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 __isl_give isl_set *isl_set_set_tuple_name(
1843 __isl_take isl_set *set, const char *s);
1844 const char *isl_basic_map_get_tuple_name(
1845 __isl_keep isl_basic_map *bmap,
1846 enum isl_dim_type type);
1847 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1848 __isl_take isl_basic_map *bmap,
1849 enum isl_dim_type type, const char *s);
1850 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1851 enum isl_dim_type type);
1852 const char *isl_map_get_tuple_name(
1853 __isl_keep isl_map *map,
1854 enum isl_dim_type type);
1855 __isl_give isl_map *isl_map_set_tuple_name(
1856 __isl_take isl_map *map,
1857 enum isl_dim_type type, const char *s);
1859 As with C<isl_space_get_tuple_name>, the value returned points to
1860 an internal data structure.
1861 The identifiers, positions or names of individual dimensions can be
1862 read off using the following functions.
1864 __isl_give isl_id *isl_basic_set_get_dim_id(
1865 __isl_keep isl_basic_set *bset,
1866 enum isl_dim_type type, unsigned pos);
1867 __isl_give isl_set *isl_set_set_dim_id(
1868 __isl_take isl_set *set, enum isl_dim_type type,
1869 unsigned pos, __isl_take isl_id *id);
1870 int isl_set_has_dim_id(__isl_keep isl_set *set,
1871 enum isl_dim_type type, unsigned pos);
1872 __isl_give isl_id *isl_set_get_dim_id(
1873 __isl_keep isl_set *set, enum isl_dim_type type,
1875 int isl_basic_map_has_dim_id(
1876 __isl_keep isl_basic_map *bmap,
1877 enum isl_dim_type type, unsigned pos);
1878 __isl_give isl_map *isl_map_set_dim_id(
1879 __isl_take isl_map *map, enum isl_dim_type type,
1880 unsigned pos, __isl_take isl_id *id);
1881 int isl_map_has_dim_id(__isl_keep isl_map *map,
1882 enum isl_dim_type type, unsigned pos);
1883 __isl_give isl_id *isl_map_get_dim_id(
1884 __isl_keep isl_map *map, enum isl_dim_type type,
1886 __isl_give isl_id *isl_union_map_get_dim_id(
1887 __isl_keep isl_union_map *umap,
1888 enum isl_dim_type type, unsigned pos);
1890 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1891 enum isl_dim_type type, __isl_keep isl_id *id);
1892 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1893 enum isl_dim_type type, __isl_keep isl_id *id);
1894 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1895 enum isl_dim_type type, const char *name);
1896 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1897 enum isl_dim_type type, const char *name);
1899 const char *isl_constraint_get_dim_name(
1900 __isl_keep isl_constraint *constraint,
1901 enum isl_dim_type type, unsigned pos);
1902 const char *isl_basic_set_get_dim_name(
1903 __isl_keep isl_basic_set *bset,
1904 enum isl_dim_type type, unsigned pos);
1905 int isl_set_has_dim_name(__isl_keep isl_set *set,
1906 enum isl_dim_type type, unsigned pos);
1907 const char *isl_set_get_dim_name(
1908 __isl_keep isl_set *set,
1909 enum isl_dim_type type, unsigned pos);
1910 const char *isl_basic_map_get_dim_name(
1911 __isl_keep isl_basic_map *bmap,
1912 enum isl_dim_type type, unsigned pos);
1913 int isl_map_has_dim_name(__isl_keep isl_map *map,
1914 enum isl_dim_type type, unsigned pos);
1915 const char *isl_map_get_dim_name(
1916 __isl_keep isl_map *map,
1917 enum isl_dim_type type, unsigned pos);
1919 These functions are mostly useful to obtain the identifiers, positions
1920 or names of the parameters. Identifiers of individual dimensions are
1921 essentially only useful for printing. They are ignored by all other
1922 operations and may not be preserved across those operations.
1924 The user pointers on all parameters and tuples can be reset
1925 using the following functions.
1927 #include <isl/set.h>
1928 __isl_give isl_set *isl_set_reset_user(
1929 __isl_take isl_set *set);
1930 #include <isl/map.h>
1931 __isl_give isl_map *isl_map_reset_user(
1932 __isl_take isl_map *map);
1933 #include <isl/union_set.h>
1934 __isl_give isl_union_set *isl_union_set_reset_user(
1935 __isl_take isl_union_set *uset);
1936 #include <isl/union_map.h>
1937 __isl_give isl_union_map *isl_union_map_reset_user(
1938 __isl_take isl_union_map *umap);
1942 =head3 Unary Properties
1948 The following functions test whether the given set or relation
1949 contains any integer points. The ``plain'' variants do not perform
1950 any computations, but simply check if the given set or relation
1951 is already known to be empty.
1953 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1954 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1955 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1956 int isl_set_is_empty(__isl_keep isl_set *set);
1957 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1958 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1959 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1960 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1961 int isl_map_is_empty(__isl_keep isl_map *map);
1962 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1964 =item * Universality
1966 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1967 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1968 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1970 =item * Single-valuedness
1972 int isl_basic_map_is_single_valued(
1973 __isl_keep isl_basic_map *bmap);
1974 int isl_map_plain_is_single_valued(
1975 __isl_keep isl_map *map);
1976 int isl_map_is_single_valued(__isl_keep isl_map *map);
1977 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1981 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1982 int isl_map_is_injective(__isl_keep isl_map *map);
1983 int isl_union_map_plain_is_injective(
1984 __isl_keep isl_union_map *umap);
1985 int isl_union_map_is_injective(
1986 __isl_keep isl_union_map *umap);
1990 int isl_map_is_bijective(__isl_keep isl_map *map);
1991 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1995 __isl_give isl_val *
1996 isl_basic_map_plain_get_val_if_fixed(
1997 __isl_keep isl_basic_map *bmap,
1998 enum isl_dim_type type, unsigned pos);
1999 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
2000 __isl_keep isl_set *set,
2001 enum isl_dim_type type, unsigned pos);
2002 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
2003 __isl_keep isl_map *map,
2004 enum isl_dim_type type, unsigned pos);
2006 If the set or relation obviously lies on a hyperplane where the given dimension
2007 has a fixed value, then return that value.
2008 Otherwise return NaN.
2012 int isl_set_dim_residue_class_val(
2013 __isl_keep isl_set *set,
2014 int pos, __isl_give isl_val **modulo,
2015 __isl_give isl_val **residue);
2017 Check if the values of the given set dimension are equal to a fixed
2018 value modulo some integer value. If so, assign the modulo to C<*modulo>
2019 and the fixed value to C<*residue>. If the given dimension attains only
2020 a single value, then assign C<0> to C<*modulo> and the fixed value to
2022 If the dimension does not attain only a single value and if no modulo
2023 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
2027 To check whether a set is a parameter domain, use this function:
2029 int isl_set_is_params(__isl_keep isl_set *set);
2030 int isl_union_set_is_params(
2031 __isl_keep isl_union_set *uset);
2035 The following functions check whether the space of the given
2036 (basic) set or relation range is a wrapped relation.
2038 #include <isl/space.h>
2039 int isl_space_is_wrapping(
2040 __isl_keep isl_space *space);
2041 int isl_space_domain_is_wrapping(
2042 __isl_keep isl_space *space);
2043 int isl_space_range_is_wrapping(
2044 __isl_keep isl_space *space);
2046 #include <isl/set.h>
2047 int isl_basic_set_is_wrapping(
2048 __isl_keep isl_basic_set *bset);
2049 int isl_set_is_wrapping(__isl_keep isl_set *set);
2051 #include <isl/map.h>
2052 int isl_map_domain_is_wrapping(
2053 __isl_keep isl_map *map);
2054 int isl_map_range_is_wrapping(
2055 __isl_keep isl_map *map);
2057 The input to C<isl_space_is_wrapping> should
2058 be the space of a set, while that of
2059 C<isl_space_domain_is_wrapping> and
2060 C<isl_space_range_is_wrapping> should be the space of a relation.
2062 =item * Internal Product
2064 int isl_basic_map_can_zip(
2065 __isl_keep isl_basic_map *bmap);
2066 int isl_map_can_zip(__isl_keep isl_map *map);
2068 Check whether the product of domain and range of the given relation
2070 i.e., whether both domain and range are nested relations.
2074 int isl_basic_map_can_curry(
2075 __isl_keep isl_basic_map *bmap);
2076 int isl_map_can_curry(__isl_keep isl_map *map);
2078 Check whether the domain of the (basic) relation is a wrapped relation.
2080 int isl_basic_map_can_uncurry(
2081 __isl_keep isl_basic_map *bmap);
2082 int isl_map_can_uncurry(__isl_keep isl_map *map);
2084 Check whether the range of the (basic) relation is a wrapped relation.
2088 =head3 Binary Properties
2094 int isl_basic_set_plain_is_equal(
2095 __isl_keep isl_basic_set *bset1,
2096 __isl_keep isl_basic_set *bset2);
2097 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2098 __isl_keep isl_set *set2);
2099 int isl_set_is_equal(__isl_keep isl_set *set1,
2100 __isl_keep isl_set *set2);
2101 int isl_union_set_is_equal(
2102 __isl_keep isl_union_set *uset1,
2103 __isl_keep isl_union_set *uset2);
2104 int isl_basic_map_is_equal(
2105 __isl_keep isl_basic_map *bmap1,
2106 __isl_keep isl_basic_map *bmap2);
2107 int isl_map_is_equal(__isl_keep isl_map *map1,
2108 __isl_keep isl_map *map2);
2109 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2110 __isl_keep isl_map *map2);
2111 int isl_union_map_is_equal(
2112 __isl_keep isl_union_map *umap1,
2113 __isl_keep isl_union_map *umap2);
2115 =item * Disjointness
2117 int isl_basic_set_is_disjoint(
2118 __isl_keep isl_basic_set *bset1,
2119 __isl_keep isl_basic_set *bset2);
2120 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2121 __isl_keep isl_set *set2);
2122 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2123 __isl_keep isl_set *set2);
2124 int isl_basic_map_is_disjoint(
2125 __isl_keep isl_basic_map *bmap1,
2126 __isl_keep isl_basic_map *bmap2);
2127 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2128 __isl_keep isl_map *map2);
2132 int isl_basic_set_is_subset(
2133 __isl_keep isl_basic_set *bset1,
2134 __isl_keep isl_basic_set *bset2);
2135 int isl_set_is_subset(__isl_keep isl_set *set1,
2136 __isl_keep isl_set *set2);
2137 int isl_set_is_strict_subset(
2138 __isl_keep isl_set *set1,
2139 __isl_keep isl_set *set2);
2140 int isl_union_set_is_subset(
2141 __isl_keep isl_union_set *uset1,
2142 __isl_keep isl_union_set *uset2);
2143 int isl_union_set_is_strict_subset(
2144 __isl_keep isl_union_set *uset1,
2145 __isl_keep isl_union_set *uset2);
2146 int isl_basic_map_is_subset(
2147 __isl_keep isl_basic_map *bmap1,
2148 __isl_keep isl_basic_map *bmap2);
2149 int isl_basic_map_is_strict_subset(
2150 __isl_keep isl_basic_map *bmap1,
2151 __isl_keep isl_basic_map *bmap2);
2152 int isl_map_is_subset(
2153 __isl_keep isl_map *map1,
2154 __isl_keep isl_map *map2);
2155 int isl_map_is_strict_subset(
2156 __isl_keep isl_map *map1,
2157 __isl_keep isl_map *map2);
2158 int isl_union_map_is_subset(
2159 __isl_keep isl_union_map *umap1,
2160 __isl_keep isl_union_map *umap2);
2161 int isl_union_map_is_strict_subset(
2162 __isl_keep isl_union_map *umap1,
2163 __isl_keep isl_union_map *umap2);
2165 Check whether the first argument is a (strict) subset of the
2170 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2171 __isl_keep isl_set *set2);
2173 This function is useful for sorting C<isl_set>s.
2174 The order depends on the internal representation of the inputs.
2175 The order is fixed over different calls to the function (assuming
2176 the internal representation of the inputs has not changed), but may
2177 change over different versions of C<isl>.
2181 =head2 Unary Operations
2187 __isl_give isl_set *isl_set_complement(
2188 __isl_take isl_set *set);
2189 __isl_give isl_map *isl_map_complement(
2190 __isl_take isl_map *map);
2194 __isl_give isl_basic_map *isl_basic_map_reverse(
2195 __isl_take isl_basic_map *bmap);
2196 __isl_give isl_map *isl_map_reverse(
2197 __isl_take isl_map *map);
2198 __isl_give isl_union_map *isl_union_map_reverse(
2199 __isl_take isl_union_map *umap);
2203 #include <isl/local_space.h>
2204 __isl_give isl_local_space *isl_local_space_domain(
2205 __isl_take isl_local_space *ls);
2206 __isl_give isl_local_space *isl_local_space_range(
2207 __isl_take isl_local_space *ls);
2209 #include <isl/set.h>
2210 __isl_give isl_basic_set *isl_basic_set_project_out(
2211 __isl_take isl_basic_set *bset,
2212 enum isl_dim_type type, unsigned first, unsigned n);
2213 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2214 enum isl_dim_type type, unsigned first, unsigned n);
2215 __isl_give isl_basic_set *isl_basic_set_params(
2216 __isl_take isl_basic_set *bset);
2217 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2219 #include <isl/map.h>
2220 __isl_give isl_basic_map *isl_basic_map_project_out(
2221 __isl_take isl_basic_map *bmap,
2222 enum isl_dim_type type, unsigned first, unsigned n);
2223 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2224 enum isl_dim_type type, unsigned first, unsigned n);
2225 __isl_give isl_basic_set *isl_basic_map_domain(
2226 __isl_take isl_basic_map *bmap);
2227 __isl_give isl_basic_set *isl_basic_map_range(
2228 __isl_take isl_basic_map *bmap);
2229 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2230 __isl_give isl_set *isl_map_domain(
2231 __isl_take isl_map *bmap);
2232 __isl_give isl_set *isl_map_range(
2233 __isl_take isl_map *map);
2235 #include <isl/union_set.h>
2236 __isl_give isl_set *isl_union_set_params(
2237 __isl_take isl_union_set *uset);
2239 #include <isl/union_map.h>
2240 __isl_give isl_union_map *isl_union_map_project_out(
2241 __isl_take isl_union_map *umap,
2242 enum isl_dim_type type, unsigned first, unsigned n);
2243 __isl_give isl_set *isl_union_map_params(
2244 __isl_take isl_union_map *umap);
2245 __isl_give isl_union_set *isl_union_map_domain(
2246 __isl_take isl_union_map *umap);
2247 __isl_give isl_union_set *isl_union_map_range(
2248 __isl_take isl_union_map *umap);
2250 The function C<isl_union_map_project_out> can only project out
2253 #include <isl/map.h>
2254 __isl_give isl_basic_map *isl_basic_map_domain_map(
2255 __isl_take isl_basic_map *bmap);
2256 __isl_give isl_basic_map *isl_basic_map_range_map(
2257 __isl_take isl_basic_map *bmap);
2258 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2259 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2261 #include <isl/union_map.h>
2262 __isl_give isl_union_map *isl_union_map_domain_map(
2263 __isl_take isl_union_map *umap);
2264 __isl_give isl_union_map *isl_union_map_range_map(
2265 __isl_take isl_union_map *umap);
2267 The functions above construct a (basic, regular or union) relation
2268 that maps (a wrapped version of) the input relation to its domain or range.
2272 __isl_give isl_basic_set *isl_basic_set_eliminate(
2273 __isl_take isl_basic_set *bset,
2274 enum isl_dim_type type,
2275 unsigned first, unsigned n);
2276 __isl_give isl_set *isl_set_eliminate(
2277 __isl_take isl_set *set, enum isl_dim_type type,
2278 unsigned first, unsigned n);
2279 __isl_give isl_basic_map *isl_basic_map_eliminate(
2280 __isl_take isl_basic_map *bmap,
2281 enum isl_dim_type type,
2282 unsigned first, unsigned n);
2283 __isl_give isl_map *isl_map_eliminate(
2284 __isl_take isl_map *map, enum isl_dim_type type,
2285 unsigned first, unsigned n);
2287 Eliminate the coefficients for the given dimensions from the constraints,
2288 without removing the dimensions.
2290 =item * Constructing a relation from a set
2292 #include <isl/local_space.h>
2293 __isl_give isl_local_space *isl_local_space_from_domain(
2294 __isl_take isl_local_space *ls);
2296 #include <isl/map.h>
2297 __isl_give isl_map *isl_map_from_domain(
2298 __isl_take isl_set *set);
2299 __isl_give isl_map *isl_map_from_range(
2300 __isl_take isl_set *set);
2302 Create a relation with the given set as domain or range.
2303 The range or domain of the created relation is a zero-dimensional
2304 flat anonymous space.
2308 __isl_give isl_basic_set *isl_basic_set_fix_si(
2309 __isl_take isl_basic_set *bset,
2310 enum isl_dim_type type, unsigned pos, int value);
2311 __isl_give isl_basic_set *isl_basic_set_fix_val(
2312 __isl_take isl_basic_set *bset,
2313 enum isl_dim_type type, unsigned pos,
2314 __isl_take isl_val *v);
2315 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2316 enum isl_dim_type type, unsigned pos, int value);
2317 __isl_give isl_set *isl_set_fix_val(
2318 __isl_take isl_set *set,
2319 enum isl_dim_type type, unsigned pos,
2320 __isl_take isl_val *v);
2321 __isl_give isl_basic_map *isl_basic_map_fix_si(
2322 __isl_take isl_basic_map *bmap,
2323 enum isl_dim_type type, unsigned pos, int value);
2324 __isl_give isl_basic_map *isl_basic_map_fix_val(
2325 __isl_take isl_basic_map *bmap,
2326 enum isl_dim_type type, unsigned pos,
2327 __isl_take isl_val *v);
2328 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2329 enum isl_dim_type type, unsigned pos, int value);
2330 __isl_give isl_map *isl_map_fix_val(
2331 __isl_take isl_map *map,
2332 enum isl_dim_type type, unsigned pos,
2333 __isl_take isl_val *v);
2335 Intersect the set or relation with the hyperplane where the given
2336 dimension has the fixed given value.
2338 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2339 __isl_take isl_basic_map *bmap,
2340 enum isl_dim_type type, unsigned pos, int value);
2341 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2342 __isl_take isl_basic_map *bmap,
2343 enum isl_dim_type type, unsigned pos, int value);
2344 __isl_give isl_set *isl_set_lower_bound_si(
2345 __isl_take isl_set *set,
2346 enum isl_dim_type type, unsigned pos, int value);
2347 __isl_give isl_set *isl_set_lower_bound_val(
2348 __isl_take isl_set *set,
2349 enum isl_dim_type type, unsigned pos,
2350 __isl_take isl_val *value);
2351 __isl_give isl_map *isl_map_lower_bound_si(
2352 __isl_take isl_map *map,
2353 enum isl_dim_type type, unsigned pos, int value);
2354 __isl_give isl_set *isl_set_upper_bound_si(
2355 __isl_take isl_set *set,
2356 enum isl_dim_type type, unsigned pos, int value);
2357 __isl_give isl_set *isl_set_upper_bound_val(
2358 __isl_take isl_set *set,
2359 enum isl_dim_type type, unsigned pos,
2360 __isl_take isl_val *value);
2361 __isl_give isl_map *isl_map_upper_bound_si(
2362 __isl_take isl_map *map,
2363 enum isl_dim_type type, unsigned pos, int value);
2365 Intersect the set or relation with the half-space where the given
2366 dimension has a value bounded by the fixed given integer value.
2368 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2369 enum isl_dim_type type1, int pos1,
2370 enum isl_dim_type type2, int pos2);
2371 __isl_give isl_basic_map *isl_basic_map_equate(
2372 __isl_take isl_basic_map *bmap,
2373 enum isl_dim_type type1, int pos1,
2374 enum isl_dim_type type2, int pos2);
2375 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2376 enum isl_dim_type type1, int pos1,
2377 enum isl_dim_type type2, int pos2);
2379 Intersect the set or relation with the hyperplane where the given
2380 dimensions are equal to each other.
2382 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2383 enum isl_dim_type type1, int pos1,
2384 enum isl_dim_type type2, int pos2);
2386 Intersect the relation with the hyperplane where the given
2387 dimensions have opposite values.
2389 __isl_give isl_map *isl_map_order_le(
2390 __isl_take isl_map *map,
2391 enum isl_dim_type type1, int pos1,
2392 enum isl_dim_type type2, int pos2);
2393 __isl_give isl_basic_map *isl_basic_map_order_ge(
2394 __isl_take isl_basic_map *bmap,
2395 enum isl_dim_type type1, int pos1,
2396 enum isl_dim_type type2, int pos2);
2397 __isl_give isl_map *isl_map_order_ge(
2398 __isl_take isl_map *map,
2399 enum isl_dim_type type1, int pos1,
2400 enum isl_dim_type type2, int pos2);
2401 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2402 enum isl_dim_type type1, int pos1,
2403 enum isl_dim_type type2, int pos2);
2404 __isl_give isl_basic_map *isl_basic_map_order_gt(
2405 __isl_take isl_basic_map *bmap,
2406 enum isl_dim_type type1, int pos1,
2407 enum isl_dim_type type2, int pos2);
2408 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2409 enum isl_dim_type type1, int pos1,
2410 enum isl_dim_type type2, int pos2);
2412 Intersect the relation with the half-space where the given
2413 dimensions satisfy the given ordering.
2417 __isl_give isl_map *isl_set_identity(
2418 __isl_take isl_set *set);
2419 __isl_give isl_union_map *isl_union_set_identity(
2420 __isl_take isl_union_set *uset);
2422 Construct an identity relation on the given (union) set.
2426 __isl_give isl_basic_set *isl_basic_map_deltas(
2427 __isl_take isl_basic_map *bmap);
2428 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2429 __isl_give isl_union_set *isl_union_map_deltas(
2430 __isl_take isl_union_map *umap);
2432 These functions return a (basic) set containing the differences
2433 between image elements and corresponding domain elements in the input.
2435 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2436 __isl_take isl_basic_map *bmap);
2437 __isl_give isl_map *isl_map_deltas_map(
2438 __isl_take isl_map *map);
2439 __isl_give isl_union_map *isl_union_map_deltas_map(
2440 __isl_take isl_union_map *umap);
2442 The functions above construct a (basic, regular or union) relation
2443 that maps (a wrapped version of) the input relation to its delta set.
2447 Simplify the representation of a set or relation by trying
2448 to combine pairs of basic sets or relations into a single
2449 basic set or relation.
2451 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2452 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2453 __isl_give isl_union_set *isl_union_set_coalesce(
2454 __isl_take isl_union_set *uset);
2455 __isl_give isl_union_map *isl_union_map_coalesce(
2456 __isl_take isl_union_map *umap);
2458 One of the methods for combining pairs of basic sets or relations
2459 can result in coefficients that are much larger than those that appear
2460 in the constraints of the input. By default, the coefficients are
2461 not allowed to grow larger, but this can be changed by unsetting
2462 the following option.
2464 int isl_options_set_coalesce_bounded_wrapping(
2465 isl_ctx *ctx, int val);
2466 int isl_options_get_coalesce_bounded_wrapping(
2469 =item * Detecting equalities
2471 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2472 __isl_take isl_basic_set *bset);
2473 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2474 __isl_take isl_basic_map *bmap);
2475 __isl_give isl_set *isl_set_detect_equalities(
2476 __isl_take isl_set *set);
2477 __isl_give isl_map *isl_map_detect_equalities(
2478 __isl_take isl_map *map);
2479 __isl_give isl_union_set *isl_union_set_detect_equalities(
2480 __isl_take isl_union_set *uset);
2481 __isl_give isl_union_map *isl_union_map_detect_equalities(
2482 __isl_take isl_union_map *umap);
2484 Simplify the representation of a set or relation by detecting implicit
2487 =item * Removing redundant constraints
2489 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2490 __isl_take isl_basic_set *bset);
2491 __isl_give isl_set *isl_set_remove_redundancies(
2492 __isl_take isl_set *set);
2493 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2494 __isl_take isl_basic_map *bmap);
2495 __isl_give isl_map *isl_map_remove_redundancies(
2496 __isl_take isl_map *map);
2500 __isl_give isl_basic_set *isl_set_convex_hull(
2501 __isl_take isl_set *set);
2502 __isl_give isl_basic_map *isl_map_convex_hull(
2503 __isl_take isl_map *map);
2505 If the input set or relation has any existentially quantified
2506 variables, then the result of these operations is currently undefined.
2510 __isl_give isl_basic_set *
2511 isl_set_unshifted_simple_hull(
2512 __isl_take isl_set *set);
2513 __isl_give isl_basic_map *
2514 isl_map_unshifted_simple_hull(
2515 __isl_take isl_map *map);
2516 __isl_give isl_basic_set *isl_set_simple_hull(
2517 __isl_take isl_set *set);
2518 __isl_give isl_basic_map *isl_map_simple_hull(
2519 __isl_take isl_map *map);
2520 __isl_give isl_union_map *isl_union_map_simple_hull(
2521 __isl_take isl_union_map *umap);
2523 These functions compute a single basic set or relation
2524 that contains the whole input set or relation.
2525 In particular, the output is described by translates
2526 of the constraints describing the basic sets or relations in the input.
2527 In case of C<isl_set_unshifted_simple_hull>, only the original
2528 constraints are used, without any translation.
2532 (See \autoref{s:simple hull}.)
2538 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2539 __isl_take isl_basic_set *bset);
2540 __isl_give isl_basic_set *isl_set_affine_hull(
2541 __isl_take isl_set *set);
2542 __isl_give isl_union_set *isl_union_set_affine_hull(
2543 __isl_take isl_union_set *uset);
2544 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2545 __isl_take isl_basic_map *bmap);
2546 __isl_give isl_basic_map *isl_map_affine_hull(
2547 __isl_take isl_map *map);
2548 __isl_give isl_union_map *isl_union_map_affine_hull(
2549 __isl_take isl_union_map *umap);
2551 In case of union sets and relations, the affine hull is computed
2554 =item * Polyhedral hull
2556 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2557 __isl_take isl_set *set);
2558 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2559 __isl_take isl_map *map);
2560 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2561 __isl_take isl_union_set *uset);
2562 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2563 __isl_take isl_union_map *umap);
2565 These functions compute a single basic set or relation
2566 not involving any existentially quantified variables
2567 that contains the whole input set or relation.
2568 In case of union sets and relations, the polyhedral hull is computed
2571 =item * Other approximations
2573 __isl_give isl_basic_set *
2574 isl_basic_set_drop_constraints_involving_dims(
2575 __isl_take isl_basic_set *bset,
2576 enum isl_dim_type type,
2577 unsigned first, unsigned n);
2578 __isl_give isl_basic_map *
2579 isl_basic_map_drop_constraints_involving_dims(
2580 __isl_take isl_basic_map *bmap,
2581 enum isl_dim_type type,
2582 unsigned first, unsigned n);
2583 __isl_give isl_basic_set *
2584 isl_basic_set_drop_constraints_not_involving_dims(
2585 __isl_take isl_basic_set *bset,
2586 enum isl_dim_type type,
2587 unsigned first, unsigned n);
2588 __isl_give isl_set *
2589 isl_set_drop_constraints_involving_dims(
2590 __isl_take isl_set *set,
2591 enum isl_dim_type type,
2592 unsigned first, unsigned n);
2593 __isl_give isl_map *
2594 isl_map_drop_constraints_involving_dims(
2595 __isl_take isl_map *map,
2596 enum isl_dim_type type,
2597 unsigned first, unsigned n);
2599 These functions drop any constraints (not) involving the specified dimensions.
2600 Note that the result depends on the representation of the input.
2604 __isl_give isl_basic_set *isl_basic_set_sample(
2605 __isl_take isl_basic_set *bset);
2606 __isl_give isl_basic_set *isl_set_sample(
2607 __isl_take isl_set *set);
2608 __isl_give isl_basic_map *isl_basic_map_sample(
2609 __isl_take isl_basic_map *bmap);
2610 __isl_give isl_basic_map *isl_map_sample(
2611 __isl_take isl_map *map);
2613 If the input (basic) set or relation is non-empty, then return
2614 a singleton subset of the input. Otherwise, return an empty set.
2616 =item * Optimization
2618 #include <isl/ilp.h>
2619 __isl_give isl_val *isl_basic_set_max_val(
2620 __isl_keep isl_basic_set *bset,
2621 __isl_keep isl_aff *obj);
2622 __isl_give isl_val *isl_set_min_val(
2623 __isl_keep isl_set *set,
2624 __isl_keep isl_aff *obj);
2625 __isl_give isl_val *isl_set_max_val(
2626 __isl_keep isl_set *set,
2627 __isl_keep isl_aff *obj);
2629 Compute the minimum or maximum of the integer affine expression C<obj>
2630 over the points in C<set>, returning the result in C<opt>.
2631 The result is C<NULL> in case of an error, the optimal value in case
2632 there is one, negative infinity or infinity if the problem is unbounded and
2633 NaN if the problem is empty.
2635 =item * Parametric optimization
2637 __isl_give isl_pw_aff *isl_set_dim_min(
2638 __isl_take isl_set *set, int pos);
2639 __isl_give isl_pw_aff *isl_set_dim_max(
2640 __isl_take isl_set *set, int pos);
2641 __isl_give isl_pw_aff *isl_map_dim_max(
2642 __isl_take isl_map *map, int pos);
2644 Compute the minimum or maximum of the given set or output dimension
2645 as a function of the parameters (and input dimensions), but independently
2646 of the other set or output dimensions.
2647 For lexicographic optimization, see L<"Lexicographic Optimization">.
2651 The following functions compute either the set of (rational) coefficient
2652 values of valid constraints for the given set or the set of (rational)
2653 values satisfying the constraints with coefficients from the given set.
2654 Internally, these two sets of functions perform essentially the
2655 same operations, except that the set of coefficients is assumed to
2656 be a cone, while the set of values may be any polyhedron.
2657 The current implementation is based on the Farkas lemma and
2658 Fourier-Motzkin elimination, but this may change or be made optional
2659 in future. In particular, future implementations may use different
2660 dualization algorithms or skip the elimination step.
2662 __isl_give isl_basic_set *isl_basic_set_coefficients(
2663 __isl_take isl_basic_set *bset);
2664 __isl_give isl_basic_set *isl_set_coefficients(
2665 __isl_take isl_set *set);
2666 __isl_give isl_union_set *isl_union_set_coefficients(
2667 __isl_take isl_union_set *bset);
2668 __isl_give isl_basic_set *isl_basic_set_solutions(
2669 __isl_take isl_basic_set *bset);
2670 __isl_give isl_basic_set *isl_set_solutions(
2671 __isl_take isl_set *set);
2672 __isl_give isl_union_set *isl_union_set_solutions(
2673 __isl_take isl_union_set *bset);
2677 __isl_give isl_map *isl_map_fixed_power_val(
2678 __isl_take isl_map *map,
2679 __isl_take isl_val *exp);
2680 __isl_give isl_union_map *
2681 isl_union_map_fixed_power_val(
2682 __isl_take isl_union_map *umap,
2683 __isl_take isl_val *exp);
2685 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2686 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2687 of C<map> is computed.
2689 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2691 __isl_give isl_union_map *isl_union_map_power(
2692 __isl_take isl_union_map *umap, int *exact);
2694 Compute a parametric representation for all positive powers I<k> of C<map>.
2695 The result maps I<k> to a nested relation corresponding to the
2696 I<k>th power of C<map>.
2697 The result may be an overapproximation. If the result is known to be exact,
2698 then C<*exact> is set to C<1>.
2700 =item * Transitive closure
2702 __isl_give isl_map *isl_map_transitive_closure(
2703 __isl_take isl_map *map, int *exact);
2704 __isl_give isl_union_map *isl_union_map_transitive_closure(
2705 __isl_take isl_union_map *umap, int *exact);
2707 Compute the transitive closure of C<map>.
2708 The result may be an overapproximation. If the result is known to be exact,
2709 then C<*exact> is set to C<1>.
2711 =item * Reaching path lengths
2713 __isl_give isl_map *isl_map_reaching_path_lengths(
2714 __isl_take isl_map *map, int *exact);
2716 Compute a relation that maps each element in the range of C<map>
2717 to the lengths of all paths composed of edges in C<map> that
2718 end up in the given element.
2719 The result may be an overapproximation. If the result is known to be exact,
2720 then C<*exact> is set to C<1>.
2721 To compute the I<maximal> path length, the resulting relation
2722 should be postprocessed by C<isl_map_lexmax>.
2723 In particular, if the input relation is a dependence relation
2724 (mapping sources to sinks), then the maximal path length corresponds
2725 to the free schedule.
2726 Note, however, that C<isl_map_lexmax> expects the maximum to be
2727 finite, so if the path lengths are unbounded (possibly due to
2728 the overapproximation), then you will get an error message.
2732 #include <isl/space.h>
2733 __isl_give isl_space *isl_space_wrap(
2734 __isl_take isl_space *space);
2735 __isl_give isl_space *isl_space_unwrap(
2736 __isl_take isl_space *space);
2738 #include <isl/set.h>
2739 __isl_give isl_basic_map *isl_basic_set_unwrap(
2740 __isl_take isl_basic_set *bset);
2741 __isl_give isl_map *isl_set_unwrap(
2742 __isl_take isl_set *set);
2744 #include <isl/map.h>
2745 __isl_give isl_basic_set *isl_basic_map_wrap(
2746 __isl_take isl_basic_map *bmap);
2747 __isl_give isl_set *isl_map_wrap(
2748 __isl_take isl_map *map);
2750 #include <isl/union_set.h>
2751 __isl_give isl_union_map *isl_union_set_unwrap(
2752 __isl_take isl_union_set *uset);
2754 #include <isl/union_map.h>
2755 __isl_give isl_union_set *isl_union_map_wrap(
2756 __isl_take isl_union_map *umap);
2758 The input to C<isl_space_unwrap> should
2759 be the space of a set, while that of
2760 C<isl_space_wrap> should be the space of a relation.
2761 Conversely, the output of C<isl_space_unwrap> is the space
2762 of a relation, while that of C<isl_space_wrap> is the space of a set.
2766 Remove any internal structure of domain (and range) of the given
2767 set or relation. If there is any such internal structure in the input,
2768 then the name of the space is also removed.
2770 #include <isl/local_space.h>
2771 __isl_give isl_local_space *
2772 isl_local_space_flatten_domain(
2773 __isl_take isl_local_space *ls);
2774 __isl_give isl_local_space *
2775 isl_local_space_flatten_range(
2776 __isl_take isl_local_space *ls);
2778 #include <isl/set.h>
2779 __isl_give isl_basic_set *isl_basic_set_flatten(
2780 __isl_take isl_basic_set *bset);
2781 __isl_give isl_set *isl_set_flatten(
2782 __isl_take isl_set *set);
2784 #include <isl/map.h>
2785 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2786 __isl_take isl_basic_map *bmap);
2787 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2788 __isl_take isl_basic_map *bmap);
2789 __isl_give isl_map *isl_map_flatten_range(
2790 __isl_take isl_map *map);
2791 __isl_give isl_map *isl_map_flatten_domain(
2792 __isl_take isl_map *map);
2793 __isl_give isl_basic_map *isl_basic_map_flatten(
2794 __isl_take isl_basic_map *bmap);
2795 __isl_give isl_map *isl_map_flatten(
2796 __isl_take isl_map *map);
2798 #include <isl/map.h>
2799 __isl_give isl_map *isl_set_flatten_map(
2800 __isl_take isl_set *set);
2802 The function above constructs a relation
2803 that maps the input set to a flattened version of the set.
2807 Lift the input set to a space with extra dimensions corresponding
2808 to the existentially quantified variables in the input.
2809 In particular, the result lives in a wrapped map where the domain
2810 is the original space and the range corresponds to the original
2811 existentially quantified variables.
2813 __isl_give isl_basic_set *isl_basic_set_lift(
2814 __isl_take isl_basic_set *bset);
2815 __isl_give isl_set *isl_set_lift(
2816 __isl_take isl_set *set);
2817 __isl_give isl_union_set *isl_union_set_lift(
2818 __isl_take isl_union_set *uset);
2820 Given a local space that contains the existentially quantified
2821 variables of a set, a basic relation that, when applied to
2822 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2823 can be constructed using the following function.
2825 #include <isl/local_space.h>
2826 __isl_give isl_basic_map *isl_local_space_lifting(
2827 __isl_take isl_local_space *ls);
2829 =item * Internal Product
2831 __isl_give isl_basic_map *isl_basic_map_zip(
2832 __isl_take isl_basic_map *bmap);
2833 __isl_give isl_map *isl_map_zip(
2834 __isl_take isl_map *map);
2835 __isl_give isl_union_map *isl_union_map_zip(
2836 __isl_take isl_union_map *umap);
2838 Given a relation with nested relations for domain and range,
2839 interchange the range of the domain with the domain of the range.
2843 __isl_give isl_basic_map *isl_basic_map_curry(
2844 __isl_take isl_basic_map *bmap);
2845 __isl_give isl_basic_map *isl_basic_map_uncurry(
2846 __isl_take isl_basic_map *bmap);
2847 __isl_give isl_map *isl_map_curry(
2848 __isl_take isl_map *map);
2849 __isl_give isl_map *isl_map_uncurry(
2850 __isl_take isl_map *map);
2851 __isl_give isl_union_map *isl_union_map_curry(
2852 __isl_take isl_union_map *umap);
2853 __isl_give isl_union_map *isl_union_map_uncurry(
2854 __isl_take isl_union_map *umap);
2856 Given a relation with a nested relation for domain,
2857 the C<curry> functions
2858 move the range of the nested relation out of the domain
2859 and use it as the domain of a nested relation in the range,
2860 with the original range as range of this nested relation.
2861 The C<uncurry> functions perform the inverse operation.
2863 =item * Aligning parameters
2865 __isl_give isl_basic_set *isl_basic_set_align_params(
2866 __isl_take isl_basic_set *bset,
2867 __isl_take isl_space *model);
2868 __isl_give isl_set *isl_set_align_params(
2869 __isl_take isl_set *set,
2870 __isl_take isl_space *model);
2871 __isl_give isl_basic_map *isl_basic_map_align_params(
2872 __isl_take isl_basic_map *bmap,
2873 __isl_take isl_space *model);
2874 __isl_give isl_map *isl_map_align_params(
2875 __isl_take isl_map *map,
2876 __isl_take isl_space *model);
2878 Change the order of the parameters of the given set or relation
2879 such that the first parameters match those of C<model>.
2880 This may involve the introduction of extra parameters.
2881 All parameters need to be named.
2883 =item * Dimension manipulation
2885 #include <isl/local_space.h>
2886 __isl_give isl_local_space *isl_local_space_add_dims(
2887 __isl_take isl_local_space *ls,
2888 enum isl_dim_type type, unsigned n);
2889 __isl_give isl_local_space *isl_local_space_insert_dims(
2890 __isl_take isl_local_space *ls,
2891 enum isl_dim_type type, unsigned first, unsigned n);
2892 __isl_give isl_local_space *isl_local_space_drop_dims(
2893 __isl_take isl_local_space *ls,
2894 enum isl_dim_type type, unsigned first, unsigned n);
2896 #include <isl/set.h>
2897 __isl_give isl_basic_set *isl_basic_set_add_dims(
2898 __isl_take isl_basic_set *bset,
2899 enum isl_dim_type type, unsigned n);
2900 __isl_give isl_set *isl_set_add_dims(
2901 __isl_take isl_set *set,
2902 enum isl_dim_type type, unsigned n);
2903 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2904 __isl_take isl_basic_set *bset,
2905 enum isl_dim_type type, unsigned pos,
2907 __isl_give isl_set *isl_set_insert_dims(
2908 __isl_take isl_set *set,
2909 enum isl_dim_type type, unsigned pos, unsigned n);
2910 __isl_give isl_basic_set *isl_basic_set_move_dims(
2911 __isl_take isl_basic_set *bset,
2912 enum isl_dim_type dst_type, unsigned dst_pos,
2913 enum isl_dim_type src_type, unsigned src_pos,
2915 __isl_give isl_set *isl_set_move_dims(
2916 __isl_take isl_set *set,
2917 enum isl_dim_type dst_type, unsigned dst_pos,
2918 enum isl_dim_type src_type, unsigned src_pos,
2921 #include <isl/map.h>
2922 __isl_give isl_map *isl_map_add_dims(
2923 __isl_take isl_map *map,
2924 enum isl_dim_type type, unsigned n);
2925 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2926 __isl_take isl_basic_map *bmap,
2927 enum isl_dim_type type, unsigned pos,
2929 __isl_give isl_map *isl_map_insert_dims(
2930 __isl_take isl_map *map,
2931 enum isl_dim_type type, unsigned pos, unsigned n);
2932 __isl_give isl_basic_map *isl_basic_map_move_dims(
2933 __isl_take isl_basic_map *bmap,
2934 enum isl_dim_type dst_type, unsigned dst_pos,
2935 enum isl_dim_type src_type, unsigned src_pos,
2937 __isl_give isl_map *isl_map_move_dims(
2938 __isl_take isl_map *map,
2939 enum isl_dim_type dst_type, unsigned dst_pos,
2940 enum isl_dim_type src_type, unsigned src_pos,
2943 It is usually not advisable to directly change the (input or output)
2944 space of a set or a relation as this removes the name and the internal
2945 structure of the space. However, the above functions can be useful
2946 to add new parameters, assuming
2947 C<isl_set_align_params> and C<isl_map_align_params>
2952 =head2 Binary Operations
2954 The two arguments of a binary operation not only need to live
2955 in the same C<isl_ctx>, they currently also need to have
2956 the same (number of) parameters.
2958 =head3 Basic Operations
2962 =item * Intersection
2964 #include <isl/local_space.h>
2965 __isl_give isl_local_space *isl_local_space_intersect(
2966 __isl_take isl_local_space *ls1,
2967 __isl_take isl_local_space *ls2);
2969 #include <isl/set.h>
2970 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2971 __isl_take isl_basic_set *bset1,
2972 __isl_take isl_basic_set *bset2);
2973 __isl_give isl_basic_set *isl_basic_set_intersect(
2974 __isl_take isl_basic_set *bset1,
2975 __isl_take isl_basic_set *bset2);
2976 __isl_give isl_set *isl_set_intersect_params(
2977 __isl_take isl_set *set,
2978 __isl_take isl_set *params);
2979 __isl_give isl_set *isl_set_intersect(
2980 __isl_take isl_set *set1,
2981 __isl_take isl_set *set2);
2983 #include <isl/map.h>
2984 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2985 __isl_take isl_basic_map *bmap,
2986 __isl_take isl_basic_set *bset);
2987 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2988 __isl_take isl_basic_map *bmap,
2989 __isl_take isl_basic_set *bset);
2990 __isl_give isl_basic_map *isl_basic_map_intersect(
2991 __isl_take isl_basic_map *bmap1,
2992 __isl_take isl_basic_map *bmap2);
2993 __isl_give isl_map *isl_map_intersect_params(
2994 __isl_take isl_map *map,
2995 __isl_take isl_set *params);
2996 __isl_give isl_map *isl_map_intersect_domain(
2997 __isl_take isl_map *map,
2998 __isl_take isl_set *set);
2999 __isl_give isl_map *isl_map_intersect_range(
3000 __isl_take isl_map *map,
3001 __isl_take isl_set *set);
3002 __isl_give isl_map *isl_map_intersect(
3003 __isl_take isl_map *map1,
3004 __isl_take isl_map *map2);
3006 #include <isl/union_set.h>
3007 __isl_give isl_union_set *isl_union_set_intersect_params(
3008 __isl_take isl_union_set *uset,
3009 __isl_take isl_set *set);
3010 __isl_give isl_union_set *isl_union_set_intersect(
3011 __isl_take isl_union_set *uset1,
3012 __isl_take isl_union_set *uset2);
3014 #include <isl/union_map.h>
3015 __isl_give isl_union_map *isl_union_map_intersect_params(
3016 __isl_take isl_union_map *umap,
3017 __isl_take isl_set *set);
3018 __isl_give isl_union_map *isl_union_map_intersect_domain(
3019 __isl_take isl_union_map *umap,
3020 __isl_take isl_union_set *uset);
3021 __isl_give isl_union_map *isl_union_map_intersect_range(
3022 __isl_take isl_union_map *umap,
3023 __isl_take isl_union_set *uset);
3024 __isl_give isl_union_map *isl_union_map_intersect(
3025 __isl_take isl_union_map *umap1,
3026 __isl_take isl_union_map *umap2);
3028 The second argument to the C<_params> functions needs to be
3029 a parametric (basic) set. For the other functions, a parametric set
3030 for either argument is only allowed if the other argument is
3031 a parametric set as well.
3035 __isl_give isl_set *isl_basic_set_union(
3036 __isl_take isl_basic_set *bset1,
3037 __isl_take isl_basic_set *bset2);
3038 __isl_give isl_map *isl_basic_map_union(
3039 __isl_take isl_basic_map *bmap1,
3040 __isl_take isl_basic_map *bmap2);
3041 __isl_give isl_set *isl_set_union(
3042 __isl_take isl_set *set1,
3043 __isl_take isl_set *set2);
3044 __isl_give isl_map *isl_map_union(
3045 __isl_take isl_map *map1,
3046 __isl_take isl_map *map2);
3047 __isl_give isl_union_set *isl_union_set_union(
3048 __isl_take isl_union_set *uset1,
3049 __isl_take isl_union_set *uset2);
3050 __isl_give isl_union_map *isl_union_map_union(
3051 __isl_take isl_union_map *umap1,
3052 __isl_take isl_union_map *umap2);
3054 =item * Set difference
3056 __isl_give isl_set *isl_set_subtract(
3057 __isl_take isl_set *set1,
3058 __isl_take isl_set *set2);
3059 __isl_give isl_map *isl_map_subtract(
3060 __isl_take isl_map *map1,
3061 __isl_take isl_map *map2);
3062 __isl_give isl_map *isl_map_subtract_domain(
3063 __isl_take isl_map *map,
3064 __isl_take isl_set *dom);
3065 __isl_give isl_map *isl_map_subtract_range(
3066 __isl_take isl_map *map,
3067 __isl_take isl_set *dom);
3068 __isl_give isl_union_set *isl_union_set_subtract(
3069 __isl_take isl_union_set *uset1,
3070 __isl_take isl_union_set *uset2);
3071 __isl_give isl_union_map *isl_union_map_subtract(
3072 __isl_take isl_union_map *umap1,
3073 __isl_take isl_union_map *umap2);
3074 __isl_give isl_union_map *isl_union_map_subtract_domain(
3075 __isl_take isl_union_map *umap,
3076 __isl_take isl_union_set *dom);
3077 __isl_give isl_union_map *isl_union_map_subtract_range(
3078 __isl_take isl_union_map *umap,
3079 __isl_take isl_union_set *dom);
3083 __isl_give isl_basic_set *isl_basic_set_apply(
3084 __isl_take isl_basic_set *bset,
3085 __isl_take isl_basic_map *bmap);
3086 __isl_give isl_set *isl_set_apply(
3087 __isl_take isl_set *set,
3088 __isl_take isl_map *map);
3089 __isl_give isl_union_set *isl_union_set_apply(
3090 __isl_take isl_union_set *uset,
3091 __isl_take isl_union_map *umap);
3092 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3093 __isl_take isl_basic_map *bmap1,
3094 __isl_take isl_basic_map *bmap2);
3095 __isl_give isl_basic_map *isl_basic_map_apply_range(
3096 __isl_take isl_basic_map *bmap1,
3097 __isl_take isl_basic_map *bmap2);
3098 __isl_give isl_map *isl_map_apply_domain(
3099 __isl_take isl_map *map1,
3100 __isl_take isl_map *map2);
3101 __isl_give isl_union_map *isl_union_map_apply_domain(
3102 __isl_take isl_union_map *umap1,
3103 __isl_take isl_union_map *umap2);
3104 __isl_give isl_map *isl_map_apply_range(
3105 __isl_take isl_map *map1,
3106 __isl_take isl_map *map2);
3107 __isl_give isl_union_map *isl_union_map_apply_range(
3108 __isl_take isl_union_map *umap1,
3109 __isl_take isl_union_map *umap2);
3113 #include <isl/set.h>
3114 __isl_give isl_basic_set *
3115 isl_basic_set_preimage_multi_aff(
3116 __isl_take isl_basic_set *bset,
3117 __isl_take isl_multi_aff *ma);
3118 __isl_give isl_set *isl_set_preimage_multi_aff(
3119 __isl_take isl_set *set,
3120 __isl_take isl_multi_aff *ma);
3121 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3122 __isl_take isl_set *set,
3123 __isl_take isl_pw_multi_aff *pma);
3124 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
3125 __isl_take isl_set *set,
3126 __isl_take isl_multi_pw_aff *mpa);
3128 #include <isl/union_set.h>
3129 __isl_give isl_union_set *
3130 isl_union_set_preimage_multi_aff(
3131 __isl_take isl_union_set *uset,
3132 __isl_take isl_multi_aff *ma);
3133 __isl_give isl_union_set *
3134 isl_union_set_preimage_pw_multi_aff(
3135 __isl_take isl_union_set *uset,
3136 __isl_take isl_pw_multi_aff *pma);
3137 __isl_give isl_union_set *
3138 isl_union_set_preimage_union_pw_multi_aff(
3139 __isl_take isl_union_set *uset,
3140 __isl_take isl_union_pw_multi_aff *upma);
3142 #include <isl/map.h>
3143 __isl_give isl_basic_map *
3144 isl_basic_map_preimage_domain_multi_aff(
3145 __isl_take isl_basic_map *bmap,
3146 __isl_take isl_multi_aff *ma);
3147 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3148 __isl_take isl_map *map,
3149 __isl_take isl_multi_aff *ma);
3150 __isl_give isl_map *isl_map_preimage_range_multi_aff(
3151 __isl_take isl_map *map,
3152 __isl_take isl_multi_aff *ma);
3153 __isl_give isl_map *
3154 isl_map_preimage_domain_pw_multi_aff(
3155 __isl_take isl_map *map,
3156 __isl_take isl_pw_multi_aff *pma);
3157 __isl_give isl_map *
3158 isl_map_preimage_range_pw_multi_aff(
3159 __isl_take isl_map *map,
3160 __isl_take isl_pw_multi_aff *pma);
3161 __isl_give isl_map *
3162 isl_map_preimage_domain_multi_pw_aff(
3163 __isl_take isl_map *map,
3164 __isl_take isl_multi_pw_aff *mpa);
3165 __isl_give isl_basic_map *
3166 isl_basic_map_preimage_range_multi_aff(
3167 __isl_take isl_basic_map *bmap,
3168 __isl_take isl_multi_aff *ma);
3170 #include <isl/union_map.h>
3171 __isl_give isl_union_map *
3172 isl_union_map_preimage_domain_multi_aff(
3173 __isl_take isl_union_map *umap,
3174 __isl_take isl_multi_aff *ma);
3175 __isl_give isl_union_map *
3176 isl_union_map_preimage_range_multi_aff(
3177 __isl_take isl_union_map *umap,
3178 __isl_take isl_multi_aff *ma);
3179 __isl_give isl_union_map *
3180 isl_union_map_preimage_domain_pw_multi_aff(
3181 __isl_take isl_union_map *umap,
3182 __isl_take isl_pw_multi_aff *pma);
3183 __isl_give isl_union_map *
3184 isl_union_map_preimage_range_pw_multi_aff(
3185 __isl_take isl_union_map *umap,
3186 __isl_take isl_pw_multi_aff *pma);
3187 __isl_give isl_union_map *
3188 isl_union_map_preimage_domain_union_pw_multi_aff(
3189 __isl_take isl_union_map *umap,
3190 __isl_take isl_union_pw_multi_aff *upma);
3191 __isl_give isl_union_map *
3192 isl_union_map_preimage_range_union_pw_multi_aff(
3193 __isl_take isl_union_map *umap,
3194 __isl_take isl_union_pw_multi_aff *upma);
3196 These functions compute the preimage of the given set or map domain/range under
3197 the given function. In other words, the expression is plugged
3198 into the set description or into the domain/range of the map.
3199 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3200 L</"Piecewise Multiple Quasi Affine Expressions">.
3202 =item * Cartesian Product
3204 #include <isl/space.h>
3205 __isl_give isl_space *isl_space_product(
3206 __isl_take isl_space *space1,
3207 __isl_take isl_space *space2);
3208 __isl_give isl_space *isl_space_domain_product(
3209 __isl_take isl_space *space1,
3210 __isl_take isl_space *space2);
3211 __isl_give isl_space *isl_space_range_product(
3212 __isl_take isl_space *space1,
3213 __isl_take isl_space *space2);
3216 C<isl_space_product>, C<isl_space_domain_product>
3217 and C<isl_space_range_product> take pairs or relation spaces and
3218 produce a single relations space, where either the domain, the range
3219 or both domain and range are wrapped spaces of relations between
3220 the domains and/or ranges of the input spaces.
3221 If the product is only constructed over the domain or the range
3222 then the ranges or the domains of the inputs should be the same.
3223 The function C<isl_space_product> also accepts a pair of set spaces,
3224 in which case it returns a wrapped space of a relation between the
3227 #include <isl/set.h>
3228 __isl_give isl_set *isl_set_product(
3229 __isl_take isl_set *set1,
3230 __isl_take isl_set *set2);
3232 #include <isl/map.h>
3233 __isl_give isl_basic_map *isl_basic_map_domain_product(
3234 __isl_take isl_basic_map *bmap1,
3235 __isl_take isl_basic_map *bmap2);
3236 __isl_give isl_basic_map *isl_basic_map_range_product(
3237 __isl_take isl_basic_map *bmap1,
3238 __isl_take isl_basic_map *bmap2);
3239 __isl_give isl_basic_map *isl_basic_map_product(
3240 __isl_take isl_basic_map *bmap1,
3241 __isl_take isl_basic_map *bmap2);
3242 __isl_give isl_map *isl_map_domain_product(
3243 __isl_take isl_map *map1,
3244 __isl_take isl_map *map2);
3245 __isl_give isl_map *isl_map_range_product(
3246 __isl_take isl_map *map1,
3247 __isl_take isl_map *map2);
3248 __isl_give isl_map *isl_map_product(
3249 __isl_take isl_map *map1,
3250 __isl_take isl_map *map2);
3252 #include <isl/union_set.h>
3253 __isl_give isl_union_set *isl_union_set_product(
3254 __isl_take isl_union_set *uset1,
3255 __isl_take isl_union_set *uset2);
3257 #include <isl/union_map.h>
3258 __isl_give isl_union_map *isl_union_map_domain_product(
3259 __isl_take isl_union_map *umap1,
3260 __isl_take isl_union_map *umap2);
3261 __isl_give isl_union_map *isl_union_map_range_product(
3262 __isl_take isl_union_map *umap1,
3263 __isl_take isl_union_map *umap2);
3264 __isl_give isl_union_map *isl_union_map_product(
3265 __isl_take isl_union_map *umap1,
3266 __isl_take isl_union_map *umap2);
3268 The above functions compute the cross product of the given
3269 sets or relations. The domains and ranges of the results
3270 are wrapped maps between domains and ranges of the inputs.
3271 To obtain a ``flat'' product, use the following functions
3274 __isl_give isl_basic_set *isl_basic_set_flat_product(
3275 __isl_take isl_basic_set *bset1,
3276 __isl_take isl_basic_set *bset2);
3277 __isl_give isl_set *isl_set_flat_product(
3278 __isl_take isl_set *set1,
3279 __isl_take isl_set *set2);
3280 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3281 __isl_take isl_basic_map *bmap1,
3282 __isl_take isl_basic_map *bmap2);
3283 __isl_give isl_map *isl_map_flat_domain_product(
3284 __isl_take isl_map *map1,
3285 __isl_take isl_map *map2);
3286 __isl_give isl_map *isl_map_flat_range_product(
3287 __isl_take isl_map *map1,
3288 __isl_take isl_map *map2);
3289 __isl_give isl_union_map *isl_union_map_flat_range_product(
3290 __isl_take isl_union_map *umap1,
3291 __isl_take isl_union_map *umap2);
3292 __isl_give isl_basic_map *isl_basic_map_flat_product(
3293 __isl_take isl_basic_map *bmap1,
3294 __isl_take isl_basic_map *bmap2);
3295 __isl_give isl_map *isl_map_flat_product(
3296 __isl_take isl_map *map1,
3297 __isl_take isl_map *map2);
3299 #include <isl/space.h>
3300 __isl_give isl_space *isl_space_domain_factor_domain(
3301 __isl_take isl_space *space);
3302 __isl_give isl_space *isl_space_range_factor_domain(
3303 __isl_take isl_space *space);
3304 __isl_give isl_space *isl_space_range_factor_range(
3305 __isl_take isl_space *space);
3307 The functions C<isl_space_range_factor_domain> and
3308 C<isl_space_range_factor_range> extract the two arguments from
3309 the result of a call to C<isl_space_range_product>.
3311 The arguments of a call to C<isl_map_range_product> can be extracted
3312 from the result using the following two functions.
3314 #include <isl/map.h>
3315 __isl_give isl_map *isl_map_range_factor_domain(
3316 __isl_take isl_map *map);
3317 __isl_give isl_map *isl_map_range_factor_range(
3318 __isl_take isl_map *map);
3320 =item * Simplification
3322 __isl_give isl_basic_set *isl_basic_set_gist(
3323 __isl_take isl_basic_set *bset,
3324 __isl_take isl_basic_set *context);
3325 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3326 __isl_take isl_set *context);
3327 __isl_give isl_set *isl_set_gist_params(
3328 __isl_take isl_set *set,
3329 __isl_take isl_set *context);
3330 __isl_give isl_union_set *isl_union_set_gist(
3331 __isl_take isl_union_set *uset,
3332 __isl_take isl_union_set *context);
3333 __isl_give isl_union_set *isl_union_set_gist_params(
3334 __isl_take isl_union_set *uset,
3335 __isl_take isl_set *set);
3336 __isl_give isl_basic_map *isl_basic_map_gist(
3337 __isl_take isl_basic_map *bmap,
3338 __isl_take isl_basic_map *context);
3339 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3340 __isl_take isl_map *context);
3341 __isl_give isl_map *isl_map_gist_params(
3342 __isl_take isl_map *map,
3343 __isl_take isl_set *context);
3344 __isl_give isl_map *isl_map_gist_domain(
3345 __isl_take isl_map *map,
3346 __isl_take isl_set *context);
3347 __isl_give isl_map *isl_map_gist_range(
3348 __isl_take isl_map *map,
3349 __isl_take isl_set *context);
3350 __isl_give isl_union_map *isl_union_map_gist(
3351 __isl_take isl_union_map *umap,
3352 __isl_take isl_union_map *context);
3353 __isl_give isl_union_map *isl_union_map_gist_params(
3354 __isl_take isl_union_map *umap,
3355 __isl_take isl_set *set);
3356 __isl_give isl_union_map *isl_union_map_gist_domain(
3357 __isl_take isl_union_map *umap,
3358 __isl_take isl_union_set *uset);
3359 __isl_give isl_union_map *isl_union_map_gist_range(
3360 __isl_take isl_union_map *umap,
3361 __isl_take isl_union_set *uset);
3363 The gist operation returns a set or relation that has the
3364 same intersection with the context as the input set or relation.
3365 Any implicit equality in the intersection is made explicit in the result,
3366 while all inequalities that are redundant with respect to the intersection
3368 In case of union sets and relations, the gist operation is performed
3373 =head3 Lexicographic Optimization
3375 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3376 the following functions
3377 compute a set that contains the lexicographic minimum or maximum
3378 of the elements in C<set> (or C<bset>) for those values of the parameters
3379 that satisfy C<dom>.
3380 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3381 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3383 In other words, the union of the parameter values
3384 for which the result is non-empty and of C<*empty>
3387 __isl_give isl_set *isl_basic_set_partial_lexmin(
3388 __isl_take isl_basic_set *bset,
3389 __isl_take isl_basic_set *dom,
3390 __isl_give isl_set **empty);
3391 __isl_give isl_set *isl_basic_set_partial_lexmax(
3392 __isl_take isl_basic_set *bset,
3393 __isl_take isl_basic_set *dom,
3394 __isl_give isl_set **empty);
3395 __isl_give isl_set *isl_set_partial_lexmin(
3396 __isl_take isl_set *set, __isl_take isl_set *dom,
3397 __isl_give isl_set **empty);
3398 __isl_give isl_set *isl_set_partial_lexmax(
3399 __isl_take isl_set *set, __isl_take isl_set *dom,
3400 __isl_give isl_set **empty);
3402 Given a (basic) set C<set> (or C<bset>), the following functions simply
3403 return a set containing the lexicographic minimum or maximum
3404 of the elements in C<set> (or C<bset>).
3405 In case of union sets, the optimum is computed per space.
3407 __isl_give isl_set *isl_basic_set_lexmin(
3408 __isl_take isl_basic_set *bset);
3409 __isl_give isl_set *isl_basic_set_lexmax(
3410 __isl_take isl_basic_set *bset);
3411 __isl_give isl_set *isl_set_lexmin(
3412 __isl_take isl_set *set);
3413 __isl_give isl_set *isl_set_lexmax(
3414 __isl_take isl_set *set);
3415 __isl_give isl_union_set *isl_union_set_lexmin(
3416 __isl_take isl_union_set *uset);
3417 __isl_give isl_union_set *isl_union_set_lexmax(
3418 __isl_take isl_union_set *uset);
3420 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3421 the following functions
3422 compute a relation that maps each element of C<dom>
3423 to the single lexicographic minimum or maximum
3424 of the elements that are associated to that same
3425 element in C<map> (or C<bmap>).
3426 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3427 that contains the elements in C<dom> that do not map
3428 to any elements in C<map> (or C<bmap>).
3429 In other words, the union of the domain of the result and of C<*empty>
3432 __isl_give isl_map *isl_basic_map_partial_lexmax(
3433 __isl_take isl_basic_map *bmap,
3434 __isl_take isl_basic_set *dom,
3435 __isl_give isl_set **empty);
3436 __isl_give isl_map *isl_basic_map_partial_lexmin(
3437 __isl_take isl_basic_map *bmap,
3438 __isl_take isl_basic_set *dom,
3439 __isl_give isl_set **empty);
3440 __isl_give isl_map *isl_map_partial_lexmax(
3441 __isl_take isl_map *map, __isl_take isl_set *dom,
3442 __isl_give isl_set **empty);
3443 __isl_give isl_map *isl_map_partial_lexmin(
3444 __isl_take isl_map *map, __isl_take isl_set *dom,
3445 __isl_give isl_set **empty);
3447 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3448 return a map mapping each element in the domain of
3449 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3450 of all elements associated to that element.
3451 In case of union relations, the optimum is computed per space.
3453 __isl_give isl_map *isl_basic_map_lexmin(
3454 __isl_take isl_basic_map *bmap);
3455 __isl_give isl_map *isl_basic_map_lexmax(
3456 __isl_take isl_basic_map *bmap);
3457 __isl_give isl_map *isl_map_lexmin(
3458 __isl_take isl_map *map);
3459 __isl_give isl_map *isl_map_lexmax(
3460 __isl_take isl_map *map);
3461 __isl_give isl_union_map *isl_union_map_lexmin(
3462 __isl_take isl_union_map *umap);
3463 __isl_give isl_union_map *isl_union_map_lexmax(
3464 __isl_take isl_union_map *umap);
3466 The following functions return their result in the form of
3467 a piecewise multi-affine expression
3468 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3469 but are otherwise equivalent to the corresponding functions
3470 returning a basic set or relation.
3472 __isl_give isl_pw_multi_aff *
3473 isl_basic_map_lexmin_pw_multi_aff(
3474 __isl_take isl_basic_map *bmap);
3475 __isl_give isl_pw_multi_aff *
3476 isl_basic_set_partial_lexmin_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_set_partial_lexmax_pw_multi_aff(
3482 __isl_take isl_basic_set *bset,
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_lexmin_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 *
3491 isl_basic_map_partial_lexmax_pw_multi_aff(
3492 __isl_take isl_basic_map *bmap,
3493 __isl_take isl_basic_set *dom,
3494 __isl_give isl_set **empty);
3495 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3496 __isl_take isl_set *set);
3497 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3498 __isl_take isl_set *set);
3499 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3500 __isl_take isl_map *map);
3501 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3502 __isl_take isl_map *map);
3506 Lists are defined over several element types, including
3507 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3508 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3509 Here we take lists of C<isl_set>s as an example.
3510 Lists can be created, copied, modified and freed using the following functions.
3512 #include <isl/list.h>
3513 __isl_give isl_set_list *isl_set_list_from_set(
3514 __isl_take isl_set *el);
3515 __isl_give isl_set_list *isl_set_list_alloc(
3516 isl_ctx *ctx, int n);
3517 __isl_give isl_set_list *isl_set_list_copy(
3518 __isl_keep isl_set_list *list);
3519 __isl_give isl_set_list *isl_set_list_insert(
3520 __isl_take isl_set_list *list, unsigned pos,
3521 __isl_take isl_set *el);
3522 __isl_give isl_set_list *isl_set_list_add(
3523 __isl_take isl_set_list *list,
3524 __isl_take isl_set *el);
3525 __isl_give isl_set_list *isl_set_list_drop(
3526 __isl_take isl_set_list *list,
3527 unsigned first, unsigned n);
3528 __isl_give isl_set_list *isl_set_list_set_set(
3529 __isl_take isl_set_list *list, int index,
3530 __isl_take isl_set *set);
3531 __isl_give isl_set_list *isl_set_list_concat(
3532 __isl_take isl_set_list *list1,
3533 __isl_take isl_set_list *list2);
3534 __isl_give isl_set_list *isl_set_list_sort(
3535 __isl_take isl_set_list *list,
3536 int (*cmp)(__isl_keep isl_set *a,
3537 __isl_keep isl_set *b, void *user),
3539 __isl_null isl_set_list *isl_set_list_free(
3540 __isl_take isl_set_list *list);
3542 C<isl_set_list_alloc> creates an empty list with a capacity for
3543 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3546 Lists can be inspected using the following functions.
3548 #include <isl/list.h>
3549 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3550 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3551 __isl_give isl_set *isl_set_list_get_set(
3552 __isl_keep isl_set_list *list, int index);
3553 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3554 int (*fn)(__isl_take isl_set *el, void *user),
3556 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3557 int (*follows)(__isl_keep isl_set *a,
3558 __isl_keep isl_set *b, void *user),
3560 int (*fn)(__isl_take isl_set *el, void *user),
3563 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3564 strongly connected components of the graph with as vertices the elements
3565 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3566 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3567 should return C<-1> on error.
3569 Lists can be printed using
3571 #include <isl/list.h>
3572 __isl_give isl_printer *isl_printer_print_set_list(
3573 __isl_take isl_printer *p,
3574 __isl_keep isl_set_list *list);
3576 =head2 Associative arrays
3578 Associative arrays map isl objects of a specific type to isl objects
3579 of some (other) specific type. They are defined for several pairs
3580 of types, including (C<isl_map>, C<isl_basic_set>),
3581 (C<isl_id>, C<isl_ast_expr>) and.
3582 (C<isl_id>, C<isl_pw_aff>).
3583 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3586 Associative arrays can be created, copied and freed using
3587 the following functions.
3589 #include <isl/id_to_ast_expr.h>
3590 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3591 isl_ctx *ctx, int min_size);
3592 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3593 __isl_keep id_to_ast_expr *id2expr);
3594 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
3595 __isl_take id_to_ast_expr *id2expr);
3597 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3598 to specify the expected size of the associative array.
3599 The associative array will be grown automatically as needed.
3601 Associative arrays can be inspected using the following functions.
3603 #include <isl/id_to_ast_expr.h>
3604 isl_ctx *isl_id_to_ast_expr_get_ctx(
3605 __isl_keep id_to_ast_expr *id2expr);
3606 int isl_id_to_ast_expr_has(
3607 __isl_keep id_to_ast_expr *id2expr,
3608 __isl_keep isl_id *key);
3609 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3610 __isl_keep id_to_ast_expr *id2expr,
3611 __isl_take isl_id *key);
3612 int isl_id_to_ast_expr_foreach(
3613 __isl_keep id_to_ast_expr *id2expr,
3614 int (*fn)(__isl_take isl_id *key,
3615 __isl_take isl_ast_expr *val, void *user),
3618 They can be modified using the following function.
3620 #include <isl/id_to_ast_expr.h>
3621 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3622 __isl_take id_to_ast_expr *id2expr,
3623 __isl_take isl_id *key,
3624 __isl_take isl_ast_expr *val);
3625 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
3626 __isl_take id_to_ast_expr *id2expr,
3627 __isl_take isl_id *key);
3629 Associative arrays can be printed using the following function.
3631 #include <isl/id_to_ast_expr.h>
3632 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3633 __isl_take isl_printer *p,
3634 __isl_keep id_to_ast_expr *id2expr);
3636 =head2 Multiple Values
3638 An C<isl_multi_val> object represents a sequence of zero or more values,
3639 living in a set space.
3641 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3642 using the following function
3644 #include <isl/val.h>
3645 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3646 __isl_take isl_space *space,
3647 __isl_take isl_val_list *list);
3649 The zero multiple value (with value zero for each set dimension)
3650 can be created using the following function.
3652 #include <isl/val.h>
3653 __isl_give isl_multi_val *isl_multi_val_zero(
3654 __isl_take isl_space *space);
3656 Multiple values can be copied and freed using
3658 #include <isl/val.h>
3659 __isl_give isl_multi_val *isl_multi_val_copy(
3660 __isl_keep isl_multi_val *mv);
3661 __isl_null isl_multi_val *isl_multi_val_free(
3662 __isl_take isl_multi_val *mv);
3664 They can be inspected using
3666 #include <isl/val.h>
3667 isl_ctx *isl_multi_val_get_ctx(
3668 __isl_keep isl_multi_val *mv);
3669 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3670 enum isl_dim_type type);
3671 __isl_give isl_val *isl_multi_val_get_val(
3672 __isl_keep isl_multi_val *mv, int pos);
3673 int isl_multi_val_find_dim_by_id(
3674 __isl_keep isl_multi_val *mv,
3675 enum isl_dim_type type, __isl_keep isl_id *id);
3676 __isl_give isl_id *isl_multi_val_get_dim_id(
3677 __isl_keep isl_multi_val *mv,
3678 enum isl_dim_type type, unsigned pos);
3679 const char *isl_multi_val_get_tuple_name(
3680 __isl_keep isl_multi_val *mv,
3681 enum isl_dim_type type);
3682 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3683 enum isl_dim_type type);
3684 __isl_give isl_id *isl_multi_val_get_tuple_id(
3685 __isl_keep isl_multi_val *mv,
3686 enum isl_dim_type type);
3687 int isl_multi_val_range_is_wrapping(
3688 __isl_keep isl_multi_val *mv);
3690 They can be modified using
3692 #include <isl/val.h>
3693 __isl_give isl_multi_val *isl_multi_val_set_val(
3694 __isl_take isl_multi_val *mv, int pos,
3695 __isl_take isl_val *val);
3696 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3697 __isl_take isl_multi_val *mv,
3698 enum isl_dim_type type, unsigned pos, const char *s);
3699 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3700 __isl_take isl_multi_val *mv,
3701 enum isl_dim_type type, unsigned pos,
3702 __isl_take isl_id *id);
3703 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3704 __isl_take isl_multi_val *mv,
3705 enum isl_dim_type type, const char *s);
3706 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3707 __isl_take isl_multi_val *mv,
3708 enum isl_dim_type type, __isl_take isl_id *id);
3709 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3710 __isl_take isl_multi_val *mv,
3711 enum isl_dim_type type);
3712 __isl_give isl_multi_val *isl_multi_val_reset_user(
3713 __isl_take isl_multi_val *mv);
3715 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3716 __isl_take isl_multi_val *mv,
3717 enum isl_dim_type type, unsigned first, unsigned n);
3718 __isl_give isl_multi_val *isl_multi_val_add_dims(
3719 __isl_take isl_multi_val *mv,
3720 enum isl_dim_type type, unsigned n);
3721 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3722 __isl_take isl_multi_val *mv,
3723 enum isl_dim_type type, unsigned first, unsigned n);
3727 #include <isl/val.h>
3728 __isl_give isl_multi_val *isl_multi_val_align_params(
3729 __isl_take isl_multi_val *mv,
3730 __isl_take isl_space *model);
3731 __isl_give isl_multi_val *isl_multi_val_from_range(
3732 __isl_take isl_multi_val *mv);
3733 __isl_give isl_multi_val *isl_multi_val_range_splice(
3734 __isl_take isl_multi_val *mv1, unsigned pos,
3735 __isl_take isl_multi_val *mv2);
3736 __isl_give isl_multi_val *isl_multi_val_range_product(
3737 __isl_take isl_multi_val *mv1,
3738 __isl_take isl_multi_val *mv2);
3739 __isl_give isl_multi_val *
3740 isl_multi_val_range_factor_domain(
3741 __isl_take isl_multi_val *mv);
3742 __isl_give isl_multi_val *
3743 isl_multi_val_range_factor_range(
3744 __isl_take isl_multi_val *mv);
3745 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3746 __isl_take isl_multi_val *mv1,
3747 __isl_take isl_multi_aff *mv2);
3748 __isl_give isl_multi_val *isl_multi_val_product(
3749 __isl_take isl_multi_val *mv1,
3750 __isl_take isl_multi_val *mv2);
3751 __isl_give isl_multi_val *isl_multi_val_add_val(
3752 __isl_take isl_multi_val *mv,
3753 __isl_take isl_val *v);
3754 __isl_give isl_multi_val *isl_multi_val_mod_val(
3755 __isl_take isl_multi_val *mv,
3756 __isl_take isl_val *v);
3757 __isl_give isl_multi_val *isl_multi_val_scale_val(
3758 __isl_take isl_multi_val *mv,
3759 __isl_take isl_val *v);
3760 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3761 __isl_take isl_multi_val *mv1,
3762 __isl_take isl_multi_val *mv2);
3763 __isl_give isl_multi_val *
3764 isl_multi_val_scale_down_multi_val(
3765 __isl_take isl_multi_val *mv1,
3766 __isl_take isl_multi_val *mv2);
3768 A multiple value can be printed using
3770 __isl_give isl_printer *isl_printer_print_multi_val(
3771 __isl_take isl_printer *p,
3772 __isl_keep isl_multi_val *mv);
3776 Vectors can be created, copied and freed using the following functions.
3778 #include <isl/vec.h>
3779 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3781 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3782 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
3784 Note that the elements of a newly created vector may have arbitrary values.
3785 The elements can be changed and inspected using the following functions.
3787 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3788 int isl_vec_size(__isl_keep isl_vec *vec);
3789 __isl_give isl_val *isl_vec_get_element_val(
3790 __isl_keep isl_vec *vec, int pos);
3791 __isl_give isl_vec *isl_vec_set_element_si(
3792 __isl_take isl_vec *vec, int pos, int v);
3793 __isl_give isl_vec *isl_vec_set_element_val(
3794 __isl_take isl_vec *vec, int pos,
3795 __isl_take isl_val *v);
3796 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3798 __isl_give isl_vec *isl_vec_set_val(
3799 __isl_take isl_vec *vec, __isl_take isl_val *v);
3800 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3801 __isl_keep isl_vec *vec2, int pos);
3803 C<isl_vec_get_element> will return a negative value if anything went wrong.
3804 In that case, the value of C<*v> is undefined.
3806 The following function can be used to concatenate two vectors.
3808 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3809 __isl_take isl_vec *vec2);
3813 Matrices can be created, copied and freed using the following functions.
3815 #include <isl/mat.h>
3816 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3817 unsigned n_row, unsigned n_col);
3818 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3819 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
3821 Note that the elements of a newly created matrix may have arbitrary values.
3822 The elements can be changed and inspected using the following functions.
3824 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3825 int isl_mat_rows(__isl_keep isl_mat *mat);
3826 int isl_mat_cols(__isl_keep isl_mat *mat);
3827 __isl_give isl_val *isl_mat_get_element_val(
3828 __isl_keep isl_mat *mat, int row, int col);
3829 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3830 int row, int col, int v);
3831 __isl_give isl_mat *isl_mat_set_element_val(
3832 __isl_take isl_mat *mat, int row, int col,
3833 __isl_take isl_val *v);
3835 C<isl_mat_get_element> will return a negative value if anything went wrong.
3836 In that case, the value of C<*v> is undefined.
3838 The following function can be used to compute the (right) inverse
3839 of a matrix, i.e., a matrix such that the product of the original
3840 and the inverse (in that order) is a multiple of the identity matrix.
3841 The input matrix is assumed to be of full row-rank.
3843 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3845 The following function can be used to compute the (right) kernel
3846 (or null space) of a matrix, i.e., a matrix such that the product of
3847 the original and the kernel (in that order) is the zero matrix.
3849 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3851 =head2 Piecewise Quasi Affine Expressions
3853 The zero quasi affine expression or the quasi affine expression
3854 that is equal to a given value or
3855 a specified dimension on a given domain can be created using
3857 __isl_give isl_aff *isl_aff_zero_on_domain(
3858 __isl_take isl_local_space *ls);
3859 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3860 __isl_take isl_local_space *ls);
3861 __isl_give isl_aff *isl_aff_val_on_domain(
3862 __isl_take isl_local_space *ls,
3863 __isl_take isl_val *val);
3864 __isl_give isl_aff *isl_aff_var_on_domain(
3865 __isl_take isl_local_space *ls,
3866 enum isl_dim_type type, unsigned pos);
3867 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3868 __isl_take isl_local_space *ls,
3869 enum isl_dim_type type, unsigned pos);
3870 __isl_give isl_aff *isl_aff_nan_on_domain(
3871 __isl_take isl_local_space *ls);
3872 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3873 __isl_take isl_local_space *ls);
3875 Note that the space in which the resulting objects live is a map space
3876 with the given space as domain and a one-dimensional range.
3878 An empty piecewise quasi affine expression (one with no cells)
3879 or a piecewise quasi affine expression with a single cell can
3880 be created using the following functions.
3882 #include <isl/aff.h>
3883 __isl_give isl_pw_aff *isl_pw_aff_empty(
3884 __isl_take isl_space *space);
3885 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3886 __isl_take isl_set *set, __isl_take isl_aff *aff);
3887 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3888 __isl_take isl_aff *aff);
3890 A piecewise quasi affine expression that is equal to 1 on a set
3891 and 0 outside the set can be created using the following function.
3893 #include <isl/aff.h>
3894 __isl_give isl_pw_aff *isl_set_indicator_function(
3895 __isl_take isl_set *set);
3897 Quasi affine expressions can be copied and freed using
3899 #include <isl/aff.h>
3900 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3901 __isl_null isl_aff *isl_aff_free(__isl_take isl_aff *aff);
3903 __isl_give isl_pw_aff *isl_pw_aff_copy(
3904 __isl_keep isl_pw_aff *pwaff);
3905 __isl_null isl_pw_aff *isl_pw_aff_free(
3906 __isl_take isl_pw_aff *pwaff);
3908 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3909 using the following function. The constraint is required to have
3910 a non-zero coefficient for the specified dimension.
3912 #include <isl/constraint.h>
3913 __isl_give isl_aff *isl_constraint_get_bound(
3914 __isl_keep isl_constraint *constraint,
3915 enum isl_dim_type type, int pos);
3917 The entire affine expression of the constraint can also be extracted
3918 using the following function.
3920 #include <isl/constraint.h>
3921 __isl_give isl_aff *isl_constraint_get_aff(
3922 __isl_keep isl_constraint *constraint);
3924 Conversely, an equality constraint equating
3925 the affine expression to zero or an inequality constraint enforcing
3926 the affine expression to be non-negative, can be constructed using
3928 __isl_give isl_constraint *isl_equality_from_aff(
3929 __isl_take isl_aff *aff);
3930 __isl_give isl_constraint *isl_inequality_from_aff(
3931 __isl_take isl_aff *aff);
3933 The expression can be inspected using
3935 #include <isl/aff.h>
3936 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3937 int isl_aff_dim(__isl_keep isl_aff *aff,
3938 enum isl_dim_type type);
3939 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3940 __isl_keep isl_aff *aff);
3941 __isl_give isl_local_space *isl_aff_get_local_space(
3942 __isl_keep isl_aff *aff);
3943 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3944 enum isl_dim_type type, unsigned pos);
3945 const char *isl_pw_aff_get_dim_name(
3946 __isl_keep isl_pw_aff *pa,
3947 enum isl_dim_type type, unsigned pos);
3948 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3949 enum isl_dim_type type, unsigned pos);
3950 __isl_give isl_id *isl_pw_aff_get_dim_id(
3951 __isl_keep isl_pw_aff *pa,
3952 enum isl_dim_type type, unsigned pos);
3953 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
3954 enum isl_dim_type type);
3955 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3956 __isl_keep isl_pw_aff *pa,
3957 enum isl_dim_type type);
3958 __isl_give isl_val *isl_aff_get_constant_val(
3959 __isl_keep isl_aff *aff);
3960 __isl_give isl_val *isl_aff_get_coefficient_val(
3961 __isl_keep isl_aff *aff,
3962 enum isl_dim_type type, int pos);
3963 __isl_give isl_val *isl_aff_get_denominator_val(
3964 __isl_keep isl_aff *aff);
3965 __isl_give isl_aff *isl_aff_get_div(
3966 __isl_keep isl_aff *aff, int pos);
3968 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3969 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3970 int (*fn)(__isl_take isl_set *set,
3971 __isl_take isl_aff *aff,
3972 void *user), void *user);
3974 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3975 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3977 int isl_aff_is_nan(__isl_keep isl_aff *aff);
3978 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
3980 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3981 enum isl_dim_type type, unsigned first, unsigned n);
3982 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3983 enum isl_dim_type type, unsigned first, unsigned n);
3985 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3986 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3987 enum isl_dim_type type);
3988 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3990 It can be modified using
3992 #include <isl/aff.h>
3993 __isl_give isl_aff *isl_aff_set_tuple_id(
3994 __isl_take isl_aff *aff,
3995 enum isl_dim_type type, __isl_take isl_id *id);
3996 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3997 __isl_take isl_pw_aff *pwaff,
3998 enum isl_dim_type type, __isl_take isl_id *id);
3999 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
4000 __isl_take isl_pw_aff *pa,
4001 enum isl_dim_type type);
4002 __isl_give isl_aff *isl_aff_set_dim_name(
4003 __isl_take isl_aff *aff, enum isl_dim_type type,
4004 unsigned pos, const char *s);
4005 __isl_give isl_aff *isl_aff_set_dim_id(
4006 __isl_take isl_aff *aff, enum isl_dim_type type,
4007 unsigned pos, __isl_take isl_id *id);
4008 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
4009 __isl_take isl_pw_aff *pma,
4010 enum isl_dim_type type, unsigned pos,
4011 __isl_take isl_id *id);
4012 __isl_give isl_aff *isl_aff_set_constant_si(
4013 __isl_take isl_aff *aff, int v);
4014 __isl_give isl_aff *isl_aff_set_constant_val(
4015 __isl_take isl_aff *aff, __isl_take isl_val *v);
4016 __isl_give isl_aff *isl_aff_set_coefficient_si(
4017 __isl_take isl_aff *aff,
4018 enum isl_dim_type type, int pos, int v);
4019 __isl_give isl_aff *isl_aff_set_coefficient_val(
4020 __isl_take isl_aff *aff,
4021 enum isl_dim_type type, int pos,
4022 __isl_take isl_val *v);
4024 __isl_give isl_aff *isl_aff_add_constant_si(
4025 __isl_take isl_aff *aff, int v);
4026 __isl_give isl_aff *isl_aff_add_constant_val(
4027 __isl_take isl_aff *aff, __isl_take isl_val *v);
4028 __isl_give isl_aff *isl_aff_add_constant_num_si(
4029 __isl_take isl_aff *aff, int v);
4030 __isl_give isl_aff *isl_aff_add_coefficient_si(
4031 __isl_take isl_aff *aff,
4032 enum isl_dim_type type, int pos, int v);
4033 __isl_give isl_aff *isl_aff_add_coefficient_val(
4034 __isl_take isl_aff *aff,
4035 enum isl_dim_type type, int pos,
4036 __isl_take isl_val *v);
4038 __isl_give isl_aff *isl_aff_insert_dims(
4039 __isl_take isl_aff *aff,
4040 enum isl_dim_type type, unsigned first, unsigned n);
4041 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
4042 __isl_take isl_pw_aff *pwaff,
4043 enum isl_dim_type type, unsigned first, unsigned n);
4044 __isl_give isl_aff *isl_aff_add_dims(
4045 __isl_take isl_aff *aff,
4046 enum isl_dim_type type, unsigned n);
4047 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
4048 __isl_take isl_pw_aff *pwaff,
4049 enum isl_dim_type type, unsigned n);
4050 __isl_give isl_aff *isl_aff_drop_dims(
4051 __isl_take isl_aff *aff,
4052 enum isl_dim_type type, unsigned first, unsigned n);
4053 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
4054 __isl_take isl_pw_aff *pwaff,
4055 enum isl_dim_type type, unsigned first, unsigned n);
4056 __isl_give isl_aff *isl_aff_move_dims(
4057 __isl_take isl_aff *aff,
4058 enum isl_dim_type dst_type, unsigned dst_pos,
4059 enum isl_dim_type src_type, unsigned src_pos,
4061 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
4062 __isl_take isl_pw_aff *pa,
4063 enum isl_dim_type dst_type, unsigned dst_pos,
4064 enum isl_dim_type src_type, unsigned src_pos,
4067 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
4068 set the I<numerator> of the constant or coefficient, while
4069 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
4070 the constant or coefficient as a whole.
4071 The C<add_constant> and C<add_coefficient> functions add an integer
4072 or rational value to
4073 the possibly rational constant or coefficient.
4074 The C<add_constant_num> functions add an integer value to
4077 To check whether an affine expressions is obviously zero
4078 or (obviously) equal to some other affine expression, use
4080 #include <isl/aff.h>
4081 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
4082 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
4083 __isl_keep isl_aff *aff2);
4084 int isl_pw_aff_plain_is_equal(
4085 __isl_keep isl_pw_aff *pwaff1,
4086 __isl_keep isl_pw_aff *pwaff2);
4087 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
4088 __isl_keep isl_pw_aff *pa2);
4089 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4090 __isl_keep isl_pw_aff *pa2);
4092 The function C<isl_pw_aff_plain_cmp> can be used to sort
4093 C<isl_pw_aff>s. The order is not strictly defined.
4094 The current order sorts expressions that only involve
4095 earlier dimensions before those that involve later dimensions.
4099 #include <isl/aff.h>
4100 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
4101 __isl_take isl_aff *aff2);
4102 __isl_give isl_pw_aff *isl_pw_aff_add(
4103 __isl_take isl_pw_aff *pwaff1,
4104 __isl_take isl_pw_aff *pwaff2);
4105 __isl_give isl_pw_aff *isl_pw_aff_min(
4106 __isl_take isl_pw_aff *pwaff1,
4107 __isl_take isl_pw_aff *pwaff2);
4108 __isl_give isl_pw_aff *isl_pw_aff_max(
4109 __isl_take isl_pw_aff *pwaff1,
4110 __isl_take isl_pw_aff *pwaff2);
4111 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
4112 __isl_take isl_aff *aff2);
4113 __isl_give isl_pw_aff *isl_pw_aff_sub(
4114 __isl_take isl_pw_aff *pwaff1,
4115 __isl_take isl_pw_aff *pwaff2);
4116 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
4117 __isl_give isl_pw_aff *isl_pw_aff_neg(
4118 __isl_take isl_pw_aff *pwaff);
4119 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
4120 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4121 __isl_take isl_pw_aff *pwaff);
4122 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
4123 __isl_give isl_pw_aff *isl_pw_aff_floor(
4124 __isl_take isl_pw_aff *pwaff);
4125 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
4126 __isl_take isl_val *mod);
4127 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
4128 __isl_take isl_pw_aff *pa,
4129 __isl_take isl_val *mod);
4130 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
4131 __isl_take isl_val *v);
4132 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
4133 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
4134 __isl_give isl_aff *isl_aff_scale_down_ui(
4135 __isl_take isl_aff *aff, unsigned f);
4136 __isl_give isl_aff *isl_aff_scale_down_val(
4137 __isl_take isl_aff *aff, __isl_take isl_val *v);
4138 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
4139 __isl_take isl_pw_aff *pa,
4140 __isl_take isl_val *f);
4142 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4143 __isl_take isl_pw_aff_list *list);
4144 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4145 __isl_take isl_pw_aff_list *list);
4147 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4148 __isl_take isl_pw_aff *pwqp);
4150 __isl_give isl_aff *isl_aff_align_params(
4151 __isl_take isl_aff *aff,
4152 __isl_take isl_space *model);
4153 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4154 __isl_take isl_pw_aff *pwaff,
4155 __isl_take isl_space *model);
4157 __isl_give isl_aff *isl_aff_project_domain_on_params(
4158 __isl_take isl_aff *aff);
4159 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4160 __isl_take isl_pw_aff *pwa);
4162 __isl_give isl_aff *isl_aff_gist_params(
4163 __isl_take isl_aff *aff,
4164 __isl_take isl_set *context);
4165 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
4166 __isl_take isl_set *context);
4167 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
4168 __isl_take isl_pw_aff *pwaff,
4169 __isl_take isl_set *context);
4170 __isl_give isl_pw_aff *isl_pw_aff_gist(
4171 __isl_take isl_pw_aff *pwaff,
4172 __isl_take isl_set *context);
4174 __isl_give isl_set *isl_pw_aff_domain(
4175 __isl_take isl_pw_aff *pwaff);
4176 __isl_give isl_set *isl_pw_aff_params(
4177 __isl_take isl_pw_aff *pwa);
4178 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4179 __isl_take isl_pw_aff *pa,
4180 __isl_take isl_set *set);
4181 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4182 __isl_take isl_pw_aff *pa,
4183 __isl_take isl_set *set);
4185 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
4186 __isl_take isl_aff *aff2);
4187 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
4188 __isl_take isl_aff *aff2);
4189 __isl_give isl_pw_aff *isl_pw_aff_mul(
4190 __isl_take isl_pw_aff *pwaff1,
4191 __isl_take isl_pw_aff *pwaff2);
4192 __isl_give isl_pw_aff *isl_pw_aff_div(
4193 __isl_take isl_pw_aff *pa1,
4194 __isl_take isl_pw_aff *pa2);
4195 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
4196 __isl_take isl_pw_aff *pa1,
4197 __isl_take isl_pw_aff *pa2);
4198 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
4199 __isl_take isl_pw_aff *pa1,
4200 __isl_take isl_pw_aff *pa2);
4202 When multiplying two affine expressions, at least one of the two needs
4203 to be a constant. Similarly, when dividing an affine expression by another,
4204 the second expression needs to be a constant.
4205 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
4206 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
4209 #include <isl/aff.h>
4210 __isl_give isl_aff *isl_aff_pullback_aff(
4211 __isl_take isl_aff *aff1,
4212 __isl_take isl_aff *aff2);
4213 __isl_give isl_aff *isl_aff_pullback_multi_aff(
4214 __isl_take isl_aff *aff,
4215 __isl_take isl_multi_aff *ma);
4216 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
4217 __isl_take isl_pw_aff *pa,
4218 __isl_take isl_multi_aff *ma);
4219 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
4220 __isl_take isl_pw_aff *pa,
4221 __isl_take isl_pw_multi_aff *pma);
4222 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
4223 __isl_take isl_pw_aff *pa,
4224 __isl_take isl_multi_pw_aff *mpa);
4226 These functions precompose the input expression by the given
4227 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
4228 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
4229 into the (piecewise) affine expression.
4230 Objects of type C<isl_multi_aff> are described in
4231 L</"Piecewise Multiple Quasi Affine Expressions">.
4233 #include <isl/aff.h>
4234 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4235 __isl_take isl_aff *aff);
4236 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4237 __isl_take isl_aff *aff);
4238 __isl_give isl_basic_set *isl_aff_le_basic_set(
4239 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4240 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4241 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4242 __isl_give isl_set *isl_pw_aff_eq_set(
4243 __isl_take isl_pw_aff *pwaff1,
4244 __isl_take isl_pw_aff *pwaff2);
4245 __isl_give isl_set *isl_pw_aff_ne_set(
4246 __isl_take isl_pw_aff *pwaff1,
4247 __isl_take isl_pw_aff *pwaff2);
4248 __isl_give isl_set *isl_pw_aff_le_set(
4249 __isl_take isl_pw_aff *pwaff1,
4250 __isl_take isl_pw_aff *pwaff2);
4251 __isl_give isl_set *isl_pw_aff_lt_set(
4252 __isl_take isl_pw_aff *pwaff1,
4253 __isl_take isl_pw_aff *pwaff2);
4254 __isl_give isl_set *isl_pw_aff_ge_set(
4255 __isl_take isl_pw_aff *pwaff1,
4256 __isl_take isl_pw_aff *pwaff2);
4257 __isl_give isl_set *isl_pw_aff_gt_set(
4258 __isl_take isl_pw_aff *pwaff1,
4259 __isl_take isl_pw_aff *pwaff2);
4261 __isl_give isl_set *isl_pw_aff_list_eq_set(
4262 __isl_take isl_pw_aff_list *list1,
4263 __isl_take isl_pw_aff_list *list2);
4264 __isl_give isl_set *isl_pw_aff_list_ne_set(
4265 __isl_take isl_pw_aff_list *list1,
4266 __isl_take isl_pw_aff_list *list2);
4267 __isl_give isl_set *isl_pw_aff_list_le_set(
4268 __isl_take isl_pw_aff_list *list1,
4269 __isl_take isl_pw_aff_list *list2);
4270 __isl_give isl_set *isl_pw_aff_list_lt_set(
4271 __isl_take isl_pw_aff_list *list1,
4272 __isl_take isl_pw_aff_list *list2);
4273 __isl_give isl_set *isl_pw_aff_list_ge_set(
4274 __isl_take isl_pw_aff_list *list1,
4275 __isl_take isl_pw_aff_list *list2);
4276 __isl_give isl_set *isl_pw_aff_list_gt_set(
4277 __isl_take isl_pw_aff_list *list1,
4278 __isl_take isl_pw_aff_list *list2);
4280 The function C<isl_aff_neg_basic_set> returns a basic set
4281 containing those elements in the domain space
4282 of C<aff> where C<aff> is negative.
4283 The function C<isl_aff_ge_basic_set> returns a basic set
4284 containing those elements in the shared space
4285 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4286 The function C<isl_pw_aff_ge_set> returns a set
4287 containing those elements in the shared domain
4288 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4289 The functions operating on C<isl_pw_aff_list> apply the corresponding
4290 C<isl_pw_aff> function to each pair of elements in the two lists.
4292 #include <isl/aff.h>
4293 __isl_give isl_set *isl_pw_aff_nonneg_set(
4294 __isl_take isl_pw_aff *pwaff);
4295 __isl_give isl_set *isl_pw_aff_zero_set(
4296 __isl_take isl_pw_aff *pwaff);
4297 __isl_give isl_set *isl_pw_aff_non_zero_set(
4298 __isl_take isl_pw_aff *pwaff);
4300 The function C<isl_pw_aff_nonneg_set> returns a set
4301 containing those elements in the domain
4302 of C<pwaff> where C<pwaff> is non-negative.
4304 #include <isl/aff.h>
4305 __isl_give isl_pw_aff *isl_pw_aff_cond(
4306 __isl_take isl_pw_aff *cond,
4307 __isl_take isl_pw_aff *pwaff_true,
4308 __isl_take isl_pw_aff *pwaff_false);
4310 The function C<isl_pw_aff_cond> performs a conditional operator
4311 and returns an expression that is equal to C<pwaff_true>
4312 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4313 where C<cond> is zero.
4315 #include <isl/aff.h>
4316 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4317 __isl_take isl_pw_aff *pwaff1,
4318 __isl_take isl_pw_aff *pwaff2);
4319 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4320 __isl_take isl_pw_aff *pwaff1,
4321 __isl_take isl_pw_aff *pwaff2);
4322 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4323 __isl_take isl_pw_aff *pwaff1,
4324 __isl_take isl_pw_aff *pwaff2);
4326 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4327 expression with a domain that is the union of those of C<pwaff1> and
4328 C<pwaff2> and such that on each cell, the quasi-affine expression is
4329 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4330 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4331 associated expression is the defined one.
4333 An expression can be read from input using
4335 #include <isl/aff.h>
4336 __isl_give isl_aff *isl_aff_read_from_str(
4337 isl_ctx *ctx, const char *str);
4338 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4339 isl_ctx *ctx, const char *str);
4341 An expression can be printed using
4343 #include <isl/aff.h>
4344 __isl_give isl_printer *isl_printer_print_aff(
4345 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4347 __isl_give isl_printer *isl_printer_print_pw_aff(
4348 __isl_take isl_printer *p,
4349 __isl_keep isl_pw_aff *pwaff);
4351 =head2 Piecewise Multiple Quasi Affine Expressions
4353 An C<isl_multi_aff> object represents a sequence of
4354 zero or more affine expressions, all defined on the same domain space.
4355 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4356 zero or more piecewise affine expressions.
4358 An C<isl_multi_aff> can be constructed from a single
4359 C<isl_aff> or an C<isl_aff_list> using the
4360 following functions. Similarly for C<isl_multi_pw_aff>
4361 and C<isl_pw_multi_aff>.
4363 #include <isl/aff.h>
4364 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4365 __isl_take isl_aff *aff);
4366 __isl_give isl_multi_pw_aff *
4367 isl_multi_pw_aff_from_multi_aff(
4368 __isl_take isl_multi_aff *ma);
4369 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4370 __isl_take isl_pw_aff *pa);
4371 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4372 __isl_take isl_pw_aff *pa);
4373 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4374 __isl_take isl_space *space,
4375 __isl_take isl_aff_list *list);
4377 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4378 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4379 Note however that the domain
4380 of the result is the intersection of the domains of the input.
4381 The reverse conversion is exact.
4383 #include <isl/aff.h>
4384 __isl_give isl_pw_multi_aff *
4385 isl_pw_multi_aff_from_multi_pw_aff(
4386 __isl_take isl_multi_pw_aff *mpa);
4387 __isl_give isl_multi_pw_aff *
4388 isl_multi_pw_aff_from_pw_multi_aff(
4389 __isl_take isl_pw_multi_aff *pma);
4391 An empty piecewise multiple quasi affine expression (one with no cells),
4392 the zero piecewise multiple quasi affine expression (with value zero
4393 for each output dimension),
4394 a piecewise multiple quasi affine expression with a single cell (with
4395 either a universe or a specified domain) or
4396 a zero-dimensional piecewise multiple quasi affine expression
4398 can be created using the following functions.
4400 #include <isl/aff.h>
4401 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4402 __isl_take isl_space *space);
4403 __isl_give isl_multi_aff *isl_multi_aff_zero(
4404 __isl_take isl_space *space);
4405 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4406 __isl_take isl_space *space);
4407 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4408 __isl_take isl_space *space);
4409 __isl_give isl_multi_aff *isl_multi_aff_identity(
4410 __isl_take isl_space *space);
4411 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4412 __isl_take isl_space *space);
4413 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4414 __isl_take isl_space *space);
4415 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4416 __isl_take isl_space *space);
4417 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4418 __isl_take isl_space *space);
4419 __isl_give isl_multi_aff *isl_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_project_out_map(
4425 __isl_take isl_space *space,
4426 enum isl_dim_type type,
4427 unsigned first, unsigned n);
4428 __isl_give isl_pw_multi_aff *
4429 isl_pw_multi_aff_from_multi_aff(
4430 __isl_take isl_multi_aff *ma);
4431 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4432 __isl_take isl_set *set,
4433 __isl_take isl_multi_aff *maff);
4434 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4435 __isl_take isl_set *set);
4437 __isl_give isl_union_pw_multi_aff *
4438 isl_union_pw_multi_aff_empty(
4439 __isl_take isl_space *space);
4440 __isl_give isl_union_pw_multi_aff *
4441 isl_union_pw_multi_aff_add_pw_multi_aff(
4442 __isl_take isl_union_pw_multi_aff *upma,
4443 __isl_take isl_pw_multi_aff *pma);
4444 __isl_give isl_union_pw_multi_aff *
4445 isl_union_pw_multi_aff_from_domain(
4446 __isl_take isl_union_set *uset);
4448 A piecewise multiple quasi affine expression can also be initialized
4449 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4450 and the C<isl_map> is single-valued.
4451 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4452 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4454 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4455 __isl_take isl_set *set);
4456 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4457 __isl_take isl_map *map);
4459 __isl_give isl_union_pw_multi_aff *
4460 isl_union_pw_multi_aff_from_union_set(
4461 __isl_take isl_union_set *uset);
4462 __isl_give isl_union_pw_multi_aff *
4463 isl_union_pw_multi_aff_from_union_map(
4464 __isl_take isl_union_map *umap);
4466 Multiple quasi affine expressions can be copied and freed using
4468 #include <isl/aff.h>
4469 __isl_give isl_multi_aff *isl_multi_aff_copy(
4470 __isl_keep isl_multi_aff *maff);
4471 __isl_null isl_multi_aff *isl_multi_aff_free(
4472 __isl_take isl_multi_aff *maff);
4474 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4475 __isl_keep isl_pw_multi_aff *pma);
4476 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
4477 __isl_take isl_pw_multi_aff *pma);
4479 __isl_give isl_union_pw_multi_aff *
4480 isl_union_pw_multi_aff_copy(
4481 __isl_keep isl_union_pw_multi_aff *upma);
4482 __isl_null isl_union_pw_multi_aff *
4483 isl_union_pw_multi_aff_free(
4484 __isl_take isl_union_pw_multi_aff *upma);
4486 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4487 __isl_keep isl_multi_pw_aff *mpa);
4488 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
4489 __isl_take isl_multi_pw_aff *mpa);
4491 The expression can be inspected using
4493 #include <isl/aff.h>
4494 isl_ctx *isl_multi_aff_get_ctx(
4495 __isl_keep isl_multi_aff *maff);
4496 isl_ctx *isl_pw_multi_aff_get_ctx(
4497 __isl_keep isl_pw_multi_aff *pma);
4498 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4499 __isl_keep isl_union_pw_multi_aff *upma);
4500 isl_ctx *isl_multi_pw_aff_get_ctx(
4501 __isl_keep isl_multi_pw_aff *mpa);
4503 int isl_multi_aff_involves_dims(
4504 __isl_keep isl_multi_aff *ma,
4505 enum isl_dim_type type, unsigned first, unsigned n);
4506 int isl_multi_pw_aff_involves_dims(
4507 __isl_keep isl_multi_pw_aff *mpa,
4508 enum isl_dim_type type, unsigned first, unsigned n);
4510 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4511 enum isl_dim_type type);
4512 unsigned isl_pw_multi_aff_dim(
4513 __isl_keep isl_pw_multi_aff *pma,
4514 enum isl_dim_type type);
4515 unsigned isl_multi_pw_aff_dim(
4516 __isl_keep isl_multi_pw_aff *mpa,
4517 enum isl_dim_type type);
4518 __isl_give isl_aff *isl_multi_aff_get_aff(
4519 __isl_keep isl_multi_aff *multi, int pos);
4520 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4521 __isl_keep isl_pw_multi_aff *pma, int pos);
4522 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4523 __isl_keep isl_multi_pw_aff *mpa, int pos);
4524 int isl_multi_aff_find_dim_by_id(
4525 __isl_keep isl_multi_aff *ma,
4526 enum isl_dim_type type, __isl_keep isl_id *id);
4527 int isl_multi_pw_aff_find_dim_by_id(
4528 __isl_keep isl_multi_pw_aff *mpa,
4529 enum isl_dim_type type, __isl_keep isl_id *id);
4530 const char *isl_pw_multi_aff_get_dim_name(
4531 __isl_keep isl_pw_multi_aff *pma,
4532 enum isl_dim_type type, unsigned pos);
4533 __isl_give isl_id *isl_multi_aff_get_dim_id(
4534 __isl_keep isl_multi_aff *ma,
4535 enum isl_dim_type type, unsigned pos);
4536 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4537 __isl_keep isl_pw_multi_aff *pma,
4538 enum isl_dim_type type, unsigned pos);
4539 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4540 __isl_keep isl_multi_pw_aff *mpa,
4541 enum isl_dim_type type, unsigned pos);
4542 const char *isl_multi_aff_get_tuple_name(
4543 __isl_keep isl_multi_aff *multi,
4544 enum isl_dim_type type);
4545 int isl_pw_multi_aff_has_tuple_name(
4546 __isl_keep isl_pw_multi_aff *pma,
4547 enum isl_dim_type type);
4548 const char *isl_pw_multi_aff_get_tuple_name(
4549 __isl_keep isl_pw_multi_aff *pma,
4550 enum isl_dim_type type);
4551 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4552 enum isl_dim_type type);
4553 int isl_pw_multi_aff_has_tuple_id(
4554 __isl_keep isl_pw_multi_aff *pma,
4555 enum isl_dim_type type);
4556 int isl_multi_pw_aff_has_tuple_id(
4557 __isl_keep isl_multi_pw_aff *mpa,
4558 enum isl_dim_type type);
4559 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4560 __isl_keep isl_multi_aff *ma,
4561 enum isl_dim_type type);
4562 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4563 __isl_keep isl_pw_multi_aff *pma,
4564 enum isl_dim_type type);
4565 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4566 __isl_keep isl_multi_pw_aff *mpa,
4567 enum isl_dim_type type);
4568 int isl_multi_aff_range_is_wrapping(
4569 __isl_keep isl_multi_aff *ma);
4570 int isl_multi_pw_aff_range_is_wrapping(
4571 __isl_keep isl_multi_pw_aff *mpa);
4573 int isl_pw_multi_aff_foreach_piece(
4574 __isl_keep isl_pw_multi_aff *pma,
4575 int (*fn)(__isl_take isl_set *set,
4576 __isl_take isl_multi_aff *maff,
4577 void *user), void *user);
4579 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4580 __isl_keep isl_union_pw_multi_aff *upma,
4581 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4582 void *user), void *user);
4584 It can be modified using
4586 #include <isl/aff.h>
4587 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4588 __isl_take isl_multi_aff *multi, int pos,
4589 __isl_take isl_aff *aff);
4590 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4591 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4592 __isl_take isl_pw_aff *pa);
4593 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4594 __isl_take isl_multi_aff *maff,
4595 enum isl_dim_type type, unsigned pos, const char *s);
4596 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4597 __isl_take isl_multi_aff *maff,
4598 enum isl_dim_type type, unsigned pos,
4599 __isl_take isl_id *id);
4600 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4601 __isl_take isl_multi_aff *maff,
4602 enum isl_dim_type type, const char *s);
4603 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4604 __isl_take isl_multi_aff *maff,
4605 enum isl_dim_type type, __isl_take isl_id *id);
4606 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4607 __isl_take isl_pw_multi_aff *pma,
4608 enum isl_dim_type type, __isl_take isl_id *id);
4609 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4610 __isl_take isl_multi_aff *ma,
4611 enum isl_dim_type type);
4612 __isl_give isl_multi_pw_aff *
4613 isl_multi_pw_aff_reset_tuple_id(
4614 __isl_take isl_multi_pw_aff *mpa,
4615 enum isl_dim_type type);
4616 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4617 __isl_take isl_multi_aff *ma);
4618 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4619 __isl_take isl_multi_pw_aff *mpa);
4621 __isl_give isl_multi_pw_aff *
4622 isl_multi_pw_aff_set_dim_name(
4623 __isl_take isl_multi_pw_aff *mpa,
4624 enum isl_dim_type type, unsigned pos, const char *s);
4625 __isl_give isl_multi_pw_aff *
4626 isl_multi_pw_aff_set_dim_id(
4627 __isl_take isl_multi_pw_aff *mpa,
4628 enum isl_dim_type type, unsigned pos,
4629 __isl_take isl_id *id);
4630 __isl_give isl_multi_pw_aff *
4631 isl_multi_pw_aff_set_tuple_name(
4632 __isl_take isl_multi_pw_aff *mpa,
4633 enum isl_dim_type type, const char *s);
4635 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4636 __isl_take isl_multi_aff *ma);
4638 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4639 __isl_take isl_multi_aff *ma,
4640 enum isl_dim_type type, unsigned first, unsigned n);
4641 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4642 __isl_take isl_multi_aff *ma,
4643 enum isl_dim_type type, unsigned n);
4644 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4645 __isl_take isl_multi_aff *maff,
4646 enum isl_dim_type type, unsigned first, unsigned n);
4647 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4648 __isl_take isl_pw_multi_aff *pma,
4649 enum isl_dim_type type, unsigned first, unsigned n);
4651 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4652 __isl_take isl_multi_pw_aff *mpa,
4653 enum isl_dim_type type, unsigned first, unsigned n);
4654 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4655 __isl_take isl_multi_pw_aff *mpa,
4656 enum isl_dim_type type, unsigned n);
4657 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4658 __isl_take isl_multi_pw_aff *pma,
4659 enum isl_dim_type dst_type, unsigned dst_pos,
4660 enum isl_dim_type src_type, unsigned src_pos,
4663 To check whether two multiple affine expressions are
4664 (obviously) equal to each other, use
4666 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4667 __isl_keep isl_multi_aff *maff2);
4668 int isl_pw_multi_aff_plain_is_equal(
4669 __isl_keep isl_pw_multi_aff *pma1,
4670 __isl_keep isl_pw_multi_aff *pma2);
4671 int isl_multi_pw_aff_plain_is_equal(
4672 __isl_keep isl_multi_pw_aff *mpa1,
4673 __isl_keep isl_multi_pw_aff *mpa2);
4674 int isl_multi_pw_aff_is_equal(
4675 __isl_keep isl_multi_pw_aff *mpa1,
4676 __isl_keep isl_multi_pw_aff *mpa2);
4680 #include <isl/aff.h>
4681 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4682 __isl_take isl_pw_multi_aff *pma1,
4683 __isl_take isl_pw_multi_aff *pma2);
4684 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4685 __isl_take isl_pw_multi_aff *pma1,
4686 __isl_take isl_pw_multi_aff *pma2);
4687 __isl_give isl_multi_aff *isl_multi_aff_floor(
4688 __isl_take isl_multi_aff *ma);
4689 __isl_give isl_multi_aff *isl_multi_aff_add(
4690 __isl_take isl_multi_aff *maff1,
4691 __isl_take isl_multi_aff *maff2);
4692 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4693 __isl_take isl_pw_multi_aff *pma1,
4694 __isl_take isl_pw_multi_aff *pma2);
4695 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4696 __isl_take isl_union_pw_multi_aff *upma1,
4697 __isl_take isl_union_pw_multi_aff *upma2);
4698 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4699 __isl_take isl_pw_multi_aff *pma1,
4700 __isl_take isl_pw_multi_aff *pma2);
4701 __isl_give isl_multi_aff *isl_multi_aff_sub(
4702 __isl_take isl_multi_aff *ma1,
4703 __isl_take isl_multi_aff *ma2);
4704 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4705 __isl_take isl_pw_multi_aff *pma1,
4706 __isl_take isl_pw_multi_aff *pma2);
4707 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4708 __isl_take isl_union_pw_multi_aff *upma1,
4709 __isl_take isl_union_pw_multi_aff *upma2);
4711 C<isl_multi_aff_sub> subtracts the second argument from the first.
4713 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4714 __isl_take isl_multi_aff *ma,
4715 __isl_take isl_val *v);
4716 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4717 __isl_take isl_pw_multi_aff *pma,
4718 __isl_take isl_val *v);
4719 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4720 __isl_take isl_multi_pw_aff *mpa,
4721 __isl_take isl_val *v);
4722 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4723 __isl_take isl_multi_aff *ma,
4724 __isl_take isl_multi_val *mv);
4725 __isl_give isl_pw_multi_aff *
4726 isl_pw_multi_aff_scale_multi_val(
4727 __isl_take isl_pw_multi_aff *pma,
4728 __isl_take isl_multi_val *mv);
4729 __isl_give isl_multi_pw_aff *
4730 isl_multi_pw_aff_scale_multi_val(
4731 __isl_take isl_multi_pw_aff *mpa,
4732 __isl_take isl_multi_val *mv);
4733 __isl_give isl_union_pw_multi_aff *
4734 isl_union_pw_multi_aff_scale_multi_val(
4735 __isl_take isl_union_pw_multi_aff *upma,
4736 __isl_take isl_multi_val *mv);
4737 __isl_give isl_multi_aff *
4738 isl_multi_aff_scale_down_multi_val(
4739 __isl_take isl_multi_aff *ma,
4740 __isl_take isl_multi_val *mv);
4741 __isl_give isl_multi_pw_aff *
4742 isl_multi_pw_aff_scale_down_multi_val(
4743 __isl_take isl_multi_pw_aff *mpa,
4744 __isl_take isl_multi_val *mv);
4746 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4747 by the corresponding elements of C<mv>.
4749 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4750 __isl_take isl_pw_multi_aff *pma,
4751 enum isl_dim_type type, unsigned pos, int value);
4752 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4753 __isl_take isl_pw_multi_aff *pma,
4754 __isl_take isl_set *set);
4755 __isl_give isl_set *isl_multi_pw_aff_domain(
4756 __isl_take isl_multi_pw_aff *mpa);
4757 __isl_give isl_multi_pw_aff *
4758 isl_multi_pw_aff_intersect_params(
4759 __isl_take isl_multi_pw_aff *mpa,
4760 __isl_take isl_set *set);
4761 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4762 __isl_take isl_pw_multi_aff *pma,
4763 __isl_take isl_set *set);
4764 __isl_give isl_multi_pw_aff *
4765 isl_multi_pw_aff_intersect_domain(
4766 __isl_take isl_multi_pw_aff *mpa,
4767 __isl_take isl_set *domain);
4768 __isl_give isl_union_pw_multi_aff *
4769 isl_union_pw_multi_aff_intersect_domain(
4770 __isl_take isl_union_pw_multi_aff *upma,
4771 __isl_take isl_union_set *uset);
4772 __isl_give isl_multi_aff *isl_multi_aff_lift(
4773 __isl_take isl_multi_aff *maff,
4774 __isl_give isl_local_space **ls);
4775 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4776 __isl_take isl_pw_multi_aff *pma);
4777 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4778 __isl_take isl_multi_pw_aff *mpa);
4779 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4780 __isl_take isl_multi_aff *multi,
4781 __isl_take isl_space *model);
4782 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4783 __isl_take isl_pw_multi_aff *pma,
4784 __isl_take isl_space *model);
4785 __isl_give isl_union_pw_multi_aff *
4786 isl_union_pw_multi_aff_align_params(
4787 __isl_take isl_union_pw_multi_aff *upma,
4788 __isl_take isl_space *model);
4789 __isl_give isl_pw_multi_aff *
4790 isl_pw_multi_aff_project_domain_on_params(
4791 __isl_take isl_pw_multi_aff *pma);
4792 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4793 __isl_take isl_multi_aff *maff,
4794 __isl_take isl_set *context);
4795 __isl_give isl_multi_aff *isl_multi_aff_gist(
4796 __isl_take isl_multi_aff *maff,
4797 __isl_take isl_set *context);
4798 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4799 __isl_take isl_pw_multi_aff *pma,
4800 __isl_take isl_set *set);
4801 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4802 __isl_take isl_pw_multi_aff *pma,
4803 __isl_take isl_set *set);
4804 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4805 __isl_take isl_multi_pw_aff *mpa,
4806 __isl_take isl_set *set);
4807 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4808 __isl_take isl_multi_pw_aff *mpa,
4809 __isl_take isl_set *set);
4810 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4811 __isl_take isl_multi_aff *ma);
4812 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4813 __isl_take isl_multi_pw_aff *mpa);
4814 __isl_give isl_set *isl_pw_multi_aff_domain(
4815 __isl_take isl_pw_multi_aff *pma);
4816 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4817 __isl_take isl_union_pw_multi_aff *upma);
4818 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4819 __isl_take isl_multi_aff *ma1, unsigned pos,
4820 __isl_take isl_multi_aff *ma2);
4821 __isl_give isl_multi_aff *isl_multi_aff_splice(
4822 __isl_take isl_multi_aff *ma1,
4823 unsigned in_pos, unsigned out_pos,
4824 __isl_take isl_multi_aff *ma2);
4825 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4826 __isl_take isl_multi_aff *ma1,
4827 __isl_take isl_multi_aff *ma2);
4828 __isl_give isl_multi_aff *
4829 isl_multi_aff_range_factor_domain(
4830 __isl_take isl_multi_aff *ma);
4831 __isl_give isl_multi_aff *
4832 isl_multi_aff_range_factor_range(
4833 __isl_take isl_multi_aff *ma);
4834 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4835 __isl_take isl_multi_aff *ma1,
4836 __isl_take isl_multi_aff *ma2);
4837 __isl_give isl_multi_aff *isl_multi_aff_product(
4838 __isl_take isl_multi_aff *ma1,
4839 __isl_take isl_multi_aff *ma2);
4840 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4841 __isl_take isl_multi_pw_aff *mpa1,
4842 __isl_take isl_multi_pw_aff *mpa2);
4843 __isl_give isl_pw_multi_aff *
4844 isl_pw_multi_aff_range_product(
4845 __isl_take isl_pw_multi_aff *pma1,
4846 __isl_take isl_pw_multi_aff *pma2);
4847 __isl_give isl_multi_pw_aff *
4848 isl_multi_pw_aff_range_factor_domain(
4849 __isl_take isl_multi_pw_aff *mpa);
4850 __isl_give isl_multi_pw_aff *
4851 isl_multi_pw_aff_range_factor_range(
4852 __isl_take isl_multi_pw_aff *mpa);
4853 __isl_give isl_pw_multi_aff *
4854 isl_pw_multi_aff_flat_range_product(
4855 __isl_take isl_pw_multi_aff *pma1,
4856 __isl_take isl_pw_multi_aff *pma2);
4857 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4858 __isl_take isl_pw_multi_aff *pma1,
4859 __isl_take isl_pw_multi_aff *pma2);
4860 __isl_give isl_union_pw_multi_aff *
4861 isl_union_pw_multi_aff_flat_range_product(
4862 __isl_take isl_union_pw_multi_aff *upma1,
4863 __isl_take isl_union_pw_multi_aff *upma2);
4864 __isl_give isl_multi_pw_aff *
4865 isl_multi_pw_aff_range_splice(
4866 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4867 __isl_take isl_multi_pw_aff *mpa2);
4868 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4869 __isl_take isl_multi_pw_aff *mpa1,
4870 unsigned in_pos, unsigned out_pos,
4871 __isl_take isl_multi_pw_aff *mpa2);
4872 __isl_give isl_multi_pw_aff *
4873 isl_multi_pw_aff_range_product(
4874 __isl_take isl_multi_pw_aff *mpa1,
4875 __isl_take isl_multi_pw_aff *mpa2);
4876 __isl_give isl_multi_pw_aff *
4877 isl_multi_pw_aff_flat_range_product(
4878 __isl_take isl_multi_pw_aff *mpa1,
4879 __isl_take isl_multi_pw_aff *mpa2);
4881 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4882 then it is assigned the local space that lies at the basis of
4883 the lifting applied.
4885 #include <isl/aff.h>
4886 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4887 __isl_take isl_multi_aff *ma1,
4888 __isl_take isl_multi_aff *ma2);
4889 __isl_give isl_pw_multi_aff *
4890 isl_pw_multi_aff_pullback_multi_aff(
4891 __isl_take isl_pw_multi_aff *pma,
4892 __isl_take isl_multi_aff *ma);
4893 __isl_give isl_multi_pw_aff *
4894 isl_multi_pw_aff_pullback_multi_aff(
4895 __isl_take isl_multi_pw_aff *mpa,
4896 __isl_take isl_multi_aff *ma);
4897 __isl_give isl_pw_multi_aff *
4898 isl_pw_multi_aff_pullback_pw_multi_aff(
4899 __isl_take isl_pw_multi_aff *pma1,
4900 __isl_take isl_pw_multi_aff *pma2);
4901 __isl_give isl_multi_pw_aff *
4902 isl_multi_pw_aff_pullback_pw_multi_aff(
4903 __isl_take isl_multi_pw_aff *mpa,
4904 __isl_take isl_pw_multi_aff *pma);
4905 __isl_give isl_multi_pw_aff *
4906 isl_multi_pw_aff_pullback_multi_pw_aff(
4907 __isl_take isl_multi_pw_aff *mpa1,
4908 __isl_take isl_multi_pw_aff *mpa2);
4910 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4911 In other words, C<ma2> is plugged
4914 __isl_give isl_set *isl_multi_aff_lex_le_set(
4915 __isl_take isl_multi_aff *ma1,
4916 __isl_take isl_multi_aff *ma2);
4917 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4918 __isl_take isl_multi_aff *ma1,
4919 __isl_take isl_multi_aff *ma2);
4921 The function C<isl_multi_aff_lex_le_set> returns a set
4922 containing those elements in the shared domain space
4923 where C<ma1> is lexicographically smaller than or
4926 An expression can be read from input using
4928 #include <isl/aff.h>
4929 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4930 isl_ctx *ctx, const char *str);
4931 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4932 isl_ctx *ctx, const char *str);
4933 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4934 isl_ctx *ctx, const char *str);
4935 __isl_give isl_union_pw_multi_aff *
4936 isl_union_pw_multi_aff_read_from_str(
4937 isl_ctx *ctx, const char *str);
4939 An expression can be printed using
4941 #include <isl/aff.h>
4942 __isl_give isl_printer *isl_printer_print_multi_aff(
4943 __isl_take isl_printer *p,
4944 __isl_keep isl_multi_aff *maff);
4945 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4946 __isl_take isl_printer *p,
4947 __isl_keep isl_pw_multi_aff *pma);
4948 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4949 __isl_take isl_printer *p,
4950 __isl_keep isl_union_pw_multi_aff *upma);
4951 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4952 __isl_take isl_printer *p,
4953 __isl_keep isl_multi_pw_aff *mpa);
4957 Points are elements of a set. They can be used to construct
4958 simple sets (boxes) or they can be used to represent the
4959 individual elements of a set.
4960 The zero point (the origin) can be created using
4962 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4964 The coordinates of a point can be inspected, set and changed
4967 __isl_give isl_val *isl_point_get_coordinate_val(
4968 __isl_keep isl_point *pnt,
4969 enum isl_dim_type type, int pos);
4970 __isl_give isl_point *isl_point_set_coordinate_val(
4971 __isl_take isl_point *pnt,
4972 enum isl_dim_type type, int pos,
4973 __isl_take isl_val *v);
4975 __isl_give isl_point *isl_point_add_ui(
4976 __isl_take isl_point *pnt,
4977 enum isl_dim_type type, int pos, unsigned val);
4978 __isl_give isl_point *isl_point_sub_ui(
4979 __isl_take isl_point *pnt,
4980 enum isl_dim_type type, int pos, unsigned val);
4982 Other properties can be obtained using
4984 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4986 Points can be copied or freed using
4988 __isl_give isl_point *isl_point_copy(
4989 __isl_keep isl_point *pnt);
4990 void isl_point_free(__isl_take isl_point *pnt);
4992 A singleton set can be created from a point using
4994 __isl_give isl_basic_set *isl_basic_set_from_point(
4995 __isl_take isl_point *pnt);
4996 __isl_give isl_set *isl_set_from_point(
4997 __isl_take isl_point *pnt);
4999 and a box can be created from two opposite extremal points using
5001 __isl_give isl_basic_set *isl_basic_set_box_from_points(
5002 __isl_take isl_point *pnt1,
5003 __isl_take isl_point *pnt2);
5004 __isl_give isl_set *isl_set_box_from_points(
5005 __isl_take isl_point *pnt1,
5006 __isl_take isl_point *pnt2);
5008 All elements of a B<bounded> (union) set can be enumerated using
5009 the following functions.
5011 int isl_set_foreach_point(__isl_keep isl_set *set,
5012 int (*fn)(__isl_take isl_point *pnt, void *user),
5014 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
5015 int (*fn)(__isl_take isl_point *pnt, void *user),
5018 The function C<fn> is called for each integer point in
5019 C<set> with as second argument the last argument of
5020 the C<isl_set_foreach_point> call. The function C<fn>
5021 should return C<0> on success and C<-1> on failure.
5022 In the latter case, C<isl_set_foreach_point> will stop
5023 enumerating and return C<-1> as well.
5024 If the enumeration is performed successfully and to completion,
5025 then C<isl_set_foreach_point> returns C<0>.
5027 To obtain a single point of a (basic) set, use
5029 __isl_give isl_point *isl_basic_set_sample_point(
5030 __isl_take isl_basic_set *bset);
5031 __isl_give isl_point *isl_set_sample_point(
5032 __isl_take isl_set *set);
5034 If C<set> does not contain any (integer) points, then the
5035 resulting point will be ``void'', a property that can be
5038 int isl_point_is_void(__isl_keep isl_point *pnt);
5040 =head2 Piecewise Quasipolynomials
5042 A piecewise quasipolynomial is a particular kind of function that maps
5043 a parametric point to a rational value.
5044 More specifically, a quasipolynomial is a polynomial expression in greatest
5045 integer parts of affine expressions of parameters and variables.
5046 A piecewise quasipolynomial is a subdivision of a given parametric
5047 domain into disjoint cells with a quasipolynomial associated to
5048 each cell. The value of the piecewise quasipolynomial at a given
5049 point is the value of the quasipolynomial associated to the cell
5050 that contains the point. Outside of the union of cells,
5051 the value is assumed to be zero.
5052 For example, the piecewise quasipolynomial
5054 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
5056 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
5057 A given piecewise quasipolynomial has a fixed domain dimension.
5058 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
5059 defined over different domains.
5060 Piecewise quasipolynomials are mainly used by the C<barvinok>
5061 library for representing the number of elements in a parametric set or map.
5062 For example, the piecewise quasipolynomial above represents
5063 the number of points in the map
5065 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
5067 =head3 Input and Output
5069 Piecewise quasipolynomials can be read from input using
5071 __isl_give isl_union_pw_qpolynomial *
5072 isl_union_pw_qpolynomial_read_from_str(
5073 isl_ctx *ctx, const char *str);
5075 Quasipolynomials and piecewise quasipolynomials can be printed
5076 using the following functions.
5078 __isl_give isl_printer *isl_printer_print_qpolynomial(
5079 __isl_take isl_printer *p,
5080 __isl_keep isl_qpolynomial *qp);
5082 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
5083 __isl_take isl_printer *p,
5084 __isl_keep isl_pw_qpolynomial *pwqp);
5086 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
5087 __isl_take isl_printer *p,
5088 __isl_keep isl_union_pw_qpolynomial *upwqp);
5090 The output format of the printer
5091 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5092 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
5094 In case of printing in C<ISL_FORMAT_C>, the user may want
5095 to set the names of all dimensions
5097 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
5098 __isl_take isl_qpolynomial *qp,
5099 enum isl_dim_type type, unsigned pos,
5101 __isl_give isl_pw_qpolynomial *
5102 isl_pw_qpolynomial_set_dim_name(
5103 __isl_take isl_pw_qpolynomial *pwqp,
5104 enum isl_dim_type type, unsigned pos,
5107 =head3 Creating New (Piecewise) Quasipolynomials
5109 Some simple quasipolynomials can be created using the following functions.
5110 More complicated quasipolynomials can be created by applying
5111 operations such as addition and multiplication
5112 on the resulting quasipolynomials
5114 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
5115 __isl_take isl_space *domain);
5116 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
5117 __isl_take isl_space *domain);
5118 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
5119 __isl_take isl_space *domain);
5120 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
5121 __isl_take isl_space *domain);
5122 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
5123 __isl_take isl_space *domain);
5124 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
5125 __isl_take isl_space *domain,
5126 __isl_take isl_val *val);
5127 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
5128 __isl_take isl_space *domain,
5129 enum isl_dim_type type, unsigned pos);
5130 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
5131 __isl_take isl_aff *aff);
5133 Note that the space in which a quasipolynomial lives is a map space
5134 with a one-dimensional range. The C<domain> argument in some of
5135 the functions above corresponds to the domain of this map space.
5137 The zero piecewise quasipolynomial or a piecewise quasipolynomial
5138 with a single cell can be created using the following functions.
5139 Multiple of these single cell piecewise quasipolynomials can
5140 be combined to create more complicated piecewise quasipolynomials.
5142 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
5143 __isl_take isl_space *space);
5144 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
5145 __isl_take isl_set *set,
5146 __isl_take isl_qpolynomial *qp);
5147 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
5148 __isl_take isl_qpolynomial *qp);
5149 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
5150 __isl_take isl_pw_aff *pwaff);
5152 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
5153 __isl_take isl_space *space);
5154 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
5155 __isl_take isl_pw_qpolynomial *pwqp);
5156 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
5157 __isl_take isl_union_pw_qpolynomial *upwqp,
5158 __isl_take isl_pw_qpolynomial *pwqp);
5160 Quasipolynomials can be copied and freed again using the following
5163 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
5164 __isl_keep isl_qpolynomial *qp);
5165 __isl_null isl_qpolynomial *isl_qpolynomial_free(
5166 __isl_take isl_qpolynomial *qp);
5168 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
5169 __isl_keep isl_pw_qpolynomial *pwqp);
5170 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
5171 __isl_take isl_pw_qpolynomial *pwqp);
5173 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
5174 __isl_keep isl_union_pw_qpolynomial *upwqp);
5175 __isl_null isl_union_pw_qpolynomial *
5176 isl_union_pw_qpolynomial_free(
5177 __isl_take isl_union_pw_qpolynomial *upwqp);
5179 =head3 Inspecting (Piecewise) Quasipolynomials
5181 To iterate over all piecewise quasipolynomials in a union
5182 piecewise quasipolynomial, use the following function
5184 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
5185 __isl_keep isl_union_pw_qpolynomial *upwqp,
5186 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
5189 To extract the piecewise quasipolynomial in a given space from a union, use
5191 __isl_give isl_pw_qpolynomial *
5192 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
5193 __isl_keep isl_union_pw_qpolynomial *upwqp,
5194 __isl_take isl_space *space);
5196 To iterate over the cells in a piecewise quasipolynomial,
5197 use either of the following two functions
5199 int isl_pw_qpolynomial_foreach_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);
5204 int isl_pw_qpolynomial_foreach_lifted_piece(
5205 __isl_keep isl_pw_qpolynomial *pwqp,
5206 int (*fn)(__isl_take isl_set *set,
5207 __isl_take isl_qpolynomial *qp,
5208 void *user), void *user);
5210 As usual, the function C<fn> should return C<0> on success
5211 and C<-1> on failure. The difference between
5212 C<isl_pw_qpolynomial_foreach_piece> and
5213 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
5214 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
5215 compute unique representations for all existentially quantified
5216 variables and then turn these existentially quantified variables
5217 into extra set variables, adapting the associated quasipolynomial
5218 accordingly. This means that the C<set> passed to C<fn>
5219 will not have any existentially quantified variables, but that
5220 the dimensions of the sets may be different for different
5221 invocations of C<fn>.
5223 The constant term of a quasipolynomial can be extracted using
5225 __isl_give isl_val *isl_qpolynomial_get_constant_val(
5226 __isl_keep isl_qpolynomial *qp);
5228 To iterate over all terms in a quasipolynomial,
5231 int isl_qpolynomial_foreach_term(
5232 __isl_keep isl_qpolynomial *qp,
5233 int (*fn)(__isl_take isl_term *term,
5234 void *user), void *user);
5236 The terms themselves can be inspected and freed using
5239 unsigned isl_term_dim(__isl_keep isl_term *term,
5240 enum isl_dim_type type);
5241 __isl_give isl_val *isl_term_get_coefficient_val(
5242 __isl_keep isl_term *term);
5243 int isl_term_get_exp(__isl_keep isl_term *term,
5244 enum isl_dim_type type, unsigned pos);
5245 __isl_give isl_aff *isl_term_get_div(
5246 __isl_keep isl_term *term, unsigned pos);
5247 void isl_term_free(__isl_take isl_term *term);
5249 Each term is a product of parameters, set variables and
5250 integer divisions. The function C<isl_term_get_exp>
5251 returns the exponent of a given dimensions in the given term.
5253 =head3 Properties of (Piecewise) Quasipolynomials
5255 To check whether two union piecewise quasipolynomials are
5256 obviously equal, use
5258 int isl_union_pw_qpolynomial_plain_is_equal(
5259 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5260 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5262 =head3 Operations on (Piecewise) Quasipolynomials
5264 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5265 __isl_take isl_qpolynomial *qp,
5266 __isl_take isl_val *v);
5267 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5268 __isl_take isl_qpolynomial *qp);
5269 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5270 __isl_take isl_qpolynomial *qp1,
5271 __isl_take isl_qpolynomial *qp2);
5272 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5273 __isl_take isl_qpolynomial *qp1,
5274 __isl_take isl_qpolynomial *qp2);
5275 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5276 __isl_take isl_qpolynomial *qp1,
5277 __isl_take isl_qpolynomial *qp2);
5278 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5279 __isl_take isl_qpolynomial *qp, unsigned exponent);
5281 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5282 __isl_take isl_pw_qpolynomial *pwqp,
5283 enum isl_dim_type type, unsigned n,
5284 __isl_take isl_val *v);
5285 __isl_give isl_pw_qpolynomial *
5286 isl_pw_qpolynomial_scale_val(
5287 __isl_take isl_pw_qpolynomial *pwqp,
5288 __isl_take isl_val *v);
5289 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5290 __isl_take isl_pw_qpolynomial *pwqp1,
5291 __isl_take isl_pw_qpolynomial *pwqp2);
5292 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5293 __isl_take isl_pw_qpolynomial *pwqp1,
5294 __isl_take isl_pw_qpolynomial *pwqp2);
5295 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5296 __isl_take isl_pw_qpolynomial *pwqp1,
5297 __isl_take isl_pw_qpolynomial *pwqp2);
5298 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5299 __isl_take isl_pw_qpolynomial *pwqp);
5300 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5301 __isl_take isl_pw_qpolynomial *pwqp1,
5302 __isl_take isl_pw_qpolynomial *pwqp2);
5303 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5304 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5306 __isl_give isl_union_pw_qpolynomial *
5307 isl_union_pw_qpolynomial_scale_val(
5308 __isl_take isl_union_pw_qpolynomial *upwqp,
5309 __isl_take isl_val *v);
5310 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5311 __isl_take isl_union_pw_qpolynomial *upwqp1,
5312 __isl_take isl_union_pw_qpolynomial *upwqp2);
5313 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5314 __isl_take isl_union_pw_qpolynomial *upwqp1,
5315 __isl_take isl_union_pw_qpolynomial *upwqp2);
5316 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5317 __isl_take isl_union_pw_qpolynomial *upwqp1,
5318 __isl_take isl_union_pw_qpolynomial *upwqp2);
5320 __isl_give isl_val *isl_pw_qpolynomial_eval(
5321 __isl_take isl_pw_qpolynomial *pwqp,
5322 __isl_take isl_point *pnt);
5324 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5325 __isl_take isl_union_pw_qpolynomial *upwqp,
5326 __isl_take isl_point *pnt);
5328 __isl_give isl_set *isl_pw_qpolynomial_domain(
5329 __isl_take isl_pw_qpolynomial *pwqp);
5330 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5331 __isl_take isl_pw_qpolynomial *pwpq,
5332 __isl_take isl_set *set);
5333 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5334 __isl_take isl_pw_qpolynomial *pwpq,
5335 __isl_take isl_set *set);
5337 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5338 __isl_take isl_union_pw_qpolynomial *upwqp);
5339 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5340 __isl_take isl_union_pw_qpolynomial *upwpq,
5341 __isl_take isl_union_set *uset);
5342 __isl_give isl_union_pw_qpolynomial *
5343 isl_union_pw_qpolynomial_intersect_params(
5344 __isl_take isl_union_pw_qpolynomial *upwpq,
5345 __isl_take isl_set *set);
5347 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5348 __isl_take isl_qpolynomial *qp,
5349 __isl_take isl_space *model);
5351 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5352 __isl_take isl_qpolynomial *qp);
5353 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5354 __isl_take isl_pw_qpolynomial *pwqp);
5356 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5357 __isl_take isl_union_pw_qpolynomial *upwqp);
5359 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5360 __isl_take isl_qpolynomial *qp,
5361 __isl_take isl_set *context);
5362 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5363 __isl_take isl_qpolynomial *qp,
5364 __isl_take isl_set *context);
5366 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5367 __isl_take isl_pw_qpolynomial *pwqp,
5368 __isl_take isl_set *context);
5369 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5370 __isl_take isl_pw_qpolynomial *pwqp,
5371 __isl_take isl_set *context);
5373 __isl_give isl_union_pw_qpolynomial *
5374 isl_union_pw_qpolynomial_gist_params(
5375 __isl_take isl_union_pw_qpolynomial *upwqp,
5376 __isl_take isl_set *context);
5377 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5378 __isl_take isl_union_pw_qpolynomial *upwqp,
5379 __isl_take isl_union_set *context);
5381 The gist operation applies the gist operation to each of
5382 the cells in the domain of the input piecewise quasipolynomial.
5383 The context is also exploited
5384 to simplify the quasipolynomials associated to each cell.
5386 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5387 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5388 __isl_give isl_union_pw_qpolynomial *
5389 isl_union_pw_qpolynomial_to_polynomial(
5390 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5392 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5393 the polynomial will be an overapproximation. If C<sign> is negative,
5394 it will be an underapproximation. If C<sign> is zero, the approximation
5395 will lie somewhere in between.
5397 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5399 A piecewise quasipolynomial reduction is a piecewise
5400 reduction (or fold) of quasipolynomials.
5401 In particular, the reduction can be maximum or a minimum.
5402 The objects are mainly used to represent the result of
5403 an upper or lower bound on a quasipolynomial over its domain,
5404 i.e., as the result of the following function.
5406 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5407 __isl_take isl_pw_qpolynomial *pwqp,
5408 enum isl_fold type, int *tight);
5410 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5411 __isl_take isl_union_pw_qpolynomial *upwqp,
5412 enum isl_fold type, int *tight);
5414 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5415 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5416 is the returned bound is known be tight, i.e., for each value
5417 of the parameters there is at least
5418 one element in the domain that reaches the bound.
5419 If the domain of C<pwqp> is not wrapping, then the bound is computed
5420 over all elements in that domain and the result has a purely parametric
5421 domain. If the domain of C<pwqp> is wrapping, then the bound is
5422 computed over the range of the wrapped relation. The domain of the
5423 wrapped relation becomes the domain of the result.
5425 A (piecewise) quasipolynomial reduction can be copied or freed using the
5426 following functions.
5428 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5429 __isl_keep isl_qpolynomial_fold *fold);
5430 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5431 __isl_keep isl_pw_qpolynomial_fold *pwf);
5432 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5433 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5434 void isl_qpolynomial_fold_free(
5435 __isl_take isl_qpolynomial_fold *fold);
5436 __isl_null isl_pw_qpolynomial_fold *
5437 isl_pw_qpolynomial_fold_free(
5438 __isl_take isl_pw_qpolynomial_fold *pwf);
5439 __isl_null isl_union_pw_qpolynomial_fold *
5440 isl_union_pw_qpolynomial_fold_free(
5441 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5443 =head3 Printing Piecewise Quasipolynomial Reductions
5445 Piecewise quasipolynomial reductions can be printed
5446 using the following function.
5448 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5449 __isl_take isl_printer *p,
5450 __isl_keep isl_pw_qpolynomial_fold *pwf);
5451 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5452 __isl_take isl_printer *p,
5453 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5455 For C<isl_printer_print_pw_qpolynomial_fold>,
5456 output format of the printer
5457 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5458 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5459 output format of the printer
5460 needs to be set to C<ISL_FORMAT_ISL>.
5461 In case of printing in C<ISL_FORMAT_C>, the user may want
5462 to set the names of all dimensions
5464 __isl_give isl_pw_qpolynomial_fold *
5465 isl_pw_qpolynomial_fold_set_dim_name(
5466 __isl_take isl_pw_qpolynomial_fold *pwf,
5467 enum isl_dim_type type, unsigned pos,
5470 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5472 To iterate over all piecewise quasipolynomial reductions in a union
5473 piecewise quasipolynomial reduction, use the following function
5475 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5476 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5477 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5478 void *user), void *user);
5480 To iterate over the cells in a piecewise quasipolynomial reduction,
5481 use either of the following two functions
5483 int isl_pw_qpolynomial_fold_foreach_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);
5488 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5489 __isl_keep isl_pw_qpolynomial_fold *pwf,
5490 int (*fn)(__isl_take isl_set *set,
5491 __isl_take isl_qpolynomial_fold *fold,
5492 void *user), void *user);
5494 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5495 of the difference between these two functions.
5497 To iterate over all quasipolynomials in a reduction, use
5499 int isl_qpolynomial_fold_foreach_qpolynomial(
5500 __isl_keep isl_qpolynomial_fold *fold,
5501 int (*fn)(__isl_take isl_qpolynomial *qp,
5502 void *user), void *user);
5504 =head3 Properties of Piecewise Quasipolynomial Reductions
5506 To check whether two union piecewise quasipolynomial reductions are
5507 obviously equal, use
5509 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5510 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5511 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5513 =head3 Operations on Piecewise Quasipolynomial Reductions
5515 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5516 __isl_take isl_qpolynomial_fold *fold,
5517 __isl_take isl_val *v);
5518 __isl_give isl_pw_qpolynomial_fold *
5519 isl_pw_qpolynomial_fold_scale_val(
5520 __isl_take isl_pw_qpolynomial_fold *pwf,
5521 __isl_take isl_val *v);
5522 __isl_give isl_union_pw_qpolynomial_fold *
5523 isl_union_pw_qpolynomial_fold_scale_val(
5524 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5525 __isl_take isl_val *v);
5527 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5528 __isl_take isl_pw_qpolynomial_fold *pwf1,
5529 __isl_take isl_pw_qpolynomial_fold *pwf2);
5531 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5532 __isl_take isl_pw_qpolynomial_fold *pwf1,
5533 __isl_take isl_pw_qpolynomial_fold *pwf2);
5535 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5536 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5537 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5539 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5540 __isl_take isl_pw_qpolynomial_fold *pwf,
5541 __isl_take isl_point *pnt);
5543 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5544 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5545 __isl_take isl_point *pnt);
5547 __isl_give isl_pw_qpolynomial_fold *
5548 isl_pw_qpolynomial_fold_intersect_params(
5549 __isl_take isl_pw_qpolynomial_fold *pwf,
5550 __isl_take isl_set *set);
5552 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5553 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5554 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5555 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5556 __isl_take isl_union_set *uset);
5557 __isl_give isl_union_pw_qpolynomial_fold *
5558 isl_union_pw_qpolynomial_fold_intersect_params(
5559 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5560 __isl_take isl_set *set);
5562 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5563 __isl_take isl_pw_qpolynomial_fold *pwf);
5565 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5566 __isl_take isl_pw_qpolynomial_fold *pwf);
5568 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5569 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5571 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5572 __isl_take isl_qpolynomial_fold *fold,
5573 __isl_take isl_set *context);
5574 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5575 __isl_take isl_qpolynomial_fold *fold,
5576 __isl_take isl_set *context);
5578 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5579 __isl_take isl_pw_qpolynomial_fold *pwf,
5580 __isl_take isl_set *context);
5581 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5582 __isl_take isl_pw_qpolynomial_fold *pwf,
5583 __isl_take isl_set *context);
5585 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5586 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5587 __isl_take isl_union_set *context);
5588 __isl_give isl_union_pw_qpolynomial_fold *
5589 isl_union_pw_qpolynomial_fold_gist_params(
5590 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5591 __isl_take isl_set *context);
5593 The gist operation applies the gist operation to each of
5594 the cells in the domain of the input piecewise quasipolynomial reduction.
5595 In future, the operation will also exploit the context
5596 to simplify the quasipolynomial reductions associated to each cell.
5598 __isl_give isl_pw_qpolynomial_fold *
5599 isl_set_apply_pw_qpolynomial_fold(
5600 __isl_take isl_set *set,
5601 __isl_take isl_pw_qpolynomial_fold *pwf,
5603 __isl_give isl_pw_qpolynomial_fold *
5604 isl_map_apply_pw_qpolynomial_fold(
5605 __isl_take isl_map *map,
5606 __isl_take isl_pw_qpolynomial_fold *pwf,
5608 __isl_give isl_union_pw_qpolynomial_fold *
5609 isl_union_set_apply_union_pw_qpolynomial_fold(
5610 __isl_take isl_union_set *uset,
5611 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5613 __isl_give isl_union_pw_qpolynomial_fold *
5614 isl_union_map_apply_union_pw_qpolynomial_fold(
5615 __isl_take isl_union_map *umap,
5616 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5619 The functions taking a map
5620 compose the given map with the given piecewise quasipolynomial reduction.
5621 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5622 over all elements in the intersection of the range of the map
5623 and the domain of the piecewise quasipolynomial reduction
5624 as a function of an element in the domain of the map.
5625 The functions taking a set compute a bound over all elements in the
5626 intersection of the set and the domain of the
5627 piecewise quasipolynomial reduction.
5629 =head2 Parametric Vertex Enumeration
5631 The parametric vertex enumeration described in this section
5632 is mainly intended to be used internally and by the C<barvinok>
5635 #include <isl/vertices.h>
5636 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5637 __isl_keep isl_basic_set *bset);
5639 The function C<isl_basic_set_compute_vertices> performs the
5640 actual computation of the parametric vertices and the chamber
5641 decomposition and store the result in an C<isl_vertices> object.
5642 This information can be queried by either iterating over all
5643 the vertices or iterating over all the chambers or cells
5644 and then iterating over all vertices that are active on the chamber.
5646 int isl_vertices_foreach_vertex(
5647 __isl_keep isl_vertices *vertices,
5648 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5651 int isl_vertices_foreach_cell(
5652 __isl_keep isl_vertices *vertices,
5653 int (*fn)(__isl_take isl_cell *cell, void *user),
5655 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5656 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5659 Other operations that can be performed on an C<isl_vertices> object are
5662 isl_ctx *isl_vertices_get_ctx(
5663 __isl_keep isl_vertices *vertices);
5664 int isl_vertices_get_n_vertices(
5665 __isl_keep isl_vertices *vertices);
5666 void isl_vertices_free(__isl_take isl_vertices *vertices);
5668 Vertices can be inspected and destroyed using the following functions.
5670 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5671 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5672 __isl_give isl_basic_set *isl_vertex_get_domain(
5673 __isl_keep isl_vertex *vertex);
5674 __isl_give isl_multi_aff *isl_vertex_get_expr(
5675 __isl_keep isl_vertex *vertex);
5676 void isl_vertex_free(__isl_take isl_vertex *vertex);
5678 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
5679 describing the vertex in terms of the parameters,
5680 while C<isl_vertex_get_domain> returns the activity domain
5683 Chambers can be inspected and destroyed using the following functions.
5685 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5686 __isl_give isl_basic_set *isl_cell_get_domain(
5687 __isl_keep isl_cell *cell);
5688 void isl_cell_free(__isl_take isl_cell *cell);
5690 =head1 Polyhedral Compilation Library
5692 This section collects functionality in C<isl> that has been specifically
5693 designed for use during polyhedral compilation.
5695 =head2 Dependence Analysis
5697 C<isl> contains specialized functionality for performing
5698 array dataflow analysis. That is, given a I<sink> access relation
5699 and a collection of possible I<source> access relations,
5700 C<isl> can compute relations that describe
5701 for each iteration of the sink access, which iteration
5702 of which of the source access relations was the last
5703 to access the same data element before the given iteration
5705 The resulting dependence relations map source iterations
5706 to the corresponding sink iterations.
5707 To compute standard flow dependences, the sink should be
5708 a read, while the sources should be writes.
5709 If any of the source accesses are marked as being I<may>
5710 accesses, then there will be a dependence from the last
5711 I<must> access B<and> from any I<may> access that follows
5712 this last I<must> access.
5713 In particular, if I<all> sources are I<may> accesses,
5714 then memory based dependence analysis is performed.
5715 If, on the other hand, all sources are I<must> accesses,
5716 then value based dependence analysis is performed.
5718 #include <isl/flow.h>
5720 typedef int (*isl_access_level_before)(void *first, void *second);
5722 __isl_give isl_access_info *isl_access_info_alloc(
5723 __isl_take isl_map *sink,
5724 void *sink_user, isl_access_level_before fn,
5726 __isl_give isl_access_info *isl_access_info_add_source(
5727 __isl_take isl_access_info *acc,
5728 __isl_take isl_map *source, int must,
5730 __isl_null isl_access_info *isl_access_info_free(
5731 __isl_take isl_access_info *acc);
5733 __isl_give isl_flow *isl_access_info_compute_flow(
5734 __isl_take isl_access_info *acc);
5736 int isl_flow_foreach(__isl_keep isl_flow *deps,
5737 int (*fn)(__isl_take isl_map *dep, int must,
5738 void *dep_user, void *user),
5740 __isl_give isl_map *isl_flow_get_no_source(
5741 __isl_keep isl_flow *deps, int must);
5742 void isl_flow_free(__isl_take isl_flow *deps);
5744 The function C<isl_access_info_compute_flow> performs the actual
5745 dependence analysis. The other functions are used to construct
5746 the input for this function or to read off the output.
5748 The input is collected in an C<isl_access_info>, which can
5749 be created through a call to C<isl_access_info_alloc>.
5750 The arguments to this functions are the sink access relation
5751 C<sink>, a token C<sink_user> used to identify the sink
5752 access to the user, a callback function for specifying the
5753 relative order of source and sink accesses, and the number
5754 of source access relations that will be added.
5755 The callback function has type C<int (*)(void *first, void *second)>.
5756 The function is called with two user supplied tokens identifying
5757 either a source or the sink and it should return the shared nesting
5758 level and the relative order of the two accesses.
5759 In particular, let I<n> be the number of loops shared by
5760 the two accesses. If C<first> precedes C<second> textually,
5761 then the function should return I<2 * n + 1>; otherwise,
5762 it should return I<2 * n>.
5763 The sources can be added to the C<isl_access_info> by performing
5764 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5765 C<must> indicates whether the source is a I<must> access
5766 or a I<may> access. Note that a multi-valued access relation
5767 should only be marked I<must> if every iteration in the domain
5768 of the relation accesses I<all> elements in its image.
5769 The C<source_user> token is again used to identify
5770 the source access. The range of the source access relation
5771 C<source> should have the same dimension as the range
5772 of the sink access relation.
5773 The C<isl_access_info_free> function should usually not be
5774 called explicitly, because it is called implicitly by
5775 C<isl_access_info_compute_flow>.
5777 The result of the dependence analysis is collected in an
5778 C<isl_flow>. There may be elements of
5779 the sink access for which no preceding source access could be
5780 found or for which all preceding sources are I<may> accesses.
5781 The relations containing these elements can be obtained through
5782 calls to C<isl_flow_get_no_source>, the first with C<must> set
5783 and the second with C<must> unset.
5784 In the case of standard flow dependence analysis,
5785 with the sink a read and the sources I<must> writes,
5786 the first relation corresponds to the reads from uninitialized
5787 array elements and the second relation is empty.
5788 The actual flow dependences can be extracted using
5789 C<isl_flow_foreach>. This function will call the user-specified
5790 callback function C<fn> for each B<non-empty> dependence between
5791 a source and the sink. The callback function is called
5792 with four arguments, the actual flow dependence relation
5793 mapping source iterations to sink iterations, a boolean that
5794 indicates whether it is a I<must> or I<may> dependence, a token
5795 identifying the source and an additional C<void *> with value
5796 equal to the third argument of the C<isl_flow_foreach> call.
5797 A dependence is marked I<must> if it originates from a I<must>
5798 source and if it is not followed by any I<may> sources.
5800 After finishing with an C<isl_flow>, the user should call
5801 C<isl_flow_free> to free all associated memory.
5803 A higher-level interface to dependence analysis is provided
5804 by the following function.
5806 #include <isl/flow.h>
5808 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5809 __isl_take isl_union_map *must_source,
5810 __isl_take isl_union_map *may_source,
5811 __isl_take isl_union_map *schedule,
5812 __isl_give isl_union_map **must_dep,
5813 __isl_give isl_union_map **may_dep,
5814 __isl_give isl_union_map **must_no_source,
5815 __isl_give isl_union_map **may_no_source);
5817 The arrays are identified by the tuple names of the ranges
5818 of the accesses. The iteration domains by the tuple names
5819 of the domains of the accesses and of the schedule.
5820 The relative order of the iteration domains is given by the
5821 schedule. The relations returned through C<must_no_source>
5822 and C<may_no_source> are subsets of C<sink>.
5823 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5824 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5825 any of the other arguments is treated as an error.
5827 =head3 Interaction with Dependence Analysis
5829 During the dependence analysis, we frequently need to perform
5830 the following operation. Given a relation between sink iterations
5831 and potential source iterations from a particular source domain,
5832 what is the last potential source iteration corresponding to each
5833 sink iteration. It can sometimes be convenient to adjust
5834 the set of potential source iterations before or after each such operation.
5835 The prototypical example is fuzzy array dataflow analysis,
5836 where we need to analyze if, based on data-dependent constraints,
5837 the sink iteration can ever be executed without one or more of
5838 the corresponding potential source iterations being executed.
5839 If so, we can introduce extra parameters and select an unknown
5840 but fixed source iteration from the potential source iterations.
5841 To be able to perform such manipulations, C<isl> provides the following
5844 #include <isl/flow.h>
5846 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5847 __isl_keep isl_map *source_map,
5848 __isl_keep isl_set *sink, void *source_user,
5850 __isl_give isl_access_info *isl_access_info_set_restrict(
5851 __isl_take isl_access_info *acc,
5852 isl_access_restrict fn, void *user);
5854 The function C<isl_access_info_set_restrict> should be called
5855 before calling C<isl_access_info_compute_flow> and registers a callback function
5856 that will be called any time C<isl> is about to compute the last
5857 potential source. The first argument is the (reverse) proto-dependence,
5858 mapping sink iterations to potential source iterations.
5859 The second argument represents the sink iterations for which
5860 we want to compute the last source iteration.
5861 The third argument is the token corresponding to the source
5862 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5863 The callback is expected to return a restriction on either the input or
5864 the output of the operation computing the last potential source.
5865 If the input needs to be restricted then restrictions are needed
5866 for both the source and the sink iterations. The sink iterations
5867 and the potential source iterations will be intersected with these sets.
5868 If the output needs to be restricted then only a restriction on the source
5869 iterations is required.
5870 If any error occurs, the callback should return C<NULL>.
5871 An C<isl_restriction> object can be created, freed and inspected
5872 using the following functions.
5874 #include <isl/flow.h>
5876 __isl_give isl_restriction *isl_restriction_input(
5877 __isl_take isl_set *source_restr,
5878 __isl_take isl_set *sink_restr);
5879 __isl_give isl_restriction *isl_restriction_output(
5880 __isl_take isl_set *source_restr);
5881 __isl_give isl_restriction *isl_restriction_none(
5882 __isl_take isl_map *source_map);
5883 __isl_give isl_restriction *isl_restriction_empty(
5884 __isl_take isl_map *source_map);
5885 __isl_null isl_restriction *isl_restriction_free(
5886 __isl_take isl_restriction *restr);
5887 isl_ctx *isl_restriction_get_ctx(
5888 __isl_keep isl_restriction *restr);
5890 C<isl_restriction_none> and C<isl_restriction_empty> are special
5891 cases of C<isl_restriction_input>. C<isl_restriction_none>
5892 is essentially equivalent to
5894 isl_restriction_input(isl_set_universe(
5895 isl_space_range(isl_map_get_space(source_map))),
5897 isl_space_domain(isl_map_get_space(source_map))));
5899 whereas C<isl_restriction_empty> is essentially equivalent to
5901 isl_restriction_input(isl_set_empty(
5902 isl_space_range(isl_map_get_space(source_map))),
5904 isl_space_domain(isl_map_get_space(source_map))));
5908 B<The functionality described in this section is fairly new
5909 and may be subject to change.>
5911 #include <isl/schedule.h>
5912 __isl_give isl_schedule *
5913 isl_schedule_constraints_compute_schedule(
5914 __isl_take isl_schedule_constraints *sc);
5915 __isl_null isl_schedule *isl_schedule_free(
5916 __isl_take isl_schedule *sched);
5918 The function C<isl_schedule_constraints_compute_schedule> can be
5919 used to compute a schedule that satisfy the given schedule constraints.
5920 These schedule constraints include the iteration domain for which
5921 a schedule should be computed and dependences between pairs of
5922 iterations. In particular, these dependences include
5923 I<validity> dependences and I<proximity> dependences.
5924 By default, the algorithm used to construct the schedule is similar
5925 to that of C<Pluto>.
5926 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5928 The generated schedule respects all validity dependences.
5929 That is, all dependence distances over these dependences in the
5930 scheduled space are lexicographically positive.
5931 The default algorithm tries to ensure that the dependence distances
5932 over coincidence constraints are zero and to minimize the
5933 dependence distances over proximity dependences.
5934 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5935 for groups of domains where the dependence distances over validity
5936 dependences have only non-negative values.
5937 When using Feautrier's algorithm, the coincidence and proximity constraints
5938 are only taken into account during the extension to a
5939 full-dimensional schedule.
5941 An C<isl_schedule_constraints> object can be constructed
5942 and manipulated using the following functions.
5944 #include <isl/schedule.h>
5945 __isl_give isl_schedule_constraints *
5946 isl_schedule_constraints_copy(
5947 __isl_keep isl_schedule_constraints *sc);
5948 __isl_give isl_schedule_constraints *
5949 isl_schedule_constraints_on_domain(
5950 __isl_take isl_union_set *domain);
5951 isl_ctx *isl_schedule_constraints_get_ctx(
5952 __isl_keep isl_schedule_constraints *sc);
5953 __isl_give isl_schedule_constraints *
5954 isl_schedule_constraints_set_validity(
5955 __isl_take isl_schedule_constraints *sc,
5956 __isl_take isl_union_map *validity);
5957 __isl_give isl_schedule_constraints *
5958 isl_schedule_constraints_set_coincidence(
5959 __isl_take isl_schedule_constraints *sc,
5960 __isl_take isl_union_map *coincidence);
5961 __isl_give isl_schedule_constraints *
5962 isl_schedule_constraints_set_proximity(
5963 __isl_take isl_schedule_constraints *sc,
5964 __isl_take isl_union_map *proximity);
5965 __isl_give isl_schedule_constraints *
5966 isl_schedule_constraints_set_conditional_validity(
5967 __isl_take isl_schedule_constraints *sc,
5968 __isl_take isl_union_map *condition,
5969 __isl_take isl_union_map *validity);
5970 __isl_null isl_schedule_constraints *
5971 isl_schedule_constraints_free(
5972 __isl_take isl_schedule_constraints *sc);
5974 The initial C<isl_schedule_constraints> object created by
5975 C<isl_schedule_constraints_on_domain> does not impose any constraints.
5976 That is, it has an empty set of dependences.
5977 The function C<isl_schedule_constraints_set_validity> replaces the
5978 validity dependences, mapping domain elements I<i> to domain
5979 elements that should be scheduled after I<i>.
5980 The function C<isl_schedule_constraints_set_coincidence> replaces the
5981 coincidence dependences, mapping domain elements I<i> to domain
5982 elements that should be scheduled together with I<I>, if possible.
5983 The function C<isl_schedule_constraints_set_proximity> replaces the
5984 proximity dependences, mapping domain elements I<i> to domain
5985 elements that should be scheduled either before I<I>
5986 or as early as possible after I<i>.
5988 The function C<isl_schedule_constraints_set_conditional_validity>
5989 replaces the conditional validity constraints.
5990 A conditional validity constraint is only imposed when any of the corresponding
5991 conditions is satisfied, i.e., when any of them is non-zero.
5992 That is, the scheduler ensures that within each band if the dependence
5993 distances over the condition constraints are not all zero
5994 then all corresponding conditional validity constraints are respected.
5995 A conditional validity constraint corresponds to a condition
5996 if the two are adjacent, i.e., if the domain of one relation intersect
5997 the range of the other relation.
5998 The typical use case of conditional validity constraints is
5999 to allow order constraints between live ranges to be violated
6000 as long as the live ranges themselves are local to the band.
6001 To allow more fine-grained control over which conditions correspond
6002 to which conditional validity constraints, the domains and ranges
6003 of these relations may include I<tags>. That is, the domains and
6004 ranges of those relation may themselves be wrapped relations
6005 where the iteration domain appears in the domain of those wrapped relations
6006 and the range of the wrapped relations can be arbitrarily chosen
6007 by the user. Conditions and conditional validity constraints are only
6008 considere adjacent to each other if the entire wrapped relation matches.
6009 In particular, a relation with a tag will never be considered adjacent
6010 to a relation without a tag.
6012 The following function computes a schedule directly from
6013 an iteration domain and validity and proximity dependences
6014 and is implemented in terms of the functions described above.
6015 The use of C<isl_union_set_compute_schedule> is discouraged.
6017 #include <isl/schedule.h>
6018 __isl_give isl_schedule *isl_union_set_compute_schedule(
6019 __isl_take isl_union_set *domain,
6020 __isl_take isl_union_map *validity,
6021 __isl_take isl_union_map *proximity);
6023 A mapping from the domains to the scheduled space can be obtained
6024 from an C<isl_schedule> using the following function.
6026 __isl_give isl_union_map *isl_schedule_get_map(
6027 __isl_keep isl_schedule *sched);
6029 A representation of the schedule can be printed using
6031 __isl_give isl_printer *isl_printer_print_schedule(
6032 __isl_take isl_printer *p,
6033 __isl_keep isl_schedule *schedule);
6035 A representation of the schedule as a forest of bands can be obtained
6036 using the following function.
6038 __isl_give isl_band_list *isl_schedule_get_band_forest(
6039 __isl_keep isl_schedule *schedule);
6041 The individual bands can be visited in depth-first post-order
6042 using the following function.
6044 #include <isl/schedule.h>
6045 int isl_schedule_foreach_band(
6046 __isl_keep isl_schedule *sched,
6047 int (*fn)(__isl_keep isl_band *band, void *user),
6050 The list can be manipulated as explained in L<"Lists">.
6051 The bands inside the list can be copied and freed using the following
6054 #include <isl/band.h>
6055 __isl_give isl_band *isl_band_copy(
6056 __isl_keep isl_band *band);
6057 __isl_null isl_band *isl_band_free(
6058 __isl_take isl_band *band);
6060 Each band contains zero or more scheduling dimensions.
6061 These are referred to as the members of the band.
6062 The section of the schedule that corresponds to the band is
6063 referred to as the partial schedule of the band.
6064 For those nodes that participate in a band, the outer scheduling
6065 dimensions form the prefix schedule, while the inner scheduling
6066 dimensions form the suffix schedule.
6067 That is, if we take a cut of the band forest, then the union of
6068 the concatenations of the prefix, partial and suffix schedules of
6069 each band in the cut is equal to the entire schedule (modulo
6070 some possible padding at the end with zero scheduling dimensions).
6071 The properties of a band can be inspected using the following functions.
6073 #include <isl/band.h>
6074 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
6076 int isl_band_has_children(__isl_keep isl_band *band);
6077 __isl_give isl_band_list *isl_band_get_children(
6078 __isl_keep isl_band *band);
6080 __isl_give isl_union_map *isl_band_get_prefix_schedule(
6081 __isl_keep isl_band *band);
6082 __isl_give isl_union_map *isl_band_get_partial_schedule(
6083 __isl_keep isl_band *band);
6084 __isl_give isl_union_map *isl_band_get_suffix_schedule(
6085 __isl_keep isl_band *band);
6087 int isl_band_n_member(__isl_keep isl_band *band);
6088 int isl_band_member_is_coincident(
6089 __isl_keep isl_band *band, int pos);
6091 int isl_band_list_foreach_band(
6092 __isl_keep isl_band_list *list,
6093 int (*fn)(__isl_keep isl_band *band, void *user),
6096 Note that a scheduling dimension is considered to be ``coincident''
6097 if it satisfies the coincidence constraints within its band.
6098 That is, if the dependence distances of the coincidence
6099 constraints are all zero in that direction (for fixed
6100 iterations of outer bands).
6101 Like C<isl_schedule_foreach_band>,
6102 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
6103 in depth-first post-order.
6105 A band can be tiled using the following function.
6107 #include <isl/band.h>
6108 int isl_band_tile(__isl_keep isl_band *band,
6109 __isl_take isl_vec *sizes);
6111 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
6113 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
6114 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
6116 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
6118 The C<isl_band_tile> function tiles the band using the given tile sizes
6119 inside its schedule.
6120 A new child band is created to represent the point loops and it is
6121 inserted between the modified band and its children.
6122 The C<tile_scale_tile_loops> option specifies whether the tile
6123 loops iterators should be scaled by the tile sizes.
6124 If the C<tile_shift_point_loops> option is set, then the point loops
6125 are shifted to start at zero.
6127 A band can be split into two nested bands using the following function.
6129 int isl_band_split(__isl_keep isl_band *band, int pos);
6131 The resulting outer band contains the first C<pos> dimensions of C<band>
6132 while the inner band contains the remaining dimensions.
6134 A representation of the band can be printed using
6136 #include <isl/band.h>
6137 __isl_give isl_printer *isl_printer_print_band(
6138 __isl_take isl_printer *p,
6139 __isl_keep isl_band *band);
6143 #include <isl/schedule.h>
6144 int isl_options_set_schedule_max_coefficient(
6145 isl_ctx *ctx, int val);
6146 int isl_options_get_schedule_max_coefficient(
6148 int isl_options_set_schedule_max_constant_term(
6149 isl_ctx *ctx, int val);
6150 int isl_options_get_schedule_max_constant_term(
6152 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
6153 int isl_options_get_schedule_fuse(isl_ctx *ctx);
6154 int isl_options_set_schedule_maximize_band_depth(
6155 isl_ctx *ctx, int val);
6156 int isl_options_get_schedule_maximize_band_depth(
6158 int isl_options_set_schedule_outer_coincidence(
6159 isl_ctx *ctx, int val);
6160 int isl_options_get_schedule_outer_coincidence(
6162 int isl_options_set_schedule_split_scaled(
6163 isl_ctx *ctx, int val);
6164 int isl_options_get_schedule_split_scaled(
6166 int isl_options_set_schedule_algorithm(
6167 isl_ctx *ctx, int val);
6168 int isl_options_get_schedule_algorithm(
6170 int isl_options_set_schedule_separate_components(
6171 isl_ctx *ctx, int val);
6172 int isl_options_get_schedule_separate_components(
6177 =item * schedule_max_coefficient
6179 This option enforces that the coefficients for variable and parameter
6180 dimensions in the calculated schedule are not larger than the specified value.
6181 This option can significantly increase the speed of the scheduling calculation
6182 and may also prevent fusing of unrelated dimensions. A value of -1 means that
6183 this option does not introduce bounds on the variable or parameter
6186 =item * schedule_max_constant_term
6188 This option enforces that the constant coefficients in the calculated schedule
6189 are not larger than the maximal constant term. This option can significantly
6190 increase the speed of the scheduling calculation and may also prevent fusing of
6191 unrelated dimensions. A value of -1 means that this option does not introduce
6192 bounds on the constant coefficients.
6194 =item * schedule_fuse
6196 This option controls the level of fusion.
6197 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6198 resulting schedule will be distributed as much as possible.
6199 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6200 try to fuse loops in the resulting schedule.
6202 =item * schedule_maximize_band_depth
6204 If this option is set, we do not split bands at the point
6205 where we detect splitting is necessary. Instead, we
6206 backtrack and split bands as early as possible. This
6207 reduces the number of splits and maximizes the width of
6208 the bands. Wider bands give more possibilities for tiling.
6209 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6210 then bands will be split as early as possible, even if there is no need.
6211 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6213 =item * schedule_outer_coincidence
6215 If this option is set, then we try to construct schedules
6216 where the outermost scheduling dimension in each band
6217 satisfies the coincidence constraints.
6219 =item * schedule_split_scaled
6221 If this option is set, then we try to construct schedules in which the
6222 constant term is split off from the linear part if the linear parts of
6223 the scheduling rows for all nodes in the graphs have a common non-trivial
6225 The constant term is then placed in a separate band and the linear
6228 =item * schedule_algorithm
6230 Selects the scheduling algorithm to be used.
6231 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6232 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6234 =item * schedule_separate_components
6236 If at any point the dependence graph contains any (weakly connected) components,
6237 then these components are scheduled separately.
6238 If this option is not set, then some iterations of the domains
6239 in these components may be scheduled together.
6240 If this option is set, then the components are given consecutive
6245 =head2 AST Generation
6247 This section describes the C<isl> functionality for generating
6248 ASTs that visit all the elements
6249 in a domain in an order specified by a schedule.
6250 In particular, given a C<isl_union_map>, an AST is generated
6251 that visits all the elements in the domain of the C<isl_union_map>
6252 according to the lexicographic order of the corresponding image
6253 element(s). If the range of the C<isl_union_map> consists of
6254 elements in more than one space, then each of these spaces is handled
6255 separately in an arbitrary order.
6256 It should be noted that the image elements only specify the I<order>
6257 in which the corresponding domain elements should be visited.
6258 No direct relation between the image elements and the loop iterators
6259 in the generated AST should be assumed.
6261 Each AST is generated within a build. The initial build
6262 simply specifies the constraints on the parameters (if any)
6263 and can be created, inspected, copied and freed using the following functions.
6265 #include <isl/ast_build.h>
6266 __isl_give isl_ast_build *isl_ast_build_from_context(
6267 __isl_take isl_set *set);
6268 isl_ctx *isl_ast_build_get_ctx(
6269 __isl_keep isl_ast_build *build);
6270 __isl_give isl_ast_build *isl_ast_build_copy(
6271 __isl_keep isl_ast_build *build);
6272 __isl_null isl_ast_build *isl_ast_build_free(
6273 __isl_take isl_ast_build *build);
6275 The C<set> argument is usually a parameter set with zero or more parameters.
6276 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6277 and L</"Fine-grained Control over AST Generation">.
6278 Finally, the AST itself can be constructed using the following
6281 #include <isl/ast_build.h>
6282 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6283 __isl_keep isl_ast_build *build,
6284 __isl_take isl_union_map *schedule);
6286 =head3 Inspecting the AST
6288 The basic properties of an AST node can be obtained as follows.
6290 #include <isl/ast.h>
6291 isl_ctx *isl_ast_node_get_ctx(
6292 __isl_keep isl_ast_node *node);
6293 enum isl_ast_node_type isl_ast_node_get_type(
6294 __isl_keep isl_ast_node *node);
6296 The type of an AST node is one of
6297 C<isl_ast_node_for>,
6299 C<isl_ast_node_block> or
6300 C<isl_ast_node_user>.
6301 An C<isl_ast_node_for> represents a for node.
6302 An C<isl_ast_node_if> represents an if node.
6303 An C<isl_ast_node_block> represents a compound node.
6304 An C<isl_ast_node_user> represents an expression statement.
6305 An expression statement typically corresponds to a domain element, i.e.,
6306 one of the elements that is visited by the AST.
6308 Each type of node has its own additional properties.
6310 #include <isl/ast.h>
6311 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6312 __isl_keep isl_ast_node *node);
6313 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6314 __isl_keep isl_ast_node *node);
6315 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6316 __isl_keep isl_ast_node *node);
6317 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6318 __isl_keep isl_ast_node *node);
6319 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6320 __isl_keep isl_ast_node *node);
6321 int isl_ast_node_for_is_degenerate(
6322 __isl_keep isl_ast_node *node);
6324 An C<isl_ast_for> is considered degenerate if it is known to execute
6327 #include <isl/ast.h>
6328 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6329 __isl_keep isl_ast_node *node);
6330 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6331 __isl_keep isl_ast_node *node);
6332 int isl_ast_node_if_has_else(
6333 __isl_keep isl_ast_node *node);
6334 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6335 __isl_keep isl_ast_node *node);
6337 __isl_give isl_ast_node_list *
6338 isl_ast_node_block_get_children(
6339 __isl_keep isl_ast_node *node);
6341 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6342 __isl_keep isl_ast_node *node);
6344 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6345 the following functions.
6347 #include <isl/ast.h>
6348 isl_ctx *isl_ast_expr_get_ctx(
6349 __isl_keep isl_ast_expr *expr);
6350 enum isl_ast_expr_type isl_ast_expr_get_type(
6351 __isl_keep isl_ast_expr *expr);
6353 The type of an AST expression is one of
6355 C<isl_ast_expr_id> or
6356 C<isl_ast_expr_int>.
6357 An C<isl_ast_expr_op> represents the result of an operation.
6358 An C<isl_ast_expr_id> represents an identifier.
6359 An C<isl_ast_expr_int> represents an integer value.
6361 Each type of expression has its own additional properties.
6363 #include <isl/ast.h>
6364 enum isl_ast_op_type isl_ast_expr_get_op_type(
6365 __isl_keep isl_ast_expr *expr);
6366 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6367 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6368 __isl_keep isl_ast_expr *expr, int pos);
6369 int isl_ast_node_foreach_ast_op_type(
6370 __isl_keep isl_ast_node *node,
6371 int (*fn)(enum isl_ast_op_type type, void *user),
6374 C<isl_ast_expr_get_op_type> returns the type of the operation
6375 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6376 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6378 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6379 C<isl_ast_op_type> that appears in C<node>.
6380 The operation type is one of the following.
6384 =item C<isl_ast_op_and>
6386 Logical I<and> of two arguments.
6387 Both arguments can be evaluated.
6389 =item C<isl_ast_op_and_then>
6391 Logical I<and> of two arguments.
6392 The second argument can only be evaluated if the first evaluates to true.
6394 =item C<isl_ast_op_or>
6396 Logical I<or> of two arguments.
6397 Both arguments can be evaluated.
6399 =item C<isl_ast_op_or_else>
6401 Logical I<or> of two arguments.
6402 The second argument can only be evaluated if the first evaluates to false.
6404 =item C<isl_ast_op_max>
6406 Maximum of two or more arguments.
6408 =item C<isl_ast_op_min>
6410 Minimum of two or more arguments.
6412 =item C<isl_ast_op_minus>
6416 =item C<isl_ast_op_add>
6418 Sum of two arguments.
6420 =item C<isl_ast_op_sub>
6422 Difference of two arguments.
6424 =item C<isl_ast_op_mul>
6426 Product of two arguments.
6428 =item C<isl_ast_op_div>
6430 Exact division. That is, the result is known to be an integer.
6432 =item C<isl_ast_op_fdiv_q>
6434 Result of integer division, rounded towards negative
6437 =item C<isl_ast_op_pdiv_q>
6439 Result of integer division, where dividend is known to be non-negative.
6441 =item C<isl_ast_op_pdiv_r>
6443 Remainder of integer division, where dividend is known to be non-negative.
6445 =item C<isl_ast_op_cond>
6447 Conditional operator defined on three arguments.
6448 If the first argument evaluates to true, then the result
6449 is equal to the second argument. Otherwise, the result
6450 is equal to the third argument.
6451 The second and third argument may only be evaluated if
6452 the first argument evaluates to true and false, respectively.
6453 Corresponds to C<a ? b : c> in C.
6455 =item C<isl_ast_op_select>
6457 Conditional operator defined on three arguments.
6458 If the first argument evaluates to true, then the result
6459 is equal to the second argument. Otherwise, the result
6460 is equal to the third argument.
6461 The second and third argument may be evaluated independently
6462 of the value of the first argument.
6463 Corresponds to C<a * b + (1 - a) * c> in C.
6465 =item C<isl_ast_op_eq>
6469 =item C<isl_ast_op_le>
6471 Less than or equal relation.
6473 =item C<isl_ast_op_lt>
6477 =item C<isl_ast_op_ge>
6479 Greater than or equal relation.
6481 =item C<isl_ast_op_gt>
6483 Greater than relation.
6485 =item C<isl_ast_op_call>
6488 The number of arguments of the C<isl_ast_expr> is one more than
6489 the number of arguments in the function call, the first argument
6490 representing the function being called.
6492 =item C<isl_ast_op_access>
6495 The number of arguments of the C<isl_ast_expr> is one more than
6496 the number of index expressions in the array access, the first argument
6497 representing the array being accessed.
6499 =item C<isl_ast_op_member>
6502 This operation has two arguments, a structure and the name of
6503 the member of the structure being accessed.
6507 #include <isl/ast.h>
6508 __isl_give isl_id *isl_ast_expr_get_id(
6509 __isl_keep isl_ast_expr *expr);
6511 Return the identifier represented by the AST expression.
6513 #include <isl/ast.h>
6514 __isl_give isl_val *isl_ast_expr_get_val(
6515 __isl_keep isl_ast_expr *expr);
6517 Return the integer represented by the AST expression.
6519 =head3 Properties of ASTs
6521 #include <isl/ast.h>
6522 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6523 __isl_keep isl_ast_expr *expr2);
6525 Check if two C<isl_ast_expr>s are equal to each other.
6527 =head3 Manipulating and printing the AST
6529 AST nodes can be copied and freed using the following functions.
6531 #include <isl/ast.h>
6532 __isl_give isl_ast_node *isl_ast_node_copy(
6533 __isl_keep isl_ast_node *node);
6534 __isl_null isl_ast_node *isl_ast_node_free(
6535 __isl_take isl_ast_node *node);
6537 AST expressions can be copied and freed using the following functions.
6539 #include <isl/ast.h>
6540 __isl_give isl_ast_expr *isl_ast_expr_copy(
6541 __isl_keep isl_ast_expr *expr);
6542 __isl_null isl_ast_expr *isl_ast_expr_free(
6543 __isl_take isl_ast_expr *expr);
6545 New AST expressions can be created either directly or within
6546 the context of an C<isl_ast_build>.
6548 #include <isl/ast.h>
6549 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6550 __isl_take isl_val *v);
6551 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6552 __isl_take isl_id *id);
6553 __isl_give isl_ast_expr *isl_ast_expr_neg(
6554 __isl_take isl_ast_expr *expr);
6555 __isl_give isl_ast_expr *isl_ast_expr_add(
6556 __isl_take isl_ast_expr *expr1,
6557 __isl_take isl_ast_expr *expr2);
6558 __isl_give isl_ast_expr *isl_ast_expr_sub(
6559 __isl_take isl_ast_expr *expr1,
6560 __isl_take isl_ast_expr *expr2);
6561 __isl_give isl_ast_expr *isl_ast_expr_mul(
6562 __isl_take isl_ast_expr *expr1,
6563 __isl_take isl_ast_expr *expr2);
6564 __isl_give isl_ast_expr *isl_ast_expr_div(
6565 __isl_take isl_ast_expr *expr1,
6566 __isl_take isl_ast_expr *expr2);
6567 __isl_give isl_ast_expr *isl_ast_expr_and(
6568 __isl_take isl_ast_expr *expr1,
6569 __isl_take isl_ast_expr *expr2)
6570 __isl_give isl_ast_expr *isl_ast_expr_or(
6571 __isl_take isl_ast_expr *expr1,
6572 __isl_take isl_ast_expr *expr2)
6573 __isl_give isl_ast_expr *isl_ast_expr_access(
6574 __isl_take isl_ast_expr *array,
6575 __isl_take isl_ast_expr_list *indices);
6577 #include <isl/ast_build.h>
6578 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6579 __isl_keep isl_ast_build *build,
6580 __isl_take isl_pw_aff *pa);
6581 __isl_give isl_ast_expr *
6582 isl_ast_build_access_from_pw_multi_aff(
6583 __isl_keep isl_ast_build *build,
6584 __isl_take isl_pw_multi_aff *pma);
6585 __isl_give isl_ast_expr *
6586 isl_ast_build_access_from_multi_pw_aff(
6587 __isl_keep isl_ast_build *build,
6588 __isl_take isl_multi_pw_aff *mpa);
6589 __isl_give isl_ast_expr *
6590 isl_ast_build_call_from_pw_multi_aff(
6591 __isl_keep isl_ast_build *build,
6592 __isl_take isl_pw_multi_aff *pma);
6593 __isl_give isl_ast_expr *
6594 isl_ast_build_call_from_multi_pw_aff(
6595 __isl_keep isl_ast_build *build,
6596 __isl_take isl_multi_pw_aff *mpa);
6598 The domains of C<pa>, C<mpa> and C<pma> should correspond
6599 to the schedule space of C<build>.
6600 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6601 the function being called.
6602 If the accessed space is a nested relation, then it is taken
6603 to represent an access of the member specified by the range
6604 of this nested relation of the structure specified by the domain
6605 of the nested relation.
6607 The following functions can be used to modify an C<isl_ast_expr>.
6609 #include <isl/ast.h>
6610 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6611 __isl_take isl_ast_expr *expr, int pos,
6612 __isl_take isl_ast_expr *arg);
6614 Replace the argument of C<expr> at position C<pos> by C<arg>.
6616 #include <isl/ast.h>
6617 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6618 __isl_take isl_ast_expr *expr,
6619 __isl_take isl_id_to_ast_expr *id2expr);
6621 The function C<isl_ast_expr_substitute_ids> replaces the
6622 subexpressions of C<expr> of type C<isl_ast_expr_id>
6623 by the corresponding expression in C<id2expr>, if there is any.
6626 User specified data can be attached to an C<isl_ast_node> and obtained
6627 from the same C<isl_ast_node> using the following functions.
6629 #include <isl/ast.h>
6630 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6631 __isl_take isl_ast_node *node,
6632 __isl_take isl_id *annotation);
6633 __isl_give isl_id *isl_ast_node_get_annotation(
6634 __isl_keep isl_ast_node *node);
6636 Basic printing can be performed using the following functions.
6638 #include <isl/ast.h>
6639 __isl_give isl_printer *isl_printer_print_ast_expr(
6640 __isl_take isl_printer *p,
6641 __isl_keep isl_ast_expr *expr);
6642 __isl_give isl_printer *isl_printer_print_ast_node(
6643 __isl_take isl_printer *p,
6644 __isl_keep isl_ast_node *node);
6646 More advanced printing can be performed using the following functions.
6648 #include <isl/ast.h>
6649 __isl_give isl_printer *isl_ast_op_type_print_macro(
6650 enum isl_ast_op_type type,
6651 __isl_take isl_printer *p);
6652 __isl_give isl_printer *isl_ast_node_print_macros(
6653 __isl_keep isl_ast_node *node,
6654 __isl_take isl_printer *p);
6655 __isl_give isl_printer *isl_ast_node_print(
6656 __isl_keep isl_ast_node *node,
6657 __isl_take isl_printer *p,
6658 __isl_take isl_ast_print_options *options);
6659 __isl_give isl_printer *isl_ast_node_for_print(
6660 __isl_keep isl_ast_node *node,
6661 __isl_take isl_printer *p,
6662 __isl_take isl_ast_print_options *options);
6663 __isl_give isl_printer *isl_ast_node_if_print(
6664 __isl_keep isl_ast_node *node,
6665 __isl_take isl_printer *p,
6666 __isl_take isl_ast_print_options *options);
6668 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6669 C<isl> may print out an AST that makes use of macros such
6670 as C<floord>, C<min> and C<max>.
6671 C<isl_ast_op_type_print_macro> prints out the macro
6672 corresponding to a specific C<isl_ast_op_type>.
6673 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6674 for expressions where these macros would be used and prints
6675 out the required macro definitions.
6676 Essentially, C<isl_ast_node_print_macros> calls
6677 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6678 as function argument.
6679 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6680 C<isl_ast_node_if_print> print an C<isl_ast_node>
6681 in C<ISL_FORMAT_C>, but allow for some extra control
6682 through an C<isl_ast_print_options> object.
6683 This object can be created using the following functions.
6685 #include <isl/ast.h>
6686 __isl_give isl_ast_print_options *
6687 isl_ast_print_options_alloc(isl_ctx *ctx);
6688 __isl_give isl_ast_print_options *
6689 isl_ast_print_options_copy(
6690 __isl_keep isl_ast_print_options *options);
6691 __isl_null isl_ast_print_options *
6692 isl_ast_print_options_free(
6693 __isl_take isl_ast_print_options *options);
6695 __isl_give isl_ast_print_options *
6696 isl_ast_print_options_set_print_user(
6697 __isl_take isl_ast_print_options *options,
6698 __isl_give isl_printer *(*print_user)(
6699 __isl_take isl_printer *p,
6700 __isl_take isl_ast_print_options *options,
6701 __isl_keep isl_ast_node *node, void *user),
6703 __isl_give isl_ast_print_options *
6704 isl_ast_print_options_set_print_for(
6705 __isl_take isl_ast_print_options *options,
6706 __isl_give isl_printer *(*print_for)(
6707 __isl_take isl_printer *p,
6708 __isl_take isl_ast_print_options *options,
6709 __isl_keep isl_ast_node *node, void *user),
6712 The callback set by C<isl_ast_print_options_set_print_user>
6713 is called whenever a node of type C<isl_ast_node_user> needs to
6715 The callback set by C<isl_ast_print_options_set_print_for>
6716 is called whenever a node of type C<isl_ast_node_for> needs to
6718 Note that C<isl_ast_node_for_print> will I<not> call the
6719 callback set by C<isl_ast_print_options_set_print_for> on the node
6720 on which C<isl_ast_node_for_print> is called, but only on nested
6721 nodes of type C<isl_ast_node_for>. It is therefore safe to
6722 call C<isl_ast_node_for_print> from within the callback set by
6723 C<isl_ast_print_options_set_print_for>.
6725 The following option determines the type to be used for iterators
6726 while printing the AST.
6728 int isl_options_set_ast_iterator_type(
6729 isl_ctx *ctx, const char *val);
6730 const char *isl_options_get_ast_iterator_type(
6735 #include <isl/ast_build.h>
6736 int isl_options_set_ast_build_atomic_upper_bound(
6737 isl_ctx *ctx, int val);
6738 int isl_options_get_ast_build_atomic_upper_bound(
6740 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6742 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6743 int isl_options_set_ast_build_exploit_nested_bounds(
6744 isl_ctx *ctx, int val);
6745 int isl_options_get_ast_build_exploit_nested_bounds(
6747 int isl_options_set_ast_build_group_coscheduled(
6748 isl_ctx *ctx, int val);
6749 int isl_options_get_ast_build_group_coscheduled(
6751 int isl_options_set_ast_build_scale_strides(
6752 isl_ctx *ctx, int val);
6753 int isl_options_get_ast_build_scale_strides(
6755 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6757 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6758 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6760 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6764 =item * ast_build_atomic_upper_bound
6766 Generate loop upper bounds that consist of the current loop iterator,
6767 an operator and an expression not involving the iterator.
6768 If this option is not set, then the current loop iterator may appear
6769 several times in the upper bound.
6770 For example, when this option is turned off, AST generation
6773 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6777 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6780 When the option is turned on, the following AST is generated
6782 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6785 =item * ast_build_prefer_pdiv
6787 If this option is turned off, then the AST generation will
6788 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6789 operators, but no C<isl_ast_op_pdiv_q> or
6790 C<isl_ast_op_pdiv_r> operators.
6791 If this options is turned on, then C<isl> will try to convert
6792 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6793 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6795 =item * ast_build_exploit_nested_bounds
6797 Simplify conditions based on bounds of nested for loops.
6798 In particular, remove conditions that are implied by the fact
6799 that one or more nested loops have at least one iteration,
6800 meaning that the upper bound is at least as large as the lower bound.
6801 For example, when this option is turned off, AST generation
6804 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6810 for (int c0 = 0; c0 <= N; c0 += 1)
6811 for (int c1 = 0; c1 <= M; c1 += 1)
6814 When the option is turned on, the following AST is generated
6816 for (int c0 = 0; c0 <= N; c0 += 1)
6817 for (int c1 = 0; c1 <= M; c1 += 1)
6820 =item * ast_build_group_coscheduled
6822 If two domain elements are assigned the same schedule point, then
6823 they may be executed in any order and they may even appear in different
6824 loops. If this options is set, then the AST generator will make
6825 sure that coscheduled domain elements do not appear in separate parts
6826 of the AST. This is useful in case of nested AST generation
6827 if the outer AST generation is given only part of a schedule
6828 and the inner AST generation should handle the domains that are
6829 coscheduled by this initial part of the schedule together.
6830 For example if an AST is generated for a schedule
6832 { A[i] -> [0]; B[i] -> [0] }
6834 then the C<isl_ast_build_set_create_leaf> callback described
6835 below may get called twice, once for each domain.
6836 Setting this option ensures that the callback is only called once
6837 on both domains together.
6839 =item * ast_build_separation_bounds
6841 This option specifies which bounds to use during separation.
6842 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6843 then all (possibly implicit) bounds on the current dimension will
6844 be used during separation.
6845 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6846 then only those bounds that are explicitly available will
6847 be used during separation.
6849 =item * ast_build_scale_strides
6851 This option specifies whether the AST generator is allowed
6852 to scale down iterators of strided loops.
6854 =item * ast_build_allow_else
6856 This option specifies whether the AST generator is allowed
6857 to construct if statements with else branches.
6859 =item * ast_build_allow_or
6861 This option specifies whether the AST generator is allowed
6862 to construct if conditions with disjunctions.
6866 =head3 Fine-grained Control over AST Generation
6868 Besides specifying the constraints on the parameters,
6869 an C<isl_ast_build> object can be used to control
6870 various aspects of the AST generation process.
6871 The most prominent way of control is through ``options'',
6872 which can be set using the following function.
6874 #include <isl/ast_build.h>
6875 __isl_give isl_ast_build *
6876 isl_ast_build_set_options(
6877 __isl_take isl_ast_build *control,
6878 __isl_take isl_union_map *options);
6880 The options are encoded in an <isl_union_map>.
6881 The domain of this union relation refers to the schedule domain,
6882 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6883 In the case of nested AST generation (see L</"Nested AST Generation">),
6884 the domain of C<options> should refer to the extra piece of the schedule.
6885 That is, it should be equal to the range of the wrapped relation in the
6886 range of the schedule.
6887 The range of the options can consist of elements in one or more spaces,
6888 the names of which determine the effect of the option.
6889 The values of the range typically also refer to the schedule dimension
6890 to which the option applies. In case of nested AST generation
6891 (see L</"Nested AST Generation">), these values refer to the position
6892 of the schedule dimension within the innermost AST generation.
6893 The constraints on the domain elements of
6894 the option should only refer to this dimension and earlier dimensions.
6895 We consider the following spaces.
6899 =item C<separation_class>
6901 This space is a wrapped relation between two one dimensional spaces.
6902 The input space represents the schedule dimension to which the option
6903 applies and the output space represents the separation class.
6904 While constructing a loop corresponding to the specified schedule
6905 dimension(s), the AST generator will try to generate separate loops
6906 for domain elements that are assigned different classes.
6907 If only some of the elements are assigned a class, then those elements
6908 that are not assigned any class will be treated as belonging to a class
6909 that is separate from the explicitly assigned classes.
6910 The typical use case for this option is to separate full tiles from
6912 The other options, described below, are applied after the separation
6915 As an example, consider the separation into full and partial tiles
6916 of a tiling of a triangular domain.
6917 Take, for example, the domain
6919 { A[i,j] : 0 <= i,j and i + j <= 100 }
6921 and a tiling into tiles of 10 by 10. The input to the AST generator
6922 is then the schedule
6924 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6927 Without any options, the following AST is generated
6929 for (int c0 = 0; c0 <= 10; c0 += 1)
6930 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6931 for (int c2 = 10 * c0;
6932 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6934 for (int c3 = 10 * c1;
6935 c3 <= min(10 * c1 + 9, -c2 + 100);
6939 Separation into full and partial tiles can be obtained by assigning
6940 a class, say C<0>, to the full tiles. The full tiles are represented by those
6941 values of the first and second schedule dimensions for which there are
6942 values of the third and fourth dimensions to cover an entire tile.
6943 That is, we need to specify the following option
6945 { [a,b,c,d] -> separation_class[[0]->[0]] :
6946 exists b': 0 <= 10a,10b' and
6947 10a+9+10b'+9 <= 100;
6948 [a,b,c,d] -> separation_class[[1]->[0]] :
6949 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6953 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6954 a >= 0 and b >= 0 and b <= 8 - a;
6955 [a, b, c, d] -> separation_class[[0] -> [0]] :
6958 With this option, the generated AST is as follows
6961 for (int c0 = 0; c0 <= 8; c0 += 1) {
6962 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6963 for (int c2 = 10 * c0;
6964 c2 <= 10 * c0 + 9; c2 += 1)
6965 for (int c3 = 10 * c1;
6966 c3 <= 10 * c1 + 9; c3 += 1)
6968 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6969 for (int c2 = 10 * c0;
6970 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6972 for (int c3 = 10 * c1;
6973 c3 <= min(-c2 + 100, 10 * c1 + 9);
6977 for (int c0 = 9; c0 <= 10; c0 += 1)
6978 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6979 for (int c2 = 10 * c0;
6980 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6982 for (int c3 = 10 * c1;
6983 c3 <= min(10 * c1 + 9, -c2 + 100);
6990 This is a single-dimensional space representing the schedule dimension(s)
6991 to which ``separation'' should be applied. Separation tries to split
6992 a loop into several pieces if this can avoid the generation of guards
6994 See also the C<atomic> option.
6998 This is a single-dimensional space representing the schedule dimension(s)
6999 for which the domains should be considered ``atomic''. That is, the
7000 AST generator will make sure that any given domain space will only appear
7001 in a single loop at the specified level.
7003 Consider the following schedule
7005 { a[i] -> [i] : 0 <= i < 10;
7006 b[i] -> [i+1] : 0 <= i < 10 }
7008 If the following option is specified
7010 { [i] -> separate[x] }
7012 then the following AST will be generated
7016 for (int c0 = 1; c0 <= 9; c0 += 1) {
7023 If, on the other hand, the following option is specified
7025 { [i] -> atomic[x] }
7027 then the following AST will be generated
7029 for (int c0 = 0; c0 <= 10; c0 += 1) {
7036 If neither C<atomic> nor C<separate> is specified, then the AST generator
7037 may produce either of these two results or some intermediate form.
7041 This is a single-dimensional space representing the schedule dimension(s)
7042 that should be I<completely> unrolled.
7043 To obtain a partial unrolling, the user should apply an additional
7044 strip-mining to the schedule and fully unroll the inner loop.
7048 Additional control is available through the following functions.
7050 #include <isl/ast_build.h>
7051 __isl_give isl_ast_build *
7052 isl_ast_build_set_iterators(
7053 __isl_take isl_ast_build *control,
7054 __isl_take isl_id_list *iterators);
7056 The function C<isl_ast_build_set_iterators> allows the user to
7057 specify a list of iterator C<isl_id>s to be used as iterators.
7058 If the input schedule is injective, then
7059 the number of elements in this list should be as large as the dimension
7060 of the schedule space, but no direct correspondence should be assumed
7061 between dimensions and elements.
7062 If the input schedule is not injective, then an additional number
7063 of C<isl_id>s equal to the largest dimension of the input domains
7065 If the number of provided C<isl_id>s is insufficient, then additional
7066 names are automatically generated.
7068 #include <isl/ast_build.h>
7069 __isl_give isl_ast_build *
7070 isl_ast_build_set_create_leaf(
7071 __isl_take isl_ast_build *control,
7072 __isl_give isl_ast_node *(*fn)(
7073 __isl_take isl_ast_build *build,
7074 void *user), void *user);
7077 C<isl_ast_build_set_create_leaf> function allows for the
7078 specification of a callback that should be called whenever the AST
7079 generator arrives at an element of the schedule domain.
7080 The callback should return an AST node that should be inserted
7081 at the corresponding position of the AST. The default action (when
7082 the callback is not set) is to continue generating parts of the AST to scan
7083 all the domain elements associated to the schedule domain element
7084 and to insert user nodes, ``calling'' the domain element, for each of them.
7085 The C<build> argument contains the current state of the C<isl_ast_build>.
7086 To ease nested AST generation (see L</"Nested AST Generation">),
7087 all control information that is
7088 specific to the current AST generation such as the options and
7089 the callbacks has been removed from this C<isl_ast_build>.
7090 The callback would typically return the result of a nested
7092 user defined node created using the following function.
7094 #include <isl/ast.h>
7095 __isl_give isl_ast_node *isl_ast_node_alloc_user(
7096 __isl_take isl_ast_expr *expr);
7098 #include <isl/ast_build.h>
7099 __isl_give isl_ast_build *
7100 isl_ast_build_set_at_each_domain(
7101 __isl_take isl_ast_build *build,
7102 __isl_give isl_ast_node *(*fn)(
7103 __isl_take isl_ast_node *node,
7104 __isl_keep isl_ast_build *build,
7105 void *user), void *user);
7106 __isl_give isl_ast_build *
7107 isl_ast_build_set_before_each_for(
7108 __isl_take isl_ast_build *build,
7109 __isl_give isl_id *(*fn)(
7110 __isl_keep isl_ast_build *build,
7111 void *user), void *user);
7112 __isl_give isl_ast_build *
7113 isl_ast_build_set_after_each_for(
7114 __isl_take isl_ast_build *build,
7115 __isl_give isl_ast_node *(*fn)(
7116 __isl_take isl_ast_node *node,
7117 __isl_keep isl_ast_build *build,
7118 void *user), void *user);
7120 The callback set by C<isl_ast_build_set_at_each_domain> will
7121 be called for each domain AST node.
7122 The callbacks set by C<isl_ast_build_set_before_each_for>
7123 and C<isl_ast_build_set_after_each_for> will be called
7124 for each for AST node. The first will be called in depth-first
7125 pre-order, while the second will be called in depth-first post-order.
7126 Since C<isl_ast_build_set_before_each_for> is called before the for
7127 node is actually constructed, it is only passed an C<isl_ast_build>.
7128 The returned C<isl_id> will be added as an annotation (using
7129 C<isl_ast_node_set_annotation>) to the constructed for node.
7130 In particular, if the user has also specified an C<after_each_for>
7131 callback, then the annotation can be retrieved from the node passed to
7132 that callback using C<isl_ast_node_get_annotation>.
7133 All callbacks should C<NULL> on failure.
7134 The given C<isl_ast_build> can be used to create new
7135 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
7136 or C<isl_ast_build_call_from_pw_multi_aff>.
7138 =head3 Nested AST Generation
7140 C<isl> allows the user to create an AST within the context
7141 of another AST. These nested ASTs are created using the
7142 same C<isl_ast_build_ast_from_schedule> function that is used to create the
7143 outer AST. The C<build> argument should be an C<isl_ast_build>
7144 passed to a callback set by
7145 C<isl_ast_build_set_create_leaf>.
7146 The space of the range of the C<schedule> argument should refer
7147 to this build. In particular, the space should be a wrapped
7148 relation and the domain of this wrapped relation should be the
7149 same as that of the range of the schedule returned by
7150 C<isl_ast_build_get_schedule> below.
7151 In practice, the new schedule is typically
7152 created by calling C<isl_union_map_range_product> on the old schedule
7153 and some extra piece of the schedule.
7154 The space of the schedule domain is also available from
7155 the C<isl_ast_build>.
7157 #include <isl/ast_build.h>
7158 __isl_give isl_union_map *isl_ast_build_get_schedule(
7159 __isl_keep isl_ast_build *build);
7160 __isl_give isl_space *isl_ast_build_get_schedule_space(
7161 __isl_keep isl_ast_build *build);
7162 __isl_give isl_ast_build *isl_ast_build_restrict(
7163 __isl_take isl_ast_build *build,
7164 __isl_take isl_set *set);
7166 The C<isl_ast_build_get_schedule> function returns a (partial)
7167 schedule for the domains elements for which part of the AST still needs to
7168 be generated in the current build.
7169 In particular, the domain elements are mapped to those iterations of the loops
7170 enclosing the current point of the AST generation inside which
7171 the domain elements are executed.
7172 No direct correspondence between
7173 the input schedule and this schedule should be assumed.
7174 The space obtained from C<isl_ast_build_get_schedule_space> can be used
7175 to create a set for C<isl_ast_build_restrict> to intersect
7176 with the current build. In particular, the set passed to
7177 C<isl_ast_build_restrict> can have additional parameters.
7178 The ids of the set dimensions in the space returned by
7179 C<isl_ast_build_get_schedule_space> correspond to the
7180 iterators of the already generated loops.
7181 The user should not rely on the ids of the output dimensions
7182 of the relations in the union relation returned by
7183 C<isl_ast_build_get_schedule> having any particular value.
7187 Although C<isl> is mainly meant to be used as a library,
7188 it also contains some basic applications that use some
7189 of the functionality of C<isl>.
7190 The input may be specified in either the L<isl format>
7191 or the L<PolyLib format>.
7193 =head2 C<isl_polyhedron_sample>
7195 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7196 an integer element of the polyhedron, if there is any.
7197 The first column in the output is the denominator and is always
7198 equal to 1. If the polyhedron contains no integer points,
7199 then a vector of length zero is printed.
7203 C<isl_pip> takes the same input as the C<example> program
7204 from the C<piplib> distribution, i.e., a set of constraints
7205 on the parameters, a line containing only -1 and finally a set
7206 of constraints on a parametric polyhedron.
7207 The coefficients of the parameters appear in the last columns
7208 (but before the final constant column).
7209 The output is the lexicographic minimum of the parametric polyhedron.
7210 As C<isl> currently does not have its own output format, the output
7211 is just a dump of the internal state.
7213 =head2 C<isl_polyhedron_minimize>
7215 C<isl_polyhedron_minimize> computes the minimum of some linear
7216 or affine objective function over the integer points in a polyhedron.
7217 If an affine objective function
7218 is given, then the constant should appear in the last column.
7220 =head2 C<isl_polytope_scan>
7222 Given a polytope, C<isl_polytope_scan> prints
7223 all integer points in the polytope.
7225 =head2 C<isl_codegen>
7227 Given a schedule, a context set and an options relation,
7228 C<isl_codegen> prints out an AST that scans the domain elements
7229 of the schedule in the order of their image(s) taking into account
7230 the constraints in the context set.