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
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 C<isl> currently 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.
243 The source of C<isl> can be obtained either as a tarball
244 or from the git repository. Both are available from
245 L<http://freshmeat.net/projects/isl/>.
246 The installation process depends on how you obtained
249 =head2 Installation from the git repository
253 =item 1 Clone or update the repository
255 The first time the source is obtained, you need to clone
258 git clone git://repo.or.cz/isl.git
260 To obtain updates, you need to pull in the latest changes
264 =item 2 Generate C<configure>
270 After performing the above steps, continue
271 with the L<Common installation instructions>.
273 =head2 Common installation instructions
277 =item 1 Obtain C<GMP>
279 Building C<isl> requires C<GMP>, including its headers files.
280 Your distribution may not provide these header files by default
281 and you may need to install a package called C<gmp-devel> or something
282 similar. Alternatively, C<GMP> can be built from
283 source, available from L<http://gmplib.org/>.
287 C<isl> uses the standard C<autoconf> C<configure> script.
292 optionally followed by some configure options.
293 A complete list of options can be obtained by running
297 Below we discuss some of the more common options.
303 Installation prefix for C<isl>
305 =item C<--with-gmp-prefix>
307 Installation prefix for C<GMP> (architecture-independent files).
309 =item C<--with-gmp-exec-prefix>
311 Installation prefix for C<GMP> (architecture-dependent files).
319 =item 4 Install (optional)
325 =head1 Integer Set Library
327 =head2 Initialization
329 All manipulations of integer sets and relations occur within
330 the context of an C<isl_ctx>.
331 A given C<isl_ctx> can only be used within a single thread.
332 All arguments of a function are required to have been allocated
333 within the same context.
334 There are currently no functions available for moving an object
335 from one C<isl_ctx> to another C<isl_ctx>. This means that
336 there is currently no way of safely moving an object from one
337 thread to another, unless the whole C<isl_ctx> is moved.
339 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
340 freed using C<isl_ctx_free>.
341 All objects allocated within an C<isl_ctx> should be freed
342 before the C<isl_ctx> itself is freed.
344 isl_ctx *isl_ctx_alloc();
345 void isl_ctx_free(isl_ctx *ctx);
347 The user can impose a bound on the number of low-level I<operations>
348 that can be performed by an C<isl_ctx>. This bound can be set and
349 retrieved using the following functions. A bound of zero means that
350 no bound is imposed. The number of operations performed can be
351 reset using C<isl_ctx_reset_operations>. Note that the number
352 of low-level operations needed to perform a high-level computation
353 may differ significantly across different versions
354 of C<isl>, but it should be the same across different platforms
355 for the same version of C<isl>.
357 Warning: This feature is experimental. C<isl> has good support to abort and
358 bail out during the computation, but this feature may exercise error code paths
359 that are normally not used that much. Consequently, it is not unlikely that
360 hidden bugs will be exposed.
362 void isl_ctx_set_max_operations(isl_ctx *ctx,
363 unsigned long max_operations);
364 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
365 void isl_ctx_reset_operations(isl_ctx *ctx);
367 =head2 Memory Management
369 Since a high-level operation on isl objects usually involves
370 several substeps and since the user is usually not interested in
371 the intermediate results, most functions that return a new object
372 will also release all the objects passed as arguments.
373 If the user still wants to use one or more of these arguments
374 after the function call, she should pass along a copy of the
375 object rather than the object itself.
376 The user is then responsible for making sure that the original
377 object gets used somewhere else or is explicitly freed.
379 The arguments and return values of all documented functions are
380 annotated to make clear which arguments are released and which
381 arguments are preserved. In particular, the following annotations
388 C<__isl_give> means that a new object is returned.
389 The user should make sure that the returned pointer is
390 used exactly once as a value for an C<__isl_take> argument.
391 In between, it can be used as a value for as many
392 C<__isl_keep> arguments as the user likes.
393 There is one exception, and that is the case where the
394 pointer returned is C<NULL>. Is this case, the user
395 is free to use it as an C<__isl_take> argument or not.
399 C<__isl_null> means that a C<NULL> value is returned.
403 C<__isl_take> means that the object the argument points to
404 is taken over by the function and may no longer be used
405 by the user as an argument to any other function.
406 The pointer value must be one returned by a function
407 returning an C<__isl_give> pointer.
408 If the user passes in a C<NULL> value, then this will
409 be treated as an error in the sense that the function will
410 not perform its usual operation. However, it will still
411 make sure that all the other C<__isl_take> arguments
416 C<__isl_keep> means that the function will only use the object
417 temporarily. After the function has finished, the user
418 can still use it as an argument to other functions.
419 A C<NULL> value will be treated in the same way as
420 a C<NULL> value for an C<__isl_take> argument.
426 An C<isl_val> represents an integer value, a rational value
427 or one of three special values, infinity, negative infinity and NaN.
428 Some predefined values can be created using the following functions.
431 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
432 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
433 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
434 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
435 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
436 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
438 Specific integer values can be created using the following functions.
441 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
443 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
445 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
446 size_t n, size_t size, const void *chunks);
448 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
449 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
450 The least significant digit is assumed to be stored first.
452 Value objects can be copied and freed using the following functions.
455 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
456 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
458 They can be inspected using the following functions.
461 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
462 long isl_val_get_num_si(__isl_keep isl_val *v);
463 long isl_val_get_den_si(__isl_keep isl_val *v);
464 double isl_val_get_d(__isl_keep isl_val *v);
465 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
467 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
468 size_t size, void *chunks);
470 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
471 of C<size> bytes needed to store the absolute value of the
473 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
474 which is assumed to have been preallocated by the caller.
475 The least significant digit is stored first.
476 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
477 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
478 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
480 An C<isl_val> can be modified using the following function.
483 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
486 The following unary properties are defined on C<isl_val>s.
489 int isl_val_sgn(__isl_keep isl_val *v);
490 int isl_val_is_zero(__isl_keep isl_val *v);
491 int isl_val_is_one(__isl_keep isl_val *v);
492 int isl_val_is_negone(__isl_keep isl_val *v);
493 int isl_val_is_nonneg(__isl_keep isl_val *v);
494 int isl_val_is_nonpos(__isl_keep isl_val *v);
495 int isl_val_is_pos(__isl_keep isl_val *v);
496 int isl_val_is_neg(__isl_keep isl_val *v);
497 int isl_val_is_int(__isl_keep isl_val *v);
498 int isl_val_is_rat(__isl_keep isl_val *v);
499 int isl_val_is_nan(__isl_keep isl_val *v);
500 int isl_val_is_infty(__isl_keep isl_val *v);
501 int isl_val_is_neginfty(__isl_keep isl_val *v);
503 Note that the sign of NaN is undefined.
505 The following binary properties are defined on pairs of C<isl_val>s.
508 int isl_val_lt(__isl_keep isl_val *v1,
509 __isl_keep isl_val *v2);
510 int isl_val_le(__isl_keep isl_val *v1,
511 __isl_keep isl_val *v2);
512 int isl_val_gt(__isl_keep isl_val *v1,
513 __isl_keep isl_val *v2);
514 int isl_val_ge(__isl_keep isl_val *v1,
515 __isl_keep isl_val *v2);
516 int isl_val_eq(__isl_keep isl_val *v1,
517 __isl_keep isl_val *v2);
518 int isl_val_ne(__isl_keep isl_val *v1,
519 __isl_keep isl_val *v2);
521 For integer C<isl_val>s we additionally have the following binary property.
524 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
525 __isl_keep isl_val *v2);
527 An C<isl_val> can also be compared to an integer using the following
528 function. The result is undefined for NaN.
531 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
533 The following unary operations are available on C<isl_val>s.
536 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
537 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
538 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
539 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
540 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
542 The following binary operations are available on C<isl_val>s.
545 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
546 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
547 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
548 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
549 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
550 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
551 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
552 __isl_take isl_val *v2);
553 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
554 __isl_take isl_val *v2);
555 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
556 __isl_take isl_val *v2);
557 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
559 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
560 __isl_take isl_val *v2);
561 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
563 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
564 __isl_take isl_val *v2);
565 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
567 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
568 __isl_take isl_val *v2);
570 On integer values, we additionally have the following operations.
573 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
574 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
575 __isl_take isl_val *v2);
576 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
577 __isl_take isl_val *v2);
578 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
579 __isl_take isl_val *v2, __isl_give isl_val **x,
580 __isl_give isl_val **y);
582 The function C<isl_val_gcdext> returns the greatest common divisor g
583 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
584 that C<*x> * C<v1> + C<*y> * C<v2> = g.
586 A value can be read from input using
589 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
592 A value can be printed using
595 __isl_give isl_printer *isl_printer_print_val(
596 __isl_take isl_printer *p, __isl_keep isl_val *v);
598 =head3 GMP specific functions
600 These functions are only available if C<isl> has been compiled with C<GMP>
603 Specific integer and rational values can be created from C<GMP> values using
604 the following functions.
606 #include <isl/val_gmp.h>
607 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
609 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
610 const mpz_t n, const mpz_t d);
612 The numerator and denominator of a rational value can be extracted as
613 C<GMP> values using the following functions.
615 #include <isl/val_gmp.h>
616 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
617 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
619 =head2 Sets and Relations
621 C<isl> uses six types of objects for representing sets and relations,
622 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
623 C<isl_union_set> and C<isl_union_map>.
624 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
625 can be described as a conjunction of affine constraints, while
626 C<isl_set> and C<isl_map> represent unions of
627 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
628 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
629 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
630 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
631 where spaces are considered different if they have a different number
632 of dimensions and/or different names (see L<"Spaces">).
633 The difference between sets and relations (maps) is that sets have
634 one set of variables, while relations have two sets of variables,
635 input variables and output variables.
637 =head2 Error Handling
639 C<isl> supports different ways to react in case a runtime error is triggered.
640 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
641 with two maps that have incompatible spaces. There are three possible ways
642 to react on error: to warn, to continue or to abort.
644 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
645 the last error in the corresponding C<isl_ctx> and the function in which the
646 error was triggered returns C<NULL>. An error does not corrupt internal state,
647 such that isl can continue to be used. C<isl> also provides functions to
648 read the last error and to reset the memory that stores the last error. The
649 last error is only stored for information purposes. Its presence does not
650 change the behavior of C<isl>. Hence, resetting an error is not required to
651 continue to use isl, but only to observe new errors.
654 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
655 void isl_ctx_reset_error(isl_ctx *ctx);
657 Another option is to continue on error. This is similar to warn on error mode,
658 except that C<isl> does not print any warning. This allows a program to
659 implement its own error reporting.
661 The last option is to directly abort the execution of the program from within
662 the isl library. This makes it obviously impossible to recover from an error,
663 but it allows to directly spot the error location. By aborting on error,
664 debuggers break at the location the error occurred and can provide a stack
665 trace. Other tools that automatically provide stack traces on abort or that do
666 not want to continue execution after an error was triggered may also prefer to
669 The on error behavior of isl can be specified by calling
670 C<isl_options_set_on_error> or by setting the command line option
671 C<--isl-on-error>. Valid arguments for the function call are
672 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
673 choices for the command line option are C<warn>, C<continue> and C<abort>.
674 It is also possible to query the current error mode.
676 #include <isl/options.h>
677 int isl_options_set_on_error(isl_ctx *ctx, int val);
678 int isl_options_get_on_error(isl_ctx *ctx);
682 Identifiers are used to identify both individual dimensions
683 and tuples of dimensions. They consist of an optional name and an optional
684 user pointer. The name and the user pointer cannot both be C<NULL>, however.
685 Identifiers with the same name but different pointer values
686 are considered to be distinct.
687 Similarly, identifiers with different names but the same pointer value
688 are also considered to be distinct.
689 Equal identifiers are represented using the same object.
690 Pairs of identifiers can therefore be tested for equality using the
692 Identifiers can be constructed, copied, freed, inspected and printed
693 using the following functions.
696 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
697 __isl_keep const char *name, void *user);
698 __isl_give isl_id *isl_id_set_free_user(
699 __isl_take isl_id *id,
700 __isl_give void (*free_user)(void *user));
701 __isl_give isl_id *isl_id_copy(isl_id *id);
702 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
704 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
705 void *isl_id_get_user(__isl_keep isl_id *id);
706 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
708 __isl_give isl_printer *isl_printer_print_id(
709 __isl_take isl_printer *p, __isl_keep isl_id *id);
711 The callback set by C<isl_id_set_free_user> is called on the user
712 pointer when the last reference to the C<isl_id> is freed.
713 Note that C<isl_id_get_name> returns a pointer to some internal
714 data structure, so the result can only be used while the
715 corresponding C<isl_id> is alive.
719 Whenever a new set, relation or similiar object is created from scratch,
720 the space in which it lives needs to be specified using an C<isl_space>.
721 Each space involves zero or more parameters and zero, one or two
722 tuples of set or input/output dimensions. The parameters and dimensions
723 are identified by an C<isl_dim_type> and a position.
724 The type C<isl_dim_param> refers to parameters,
725 the type C<isl_dim_set> refers to set dimensions (for spaces
726 with a single tuple of dimensions) and the types C<isl_dim_in>
727 and C<isl_dim_out> refer to input and output dimensions
728 (for spaces with two tuples of dimensions).
729 Local spaces (see L</"Local Spaces">) also contain dimensions
730 of type C<isl_dim_div>.
731 Note that parameters are only identified by their position within
732 a given object. Across different objects, parameters are (usually)
733 identified by their names or identifiers. Only unnamed parameters
734 are identified by their positions across objects. The use of unnamed
735 parameters is discouraged.
737 #include <isl/space.h>
738 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
739 unsigned nparam, unsigned n_in, unsigned n_out);
740 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
742 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
743 unsigned nparam, unsigned dim);
744 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
745 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
746 unsigned isl_space_dim(__isl_keep isl_space *space,
747 enum isl_dim_type type);
749 The space used for creating a parameter domain
750 needs to be created using C<isl_space_params_alloc>.
751 For other sets, the space
752 needs to be created using C<isl_space_set_alloc>, while
753 for a relation, the space
754 needs to be created using C<isl_space_alloc>.
755 C<isl_space_dim> can be used
756 to find out the number of dimensions of each type in
757 a space, where type may be
758 C<isl_dim_param>, C<isl_dim_in> (only for relations),
759 C<isl_dim_out> (only for relations), C<isl_dim_set>
760 (only for sets) or C<isl_dim_all>.
762 To check whether a given space is that of a set or a map
763 or whether it is a parameter space, use these functions:
765 #include <isl/space.h>
766 int isl_space_is_params(__isl_keep isl_space *space);
767 int isl_space_is_set(__isl_keep isl_space *space);
768 int isl_space_is_map(__isl_keep isl_space *space);
770 Spaces can be compared using the following functions:
772 #include <isl/space.h>
773 int isl_space_is_equal(__isl_keep isl_space *space1,
774 __isl_keep isl_space *space2);
775 int isl_space_is_domain(__isl_keep isl_space *space1,
776 __isl_keep isl_space *space2);
777 int isl_space_is_range(__isl_keep isl_space *space1,
778 __isl_keep isl_space *space2);
780 C<isl_space_is_domain> checks whether the first argument is equal
781 to the domain of the second argument. This requires in particular that
782 the first argument is a set space and that the second argument
785 It is often useful to create objects that live in the
786 same space as some other object. This can be accomplished
787 by creating the new objects
788 (see L</"Creating New Sets and Relations"> or
789 L</"Creating New (Piecewise) Quasipolynomials">) based on the space
790 of the original object.
793 __isl_give isl_space *isl_basic_set_get_space(
794 __isl_keep isl_basic_set *bset);
795 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
797 #include <isl/union_set.h>
798 __isl_give isl_space *isl_union_set_get_space(
799 __isl_keep isl_union_set *uset);
802 __isl_give isl_space *isl_basic_map_get_space(
803 __isl_keep isl_basic_map *bmap);
804 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
806 #include <isl/union_map.h>
807 __isl_give isl_space *isl_union_map_get_space(
808 __isl_keep isl_union_map *umap);
810 #include <isl/constraint.h>
811 __isl_give isl_space *isl_constraint_get_space(
812 __isl_keep isl_constraint *constraint);
814 #include <isl/polynomial.h>
815 __isl_give isl_space *isl_qpolynomial_get_domain_space(
816 __isl_keep isl_qpolynomial *qp);
817 __isl_give isl_space *isl_qpolynomial_get_space(
818 __isl_keep isl_qpolynomial *qp);
819 __isl_give isl_space *isl_qpolynomial_fold_get_space(
820 __isl_keep isl_qpolynomial_fold *fold);
821 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
822 __isl_keep isl_pw_qpolynomial *pwqp);
823 __isl_give isl_space *isl_pw_qpolynomial_get_space(
824 __isl_keep isl_pw_qpolynomial *pwqp);
825 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
826 __isl_keep isl_pw_qpolynomial_fold *pwf);
827 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
828 __isl_keep isl_pw_qpolynomial_fold *pwf);
829 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
830 __isl_keep isl_union_pw_qpolynomial *upwqp);
831 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
832 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
835 __isl_give isl_space *isl_multi_val_get_space(
836 __isl_keep isl_multi_val *mv);
839 __isl_give isl_space *isl_aff_get_domain_space(
840 __isl_keep isl_aff *aff);
841 __isl_give isl_space *isl_aff_get_space(
842 __isl_keep isl_aff *aff);
843 __isl_give isl_space *isl_pw_aff_get_domain_space(
844 __isl_keep isl_pw_aff *pwaff);
845 __isl_give isl_space *isl_pw_aff_get_space(
846 __isl_keep isl_pw_aff *pwaff);
847 __isl_give isl_space *isl_multi_aff_get_domain_space(
848 __isl_keep isl_multi_aff *maff);
849 __isl_give isl_space *isl_multi_aff_get_space(
850 __isl_keep isl_multi_aff *maff);
851 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
852 __isl_keep isl_pw_multi_aff *pma);
853 __isl_give isl_space *isl_pw_multi_aff_get_space(
854 __isl_keep isl_pw_multi_aff *pma);
855 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
856 __isl_keep isl_union_pw_multi_aff *upma);
857 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
858 __isl_keep isl_multi_pw_aff *mpa);
859 __isl_give isl_space *isl_multi_pw_aff_get_space(
860 __isl_keep isl_multi_pw_aff *mpa);
862 #include <isl/point.h>
863 __isl_give isl_space *isl_point_get_space(
864 __isl_keep isl_point *pnt);
866 The identifiers or names of the individual dimensions may be set or read off
867 using the following functions.
869 #include <isl/space.h>
870 __isl_give isl_space *isl_space_set_dim_id(
871 __isl_take isl_space *space,
872 enum isl_dim_type type, unsigned pos,
873 __isl_take isl_id *id);
874 int isl_space_has_dim_id(__isl_keep isl_space *space,
875 enum isl_dim_type type, unsigned pos);
876 __isl_give isl_id *isl_space_get_dim_id(
877 __isl_keep isl_space *space,
878 enum isl_dim_type type, unsigned pos);
879 __isl_give isl_space *isl_space_set_dim_name(
880 __isl_take isl_space *space,
881 enum isl_dim_type type, unsigned pos,
882 __isl_keep const char *name);
883 int isl_space_has_dim_name(__isl_keep isl_space *space,
884 enum isl_dim_type type, unsigned pos);
885 __isl_keep const char *isl_space_get_dim_name(
886 __isl_keep isl_space *space,
887 enum isl_dim_type type, unsigned pos);
889 Note that C<isl_space_get_name> returns a pointer to some internal
890 data structure, so the result can only be used while the
891 corresponding C<isl_space> is alive.
892 Also note that every function that operates on two sets or relations
893 requires that both arguments have the same parameters. This also
894 means that if one of the arguments has named parameters, then the
895 other needs to have named parameters too and the names need to match.
896 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
897 arguments may have different parameters (as long as they are named),
898 in which case the result will have as parameters the union of the parameters of
901 Given the identifier or name of a dimension (typically a parameter),
902 its position can be obtained from the following function.
904 #include <isl/space.h>
905 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
906 enum isl_dim_type type, __isl_keep isl_id *id);
907 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
908 enum isl_dim_type type, const char *name);
910 The identifiers or names of entire spaces may be set or read off
911 using the following functions.
913 #include <isl/space.h>
914 __isl_give isl_space *isl_space_set_tuple_id(
915 __isl_take isl_space *space,
916 enum isl_dim_type type, __isl_take isl_id *id);
917 __isl_give isl_space *isl_space_reset_tuple_id(
918 __isl_take isl_space *space, enum isl_dim_type type);
919 int isl_space_has_tuple_id(__isl_keep isl_space *space,
920 enum isl_dim_type type);
921 __isl_give isl_id *isl_space_get_tuple_id(
922 __isl_keep isl_space *space, enum isl_dim_type type);
923 __isl_give isl_space *isl_space_set_tuple_name(
924 __isl_take isl_space *space,
925 enum isl_dim_type type, const char *s);
926 int isl_space_has_tuple_name(__isl_keep isl_space *space,
927 enum isl_dim_type type);
928 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
929 enum isl_dim_type type);
931 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
932 or C<isl_dim_set>. As with C<isl_space_get_name>,
933 the C<isl_space_get_tuple_name> function returns a pointer to some internal
935 Binary operations require the corresponding spaces of their arguments
936 to have the same name.
938 To keep the names of all parameters and tuples, but reset the user pointers
939 of all the corresponding identifiers, use the following function.
941 __isl_give isl_space *isl_space_reset_user(
942 __isl_take isl_space *space);
944 Spaces can be nested. In particular, the domain of a set or
945 the domain or range of a relation can be a nested relation.
946 This process is also called I<wrapping>.
947 The functions for detecting, constructing and deconstructing
948 such nested spaces can be found in the wrapping properties
949 of L</"Unary Properties">, the wrapping operations
950 of L</"Unary Operations"> and the Cartesian product operations
951 of L</"Basic Operations">.
953 Spaces can be created from other spaces
954 using the following functions.
956 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
957 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
958 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
959 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
960 __isl_give isl_space *isl_space_domain_map(
961 __isl_take isl_space *space);
962 __isl_give isl_space *isl_space_range_map(
963 __isl_take isl_space *space);
964 __isl_give isl_space *isl_space_params(
965 __isl_take isl_space *space);
966 __isl_give isl_space *isl_space_set_from_params(
967 __isl_take isl_space *space);
968 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
969 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
970 __isl_take isl_space *right);
971 __isl_give isl_space *isl_space_align_params(
972 __isl_take isl_space *space1, __isl_take isl_space *space2)
973 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
974 enum isl_dim_type type, unsigned pos, unsigned n);
975 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
976 enum isl_dim_type type, unsigned n);
977 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
978 enum isl_dim_type type, unsigned first, unsigned n);
979 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
980 enum isl_dim_type dst_type, unsigned dst_pos,
981 enum isl_dim_type src_type, unsigned src_pos,
983 __isl_give isl_space *isl_space_map_from_set(
984 __isl_take isl_space *space);
985 __isl_give isl_space *isl_space_map_from_domain_and_range(
986 __isl_take isl_space *domain,
987 __isl_take isl_space *range);
988 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
989 __isl_give isl_space *isl_space_curry(
990 __isl_take isl_space *space);
991 __isl_give isl_space *isl_space_uncurry(
992 __isl_take isl_space *space);
994 Note that if dimensions are added or removed from a space, then
995 the name and the internal structure are lost.
999 A local space is essentially a space with
1000 zero or more existentially quantified variables.
1001 The local space of a (constraint of a) basic set or relation can be obtained
1002 using the following functions.
1004 #include <isl/constraint.h>
1005 __isl_give isl_local_space *isl_constraint_get_local_space(
1006 __isl_keep isl_constraint *constraint);
1008 #include <isl/set.h>
1009 __isl_give isl_local_space *isl_basic_set_get_local_space(
1010 __isl_keep isl_basic_set *bset);
1012 #include <isl/map.h>
1013 __isl_give isl_local_space *isl_basic_map_get_local_space(
1014 __isl_keep isl_basic_map *bmap);
1016 A new local space can be created from a space using
1018 #include <isl/local_space.h>
1019 __isl_give isl_local_space *isl_local_space_from_space(
1020 __isl_take isl_space *space);
1022 They can be inspected, modified, copied and freed using the following functions.
1024 #include <isl/local_space.h>
1025 isl_ctx *isl_local_space_get_ctx(
1026 __isl_keep isl_local_space *ls);
1027 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1028 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1029 enum isl_dim_type type);
1030 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1031 __isl_take isl_local_space *ls,
1032 enum isl_dim_type type, __isl_take isl_id *id);
1033 int isl_local_space_has_dim_id(
1034 __isl_keep isl_local_space *ls,
1035 enum isl_dim_type type, unsigned pos);
1036 __isl_give isl_id *isl_local_space_get_dim_id(
1037 __isl_keep isl_local_space *ls,
1038 enum isl_dim_type type, unsigned pos);
1039 int isl_local_space_has_dim_name(
1040 __isl_keep isl_local_space *ls,
1041 enum isl_dim_type type, unsigned pos)
1042 const char *isl_local_space_get_dim_name(
1043 __isl_keep isl_local_space *ls,
1044 enum isl_dim_type type, unsigned pos);
1045 __isl_give isl_local_space *isl_local_space_set_dim_name(
1046 __isl_take isl_local_space *ls,
1047 enum isl_dim_type type, unsigned pos, const char *s);
1048 __isl_give isl_local_space *isl_local_space_set_dim_id(
1049 __isl_take isl_local_space *ls,
1050 enum isl_dim_type type, unsigned pos,
1051 __isl_take isl_id *id);
1052 __isl_give isl_space *isl_local_space_get_space(
1053 __isl_keep isl_local_space *ls);
1054 __isl_give isl_aff *isl_local_space_get_div(
1055 __isl_keep isl_local_space *ls, int pos);
1056 __isl_give isl_local_space *isl_local_space_copy(
1057 __isl_keep isl_local_space *ls);
1058 __isl_null isl_local_space *isl_local_space_free(
1059 __isl_take isl_local_space *ls);
1061 Note that C<isl_local_space_get_div> can only be used on local spaces
1064 Two local spaces can be compared using
1066 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1067 __isl_keep isl_local_space *ls2);
1069 Local spaces can be created from other local spaces
1070 using the functions described in L</"Unary Operations">
1071 and L</"Binary Operations">.
1073 =head2 Input and Output
1075 C<isl> supports its own input/output format, which is similar
1076 to the C<Omega> format, but also supports the C<PolyLib> format
1079 =head3 C<isl> format
1081 The C<isl> format is similar to that of C<Omega>, but has a different
1082 syntax for describing the parameters and allows for the definition
1083 of an existentially quantified variable as the integer division
1084 of an affine expression.
1085 For example, the set of integers C<i> between C<0> and C<n>
1086 such that C<i % 10 <= 6> can be described as
1088 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1091 A set or relation can have several disjuncts, separated
1092 by the keyword C<or>. Each disjunct is either a conjunction
1093 of constraints or a projection (C<exists>) of a conjunction
1094 of constraints. The constraints are separated by the keyword
1097 =head3 C<PolyLib> format
1099 If the represented set is a union, then the first line
1100 contains a single number representing the number of disjuncts.
1101 Otherwise, a line containing the number C<1> is optional.
1103 Each disjunct is represented by a matrix of constraints.
1104 The first line contains two numbers representing
1105 the number of rows and columns,
1106 where the number of rows is equal to the number of constraints
1107 and the number of columns is equal to two plus the number of variables.
1108 The following lines contain the actual rows of the constraint matrix.
1109 In each row, the first column indicates whether the constraint
1110 is an equality (C<0>) or inequality (C<1>). The final column
1111 corresponds to the constant term.
1113 If the set is parametric, then the coefficients of the parameters
1114 appear in the last columns before the constant column.
1115 The coefficients of any existentially quantified variables appear
1116 between those of the set variables and those of the parameters.
1118 =head3 Extended C<PolyLib> format
1120 The extended C<PolyLib> format is nearly identical to the
1121 C<PolyLib> format. The only difference is that the line
1122 containing the number of rows and columns of a constraint matrix
1123 also contains four additional numbers:
1124 the number of output dimensions, the number of input dimensions,
1125 the number of local dimensions (i.e., the number of existentially
1126 quantified variables) and the number of parameters.
1127 For sets, the number of ``output'' dimensions is equal
1128 to the number of set dimensions, while the number of ``input''
1133 #include <isl/set.h>
1134 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1135 isl_ctx *ctx, FILE *input);
1136 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1137 isl_ctx *ctx, const char *str);
1138 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1140 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1143 #include <isl/map.h>
1144 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1145 isl_ctx *ctx, FILE *input);
1146 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1147 isl_ctx *ctx, const char *str);
1148 __isl_give isl_map *isl_map_read_from_file(
1149 isl_ctx *ctx, FILE *input);
1150 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1153 #include <isl/union_set.h>
1154 __isl_give isl_union_set *isl_union_set_read_from_file(
1155 isl_ctx *ctx, FILE *input);
1156 __isl_give isl_union_set *isl_union_set_read_from_str(
1157 isl_ctx *ctx, const char *str);
1159 #include <isl/union_map.h>
1160 __isl_give isl_union_map *isl_union_map_read_from_file(
1161 isl_ctx *ctx, FILE *input);
1162 __isl_give isl_union_map *isl_union_map_read_from_str(
1163 isl_ctx *ctx, const char *str);
1165 The input format is autodetected and may be either the C<PolyLib> format
1166 or the C<isl> format.
1170 Before anything can be printed, an C<isl_printer> needs to
1173 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1175 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1176 __isl_null isl_printer *isl_printer_free(
1177 __isl_take isl_printer *printer);
1178 __isl_give char *isl_printer_get_str(
1179 __isl_keep isl_printer *printer);
1181 The printer can be inspected using the following functions.
1183 FILE *isl_printer_get_file(
1184 __isl_keep isl_printer *printer);
1185 int isl_printer_get_output_format(
1186 __isl_keep isl_printer *p);
1188 The behavior of the printer can be modified in various ways
1190 __isl_give isl_printer *isl_printer_set_output_format(
1191 __isl_take isl_printer *p, int output_format);
1192 __isl_give isl_printer *isl_printer_set_indent(
1193 __isl_take isl_printer *p, int indent);
1194 __isl_give isl_printer *isl_printer_set_indent_prefix(
1195 __isl_take isl_printer *p, const char *prefix);
1196 __isl_give isl_printer *isl_printer_indent(
1197 __isl_take isl_printer *p, int indent);
1198 __isl_give isl_printer *isl_printer_set_prefix(
1199 __isl_take isl_printer *p, const char *prefix);
1200 __isl_give isl_printer *isl_printer_set_suffix(
1201 __isl_take isl_printer *p, const char *suffix);
1203 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1204 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1205 and defaults to C<ISL_FORMAT_ISL>.
1206 Each line in the output is prefixed by C<indent_prefix>,
1207 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
1208 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1209 In the C<PolyLib> format output,
1210 the coefficients of the existentially quantified variables
1211 appear between those of the set variables and those
1213 The function C<isl_printer_indent> increases the indentation
1214 by the specified amount (which may be negative).
1216 To actually print something, use
1218 #include <isl/printer.h>
1219 __isl_give isl_printer *isl_printer_print_double(
1220 __isl_take isl_printer *p, double d);
1222 #include <isl/set.h>
1223 __isl_give isl_printer *isl_printer_print_basic_set(
1224 __isl_take isl_printer *printer,
1225 __isl_keep isl_basic_set *bset);
1226 __isl_give isl_printer *isl_printer_print_set(
1227 __isl_take isl_printer *printer,
1228 __isl_keep isl_set *set);
1230 #include <isl/map.h>
1231 __isl_give isl_printer *isl_printer_print_basic_map(
1232 __isl_take isl_printer *printer,
1233 __isl_keep isl_basic_map *bmap);
1234 __isl_give isl_printer *isl_printer_print_map(
1235 __isl_take isl_printer *printer,
1236 __isl_keep isl_map *map);
1238 #include <isl/union_set.h>
1239 __isl_give isl_printer *isl_printer_print_union_set(
1240 __isl_take isl_printer *p,
1241 __isl_keep isl_union_set *uset);
1243 #include <isl/union_map.h>
1244 __isl_give isl_printer *isl_printer_print_union_map(
1245 __isl_take isl_printer *p,
1246 __isl_keep isl_union_map *umap);
1248 When called on a file printer, the following function flushes
1249 the file. When called on a string printer, the buffer is cleared.
1251 __isl_give isl_printer *isl_printer_flush(
1252 __isl_take isl_printer *p);
1254 =head2 Creating New Sets and Relations
1256 C<isl> has functions for creating some standard sets and relations.
1260 =item * Empty sets and relations
1262 __isl_give isl_basic_set *isl_basic_set_empty(
1263 __isl_take isl_space *space);
1264 __isl_give isl_basic_map *isl_basic_map_empty(
1265 __isl_take isl_space *space);
1266 __isl_give isl_set *isl_set_empty(
1267 __isl_take isl_space *space);
1268 __isl_give isl_map *isl_map_empty(
1269 __isl_take isl_space *space);
1270 __isl_give isl_union_set *isl_union_set_empty(
1271 __isl_take isl_space *space);
1272 __isl_give isl_union_map *isl_union_map_empty(
1273 __isl_take isl_space *space);
1275 For C<isl_union_set>s and C<isl_union_map>s, the space
1276 is only used to specify the parameters.
1278 =item * Universe sets and relations
1280 __isl_give isl_basic_set *isl_basic_set_universe(
1281 __isl_take isl_space *space);
1282 __isl_give isl_basic_map *isl_basic_map_universe(
1283 __isl_take isl_space *space);
1284 __isl_give isl_set *isl_set_universe(
1285 __isl_take isl_space *space);
1286 __isl_give isl_map *isl_map_universe(
1287 __isl_take isl_space *space);
1288 __isl_give isl_union_set *isl_union_set_universe(
1289 __isl_take isl_union_set *uset);
1290 __isl_give isl_union_map *isl_union_map_universe(
1291 __isl_take isl_union_map *umap);
1293 The sets and relations constructed by the functions above
1294 contain all integer values, while those constructed by the
1295 functions below only contain non-negative values.
1297 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1298 __isl_take isl_space *space);
1299 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1300 __isl_take isl_space *space);
1301 __isl_give isl_set *isl_set_nat_universe(
1302 __isl_take isl_space *space);
1303 __isl_give isl_map *isl_map_nat_universe(
1304 __isl_take isl_space *space);
1306 =item * Identity relations
1308 __isl_give isl_basic_map *isl_basic_map_identity(
1309 __isl_take isl_space *space);
1310 __isl_give isl_map *isl_map_identity(
1311 __isl_take isl_space *space);
1313 The number of input and output dimensions in C<space> needs
1316 =item * Lexicographic order
1318 __isl_give isl_map *isl_map_lex_lt(
1319 __isl_take isl_space *set_space);
1320 __isl_give isl_map *isl_map_lex_le(
1321 __isl_take isl_space *set_space);
1322 __isl_give isl_map *isl_map_lex_gt(
1323 __isl_take isl_space *set_space);
1324 __isl_give isl_map *isl_map_lex_ge(
1325 __isl_take isl_space *set_space);
1326 __isl_give isl_map *isl_map_lex_lt_first(
1327 __isl_take isl_space *space, unsigned n);
1328 __isl_give isl_map *isl_map_lex_le_first(
1329 __isl_take isl_space *space, unsigned n);
1330 __isl_give isl_map *isl_map_lex_gt_first(
1331 __isl_take isl_space *space, unsigned n);
1332 __isl_give isl_map *isl_map_lex_ge_first(
1333 __isl_take isl_space *space, unsigned n);
1335 The first four functions take a space for a B<set>
1336 and return relations that express that the elements in the domain
1337 are lexicographically less
1338 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1339 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1340 than the elements in the range.
1341 The last four functions take a space for a map
1342 and return relations that express that the first C<n> dimensions
1343 in the domain are lexicographically less
1344 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1345 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1346 than the first C<n> dimensions in the range.
1350 A basic set or relation can be converted to a set or relation
1351 using the following functions.
1353 __isl_give isl_set *isl_set_from_basic_set(
1354 __isl_take isl_basic_set *bset);
1355 __isl_give isl_map *isl_map_from_basic_map(
1356 __isl_take isl_basic_map *bmap);
1358 Sets and relations can be converted to union sets and relations
1359 using the following functions.
1361 __isl_give isl_union_set *isl_union_set_from_basic_set(
1362 __isl_take isl_basic_set *bset);
1363 __isl_give isl_union_map *isl_union_map_from_basic_map(
1364 __isl_take isl_basic_map *bmap);
1365 __isl_give isl_union_set *isl_union_set_from_set(
1366 __isl_take isl_set *set);
1367 __isl_give isl_union_map *isl_union_map_from_map(
1368 __isl_take isl_map *map);
1370 The inverse conversions below can only be used if the input
1371 union set or relation is known to contain elements in exactly one
1374 __isl_give isl_set *isl_set_from_union_set(
1375 __isl_take isl_union_set *uset);
1376 __isl_give isl_map *isl_map_from_union_map(
1377 __isl_take isl_union_map *umap);
1379 A zero-dimensional (basic) set can be constructed on a given parameter domain
1380 using the following function.
1382 __isl_give isl_basic_set *isl_basic_set_from_params(
1383 __isl_take isl_basic_set *bset);
1384 __isl_give isl_set *isl_set_from_params(
1385 __isl_take isl_set *set);
1387 Sets and relations can be copied and freed again using the following
1390 __isl_give isl_basic_set *isl_basic_set_copy(
1391 __isl_keep isl_basic_set *bset);
1392 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1393 __isl_give isl_union_set *isl_union_set_copy(
1394 __isl_keep isl_union_set *uset);
1395 __isl_give isl_basic_map *isl_basic_map_copy(
1396 __isl_keep isl_basic_map *bmap);
1397 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1398 __isl_give isl_union_map *isl_union_map_copy(
1399 __isl_keep isl_union_map *umap);
1400 __isl_null isl_basic_set *isl_basic_set_free(
1401 __isl_take isl_basic_set *bset);
1402 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1403 __isl_null isl_union_set *isl_union_set_free(
1404 __isl_take isl_union_set *uset);
1405 __isl_null isl_basic_map *isl_basic_map_free(
1406 __isl_take isl_basic_map *bmap);
1407 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1408 __isl_null isl_union_map *isl_union_map_free(
1409 __isl_take isl_union_map *umap);
1411 Other sets and relations can be constructed by starting
1412 from a universe set or relation, adding equality and/or
1413 inequality constraints and then projecting out the
1414 existentially quantified variables, if any.
1415 Constraints can be constructed, manipulated and
1416 added to (or removed from) (basic) sets and relations
1417 using the following functions.
1419 #include <isl/constraint.h>
1420 __isl_give isl_constraint *isl_equality_alloc(
1421 __isl_take isl_local_space *ls);
1422 __isl_give isl_constraint *isl_inequality_alloc(
1423 __isl_take isl_local_space *ls);
1424 __isl_give isl_constraint *isl_constraint_set_constant_si(
1425 __isl_take isl_constraint *constraint, int v);
1426 __isl_give isl_constraint *isl_constraint_set_constant_val(
1427 __isl_take isl_constraint *constraint,
1428 __isl_take isl_val *v);
1429 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1430 __isl_take isl_constraint *constraint,
1431 enum isl_dim_type type, int pos, int v);
1432 __isl_give isl_constraint *
1433 isl_constraint_set_coefficient_val(
1434 __isl_take isl_constraint *constraint,
1435 enum isl_dim_type type, int pos,
1436 __isl_take isl_val *v);
1437 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1438 __isl_take isl_basic_map *bmap,
1439 __isl_take isl_constraint *constraint);
1440 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1441 __isl_take isl_basic_set *bset,
1442 __isl_take isl_constraint *constraint);
1443 __isl_give isl_map *isl_map_add_constraint(
1444 __isl_take isl_map *map,
1445 __isl_take isl_constraint *constraint);
1446 __isl_give isl_set *isl_set_add_constraint(
1447 __isl_take isl_set *set,
1448 __isl_take isl_constraint *constraint);
1449 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1450 __isl_take isl_basic_set *bset,
1451 __isl_take isl_constraint *constraint);
1453 For example, to create a set containing the even integers
1454 between 10 and 42, you would use the following code.
1457 isl_local_space *ls;
1459 isl_basic_set *bset;
1461 space = isl_space_set_alloc(ctx, 0, 2);
1462 bset = isl_basic_set_universe(isl_space_copy(space));
1463 ls = isl_local_space_from_space(space);
1465 c = isl_equality_alloc(isl_local_space_copy(ls));
1466 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1467 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1468 bset = isl_basic_set_add_constraint(bset, c);
1470 c = isl_inequality_alloc(isl_local_space_copy(ls));
1471 c = isl_constraint_set_constant_si(c, -10);
1472 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1473 bset = isl_basic_set_add_constraint(bset, c);
1475 c = isl_inequality_alloc(ls);
1476 c = isl_constraint_set_constant_si(c, 42);
1477 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1478 bset = isl_basic_set_add_constraint(bset, c);
1480 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1484 isl_basic_set *bset;
1485 bset = isl_basic_set_read_from_str(ctx,
1486 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1488 A basic set or relation can also be constructed from two matrices
1489 describing the equalities and the inequalities.
1491 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1492 __isl_take isl_space *space,
1493 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1494 enum isl_dim_type c1,
1495 enum isl_dim_type c2, enum isl_dim_type c3,
1496 enum isl_dim_type c4);
1497 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1498 __isl_take isl_space *space,
1499 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1500 enum isl_dim_type c1,
1501 enum isl_dim_type c2, enum isl_dim_type c3,
1502 enum isl_dim_type c4, enum isl_dim_type c5);
1504 The C<isl_dim_type> arguments indicate the order in which
1505 different kinds of variables appear in the input matrices
1506 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1507 C<isl_dim_set> and C<isl_dim_div> for sets and
1508 of C<isl_dim_cst>, C<isl_dim_param>,
1509 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1511 A (basic or union) set or relation can also be constructed from a
1512 (union) (piecewise) (multiple) affine expression
1513 or a list of affine expressions
1514 (See L<"Piecewise Quasi Affine Expressions"> and
1515 L<"Piecewise Multiple Quasi Affine Expressions">).
1517 __isl_give isl_basic_map *isl_basic_map_from_aff(
1518 __isl_take isl_aff *aff);
1519 __isl_give isl_map *isl_map_from_aff(
1520 __isl_take isl_aff *aff);
1521 __isl_give isl_set *isl_set_from_pw_aff(
1522 __isl_take isl_pw_aff *pwaff);
1523 __isl_give isl_map *isl_map_from_pw_aff(
1524 __isl_take isl_pw_aff *pwaff);
1525 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1526 __isl_take isl_space *domain_space,
1527 __isl_take isl_aff_list *list);
1528 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1529 __isl_take isl_multi_aff *maff)
1530 __isl_give isl_map *isl_map_from_multi_aff(
1531 __isl_take isl_multi_aff *maff)
1532 __isl_give isl_set *isl_set_from_pw_multi_aff(
1533 __isl_take isl_pw_multi_aff *pma);
1534 __isl_give isl_map *isl_map_from_pw_multi_aff(
1535 __isl_take isl_pw_multi_aff *pma);
1536 __isl_give isl_set *isl_set_from_multi_pw_aff(
1537 __isl_take isl_multi_pw_aff *mpa);
1538 __isl_give isl_map *isl_map_from_multi_pw_aff(
1539 __isl_take isl_multi_pw_aff *mpa);
1540 __isl_give isl_union_map *
1541 isl_union_map_from_union_pw_multi_aff(
1542 __isl_take isl_union_pw_multi_aff *upma);
1544 The C<domain_space> argument describes the domain of the resulting
1545 basic relation. It is required because the C<list> may consist
1546 of zero affine expressions.
1548 =head2 Inspecting Sets and Relations
1550 Usually, the user should not have to care about the actual constraints
1551 of the sets and maps, but should instead apply the abstract operations
1552 explained in the following sections.
1553 Occasionally, however, it may be required to inspect the individual
1554 coefficients of the constraints. This section explains how to do so.
1555 In these cases, it may also be useful to have C<isl> compute
1556 an explicit representation of the existentially quantified variables.
1558 __isl_give isl_set *isl_set_compute_divs(
1559 __isl_take isl_set *set);
1560 __isl_give isl_map *isl_map_compute_divs(
1561 __isl_take isl_map *map);
1562 __isl_give isl_union_set *isl_union_set_compute_divs(
1563 __isl_take isl_union_set *uset);
1564 __isl_give isl_union_map *isl_union_map_compute_divs(
1565 __isl_take isl_union_map *umap);
1567 This explicit representation defines the existentially quantified
1568 variables as integer divisions of the other variables, possibly
1569 including earlier existentially quantified variables.
1570 An explicitly represented existentially quantified variable therefore
1571 has a unique value when the values of the other variables are known.
1572 If, furthermore, the same existentials, i.e., existentials
1573 with the same explicit representations, should appear in the
1574 same order in each of the disjuncts of a set or map, then the user should call
1575 either of the following functions.
1577 __isl_give isl_set *isl_set_align_divs(
1578 __isl_take isl_set *set);
1579 __isl_give isl_map *isl_map_align_divs(
1580 __isl_take isl_map *map);
1582 Alternatively, the existentially quantified variables can be removed
1583 using the following functions, which compute an overapproximation.
1585 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1586 __isl_take isl_basic_set *bset);
1587 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1588 __isl_take isl_basic_map *bmap);
1589 __isl_give isl_set *isl_set_remove_divs(
1590 __isl_take isl_set *set);
1591 __isl_give isl_map *isl_map_remove_divs(
1592 __isl_take isl_map *map);
1594 It is also possible to only remove those divs that are defined
1595 in terms of a given range of dimensions or only those for which
1596 no explicit representation is known.
1598 __isl_give isl_basic_set *
1599 isl_basic_set_remove_divs_involving_dims(
1600 __isl_take isl_basic_set *bset,
1601 enum isl_dim_type type,
1602 unsigned first, unsigned n);
1603 __isl_give isl_basic_map *
1604 isl_basic_map_remove_divs_involving_dims(
1605 __isl_take isl_basic_map *bmap,
1606 enum isl_dim_type type,
1607 unsigned first, unsigned n);
1608 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1609 __isl_take isl_set *set, enum isl_dim_type type,
1610 unsigned first, unsigned n);
1611 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1612 __isl_take isl_map *map, enum isl_dim_type type,
1613 unsigned first, unsigned n);
1615 __isl_give isl_basic_set *
1616 isl_basic_set_remove_unknown_divs(
1617 __isl_take isl_basic_set *bset);
1618 __isl_give isl_set *isl_set_remove_unknown_divs(
1619 __isl_take isl_set *set);
1620 __isl_give isl_map *isl_map_remove_unknown_divs(
1621 __isl_take isl_map *map);
1623 To iterate over all the sets or maps in a union set or map, use
1625 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1626 int (*fn)(__isl_take isl_set *set, void *user),
1628 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1629 int (*fn)(__isl_take isl_map *map, void *user),
1632 The number of sets or maps in a union set or map can be obtained
1635 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1636 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1638 To extract the set or map in a given space from a union, use
1640 __isl_give isl_set *isl_union_set_extract_set(
1641 __isl_keep isl_union_set *uset,
1642 __isl_take isl_space *space);
1643 __isl_give isl_map *isl_union_map_extract_map(
1644 __isl_keep isl_union_map *umap,
1645 __isl_take isl_space *space);
1647 To iterate over all the basic sets or maps in a set or map, use
1649 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1650 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1652 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1653 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1656 The callback function C<fn> should return 0 if successful and
1657 -1 if an error occurs. In the latter case, or if any other error
1658 occurs, the above functions will return -1.
1660 It should be noted that C<isl> does not guarantee that
1661 the basic sets or maps passed to C<fn> are disjoint.
1662 If this is required, then the user should call one of
1663 the following functions first.
1665 __isl_give isl_set *isl_set_make_disjoint(
1666 __isl_take isl_set *set);
1667 __isl_give isl_map *isl_map_make_disjoint(
1668 __isl_take isl_map *map);
1670 The number of basic sets in a set can be obtained
1673 int isl_set_n_basic_set(__isl_keep isl_set *set);
1675 To iterate over the constraints of a basic set or map, use
1677 #include <isl/constraint.h>
1679 int isl_basic_set_n_constraint(
1680 __isl_keep isl_basic_set *bset);
1681 int isl_basic_set_foreach_constraint(
1682 __isl_keep isl_basic_set *bset,
1683 int (*fn)(__isl_take isl_constraint *c, void *user),
1685 int isl_basic_map_foreach_constraint(
1686 __isl_keep isl_basic_map *bmap,
1687 int (*fn)(__isl_take isl_constraint *c, void *user),
1689 __isl_null isl_constraint *isl_constraint_free(
1690 __isl_take isl_constraint *c);
1692 Again, the callback function C<fn> should return 0 if successful and
1693 -1 if an error occurs. In the latter case, or if any other error
1694 occurs, the above functions will return -1.
1695 The constraint C<c> represents either an equality or an inequality.
1696 Use the following function to find out whether a constraint
1697 represents an equality. If not, it represents an inequality.
1699 int isl_constraint_is_equality(
1700 __isl_keep isl_constraint *constraint);
1702 The coefficients of the constraints can be inspected using
1703 the following functions.
1705 int isl_constraint_is_lower_bound(
1706 __isl_keep isl_constraint *constraint,
1707 enum isl_dim_type type, unsigned pos);
1708 int isl_constraint_is_upper_bound(
1709 __isl_keep isl_constraint *constraint,
1710 enum isl_dim_type type, unsigned pos);
1711 __isl_give isl_val *isl_constraint_get_constant_val(
1712 __isl_keep isl_constraint *constraint);
1713 __isl_give isl_val *isl_constraint_get_coefficient_val(
1714 __isl_keep isl_constraint *constraint,
1715 enum isl_dim_type type, int pos);
1716 int isl_constraint_involves_dims(
1717 __isl_keep isl_constraint *constraint,
1718 enum isl_dim_type type, unsigned first, unsigned n);
1720 The explicit representations of the existentially quantified
1721 variables can be inspected using the following function.
1722 Note that the user is only allowed to use this function
1723 if the inspected set or map is the result of a call
1724 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1725 The existentially quantified variable is equal to the floor
1726 of the returned affine expression. The affine expression
1727 itself can be inspected using the functions in
1728 L<"Piecewise Quasi Affine Expressions">.
1730 __isl_give isl_aff *isl_constraint_get_div(
1731 __isl_keep isl_constraint *constraint, int pos);
1733 To obtain the constraints of a basic set or map in matrix
1734 form, use the following functions.
1736 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1737 __isl_keep isl_basic_set *bset,
1738 enum isl_dim_type c1, enum isl_dim_type c2,
1739 enum isl_dim_type c3, enum isl_dim_type c4);
1740 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1741 __isl_keep isl_basic_set *bset,
1742 enum isl_dim_type c1, enum isl_dim_type c2,
1743 enum isl_dim_type c3, enum isl_dim_type c4);
1744 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1745 __isl_keep isl_basic_map *bmap,
1746 enum isl_dim_type c1,
1747 enum isl_dim_type c2, enum isl_dim_type c3,
1748 enum isl_dim_type c4, enum isl_dim_type c5);
1749 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1750 __isl_keep isl_basic_map *bmap,
1751 enum isl_dim_type c1,
1752 enum isl_dim_type c2, enum isl_dim_type c3,
1753 enum isl_dim_type c4, enum isl_dim_type c5);
1755 The C<isl_dim_type> arguments dictate the order in which
1756 different kinds of variables appear in the resulting matrix
1757 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1758 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1760 The number of parameters, input, output or set dimensions can
1761 be obtained using the following functions.
1763 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1764 enum isl_dim_type type);
1765 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1766 enum isl_dim_type type);
1767 unsigned isl_set_dim(__isl_keep isl_set *set,
1768 enum isl_dim_type type);
1769 unsigned isl_map_dim(__isl_keep isl_map *map,
1770 enum isl_dim_type type);
1771 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1772 enum isl_dim_type type);
1774 Note that a C<isl_union_map> only has parameters.
1776 To check whether the description of a set or relation depends
1777 on one or more given dimensions, it is not necessary to iterate over all
1778 constraints. Instead the following functions can be used.
1780 int isl_basic_set_involves_dims(
1781 __isl_keep isl_basic_set *bset,
1782 enum isl_dim_type type, unsigned first, unsigned n);
1783 int isl_set_involves_dims(__isl_keep isl_set *set,
1784 enum isl_dim_type type, unsigned first, unsigned n);
1785 int isl_basic_map_involves_dims(
1786 __isl_keep isl_basic_map *bmap,
1787 enum isl_dim_type type, unsigned first, unsigned n);
1788 int isl_map_involves_dims(__isl_keep isl_map *map,
1789 enum isl_dim_type type, unsigned first, unsigned n);
1791 Similarly, the following functions can be used to check whether
1792 a given dimension is involved in any lower or upper bound.
1794 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1795 enum isl_dim_type type, unsigned pos);
1796 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1797 enum isl_dim_type type, unsigned pos);
1799 Note that these functions return true even if there is a bound on
1800 the dimension on only some of the basic sets of C<set>.
1801 To check if they have a bound for all of the basic sets in C<set>,
1802 use the following functions instead.
1804 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1805 enum isl_dim_type type, unsigned pos);
1806 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1807 enum isl_dim_type type, unsigned pos);
1809 The identifiers or names of the domain and range spaces of a set
1810 or relation can be read off or set using the following functions.
1812 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1813 __isl_take isl_basic_set *bset,
1814 __isl_take isl_id *id);
1815 __isl_give isl_set *isl_set_set_tuple_id(
1816 __isl_take isl_set *set, __isl_take isl_id *id);
1817 __isl_give isl_set *isl_set_reset_tuple_id(
1818 __isl_take isl_set *set);
1819 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1820 __isl_give isl_id *isl_set_get_tuple_id(
1821 __isl_keep isl_set *set);
1822 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1823 __isl_take isl_basic_map *bmap,
1824 enum isl_dim_type type, __isl_take isl_id *id);
1825 __isl_give isl_map *isl_map_set_tuple_id(
1826 __isl_take isl_map *map, enum isl_dim_type type,
1827 __isl_take isl_id *id);
1828 __isl_give isl_map *isl_map_reset_tuple_id(
1829 __isl_take isl_map *map, enum isl_dim_type type);
1830 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1831 enum isl_dim_type type);
1832 __isl_give isl_id *isl_map_get_tuple_id(
1833 __isl_keep isl_map *map, enum isl_dim_type type);
1835 const char *isl_basic_set_get_tuple_name(
1836 __isl_keep isl_basic_set *bset);
1837 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1838 __isl_take isl_basic_set *set, const char *s);
1839 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1840 const char *isl_set_get_tuple_name(
1841 __isl_keep isl_set *set);
1842 const char *isl_basic_map_get_tuple_name(
1843 __isl_keep isl_basic_map *bmap,
1844 enum isl_dim_type type);
1845 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1846 __isl_take isl_basic_map *bmap,
1847 enum isl_dim_type type, const char *s);
1848 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1849 enum isl_dim_type type);
1850 const char *isl_map_get_tuple_name(
1851 __isl_keep isl_map *map,
1852 enum isl_dim_type type);
1854 As with C<isl_space_get_tuple_name>, the value returned points to
1855 an internal data structure.
1856 The identifiers, positions or names of individual dimensions can be
1857 read off using the following functions.
1859 __isl_give isl_id *isl_basic_set_get_dim_id(
1860 __isl_keep isl_basic_set *bset,
1861 enum isl_dim_type type, unsigned pos);
1862 __isl_give isl_set *isl_set_set_dim_id(
1863 __isl_take isl_set *set, enum isl_dim_type type,
1864 unsigned pos, __isl_take isl_id *id);
1865 int isl_set_has_dim_id(__isl_keep isl_set *set,
1866 enum isl_dim_type type, unsigned pos);
1867 __isl_give isl_id *isl_set_get_dim_id(
1868 __isl_keep isl_set *set, enum isl_dim_type type,
1870 int isl_basic_map_has_dim_id(
1871 __isl_keep isl_basic_map *bmap,
1872 enum isl_dim_type type, unsigned pos);
1873 __isl_give isl_map *isl_map_set_dim_id(
1874 __isl_take isl_map *map, enum isl_dim_type type,
1875 unsigned pos, __isl_take isl_id *id);
1876 int isl_map_has_dim_id(__isl_keep isl_map *map,
1877 enum isl_dim_type type, unsigned pos);
1878 __isl_give isl_id *isl_map_get_dim_id(
1879 __isl_keep isl_map *map, enum isl_dim_type type,
1881 __isl_give isl_id *isl_union_map_get_dim_id(
1882 __isl_keep isl_union_map *umap,
1883 enum isl_dim_type type, unsigned pos);
1885 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1886 enum isl_dim_type type, __isl_keep isl_id *id);
1887 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1888 enum isl_dim_type type, __isl_keep isl_id *id);
1889 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1890 enum isl_dim_type type, const char *name);
1891 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1892 enum isl_dim_type type, const char *name);
1894 const char *isl_constraint_get_dim_name(
1895 __isl_keep isl_constraint *constraint,
1896 enum isl_dim_type type, unsigned pos);
1897 const char *isl_basic_set_get_dim_name(
1898 __isl_keep isl_basic_set *bset,
1899 enum isl_dim_type type, unsigned pos);
1900 int isl_set_has_dim_name(__isl_keep isl_set *set,
1901 enum isl_dim_type type, unsigned pos);
1902 const char *isl_set_get_dim_name(
1903 __isl_keep isl_set *set,
1904 enum isl_dim_type type, unsigned pos);
1905 const char *isl_basic_map_get_dim_name(
1906 __isl_keep isl_basic_map *bmap,
1907 enum isl_dim_type type, unsigned pos);
1908 int isl_map_has_dim_name(__isl_keep isl_map *map,
1909 enum isl_dim_type type, unsigned pos);
1910 const char *isl_map_get_dim_name(
1911 __isl_keep isl_map *map,
1912 enum isl_dim_type type, unsigned pos);
1914 These functions are mostly useful to obtain the identifiers, positions
1915 or names of the parameters. Identifiers of individual dimensions are
1916 essentially only useful for printing. They are ignored by all other
1917 operations and may not be preserved across those operations.
1919 The user pointers on all parameters and tuples can be reset
1920 using the following functions.
1922 #include <isl/set.h>
1923 __isl_give isl_set *isl_set_reset_user(
1924 __isl_take isl_set *set);
1925 #include <isl/map.h>
1926 __isl_give isl_map *isl_map_reset_user(
1927 __isl_take isl_map *map);
1928 #include <isl/union_set.h>
1929 __isl_give isl_union_set *isl_union_set_reset_user(
1930 __isl_take isl_union_set *uset);
1931 #include <isl/union_map.h>
1932 __isl_give isl_union_map *isl_union_map_reset_user(
1933 __isl_take isl_union_map *umap);
1937 =head3 Unary Properties
1943 The following functions test whether the given set or relation
1944 contains any integer points. The ``plain'' variants do not perform
1945 any computations, but simply check if the given set or relation
1946 is already known to be empty.
1948 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1949 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1950 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1951 int isl_set_is_empty(__isl_keep isl_set *set);
1952 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1953 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1954 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1955 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1956 int isl_map_is_empty(__isl_keep isl_map *map);
1957 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1959 =item * Universality
1961 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1962 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1963 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1965 =item * Single-valuedness
1967 int isl_basic_map_is_single_valued(
1968 __isl_keep isl_basic_map *bmap);
1969 int isl_map_plain_is_single_valued(
1970 __isl_keep isl_map *map);
1971 int isl_map_is_single_valued(__isl_keep isl_map *map);
1972 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1976 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1977 int isl_map_is_injective(__isl_keep isl_map *map);
1978 int isl_union_map_plain_is_injective(
1979 __isl_keep isl_union_map *umap);
1980 int isl_union_map_is_injective(
1981 __isl_keep isl_union_map *umap);
1985 int isl_map_is_bijective(__isl_keep isl_map *map);
1986 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1990 __isl_give isl_val *
1991 isl_basic_map_plain_get_val_if_fixed(
1992 __isl_keep isl_basic_map *bmap,
1993 enum isl_dim_type type, unsigned pos);
1994 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
1995 __isl_keep isl_set *set,
1996 enum isl_dim_type type, unsigned pos);
1997 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
1998 __isl_keep isl_map *map,
1999 enum isl_dim_type type, unsigned pos);
2001 If the set or relation obviously lies on a hyperplane where the given dimension
2002 has a fixed value, then return that value.
2003 Otherwise return NaN.
2007 int isl_set_dim_residue_class_val(
2008 __isl_keep isl_set *set,
2009 int pos, __isl_give isl_val **modulo,
2010 __isl_give isl_val **residue);
2012 Check if the values of the given set dimension are equal to a fixed
2013 value modulo some integer value. If so, assign the modulo to C<*modulo>
2014 and the fixed value to C<*residue>. If the given dimension attains only
2015 a single value, then assign C<0> to C<*modulo> and the fixed value to
2017 If the dimension does not attain only a single value and if no modulo
2018 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
2022 To check whether a set is a parameter domain, use this function:
2024 int isl_set_is_params(__isl_keep isl_set *set);
2025 int isl_union_set_is_params(
2026 __isl_keep isl_union_set *uset);
2030 The following functions check whether the space of the given
2031 (basic) set or relation range is a wrapped relation.
2033 #include <isl/space.h>
2034 int isl_space_is_wrapping(
2035 __isl_keep isl_space *space);
2036 int isl_space_domain_is_wrapping(
2037 __isl_keep isl_space *space);
2038 int isl_space_range_is_wrapping(
2039 __isl_keep isl_space *space);
2041 #include <isl/set.h>
2042 int isl_basic_set_is_wrapping(
2043 __isl_keep isl_basic_set *bset);
2044 int isl_set_is_wrapping(__isl_keep isl_set *set);
2046 #include <isl/map.h>
2047 int isl_map_domain_is_wrapping(
2048 __isl_keep isl_map *map);
2049 int isl_map_range_is_wrapping(
2050 __isl_keep isl_map *map);
2052 The input to C<isl_space_is_wrapping> should
2053 be the space of a set, while that of
2054 C<isl_space_domain_is_wrapping> and
2055 C<isl_space_range_is_wrapping> should be the space of a relation.
2057 =item * Internal Product
2059 int isl_basic_map_can_zip(
2060 __isl_keep isl_basic_map *bmap);
2061 int isl_map_can_zip(__isl_keep isl_map *map);
2063 Check whether the product of domain and range of the given relation
2065 i.e., whether both domain and range are nested relations.
2069 int isl_basic_map_can_curry(
2070 __isl_keep isl_basic_map *bmap);
2071 int isl_map_can_curry(__isl_keep isl_map *map);
2073 Check whether the domain of the (basic) relation is a wrapped relation.
2075 int isl_basic_map_can_uncurry(
2076 __isl_keep isl_basic_map *bmap);
2077 int isl_map_can_uncurry(__isl_keep isl_map *map);
2079 Check whether the range of the (basic) relation is a wrapped relation.
2083 =head3 Binary Properties
2089 int isl_basic_set_plain_is_equal(
2090 __isl_keep isl_basic_set *bset1,
2091 __isl_keep isl_basic_set *bset2);
2092 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2093 __isl_keep isl_set *set2);
2094 int isl_set_is_equal(__isl_keep isl_set *set1,
2095 __isl_keep isl_set *set2);
2096 int isl_union_set_is_equal(
2097 __isl_keep isl_union_set *uset1,
2098 __isl_keep isl_union_set *uset2);
2099 int isl_basic_map_is_equal(
2100 __isl_keep isl_basic_map *bmap1,
2101 __isl_keep isl_basic_map *bmap2);
2102 int isl_map_is_equal(__isl_keep isl_map *map1,
2103 __isl_keep isl_map *map2);
2104 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2105 __isl_keep isl_map *map2);
2106 int isl_union_map_is_equal(
2107 __isl_keep isl_union_map *umap1,
2108 __isl_keep isl_union_map *umap2);
2110 =item * Disjointness
2112 int isl_basic_set_is_disjoint(
2113 __isl_keep isl_basic_set *bset1,
2114 __isl_keep isl_basic_set *bset2);
2115 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2116 __isl_keep isl_set *set2);
2117 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2118 __isl_keep isl_set *set2);
2119 int isl_basic_map_is_disjoint(
2120 __isl_keep isl_basic_map *bmap1,
2121 __isl_keep isl_basic_map *bmap2);
2122 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2123 __isl_keep isl_map *map2);
2127 int isl_basic_set_is_subset(
2128 __isl_keep isl_basic_set *bset1,
2129 __isl_keep isl_basic_set *bset2);
2130 int isl_set_is_subset(__isl_keep isl_set *set1,
2131 __isl_keep isl_set *set2);
2132 int isl_set_is_strict_subset(
2133 __isl_keep isl_set *set1,
2134 __isl_keep isl_set *set2);
2135 int isl_union_set_is_subset(
2136 __isl_keep isl_union_set *uset1,
2137 __isl_keep isl_union_set *uset2);
2138 int isl_union_set_is_strict_subset(
2139 __isl_keep isl_union_set *uset1,
2140 __isl_keep isl_union_set *uset2);
2141 int isl_basic_map_is_subset(
2142 __isl_keep isl_basic_map *bmap1,
2143 __isl_keep isl_basic_map *bmap2);
2144 int isl_basic_map_is_strict_subset(
2145 __isl_keep isl_basic_map *bmap1,
2146 __isl_keep isl_basic_map *bmap2);
2147 int isl_map_is_subset(
2148 __isl_keep isl_map *map1,
2149 __isl_keep isl_map *map2);
2150 int isl_map_is_strict_subset(
2151 __isl_keep isl_map *map1,
2152 __isl_keep isl_map *map2);
2153 int isl_union_map_is_subset(
2154 __isl_keep isl_union_map *umap1,
2155 __isl_keep isl_union_map *umap2);
2156 int isl_union_map_is_strict_subset(
2157 __isl_keep isl_union_map *umap1,
2158 __isl_keep isl_union_map *umap2);
2160 Check whether the first argument is a (strict) subset of the
2165 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2166 __isl_keep isl_set *set2);
2168 This function is useful for sorting C<isl_set>s.
2169 The order depends on the internal representation of the inputs.
2170 The order is fixed over different calls to the function (assuming
2171 the internal representation of the inputs has not changed), but may
2172 change over different versions of C<isl>.
2176 =head2 Unary Operations
2182 __isl_give isl_set *isl_set_complement(
2183 __isl_take isl_set *set);
2184 __isl_give isl_map *isl_map_complement(
2185 __isl_take isl_map *map);
2189 __isl_give isl_basic_map *isl_basic_map_reverse(
2190 __isl_take isl_basic_map *bmap);
2191 __isl_give isl_map *isl_map_reverse(
2192 __isl_take isl_map *map);
2193 __isl_give isl_union_map *isl_union_map_reverse(
2194 __isl_take isl_union_map *umap);
2198 #include <isl/local_space.h>
2199 __isl_give isl_local_space *isl_local_space_domain(
2200 __isl_take isl_local_space *ls);
2201 __isl_give isl_local_space *isl_local_space_range(
2202 __isl_take isl_local_space *ls);
2204 #include <isl/set.h>
2205 __isl_give isl_basic_set *isl_basic_set_project_out(
2206 __isl_take isl_basic_set *bset,
2207 enum isl_dim_type type, unsigned first, unsigned n);
2208 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2209 enum isl_dim_type type, unsigned first, unsigned n);
2210 __isl_give isl_basic_set *isl_basic_set_params(
2211 __isl_take isl_basic_set *bset);
2212 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2214 #include <isl/map.h>
2215 __isl_give isl_basic_map *isl_basic_map_project_out(
2216 __isl_take isl_basic_map *bmap,
2217 enum isl_dim_type type, unsigned first, unsigned n);
2218 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2219 enum isl_dim_type type, unsigned first, unsigned n);
2220 __isl_give isl_basic_set *isl_basic_map_domain(
2221 __isl_take isl_basic_map *bmap);
2222 __isl_give isl_basic_set *isl_basic_map_range(
2223 __isl_take isl_basic_map *bmap);
2224 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2225 __isl_give isl_set *isl_map_domain(
2226 __isl_take isl_map *bmap);
2227 __isl_give isl_set *isl_map_range(
2228 __isl_take isl_map *map);
2230 #include <isl/union_set.h>
2231 __isl_give isl_set *isl_union_set_params(
2232 __isl_take isl_union_set *uset);
2234 #include <isl/union_map.h>
2235 __isl_give isl_union_map *isl_union_map_project_out(
2236 __isl_take isl_union_map *umap,
2237 enum isl_dim_type type, unsigned first, unsigned n);
2238 __isl_give isl_set *isl_union_map_params(
2239 __isl_take isl_union_map *umap);
2240 __isl_give isl_union_set *isl_union_map_domain(
2241 __isl_take isl_union_map *umap);
2242 __isl_give isl_union_set *isl_union_map_range(
2243 __isl_take isl_union_map *umap);
2245 The function C<isl_union_map_project_out> can only project out
2248 #include <isl/map.h>
2249 __isl_give isl_basic_map *isl_basic_map_domain_map(
2250 __isl_take isl_basic_map *bmap);
2251 __isl_give isl_basic_map *isl_basic_map_range_map(
2252 __isl_take isl_basic_map *bmap);
2253 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2254 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2256 #include <isl/union_map.h>
2257 __isl_give isl_union_map *isl_union_map_domain_map(
2258 __isl_take isl_union_map *umap);
2259 __isl_give isl_union_map *isl_union_map_range_map(
2260 __isl_take isl_union_map *umap);
2262 The functions above construct a (basic, regular or union) relation
2263 that maps (a wrapped version of) the input relation to its domain or range.
2267 __isl_give isl_basic_set *isl_basic_set_eliminate(
2268 __isl_take isl_basic_set *bset,
2269 enum isl_dim_type type,
2270 unsigned first, unsigned n);
2271 __isl_give isl_set *isl_set_eliminate(
2272 __isl_take isl_set *set, enum isl_dim_type type,
2273 unsigned first, unsigned n);
2274 __isl_give isl_basic_map *isl_basic_map_eliminate(
2275 __isl_take isl_basic_map *bmap,
2276 enum isl_dim_type type,
2277 unsigned first, unsigned n);
2278 __isl_give isl_map *isl_map_eliminate(
2279 __isl_take isl_map *map, enum isl_dim_type type,
2280 unsigned first, unsigned n);
2282 Eliminate the coefficients for the given dimensions from the constraints,
2283 without removing the dimensions.
2285 =item * Constructing a relation from a set
2287 #include <isl/local_space.h>
2288 __isl_give isl_local_space *isl_local_space_from_domain(
2289 __isl_take isl_local_space *ls);
2291 #include <isl/map.h>
2292 __isl_give isl_map *isl_map_from_domain(
2293 __isl_take isl_set *set);
2294 __isl_give isl_map *isl_map_from_range(
2295 __isl_take isl_set *set);
2297 Create a relation with the given set as domain or range.
2298 The range or domain of the created relation is a zero-dimensional
2299 flat anonymous space.
2303 __isl_give isl_basic_set *isl_basic_set_fix_si(
2304 __isl_take isl_basic_set *bset,
2305 enum isl_dim_type type, unsigned pos, int value);
2306 __isl_give isl_basic_set *isl_basic_set_fix_val(
2307 __isl_take isl_basic_set *bset,
2308 enum isl_dim_type type, unsigned pos,
2309 __isl_take isl_val *v);
2310 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2311 enum isl_dim_type type, unsigned pos, int value);
2312 __isl_give isl_set *isl_set_fix_val(
2313 __isl_take isl_set *set,
2314 enum isl_dim_type type, unsigned pos,
2315 __isl_take isl_val *v);
2316 __isl_give isl_basic_map *isl_basic_map_fix_si(
2317 __isl_take isl_basic_map *bmap,
2318 enum isl_dim_type type, unsigned pos, int value);
2319 __isl_give isl_basic_map *isl_basic_map_fix_val(
2320 __isl_take isl_basic_map *bmap,
2321 enum isl_dim_type type, unsigned pos,
2322 __isl_take isl_val *v);
2323 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2324 enum isl_dim_type type, unsigned pos, int value);
2325 __isl_give isl_map *isl_map_fix_val(
2326 __isl_take isl_map *map,
2327 enum isl_dim_type type, unsigned pos,
2328 __isl_take isl_val *v);
2330 Intersect the set or relation with the hyperplane where the given
2331 dimension has the fixed given value.
2333 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2334 __isl_take isl_basic_map *bmap,
2335 enum isl_dim_type type, unsigned pos, int value);
2336 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2337 __isl_take isl_basic_map *bmap,
2338 enum isl_dim_type type, unsigned pos, int value);
2339 __isl_give isl_set *isl_set_lower_bound_si(
2340 __isl_take isl_set *set,
2341 enum isl_dim_type type, unsigned pos, int value);
2342 __isl_give isl_set *isl_set_lower_bound_val(
2343 __isl_take isl_set *set,
2344 enum isl_dim_type type, unsigned pos,
2345 __isl_take isl_val *value);
2346 __isl_give isl_map *isl_map_lower_bound_si(
2347 __isl_take isl_map *map,
2348 enum isl_dim_type type, unsigned pos, int value);
2349 __isl_give isl_set *isl_set_upper_bound_si(
2350 __isl_take isl_set *set,
2351 enum isl_dim_type type, unsigned pos, int value);
2352 __isl_give isl_set *isl_set_upper_bound_val(
2353 __isl_take isl_set *set,
2354 enum isl_dim_type type, unsigned pos,
2355 __isl_take isl_val *value);
2356 __isl_give isl_map *isl_map_upper_bound_si(
2357 __isl_take isl_map *map,
2358 enum isl_dim_type type, unsigned pos, int value);
2360 Intersect the set or relation with the half-space where the given
2361 dimension has a value bounded by the fixed given integer value.
2363 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2364 enum isl_dim_type type1, int pos1,
2365 enum isl_dim_type type2, int pos2);
2366 __isl_give isl_basic_map *isl_basic_map_equate(
2367 __isl_take isl_basic_map *bmap,
2368 enum isl_dim_type type1, int pos1,
2369 enum isl_dim_type type2, int pos2);
2370 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2371 enum isl_dim_type type1, int pos1,
2372 enum isl_dim_type type2, int pos2);
2374 Intersect the set or relation with the hyperplane where the given
2375 dimensions are equal to each other.
2377 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2378 enum isl_dim_type type1, int pos1,
2379 enum isl_dim_type type2, int pos2);
2381 Intersect the relation with the hyperplane where the given
2382 dimensions have opposite values.
2384 __isl_give isl_map *isl_map_order_le(
2385 __isl_take isl_map *map,
2386 enum isl_dim_type type1, int pos1,
2387 enum isl_dim_type type2, int pos2);
2388 __isl_give isl_basic_map *isl_basic_map_order_ge(
2389 __isl_take isl_basic_map *bmap,
2390 enum isl_dim_type type1, int pos1,
2391 enum isl_dim_type type2, int pos2);
2392 __isl_give isl_map *isl_map_order_ge(
2393 __isl_take isl_map *map,
2394 enum isl_dim_type type1, int pos1,
2395 enum isl_dim_type type2, int pos2);
2396 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2397 enum isl_dim_type type1, int pos1,
2398 enum isl_dim_type type2, int pos2);
2399 __isl_give isl_basic_map *isl_basic_map_order_gt(
2400 __isl_take isl_basic_map *bmap,
2401 enum isl_dim_type type1, int pos1,
2402 enum isl_dim_type type2, int pos2);
2403 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2404 enum isl_dim_type type1, int pos1,
2405 enum isl_dim_type type2, int pos2);
2407 Intersect the relation with the half-space where the given
2408 dimensions satisfy the given ordering.
2412 __isl_give isl_map *isl_set_identity(
2413 __isl_take isl_set *set);
2414 __isl_give isl_union_map *isl_union_set_identity(
2415 __isl_take isl_union_set *uset);
2417 Construct an identity relation on the given (union) set.
2421 __isl_give isl_basic_set *isl_basic_map_deltas(
2422 __isl_take isl_basic_map *bmap);
2423 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2424 __isl_give isl_union_set *isl_union_map_deltas(
2425 __isl_take isl_union_map *umap);
2427 These functions return a (basic) set containing the differences
2428 between image elements and corresponding domain elements in the input.
2430 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2431 __isl_take isl_basic_map *bmap);
2432 __isl_give isl_map *isl_map_deltas_map(
2433 __isl_take isl_map *map);
2434 __isl_give isl_union_map *isl_union_map_deltas_map(
2435 __isl_take isl_union_map *umap);
2437 The functions above construct a (basic, regular or union) relation
2438 that maps (a wrapped version of) the input relation to its delta set.
2442 Simplify the representation of a set or relation by trying
2443 to combine pairs of basic sets or relations into a single
2444 basic set or relation.
2446 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2447 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2448 __isl_give isl_union_set *isl_union_set_coalesce(
2449 __isl_take isl_union_set *uset);
2450 __isl_give isl_union_map *isl_union_map_coalesce(
2451 __isl_take isl_union_map *umap);
2453 One of the methods for combining pairs of basic sets or relations
2454 can result in coefficients that are much larger than those that appear
2455 in the constraints of the input. By default, the coefficients are
2456 not allowed to grow larger, but this can be changed by unsetting
2457 the following option.
2459 int isl_options_set_coalesce_bounded_wrapping(
2460 isl_ctx *ctx, int val);
2461 int isl_options_get_coalesce_bounded_wrapping(
2464 =item * Detecting equalities
2466 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2467 __isl_take isl_basic_set *bset);
2468 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2469 __isl_take isl_basic_map *bmap);
2470 __isl_give isl_set *isl_set_detect_equalities(
2471 __isl_take isl_set *set);
2472 __isl_give isl_map *isl_map_detect_equalities(
2473 __isl_take isl_map *map);
2474 __isl_give isl_union_set *isl_union_set_detect_equalities(
2475 __isl_take isl_union_set *uset);
2476 __isl_give isl_union_map *isl_union_map_detect_equalities(
2477 __isl_take isl_union_map *umap);
2479 Simplify the representation of a set or relation by detecting implicit
2482 =item * Removing redundant constraints
2484 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2485 __isl_take isl_basic_set *bset);
2486 __isl_give isl_set *isl_set_remove_redundancies(
2487 __isl_take isl_set *set);
2488 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2489 __isl_take isl_basic_map *bmap);
2490 __isl_give isl_map *isl_map_remove_redundancies(
2491 __isl_take isl_map *map);
2495 __isl_give isl_basic_set *isl_set_convex_hull(
2496 __isl_take isl_set *set);
2497 __isl_give isl_basic_map *isl_map_convex_hull(
2498 __isl_take isl_map *map);
2500 If the input set or relation has any existentially quantified
2501 variables, then the result of these operations is currently undefined.
2505 __isl_give isl_basic_set *
2506 isl_set_unshifted_simple_hull(
2507 __isl_take isl_set *set);
2508 __isl_give isl_basic_map *
2509 isl_map_unshifted_simple_hull(
2510 __isl_take isl_map *map);
2511 __isl_give isl_basic_set *isl_set_simple_hull(
2512 __isl_take isl_set *set);
2513 __isl_give isl_basic_map *isl_map_simple_hull(
2514 __isl_take isl_map *map);
2515 __isl_give isl_union_map *isl_union_map_simple_hull(
2516 __isl_take isl_union_map *umap);
2518 These functions compute a single basic set or relation
2519 that contains the whole input set or relation.
2520 In particular, the output is described by translates
2521 of the constraints describing the basic sets or relations in the input.
2522 In case of C<isl_set_unshifted_simple_hull>, only the original
2523 constraints are used, without any translation.
2527 (See \autoref{s:simple hull}.)
2533 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2534 __isl_take isl_basic_set *bset);
2535 __isl_give isl_basic_set *isl_set_affine_hull(
2536 __isl_take isl_set *set);
2537 __isl_give isl_union_set *isl_union_set_affine_hull(
2538 __isl_take isl_union_set *uset);
2539 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2540 __isl_take isl_basic_map *bmap);
2541 __isl_give isl_basic_map *isl_map_affine_hull(
2542 __isl_take isl_map *map);
2543 __isl_give isl_union_map *isl_union_map_affine_hull(
2544 __isl_take isl_union_map *umap);
2546 In case of union sets and relations, the affine hull is computed
2549 =item * Polyhedral hull
2551 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2552 __isl_take isl_set *set);
2553 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2554 __isl_take isl_map *map);
2555 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2556 __isl_take isl_union_set *uset);
2557 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2558 __isl_take isl_union_map *umap);
2560 These functions compute a single basic set or relation
2561 not involving any existentially quantified variables
2562 that contains the whole input set or relation.
2563 In case of union sets and relations, the polyhedral hull is computed
2566 =item * Other approximations
2568 __isl_give isl_basic_set *
2569 isl_basic_set_drop_constraints_involving_dims(
2570 __isl_take isl_basic_set *bset,
2571 enum isl_dim_type type,
2572 unsigned first, unsigned n);
2573 __isl_give isl_basic_map *
2574 isl_basic_map_drop_constraints_involving_dims(
2575 __isl_take isl_basic_map *bmap,
2576 enum isl_dim_type type,
2577 unsigned first, unsigned n);
2578 __isl_give isl_basic_set *
2579 isl_basic_set_drop_constraints_not_involving_dims(
2580 __isl_take isl_basic_set *bset,
2581 enum isl_dim_type type,
2582 unsigned first, unsigned n);
2583 __isl_give isl_set *
2584 isl_set_drop_constraints_involving_dims(
2585 __isl_take isl_set *set,
2586 enum isl_dim_type type,
2587 unsigned first, unsigned n);
2588 __isl_give isl_map *
2589 isl_map_drop_constraints_involving_dims(
2590 __isl_take isl_map *map,
2591 enum isl_dim_type type,
2592 unsigned first, unsigned n);
2594 These functions drop any constraints (not) involving the specified dimensions.
2595 Note that the result depends on the representation of the input.
2599 __isl_give isl_basic_set *isl_basic_set_sample(
2600 __isl_take isl_basic_set *bset);
2601 __isl_give isl_basic_set *isl_set_sample(
2602 __isl_take isl_set *set);
2603 __isl_give isl_basic_map *isl_basic_map_sample(
2604 __isl_take isl_basic_map *bmap);
2605 __isl_give isl_basic_map *isl_map_sample(
2606 __isl_take isl_map *map);
2608 If the input (basic) set or relation is non-empty, then return
2609 a singleton subset of the input. Otherwise, return an empty set.
2611 =item * Optimization
2613 #include <isl/ilp.h>
2614 __isl_give isl_val *isl_basic_set_max_val(
2615 __isl_keep isl_basic_set *bset,
2616 __isl_keep isl_aff *obj);
2617 __isl_give isl_val *isl_set_min_val(
2618 __isl_keep isl_set *set,
2619 __isl_keep isl_aff *obj);
2620 __isl_give isl_val *isl_set_max_val(
2621 __isl_keep isl_set *set,
2622 __isl_keep isl_aff *obj);
2624 Compute the minimum or maximum of the integer affine expression C<obj>
2625 over the points in C<set>, returning the result in C<opt>.
2626 The result is C<NULL> in case of an error, the optimal value in case
2627 there is one, negative infinity or infinity if the problem is unbounded and
2628 NaN if the problem is empty.
2630 =item * Parametric optimization
2632 __isl_give isl_pw_aff *isl_set_dim_min(
2633 __isl_take isl_set *set, int pos);
2634 __isl_give isl_pw_aff *isl_set_dim_max(
2635 __isl_take isl_set *set, int pos);
2636 __isl_give isl_pw_aff *isl_map_dim_max(
2637 __isl_take isl_map *map, int pos);
2639 Compute the minimum or maximum of the given set or output dimension
2640 as a function of the parameters (and input dimensions), but independently
2641 of the other set or output dimensions.
2642 For lexicographic optimization, see L<"Lexicographic Optimization">.
2646 The following functions compute either the set of (rational) coefficient
2647 values of valid constraints for the given set or the set of (rational)
2648 values satisfying the constraints with coefficients from the given set.
2649 Internally, these two sets of functions perform essentially the
2650 same operations, except that the set of coefficients is assumed to
2651 be a cone, while the set of values may be any polyhedron.
2652 The current implementation is based on the Farkas lemma and
2653 Fourier-Motzkin elimination, but this may change or be made optional
2654 in future. In particular, future implementations may use different
2655 dualization algorithms or skip the elimination step.
2657 __isl_give isl_basic_set *isl_basic_set_coefficients(
2658 __isl_take isl_basic_set *bset);
2659 __isl_give isl_basic_set *isl_set_coefficients(
2660 __isl_take isl_set *set);
2661 __isl_give isl_union_set *isl_union_set_coefficients(
2662 __isl_take isl_union_set *bset);
2663 __isl_give isl_basic_set *isl_basic_set_solutions(
2664 __isl_take isl_basic_set *bset);
2665 __isl_give isl_basic_set *isl_set_solutions(
2666 __isl_take isl_set *set);
2667 __isl_give isl_union_set *isl_union_set_solutions(
2668 __isl_take isl_union_set *bset);
2672 __isl_give isl_map *isl_map_fixed_power_val(
2673 __isl_take isl_map *map,
2674 __isl_take isl_val *exp);
2675 __isl_give isl_union_map *
2676 isl_union_map_fixed_power_val(
2677 __isl_take isl_union_map *umap,
2678 __isl_take isl_val *exp);
2680 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2681 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2682 of C<map> is computed.
2684 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2686 __isl_give isl_union_map *isl_union_map_power(
2687 __isl_take isl_union_map *umap, int *exact);
2689 Compute a parametric representation for all positive powers I<k> of C<map>.
2690 The result maps I<k> to a nested relation corresponding to the
2691 I<k>th power of C<map>.
2692 The result may be an overapproximation. If the result is known to be exact,
2693 then C<*exact> is set to C<1>.
2695 =item * Transitive closure
2697 __isl_give isl_map *isl_map_transitive_closure(
2698 __isl_take isl_map *map, int *exact);
2699 __isl_give isl_union_map *isl_union_map_transitive_closure(
2700 __isl_take isl_union_map *umap, int *exact);
2702 Compute the transitive closure of C<map>.
2703 The result may be an overapproximation. If the result is known to be exact,
2704 then C<*exact> is set to C<1>.
2706 =item * Reaching path lengths
2708 __isl_give isl_map *isl_map_reaching_path_lengths(
2709 __isl_take isl_map *map, int *exact);
2711 Compute a relation that maps each element in the range of C<map>
2712 to the lengths of all paths composed of edges in C<map> that
2713 end up in the given element.
2714 The result may be an overapproximation. If the result is known to be exact,
2715 then C<*exact> is set to C<1>.
2716 To compute the I<maximal> path length, the resulting relation
2717 should be postprocessed by C<isl_map_lexmax>.
2718 In particular, if the input relation is a dependence relation
2719 (mapping sources to sinks), then the maximal path length corresponds
2720 to the free schedule.
2721 Note, however, that C<isl_map_lexmax> expects the maximum to be
2722 finite, so if the path lengths are unbounded (possibly due to
2723 the overapproximation), then you will get an error message.
2727 #include <isl/space.h>
2728 __isl_give isl_space *isl_space_wrap(
2729 __isl_take isl_space *space);
2730 __isl_give isl_space *isl_space_unwrap(
2731 __isl_take isl_space *space);
2733 #include <isl/set.h>
2734 __isl_give isl_basic_map *isl_basic_set_unwrap(
2735 __isl_take isl_basic_set *bset);
2736 __isl_give isl_map *isl_set_unwrap(
2737 __isl_take isl_set *set);
2739 #include <isl/map.h>
2740 __isl_give isl_basic_set *isl_basic_map_wrap(
2741 __isl_take isl_basic_map *bmap);
2742 __isl_give isl_set *isl_map_wrap(
2743 __isl_take isl_map *map);
2745 #include <isl/union_set.h>
2746 __isl_give isl_union_map *isl_union_set_unwrap(
2747 __isl_take isl_union_set *uset);
2749 #include <isl/union_map.h>
2750 __isl_give isl_union_set *isl_union_map_wrap(
2751 __isl_take isl_union_map *umap);
2753 The input to C<isl_space_unwrap> should
2754 be the space of a set, while that of
2755 C<isl_space_wrap> should be the space of a relation.
2756 Conversely, the output of C<isl_space_unwrap> is the space
2757 of a relation, while that of C<isl_space_wrap> is the space of a set.
2761 Remove any internal structure of domain (and range) of the given
2762 set or relation. If there is any such internal structure in the input,
2763 then the name of the space is also removed.
2765 #include <isl/local_space.h>
2766 __isl_give isl_local_space *
2767 isl_local_space_flatten_domain(
2768 __isl_take isl_local_space *ls);
2769 __isl_give isl_local_space *
2770 isl_local_space_flatten_range(
2771 __isl_take isl_local_space *ls);
2773 #include <isl/set.h>
2774 __isl_give isl_basic_set *isl_basic_set_flatten(
2775 __isl_take isl_basic_set *bset);
2776 __isl_give isl_set *isl_set_flatten(
2777 __isl_take isl_set *set);
2779 #include <isl/map.h>
2780 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2781 __isl_take isl_basic_map *bmap);
2782 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2783 __isl_take isl_basic_map *bmap);
2784 __isl_give isl_map *isl_map_flatten_range(
2785 __isl_take isl_map *map);
2786 __isl_give isl_map *isl_map_flatten_domain(
2787 __isl_take isl_map *map);
2788 __isl_give isl_basic_map *isl_basic_map_flatten(
2789 __isl_take isl_basic_map *bmap);
2790 __isl_give isl_map *isl_map_flatten(
2791 __isl_take isl_map *map);
2793 #include <isl/map.h>
2794 __isl_give isl_map *isl_set_flatten_map(
2795 __isl_take isl_set *set);
2797 The function above constructs a relation
2798 that maps the input set to a flattened version of the set.
2802 Lift the input set to a space with extra dimensions corresponding
2803 to the existentially quantified variables in the input.
2804 In particular, the result lives in a wrapped map where the domain
2805 is the original space and the range corresponds to the original
2806 existentially quantified variables.
2808 __isl_give isl_basic_set *isl_basic_set_lift(
2809 __isl_take isl_basic_set *bset);
2810 __isl_give isl_set *isl_set_lift(
2811 __isl_take isl_set *set);
2812 __isl_give isl_union_set *isl_union_set_lift(
2813 __isl_take isl_union_set *uset);
2815 Given a local space that contains the existentially quantified
2816 variables of a set, a basic relation that, when applied to
2817 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2818 can be constructed using the following function.
2820 #include <isl/local_space.h>
2821 __isl_give isl_basic_map *isl_local_space_lifting(
2822 __isl_take isl_local_space *ls);
2824 =item * Internal Product
2826 __isl_give isl_basic_map *isl_basic_map_zip(
2827 __isl_take isl_basic_map *bmap);
2828 __isl_give isl_map *isl_map_zip(
2829 __isl_take isl_map *map);
2830 __isl_give isl_union_map *isl_union_map_zip(
2831 __isl_take isl_union_map *umap);
2833 Given a relation with nested relations for domain and range,
2834 interchange the range of the domain with the domain of the range.
2838 __isl_give isl_basic_map *isl_basic_map_curry(
2839 __isl_take isl_basic_map *bmap);
2840 __isl_give isl_basic_map *isl_basic_map_uncurry(
2841 __isl_take isl_basic_map *bmap);
2842 __isl_give isl_map *isl_map_curry(
2843 __isl_take isl_map *map);
2844 __isl_give isl_map *isl_map_uncurry(
2845 __isl_take isl_map *map);
2846 __isl_give isl_union_map *isl_union_map_curry(
2847 __isl_take isl_union_map *umap);
2848 __isl_give isl_union_map *isl_union_map_uncurry(
2849 __isl_take isl_union_map *umap);
2851 Given a relation with a nested relation for domain,
2852 the C<curry> functions
2853 move the range of the nested relation out of the domain
2854 and use it as the domain of a nested relation in the range,
2855 with the original range as range of this nested relation.
2856 The C<uncurry> functions perform the inverse operation.
2858 =item * Aligning parameters
2860 __isl_give isl_basic_set *isl_basic_set_align_params(
2861 __isl_take isl_basic_set *bset,
2862 __isl_take isl_space *model);
2863 __isl_give isl_set *isl_set_align_params(
2864 __isl_take isl_set *set,
2865 __isl_take isl_space *model);
2866 __isl_give isl_basic_map *isl_basic_map_align_params(
2867 __isl_take isl_basic_map *bmap,
2868 __isl_take isl_space *model);
2869 __isl_give isl_map *isl_map_align_params(
2870 __isl_take isl_map *map,
2871 __isl_take isl_space *model);
2873 Change the order of the parameters of the given set or relation
2874 such that the first parameters match those of C<model>.
2875 This may involve the introduction of extra parameters.
2876 All parameters need to be named.
2878 =item * Dimension manipulation
2880 #include <isl/local_space.h>
2881 __isl_give isl_local_space *isl_local_space_add_dims(
2882 __isl_take isl_local_space *ls,
2883 enum isl_dim_type type, unsigned n);
2884 __isl_give isl_local_space *isl_local_space_insert_dims(
2885 __isl_take isl_local_space *ls,
2886 enum isl_dim_type type, unsigned first, unsigned n);
2887 __isl_give isl_local_space *isl_local_space_drop_dims(
2888 __isl_take isl_local_space *ls,
2889 enum isl_dim_type type, unsigned first, unsigned n);
2891 #include <isl/set.h>
2892 __isl_give isl_basic_set *isl_basic_set_add_dims(
2893 __isl_take isl_basic_set *bset,
2894 enum isl_dim_type type, unsigned n);
2895 __isl_give isl_set *isl_set_add_dims(
2896 __isl_take isl_set *set,
2897 enum isl_dim_type type, unsigned n);
2898 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2899 __isl_take isl_basic_set *bset,
2900 enum isl_dim_type type, unsigned pos,
2902 __isl_give isl_set *isl_set_insert_dims(
2903 __isl_take isl_set *set,
2904 enum isl_dim_type type, unsigned pos, unsigned n);
2905 __isl_give isl_basic_set *isl_basic_set_move_dims(
2906 __isl_take isl_basic_set *bset,
2907 enum isl_dim_type dst_type, unsigned dst_pos,
2908 enum isl_dim_type src_type, unsigned src_pos,
2910 __isl_give isl_set *isl_set_move_dims(
2911 __isl_take isl_set *set,
2912 enum isl_dim_type dst_type, unsigned dst_pos,
2913 enum isl_dim_type src_type, unsigned src_pos,
2916 #include <isl/map.h>
2917 __isl_give isl_map *isl_map_add_dims(
2918 __isl_take isl_map *map,
2919 enum isl_dim_type type, unsigned n);
2920 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2921 __isl_take isl_basic_map *bmap,
2922 enum isl_dim_type type, unsigned pos,
2924 __isl_give isl_map *isl_map_insert_dims(
2925 __isl_take isl_map *map,
2926 enum isl_dim_type type, unsigned pos, unsigned n);
2927 __isl_give isl_basic_map *isl_basic_map_move_dims(
2928 __isl_take isl_basic_map *bmap,
2929 enum isl_dim_type dst_type, unsigned dst_pos,
2930 enum isl_dim_type src_type, unsigned src_pos,
2932 __isl_give isl_map *isl_map_move_dims(
2933 __isl_take isl_map *map,
2934 enum isl_dim_type dst_type, unsigned dst_pos,
2935 enum isl_dim_type src_type, unsigned src_pos,
2938 It is usually not advisable to directly change the (input or output)
2939 space of a set or a relation as this removes the name and the internal
2940 structure of the space. However, the above functions can be useful
2941 to add new parameters, assuming
2942 C<isl_set_align_params> and C<isl_map_align_params>
2947 =head2 Binary Operations
2949 The two arguments of a binary operation not only need to live
2950 in the same C<isl_ctx>, they currently also need to have
2951 the same (number of) parameters.
2953 =head3 Basic Operations
2957 =item * Intersection
2959 #include <isl/local_space.h>
2960 __isl_give isl_local_space *isl_local_space_intersect(
2961 __isl_take isl_local_space *ls1,
2962 __isl_take isl_local_space *ls2);
2964 #include <isl/set.h>
2965 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2966 __isl_take isl_basic_set *bset1,
2967 __isl_take isl_basic_set *bset2);
2968 __isl_give isl_basic_set *isl_basic_set_intersect(
2969 __isl_take isl_basic_set *bset1,
2970 __isl_take isl_basic_set *bset2);
2971 __isl_give isl_set *isl_set_intersect_params(
2972 __isl_take isl_set *set,
2973 __isl_take isl_set *params);
2974 __isl_give isl_set *isl_set_intersect(
2975 __isl_take isl_set *set1,
2976 __isl_take isl_set *set2);
2978 #include <isl/map.h>
2979 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2980 __isl_take isl_basic_map *bmap,
2981 __isl_take isl_basic_set *bset);
2982 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2983 __isl_take isl_basic_map *bmap,
2984 __isl_take isl_basic_set *bset);
2985 __isl_give isl_basic_map *isl_basic_map_intersect(
2986 __isl_take isl_basic_map *bmap1,
2987 __isl_take isl_basic_map *bmap2);
2988 __isl_give isl_map *isl_map_intersect_params(
2989 __isl_take isl_map *map,
2990 __isl_take isl_set *params);
2991 __isl_give isl_map *isl_map_intersect_domain(
2992 __isl_take isl_map *map,
2993 __isl_take isl_set *set);
2994 __isl_give isl_map *isl_map_intersect_range(
2995 __isl_take isl_map *map,
2996 __isl_take isl_set *set);
2997 __isl_give isl_map *isl_map_intersect(
2998 __isl_take isl_map *map1,
2999 __isl_take isl_map *map2);
3001 #include <isl/union_set.h>
3002 __isl_give isl_union_set *isl_union_set_intersect_params(
3003 __isl_take isl_union_set *uset,
3004 __isl_take isl_set *set);
3005 __isl_give isl_union_set *isl_union_set_intersect(
3006 __isl_take isl_union_set *uset1,
3007 __isl_take isl_union_set *uset2);
3009 #include <isl/union_map.h>
3010 __isl_give isl_union_map *isl_union_map_intersect_params(
3011 __isl_take isl_union_map *umap,
3012 __isl_take isl_set *set);
3013 __isl_give isl_union_map *isl_union_map_intersect_domain(
3014 __isl_take isl_union_map *umap,
3015 __isl_take isl_union_set *uset);
3016 __isl_give isl_union_map *isl_union_map_intersect_range(
3017 __isl_take isl_union_map *umap,
3018 __isl_take isl_union_set *uset);
3019 __isl_give isl_union_map *isl_union_map_intersect(
3020 __isl_take isl_union_map *umap1,
3021 __isl_take isl_union_map *umap2);
3023 The second argument to the C<_params> functions needs to be
3024 a parametric (basic) set. For the other functions, a parametric set
3025 for either argument is only allowed if the other argument is
3026 a parametric set as well.
3030 __isl_give isl_set *isl_basic_set_union(
3031 __isl_take isl_basic_set *bset1,
3032 __isl_take isl_basic_set *bset2);
3033 __isl_give isl_map *isl_basic_map_union(
3034 __isl_take isl_basic_map *bmap1,
3035 __isl_take isl_basic_map *bmap2);
3036 __isl_give isl_set *isl_set_union(
3037 __isl_take isl_set *set1,
3038 __isl_take isl_set *set2);
3039 __isl_give isl_map *isl_map_union(
3040 __isl_take isl_map *map1,
3041 __isl_take isl_map *map2);
3042 __isl_give isl_union_set *isl_union_set_union(
3043 __isl_take isl_union_set *uset1,
3044 __isl_take isl_union_set *uset2);
3045 __isl_give isl_union_map *isl_union_map_union(
3046 __isl_take isl_union_map *umap1,
3047 __isl_take isl_union_map *umap2);
3049 =item * Set difference
3051 __isl_give isl_set *isl_set_subtract(
3052 __isl_take isl_set *set1,
3053 __isl_take isl_set *set2);
3054 __isl_give isl_map *isl_map_subtract(
3055 __isl_take isl_map *map1,
3056 __isl_take isl_map *map2);
3057 __isl_give isl_map *isl_map_subtract_domain(
3058 __isl_take isl_map *map,
3059 __isl_take isl_set *dom);
3060 __isl_give isl_map *isl_map_subtract_range(
3061 __isl_take isl_map *map,
3062 __isl_take isl_set *dom);
3063 __isl_give isl_union_set *isl_union_set_subtract(
3064 __isl_take isl_union_set *uset1,
3065 __isl_take isl_union_set *uset2);
3066 __isl_give isl_union_map *isl_union_map_subtract(
3067 __isl_take isl_union_map *umap1,
3068 __isl_take isl_union_map *umap2);
3069 __isl_give isl_union_map *isl_union_map_subtract_domain(
3070 __isl_take isl_union_map *umap,
3071 __isl_take isl_union_set *dom);
3072 __isl_give isl_union_map *isl_union_map_subtract_range(
3073 __isl_take isl_union_map *umap,
3074 __isl_take isl_union_set *dom);
3078 __isl_give isl_basic_set *isl_basic_set_apply(
3079 __isl_take isl_basic_set *bset,
3080 __isl_take isl_basic_map *bmap);
3081 __isl_give isl_set *isl_set_apply(
3082 __isl_take isl_set *set,
3083 __isl_take isl_map *map);
3084 __isl_give isl_union_set *isl_union_set_apply(
3085 __isl_take isl_union_set *uset,
3086 __isl_take isl_union_map *umap);
3087 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3088 __isl_take isl_basic_map *bmap1,
3089 __isl_take isl_basic_map *bmap2);
3090 __isl_give isl_basic_map *isl_basic_map_apply_range(
3091 __isl_take isl_basic_map *bmap1,
3092 __isl_take isl_basic_map *bmap2);
3093 __isl_give isl_map *isl_map_apply_domain(
3094 __isl_take isl_map *map1,
3095 __isl_take isl_map *map2);
3096 __isl_give isl_union_map *isl_union_map_apply_domain(
3097 __isl_take isl_union_map *umap1,
3098 __isl_take isl_union_map *umap2);
3099 __isl_give isl_map *isl_map_apply_range(
3100 __isl_take isl_map *map1,
3101 __isl_take isl_map *map2);
3102 __isl_give isl_union_map *isl_union_map_apply_range(
3103 __isl_take isl_union_map *umap1,
3104 __isl_take isl_union_map *umap2);
3108 #include <isl/set.h>
3109 __isl_give isl_basic_set *
3110 isl_basic_set_preimage_multi_aff(
3111 __isl_take isl_basic_set *bset,
3112 __isl_take isl_multi_aff *ma);
3113 __isl_give isl_set *isl_set_preimage_multi_aff(
3114 __isl_take isl_set *set,
3115 __isl_take isl_multi_aff *ma);
3116 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3117 __isl_take isl_set *set,
3118 __isl_take isl_pw_multi_aff *pma);
3119 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
3120 __isl_take isl_set *set,
3121 __isl_take isl_multi_pw_aff *mpa);
3123 #include <isl/union_set.h>
3124 __isl_give isl_union_set *
3125 isl_union_set_preimage_multi_aff(
3126 __isl_take isl_union_set *uset,
3127 __isl_take isl_multi_aff *ma);
3128 __isl_give isl_union_set *
3129 isl_union_set_preimage_pw_multi_aff(
3130 __isl_take isl_union_set *uset,
3131 __isl_take isl_pw_multi_aff *pma);
3132 __isl_give isl_union_set *
3133 isl_union_set_preimage_union_pw_multi_aff(
3134 __isl_take isl_union_set *uset,
3135 __isl_take isl_union_pw_multi_aff *upma);
3137 #include <isl/map.h>
3138 __isl_give isl_basic_map *
3139 isl_basic_map_preimage_domain_multi_aff(
3140 __isl_take isl_basic_map *bmap,
3141 __isl_take isl_multi_aff *ma);
3142 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3143 __isl_take isl_map *map,
3144 __isl_take isl_multi_aff *ma);
3145 __isl_give isl_map *isl_map_preimage_range_multi_aff(
3146 __isl_take isl_map *map,
3147 __isl_take isl_multi_aff *ma);
3148 __isl_give isl_map *
3149 isl_map_preimage_domain_pw_multi_aff(
3150 __isl_take isl_map *map,
3151 __isl_take isl_pw_multi_aff *pma);
3152 __isl_give isl_map *
3153 isl_map_preimage_range_pw_multi_aff(
3154 __isl_take isl_map *map,
3155 __isl_take isl_pw_multi_aff *pma);
3156 __isl_give isl_map *
3157 isl_map_preimage_domain_multi_pw_aff(
3158 __isl_take isl_map *map,
3159 __isl_take isl_multi_pw_aff *mpa);
3160 __isl_give isl_basic_map *
3161 isl_basic_map_preimage_range_multi_aff(
3162 __isl_take isl_basic_map *bmap,
3163 __isl_take isl_multi_aff *ma);
3165 #include <isl/union_map.h>
3166 __isl_give isl_union_map *
3167 isl_union_map_preimage_domain_multi_aff(
3168 __isl_take isl_union_map *umap,
3169 __isl_take isl_multi_aff *ma);
3170 __isl_give isl_union_map *
3171 isl_union_map_preimage_range_multi_aff(
3172 __isl_take isl_union_map *umap,
3173 __isl_take isl_multi_aff *ma);
3174 __isl_give isl_union_map *
3175 isl_union_map_preimage_domain_pw_multi_aff(
3176 __isl_take isl_union_map *umap,
3177 __isl_take isl_pw_multi_aff *pma);
3178 __isl_give isl_union_map *
3179 isl_union_map_preimage_range_pw_multi_aff(
3180 __isl_take isl_union_map *umap,
3181 __isl_take isl_pw_multi_aff *pma);
3182 __isl_give isl_union_map *
3183 isl_union_map_preimage_domain_union_pw_multi_aff(
3184 __isl_take isl_union_map *umap,
3185 __isl_take isl_union_pw_multi_aff *upma);
3186 __isl_give isl_union_map *
3187 isl_union_map_preimage_range_union_pw_multi_aff(
3188 __isl_take isl_union_map *umap,
3189 __isl_take isl_union_pw_multi_aff *upma);
3191 These functions compute the preimage of the given set or map domain/range under
3192 the given function. In other words, the expression is plugged
3193 into the set description or into the domain/range of the map.
3194 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3195 L</"Piecewise Multiple Quasi Affine Expressions">.
3197 =item * Cartesian Product
3199 #include <isl/space.h>
3200 __isl_give isl_space *isl_space_product(
3201 __isl_take isl_space *space1,
3202 __isl_take isl_space *space2);
3203 __isl_give isl_space *isl_space_domain_product(
3204 __isl_take isl_space *space1,
3205 __isl_take isl_space *space2);
3206 __isl_give isl_space *isl_space_range_product(
3207 __isl_take isl_space *space1,
3208 __isl_take isl_space *space2);
3211 C<isl_space_product>, C<isl_space_domain_product>
3212 and C<isl_space_range_product> take pairs or relation spaces and
3213 produce a single relations space, where either the domain, the range
3214 or both domain and range are wrapped spaces of relations between
3215 the domains and/or ranges of the input spaces.
3216 If the product is only constructed over the domain or the range
3217 then the ranges or the domains of the inputs should be the same.
3218 The function C<isl_space_product> also accepts a pair of set spaces,
3219 in which case it returns a wrapped space of a relation between the
3222 #include <isl/set.h>
3223 __isl_give isl_set *isl_set_product(
3224 __isl_take isl_set *set1,
3225 __isl_take isl_set *set2);
3227 #include <isl/map.h>
3228 __isl_give isl_basic_map *isl_basic_map_domain_product(
3229 __isl_take isl_basic_map *bmap1,
3230 __isl_take isl_basic_map *bmap2);
3231 __isl_give isl_basic_map *isl_basic_map_range_product(
3232 __isl_take isl_basic_map *bmap1,
3233 __isl_take isl_basic_map *bmap2);
3234 __isl_give isl_basic_map *isl_basic_map_product(
3235 __isl_take isl_basic_map *bmap1,
3236 __isl_take isl_basic_map *bmap2);
3237 __isl_give isl_map *isl_map_domain_product(
3238 __isl_take isl_map *map1,
3239 __isl_take isl_map *map2);
3240 __isl_give isl_map *isl_map_range_product(
3241 __isl_take isl_map *map1,
3242 __isl_take isl_map *map2);
3243 __isl_give isl_map *isl_map_product(
3244 __isl_take isl_map *map1,
3245 __isl_take isl_map *map2);
3247 #include <isl/union_set.h>
3248 __isl_give isl_union_set *isl_union_set_product(
3249 __isl_take isl_union_set *uset1,
3250 __isl_take isl_union_set *uset2);
3252 #include <isl/union_map.h>
3253 __isl_give isl_union_map *isl_union_map_domain_product(
3254 __isl_take isl_union_map *umap1,
3255 __isl_take isl_union_map *umap2);
3256 __isl_give isl_union_map *isl_union_map_range_product(
3257 __isl_take isl_union_map *umap1,
3258 __isl_take isl_union_map *umap2);
3259 __isl_give isl_union_map *isl_union_map_product(
3260 __isl_take isl_union_map *umap1,
3261 __isl_take isl_union_map *umap2);
3263 The above functions compute the cross product of the given
3264 sets or relations. The domains and ranges of the results
3265 are wrapped maps between domains and ranges of the inputs.
3266 To obtain a ``flat'' product, use the following functions
3269 __isl_give isl_basic_set *isl_basic_set_flat_product(
3270 __isl_take isl_basic_set *bset1,
3271 __isl_take isl_basic_set *bset2);
3272 __isl_give isl_set *isl_set_flat_product(
3273 __isl_take isl_set *set1,
3274 __isl_take isl_set *set2);
3275 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3276 __isl_take isl_basic_map *bmap1,
3277 __isl_take isl_basic_map *bmap2);
3278 __isl_give isl_map *isl_map_flat_domain_product(
3279 __isl_take isl_map *map1,
3280 __isl_take isl_map *map2);
3281 __isl_give isl_map *isl_map_flat_range_product(
3282 __isl_take isl_map *map1,
3283 __isl_take isl_map *map2);
3284 __isl_give isl_union_map *isl_union_map_flat_range_product(
3285 __isl_take isl_union_map *umap1,
3286 __isl_take isl_union_map *umap2);
3287 __isl_give isl_basic_map *isl_basic_map_flat_product(
3288 __isl_take isl_basic_map *bmap1,
3289 __isl_take isl_basic_map *bmap2);
3290 __isl_give isl_map *isl_map_flat_product(
3291 __isl_take isl_map *map1,
3292 __isl_take isl_map *map2);
3294 #include <isl/space.h>
3295 __isl_give isl_space *isl_space_domain_factor_domain(
3296 __isl_take isl_space *space);
3297 __isl_give isl_space *isl_space_range_factor_domain(
3298 __isl_take isl_space *space);
3299 __isl_give isl_space *isl_space_range_factor_range(
3300 __isl_take isl_space *space);
3302 The functions C<isl_space_range_factor_domain> and
3303 C<isl_space_range_factor_range> extract the two arguments from
3304 the result of a call to C<isl_space_range_product>.
3306 The arguments of a call to C<isl_map_range_product> can be extracted
3307 from the result using the following two functions.
3309 #include <isl/map.h>
3310 __isl_give isl_map *isl_map_range_factor_domain(
3311 __isl_take isl_map *map);
3312 __isl_give isl_map *isl_map_range_factor_range(
3313 __isl_take isl_map *map);
3315 =item * Simplification
3317 __isl_give isl_basic_set *isl_basic_set_gist(
3318 __isl_take isl_basic_set *bset,
3319 __isl_take isl_basic_set *context);
3320 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3321 __isl_take isl_set *context);
3322 __isl_give isl_set *isl_set_gist_params(
3323 __isl_take isl_set *set,
3324 __isl_take isl_set *context);
3325 __isl_give isl_union_set *isl_union_set_gist(
3326 __isl_take isl_union_set *uset,
3327 __isl_take isl_union_set *context);
3328 __isl_give isl_union_set *isl_union_set_gist_params(
3329 __isl_take isl_union_set *uset,
3330 __isl_take isl_set *set);
3331 __isl_give isl_basic_map *isl_basic_map_gist(
3332 __isl_take isl_basic_map *bmap,
3333 __isl_take isl_basic_map *context);
3334 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3335 __isl_take isl_map *context);
3336 __isl_give isl_map *isl_map_gist_params(
3337 __isl_take isl_map *map,
3338 __isl_take isl_set *context);
3339 __isl_give isl_map *isl_map_gist_domain(
3340 __isl_take isl_map *map,
3341 __isl_take isl_set *context);
3342 __isl_give isl_map *isl_map_gist_range(
3343 __isl_take isl_map *map,
3344 __isl_take isl_set *context);
3345 __isl_give isl_union_map *isl_union_map_gist(
3346 __isl_take isl_union_map *umap,
3347 __isl_take isl_union_map *context);
3348 __isl_give isl_union_map *isl_union_map_gist_params(
3349 __isl_take isl_union_map *umap,
3350 __isl_take isl_set *set);
3351 __isl_give isl_union_map *isl_union_map_gist_domain(
3352 __isl_take isl_union_map *umap,
3353 __isl_take isl_union_set *uset);
3354 __isl_give isl_union_map *isl_union_map_gist_range(
3355 __isl_take isl_union_map *umap,
3356 __isl_take isl_union_set *uset);
3358 The gist operation returns a set or relation that has the
3359 same intersection with the context as the input set or relation.
3360 Any implicit equality in the intersection is made explicit in the result,
3361 while all inequalities that are redundant with respect to the intersection
3363 In case of union sets and relations, the gist operation is performed
3368 =head3 Lexicographic Optimization
3370 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3371 the following functions
3372 compute a set that contains the lexicographic minimum or maximum
3373 of the elements in C<set> (or C<bset>) for those values of the parameters
3374 that satisfy C<dom>.
3375 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3376 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3378 In other words, the union of the parameter values
3379 for which the result is non-empty and of C<*empty>
3382 __isl_give isl_set *isl_basic_set_partial_lexmin(
3383 __isl_take isl_basic_set *bset,
3384 __isl_take isl_basic_set *dom,
3385 __isl_give isl_set **empty);
3386 __isl_give isl_set *isl_basic_set_partial_lexmax(
3387 __isl_take isl_basic_set *bset,
3388 __isl_take isl_basic_set *dom,
3389 __isl_give isl_set **empty);
3390 __isl_give isl_set *isl_set_partial_lexmin(
3391 __isl_take isl_set *set, __isl_take isl_set *dom,
3392 __isl_give isl_set **empty);
3393 __isl_give isl_set *isl_set_partial_lexmax(
3394 __isl_take isl_set *set, __isl_take isl_set *dom,
3395 __isl_give isl_set **empty);
3397 Given a (basic) set C<set> (or C<bset>), the following functions simply
3398 return a set containing the lexicographic minimum or maximum
3399 of the elements in C<set> (or C<bset>).
3400 In case of union sets, the optimum is computed per space.
3402 __isl_give isl_set *isl_basic_set_lexmin(
3403 __isl_take isl_basic_set *bset);
3404 __isl_give isl_set *isl_basic_set_lexmax(
3405 __isl_take isl_basic_set *bset);
3406 __isl_give isl_set *isl_set_lexmin(
3407 __isl_take isl_set *set);
3408 __isl_give isl_set *isl_set_lexmax(
3409 __isl_take isl_set *set);
3410 __isl_give isl_union_set *isl_union_set_lexmin(
3411 __isl_take isl_union_set *uset);
3412 __isl_give isl_union_set *isl_union_set_lexmax(
3413 __isl_take isl_union_set *uset);
3415 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3416 the following functions
3417 compute a relation that maps each element of C<dom>
3418 to the single lexicographic minimum or maximum
3419 of the elements that are associated to that same
3420 element in C<map> (or C<bmap>).
3421 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3422 that contains the elements in C<dom> that do not map
3423 to any elements in C<map> (or C<bmap>).
3424 In other words, the union of the domain of the result and of C<*empty>
3427 __isl_give isl_map *isl_basic_map_partial_lexmax(
3428 __isl_take isl_basic_map *bmap,
3429 __isl_take isl_basic_set *dom,
3430 __isl_give isl_set **empty);
3431 __isl_give isl_map *isl_basic_map_partial_lexmin(
3432 __isl_take isl_basic_map *bmap,
3433 __isl_take isl_basic_set *dom,
3434 __isl_give isl_set **empty);
3435 __isl_give isl_map *isl_map_partial_lexmax(
3436 __isl_take isl_map *map, __isl_take isl_set *dom,
3437 __isl_give isl_set **empty);
3438 __isl_give isl_map *isl_map_partial_lexmin(
3439 __isl_take isl_map *map, __isl_take isl_set *dom,
3440 __isl_give isl_set **empty);
3442 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3443 return a map mapping each element in the domain of
3444 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3445 of all elements associated to that element.
3446 In case of union relations, the optimum is computed per space.
3448 __isl_give isl_map *isl_basic_map_lexmin(
3449 __isl_take isl_basic_map *bmap);
3450 __isl_give isl_map *isl_basic_map_lexmax(
3451 __isl_take isl_basic_map *bmap);
3452 __isl_give isl_map *isl_map_lexmin(
3453 __isl_take isl_map *map);
3454 __isl_give isl_map *isl_map_lexmax(
3455 __isl_take isl_map *map);
3456 __isl_give isl_union_map *isl_union_map_lexmin(
3457 __isl_take isl_union_map *umap);
3458 __isl_give isl_union_map *isl_union_map_lexmax(
3459 __isl_take isl_union_map *umap);
3461 The following functions return their result in the form of
3462 a piecewise multi-affine expression
3463 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3464 but are otherwise equivalent to the corresponding functions
3465 returning a basic set or relation.
3467 __isl_give isl_pw_multi_aff *
3468 isl_basic_map_lexmin_pw_multi_aff(
3469 __isl_take isl_basic_map *bmap);
3470 __isl_give isl_pw_multi_aff *
3471 isl_basic_set_partial_lexmin_pw_multi_aff(
3472 __isl_take isl_basic_set *bset,
3473 __isl_take isl_basic_set *dom,
3474 __isl_give isl_set **empty);
3475 __isl_give isl_pw_multi_aff *
3476 isl_basic_set_partial_lexmax_pw_multi_aff(
3477 __isl_take isl_basic_set *bset,
3478 __isl_take isl_basic_set *dom,
3479 __isl_give isl_set **empty);
3480 __isl_give isl_pw_multi_aff *
3481 isl_basic_map_partial_lexmin_pw_multi_aff(
3482 __isl_take isl_basic_map *bmap,
3483 __isl_take isl_basic_set *dom,
3484 __isl_give isl_set **empty);
3485 __isl_give isl_pw_multi_aff *
3486 isl_basic_map_partial_lexmax_pw_multi_aff(
3487 __isl_take isl_basic_map *bmap,
3488 __isl_take isl_basic_set *dom,
3489 __isl_give isl_set **empty);
3490 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3491 __isl_take isl_set *set);
3492 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3493 __isl_take isl_set *set);
3494 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3495 __isl_take isl_map *map);
3496 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3497 __isl_take isl_map *map);
3501 Lists are defined over several element types, including
3502 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3503 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3504 Here we take lists of C<isl_set>s as an example.
3505 Lists can be created, copied, modified and freed using the following functions.
3507 #include <isl/list.h>
3508 __isl_give isl_set_list *isl_set_list_from_set(
3509 __isl_take isl_set *el);
3510 __isl_give isl_set_list *isl_set_list_alloc(
3511 isl_ctx *ctx, int n);
3512 __isl_give isl_set_list *isl_set_list_copy(
3513 __isl_keep isl_set_list *list);
3514 __isl_give isl_set_list *isl_set_list_insert(
3515 __isl_take isl_set_list *list, unsigned pos,
3516 __isl_take isl_set *el);
3517 __isl_give isl_set_list *isl_set_list_add(
3518 __isl_take isl_set_list *list,
3519 __isl_take isl_set *el);
3520 __isl_give isl_set_list *isl_set_list_drop(
3521 __isl_take isl_set_list *list,
3522 unsigned first, unsigned n);
3523 __isl_give isl_set_list *isl_set_list_set_set(
3524 __isl_take isl_set_list *list, int index,
3525 __isl_take isl_set *set);
3526 __isl_give isl_set_list *isl_set_list_concat(
3527 __isl_take isl_set_list *list1,
3528 __isl_take isl_set_list *list2);
3529 __isl_give isl_set_list *isl_set_list_sort(
3530 __isl_take isl_set_list *list,
3531 int (*cmp)(__isl_keep isl_set *a,
3532 __isl_keep isl_set *b, void *user),
3534 __isl_null isl_set_list *isl_set_list_free(
3535 __isl_take isl_set_list *list);
3537 C<isl_set_list_alloc> creates an empty list with a capacity for
3538 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3541 Lists can be inspected using the following functions.
3543 #include <isl/list.h>
3544 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3545 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3546 __isl_give isl_set *isl_set_list_get_set(
3547 __isl_keep isl_set_list *list, int index);
3548 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3549 int (*fn)(__isl_take isl_set *el, void *user),
3551 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3552 int (*follows)(__isl_keep isl_set *a,
3553 __isl_keep isl_set *b, void *user),
3555 int (*fn)(__isl_take isl_set *el, void *user),
3558 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3559 strongly connected components of the graph with as vertices the elements
3560 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3561 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3562 should return C<-1> on error.
3564 Lists can be printed using
3566 #include <isl/list.h>
3567 __isl_give isl_printer *isl_printer_print_set_list(
3568 __isl_take isl_printer *p,
3569 __isl_keep isl_set_list *list);
3571 =head2 Associative arrays
3573 Associative arrays map isl objects of a specific type to isl objects
3574 of some (other) specific type. They are defined for several pairs
3575 of types, including (C<isl_map>, C<isl_basic_set>),
3576 (C<isl_id>, C<isl_ast_expr>) and.
3577 (C<isl_id>, C<isl_pw_aff>).
3578 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3581 Associative arrays can be created, copied and freed using
3582 the following functions.
3584 #include <isl/id_to_ast_expr.h>
3585 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3586 isl_ctx *ctx, int min_size);
3587 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3588 __isl_keep id_to_ast_expr *id2expr);
3589 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
3590 __isl_take id_to_ast_expr *id2expr);
3592 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3593 to specify the expected size of the associative array.
3594 The associative array will be grown automatically as needed.
3596 Associative arrays can be inspected using the following functions.
3598 #include <isl/id_to_ast_expr.h>
3599 isl_ctx *isl_id_to_ast_expr_get_ctx(
3600 __isl_keep id_to_ast_expr *id2expr);
3601 int isl_id_to_ast_expr_has(
3602 __isl_keep id_to_ast_expr *id2expr,
3603 __isl_keep isl_id *key);
3604 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3605 __isl_keep id_to_ast_expr *id2expr,
3606 __isl_take isl_id *key);
3607 int isl_id_to_ast_expr_foreach(
3608 __isl_keep id_to_ast_expr *id2expr,
3609 int (*fn)(__isl_take isl_id *key,
3610 __isl_take isl_ast_expr *val, void *user),
3613 They can be modified using the following function.
3615 #include <isl/id_to_ast_expr.h>
3616 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3617 __isl_take id_to_ast_expr *id2expr,
3618 __isl_take isl_id *key,
3619 __isl_take isl_ast_expr *val);
3620 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
3621 __isl_take id_to_ast_expr *id2expr,
3622 __isl_take isl_id *key);
3624 Associative arrays can be printed using the following function.
3626 #include <isl/id_to_ast_expr.h>
3627 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3628 __isl_take isl_printer *p,
3629 __isl_keep id_to_ast_expr *id2expr);
3631 =head2 Multiple Values
3633 An C<isl_multi_val> object represents a sequence of zero or more values,
3634 living in a set space.
3636 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3637 using the following function
3639 #include <isl/val.h>
3640 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3641 __isl_take isl_space *space,
3642 __isl_take isl_val_list *list);
3644 The zero multiple value (with value zero for each set dimension)
3645 can be created using the following function.
3647 #include <isl/val.h>
3648 __isl_give isl_multi_val *isl_multi_val_zero(
3649 __isl_take isl_space *space);
3651 Multiple values can be copied and freed using
3653 #include <isl/val.h>
3654 __isl_give isl_multi_val *isl_multi_val_copy(
3655 __isl_keep isl_multi_val *mv);
3656 __isl_null isl_multi_val *isl_multi_val_free(
3657 __isl_take isl_multi_val *mv);
3659 They can be inspected using
3661 #include <isl/val.h>
3662 isl_ctx *isl_multi_val_get_ctx(
3663 __isl_keep isl_multi_val *mv);
3664 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3665 enum isl_dim_type type);
3666 __isl_give isl_val *isl_multi_val_get_val(
3667 __isl_keep isl_multi_val *mv, int pos);
3668 int isl_multi_val_find_dim_by_id(
3669 __isl_keep isl_multi_val *mv,
3670 enum isl_dim_type type, __isl_keep isl_id *id);
3671 __isl_give isl_id *isl_multi_val_get_dim_id(
3672 __isl_keep isl_multi_val *mv,
3673 enum isl_dim_type type, unsigned pos);
3674 const char *isl_multi_val_get_tuple_name(
3675 __isl_keep isl_multi_val *mv,
3676 enum isl_dim_type type);
3677 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3678 enum isl_dim_type type);
3679 __isl_give isl_id *isl_multi_val_get_tuple_id(
3680 __isl_keep isl_multi_val *mv,
3681 enum isl_dim_type type);
3682 int isl_multi_val_range_is_wrapping(
3683 __isl_keep isl_multi_val *mv);
3685 They can be modified using
3687 #include <isl/val.h>
3688 __isl_give isl_multi_val *isl_multi_val_set_val(
3689 __isl_take isl_multi_val *mv, int pos,
3690 __isl_take isl_val *val);
3691 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3692 __isl_take isl_multi_val *mv,
3693 enum isl_dim_type type, unsigned pos, const char *s);
3694 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3695 __isl_take isl_multi_val *mv,
3696 enum isl_dim_type type, unsigned pos,
3697 __isl_take isl_id *id);
3698 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3699 __isl_take isl_multi_val *mv,
3700 enum isl_dim_type type, const char *s);
3701 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3702 __isl_take isl_multi_val *mv,
3703 enum isl_dim_type type, __isl_take isl_id *id);
3704 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3705 __isl_take isl_multi_val *mv,
3706 enum isl_dim_type type);
3707 __isl_give isl_multi_val *isl_multi_val_reset_user(
3708 __isl_take isl_multi_val *mv);
3710 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3711 __isl_take isl_multi_val *mv,
3712 enum isl_dim_type type, unsigned first, unsigned n);
3713 __isl_give isl_multi_val *isl_multi_val_add_dims(
3714 __isl_take isl_multi_val *mv,
3715 enum isl_dim_type type, unsigned n);
3716 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3717 __isl_take isl_multi_val *mv,
3718 enum isl_dim_type type, unsigned first, unsigned n);
3722 #include <isl/val.h>
3723 __isl_give isl_multi_val *isl_multi_val_align_params(
3724 __isl_take isl_multi_val *mv,
3725 __isl_take isl_space *model);
3726 __isl_give isl_multi_val *isl_multi_val_from_range(
3727 __isl_take isl_multi_val *mv);
3728 __isl_give isl_multi_val *isl_multi_val_range_splice(
3729 __isl_take isl_multi_val *mv1, unsigned pos,
3730 __isl_take isl_multi_val *mv2);
3731 __isl_give isl_multi_val *isl_multi_val_range_product(
3732 __isl_take isl_multi_val *mv1,
3733 __isl_take isl_multi_val *mv2);
3734 __isl_give isl_multi_val *
3735 isl_multi_val_range_factor_domain(
3736 __isl_take isl_multi_val *mv);
3737 __isl_give isl_multi_val *
3738 isl_multi_val_range_factor_range(
3739 __isl_take isl_multi_val *mv);
3740 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3741 __isl_take isl_multi_val *mv1,
3742 __isl_take isl_multi_aff *mv2);
3743 __isl_give isl_multi_val *isl_multi_val_product(
3744 __isl_take isl_multi_val *mv1,
3745 __isl_take isl_multi_val *mv2);
3746 __isl_give isl_multi_val *isl_multi_val_add_val(
3747 __isl_take isl_multi_val *mv,
3748 __isl_take isl_val *v);
3749 __isl_give isl_multi_val *isl_multi_val_mod_val(
3750 __isl_take isl_multi_val *mv,
3751 __isl_take isl_val *v);
3752 __isl_give isl_multi_val *isl_multi_val_scale_val(
3753 __isl_take isl_multi_val *mv,
3754 __isl_take isl_val *v);
3755 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3756 __isl_take isl_multi_val *mv1,
3757 __isl_take isl_multi_val *mv2);
3758 __isl_give isl_multi_val *
3759 isl_multi_val_scale_down_multi_val(
3760 __isl_take isl_multi_val *mv1,
3761 __isl_take isl_multi_val *mv2);
3763 A multiple value can be printed using
3765 __isl_give isl_printer *isl_printer_print_multi_val(
3766 __isl_take isl_printer *p,
3767 __isl_keep isl_multi_val *mv);
3771 Vectors can be created, copied and freed using the following functions.
3773 #include <isl/vec.h>
3774 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3776 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3777 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
3779 Note that the elements of a newly created vector may have arbitrary values.
3780 The elements can be changed and inspected using the following functions.
3782 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3783 int isl_vec_size(__isl_keep isl_vec *vec);
3784 __isl_give isl_val *isl_vec_get_element_val(
3785 __isl_keep isl_vec *vec, int pos);
3786 __isl_give isl_vec *isl_vec_set_element_si(
3787 __isl_take isl_vec *vec, int pos, int v);
3788 __isl_give isl_vec *isl_vec_set_element_val(
3789 __isl_take isl_vec *vec, int pos,
3790 __isl_take isl_val *v);
3791 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3793 __isl_give isl_vec *isl_vec_set_val(
3794 __isl_take isl_vec *vec, __isl_take isl_val *v);
3795 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3796 __isl_keep isl_vec *vec2, int pos);
3798 C<isl_vec_get_element> will return a negative value if anything went wrong.
3799 In that case, the value of C<*v> is undefined.
3801 The following function can be used to concatenate two vectors.
3803 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3804 __isl_take isl_vec *vec2);
3808 Matrices can be created, copied and freed using the following functions.
3810 #include <isl/mat.h>
3811 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3812 unsigned n_row, unsigned n_col);
3813 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3814 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
3816 Note that the elements of a newly created matrix may have arbitrary values.
3817 The elements can be changed and inspected using the following functions.
3819 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3820 int isl_mat_rows(__isl_keep isl_mat *mat);
3821 int isl_mat_cols(__isl_keep isl_mat *mat);
3822 __isl_give isl_val *isl_mat_get_element_val(
3823 __isl_keep isl_mat *mat, int row, int col);
3824 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3825 int row, int col, int v);
3826 __isl_give isl_mat *isl_mat_set_element_val(
3827 __isl_take isl_mat *mat, int row, int col,
3828 __isl_take isl_val *v);
3830 C<isl_mat_get_element> will return a negative value if anything went wrong.
3831 In that case, the value of C<*v> is undefined.
3833 The following function can be used to compute the (right) inverse
3834 of a matrix, i.e., a matrix such that the product of the original
3835 and the inverse (in that order) is a multiple of the identity matrix.
3836 The input matrix is assumed to be of full row-rank.
3838 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3840 The following function can be used to compute the (right) kernel
3841 (or null space) of a matrix, i.e., a matrix such that the product of
3842 the original and the kernel (in that order) is the zero matrix.
3844 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3846 =head2 Piecewise Quasi Affine Expressions
3848 The zero quasi affine expression or the quasi affine expression
3849 that is equal to a given value or
3850 a specified dimension on a given domain can be created using
3852 __isl_give isl_aff *isl_aff_zero_on_domain(
3853 __isl_take isl_local_space *ls);
3854 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3855 __isl_take isl_local_space *ls);
3856 __isl_give isl_aff *isl_aff_val_on_domain(
3857 __isl_take isl_local_space *ls,
3858 __isl_take isl_val *val);
3859 __isl_give isl_aff *isl_aff_var_on_domain(
3860 __isl_take isl_local_space *ls,
3861 enum isl_dim_type type, unsigned pos);
3862 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3863 __isl_take isl_local_space *ls,
3864 enum isl_dim_type type, unsigned pos);
3865 __isl_give isl_aff *isl_aff_nan_on_domain(
3866 __isl_take isl_local_space *ls);
3867 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3868 __isl_take isl_local_space *ls);
3870 Note that the space in which the resulting objects live is a map space
3871 with the given space as domain and a one-dimensional range.
3873 An empty piecewise quasi affine expression (one with no cells)
3874 or a piecewise quasi affine expression with a single cell can
3875 be created using the following functions.
3877 #include <isl/aff.h>
3878 __isl_give isl_pw_aff *isl_pw_aff_empty(
3879 __isl_take isl_space *space);
3880 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3881 __isl_take isl_set *set, __isl_take isl_aff *aff);
3882 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3883 __isl_take isl_aff *aff);
3885 A piecewise quasi affine expression that is equal to 1 on a set
3886 and 0 outside the set can be created using the following function.
3888 #include <isl/aff.h>
3889 __isl_give isl_pw_aff *isl_set_indicator_function(
3890 __isl_take isl_set *set);
3892 Quasi affine expressions can be copied and freed using
3894 #include <isl/aff.h>
3895 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3896 __isl_null isl_aff *isl_aff_free(__isl_take isl_aff *aff);
3898 __isl_give isl_pw_aff *isl_pw_aff_copy(
3899 __isl_keep isl_pw_aff *pwaff);
3900 __isl_null isl_pw_aff *isl_pw_aff_free(
3901 __isl_take isl_pw_aff *pwaff);
3903 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3904 using the following function. The constraint is required to have
3905 a non-zero coefficient for the specified dimension.
3907 #include <isl/constraint.h>
3908 __isl_give isl_aff *isl_constraint_get_bound(
3909 __isl_keep isl_constraint *constraint,
3910 enum isl_dim_type type, int pos);
3912 The entire affine expression of the constraint can also be extracted
3913 using the following function.
3915 #include <isl/constraint.h>
3916 __isl_give isl_aff *isl_constraint_get_aff(
3917 __isl_keep isl_constraint *constraint);
3919 Conversely, an equality constraint equating
3920 the affine expression to zero or an inequality constraint enforcing
3921 the affine expression to be non-negative, can be constructed using
3923 __isl_give isl_constraint *isl_equality_from_aff(
3924 __isl_take isl_aff *aff);
3925 __isl_give isl_constraint *isl_inequality_from_aff(
3926 __isl_take isl_aff *aff);
3928 The expression can be inspected using
3930 #include <isl/aff.h>
3931 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3932 int isl_aff_dim(__isl_keep isl_aff *aff,
3933 enum isl_dim_type type);
3934 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3935 __isl_keep isl_aff *aff);
3936 __isl_give isl_local_space *isl_aff_get_local_space(
3937 __isl_keep isl_aff *aff);
3938 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3939 enum isl_dim_type type, unsigned pos);
3940 const char *isl_pw_aff_get_dim_name(
3941 __isl_keep isl_pw_aff *pa,
3942 enum isl_dim_type type, unsigned pos);
3943 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3944 enum isl_dim_type type, unsigned pos);
3945 __isl_give isl_id *isl_pw_aff_get_dim_id(
3946 __isl_keep isl_pw_aff *pa,
3947 enum isl_dim_type type, unsigned pos);
3948 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
3949 enum isl_dim_type type);
3950 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3951 __isl_keep isl_pw_aff *pa,
3952 enum isl_dim_type type);
3953 __isl_give isl_val *isl_aff_get_constant_val(
3954 __isl_keep isl_aff *aff);
3955 __isl_give isl_val *isl_aff_get_coefficient_val(
3956 __isl_keep isl_aff *aff,
3957 enum isl_dim_type type, int pos);
3958 __isl_give isl_val *isl_aff_get_denominator_val(
3959 __isl_keep isl_aff *aff);
3960 __isl_give isl_aff *isl_aff_get_div(
3961 __isl_keep isl_aff *aff, int pos);
3963 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3964 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3965 int (*fn)(__isl_take isl_set *set,
3966 __isl_take isl_aff *aff,
3967 void *user), void *user);
3969 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3970 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3972 int isl_aff_is_nan(__isl_keep isl_aff *aff);
3973 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
3975 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3976 enum isl_dim_type type, unsigned first, unsigned n);
3977 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3978 enum isl_dim_type type, unsigned first, unsigned n);
3980 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3981 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3982 enum isl_dim_type type);
3983 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3985 It can be modified using
3987 #include <isl/aff.h>
3988 __isl_give isl_aff *isl_aff_set_tuple_id(
3989 __isl_take isl_aff *aff,
3990 enum isl_dim_type type, __isl_take isl_id *id);
3991 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3992 __isl_take isl_pw_aff *pwaff,
3993 enum isl_dim_type type, __isl_take isl_id *id);
3994 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
3995 __isl_take isl_pw_aff *pa,
3996 enum isl_dim_type type);
3997 __isl_give isl_aff *isl_aff_set_dim_name(
3998 __isl_take isl_aff *aff, enum isl_dim_type type,
3999 unsigned pos, const char *s);
4000 __isl_give isl_aff *isl_aff_set_dim_id(
4001 __isl_take isl_aff *aff, enum isl_dim_type type,
4002 unsigned pos, __isl_take isl_id *id);
4003 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
4004 __isl_take isl_pw_aff *pma,
4005 enum isl_dim_type type, unsigned pos,
4006 __isl_take isl_id *id);
4007 __isl_give isl_aff *isl_aff_set_constant_si(
4008 __isl_take isl_aff *aff, int v);
4009 __isl_give isl_aff *isl_aff_set_constant_val(
4010 __isl_take isl_aff *aff, __isl_take isl_val *v);
4011 __isl_give isl_aff *isl_aff_set_coefficient_si(
4012 __isl_take isl_aff *aff,
4013 enum isl_dim_type type, int pos, int v);
4014 __isl_give isl_aff *isl_aff_set_coefficient_val(
4015 __isl_take isl_aff *aff,
4016 enum isl_dim_type type, int pos,
4017 __isl_take isl_val *v);
4019 __isl_give isl_aff *isl_aff_add_constant_si(
4020 __isl_take isl_aff *aff, int v);
4021 __isl_give isl_aff *isl_aff_add_constant_val(
4022 __isl_take isl_aff *aff, __isl_take isl_val *v);
4023 __isl_give isl_aff *isl_aff_add_constant_num_si(
4024 __isl_take isl_aff *aff, int v);
4025 __isl_give isl_aff *isl_aff_add_coefficient_si(
4026 __isl_take isl_aff *aff,
4027 enum isl_dim_type type, int pos, int v);
4028 __isl_give isl_aff *isl_aff_add_coefficient_val(
4029 __isl_take isl_aff *aff,
4030 enum isl_dim_type type, int pos,
4031 __isl_take isl_val *v);
4033 __isl_give isl_aff *isl_aff_insert_dims(
4034 __isl_take isl_aff *aff,
4035 enum isl_dim_type type, unsigned first, unsigned n);
4036 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
4037 __isl_take isl_pw_aff *pwaff,
4038 enum isl_dim_type type, unsigned first, unsigned n);
4039 __isl_give isl_aff *isl_aff_add_dims(
4040 __isl_take isl_aff *aff,
4041 enum isl_dim_type type, unsigned n);
4042 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
4043 __isl_take isl_pw_aff *pwaff,
4044 enum isl_dim_type type, unsigned n);
4045 __isl_give isl_aff *isl_aff_drop_dims(
4046 __isl_take isl_aff *aff,
4047 enum isl_dim_type type, unsigned first, unsigned n);
4048 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
4049 __isl_take isl_pw_aff *pwaff,
4050 enum isl_dim_type type, unsigned first, unsigned n);
4051 __isl_give isl_aff *isl_aff_move_dims(
4052 __isl_take isl_aff *aff,
4053 enum isl_dim_type dst_type, unsigned dst_pos,
4054 enum isl_dim_type src_type, unsigned src_pos,
4056 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
4057 __isl_take isl_pw_aff *pa,
4058 enum isl_dim_type dst_type, unsigned dst_pos,
4059 enum isl_dim_type src_type, unsigned src_pos,
4062 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
4063 set the I<numerator> of the constant or coefficient, while
4064 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
4065 the constant or coefficient as a whole.
4066 The C<add_constant> and C<add_coefficient> functions add an integer
4067 or rational value to
4068 the possibly rational constant or coefficient.
4069 The C<add_constant_num> functions add an integer value to
4072 To check whether an affine expressions is obviously zero
4073 or (obviously) equal to some other affine expression, use
4075 #include <isl/aff.h>
4076 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
4077 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
4078 __isl_keep isl_aff *aff2);
4079 int isl_pw_aff_plain_is_equal(
4080 __isl_keep isl_pw_aff *pwaff1,
4081 __isl_keep isl_pw_aff *pwaff2);
4082 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
4083 __isl_keep isl_pw_aff *pa2);
4084 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4085 __isl_keep isl_pw_aff *pa2);
4087 The function C<isl_pw_aff_plain_cmp> can be used to sort
4088 C<isl_pw_aff>s. The order is not strictly defined.
4089 The current order sorts expressions that only involve
4090 earlier dimensions before those that involve later dimensions.
4094 #include <isl/aff.h>
4095 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
4096 __isl_take isl_aff *aff2);
4097 __isl_give isl_pw_aff *isl_pw_aff_add(
4098 __isl_take isl_pw_aff *pwaff1,
4099 __isl_take isl_pw_aff *pwaff2);
4100 __isl_give isl_pw_aff *isl_pw_aff_min(
4101 __isl_take isl_pw_aff *pwaff1,
4102 __isl_take isl_pw_aff *pwaff2);
4103 __isl_give isl_pw_aff *isl_pw_aff_max(
4104 __isl_take isl_pw_aff *pwaff1,
4105 __isl_take isl_pw_aff *pwaff2);
4106 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
4107 __isl_take isl_aff *aff2);
4108 __isl_give isl_pw_aff *isl_pw_aff_sub(
4109 __isl_take isl_pw_aff *pwaff1,
4110 __isl_take isl_pw_aff *pwaff2);
4111 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
4112 __isl_give isl_pw_aff *isl_pw_aff_neg(
4113 __isl_take isl_pw_aff *pwaff);
4114 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
4115 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4116 __isl_take isl_pw_aff *pwaff);
4117 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
4118 __isl_give isl_pw_aff *isl_pw_aff_floor(
4119 __isl_take isl_pw_aff *pwaff);
4120 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
4121 __isl_take isl_val *mod);
4122 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
4123 __isl_take isl_pw_aff *pa,
4124 __isl_take isl_val *mod);
4125 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
4126 __isl_take isl_val *v);
4127 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
4128 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
4129 __isl_give isl_aff *isl_aff_scale_down_ui(
4130 __isl_take isl_aff *aff, unsigned f);
4131 __isl_give isl_aff *isl_aff_scale_down_val(
4132 __isl_take isl_aff *aff, __isl_take isl_val *v);
4133 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
4134 __isl_take isl_pw_aff *pa,
4135 __isl_take isl_val *f);
4137 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4138 __isl_take isl_pw_aff_list *list);
4139 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4140 __isl_take isl_pw_aff_list *list);
4142 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4143 __isl_take isl_pw_aff *pwqp);
4145 __isl_give isl_aff *isl_aff_align_params(
4146 __isl_take isl_aff *aff,
4147 __isl_take isl_space *model);
4148 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4149 __isl_take isl_pw_aff *pwaff,
4150 __isl_take isl_space *model);
4152 __isl_give isl_aff *isl_aff_project_domain_on_params(
4153 __isl_take isl_aff *aff);
4154 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4155 __isl_take isl_pw_aff *pwa);
4157 __isl_give isl_aff *isl_aff_gist_params(
4158 __isl_take isl_aff *aff,
4159 __isl_take isl_set *context);
4160 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
4161 __isl_take isl_set *context);
4162 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
4163 __isl_take isl_pw_aff *pwaff,
4164 __isl_take isl_set *context);
4165 __isl_give isl_pw_aff *isl_pw_aff_gist(
4166 __isl_take isl_pw_aff *pwaff,
4167 __isl_take isl_set *context);
4169 __isl_give isl_set *isl_pw_aff_domain(
4170 __isl_take isl_pw_aff *pwaff);
4171 __isl_give isl_set *isl_pw_aff_params(
4172 __isl_take isl_pw_aff *pwa);
4173 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4174 __isl_take isl_pw_aff *pa,
4175 __isl_take isl_set *set);
4176 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4177 __isl_take isl_pw_aff *pa,
4178 __isl_take isl_set *set);
4180 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
4181 __isl_take isl_aff *aff2);
4182 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
4183 __isl_take isl_aff *aff2);
4184 __isl_give isl_pw_aff *isl_pw_aff_mul(
4185 __isl_take isl_pw_aff *pwaff1,
4186 __isl_take isl_pw_aff *pwaff2);
4187 __isl_give isl_pw_aff *isl_pw_aff_div(
4188 __isl_take isl_pw_aff *pa1,
4189 __isl_take isl_pw_aff *pa2);
4190 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
4191 __isl_take isl_pw_aff *pa1,
4192 __isl_take isl_pw_aff *pa2);
4193 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
4194 __isl_take isl_pw_aff *pa1,
4195 __isl_take isl_pw_aff *pa2);
4197 When multiplying two affine expressions, at least one of the two needs
4198 to be a constant. Similarly, when dividing an affine expression by another,
4199 the second expression needs to be a constant.
4200 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
4201 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
4204 #include <isl/aff.h>
4205 __isl_give isl_aff *isl_aff_pullback_aff(
4206 __isl_take isl_aff *aff1,
4207 __isl_take isl_aff *aff2);
4208 __isl_give isl_aff *isl_aff_pullback_multi_aff(
4209 __isl_take isl_aff *aff,
4210 __isl_take isl_multi_aff *ma);
4211 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
4212 __isl_take isl_pw_aff *pa,
4213 __isl_take isl_multi_aff *ma);
4214 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
4215 __isl_take isl_pw_aff *pa,
4216 __isl_take isl_pw_multi_aff *pma);
4217 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
4218 __isl_take isl_pw_aff *pa,
4219 __isl_take isl_multi_pw_aff *mpa);
4221 These functions precompose the input expression by the given
4222 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
4223 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
4224 into the (piecewise) affine expression.
4225 Objects of type C<isl_multi_aff> are described in
4226 L</"Piecewise Multiple Quasi Affine Expressions">.
4228 #include <isl/aff.h>
4229 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4230 __isl_take isl_aff *aff);
4231 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4232 __isl_take isl_aff *aff);
4233 __isl_give isl_basic_set *isl_aff_le_basic_set(
4234 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4235 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4236 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4237 __isl_give isl_set *isl_pw_aff_eq_set(
4238 __isl_take isl_pw_aff *pwaff1,
4239 __isl_take isl_pw_aff *pwaff2);
4240 __isl_give isl_set *isl_pw_aff_ne_set(
4241 __isl_take isl_pw_aff *pwaff1,
4242 __isl_take isl_pw_aff *pwaff2);
4243 __isl_give isl_set *isl_pw_aff_le_set(
4244 __isl_take isl_pw_aff *pwaff1,
4245 __isl_take isl_pw_aff *pwaff2);
4246 __isl_give isl_set *isl_pw_aff_lt_set(
4247 __isl_take isl_pw_aff *pwaff1,
4248 __isl_take isl_pw_aff *pwaff2);
4249 __isl_give isl_set *isl_pw_aff_ge_set(
4250 __isl_take isl_pw_aff *pwaff1,
4251 __isl_take isl_pw_aff *pwaff2);
4252 __isl_give isl_set *isl_pw_aff_gt_set(
4253 __isl_take isl_pw_aff *pwaff1,
4254 __isl_take isl_pw_aff *pwaff2);
4256 __isl_give isl_set *isl_pw_aff_list_eq_set(
4257 __isl_take isl_pw_aff_list *list1,
4258 __isl_take isl_pw_aff_list *list2);
4259 __isl_give isl_set *isl_pw_aff_list_ne_set(
4260 __isl_take isl_pw_aff_list *list1,
4261 __isl_take isl_pw_aff_list *list2);
4262 __isl_give isl_set *isl_pw_aff_list_le_set(
4263 __isl_take isl_pw_aff_list *list1,
4264 __isl_take isl_pw_aff_list *list2);
4265 __isl_give isl_set *isl_pw_aff_list_lt_set(
4266 __isl_take isl_pw_aff_list *list1,
4267 __isl_take isl_pw_aff_list *list2);
4268 __isl_give isl_set *isl_pw_aff_list_ge_set(
4269 __isl_take isl_pw_aff_list *list1,
4270 __isl_take isl_pw_aff_list *list2);
4271 __isl_give isl_set *isl_pw_aff_list_gt_set(
4272 __isl_take isl_pw_aff_list *list1,
4273 __isl_take isl_pw_aff_list *list2);
4275 The function C<isl_aff_neg_basic_set> returns a basic set
4276 containing those elements in the domain space
4277 of C<aff> where C<aff> is negative.
4278 The function C<isl_aff_ge_basic_set> returns a basic set
4279 containing those elements in the shared space
4280 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4281 The function C<isl_pw_aff_ge_set> returns a set
4282 containing those elements in the shared domain
4283 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4284 The functions operating on C<isl_pw_aff_list> apply the corresponding
4285 C<isl_pw_aff> function to each pair of elements in the two lists.
4287 #include <isl/aff.h>
4288 __isl_give isl_set *isl_pw_aff_nonneg_set(
4289 __isl_take isl_pw_aff *pwaff);
4290 __isl_give isl_set *isl_pw_aff_zero_set(
4291 __isl_take isl_pw_aff *pwaff);
4292 __isl_give isl_set *isl_pw_aff_non_zero_set(
4293 __isl_take isl_pw_aff *pwaff);
4295 The function C<isl_pw_aff_nonneg_set> returns a set
4296 containing those elements in the domain
4297 of C<pwaff> where C<pwaff> is non-negative.
4299 #include <isl/aff.h>
4300 __isl_give isl_pw_aff *isl_pw_aff_cond(
4301 __isl_take isl_pw_aff *cond,
4302 __isl_take isl_pw_aff *pwaff_true,
4303 __isl_take isl_pw_aff *pwaff_false);
4305 The function C<isl_pw_aff_cond> performs a conditional operator
4306 and returns an expression that is equal to C<pwaff_true>
4307 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4308 where C<cond> is zero.
4310 #include <isl/aff.h>
4311 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4312 __isl_take isl_pw_aff *pwaff1,
4313 __isl_take isl_pw_aff *pwaff2);
4314 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4315 __isl_take isl_pw_aff *pwaff1,
4316 __isl_take isl_pw_aff *pwaff2);
4317 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4318 __isl_take isl_pw_aff *pwaff1,
4319 __isl_take isl_pw_aff *pwaff2);
4321 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4322 expression with a domain that is the union of those of C<pwaff1> and
4323 C<pwaff2> and such that on each cell, the quasi-affine expression is
4324 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4325 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4326 associated expression is the defined one.
4328 An expression can be read from input using
4330 #include <isl/aff.h>
4331 __isl_give isl_aff *isl_aff_read_from_str(
4332 isl_ctx *ctx, const char *str);
4333 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4334 isl_ctx *ctx, const char *str);
4336 An expression can be printed using
4338 #include <isl/aff.h>
4339 __isl_give isl_printer *isl_printer_print_aff(
4340 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4342 __isl_give isl_printer *isl_printer_print_pw_aff(
4343 __isl_take isl_printer *p,
4344 __isl_keep isl_pw_aff *pwaff);
4346 =head2 Piecewise Multiple Quasi Affine Expressions
4348 An C<isl_multi_aff> object represents a sequence of
4349 zero or more affine expressions, all defined on the same domain space.
4350 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4351 zero or more piecewise affine expressions.
4353 An C<isl_multi_aff> can be constructed from a single
4354 C<isl_aff> or an C<isl_aff_list> using the
4355 following functions. Similarly for C<isl_multi_pw_aff>
4356 and C<isl_pw_multi_aff>.
4358 #include <isl/aff.h>
4359 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4360 __isl_take isl_aff *aff);
4361 __isl_give isl_multi_pw_aff *
4362 isl_multi_pw_aff_from_multi_aff(
4363 __isl_take isl_multi_aff *ma);
4364 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4365 __isl_take isl_pw_aff *pa);
4366 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4367 __isl_take isl_pw_aff *pa);
4368 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4369 __isl_take isl_space *space,
4370 __isl_take isl_aff_list *list);
4372 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4373 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4374 Note however that the domain
4375 of the result is the intersection of the domains of the input.
4376 The reverse conversion is exact.
4378 #include <isl/aff.h>
4379 __isl_give isl_pw_multi_aff *
4380 isl_pw_multi_aff_from_multi_pw_aff(
4381 __isl_take isl_multi_pw_aff *mpa);
4382 __isl_give isl_multi_pw_aff *
4383 isl_multi_pw_aff_from_pw_multi_aff(
4384 __isl_take isl_pw_multi_aff *pma);
4386 An empty piecewise multiple quasi affine expression (one with no cells),
4387 the zero piecewise multiple quasi affine expression (with value zero
4388 for each output dimension),
4389 a piecewise multiple quasi affine expression with a single cell (with
4390 either a universe or a specified domain) or
4391 a zero-dimensional piecewise multiple quasi affine expression
4393 can be created using the following functions.
4395 #include <isl/aff.h>
4396 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4397 __isl_take isl_space *space);
4398 __isl_give isl_multi_aff *isl_multi_aff_zero(
4399 __isl_take isl_space *space);
4400 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4401 __isl_take isl_space *space);
4402 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4403 __isl_take isl_space *space);
4404 __isl_give isl_multi_aff *isl_multi_aff_identity(
4405 __isl_take isl_space *space);
4406 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4407 __isl_take isl_space *space);
4408 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4409 __isl_take isl_space *space);
4410 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4411 __isl_take isl_space *space);
4412 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4413 __isl_take isl_space *space);
4414 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4415 __isl_take isl_space *space,
4416 enum isl_dim_type type,
4417 unsigned first, unsigned n);
4418 __isl_give isl_pw_multi_aff *
4419 isl_pw_multi_aff_project_out_map(
4420 __isl_take isl_space *space,
4421 enum isl_dim_type type,
4422 unsigned first, unsigned n);
4423 __isl_give isl_pw_multi_aff *
4424 isl_pw_multi_aff_from_multi_aff(
4425 __isl_take isl_multi_aff *ma);
4426 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4427 __isl_take isl_set *set,
4428 __isl_take isl_multi_aff *maff);
4429 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4430 __isl_take isl_set *set);
4432 __isl_give isl_union_pw_multi_aff *
4433 isl_union_pw_multi_aff_empty(
4434 __isl_take isl_space *space);
4435 __isl_give isl_union_pw_multi_aff *
4436 isl_union_pw_multi_aff_add_pw_multi_aff(
4437 __isl_take isl_union_pw_multi_aff *upma,
4438 __isl_take isl_pw_multi_aff *pma);
4439 __isl_give isl_union_pw_multi_aff *
4440 isl_union_pw_multi_aff_from_domain(
4441 __isl_take isl_union_set *uset);
4443 A piecewise multiple quasi affine expression can also be initialized
4444 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4445 and the C<isl_map> is single-valued.
4446 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4447 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4449 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4450 __isl_take isl_set *set);
4451 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4452 __isl_take isl_map *map);
4454 __isl_give isl_union_pw_multi_aff *
4455 isl_union_pw_multi_aff_from_union_set(
4456 __isl_take isl_union_set *uset);
4457 __isl_give isl_union_pw_multi_aff *
4458 isl_union_pw_multi_aff_from_union_map(
4459 __isl_take isl_union_map *umap);
4461 Multiple quasi affine expressions can be copied and freed using
4463 #include <isl/aff.h>
4464 __isl_give isl_multi_aff *isl_multi_aff_copy(
4465 __isl_keep isl_multi_aff *maff);
4466 __isl_null isl_multi_aff *isl_multi_aff_free(
4467 __isl_take isl_multi_aff *maff);
4469 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4470 __isl_keep isl_pw_multi_aff *pma);
4471 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
4472 __isl_take isl_pw_multi_aff *pma);
4474 __isl_give isl_union_pw_multi_aff *
4475 isl_union_pw_multi_aff_copy(
4476 __isl_keep isl_union_pw_multi_aff *upma);
4477 __isl_null isl_union_pw_multi_aff *
4478 isl_union_pw_multi_aff_free(
4479 __isl_take isl_union_pw_multi_aff *upma);
4481 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4482 __isl_keep isl_multi_pw_aff *mpa);
4483 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
4484 __isl_take isl_multi_pw_aff *mpa);
4486 The expression can be inspected using
4488 #include <isl/aff.h>
4489 isl_ctx *isl_multi_aff_get_ctx(
4490 __isl_keep isl_multi_aff *maff);
4491 isl_ctx *isl_pw_multi_aff_get_ctx(
4492 __isl_keep isl_pw_multi_aff *pma);
4493 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4494 __isl_keep isl_union_pw_multi_aff *upma);
4495 isl_ctx *isl_multi_pw_aff_get_ctx(
4496 __isl_keep isl_multi_pw_aff *mpa);
4498 int isl_multi_aff_involves_dims(
4499 __isl_keep isl_multi_aff *ma,
4500 enum isl_dim_type type, unsigned first, unsigned n);
4501 int isl_multi_pw_aff_involves_dims(
4502 __isl_keep isl_multi_pw_aff *mpa,
4503 enum isl_dim_type type, unsigned first, unsigned n);
4505 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4506 enum isl_dim_type type);
4507 unsigned isl_pw_multi_aff_dim(
4508 __isl_keep isl_pw_multi_aff *pma,
4509 enum isl_dim_type type);
4510 unsigned isl_multi_pw_aff_dim(
4511 __isl_keep isl_multi_pw_aff *mpa,
4512 enum isl_dim_type type);
4513 __isl_give isl_aff *isl_multi_aff_get_aff(
4514 __isl_keep isl_multi_aff *multi, int pos);
4515 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4516 __isl_keep isl_pw_multi_aff *pma, int pos);
4517 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4518 __isl_keep isl_multi_pw_aff *mpa, int pos);
4519 int isl_multi_aff_find_dim_by_id(
4520 __isl_keep isl_multi_aff *ma,
4521 enum isl_dim_type type, __isl_keep isl_id *id);
4522 int isl_multi_pw_aff_find_dim_by_id(
4523 __isl_keep isl_multi_pw_aff *mpa,
4524 enum isl_dim_type type, __isl_keep isl_id *id);
4525 const char *isl_pw_multi_aff_get_dim_name(
4526 __isl_keep isl_pw_multi_aff *pma,
4527 enum isl_dim_type type, unsigned pos);
4528 __isl_give isl_id *isl_multi_aff_get_dim_id(
4529 __isl_keep isl_multi_aff *ma,
4530 enum isl_dim_type type, unsigned pos);
4531 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4532 __isl_keep isl_pw_multi_aff *pma,
4533 enum isl_dim_type type, unsigned pos);
4534 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4535 __isl_keep isl_multi_pw_aff *mpa,
4536 enum isl_dim_type type, unsigned pos);
4537 const char *isl_multi_aff_get_tuple_name(
4538 __isl_keep isl_multi_aff *multi,
4539 enum isl_dim_type type);
4540 int isl_pw_multi_aff_has_tuple_name(
4541 __isl_keep isl_pw_multi_aff *pma,
4542 enum isl_dim_type type);
4543 const char *isl_pw_multi_aff_get_tuple_name(
4544 __isl_keep isl_pw_multi_aff *pma,
4545 enum isl_dim_type type);
4546 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4547 enum isl_dim_type type);
4548 int isl_pw_multi_aff_has_tuple_id(
4549 __isl_keep isl_pw_multi_aff *pma,
4550 enum isl_dim_type type);
4551 int isl_multi_pw_aff_has_tuple_id(
4552 __isl_keep isl_multi_pw_aff *mpa,
4553 enum isl_dim_type type);
4554 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4555 __isl_keep isl_multi_aff *ma,
4556 enum isl_dim_type type);
4557 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4558 __isl_keep isl_pw_multi_aff *pma,
4559 enum isl_dim_type type);
4560 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4561 __isl_keep isl_multi_pw_aff *mpa,
4562 enum isl_dim_type type);
4563 int isl_multi_aff_range_is_wrapping(
4564 __isl_keep isl_multi_aff *ma);
4565 int isl_multi_pw_aff_range_is_wrapping(
4566 __isl_keep isl_multi_pw_aff *mpa);
4568 int isl_pw_multi_aff_foreach_piece(
4569 __isl_keep isl_pw_multi_aff *pma,
4570 int (*fn)(__isl_take isl_set *set,
4571 __isl_take isl_multi_aff *maff,
4572 void *user), void *user);
4574 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4575 __isl_keep isl_union_pw_multi_aff *upma,
4576 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4577 void *user), void *user);
4579 It can be modified using
4581 #include <isl/aff.h>
4582 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4583 __isl_take isl_multi_aff *multi, int pos,
4584 __isl_take isl_aff *aff);
4585 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4586 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4587 __isl_take isl_pw_aff *pa);
4588 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4589 __isl_take isl_multi_aff *maff,
4590 enum isl_dim_type type, unsigned pos, const char *s);
4591 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4592 __isl_take isl_multi_aff *maff,
4593 enum isl_dim_type type, unsigned pos,
4594 __isl_take isl_id *id);
4595 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4596 __isl_take isl_multi_aff *maff,
4597 enum isl_dim_type type, const char *s);
4598 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4599 __isl_take isl_multi_aff *maff,
4600 enum isl_dim_type type, __isl_take isl_id *id);
4601 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4602 __isl_take isl_pw_multi_aff *pma,
4603 enum isl_dim_type type, __isl_take isl_id *id);
4604 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4605 __isl_take isl_multi_aff *ma,
4606 enum isl_dim_type type);
4607 __isl_give isl_multi_pw_aff *
4608 isl_multi_pw_aff_reset_tuple_id(
4609 __isl_take isl_multi_pw_aff *mpa,
4610 enum isl_dim_type type);
4611 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4612 __isl_take isl_multi_aff *ma);
4613 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4614 __isl_take isl_multi_pw_aff *mpa);
4616 __isl_give isl_multi_pw_aff *
4617 isl_multi_pw_aff_set_dim_name(
4618 __isl_take isl_multi_pw_aff *mpa,
4619 enum isl_dim_type type, unsigned pos, const char *s);
4620 __isl_give isl_multi_pw_aff *
4621 isl_multi_pw_aff_set_dim_id(
4622 __isl_take isl_multi_pw_aff *mpa,
4623 enum isl_dim_type type, unsigned pos,
4624 __isl_take isl_id *id);
4625 __isl_give isl_multi_pw_aff *
4626 isl_multi_pw_aff_set_tuple_name(
4627 __isl_take isl_multi_pw_aff *mpa,
4628 enum isl_dim_type type, const char *s);
4630 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4631 __isl_take isl_multi_aff *ma);
4633 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4634 __isl_take isl_multi_aff *ma,
4635 enum isl_dim_type type, unsigned first, unsigned n);
4636 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4637 __isl_take isl_multi_aff *ma,
4638 enum isl_dim_type type, unsigned n);
4639 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4640 __isl_take isl_multi_aff *maff,
4641 enum isl_dim_type type, unsigned first, unsigned n);
4642 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4643 __isl_take isl_pw_multi_aff *pma,
4644 enum isl_dim_type type, unsigned first, unsigned n);
4646 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4647 __isl_take isl_multi_pw_aff *mpa,
4648 enum isl_dim_type type, unsigned first, unsigned n);
4649 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4650 __isl_take isl_multi_pw_aff *mpa,
4651 enum isl_dim_type type, unsigned n);
4652 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4653 __isl_take isl_multi_pw_aff *pma,
4654 enum isl_dim_type dst_type, unsigned dst_pos,
4655 enum isl_dim_type src_type, unsigned src_pos,
4658 To check whether two multiple affine expressions are
4659 (obviously) equal to each other, use
4661 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4662 __isl_keep isl_multi_aff *maff2);
4663 int isl_pw_multi_aff_plain_is_equal(
4664 __isl_keep isl_pw_multi_aff *pma1,
4665 __isl_keep isl_pw_multi_aff *pma2);
4666 int isl_multi_pw_aff_plain_is_equal(
4667 __isl_keep isl_multi_pw_aff *mpa1,
4668 __isl_keep isl_multi_pw_aff *mpa2);
4669 int isl_multi_pw_aff_is_equal(
4670 __isl_keep isl_multi_pw_aff *mpa1,
4671 __isl_keep isl_multi_pw_aff *mpa2);
4675 #include <isl/aff.h>
4676 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4677 __isl_take isl_pw_multi_aff *pma1,
4678 __isl_take isl_pw_multi_aff *pma2);
4679 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4680 __isl_take isl_pw_multi_aff *pma1,
4681 __isl_take isl_pw_multi_aff *pma2);
4682 __isl_give isl_multi_aff *isl_multi_aff_floor(
4683 __isl_take isl_multi_aff *ma);
4684 __isl_give isl_multi_aff *isl_multi_aff_add(
4685 __isl_take isl_multi_aff *maff1,
4686 __isl_take isl_multi_aff *maff2);
4687 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4688 __isl_take isl_pw_multi_aff *pma1,
4689 __isl_take isl_pw_multi_aff *pma2);
4690 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4691 __isl_take isl_union_pw_multi_aff *upma1,
4692 __isl_take isl_union_pw_multi_aff *upma2);
4693 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4694 __isl_take isl_pw_multi_aff *pma1,
4695 __isl_take isl_pw_multi_aff *pma2);
4696 __isl_give isl_multi_aff *isl_multi_aff_sub(
4697 __isl_take isl_multi_aff *ma1,
4698 __isl_take isl_multi_aff *ma2);
4699 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4700 __isl_take isl_pw_multi_aff *pma1,
4701 __isl_take isl_pw_multi_aff *pma2);
4702 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4703 __isl_take isl_union_pw_multi_aff *upma1,
4704 __isl_take isl_union_pw_multi_aff *upma2);
4706 C<isl_multi_aff_sub> subtracts the second argument from the first.
4708 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4709 __isl_take isl_multi_aff *ma,
4710 __isl_take isl_val *v);
4711 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4712 __isl_take isl_pw_multi_aff *pma,
4713 __isl_take isl_val *v);
4714 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4715 __isl_take isl_multi_pw_aff *mpa,
4716 __isl_take isl_val *v);
4717 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4718 __isl_take isl_multi_aff *ma,
4719 __isl_take isl_multi_val *mv);
4720 __isl_give isl_pw_multi_aff *
4721 isl_pw_multi_aff_scale_multi_val(
4722 __isl_take isl_pw_multi_aff *pma,
4723 __isl_take isl_multi_val *mv);
4724 __isl_give isl_multi_pw_aff *
4725 isl_multi_pw_aff_scale_multi_val(
4726 __isl_take isl_multi_pw_aff *mpa,
4727 __isl_take isl_multi_val *mv);
4728 __isl_give isl_union_pw_multi_aff *
4729 isl_union_pw_multi_aff_scale_multi_val(
4730 __isl_take isl_union_pw_multi_aff *upma,
4731 __isl_take isl_multi_val *mv);
4732 __isl_give isl_multi_aff *
4733 isl_multi_aff_scale_down_multi_val(
4734 __isl_take isl_multi_aff *ma,
4735 __isl_take isl_multi_val *mv);
4736 __isl_give isl_multi_pw_aff *
4737 isl_multi_pw_aff_scale_down_multi_val(
4738 __isl_take isl_multi_pw_aff *mpa,
4739 __isl_take isl_multi_val *mv);
4741 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4742 by the corresponding elements of C<mv>.
4744 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4745 __isl_take isl_pw_multi_aff *pma,
4746 enum isl_dim_type type, unsigned pos, int value);
4747 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4748 __isl_take isl_pw_multi_aff *pma,
4749 __isl_take isl_set *set);
4750 __isl_give isl_set *isl_multi_pw_aff_domain(
4751 __isl_take isl_multi_pw_aff *mpa);
4752 __isl_give isl_multi_pw_aff *
4753 isl_multi_pw_aff_intersect_params(
4754 __isl_take isl_multi_pw_aff *mpa,
4755 __isl_take isl_set *set);
4756 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4757 __isl_take isl_pw_multi_aff *pma,
4758 __isl_take isl_set *set);
4759 __isl_give isl_multi_pw_aff *
4760 isl_multi_pw_aff_intersect_domain(
4761 __isl_take isl_multi_pw_aff *mpa,
4762 __isl_take isl_set *domain);
4763 __isl_give isl_union_pw_multi_aff *
4764 isl_union_pw_multi_aff_intersect_domain(
4765 __isl_take isl_union_pw_multi_aff *upma,
4766 __isl_take isl_union_set *uset);
4767 __isl_give isl_multi_aff *isl_multi_aff_lift(
4768 __isl_take isl_multi_aff *maff,
4769 __isl_give isl_local_space **ls);
4770 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4771 __isl_take isl_pw_multi_aff *pma);
4772 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4773 __isl_take isl_multi_pw_aff *mpa);
4774 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4775 __isl_take isl_multi_aff *multi,
4776 __isl_take isl_space *model);
4777 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4778 __isl_take isl_pw_multi_aff *pma,
4779 __isl_take isl_space *model);
4780 __isl_give isl_union_pw_multi_aff *
4781 isl_union_pw_multi_aff_align_params(
4782 __isl_take isl_union_pw_multi_aff *upma,
4783 __isl_take isl_space *model);
4784 __isl_give isl_pw_multi_aff *
4785 isl_pw_multi_aff_project_domain_on_params(
4786 __isl_take isl_pw_multi_aff *pma);
4787 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4788 __isl_take isl_multi_aff *maff,
4789 __isl_take isl_set *context);
4790 __isl_give isl_multi_aff *isl_multi_aff_gist(
4791 __isl_take isl_multi_aff *maff,
4792 __isl_take isl_set *context);
4793 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4794 __isl_take isl_pw_multi_aff *pma,
4795 __isl_take isl_set *set);
4796 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4797 __isl_take isl_pw_multi_aff *pma,
4798 __isl_take isl_set *set);
4799 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4800 __isl_take isl_multi_pw_aff *mpa,
4801 __isl_take isl_set *set);
4802 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4803 __isl_take isl_multi_pw_aff *mpa,
4804 __isl_take isl_set *set);
4805 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4806 __isl_take isl_multi_aff *ma);
4807 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4808 __isl_take isl_multi_pw_aff *mpa);
4809 __isl_give isl_set *isl_pw_multi_aff_domain(
4810 __isl_take isl_pw_multi_aff *pma);
4811 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4812 __isl_take isl_union_pw_multi_aff *upma);
4813 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4814 __isl_take isl_multi_aff *ma1, unsigned pos,
4815 __isl_take isl_multi_aff *ma2);
4816 __isl_give isl_multi_aff *isl_multi_aff_splice(
4817 __isl_take isl_multi_aff *ma1,
4818 unsigned in_pos, unsigned out_pos,
4819 __isl_take isl_multi_aff *ma2);
4820 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4821 __isl_take isl_multi_aff *ma1,
4822 __isl_take isl_multi_aff *ma2);
4823 __isl_give isl_multi_aff *
4824 isl_multi_aff_range_factor_domain(
4825 __isl_take isl_multi_aff *ma);
4826 __isl_give isl_multi_aff *
4827 isl_multi_aff_range_factor_range(
4828 __isl_take isl_multi_aff *ma);
4829 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4830 __isl_take isl_multi_aff *ma1,
4831 __isl_take isl_multi_aff *ma2);
4832 __isl_give isl_multi_aff *isl_multi_aff_product(
4833 __isl_take isl_multi_aff *ma1,
4834 __isl_take isl_multi_aff *ma2);
4835 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4836 __isl_take isl_multi_pw_aff *mpa1,
4837 __isl_take isl_multi_pw_aff *mpa2);
4838 __isl_give isl_pw_multi_aff *
4839 isl_pw_multi_aff_range_product(
4840 __isl_take isl_pw_multi_aff *pma1,
4841 __isl_take isl_pw_multi_aff *pma2);
4842 __isl_give isl_multi_pw_aff *
4843 isl_multi_pw_aff_range_factor_domain(
4844 __isl_take isl_multi_pw_aff *mpa);
4845 __isl_give isl_multi_pw_aff *
4846 isl_multi_pw_aff_range_factor_range(
4847 __isl_take isl_multi_pw_aff *mpa);
4848 __isl_give isl_pw_multi_aff *
4849 isl_pw_multi_aff_flat_range_product(
4850 __isl_take isl_pw_multi_aff *pma1,
4851 __isl_take isl_pw_multi_aff *pma2);
4852 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4853 __isl_take isl_pw_multi_aff *pma1,
4854 __isl_take isl_pw_multi_aff *pma2);
4855 __isl_give isl_union_pw_multi_aff *
4856 isl_union_pw_multi_aff_flat_range_product(
4857 __isl_take isl_union_pw_multi_aff *upma1,
4858 __isl_take isl_union_pw_multi_aff *upma2);
4859 __isl_give isl_multi_pw_aff *
4860 isl_multi_pw_aff_range_splice(
4861 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4862 __isl_take isl_multi_pw_aff *mpa2);
4863 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4864 __isl_take isl_multi_pw_aff *mpa1,
4865 unsigned in_pos, unsigned out_pos,
4866 __isl_take isl_multi_pw_aff *mpa2);
4867 __isl_give isl_multi_pw_aff *
4868 isl_multi_pw_aff_range_product(
4869 __isl_take isl_multi_pw_aff *mpa1,
4870 __isl_take isl_multi_pw_aff *mpa2);
4871 __isl_give isl_multi_pw_aff *
4872 isl_multi_pw_aff_flat_range_product(
4873 __isl_take isl_multi_pw_aff *mpa1,
4874 __isl_take isl_multi_pw_aff *mpa2);
4876 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4877 then it is assigned the local space that lies at the basis of
4878 the lifting applied.
4880 #include <isl/aff.h>
4881 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4882 __isl_take isl_multi_aff *ma1,
4883 __isl_take isl_multi_aff *ma2);
4884 __isl_give isl_pw_multi_aff *
4885 isl_pw_multi_aff_pullback_multi_aff(
4886 __isl_take isl_pw_multi_aff *pma,
4887 __isl_take isl_multi_aff *ma);
4888 __isl_give isl_multi_pw_aff *
4889 isl_multi_pw_aff_pullback_multi_aff(
4890 __isl_take isl_multi_pw_aff *mpa,
4891 __isl_take isl_multi_aff *ma);
4892 __isl_give isl_pw_multi_aff *
4893 isl_pw_multi_aff_pullback_pw_multi_aff(
4894 __isl_take isl_pw_multi_aff *pma1,
4895 __isl_take isl_pw_multi_aff *pma2);
4896 __isl_give isl_multi_pw_aff *
4897 isl_multi_pw_aff_pullback_pw_multi_aff(
4898 __isl_take isl_multi_pw_aff *mpa,
4899 __isl_take isl_pw_multi_aff *pma);
4900 __isl_give isl_multi_pw_aff *
4901 isl_multi_pw_aff_pullback_multi_pw_aff(
4902 __isl_take isl_multi_pw_aff *mpa1,
4903 __isl_take isl_multi_pw_aff *mpa2);
4905 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4906 In other words, C<ma2> is plugged
4909 __isl_give isl_set *isl_multi_aff_lex_le_set(
4910 __isl_take isl_multi_aff *ma1,
4911 __isl_take isl_multi_aff *ma2);
4912 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4913 __isl_take isl_multi_aff *ma1,
4914 __isl_take isl_multi_aff *ma2);
4916 The function C<isl_multi_aff_lex_le_set> returns a set
4917 containing those elements in the shared domain space
4918 where C<ma1> is lexicographically smaller than or
4921 An expression can be read from input using
4923 #include <isl/aff.h>
4924 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4925 isl_ctx *ctx, const char *str);
4926 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4927 isl_ctx *ctx, const char *str);
4928 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4929 isl_ctx *ctx, const char *str);
4930 __isl_give isl_union_pw_multi_aff *
4931 isl_union_pw_multi_aff_read_from_str(
4932 isl_ctx *ctx, const char *str);
4934 An expression can be printed using
4936 #include <isl/aff.h>
4937 __isl_give isl_printer *isl_printer_print_multi_aff(
4938 __isl_take isl_printer *p,
4939 __isl_keep isl_multi_aff *maff);
4940 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4941 __isl_take isl_printer *p,
4942 __isl_keep isl_pw_multi_aff *pma);
4943 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4944 __isl_take isl_printer *p,
4945 __isl_keep isl_union_pw_multi_aff *upma);
4946 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4947 __isl_take isl_printer *p,
4948 __isl_keep isl_multi_pw_aff *mpa);
4952 Points are elements of a set. They can be used to construct
4953 simple sets (boxes) or they can be used to represent the
4954 individual elements of a set.
4955 The zero point (the origin) can be created using
4957 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4959 The coordinates of a point can be inspected, set and changed
4962 __isl_give isl_val *isl_point_get_coordinate_val(
4963 __isl_keep isl_point *pnt,
4964 enum isl_dim_type type, int pos);
4965 __isl_give isl_point *isl_point_set_coordinate_val(
4966 __isl_take isl_point *pnt,
4967 enum isl_dim_type type, int pos,
4968 __isl_take isl_val *v);
4970 __isl_give isl_point *isl_point_add_ui(
4971 __isl_take isl_point *pnt,
4972 enum isl_dim_type type, int pos, unsigned val);
4973 __isl_give isl_point *isl_point_sub_ui(
4974 __isl_take isl_point *pnt,
4975 enum isl_dim_type type, int pos, unsigned val);
4977 Other properties can be obtained using
4979 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4981 Points can be copied or freed using
4983 __isl_give isl_point *isl_point_copy(
4984 __isl_keep isl_point *pnt);
4985 void isl_point_free(__isl_take isl_point *pnt);
4987 A singleton set can be created from a point using
4989 __isl_give isl_basic_set *isl_basic_set_from_point(
4990 __isl_take isl_point *pnt);
4991 __isl_give isl_set *isl_set_from_point(
4992 __isl_take isl_point *pnt);
4994 and a box can be created from two opposite extremal points using
4996 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4997 __isl_take isl_point *pnt1,
4998 __isl_take isl_point *pnt2);
4999 __isl_give isl_set *isl_set_box_from_points(
5000 __isl_take isl_point *pnt1,
5001 __isl_take isl_point *pnt2);
5003 All elements of a B<bounded> (union) set can be enumerated using
5004 the following functions.
5006 int isl_set_foreach_point(__isl_keep isl_set *set,
5007 int (*fn)(__isl_take isl_point *pnt, void *user),
5009 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
5010 int (*fn)(__isl_take isl_point *pnt, void *user),
5013 The function C<fn> is called for each integer point in
5014 C<set> with as second argument the last argument of
5015 the C<isl_set_foreach_point> call. The function C<fn>
5016 should return C<0> on success and C<-1> on failure.
5017 In the latter case, C<isl_set_foreach_point> will stop
5018 enumerating and return C<-1> as well.
5019 If the enumeration is performed successfully and to completion,
5020 then C<isl_set_foreach_point> returns C<0>.
5022 To obtain a single point of a (basic) set, use
5024 __isl_give isl_point *isl_basic_set_sample_point(
5025 __isl_take isl_basic_set *bset);
5026 __isl_give isl_point *isl_set_sample_point(
5027 __isl_take isl_set *set);
5029 If C<set> does not contain any (integer) points, then the
5030 resulting point will be ``void'', a property that can be
5033 int isl_point_is_void(__isl_keep isl_point *pnt);
5035 =head2 Piecewise Quasipolynomials
5037 A piecewise quasipolynomial is a particular kind of function that maps
5038 a parametric point to a rational value.
5039 More specifically, a quasipolynomial is a polynomial expression in greatest
5040 integer parts of affine expressions of parameters and variables.
5041 A piecewise quasipolynomial is a subdivision of a given parametric
5042 domain into disjoint cells with a quasipolynomial associated to
5043 each cell. The value of the piecewise quasipolynomial at a given
5044 point is the value of the quasipolynomial associated to the cell
5045 that contains the point. Outside of the union of cells,
5046 the value is assumed to be zero.
5047 For example, the piecewise quasipolynomial
5049 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
5051 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
5052 A given piecewise quasipolynomial has a fixed domain dimension.
5053 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
5054 defined over different domains.
5055 Piecewise quasipolynomials are mainly used by the C<barvinok>
5056 library for representing the number of elements in a parametric set or map.
5057 For example, the piecewise quasipolynomial above represents
5058 the number of points in the map
5060 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
5062 =head3 Input and Output
5064 Piecewise quasipolynomials can be read from input using
5066 __isl_give isl_union_pw_qpolynomial *
5067 isl_union_pw_qpolynomial_read_from_str(
5068 isl_ctx *ctx, const char *str);
5070 Quasipolynomials and piecewise quasipolynomials can be printed
5071 using the following functions.
5073 __isl_give isl_printer *isl_printer_print_qpolynomial(
5074 __isl_take isl_printer *p,
5075 __isl_keep isl_qpolynomial *qp);
5077 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
5078 __isl_take isl_printer *p,
5079 __isl_keep isl_pw_qpolynomial *pwqp);
5081 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
5082 __isl_take isl_printer *p,
5083 __isl_keep isl_union_pw_qpolynomial *upwqp);
5085 The output format of the printer
5086 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5087 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
5089 In case of printing in C<ISL_FORMAT_C>, the user may want
5090 to set the names of all dimensions
5092 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
5093 __isl_take isl_qpolynomial *qp,
5094 enum isl_dim_type type, unsigned pos,
5096 __isl_give isl_pw_qpolynomial *
5097 isl_pw_qpolynomial_set_dim_name(
5098 __isl_take isl_pw_qpolynomial *pwqp,
5099 enum isl_dim_type type, unsigned pos,
5102 =head3 Creating New (Piecewise) Quasipolynomials
5104 Some simple quasipolynomials can be created using the following functions.
5105 More complicated quasipolynomials can be created by applying
5106 operations such as addition and multiplication
5107 on the resulting quasipolynomials
5109 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
5110 __isl_take isl_space *domain);
5111 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
5112 __isl_take isl_space *domain);
5113 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
5114 __isl_take isl_space *domain);
5115 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
5116 __isl_take isl_space *domain);
5117 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
5118 __isl_take isl_space *domain);
5119 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
5120 __isl_take isl_space *domain,
5121 __isl_take isl_val *val);
5122 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
5123 __isl_take isl_space *domain,
5124 enum isl_dim_type type, unsigned pos);
5125 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
5126 __isl_take isl_aff *aff);
5128 Note that the space in which a quasipolynomial lives is a map space
5129 with a one-dimensional range. The C<domain> argument in some of
5130 the functions above corresponds to the domain of this map space.
5132 The zero piecewise quasipolynomial or a piecewise quasipolynomial
5133 with a single cell can be created using the following functions.
5134 Multiple of these single cell piecewise quasipolynomials can
5135 be combined to create more complicated piecewise quasipolynomials.
5137 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
5138 __isl_take isl_space *space);
5139 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
5140 __isl_take isl_set *set,
5141 __isl_take isl_qpolynomial *qp);
5142 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
5143 __isl_take isl_qpolynomial *qp);
5144 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
5145 __isl_take isl_pw_aff *pwaff);
5147 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
5148 __isl_take isl_space *space);
5149 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
5150 __isl_take isl_pw_qpolynomial *pwqp);
5151 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
5152 __isl_take isl_union_pw_qpolynomial *upwqp,
5153 __isl_take isl_pw_qpolynomial *pwqp);
5155 Quasipolynomials can be copied and freed again using the following
5158 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
5159 __isl_keep isl_qpolynomial *qp);
5160 __isl_null isl_qpolynomial *isl_qpolynomial_free(
5161 __isl_take isl_qpolynomial *qp);
5163 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
5164 __isl_keep isl_pw_qpolynomial *pwqp);
5165 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
5166 __isl_take isl_pw_qpolynomial *pwqp);
5168 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
5169 __isl_keep isl_union_pw_qpolynomial *upwqp);
5170 __isl_null isl_union_pw_qpolynomial *
5171 isl_union_pw_qpolynomial_free(
5172 __isl_take isl_union_pw_qpolynomial *upwqp);
5174 =head3 Inspecting (Piecewise) Quasipolynomials
5176 To iterate over all piecewise quasipolynomials in a union
5177 piecewise quasipolynomial, use the following function
5179 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
5180 __isl_keep isl_union_pw_qpolynomial *upwqp,
5181 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
5184 To extract the piecewise quasipolynomial in a given space from a union, use
5186 __isl_give isl_pw_qpolynomial *
5187 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
5188 __isl_keep isl_union_pw_qpolynomial *upwqp,
5189 __isl_take isl_space *space);
5191 To iterate over the cells in a piecewise quasipolynomial,
5192 use either of the following two functions
5194 int isl_pw_qpolynomial_foreach_piece(
5195 __isl_keep isl_pw_qpolynomial *pwqp,
5196 int (*fn)(__isl_take isl_set *set,
5197 __isl_take isl_qpolynomial *qp,
5198 void *user), void *user);
5199 int isl_pw_qpolynomial_foreach_lifted_piece(
5200 __isl_keep isl_pw_qpolynomial *pwqp,
5201 int (*fn)(__isl_take isl_set *set,
5202 __isl_take isl_qpolynomial *qp,
5203 void *user), void *user);
5205 As usual, the function C<fn> should return C<0> on success
5206 and C<-1> on failure. The difference between
5207 C<isl_pw_qpolynomial_foreach_piece> and
5208 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
5209 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
5210 compute unique representations for all existentially quantified
5211 variables and then turn these existentially quantified variables
5212 into extra set variables, adapting the associated quasipolynomial
5213 accordingly. This means that the C<set> passed to C<fn>
5214 will not have any existentially quantified variables, but that
5215 the dimensions of the sets may be different for different
5216 invocations of C<fn>.
5218 The constant term of a quasipolynomial can be extracted using
5220 __isl_give isl_val *isl_qpolynomial_get_constant_val(
5221 __isl_keep isl_qpolynomial *qp);
5223 To iterate over all terms in a quasipolynomial,
5226 int isl_qpolynomial_foreach_term(
5227 __isl_keep isl_qpolynomial *qp,
5228 int (*fn)(__isl_take isl_term *term,
5229 void *user), void *user);
5231 The terms themselves can be inspected and freed using
5234 unsigned isl_term_dim(__isl_keep isl_term *term,
5235 enum isl_dim_type type);
5236 __isl_give isl_val *isl_term_get_coefficient_val(
5237 __isl_keep isl_term *term);
5238 int isl_term_get_exp(__isl_keep isl_term *term,
5239 enum isl_dim_type type, unsigned pos);
5240 __isl_give isl_aff *isl_term_get_div(
5241 __isl_keep isl_term *term, unsigned pos);
5242 void isl_term_free(__isl_take isl_term *term);
5244 Each term is a product of parameters, set variables and
5245 integer divisions. The function C<isl_term_get_exp>
5246 returns the exponent of a given dimensions in the given term.
5248 =head3 Properties of (Piecewise) Quasipolynomials
5250 To check whether two union piecewise quasipolynomials are
5251 obviously equal, use
5253 int isl_union_pw_qpolynomial_plain_is_equal(
5254 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5255 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5257 =head3 Operations on (Piecewise) Quasipolynomials
5259 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5260 __isl_take isl_qpolynomial *qp,
5261 __isl_take isl_val *v);
5262 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5263 __isl_take isl_qpolynomial *qp);
5264 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5265 __isl_take isl_qpolynomial *qp1,
5266 __isl_take isl_qpolynomial *qp2);
5267 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5268 __isl_take isl_qpolynomial *qp1,
5269 __isl_take isl_qpolynomial *qp2);
5270 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5271 __isl_take isl_qpolynomial *qp1,
5272 __isl_take isl_qpolynomial *qp2);
5273 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5274 __isl_take isl_qpolynomial *qp, unsigned exponent);
5276 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5277 __isl_take isl_pw_qpolynomial *pwqp,
5278 enum isl_dim_type type, unsigned n,
5279 __isl_take isl_val *v);
5280 __isl_give isl_pw_qpolynomial *
5281 isl_pw_qpolynomial_scale_val(
5282 __isl_take isl_pw_qpolynomial *pwqp,
5283 __isl_take isl_val *v);
5284 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5285 __isl_take isl_pw_qpolynomial *pwqp1,
5286 __isl_take isl_pw_qpolynomial *pwqp2);
5287 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5288 __isl_take isl_pw_qpolynomial *pwqp1,
5289 __isl_take isl_pw_qpolynomial *pwqp2);
5290 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5291 __isl_take isl_pw_qpolynomial *pwqp1,
5292 __isl_take isl_pw_qpolynomial *pwqp2);
5293 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5294 __isl_take isl_pw_qpolynomial *pwqp);
5295 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5296 __isl_take isl_pw_qpolynomial *pwqp1,
5297 __isl_take isl_pw_qpolynomial *pwqp2);
5298 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5299 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5301 __isl_give isl_union_pw_qpolynomial *
5302 isl_union_pw_qpolynomial_scale_val(
5303 __isl_take isl_union_pw_qpolynomial *upwqp,
5304 __isl_take isl_val *v);
5305 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5306 __isl_take isl_union_pw_qpolynomial *upwqp1,
5307 __isl_take isl_union_pw_qpolynomial *upwqp2);
5308 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5309 __isl_take isl_union_pw_qpolynomial *upwqp1,
5310 __isl_take isl_union_pw_qpolynomial *upwqp2);
5311 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5312 __isl_take isl_union_pw_qpolynomial *upwqp1,
5313 __isl_take isl_union_pw_qpolynomial *upwqp2);
5315 __isl_give isl_val *isl_pw_qpolynomial_eval(
5316 __isl_take isl_pw_qpolynomial *pwqp,
5317 __isl_take isl_point *pnt);
5319 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5320 __isl_take isl_union_pw_qpolynomial *upwqp,
5321 __isl_take isl_point *pnt);
5323 __isl_give isl_set *isl_pw_qpolynomial_domain(
5324 __isl_take isl_pw_qpolynomial *pwqp);
5325 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5326 __isl_take isl_pw_qpolynomial *pwpq,
5327 __isl_take isl_set *set);
5328 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5329 __isl_take isl_pw_qpolynomial *pwpq,
5330 __isl_take isl_set *set);
5332 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5333 __isl_take isl_union_pw_qpolynomial *upwqp);
5334 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5335 __isl_take isl_union_pw_qpolynomial *upwpq,
5336 __isl_take isl_union_set *uset);
5337 __isl_give isl_union_pw_qpolynomial *
5338 isl_union_pw_qpolynomial_intersect_params(
5339 __isl_take isl_union_pw_qpolynomial *upwpq,
5340 __isl_take isl_set *set);
5342 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5343 __isl_take isl_qpolynomial *qp,
5344 __isl_take isl_space *model);
5346 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5347 __isl_take isl_qpolynomial *qp);
5348 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5349 __isl_take isl_pw_qpolynomial *pwqp);
5351 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5352 __isl_take isl_union_pw_qpolynomial *upwqp);
5354 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5355 __isl_take isl_qpolynomial *qp,
5356 __isl_take isl_set *context);
5357 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5358 __isl_take isl_qpolynomial *qp,
5359 __isl_take isl_set *context);
5361 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5362 __isl_take isl_pw_qpolynomial *pwqp,
5363 __isl_take isl_set *context);
5364 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5365 __isl_take isl_pw_qpolynomial *pwqp,
5366 __isl_take isl_set *context);
5368 __isl_give isl_union_pw_qpolynomial *
5369 isl_union_pw_qpolynomial_gist_params(
5370 __isl_take isl_union_pw_qpolynomial *upwqp,
5371 __isl_take isl_set *context);
5372 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5373 __isl_take isl_union_pw_qpolynomial *upwqp,
5374 __isl_take isl_union_set *context);
5376 The gist operation applies the gist operation to each of
5377 the cells in the domain of the input piecewise quasipolynomial.
5378 The context is also exploited
5379 to simplify the quasipolynomials associated to each cell.
5381 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5382 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5383 __isl_give isl_union_pw_qpolynomial *
5384 isl_union_pw_qpolynomial_to_polynomial(
5385 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5387 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5388 the polynomial will be an overapproximation. If C<sign> is negative,
5389 it will be an underapproximation. If C<sign> is zero, the approximation
5390 will lie somewhere in between.
5392 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5394 A piecewise quasipolynomial reduction is a piecewise
5395 reduction (or fold) of quasipolynomials.
5396 In particular, the reduction can be maximum or a minimum.
5397 The objects are mainly used to represent the result of
5398 an upper or lower bound on a quasipolynomial over its domain,
5399 i.e., as the result of the following function.
5401 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5402 __isl_take isl_pw_qpolynomial *pwqp,
5403 enum isl_fold type, int *tight);
5405 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5406 __isl_take isl_union_pw_qpolynomial *upwqp,
5407 enum isl_fold type, int *tight);
5409 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5410 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5411 is the returned bound is known be tight, i.e., for each value
5412 of the parameters there is at least
5413 one element in the domain that reaches the bound.
5414 If the domain of C<pwqp> is not wrapping, then the bound is computed
5415 over all elements in that domain and the result has a purely parametric
5416 domain. If the domain of C<pwqp> is wrapping, then the bound is
5417 computed over the range of the wrapped relation. The domain of the
5418 wrapped relation becomes the domain of the result.
5420 A (piecewise) quasipolynomial reduction can be copied or freed using the
5421 following functions.
5423 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5424 __isl_keep isl_qpolynomial_fold *fold);
5425 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5426 __isl_keep isl_pw_qpolynomial_fold *pwf);
5427 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5428 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5429 void isl_qpolynomial_fold_free(
5430 __isl_take isl_qpolynomial_fold *fold);
5431 __isl_null isl_pw_qpolynomial_fold *
5432 isl_pw_qpolynomial_fold_free(
5433 __isl_take isl_pw_qpolynomial_fold *pwf);
5434 __isl_null isl_union_pw_qpolynomial_fold *
5435 isl_union_pw_qpolynomial_fold_free(
5436 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5438 =head3 Printing Piecewise Quasipolynomial Reductions
5440 Piecewise quasipolynomial reductions can be printed
5441 using the following function.
5443 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5444 __isl_take isl_printer *p,
5445 __isl_keep isl_pw_qpolynomial_fold *pwf);
5446 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5447 __isl_take isl_printer *p,
5448 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5450 For C<isl_printer_print_pw_qpolynomial_fold>,
5451 output format of the printer
5452 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5453 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5454 output format of the printer
5455 needs to be set to C<ISL_FORMAT_ISL>.
5456 In case of printing in C<ISL_FORMAT_C>, the user may want
5457 to set the names of all dimensions
5459 __isl_give isl_pw_qpolynomial_fold *
5460 isl_pw_qpolynomial_fold_set_dim_name(
5461 __isl_take isl_pw_qpolynomial_fold *pwf,
5462 enum isl_dim_type type, unsigned pos,
5465 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5467 To iterate over all piecewise quasipolynomial reductions in a union
5468 piecewise quasipolynomial reduction, use the following function
5470 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5471 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5472 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5473 void *user), void *user);
5475 To iterate over the cells in a piecewise quasipolynomial reduction,
5476 use either of the following two functions
5478 int isl_pw_qpolynomial_fold_foreach_piece(
5479 __isl_keep isl_pw_qpolynomial_fold *pwf,
5480 int (*fn)(__isl_take isl_set *set,
5481 __isl_take isl_qpolynomial_fold *fold,
5482 void *user), void *user);
5483 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5484 __isl_keep isl_pw_qpolynomial_fold *pwf,
5485 int (*fn)(__isl_take isl_set *set,
5486 __isl_take isl_qpolynomial_fold *fold,
5487 void *user), void *user);
5489 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5490 of the difference between these two functions.
5492 To iterate over all quasipolynomials in a reduction, use
5494 int isl_qpolynomial_fold_foreach_qpolynomial(
5495 __isl_keep isl_qpolynomial_fold *fold,
5496 int (*fn)(__isl_take isl_qpolynomial *qp,
5497 void *user), void *user);
5499 =head3 Properties of Piecewise Quasipolynomial Reductions
5501 To check whether two union piecewise quasipolynomial reductions are
5502 obviously equal, use
5504 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5505 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5506 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5508 =head3 Operations on Piecewise Quasipolynomial Reductions
5510 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5511 __isl_take isl_qpolynomial_fold *fold,
5512 __isl_take isl_val *v);
5513 __isl_give isl_pw_qpolynomial_fold *
5514 isl_pw_qpolynomial_fold_scale_val(
5515 __isl_take isl_pw_qpolynomial_fold *pwf,
5516 __isl_take isl_val *v);
5517 __isl_give isl_union_pw_qpolynomial_fold *
5518 isl_union_pw_qpolynomial_fold_scale_val(
5519 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5520 __isl_take isl_val *v);
5522 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5523 __isl_take isl_pw_qpolynomial_fold *pwf1,
5524 __isl_take isl_pw_qpolynomial_fold *pwf2);
5526 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5527 __isl_take isl_pw_qpolynomial_fold *pwf1,
5528 __isl_take isl_pw_qpolynomial_fold *pwf2);
5530 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5531 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5532 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5534 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5535 __isl_take isl_pw_qpolynomial_fold *pwf,
5536 __isl_take isl_point *pnt);
5538 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5539 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5540 __isl_take isl_point *pnt);
5542 __isl_give isl_pw_qpolynomial_fold *
5543 isl_pw_qpolynomial_fold_intersect_params(
5544 __isl_take isl_pw_qpolynomial_fold *pwf,
5545 __isl_take isl_set *set);
5547 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5548 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5549 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5550 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5551 __isl_take isl_union_set *uset);
5552 __isl_give isl_union_pw_qpolynomial_fold *
5553 isl_union_pw_qpolynomial_fold_intersect_params(
5554 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5555 __isl_take isl_set *set);
5557 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5558 __isl_take isl_pw_qpolynomial_fold *pwf);
5560 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5561 __isl_take isl_pw_qpolynomial_fold *pwf);
5563 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5564 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5566 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5567 __isl_take isl_qpolynomial_fold *fold,
5568 __isl_take isl_set *context);
5569 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5570 __isl_take isl_qpolynomial_fold *fold,
5571 __isl_take isl_set *context);
5573 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5574 __isl_take isl_pw_qpolynomial_fold *pwf,
5575 __isl_take isl_set *context);
5576 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5577 __isl_take isl_pw_qpolynomial_fold *pwf,
5578 __isl_take isl_set *context);
5580 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5581 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5582 __isl_take isl_union_set *context);
5583 __isl_give isl_union_pw_qpolynomial_fold *
5584 isl_union_pw_qpolynomial_fold_gist_params(
5585 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5586 __isl_take isl_set *context);
5588 The gist operation applies the gist operation to each of
5589 the cells in the domain of the input piecewise quasipolynomial reduction.
5590 In future, the operation will also exploit the context
5591 to simplify the quasipolynomial reductions associated to each cell.
5593 __isl_give isl_pw_qpolynomial_fold *
5594 isl_set_apply_pw_qpolynomial_fold(
5595 __isl_take isl_set *set,
5596 __isl_take isl_pw_qpolynomial_fold *pwf,
5598 __isl_give isl_pw_qpolynomial_fold *
5599 isl_map_apply_pw_qpolynomial_fold(
5600 __isl_take isl_map *map,
5601 __isl_take isl_pw_qpolynomial_fold *pwf,
5603 __isl_give isl_union_pw_qpolynomial_fold *
5604 isl_union_set_apply_union_pw_qpolynomial_fold(
5605 __isl_take isl_union_set *uset,
5606 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5608 __isl_give isl_union_pw_qpolynomial_fold *
5609 isl_union_map_apply_union_pw_qpolynomial_fold(
5610 __isl_take isl_union_map *umap,
5611 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5614 The functions taking a map
5615 compose the given map with the given piecewise quasipolynomial reduction.
5616 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5617 over all elements in the intersection of the range of the map
5618 and the domain of the piecewise quasipolynomial reduction
5619 as a function of an element in the domain of the map.
5620 The functions taking a set compute a bound over all elements in the
5621 intersection of the set and the domain of the
5622 piecewise quasipolynomial reduction.
5624 =head2 Parametric Vertex Enumeration
5626 The parametric vertex enumeration described in this section
5627 is mainly intended to be used internally and by the C<barvinok>
5630 #include <isl/vertices.h>
5631 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5632 __isl_keep isl_basic_set *bset);
5634 The function C<isl_basic_set_compute_vertices> performs the
5635 actual computation of the parametric vertices and the chamber
5636 decomposition and store the result in an C<isl_vertices> object.
5637 This information can be queried by either iterating over all
5638 the vertices or iterating over all the chambers or cells
5639 and then iterating over all vertices that are active on the chamber.
5641 int isl_vertices_foreach_vertex(
5642 __isl_keep isl_vertices *vertices,
5643 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5646 int isl_vertices_foreach_cell(
5647 __isl_keep isl_vertices *vertices,
5648 int (*fn)(__isl_take isl_cell *cell, void *user),
5650 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5651 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5654 Other operations that can be performed on an C<isl_vertices> object are
5657 isl_ctx *isl_vertices_get_ctx(
5658 __isl_keep isl_vertices *vertices);
5659 int isl_vertices_get_n_vertices(
5660 __isl_keep isl_vertices *vertices);
5661 void isl_vertices_free(__isl_take isl_vertices *vertices);
5663 Vertices can be inspected and destroyed using the following functions.
5665 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5666 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5667 __isl_give isl_basic_set *isl_vertex_get_domain(
5668 __isl_keep isl_vertex *vertex);
5669 __isl_give isl_multi_aff *isl_vertex_get_expr(
5670 __isl_keep isl_vertex *vertex);
5671 void isl_vertex_free(__isl_take isl_vertex *vertex);
5673 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
5674 describing the vertex in terms of the parameters,
5675 while C<isl_vertex_get_domain> returns the activity domain
5678 Chambers can be inspected and destroyed using the following functions.
5680 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5681 __isl_give isl_basic_set *isl_cell_get_domain(
5682 __isl_keep isl_cell *cell);
5683 void isl_cell_free(__isl_take isl_cell *cell);
5685 =head1 Polyhedral Compilation Library
5687 This section collects functionality in C<isl> that has been specifically
5688 designed for use during polyhedral compilation.
5690 =head2 Dependence Analysis
5692 C<isl> contains specialized functionality for performing
5693 array dataflow analysis. That is, given a I<sink> access relation
5694 and a collection of possible I<source> access relations,
5695 C<isl> can compute relations that describe
5696 for each iteration of the sink access, which iteration
5697 of which of the source access relations was the last
5698 to access the same data element before the given iteration
5700 The resulting dependence relations map source iterations
5701 to the corresponding sink iterations.
5702 To compute standard flow dependences, the sink should be
5703 a read, while the sources should be writes.
5704 If any of the source accesses are marked as being I<may>
5705 accesses, then there will be a dependence from the last
5706 I<must> access B<and> from any I<may> access that follows
5707 this last I<must> access.
5708 In particular, if I<all> sources are I<may> accesses,
5709 then memory based dependence analysis is performed.
5710 If, on the other hand, all sources are I<must> accesses,
5711 then value based dependence analysis is performed.
5713 #include <isl/flow.h>
5715 typedef int (*isl_access_level_before)(void *first, void *second);
5717 __isl_give isl_access_info *isl_access_info_alloc(
5718 __isl_take isl_map *sink,
5719 void *sink_user, isl_access_level_before fn,
5721 __isl_give isl_access_info *isl_access_info_add_source(
5722 __isl_take isl_access_info *acc,
5723 __isl_take isl_map *source, int must,
5725 __isl_null isl_access_info *isl_access_info_free(
5726 __isl_take isl_access_info *acc);
5728 __isl_give isl_flow *isl_access_info_compute_flow(
5729 __isl_take isl_access_info *acc);
5731 int isl_flow_foreach(__isl_keep isl_flow *deps,
5732 int (*fn)(__isl_take isl_map *dep, int must,
5733 void *dep_user, void *user),
5735 __isl_give isl_map *isl_flow_get_no_source(
5736 __isl_keep isl_flow *deps, int must);
5737 void isl_flow_free(__isl_take isl_flow *deps);
5739 The function C<isl_access_info_compute_flow> performs the actual
5740 dependence analysis. The other functions are used to construct
5741 the input for this function or to read off the output.
5743 The input is collected in an C<isl_access_info>, which can
5744 be created through a call to C<isl_access_info_alloc>.
5745 The arguments to this functions are the sink access relation
5746 C<sink>, a token C<sink_user> used to identify the sink
5747 access to the user, a callback function for specifying the
5748 relative order of source and sink accesses, and the number
5749 of source access relations that will be added.
5750 The callback function has type C<int (*)(void *first, void *second)>.
5751 The function is called with two user supplied tokens identifying
5752 either a source or the sink and it should return the shared nesting
5753 level and the relative order of the two accesses.
5754 In particular, let I<n> be the number of loops shared by
5755 the two accesses. If C<first> precedes C<second> textually,
5756 then the function should return I<2 * n + 1>; otherwise,
5757 it should return I<2 * n>.
5758 The sources can be added to the C<isl_access_info> by performing
5759 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5760 C<must> indicates whether the source is a I<must> access
5761 or a I<may> access. Note that a multi-valued access relation
5762 should only be marked I<must> if every iteration in the domain
5763 of the relation accesses I<all> elements in its image.
5764 The C<source_user> token is again used to identify
5765 the source access. The range of the source access relation
5766 C<source> should have the same dimension as the range
5767 of the sink access relation.
5768 The C<isl_access_info_free> function should usually not be
5769 called explicitly, because it is called implicitly by
5770 C<isl_access_info_compute_flow>.
5772 The result of the dependence analysis is collected in an
5773 C<isl_flow>. There may be elements of
5774 the sink access for which no preceding source access could be
5775 found or for which all preceding sources are I<may> accesses.
5776 The relations containing these elements can be obtained through
5777 calls to C<isl_flow_get_no_source>, the first with C<must> set
5778 and the second with C<must> unset.
5779 In the case of standard flow dependence analysis,
5780 with the sink a read and the sources I<must> writes,
5781 the first relation corresponds to the reads from uninitialized
5782 array elements and the second relation is empty.
5783 The actual flow dependences can be extracted using
5784 C<isl_flow_foreach>. This function will call the user-specified
5785 callback function C<fn> for each B<non-empty> dependence between
5786 a source and the sink. The callback function is called
5787 with four arguments, the actual flow dependence relation
5788 mapping source iterations to sink iterations, a boolean that
5789 indicates whether it is a I<must> or I<may> dependence, a token
5790 identifying the source and an additional C<void *> with value
5791 equal to the third argument of the C<isl_flow_foreach> call.
5792 A dependence is marked I<must> if it originates from a I<must>
5793 source and if it is not followed by any I<may> sources.
5795 After finishing with an C<isl_flow>, the user should call
5796 C<isl_flow_free> to free all associated memory.
5798 A higher-level interface to dependence analysis is provided
5799 by the following function.
5801 #include <isl/flow.h>
5803 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5804 __isl_take isl_union_map *must_source,
5805 __isl_take isl_union_map *may_source,
5806 __isl_take isl_union_map *schedule,
5807 __isl_give isl_union_map **must_dep,
5808 __isl_give isl_union_map **may_dep,
5809 __isl_give isl_union_map **must_no_source,
5810 __isl_give isl_union_map **may_no_source);
5812 The arrays are identified by the tuple names of the ranges
5813 of the accesses. The iteration domains by the tuple names
5814 of the domains of the accesses and of the schedule.
5815 The relative order of the iteration domains is given by the
5816 schedule. The relations returned through C<must_no_source>
5817 and C<may_no_source> are subsets of C<sink>.
5818 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5819 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5820 any of the other arguments is treated as an error.
5822 =head3 Interaction with Dependence Analysis
5824 During the dependence analysis, we frequently need to perform
5825 the following operation. Given a relation between sink iterations
5826 and potential source iterations from a particular source domain,
5827 what is the last potential source iteration corresponding to each
5828 sink iteration. It can sometimes be convenient to adjust
5829 the set of potential source iterations before or after each such operation.
5830 The prototypical example is fuzzy array dataflow analysis,
5831 where we need to analyze if, based on data-dependent constraints,
5832 the sink iteration can ever be executed without one or more of
5833 the corresponding potential source iterations being executed.
5834 If so, we can introduce extra parameters and select an unknown
5835 but fixed source iteration from the potential source iterations.
5836 To be able to perform such manipulations, C<isl> provides the following
5839 #include <isl/flow.h>
5841 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5842 __isl_keep isl_map *source_map,
5843 __isl_keep isl_set *sink, void *source_user,
5845 __isl_give isl_access_info *isl_access_info_set_restrict(
5846 __isl_take isl_access_info *acc,
5847 isl_access_restrict fn, void *user);
5849 The function C<isl_access_info_set_restrict> should be called
5850 before calling C<isl_access_info_compute_flow> and registers a callback function
5851 that will be called any time C<isl> is about to compute the last
5852 potential source. The first argument is the (reverse) proto-dependence,
5853 mapping sink iterations to potential source iterations.
5854 The second argument represents the sink iterations for which
5855 we want to compute the last source iteration.
5856 The third argument is the token corresponding to the source
5857 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5858 The callback is expected to return a restriction on either the input or
5859 the output of the operation computing the last potential source.
5860 If the input needs to be restricted then restrictions are needed
5861 for both the source and the sink iterations. The sink iterations
5862 and the potential source iterations will be intersected with these sets.
5863 If the output needs to be restricted then only a restriction on the source
5864 iterations is required.
5865 If any error occurs, the callback should return C<NULL>.
5866 An C<isl_restriction> object can be created, freed and inspected
5867 using the following functions.
5869 #include <isl/flow.h>
5871 __isl_give isl_restriction *isl_restriction_input(
5872 __isl_take isl_set *source_restr,
5873 __isl_take isl_set *sink_restr);
5874 __isl_give isl_restriction *isl_restriction_output(
5875 __isl_take isl_set *source_restr);
5876 __isl_give isl_restriction *isl_restriction_none(
5877 __isl_take isl_map *source_map);
5878 __isl_give isl_restriction *isl_restriction_empty(
5879 __isl_take isl_map *source_map);
5880 __isl_null isl_restriction *isl_restriction_free(
5881 __isl_take isl_restriction *restr);
5882 isl_ctx *isl_restriction_get_ctx(
5883 __isl_keep isl_restriction *restr);
5885 C<isl_restriction_none> and C<isl_restriction_empty> are special
5886 cases of C<isl_restriction_input>. C<isl_restriction_none>
5887 is essentially equivalent to
5889 isl_restriction_input(isl_set_universe(
5890 isl_space_range(isl_map_get_space(source_map))),
5892 isl_space_domain(isl_map_get_space(source_map))));
5894 whereas C<isl_restriction_empty> is essentially equivalent to
5896 isl_restriction_input(isl_set_empty(
5897 isl_space_range(isl_map_get_space(source_map))),
5899 isl_space_domain(isl_map_get_space(source_map))));
5903 B<The functionality described in this section is fairly new
5904 and may be subject to change.>
5906 #include <isl/schedule.h>
5907 __isl_give isl_schedule *
5908 isl_schedule_constraints_compute_schedule(
5909 __isl_take isl_schedule_constraints *sc);
5910 __isl_null isl_schedule *isl_schedule_free(
5911 __isl_take isl_schedule *sched);
5913 The function C<isl_schedule_constraints_compute_schedule> can be
5914 used to compute a schedule that satisfy the given schedule constraints.
5915 These schedule constraints include the iteration domain for which
5916 a schedule should be computed and dependences between pairs of
5917 iterations. In particular, these dependences include
5918 I<validity> dependences and I<proximity> dependences.
5919 By default, the algorithm used to construct the schedule is similar
5920 to that of C<Pluto>.
5921 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5923 The generated schedule respects all validity dependences.
5924 That is, all dependence distances over these dependences in the
5925 scheduled space are lexicographically positive.
5926 The default algorithm tries to ensure that the dependence distances
5927 over coincidence constraints are zero and to minimize the
5928 dependence distances over proximity dependences.
5929 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5930 for groups of domains where the dependence distances over validity
5931 dependences have only non-negative values.
5932 When using Feautrier's algorithm, the coincidence and proximity constraints
5933 are only taken into account during the extension to a
5934 full-dimensional schedule.
5936 An C<isl_schedule_constraints> object can be constructed
5937 and manipulated using the following functions.
5939 #include <isl/schedule.h>
5940 __isl_give isl_schedule_constraints *
5941 isl_schedule_constraints_copy(
5942 __isl_keep isl_schedule_constraints *sc);
5943 __isl_give isl_schedule_constraints *
5944 isl_schedule_constraints_on_domain(
5945 __isl_take isl_union_set *domain);
5946 isl_ctx *isl_schedule_constraints_get_ctx(
5947 __isl_keep isl_schedule_constraints *sc);
5948 __isl_give isl_schedule_constraints *
5949 isl_schedule_constraints_set_validity(
5950 __isl_take isl_schedule_constraints *sc,
5951 __isl_take isl_union_map *validity);
5952 __isl_give isl_schedule_constraints *
5953 isl_schedule_constraints_set_coincidence(
5954 __isl_take isl_schedule_constraints *sc,
5955 __isl_take isl_union_map *coincidence);
5956 __isl_give isl_schedule_constraints *
5957 isl_schedule_constraints_set_proximity(
5958 __isl_take isl_schedule_constraints *sc,
5959 __isl_take isl_union_map *proximity);
5960 __isl_give isl_schedule_constraints *
5961 isl_schedule_constraints_set_conditional_validity(
5962 __isl_take isl_schedule_constraints *sc,
5963 __isl_take isl_union_map *condition,
5964 __isl_take isl_union_map *validity);
5965 __isl_null isl_schedule_constraints *
5966 isl_schedule_constraints_free(
5967 __isl_take isl_schedule_constraints *sc);
5969 The initial C<isl_schedule_constraints> object created by
5970 C<isl_schedule_constraints_on_domain> does not impose any constraints.
5971 That is, it has an empty set of dependences.
5972 The function C<isl_schedule_constraints_set_validity> replaces the
5973 validity dependences, mapping domain elements I<i> to domain
5974 elements that should be scheduled after I<i>.
5975 The function C<isl_schedule_constraints_set_coincidence> replaces the
5976 coincidence dependences, mapping domain elements I<i> to domain
5977 elements that should be scheduled together with I<I>, if possible.
5978 The function C<isl_schedule_constraints_set_proximity> replaces the
5979 proximity dependences, mapping domain elements I<i> to domain
5980 elements that should be scheduled either before I<I>
5981 or as early as possible after I<i>.
5983 The function C<isl_schedule_constraints_set_conditional_validity>
5984 replaces the conditional validity constraints.
5985 A conditional validity constraint is only imposed when any of the corresponding
5986 conditions is satisfied, i.e., when any of them is non-zero.
5987 That is, the scheduler ensures that within each band if the dependence
5988 distances over the condition constraints are not all zero
5989 then all corresponding conditional validity constraints are respected.
5990 A conditional validity constraint corresponds to a condition
5991 if the two are adjacent, i.e., if the domain of one relation intersect
5992 the range of the other relation.
5993 The typical use case of conditional validity constraints is
5994 to allow order constraints between live ranges to be violated
5995 as long as the live ranges themselves are local to the band.
5996 To allow more fine-grained control over which conditions correspond
5997 to which conditional validity constraints, the domains and ranges
5998 of these relations may include I<tags>. That is, the domains and
5999 ranges of those relation may themselves be wrapped relations
6000 where the iteration domain appears in the domain of those wrapped relations
6001 and the range of the wrapped relations can be arbitrarily chosen
6002 by the user. Conditions and conditional validity constraints are only
6003 considere adjacent to each other if the entire wrapped relation matches.
6004 In particular, a relation with a tag will never be considered adjacent
6005 to a relation without a tag.
6007 The following function computes a schedule directly from
6008 an iteration domain and validity and proximity dependences
6009 and is implemented in terms of the functions described above.
6010 The use of C<isl_union_set_compute_schedule> is discouraged.
6012 #include <isl/schedule.h>
6013 __isl_give isl_schedule *isl_union_set_compute_schedule(
6014 __isl_take isl_union_set *domain,
6015 __isl_take isl_union_map *validity,
6016 __isl_take isl_union_map *proximity);
6018 A mapping from the domains to the scheduled space can be obtained
6019 from an C<isl_schedule> using the following function.
6021 __isl_give isl_union_map *isl_schedule_get_map(
6022 __isl_keep isl_schedule *sched);
6024 A representation of the schedule can be printed using
6026 __isl_give isl_printer *isl_printer_print_schedule(
6027 __isl_take isl_printer *p,
6028 __isl_keep isl_schedule *schedule);
6030 A representation of the schedule as a forest of bands can be obtained
6031 using the following function.
6033 __isl_give isl_band_list *isl_schedule_get_band_forest(
6034 __isl_keep isl_schedule *schedule);
6036 The individual bands can be visited in depth-first post-order
6037 using the following function.
6039 #include <isl/schedule.h>
6040 int isl_schedule_foreach_band(
6041 __isl_keep isl_schedule *sched,
6042 int (*fn)(__isl_keep isl_band *band, void *user),
6045 The list can be manipulated as explained in L<"Lists">.
6046 The bands inside the list can be copied and freed using the following
6049 #include <isl/band.h>
6050 __isl_give isl_band *isl_band_copy(
6051 __isl_keep isl_band *band);
6052 __isl_null isl_band *isl_band_free(
6053 __isl_take isl_band *band);
6055 Each band contains zero or more scheduling dimensions.
6056 These are referred to as the members of the band.
6057 The section of the schedule that corresponds to the band is
6058 referred to as the partial schedule of the band.
6059 For those nodes that participate in a band, the outer scheduling
6060 dimensions form the prefix schedule, while the inner scheduling
6061 dimensions form the suffix schedule.
6062 That is, if we take a cut of the band forest, then the union of
6063 the concatenations of the prefix, partial and suffix schedules of
6064 each band in the cut is equal to the entire schedule (modulo
6065 some possible padding at the end with zero scheduling dimensions).
6066 The properties of a band can be inspected using the following functions.
6068 #include <isl/band.h>
6069 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
6071 int isl_band_has_children(__isl_keep isl_band *band);
6072 __isl_give isl_band_list *isl_band_get_children(
6073 __isl_keep isl_band *band);
6075 __isl_give isl_union_map *isl_band_get_prefix_schedule(
6076 __isl_keep isl_band *band);
6077 __isl_give isl_union_map *isl_band_get_partial_schedule(
6078 __isl_keep isl_band *band);
6079 __isl_give isl_union_map *isl_band_get_suffix_schedule(
6080 __isl_keep isl_band *band);
6082 int isl_band_n_member(__isl_keep isl_band *band);
6083 int isl_band_member_is_coincident(
6084 __isl_keep isl_band *band, int pos);
6086 int isl_band_list_foreach_band(
6087 __isl_keep isl_band_list *list,
6088 int (*fn)(__isl_keep isl_band *band, void *user),
6091 Note that a scheduling dimension is considered to be ``coincident''
6092 if it satisfies the coincidence constraints within its band.
6093 That is, if the dependence distances of the coincidence
6094 constraints are all zero in that direction (for fixed
6095 iterations of outer bands).
6096 Like C<isl_schedule_foreach_band>,
6097 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
6098 in depth-first post-order.
6100 A band can be tiled using the following function.
6102 #include <isl/band.h>
6103 int isl_band_tile(__isl_keep isl_band *band,
6104 __isl_take isl_vec *sizes);
6106 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
6108 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
6109 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
6111 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
6113 The C<isl_band_tile> function tiles the band using the given tile sizes
6114 inside its schedule.
6115 A new child band is created to represent the point loops and it is
6116 inserted between the modified band and its children.
6117 The C<tile_scale_tile_loops> option specifies whether the tile
6118 loops iterators should be scaled by the tile sizes.
6119 If the C<tile_shift_point_loops> option is set, then the point loops
6120 are shifted to start at zero.
6122 A band can be split into two nested bands using the following function.
6124 int isl_band_split(__isl_keep isl_band *band, int pos);
6126 The resulting outer band contains the first C<pos> dimensions of C<band>
6127 while the inner band contains the remaining dimensions.
6129 A representation of the band can be printed using
6131 #include <isl/band.h>
6132 __isl_give isl_printer *isl_printer_print_band(
6133 __isl_take isl_printer *p,
6134 __isl_keep isl_band *band);
6138 #include <isl/schedule.h>
6139 int isl_options_set_schedule_max_coefficient(
6140 isl_ctx *ctx, int val);
6141 int isl_options_get_schedule_max_coefficient(
6143 int isl_options_set_schedule_max_constant_term(
6144 isl_ctx *ctx, int val);
6145 int isl_options_get_schedule_max_constant_term(
6147 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
6148 int isl_options_get_schedule_fuse(isl_ctx *ctx);
6149 int isl_options_set_schedule_maximize_band_depth(
6150 isl_ctx *ctx, int val);
6151 int isl_options_get_schedule_maximize_band_depth(
6153 int isl_options_set_schedule_outer_coincidence(
6154 isl_ctx *ctx, int val);
6155 int isl_options_get_schedule_outer_coincidence(
6157 int isl_options_set_schedule_split_scaled(
6158 isl_ctx *ctx, int val);
6159 int isl_options_get_schedule_split_scaled(
6161 int isl_options_set_schedule_algorithm(
6162 isl_ctx *ctx, int val);
6163 int isl_options_get_schedule_algorithm(
6165 int isl_options_set_schedule_separate_components(
6166 isl_ctx *ctx, int val);
6167 int isl_options_get_schedule_separate_components(
6172 =item * schedule_max_coefficient
6174 This option enforces that the coefficients for variable and parameter
6175 dimensions in the calculated schedule are not larger than the specified value.
6176 This option can significantly increase the speed of the scheduling calculation
6177 and may also prevent fusing of unrelated dimensions. A value of -1 means that
6178 this option does not introduce bounds on the variable or parameter
6181 =item * schedule_max_constant_term
6183 This option enforces that the constant coefficients in the calculated schedule
6184 are not larger than the maximal constant term. This option can significantly
6185 increase the speed of the scheduling calculation and may also prevent fusing of
6186 unrelated dimensions. A value of -1 means that this option does not introduce
6187 bounds on the constant coefficients.
6189 =item * schedule_fuse
6191 This option controls the level of fusion.
6192 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6193 resulting schedule will be distributed as much as possible.
6194 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6195 try to fuse loops in the resulting schedule.
6197 =item * schedule_maximize_band_depth
6199 If this option is set, we do not split bands at the point
6200 where we detect splitting is necessary. Instead, we
6201 backtrack and split bands as early as possible. This
6202 reduces the number of splits and maximizes the width of
6203 the bands. Wider bands give more possibilities for tiling.
6204 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6205 then bands will be split as early as possible, even if there is no need.
6206 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6208 =item * schedule_outer_coincidence
6210 If this option is set, then we try to construct schedules
6211 where the outermost scheduling dimension in each band
6212 satisfies the coincidence constraints.
6214 =item * schedule_split_scaled
6216 If this option is set, then we try to construct schedules in which the
6217 constant term is split off from the linear part if the linear parts of
6218 the scheduling rows for all nodes in the graphs have a common non-trivial
6220 The constant term is then placed in a separate band and the linear
6223 =item * schedule_algorithm
6225 Selects the scheduling algorithm to be used.
6226 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6227 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6229 =item * schedule_separate_components
6231 If at any point the dependence graph contains any (weakly connected) components,
6232 then these components are scheduled separately.
6233 If this option is not set, then some iterations of the domains
6234 in these components may be scheduled together.
6235 If this option is set, then the components are given consecutive
6240 =head2 AST Generation
6242 This section describes the C<isl> functionality for generating
6243 ASTs that visit all the elements
6244 in a domain in an order specified by a schedule.
6245 In particular, given a C<isl_union_map>, an AST is generated
6246 that visits all the elements in the domain of the C<isl_union_map>
6247 according to the lexicographic order of the corresponding image
6248 element(s). If the range of the C<isl_union_map> consists of
6249 elements in more than one space, then each of these spaces is handled
6250 separately in an arbitrary order.
6251 It should be noted that the image elements only specify the I<order>
6252 in which the corresponding domain elements should be visited.
6253 No direct relation between the image elements and the loop iterators
6254 in the generated AST should be assumed.
6256 Each AST is generated within a build. The initial build
6257 simply specifies the constraints on the parameters (if any)
6258 and can be created, inspected, copied and freed using the following functions.
6260 #include <isl/ast_build.h>
6261 __isl_give isl_ast_build *isl_ast_build_from_context(
6262 __isl_take isl_set *set);
6263 isl_ctx *isl_ast_build_get_ctx(
6264 __isl_keep isl_ast_build *build);
6265 __isl_give isl_ast_build *isl_ast_build_copy(
6266 __isl_keep isl_ast_build *build);
6267 __isl_null isl_ast_build *isl_ast_build_free(
6268 __isl_take isl_ast_build *build);
6270 The C<set> argument is usually a parameter set with zero or more parameters.
6271 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6272 and L</"Fine-grained Control over AST Generation">.
6273 Finally, the AST itself can be constructed using the following
6276 #include <isl/ast_build.h>
6277 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6278 __isl_keep isl_ast_build *build,
6279 __isl_take isl_union_map *schedule);
6281 =head3 Inspecting the AST
6283 The basic properties of an AST node can be obtained as follows.
6285 #include <isl/ast.h>
6286 isl_ctx *isl_ast_node_get_ctx(
6287 __isl_keep isl_ast_node *node);
6288 enum isl_ast_node_type isl_ast_node_get_type(
6289 __isl_keep isl_ast_node *node);
6291 The type of an AST node is one of
6292 C<isl_ast_node_for>,
6294 C<isl_ast_node_block> or
6295 C<isl_ast_node_user>.
6296 An C<isl_ast_node_for> represents a for node.
6297 An C<isl_ast_node_if> represents an if node.
6298 An C<isl_ast_node_block> represents a compound node.
6299 An C<isl_ast_node_user> represents an expression statement.
6300 An expression statement typically corresponds to a domain element, i.e.,
6301 one of the elements that is visited by the AST.
6303 Each type of node has its own additional properties.
6305 #include <isl/ast.h>
6306 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6307 __isl_keep isl_ast_node *node);
6308 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6309 __isl_keep isl_ast_node *node);
6310 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6311 __isl_keep isl_ast_node *node);
6312 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6313 __isl_keep isl_ast_node *node);
6314 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6315 __isl_keep isl_ast_node *node);
6316 int isl_ast_node_for_is_degenerate(
6317 __isl_keep isl_ast_node *node);
6319 An C<isl_ast_for> is considered degenerate if it is known to execute
6322 #include <isl/ast.h>
6323 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6324 __isl_keep isl_ast_node *node);
6325 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6326 __isl_keep isl_ast_node *node);
6327 int isl_ast_node_if_has_else(
6328 __isl_keep isl_ast_node *node);
6329 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6330 __isl_keep isl_ast_node *node);
6332 __isl_give isl_ast_node_list *
6333 isl_ast_node_block_get_children(
6334 __isl_keep isl_ast_node *node);
6336 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6337 __isl_keep isl_ast_node *node);
6339 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6340 the following functions.
6342 #include <isl/ast.h>
6343 isl_ctx *isl_ast_expr_get_ctx(
6344 __isl_keep isl_ast_expr *expr);
6345 enum isl_ast_expr_type isl_ast_expr_get_type(
6346 __isl_keep isl_ast_expr *expr);
6348 The type of an AST expression is one of
6350 C<isl_ast_expr_id> or
6351 C<isl_ast_expr_int>.
6352 An C<isl_ast_expr_op> represents the result of an operation.
6353 An C<isl_ast_expr_id> represents an identifier.
6354 An C<isl_ast_expr_int> represents an integer value.
6356 Each type of expression has its own additional properties.
6358 #include <isl/ast.h>
6359 enum isl_ast_op_type isl_ast_expr_get_op_type(
6360 __isl_keep isl_ast_expr *expr);
6361 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6362 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6363 __isl_keep isl_ast_expr *expr, int pos);
6364 int isl_ast_node_foreach_ast_op_type(
6365 __isl_keep isl_ast_node *node,
6366 int (*fn)(enum isl_ast_op_type type, void *user),
6369 C<isl_ast_expr_get_op_type> returns the type of the operation
6370 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6371 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6373 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6374 C<isl_ast_op_type> that appears in C<node>.
6375 The operation type is one of the following.
6379 =item C<isl_ast_op_and>
6381 Logical I<and> of two arguments.
6382 Both arguments can be evaluated.
6384 =item C<isl_ast_op_and_then>
6386 Logical I<and> of two arguments.
6387 The second argument can only be evaluated if the first evaluates to true.
6389 =item C<isl_ast_op_or>
6391 Logical I<or> of two arguments.
6392 Both arguments can be evaluated.
6394 =item C<isl_ast_op_or_else>
6396 Logical I<or> of two arguments.
6397 The second argument can only be evaluated if the first evaluates to false.
6399 =item C<isl_ast_op_max>
6401 Maximum of two or more arguments.
6403 =item C<isl_ast_op_min>
6405 Minimum of two or more arguments.
6407 =item C<isl_ast_op_minus>
6411 =item C<isl_ast_op_add>
6413 Sum of two arguments.
6415 =item C<isl_ast_op_sub>
6417 Difference of two arguments.
6419 =item C<isl_ast_op_mul>
6421 Product of two arguments.
6423 =item C<isl_ast_op_div>
6425 Exact division. That is, the result is known to be an integer.
6427 =item C<isl_ast_op_fdiv_q>
6429 Result of integer division, rounded towards negative
6432 =item C<isl_ast_op_pdiv_q>
6434 Result of integer division, where dividend is known to be non-negative.
6436 =item C<isl_ast_op_pdiv_r>
6438 Remainder of integer division, where dividend is known to be non-negative.
6440 =item C<isl_ast_op_cond>
6442 Conditional operator defined on three arguments.
6443 If the first argument evaluates to true, then the result
6444 is equal to the second argument. Otherwise, the result
6445 is equal to the third argument.
6446 The second and third argument may only be evaluated if
6447 the first argument evaluates to true and false, respectively.
6448 Corresponds to C<a ? b : c> in C.
6450 =item C<isl_ast_op_select>
6452 Conditional operator defined on three arguments.
6453 If the first argument evaluates to true, then the result
6454 is equal to the second argument. Otherwise, the result
6455 is equal to the third argument.
6456 The second and third argument may be evaluated independently
6457 of the value of the first argument.
6458 Corresponds to C<a * b + (1 - a) * c> in C.
6460 =item C<isl_ast_op_eq>
6464 =item C<isl_ast_op_le>
6466 Less than or equal relation.
6468 =item C<isl_ast_op_lt>
6472 =item C<isl_ast_op_ge>
6474 Greater than or equal relation.
6476 =item C<isl_ast_op_gt>
6478 Greater than relation.
6480 =item C<isl_ast_op_call>
6483 The number of arguments of the C<isl_ast_expr> is one more than
6484 the number of arguments in the function call, the first argument
6485 representing the function being called.
6487 =item C<isl_ast_op_access>
6490 The number of arguments of the C<isl_ast_expr> is one more than
6491 the number of index expressions in the array access, the first argument
6492 representing the array being accessed.
6494 =item C<isl_ast_op_member>
6497 This operation has two arguments, a structure and the name of
6498 the member of the structure being accessed.
6502 #include <isl/ast.h>
6503 __isl_give isl_id *isl_ast_expr_get_id(
6504 __isl_keep isl_ast_expr *expr);
6506 Return the identifier represented by the AST expression.
6508 #include <isl/ast.h>
6509 __isl_give isl_val *isl_ast_expr_get_val(
6510 __isl_keep isl_ast_expr *expr);
6512 Return the integer represented by the AST expression.
6514 =head3 Properties of ASTs
6516 #include <isl/ast.h>
6517 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6518 __isl_keep isl_ast_expr *expr2);
6520 Check if two C<isl_ast_expr>s are equal to each other.
6522 =head3 Manipulating and printing the AST
6524 AST nodes can be copied and freed using the following functions.
6526 #include <isl/ast.h>
6527 __isl_give isl_ast_node *isl_ast_node_copy(
6528 __isl_keep isl_ast_node *node);
6529 __isl_null isl_ast_node *isl_ast_node_free(
6530 __isl_take isl_ast_node *node);
6532 AST expressions can be copied and freed using the following functions.
6534 #include <isl/ast.h>
6535 __isl_give isl_ast_expr *isl_ast_expr_copy(
6536 __isl_keep isl_ast_expr *expr);
6537 __isl_null isl_ast_expr *isl_ast_expr_free(
6538 __isl_take isl_ast_expr *expr);
6540 New AST expressions can be created either directly or within
6541 the context of an C<isl_ast_build>.
6543 #include <isl/ast.h>
6544 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6545 __isl_take isl_val *v);
6546 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6547 __isl_take isl_id *id);
6548 __isl_give isl_ast_expr *isl_ast_expr_neg(
6549 __isl_take isl_ast_expr *expr);
6550 __isl_give isl_ast_expr *isl_ast_expr_add(
6551 __isl_take isl_ast_expr *expr1,
6552 __isl_take isl_ast_expr *expr2);
6553 __isl_give isl_ast_expr *isl_ast_expr_sub(
6554 __isl_take isl_ast_expr *expr1,
6555 __isl_take isl_ast_expr *expr2);
6556 __isl_give isl_ast_expr *isl_ast_expr_mul(
6557 __isl_take isl_ast_expr *expr1,
6558 __isl_take isl_ast_expr *expr2);
6559 __isl_give isl_ast_expr *isl_ast_expr_div(
6560 __isl_take isl_ast_expr *expr1,
6561 __isl_take isl_ast_expr *expr2);
6562 __isl_give isl_ast_expr *isl_ast_expr_and(
6563 __isl_take isl_ast_expr *expr1,
6564 __isl_take isl_ast_expr *expr2)
6565 __isl_give isl_ast_expr *isl_ast_expr_or(
6566 __isl_take isl_ast_expr *expr1,
6567 __isl_take isl_ast_expr *expr2)
6568 __isl_give isl_ast_expr *isl_ast_expr_access(
6569 __isl_take isl_ast_expr *array,
6570 __isl_take isl_ast_expr_list *indices);
6572 #include <isl/ast_build.h>
6573 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6574 __isl_keep isl_ast_build *build,
6575 __isl_take isl_pw_aff *pa);
6576 __isl_give isl_ast_expr *
6577 isl_ast_build_access_from_pw_multi_aff(
6578 __isl_keep isl_ast_build *build,
6579 __isl_take isl_pw_multi_aff *pma);
6580 __isl_give isl_ast_expr *
6581 isl_ast_build_access_from_multi_pw_aff(
6582 __isl_keep isl_ast_build *build,
6583 __isl_take isl_multi_pw_aff *mpa);
6584 __isl_give isl_ast_expr *
6585 isl_ast_build_call_from_pw_multi_aff(
6586 __isl_keep isl_ast_build *build,
6587 __isl_take isl_pw_multi_aff *pma);
6588 __isl_give isl_ast_expr *
6589 isl_ast_build_call_from_multi_pw_aff(
6590 __isl_keep isl_ast_build *build,
6591 __isl_take isl_multi_pw_aff *mpa);
6593 The domains of C<pa>, C<mpa> and C<pma> should correspond
6594 to the schedule space of C<build>.
6595 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6596 the function being called.
6597 If the accessed space is a nested relation, then it is taken
6598 to represent an access of the member specified by the range
6599 of this nested relation of the structure specified by the domain
6600 of the nested relation.
6602 The following functions can be used to modify an C<isl_ast_expr>.
6604 #include <isl/ast.h>
6605 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6606 __isl_take isl_ast_expr *expr, int pos,
6607 __isl_take isl_ast_expr *arg);
6609 Replace the argument of C<expr> at position C<pos> by C<arg>.
6611 #include <isl/ast.h>
6612 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6613 __isl_take isl_ast_expr *expr,
6614 __isl_take isl_id_to_ast_expr *id2expr);
6616 The function C<isl_ast_expr_substitute_ids> replaces the
6617 subexpressions of C<expr> of type C<isl_ast_expr_id>
6618 by the corresponding expression in C<id2expr>, if there is any.
6621 User specified data can be attached to an C<isl_ast_node> and obtained
6622 from the same C<isl_ast_node> using the following functions.
6624 #include <isl/ast.h>
6625 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6626 __isl_take isl_ast_node *node,
6627 __isl_take isl_id *annotation);
6628 __isl_give isl_id *isl_ast_node_get_annotation(
6629 __isl_keep isl_ast_node *node);
6631 Basic printing can be performed using the following functions.
6633 #include <isl/ast.h>
6634 __isl_give isl_printer *isl_printer_print_ast_expr(
6635 __isl_take isl_printer *p,
6636 __isl_keep isl_ast_expr *expr);
6637 __isl_give isl_printer *isl_printer_print_ast_node(
6638 __isl_take isl_printer *p,
6639 __isl_keep isl_ast_node *node);
6641 More advanced printing can be performed using the following functions.
6643 #include <isl/ast.h>
6644 __isl_give isl_printer *isl_ast_op_type_print_macro(
6645 enum isl_ast_op_type type,
6646 __isl_take isl_printer *p);
6647 __isl_give isl_printer *isl_ast_node_print_macros(
6648 __isl_keep isl_ast_node *node,
6649 __isl_take isl_printer *p);
6650 __isl_give isl_printer *isl_ast_node_print(
6651 __isl_keep isl_ast_node *node,
6652 __isl_take isl_printer *p,
6653 __isl_take isl_ast_print_options *options);
6654 __isl_give isl_printer *isl_ast_node_for_print(
6655 __isl_keep isl_ast_node *node,
6656 __isl_take isl_printer *p,
6657 __isl_take isl_ast_print_options *options);
6658 __isl_give isl_printer *isl_ast_node_if_print(
6659 __isl_keep isl_ast_node *node,
6660 __isl_take isl_printer *p,
6661 __isl_take isl_ast_print_options *options);
6663 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6664 C<isl> may print out an AST that makes use of macros such
6665 as C<floord>, C<min> and C<max>.
6666 C<isl_ast_op_type_print_macro> prints out the macro
6667 corresponding to a specific C<isl_ast_op_type>.
6668 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6669 for expressions where these macros would be used and prints
6670 out the required macro definitions.
6671 Essentially, C<isl_ast_node_print_macros> calls
6672 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6673 as function argument.
6674 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6675 C<isl_ast_node_if_print> print an C<isl_ast_node>
6676 in C<ISL_FORMAT_C>, but allow for some extra control
6677 through an C<isl_ast_print_options> object.
6678 This object can be created using the following functions.
6680 #include <isl/ast.h>
6681 __isl_give isl_ast_print_options *
6682 isl_ast_print_options_alloc(isl_ctx *ctx);
6683 __isl_give isl_ast_print_options *
6684 isl_ast_print_options_copy(
6685 __isl_keep isl_ast_print_options *options);
6686 __isl_null isl_ast_print_options *
6687 isl_ast_print_options_free(
6688 __isl_take isl_ast_print_options *options);
6690 __isl_give isl_ast_print_options *
6691 isl_ast_print_options_set_print_user(
6692 __isl_take isl_ast_print_options *options,
6693 __isl_give isl_printer *(*print_user)(
6694 __isl_take isl_printer *p,
6695 __isl_take isl_ast_print_options *options,
6696 __isl_keep isl_ast_node *node, void *user),
6698 __isl_give isl_ast_print_options *
6699 isl_ast_print_options_set_print_for(
6700 __isl_take isl_ast_print_options *options,
6701 __isl_give isl_printer *(*print_for)(
6702 __isl_take isl_printer *p,
6703 __isl_take isl_ast_print_options *options,
6704 __isl_keep isl_ast_node *node, void *user),
6707 The callback set by C<isl_ast_print_options_set_print_user>
6708 is called whenever a node of type C<isl_ast_node_user> needs to
6710 The callback set by C<isl_ast_print_options_set_print_for>
6711 is called whenever a node of type C<isl_ast_node_for> needs to
6713 Note that C<isl_ast_node_for_print> will I<not> call the
6714 callback set by C<isl_ast_print_options_set_print_for> on the node
6715 on which C<isl_ast_node_for_print> is called, but only on nested
6716 nodes of type C<isl_ast_node_for>. It is therefore safe to
6717 call C<isl_ast_node_for_print> from within the callback set by
6718 C<isl_ast_print_options_set_print_for>.
6720 The following option determines the type to be used for iterators
6721 while printing the AST.
6723 int isl_options_set_ast_iterator_type(
6724 isl_ctx *ctx, const char *val);
6725 const char *isl_options_get_ast_iterator_type(
6730 #include <isl/ast_build.h>
6731 int isl_options_set_ast_build_atomic_upper_bound(
6732 isl_ctx *ctx, int val);
6733 int isl_options_get_ast_build_atomic_upper_bound(
6735 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6737 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6738 int isl_options_set_ast_build_exploit_nested_bounds(
6739 isl_ctx *ctx, int val);
6740 int isl_options_get_ast_build_exploit_nested_bounds(
6742 int isl_options_set_ast_build_group_coscheduled(
6743 isl_ctx *ctx, int val);
6744 int isl_options_get_ast_build_group_coscheduled(
6746 int isl_options_set_ast_build_scale_strides(
6747 isl_ctx *ctx, int val);
6748 int isl_options_get_ast_build_scale_strides(
6750 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6752 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6753 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6755 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6759 =item * ast_build_atomic_upper_bound
6761 Generate loop upper bounds that consist of the current loop iterator,
6762 an operator and an expression not involving the iterator.
6763 If this option is not set, then the current loop iterator may appear
6764 several times in the upper bound.
6765 For example, when this option is turned off, AST generation
6768 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6772 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6775 When the option is turned on, the following AST is generated
6777 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6780 =item * ast_build_prefer_pdiv
6782 If this option is turned off, then the AST generation will
6783 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6784 operators, but no C<isl_ast_op_pdiv_q> or
6785 C<isl_ast_op_pdiv_r> operators.
6786 If this options is turned on, then C<isl> will try to convert
6787 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6788 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6790 =item * ast_build_exploit_nested_bounds
6792 Simplify conditions based on bounds of nested for loops.
6793 In particular, remove conditions that are implied by the fact
6794 that one or more nested loops have at least one iteration,
6795 meaning that the upper bound is at least as large as the lower bound.
6796 For example, when this option is turned off, AST generation
6799 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6805 for (int c0 = 0; c0 <= N; c0 += 1)
6806 for (int c1 = 0; c1 <= M; c1 += 1)
6809 When the option is turned on, the following AST is generated
6811 for (int c0 = 0; c0 <= N; c0 += 1)
6812 for (int c1 = 0; c1 <= M; c1 += 1)
6815 =item * ast_build_group_coscheduled
6817 If two domain elements are assigned the same schedule point, then
6818 they may be executed in any order and they may even appear in different
6819 loops. If this options is set, then the AST generator will make
6820 sure that coscheduled domain elements do not appear in separate parts
6821 of the AST. This is useful in case of nested AST generation
6822 if the outer AST generation is given only part of a schedule
6823 and the inner AST generation should handle the domains that are
6824 coscheduled by this initial part of the schedule together.
6825 For example if an AST is generated for a schedule
6827 { A[i] -> [0]; B[i] -> [0] }
6829 then the C<isl_ast_build_set_create_leaf> callback described
6830 below may get called twice, once for each domain.
6831 Setting this option ensures that the callback is only called once
6832 on both domains together.
6834 =item * ast_build_separation_bounds
6836 This option specifies which bounds to use during separation.
6837 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6838 then all (possibly implicit) bounds on the current dimension will
6839 be used during separation.
6840 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6841 then only those bounds that are explicitly available will
6842 be used during separation.
6844 =item * ast_build_scale_strides
6846 This option specifies whether the AST generator is allowed
6847 to scale down iterators of strided loops.
6849 =item * ast_build_allow_else
6851 This option specifies whether the AST generator is allowed
6852 to construct if statements with else branches.
6854 =item * ast_build_allow_or
6856 This option specifies whether the AST generator is allowed
6857 to construct if conditions with disjunctions.
6861 =head3 Fine-grained Control over AST Generation
6863 Besides specifying the constraints on the parameters,
6864 an C<isl_ast_build> object can be used to control
6865 various aspects of the AST generation process.
6866 The most prominent way of control is through ``options'',
6867 which can be set using the following function.
6869 #include <isl/ast_build.h>
6870 __isl_give isl_ast_build *
6871 isl_ast_build_set_options(
6872 __isl_take isl_ast_build *control,
6873 __isl_take isl_union_map *options);
6875 The options are encoded in an <isl_union_map>.
6876 The domain of this union relation refers to the schedule domain,
6877 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6878 In the case of nested AST generation (see L</"Nested AST Generation">),
6879 the domain of C<options> should refer to the extra piece of the schedule.
6880 That is, it should be equal to the range of the wrapped relation in the
6881 range of the schedule.
6882 The range of the options can consist of elements in one or more spaces,
6883 the names of which determine the effect of the option.
6884 The values of the range typically also refer to the schedule dimension
6885 to which the option applies. In case of nested AST generation
6886 (see L</"Nested AST Generation">), these values refer to the position
6887 of the schedule dimension within the innermost AST generation.
6888 The constraints on the domain elements of
6889 the option should only refer to this dimension and earlier dimensions.
6890 We consider the following spaces.
6894 =item C<separation_class>
6896 This space is a wrapped relation between two one dimensional spaces.
6897 The input space represents the schedule dimension to which the option
6898 applies and the output space represents the separation class.
6899 While constructing a loop corresponding to the specified schedule
6900 dimension(s), the AST generator will try to generate separate loops
6901 for domain elements that are assigned different classes.
6902 If only some of the elements are assigned a class, then those elements
6903 that are not assigned any class will be treated as belonging to a class
6904 that is separate from the explicitly assigned classes.
6905 The typical use case for this option is to separate full tiles from
6907 The other options, described below, are applied after the separation
6910 As an example, consider the separation into full and partial tiles
6911 of a tiling of a triangular domain.
6912 Take, for example, the domain
6914 { A[i,j] : 0 <= i,j and i + j <= 100 }
6916 and a tiling into tiles of 10 by 10. The input to the AST generator
6917 is then the schedule
6919 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6922 Without any options, the following AST is generated
6924 for (int c0 = 0; c0 <= 10; c0 += 1)
6925 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6926 for (int c2 = 10 * c0;
6927 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6929 for (int c3 = 10 * c1;
6930 c3 <= min(10 * c1 + 9, -c2 + 100);
6934 Separation into full and partial tiles can be obtained by assigning
6935 a class, say C<0>, to the full tiles. The full tiles are represented by those
6936 values of the first and second schedule dimensions for which there are
6937 values of the third and fourth dimensions to cover an entire tile.
6938 That is, we need to specify the following option
6940 { [a,b,c,d] -> separation_class[[0]->[0]] :
6941 exists b': 0 <= 10a,10b' and
6942 10a+9+10b'+9 <= 100;
6943 [a,b,c,d] -> separation_class[[1]->[0]] :
6944 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6948 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6949 a >= 0 and b >= 0 and b <= 8 - a;
6950 [a, b, c, d] -> separation_class[[0] -> [0]] :
6953 With this option, the generated AST is as follows
6956 for (int c0 = 0; c0 <= 8; c0 += 1) {
6957 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6958 for (int c2 = 10 * c0;
6959 c2 <= 10 * c0 + 9; c2 += 1)
6960 for (int c3 = 10 * c1;
6961 c3 <= 10 * c1 + 9; c3 += 1)
6963 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6964 for (int c2 = 10 * c0;
6965 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6967 for (int c3 = 10 * c1;
6968 c3 <= min(-c2 + 100, 10 * c1 + 9);
6972 for (int c0 = 9; c0 <= 10; c0 += 1)
6973 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6974 for (int c2 = 10 * c0;
6975 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6977 for (int c3 = 10 * c1;
6978 c3 <= min(10 * c1 + 9, -c2 + 100);
6985 This is a single-dimensional space representing the schedule dimension(s)
6986 to which ``separation'' should be applied. Separation tries to split
6987 a loop into several pieces if this can avoid the generation of guards
6989 See also the C<atomic> option.
6993 This is a single-dimensional space representing the schedule dimension(s)
6994 for which the domains should be considered ``atomic''. That is, the
6995 AST generator will make sure that any given domain space will only appear
6996 in a single loop at the specified level.
6998 Consider the following schedule
7000 { a[i] -> [i] : 0 <= i < 10;
7001 b[i] -> [i+1] : 0 <= i < 10 }
7003 If the following option is specified
7005 { [i] -> separate[x] }
7007 then the following AST will be generated
7011 for (int c0 = 1; c0 <= 9; c0 += 1) {
7018 If, on the other hand, the following option is specified
7020 { [i] -> atomic[x] }
7022 then the following AST will be generated
7024 for (int c0 = 0; c0 <= 10; c0 += 1) {
7031 If neither C<atomic> nor C<separate> is specified, then the AST generator
7032 may produce either of these two results or some intermediate form.
7036 This is a single-dimensional space representing the schedule dimension(s)
7037 that should be I<completely> unrolled.
7038 To obtain a partial unrolling, the user should apply an additional
7039 strip-mining to the schedule and fully unroll the inner loop.
7043 Additional control is available through the following functions.
7045 #include <isl/ast_build.h>
7046 __isl_give isl_ast_build *
7047 isl_ast_build_set_iterators(
7048 __isl_take isl_ast_build *control,
7049 __isl_take isl_id_list *iterators);
7051 The function C<isl_ast_build_set_iterators> allows the user to
7052 specify a list of iterator C<isl_id>s to be used as iterators.
7053 If the input schedule is injective, then
7054 the number of elements in this list should be as large as the dimension
7055 of the schedule space, but no direct correspondence should be assumed
7056 between dimensions and elements.
7057 If the input schedule is not injective, then an additional number
7058 of C<isl_id>s equal to the largest dimension of the input domains
7060 If the number of provided C<isl_id>s is insufficient, then additional
7061 names are automatically generated.
7063 #include <isl/ast_build.h>
7064 __isl_give isl_ast_build *
7065 isl_ast_build_set_create_leaf(
7066 __isl_take isl_ast_build *control,
7067 __isl_give isl_ast_node *(*fn)(
7068 __isl_take isl_ast_build *build,
7069 void *user), void *user);
7072 C<isl_ast_build_set_create_leaf> function allows for the
7073 specification of a callback that should be called whenever the AST
7074 generator arrives at an element of the schedule domain.
7075 The callback should return an AST node that should be inserted
7076 at the corresponding position of the AST. The default action (when
7077 the callback is not set) is to continue generating parts of the AST to scan
7078 all the domain elements associated to the schedule domain element
7079 and to insert user nodes, ``calling'' the domain element, for each of them.
7080 The C<build> argument contains the current state of the C<isl_ast_build>.
7081 To ease nested AST generation (see L</"Nested AST Generation">),
7082 all control information that is
7083 specific to the current AST generation such as the options and
7084 the callbacks has been removed from this C<isl_ast_build>.
7085 The callback would typically return the result of a nested
7087 user defined node created using the following function.
7089 #include <isl/ast.h>
7090 __isl_give isl_ast_node *isl_ast_node_alloc_user(
7091 __isl_take isl_ast_expr *expr);
7093 #include <isl/ast_build.h>
7094 __isl_give isl_ast_build *
7095 isl_ast_build_set_at_each_domain(
7096 __isl_take isl_ast_build *build,
7097 __isl_give isl_ast_node *(*fn)(
7098 __isl_take isl_ast_node *node,
7099 __isl_keep isl_ast_build *build,
7100 void *user), void *user);
7101 __isl_give isl_ast_build *
7102 isl_ast_build_set_before_each_for(
7103 __isl_take isl_ast_build *build,
7104 __isl_give isl_id *(*fn)(
7105 __isl_keep isl_ast_build *build,
7106 void *user), void *user);
7107 __isl_give isl_ast_build *
7108 isl_ast_build_set_after_each_for(
7109 __isl_take isl_ast_build *build,
7110 __isl_give isl_ast_node *(*fn)(
7111 __isl_take isl_ast_node *node,
7112 __isl_keep isl_ast_build *build,
7113 void *user), void *user);
7115 The callback set by C<isl_ast_build_set_at_each_domain> will
7116 be called for each domain AST node.
7117 The callbacks set by C<isl_ast_build_set_before_each_for>
7118 and C<isl_ast_build_set_after_each_for> will be called
7119 for each for AST node. The first will be called in depth-first
7120 pre-order, while the second will be called in depth-first post-order.
7121 Since C<isl_ast_build_set_before_each_for> is called before the for
7122 node is actually constructed, it is only passed an C<isl_ast_build>.
7123 The returned C<isl_id> will be added as an annotation (using
7124 C<isl_ast_node_set_annotation>) to the constructed for node.
7125 In particular, if the user has also specified an C<after_each_for>
7126 callback, then the annotation can be retrieved from the node passed to
7127 that callback using C<isl_ast_node_get_annotation>.
7128 All callbacks should C<NULL> on failure.
7129 The given C<isl_ast_build> can be used to create new
7130 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
7131 or C<isl_ast_build_call_from_pw_multi_aff>.
7133 =head3 Nested AST Generation
7135 C<isl> allows the user to create an AST within the context
7136 of another AST. These nested ASTs are created using the
7137 same C<isl_ast_build_ast_from_schedule> function that is used to create the
7138 outer AST. The C<build> argument should be an C<isl_ast_build>
7139 passed to a callback set by
7140 C<isl_ast_build_set_create_leaf>.
7141 The space of the range of the C<schedule> argument should refer
7142 to this build. In particular, the space should be a wrapped
7143 relation and the domain of this wrapped relation should be the
7144 same as that of the range of the schedule returned by
7145 C<isl_ast_build_get_schedule> below.
7146 In practice, the new schedule is typically
7147 created by calling C<isl_union_map_range_product> on the old schedule
7148 and some extra piece of the schedule.
7149 The space of the schedule domain is also available from
7150 the C<isl_ast_build>.
7152 #include <isl/ast_build.h>
7153 __isl_give isl_union_map *isl_ast_build_get_schedule(
7154 __isl_keep isl_ast_build *build);
7155 __isl_give isl_space *isl_ast_build_get_schedule_space(
7156 __isl_keep isl_ast_build *build);
7157 __isl_give isl_ast_build *isl_ast_build_restrict(
7158 __isl_take isl_ast_build *build,
7159 __isl_take isl_set *set);
7161 The C<isl_ast_build_get_schedule> function returns a (partial)
7162 schedule for the domains elements for which part of the AST still needs to
7163 be generated in the current build.
7164 In particular, the domain elements are mapped to those iterations of the loops
7165 enclosing the current point of the AST generation inside which
7166 the domain elements are executed.
7167 No direct correspondence between
7168 the input schedule and this schedule should be assumed.
7169 The space obtained from C<isl_ast_build_get_schedule_space> can be used
7170 to create a set for C<isl_ast_build_restrict> to intersect
7171 with the current build. In particular, the set passed to
7172 C<isl_ast_build_restrict> can have additional parameters.
7173 The ids of the set dimensions in the space returned by
7174 C<isl_ast_build_get_schedule_space> correspond to the
7175 iterators of the already generated loops.
7176 The user should not rely on the ids of the output dimensions
7177 of the relations in the union relation returned by
7178 C<isl_ast_build_get_schedule> having any particular value.
7182 Although C<isl> is mainly meant to be used as a library,
7183 it also contains some basic applications that use some
7184 of the functionality of C<isl>.
7185 The input may be specified in either the L<isl format>
7186 or the L<PolyLib format>.
7188 =head2 C<isl_polyhedron_sample>
7190 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7191 an integer element of the polyhedron, if there is any.
7192 The first column in the output is the denominator and is always
7193 equal to 1. If the polyhedron contains no integer points,
7194 then a vector of length zero is printed.
7198 C<isl_pip> takes the same input as the C<example> program
7199 from the C<piplib> distribution, i.e., a set of constraints
7200 on the parameters, a line containing only -1 and finally a set
7201 of constraints on a parametric polyhedron.
7202 The coefficients of the parameters appear in the last columns
7203 (but before the final constant column).
7204 The output is the lexicographic minimum of the parametric polyhedron.
7205 As C<isl> currently does not have its own output format, the output
7206 is just a dump of the internal state.
7208 =head2 C<isl_polyhedron_minimize>
7210 C<isl_polyhedron_minimize> computes the minimum of some linear
7211 or affine objective function over the integer points in a polyhedron.
7212 If an affine objective function
7213 is given, then the constant should appear in the last column.
7215 =head2 C<isl_polytope_scan>
7217 Given a polytope, C<isl_polytope_scan> prints
7218 all integer points in the polytope.
7220 =head2 C<isl_codegen>
7222 Given a schedule, a context set and an options relation,
7223 C<isl_codegen> prints out an AST that scans the domain elements
7224 of the schedule in the order of their image(s) taking into account
7225 the constraints in the context set.