and ranges
6089 of these relations may include I<tags>. That is, the domains and
6090 ranges of those relation may themselves be wrapped relations
6091 where the iteration domain appears in the domain of those wrapped relations
6092 and the range of the wrapped relations can be arbitrarily chosen
6093 by the user. Conditions and conditional validity constraints are only
6094 considere adjacent to each other if the entire wrapped relation matches.
6095 In particular, a relation with a tag will never be considered adjacent
6096 to a relation without a tag.
6098 The following function computes a schedule directly from
6099 an iteration domain and validity and proximity dependences
6100 and is implemented in terms of the functions described above.
6101 The use of C<isl_union_set_compute_schedule> is discouraged.
6103 #include <isl/schedule.h>
6104 __isl_give isl_schedule *isl_union_set_compute_schedule(
6105 __isl_take isl_union_set *domain,
6106 __isl_take isl_union_map *validity,
6107 __isl_take isl_union_map *proximity);
6109 A mapping from the domains to the scheduled space can be obtained
6110 from an C<isl_schedule> using the following function.
6112 __isl_give isl_union_map *isl_schedule_get_map(
6113 __isl_keep isl_schedule *sched);
6115 A representation of the schedule can be printed using
6117 __isl_give isl_printer *isl_printer_print_schedule(
6118 __isl_take isl_printer *p,
6119 __isl_keep isl_schedule *schedule);
6121 A representation of the schedule as a forest of bands can be obtained
6122 using the following function.
6124 __isl_give isl_band_list *isl_schedule_get_band_forest(
6125 __isl_keep isl_schedule *schedule);
6127 The individual bands can be visited in depth-first post-order
6128 using the following function.
6130 #include <isl/schedule.h>
6131 int isl_schedule_foreach_band(
6132 __isl_keep isl_schedule *sched,
6133 int (*fn)(__isl_keep isl_band *band, void *user),
6136 The list can be manipulated as explained in L<"Lists">.
6137 The bands inside the list can be copied and freed using the following
6140 #include <isl/band.h>
6141 __isl_give isl_band *isl_band_copy(
6142 __isl_keep isl_band *band);
6143 __isl_null isl_band *isl_band_free(
6144 __isl_take isl_band *band);
6146 Each band contains zero or more scheduling dimensions.
6147 These are referred to as the members of the band.
6148 The section of the schedule that corresponds to the band is
6149 referred to as the partial schedule of the band.
6150 For those nodes that participate in a band, the outer scheduling
6151 dimensions form the prefix schedule, while the inner scheduling
6152 dimensions form the suffix schedule.
6153 That is, if we take a cut of the band forest, then the union of
6154 the concatenations of the prefix, partial and suffix schedules of
6155 each band in the cut is equal to the entire schedule (modulo
6156 some possible padding at the end with zero scheduling dimensions).
6157 The properties of a band can be inspected using the following functions.
6159 #include <isl/band.h>
6160 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
6162 int isl_band_has_children(__isl_keep isl_band *band);
6163 __isl_give isl_band_list *isl_band_get_children(
6164 __isl_keep isl_band *band);
6166 __isl_give isl_union_map *isl_band_get_prefix_schedule(
6167 __isl_keep isl_band *band);
6168 __isl_give isl_union_map *isl_band_get_partial_schedule(
6169 __isl_keep isl_band *band);
6170 __isl_give isl_union_map *isl_band_get_suffix_schedule(
6171 __isl_keep isl_band *band);
6173 int isl_band_n_member(__isl_keep isl_band *band);
6174 int isl_band_member_is_coincident(
6175 __isl_keep isl_band *band, int pos);
6177 int isl_band_list_foreach_band(
6178 __isl_keep isl_band_list *list,
6179 int (*fn)(__isl_keep isl_band *band, void *user),
6182 Note that a scheduling dimension is considered to be ``coincident''
6183 if it satisfies the coincidence constraints within its band.
6184 That is, if the dependence distances of the coincidence
6185 constraints are all zero in that direction (for fixed
6186 iterations of outer bands).
6187 Like C<isl_schedule_foreach_band>,
6188 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
6189 in depth-first post-order.
6191 A band can be tiled using the following function.
6193 #include <isl/band.h>
6194 int isl_band_tile(__isl_keep isl_band *band,
6195 __isl_take isl_vec *sizes);
6197 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
6199 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
6200 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
6202 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
6204 The C<isl_band_tile> function tiles the band using the given tile sizes
6205 inside its schedule.
6206 A new child band is created to represent the point loops and it is
6207 inserted between the modified band and its children.
6208 The C<tile_scale_tile_loops> option specifies whether the tile
6209 loops iterators should be scaled by the tile sizes.
6210 If the C<tile_shift_point_loops> option is set, then the point loops
6211 are shifted to start at zero.
6213 A band can be split into two nested bands using the following function.
6215 int isl_band_split(__isl_keep isl_band *band, int pos);
6217 The resulting outer band contains the first C<pos> dimensions of C<band>
6218 while the inner band contains the remaining dimensions.
6220 A representation of the band can be printed using
6222 #include <isl/band.h>
6223 __isl_give isl_printer *isl_printer_print_band(
6224 __isl_take isl_printer *p,
6225 __isl_keep isl_band *band);
6229 #include <isl/schedule.h>
6230 int isl_options_set_schedule_max_coefficient(
6231 isl_ctx *ctx, int val);
6232 int isl_options_get_schedule_max_coefficient(
6234 int isl_options_set_schedule_max_constant_term(
6235 isl_ctx *ctx, int val);
6236 int isl_options_get_schedule_max_constant_term(
6238 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
6239 int isl_options_get_schedule_fuse(isl_ctx *ctx);
6240 int isl_options_set_schedule_maximize_band_depth(
6241 isl_ctx *ctx, int val);
6242 int isl_options_get_schedule_maximize_band_depth(
6244 int isl_options_set_schedule_outer_coincidence(
6245 isl_ctx *ctx, int val);
6246 int isl_options_get_schedule_outer_coincidence(
6248 int isl_options_set_schedule_split_scaled(
6249 isl_ctx *ctx, int val);
6250 int isl_options_get_schedule_split_scaled(
6252 int isl_options_set_schedule_algorithm(
6253 isl_ctx *ctx, int val);
6254 int isl_options_get_schedule_algorithm(
6256 int isl_options_set_schedule_separate_components(
6257 isl_ctx *ctx, int val);
6258 int isl_options_get_schedule_separate_components(
6263 =item * schedule_max_coefficient
6265 This option enforces that the coefficients for variable and parameter
6266 dimensions in the calculated schedule are not larger than the specified value.
6267 This option can significantly increase the speed of the scheduling calculation
6268 and may also prevent fusing of unrelated dimensions. A value of -1 means that
6269 this option does not introduce bounds on the variable or parameter
6272 =item * schedule_max_constant_term
6274 This option enforces that the constant coefficients in the calculated schedule
6275 are not larger than the maximal constant term. This option can significantly
6276 increase the speed of the scheduling calculation and may also prevent fusing of
6277 unrelated dimensions. A value of -1 means that this option does not introduce
6278 bounds on the constant coefficients.
6280 =item * schedule_fuse
6282 This option controls the level of fusion.
6283 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6284 resulting schedule will be distributed as much as possible.
6285 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6286 try to fuse loops in the resulting schedule.
6288 =item * schedule_maximize_band_depth
6290 If this option is set, we do not split bands at the point
6291 where we detect splitting is necessary. Instead, we
6292 backtrack and split bands as early as possible. This
6293 reduces the number of splits and maximizes the width of
6294 the bands. Wider bands give more possibilities for tiling.
6295 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6296 then bands will be split as early as possible, even if there is no need.
6297 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6299 =item * schedule_outer_coincidence
6301 If this option is set, then we try to construct schedules
6302 where the outermost scheduling dimension in each band
6303 satisfies the coincidence constraints.
6305 =item * schedule_split_scaled
6307 If this option is set, then we try to construct schedules in which the
6308 constant term is split off from the linear part if the linear parts of
6309 the scheduling rows for all nodes in the graphs have a common non-trivial
6311 The constant term is then placed in a separate band and the linear
6314 =item * schedule_algorithm
6316 Selects the scheduling algorithm to be used.
6317 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6318 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6320 =item * schedule_separate_components
6322 If at any point the dependence graph contains any (weakly connected) components,
6323 then these components are scheduled separately.
6324 If this option is not set, then some iterations of the domains
6325 in these components may be scheduled together.
6326 If this option is set, then the components are given consecutive
6331 =head2 AST Generation
6333 This section describes the C<isl> functionality for generating
6334 ASTs that visit all the elements
6335 in a domain in an order specified by a schedule.
6336 In particular, given a C<isl_union_map>, an AST is generated
6337 that visits all the elements in the domain of the C<isl_union_map>
6338 according to the lexicographic order of the corresponding image
6339 element(s). If the range of the C<isl_union_map> consists of
6340 elements in more than one space, then each of these spaces is handled
6341 separately in an arbitrary order.
6342 It should be noted that the image elements only specify the I<order>
6343 in which the corresponding domain elements should be visited.
6344 No direct relation between the image elements and the loop iterators
6345 in the generated AST should be assumed.
6347 Each AST is generated within a build. The initial build
6348 simply specifies the constraints on the parameters (if any)
6349 and can be created, inspected, copied and freed using the following functions.
6351 #include <isl/ast_build.h>
6352 __isl_give isl_ast_build *isl_ast_build_from_context(
6353 __isl_take isl_set *set);
6354 isl_ctx *isl_ast_build_get_ctx(
6355 __isl_keep isl_ast_build *build);
6356 __isl_give isl_ast_build *isl_ast_build_copy(
6357 __isl_keep isl_ast_build *build);
6358 __isl_null isl_ast_build *isl_ast_build_free(
6359 __isl_take isl_ast_build *build);
6361 The C<set> argument is usually a parameter set with zero or more parameters.
6362 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6363 and L</"Fine-grained Control over AST Generation">.
6364 Finally, the AST itself can be constructed using the following
6367 #include <isl/ast_build.h>
6368 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6369 __isl_keep isl_ast_build *build,
6370 __isl_take isl_union_map *schedule);
6372 =head3 Inspecting the AST
6374 The basic properties of an AST node can be obtained as follows.
6376 #include <isl/ast.h>
6377 isl_ctx *isl_ast_node_get_ctx(
6378 __isl_keep isl_ast_node *node);
6379 enum isl_ast_node_type isl_ast_node_get_type(
6380 __isl_keep isl_ast_node *node);
6382 The type of an AST node is one of
6383 C<isl_ast_node_for>,
6385 C<isl_ast_node_block> or
6386 C<isl_ast_node_user>.
6387 An C<isl_ast_node_for> represents a for node.
6388 An C<isl_ast_node_if> represents an if node.
6389 An C<isl_ast_node_block> represents a compound node.
6390 An C<isl_ast_node_user> represents an expression statement.
6391 An expression statement typically corresponds to a domain element, i.e.,
6392 one of the elements that is visited by the AST.
6394 Each type of node has its own additional properties.
6396 #include <isl/ast.h>
6397 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6398 __isl_keep isl_ast_node *node);
6399 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6400 __isl_keep isl_ast_node *node);
6401 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6402 __isl_keep isl_ast_node *node);
6403 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6404 __isl_keep isl_ast_node *node);
6405 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6406 __isl_keep isl_ast_node *node);
6407 int isl_ast_node_for_is_degenerate(
6408 __isl_keep isl_ast_node *node);
6410 An C<isl_ast_for> is considered degenerate if it is known to execute
6413 #include <isl/ast.h>
6414 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6415 __isl_keep isl_ast_node *node);
6416 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6417 __isl_keep isl_ast_node *node);
6418 int isl_ast_node_if_has_else(
6419 __isl_keep isl_ast_node *node);
6420 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6421 __isl_keep isl_ast_node *node);
6423 __isl_give isl_ast_node_list *
6424 isl_ast_node_block_get_children(
6425 __isl_keep isl_ast_node *node);
6427 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6428 __isl_keep isl_ast_node *node);
6430 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6431 the following functions.
6433 #include <isl/ast.h>
6434 isl_ctx *isl_ast_expr_get_ctx(
6435 __isl_keep isl_ast_expr *expr);
6436 enum isl_ast_expr_type isl_ast_expr_get_type(
6437 __isl_keep isl_ast_expr *expr);
6439 The type of an AST expression is one of
6441 C<isl_ast_expr_id> or
6442 C<isl_ast_expr_int>.
6443 An C<isl_ast_expr_op> represents the result of an operation.
6444 An C<isl_ast_expr_id> represents an identifier.
6445 An C<isl_ast_expr_int> represents an integer value.
6447 Each type of expression has its own additional properties.
6449 #include <isl/ast.h>
6450 enum isl_ast_op_type isl_ast_expr_get_op_type(
6451 __isl_keep isl_ast_expr *expr);
6452 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6453 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6454 __isl_keep isl_ast_expr *expr, int pos);
6455 int isl_ast_node_foreach_ast_op_type(
6456 __isl_keep isl_ast_node *node,
6457 int (*fn)(enum isl_ast_op_type type, void *user),
6460 C<isl_ast_expr_get_op_type> returns the type of the operation
6461 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6462 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6464 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6465 C<isl_ast_op_type> that appears in C<node>.
6466 The operation type is one of the following.
6470 =item C<isl_ast_op_and>
6472 Logical I<and> of two arguments.
6473 Both arguments can be evaluated.
6475 =item C<isl_ast_op_and_then>
6477 Logical I<and> of two arguments.
6478 The second argument can only be evaluated if the first evaluates to true.
6480 =item C<isl_ast_op_or>
6482 Logical I<or> of two arguments.
6483 Both arguments can be evaluated.
6485 =item C<isl_ast_op_or_else>
6487 Logical I<or> of two arguments.
6488 The second argument can only be evaluated if the first evaluates to false.
6490 =item C<isl_ast_op_max>
6492 Maximum of two or more arguments.
6494 =item C<isl_ast_op_min>
6496 Minimum of two or more arguments.
6498 =item C<isl_ast_op_minus>
6502 =item C<isl_ast_op_add>
6504 Sum of two arguments.
6506 =item C<isl_ast_op_sub>
6508 Difference of two arguments.
6510 =item C<isl_ast_op_mul>
6512 Product of two arguments.
6514 =item C<isl_ast_op_div>
6516 Exact division. That is, the result is known to be an integer.
6518 =item C<isl_ast_op_fdiv_q>
6520 Result of integer division, rounded towards negative
6523 =item C<isl_ast_op_pdiv_q>
6525 Result of integer division, where dividend is known to be non-negative.
6527 =item C<isl_ast_op_pdiv_r>
6529 Remainder of integer division, where dividend is known to be non-negative.
6531 =item C<isl_ast_op_cond>
6533 Conditional operator defined on three arguments.
6534 If the first argument evaluates to true, then the result
6535 is equal to the second argument. Otherwise, the result
6536 is equal to the third argument.
6537 The second and third argument may only be evaluated if
6538 the first argument evaluates to true and false, respectively.
6539 Corresponds to C<a ? b : c> in C.
6541 =item C<isl_ast_op_select>
6543 Conditional operator defined on three arguments.
6544 If the first argument evaluates to true, then the result
6545 is equal to the second argument. Otherwise, the result
6546 is equal to the third argument.
6547 The second and third argument may be evaluated independently
6548 of the value of the first argument.
6549 Corresponds to C<a * b + (1 - a) * c> in C.
6551 =item C<isl_ast_op_eq>
6555 =item C<isl_ast_op_le>
6557 Less than or equal relation.
6559 =item C<isl_ast_op_lt>
6563 =item C<isl_ast_op_ge>
6565 Greater than or equal relation.
6567 =item C<isl_ast_op_gt>
6569 Greater than relation.
6571 =item C<isl_ast_op_call>
6574 The number of arguments of the C<isl_ast_expr> is one more than
6575 the number of arguments in the function call, the first argument
6576 representing the function being called.
6578 =item C<isl_ast_op_access>
6581 The number of arguments of the C<isl_ast_expr> is one more than
6582 the number of index expressions in the array access, the first argument
6583 representing the array being accessed.
6585 =item C<isl_ast_op_member>
6588 This operation has two arguments, a structure and the name of
6589 the member of the structure being accessed.
6593 #include <isl/ast.h>
6594 __isl_give isl_id *isl_ast_expr_get_id(
6595 __isl_keep isl_ast_expr *expr);
6597 Return the identifier represented by the AST expression.
6599 #include <isl/ast.h>
6600 __isl_give isl_val *isl_ast_expr_get_val(
6601 __isl_keep isl_ast_expr *expr);
6603 Return the integer represented by the AST expression.
6605 =head3 Properties of ASTs
6607 #include <isl/ast.h>
6608 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6609 __isl_keep isl_ast_expr *expr2);
6611 Check if two C<isl_ast_expr>s are equal to each other.
6613 =head3 Manipulating and printing the AST
6615 AST nodes can be copied and freed using the following functions.
6617 #include <isl/ast.h>
6618 __isl_give isl_ast_node *isl_ast_node_copy(
6619 __isl_keep isl_ast_node *node);
6620 __isl_null isl_ast_node *isl_ast_node_free(
6621 __isl_take isl_ast_node *node);
6623 AST expressions can be copied and freed using the following functions.
6625 #include <isl/ast.h>
6626 __isl_give isl_ast_expr *isl_ast_expr_copy(
6627 __isl_keep isl_ast_expr *expr);
6628 __isl_null isl_ast_expr *isl_ast_expr_free(
6629 __isl_take isl_ast_expr *expr);
6631 New AST expressions can be created either directly or within
6632 the context of an C<isl_ast_build>.
6634 #include <isl/ast.h>
6635 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6636 __isl_take isl_val *v);
6637 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6638 __isl_take isl_id *id);
6639 __isl_give isl_ast_expr *isl_ast_expr_neg(
6640 __isl_take isl_ast_expr *expr);
6641 __isl_give isl_ast_expr *isl_ast_expr_address_of(
6642 __isl_take isl_ast_expr *expr);
6643 __isl_give isl_ast_expr *isl_ast_expr_add(
6644 __isl_take isl_ast_expr *expr1,
6645 __isl_take isl_ast_expr *expr2);
6646 __isl_give isl_ast_expr *isl_ast_expr_sub(
6647 __isl_take isl_ast_expr *expr1,
6648 __isl_take isl_ast_expr *expr2);
6649 __isl_give isl_ast_expr *isl_ast_expr_mul(
6650 __isl_take isl_ast_expr *expr1,
6651 __isl_take isl_ast_expr *expr2);
6652 __isl_give isl_ast_expr *isl_ast_expr_div(
6653 __isl_take isl_ast_expr *expr1,
6654 __isl_take isl_ast_expr *expr2);
6655 __isl_give isl_ast_expr *isl_ast_expr_and(
6656 __isl_take isl_ast_expr *expr1,
6657 __isl_take isl_ast_expr *expr2)
6658 __isl_give isl_ast_expr *isl_ast_expr_or(
6659 __isl_take isl_ast_expr *expr1,
6660 __isl_take isl_ast_expr *expr2)
6661 __isl_give isl_ast_expr *isl_ast_expr_eq(
6662 __isl_take isl_ast_expr *expr1,
6663 __isl_take isl_ast_expr *expr2);
6664 __isl_give isl_ast_expr *isl_ast_expr_le(
6665 __isl_take isl_ast_expr *expr1,
6666 __isl_take isl_ast_expr *expr2);
6667 __isl_give isl_ast_expr *isl_ast_expr_lt(
6668 __isl_take isl_ast_expr *expr1,
6669 __isl_take isl_ast_expr *expr2);
6670 __isl_give isl_ast_expr *isl_ast_expr_ge(
6671 __isl_take isl_ast_expr *expr1,
6672 __isl_take isl_ast_expr *expr2);
6673 __isl_give isl_ast_expr *isl_ast_expr_gt(
6674 __isl_take isl_ast_expr *expr1,
6675 __isl_take isl_ast_expr *expr2);
6676 __isl_give isl_ast_expr *isl_ast_expr_access(
6677 __isl_take isl_ast_expr *array,
6678 __isl_take isl_ast_expr_list *indices);
6680 The function C<isl_ast_expr_address_of> can be applied to an
6681 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
6682 to represent the address of the C<isl_ast_expr_access>.
6684 #include <isl/ast_build.h>
6685 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6686 __isl_keep isl_ast_build *build,
6687 __isl_take isl_pw_aff *pa);
6688 __isl_give isl_ast_expr *
6689 isl_ast_build_access_from_pw_multi_aff(
6690 __isl_keep isl_ast_build *build,
6691 __isl_take isl_pw_multi_aff *pma);
6692 __isl_give isl_ast_expr *
6693 isl_ast_build_access_from_multi_pw_aff(
6694 __isl_keep isl_ast_build *build,
6695 __isl_take isl_multi_pw_aff *mpa);
6696 __isl_give isl_ast_expr *
6697 isl_ast_build_call_from_pw_multi_aff(
6698 __isl_keep isl_ast_build *build,
6699 __isl_take isl_pw_multi_aff *pma);
6700 __isl_give isl_ast_expr *
6701 isl_ast_build_call_from_multi_pw_aff(
6702 __isl_keep isl_ast_build *build,
6703 __isl_take isl_multi_pw_aff *mpa);
6705 The domains of C<pa>, C<mpa> and C<pma> should correspond
6706 to the schedule space of C<build>.
6707 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6708 the function being called.
6709 If the accessed space is a nested relation, then it is taken
6710 to represent an access of the member specified by the range
6711 of this nested relation of the structure specified by the domain
6712 of the nested relation.
6714 The following functions can be used to modify an C<isl_ast_expr>.
6716 #include <isl/ast.h>
6717 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6718 __isl_take isl_ast_expr *expr, int pos,
6719 __isl_take isl_ast_expr *arg);
6721 Replace the argument of C<expr> at position C<pos> by C<arg>.
6723 #include <isl/ast.h>
6724 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6725 __isl_take isl_ast_expr *expr,
6726 __isl_take isl_id_to_ast_expr *id2expr);
6728 The function C<isl_ast_expr_substitute_ids> replaces the
6729 subexpressions of C<expr> of type C<isl_ast_expr_id>
6730 by the corresponding expression in C<id2expr>, if there is any.
6733 User specified data can be attached to an C<isl_ast_node> and obtained
6734 from the same C<isl_ast_node> using the following functions.
6736 #include <isl/ast.h>
6737 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6738 __isl_take isl_ast_node *node,
6739 __isl_take isl_id *annotation);
6740 __isl_give isl_id *isl_ast_node_get_annotation(
6741 __isl_keep isl_ast_node *node);
6743 Basic printing can be performed using the following functions.
6745 #include <isl/ast.h>
6746 __isl_give isl_printer *isl_printer_print_ast_expr(
6747 __isl_take isl_printer *p,
6748 __isl_keep isl_ast_expr *expr);
6749 __isl_give isl_printer *isl_printer_print_ast_node(
6750 __isl_take isl_printer *p,
6751 __isl_keep isl_ast_node *node);
6753 More advanced printing can be performed using the following functions.
6755 #include <isl/ast.h>
6756 __isl_give isl_printer *isl_ast_op_type_print_macro(
6757 enum isl_ast_op_type type,
6758 __isl_take isl_printer *p);
6759 __isl_give isl_printer *isl_ast_node_print_macros(
6760 __isl_keep isl_ast_node *node,
6761 __isl_take isl_printer *p);
6762 __isl_give isl_printer *isl_ast_node_print(
6763 __isl_keep isl_ast_node *node,
6764 __isl_take isl_printer *p,
6765 __isl_take isl_ast_print_options *options);
6766 __isl_give isl_printer *isl_ast_node_for_print(
6767 __isl_keep isl_ast_node *node,
6768 __isl_take isl_printer *p,
6769 __isl_take isl_ast_print_options *options);
6770 __isl_give isl_printer *isl_ast_node_if_print(
6771 __isl_keep isl_ast_node *node,
6772 __isl_take isl_printer *p,
6773 __isl_take isl_ast_print_options *options);
6775 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6776 C<isl> may print out an AST that makes use of macros such
6777 as C<floord>, C<min> and C<max>.
6778 C<isl_ast_op_type_print_macro> prints out the macro
6779 corresponding to a specific C<isl_ast_op_type>.
6780 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6781 for expressions where these macros would be used and prints
6782 out the required macro definitions.
6783 Essentially, C<isl_ast_node_print_macros> calls
6784 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6785 as function argument.
6786 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6787 C<isl_ast_node_if_print> print an C<isl_ast_node>
6788 in C<ISL_FORMAT_C>, but allow for some extra control
6789 through an C<isl_ast_print_options> object.
6790 This object can be created using the following functions.
6792 #include <isl/ast.h>
6793 __isl_give isl_ast_print_options *
6794 isl_ast_print_options_alloc(isl_ctx *ctx);
6795 __isl_give isl_ast_print_options *
6796 isl_ast_print_options_copy(
6797 __isl_keep isl_ast_print_options *options);
6798 __isl_null isl_ast_print_options *
6799 isl_ast_print_options_free(
6800 __isl_take isl_ast_print_options *options);
6802 __isl_give isl_ast_print_options *
6803 isl_ast_print_options_set_print_user(
6804 __isl_take isl_ast_print_options *options,
6805 __isl_give isl_printer *(*print_user)(
6806 __isl_take isl_printer *p,
6807 __isl_take isl_ast_print_options *options,
6808 __isl_keep isl_ast_node *node, void *user),
6810 __isl_give isl_ast_print_options *
6811 isl_ast_print_options_set_print_for(
6812 __isl_take isl_ast_print_options *options,
6813 __isl_give isl_printer *(*print_for)(
6814 __isl_take isl_printer *p,
6815 __isl_take isl_ast_print_options *options,
6816 __isl_keep isl_ast_node *node, void *user),
6819 The callback set by C<isl_ast_print_options_set_print_user>
6820 is called whenever a node of type C<isl_ast_node_user> needs to
6822 The callback set by C<isl_ast_print_options_set_print_for>
6823 is called whenever a node of type C<isl_ast_node_for> needs to
6825 Note that C<isl_ast_node_for_print> will I<not> call the
6826 callback set by C<isl_ast_print_options_set_print_for> on the node
6827 on which C<isl_ast_node_for_print> is called, but only on nested
6828 nodes of type C<isl_ast_node_for>. It is therefore safe to
6829 call C<isl_ast_node_for_print> from within the callback set by
6830 C<isl_ast_print_options_set_print_for>.
6832 The following option determines the type to be used for iterators
6833 while printing the AST.
6835 int isl_options_set_ast_iterator_type(
6836 isl_ctx *ctx, const char *val);
6837 const char *isl_options_get_ast_iterator_type(
6840 The AST printer only prints body nodes as blocks if these
6841 blocks cannot be safely omitted.
6842 For example, a C<for> node with one body node will not be
6843 surrounded with braces in C<ISL_FORMAT_C>.
6844 A block will always be printed by setting the following option.
6846 int isl_options_set_ast_always_print_block(isl_ctx *ctx,
6848 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
6852 #include <isl/ast_build.h>
6853 int isl_options_set_ast_build_atomic_upper_bound(
6854 isl_ctx *ctx, int val);
6855 int isl_options_get_ast_build_atomic_upper_bound(
6857 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6859 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6860 int isl_options_set_ast_build_exploit_nested_bounds(
6861 isl_ctx *ctx, int val);
6862 int isl_options_get_ast_build_exploit_nested_bounds(
6864 int isl_options_set_ast_build_group_coscheduled(
6865 isl_ctx *ctx, int val);
6866 int isl_options_get_ast_build_group_coscheduled(
6868 int isl_options_set_ast_build_scale_strides(
6869 isl_ctx *ctx, int val);
6870 int isl_options_get_ast_build_scale_strides(
6872 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6874 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6875 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6877 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6881 =item * ast_build_atomic_upper_bound
6883 Generate loop upper bounds that consist of the current loop iterator,
6884 an operator and an expression not involving the iterator.
6885 If this option is not set, then the current loop iterator may appear
6886 several times in the upper bound.
6887 For example, when this option is turned off, AST generation
6890 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6894 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6897 When the option is turned on, the following AST is generated
6899 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6902 =item * ast_build_prefer_pdiv
6904 If this option is turned off, then the AST generation will
6905 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6906 operators, but no C<isl_ast_op_pdiv_q> or
6907 C<isl_ast_op_pdiv_r> operators.
6908 If this options is turned on, then C<isl> will try to convert
6909 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6910 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6912 =item * ast_build_exploit_nested_bounds
6914 Simplify conditions based on bounds of nested for loops.
6915 In particular, remove conditions that are implied by the fact
6916 that one or more nested loops have at least one iteration,
6917 meaning that the upper bound is at least as large as the lower bound.
6918 For example, when this option is turned off, AST generation
6921 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6927 for (int c0 = 0; c0 <= N; c0 += 1)
6928 for (int c1 = 0; c1 <= M; c1 += 1)
6931 When the option is turned on, the following AST is generated
6933 for (int c0 = 0; c0 <= N; c0 += 1)
6934 for (int c1 = 0; c1 <= M; c1 += 1)
6937 =item * ast_build_group_coscheduled
6939 If two domain elements are assigned the same schedule point, then
6940 they may be executed in any order and they may even appear in different
6941 loops. If this options is set, then the AST generator will make
6942 sure that coscheduled domain elements do not appear in separate parts
6943 of the AST. This is useful in case of nested AST generation
6944 if the outer AST generation is given only part of a schedule
6945 and the inner AST generation should handle the domains that are
6946 coscheduled by this initial part of the schedule together.
6947 For example if an AST is generated for a schedule
6949 { A[i] -> [0]; B[i] -> [0] }
6951 then the C<isl_ast_build_set_create_leaf> callback described
6952 below may get called twice, once for each domain.
6953 Setting this option ensures that the callback is only called once
6954 on both domains together.
6956 =item * ast_build_separation_bounds
6958 This option specifies which bounds to use during separation.
6959 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6960 then all (possibly implicit) bounds on the current dimension will
6961 be used during separation.
6962 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6963 then only those bounds that are explicitly available will
6964 be used during separation.
6966 =item * ast_build_scale_strides
6968 This option specifies whether the AST generator is allowed
6969 to scale down iterators of strided loops.
6971 =item * ast_build_allow_else
6973 This option specifies whether the AST generator is allowed
6974 to construct if statements with else branches.
6976 =item * ast_build_allow_or
6978 This option specifies whether the AST generator is allowed
6979 to construct if conditions with disjunctions.
6983 =head3 Fine-grained Control over AST Generation
6985 Besides specifying the constraints on the parameters,
6986 an C<isl_ast_build> object can be used to control
6987 various aspects of the AST generation process.
6988 The most prominent way of control is through ``options'',
6989 which can be set using the following function.
6991 #include <isl/ast_build.h>
6992 __isl_give isl_ast_build *
6993 isl_ast_build_set_options(
6994 __isl_take isl_ast_build *control,
6995 __isl_take isl_union_map *options);
6997 The options are encoded in an <isl_union_map>.
6998 The domain of this union relation refers to the schedule domain,
6999 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
7000 In the case of nested AST generation (see L</"Nested AST Generation">),
7001 the domain of C<options> should refer to the extra piece of the schedule.
7002 That is, it should be equal to the range of the wrapped relation in the
7003 range of the schedule.
7004 The range of the options can consist of elements in one or more spaces,
7005 the names of which determine the effect of the option.
7006 The values of the range typically also refer to the schedule dimension
7007 to which the option applies. In case of nested AST generation
7008 (see L</"Nested AST Generation">), these values refer to the position
7009 of the schedule dimension within the innermost AST generation.
7010 The constraints on the domain elements of
7011 the option should only refer to this dimension and earlier dimensions.
7012 We consider the following spaces.
7016 =item C<separation_class>
7018 This space is a wrapped relation between two one dimensional spaces.
7019 The input space represents the schedule dimension to which the option
7020 applies and the output space represents the separation class.
7021 While constructing a loop corresponding to the specified schedule
7022 dimension(s), the AST generator will try to generate separate loops
7023 for domain elements that are assigned different classes.
7024 If only some of the elements are assigned a class, then those elements
7025 that are not assigned any class will be treated as belonging to a class
7026 that is separate from the explicitly assigned classes.
7027 The typical use case for this option is to separate full tiles from
7029 The other options, described below, are applied after the separation
7032 As an example, consider the separation into full and partial tiles
7033 of a tiling of a triangular domain.
7034 Take, for example, the domain
7036 { A[i,j] : 0 <= i,j and i + j <= 100 }
7038 and a tiling into tiles of 10 by 10. The input to the AST generator
7039 is then the schedule
7041 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
7044 Without any options, the following AST is generated
7046 for (int c0 = 0; c0 <= 10; c0 += 1)
7047 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
7048 for (int c2 = 10 * c0;
7049 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7051 for (int c3 = 10 * c1;
7052 c3 <= min(10 * c1 + 9, -c2 + 100);
7056 Separation into full and partial tiles can be obtained by assigning
7057 a class, say C<0>, to the full tiles. The full tiles are represented by those
7058 values of the first and second schedule dimensions for which there are
7059 values of the third and fourth dimensions to cover an entire tile.
7060 That is, we need to specify the following option
7062 { [a,b,c,d] -> separation_class[[0]->[0]] :
7063 exists b': 0 <= 10a,10b' and
7064 10a+9+10b'+9 <= 100;
7065 [a,b,c,d] -> separation_class[[1]->[0]] :
7066 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
7070 { [a, b, c, d] -> separation_class[[1] -> [0]] :
7071 a >= 0 and b >= 0 and b <= 8 - a;
7072 [a, b, c, d] -> separation_class[[0] -> [0]] :
7075 With this option, the generated AST is as follows
7078 for (int c0 = 0; c0 <= 8; c0 += 1) {
7079 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
7080 for (int c2 = 10 * c0;
7081 c2 <= 10 * c0 + 9; c2 += 1)
7082 for (int c3 = 10 * c1;
7083 c3 <= 10 * c1 + 9; c3 += 1)
7085 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
7086 for (int c2 = 10 * c0;
7087 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7089 for (int c3 = 10 * c1;
7090 c3 <= min(-c2 + 100, 10 * c1 + 9);
7094 for (int c0 = 9; c0 <= 10; c0 += 1)
7095 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
7096 for (int c2 = 10 * c0;
7097 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7099 for (int c3 = 10 * c1;
7100 c3 <= min(10 * c1 + 9, -c2 + 100);
7107 This is a single-dimensional space representing the schedule dimension(s)
7108 to which ``separation'' should be applied. Separation tries to split
7109 a loop into several pieces if this can avoid the generation of guards
7111 See also the C<atomic> option.
7115 This is a single-dimensional space representing the schedule dimension(s)
7116 for which the domains should be considered ``atomic''. That is, the
7117 AST generator will make sure that any given domain space will only appear
7118 in a single loop at the specified level.
7120 Consider the following schedule
7122 { a[i] -> [i] : 0 <= i < 10;
7123 b[i] -> [i+1] : 0 <= i < 10 }
7125 If the following option is specified
7127 { [i] -> separate[x] }
7129 then the following AST will be generated
7133 for (int c0 = 1; c0 <= 9; c0 += 1) {
7140 If, on the other hand, the following option is specified
7142 { [i] -> atomic[x] }
7144 then the following AST will be generated
7146 for (int c0 = 0; c0 <= 10; c0 += 1) {
7153 If neither C<atomic> nor C<separate> is specified, then the AST generator
7154 may produce either of these two results or some intermediate form.
7158 This is a single-dimensional space representing the schedule dimension(s)
7159 that should be I<completely> unrolled.
7160 To obtain a partial unrolling, the user should apply an additional
7161 strip-mining to the schedule and fully unroll the inner loop.
7165 Additional control is available through the following functions.
7167 #include <isl/ast_build.h>
7168 __isl_give isl_ast_build *
7169 isl_ast_build_set_iterators(
7170 __isl_take isl_ast_build *control,
7171 __isl_take isl_id_list *iterators);
7173 The function C<isl_ast_build_set_iterators> allows the user to
7174 specify a list of iterator C<isl_id>s to be used as iterators.
7175 If the input schedule is injective, then
7176 the number of elements in this list should be as large as the dimension
7177 of the schedule space, but no direct correspondence should be assumed
7178 between dimensions and elements.
7179 If the input schedule is not injective, then an additional number
7180 of C<isl_id>s equal to the largest dimension of the input domains
7182 If the number of provided C<isl_id>s is insufficient, then additional
7183 names are automatically generated.
7185 #include <isl/ast_build.h>
7186 __isl_give isl_ast_build *
7187 isl_ast_build_set_create_leaf(
7188 __isl_take isl_ast_build *control,
7189 __isl_give isl_ast_node *(*fn)(
7190 __isl_take isl_ast_build *build,
7191 void *user), void *user);
7194 C<isl_ast_build_set_create_leaf> function allows for the
7195 specification of a callback that should be called whenever the AST
7196 generator arrives at an element of the schedule domain.
7197 The callback should return an AST node that should be inserted
7198 at the corresponding position of the AST. The default action (when
7199 the callback is not set) is to continue generating parts of the AST to scan
7200 all the domain elements associated to the schedule domain element
7201 and to insert user nodes, ``calling'' the domain element, for each of them.
7202 The C<build> argument contains the current state of the C<isl_ast_build>.
7203 To ease nested AST generation (see L</"Nested AST Generation">),
7204 all control information that is
7205 specific to the current AST generation such as the options and
7206 the callbacks has been removed from this C<isl_ast_build>.
7207 The callback would typically return the result of a nested
7209 user defined node created using the following function.
7211 #include <isl/ast.h>
7212 __isl_give isl_ast_node *isl_ast_node_alloc_user(
7213 __isl_take isl_ast_expr *expr);
7215 #include <isl/ast_build.h>
7216 __isl_give isl_ast_build *
7217 isl_ast_build_set_at_each_domain(
7218 __isl_take isl_ast_build *build,
7219 __isl_give isl_ast_node *(*fn)(
7220 __isl_take isl_ast_node *node,
7221 __isl_keep isl_ast_build *build,
7222 void *user), void *user);
7223 __isl_give isl_ast_build *
7224 isl_ast_build_set_before_each_for(
7225 __isl_take isl_ast_build *build,
7226 __isl_give isl_id *(*fn)(
7227 __isl_keep isl_ast_build *build,
7228 void *user), void *user);
7229 __isl_give isl_ast_build *
7230 isl_ast_build_set_after_each_for(
7231 __isl_take isl_ast_build *build,
7232 __isl_give isl_ast_node *(*fn)(
7233 __isl_take isl_ast_node *node,
7234 __isl_keep isl_ast_build *build,
7235 void *user), void *user);
7237 The callback set by C<isl_ast_build_set_at_each_domain> will
7238 be called for each domain AST node.
7239 The callbacks set by C<isl_ast_build_set_before_each_for>
7240 and C<isl_ast_build_set_after_each_for> will be called
7241 for each for AST node. The first will be called in depth-first
7242 pre-order, while the second will be called in depth-first post-order.
7243 Since C<isl_ast_build_set_before_each_for> is called before the for
7244 node is actually constructed, it is only passed an C<isl_ast_build>.
7245 The returned C<isl_id> will be added as an annotation (using
7246 C<isl_ast_node_set_annotation>) to the constructed for node.
7247 In particular, if the user has also specified an C<after_each_for>
7248 callback, then the annotation can be retrieved from the node passed to
7249 that callback using C<isl_ast_node_get_annotation>.
7250 All callbacks should C<NULL> on failure.
7251 The given C<isl_ast_build> can be used to create new
7252 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
7253 or C<isl_ast_build_call_from_pw_multi_aff>.
7255 =head3 Nested AST Generation
7257 C<isl> allows the user to create an AST within the context
7258 of another AST. These nested ASTs are created using the
7259 same C<isl_ast_build_ast_from_schedule> function that is used to create the
7260 outer AST. The C<build> argument should be an C<isl_ast_build>
7261 passed to a callback set by
7262 C<isl_ast_build_set_create_leaf>.
7263 The space of the range of the C<schedule> argument should refer
7264 to this build. In particular, the space should be a wrapped
7265 relation and the domain of this wrapped relation should be the
7266 same as that of the range of the schedule returned by
7267 C<isl_ast_build_get_schedule> below.
7268 In practice, the new schedule is typically
7269 created by calling C<isl_union_map_range_product> on the old schedule
7270 and some extra piece of the schedule.
7271 The space of the schedule domain is also available from
7272 the C<isl_ast_build>.
7274 #include <isl/ast_build.h>
7275 __isl_give isl_union_map *isl_ast_build_get_schedule(
7276 __isl_keep isl_ast_build *build);
7277 __isl_give isl_space *isl_ast_build_get_schedule_space(
7278 __isl_keep isl_ast_build *build);
7279 __isl_give isl_ast_build *isl_ast_build_restrict(
7280 __isl_take isl_ast_build *build,
7281 __isl_take isl_set *set);
7283 The C<isl_ast_build_get_schedule> function returns a (partial)
7284 schedule for the domains elements for which part of the AST still needs to
7285 be generated in the current build.
7286 In particular, the domain elements are mapped to those iterations of the loops
7287 enclosing the current point of the AST generation inside which
7288 the domain elements are executed.
7289 No direct correspondence between
7290 the input schedule and this schedule should be assumed.
7291 The space obtained from C<isl_ast_build_get_schedule_space> can be used
7292 to create a set for C<isl_ast_build_restrict> to intersect
7293 with the current build. In particular, the set passed to
7294 C<isl_ast_build_restrict> can have additional parameters.
7295 The ids of the set dimensions in the space returned by
7296 C<isl_ast_build_get_schedule_space> correspond to the
7297 iterators of the already generated loops.
7298 The user should not rely on the ids of the output dimensions
7299 of the relations in the union relation returned by
7300 C<isl_ast_build_get_schedule> having any particular value.
7304 Although C<isl> is mainly meant to be used as a library,
7305 it also contains some basic applications that use some
7306 of the functionality of C<isl>.
7307 The input may be specified in either the L<isl format>
7308 or the L<PolyLib format>.
7310 =head2 C<isl_polyhedron_sample>
7312 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7313 an integer element of the polyhedron, if there is any.
7314 The first column in the output is the denominator and is always
7315 equal to 1. If the polyhedron contains no integer points,
7316 then a vector of length zero is printed.
7320 C<isl_pip> takes the same input as the C<example> program
7321 from the C<piplib> distribution, i.e., a set of constraints
7322 on the parameters, a line containing only -1 and finally a set
7323 of constraints on a parametric polyhedron.
7324 The coefficients of the parameters appear in the last columns
7325 (but before the final constant column).
7326 The output is the lexicographic minimum of the parametric polyhedron.
7327 As C<isl> currently does not have its own output format, the output
7328 is just a dump of the internal state.
7330 =head2 C<isl_polyhedron_minimize>
7332 C<isl_polyhedron_minimize> computes the minimum of some linear
7333 or affine objective function over the integer points in a polyhedron.
7334 If an affine objective function
7335 is given, then the constant should appear in the last column.
7337 =head2 C<isl_polytope_scan>
7339 Given a polytope, C<isl_polytope_scan> prints
7340 all integer points in the polytope.
7342 =head2 C<isl_codegen>
7344 Given a schedule, a context set and an options relation,
7345 C<isl_codegen> prints out an AST that scans the domain elements
7346 of the schedule in the order of their image(s) taking into account
7347 the constraints in the context set.