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>.
208 C<isl> is released under the MIT license.
212 Permission is hereby granted, free of charge, to any person obtaining a copy of
213 this software and associated documentation files (the "Software"), to deal in
214 the Software without restriction, including without limitation the rights to
215 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
216 of the Software, and to permit persons to whom the Software is furnished to do
217 so, subject to the following conditions:
219 The above copyright notice and this permission notice shall be included in all
220 copies or substantial portions of the Software.
222 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
223 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
224 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
225 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
226 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
227 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
232 Note that C<isl> currently requires C<GMP>, which is released
233 under the GNU Lesser General Public License (LGPL). This means
234 that code linked against C<isl> is also linked against LGPL code.
238 The source of C<isl> can be obtained either as a tarball
239 or from the git repository. Both are available from
240 L<http://freshmeat.net/projects/isl/>.
241 The installation process depends on how you obtained
244 =head2 Installation from the git repository
248 =item 1 Clone or update the repository
250 The first time the source is obtained, you need to clone
253 git clone git://repo.or.cz/isl.git
255 To obtain updates, you need to pull in the latest changes
259 =item 2 Generate C<configure>
265 After performing the above steps, continue
266 with the L<Common installation instructions>.
268 =head2 Common installation instructions
272 =item 1 Obtain C<GMP>
274 Building C<isl> requires C<GMP>, including its headers files.
275 Your distribution may not provide these header files by default
276 and you may need to install a package called C<gmp-devel> or something
277 similar. Alternatively, C<GMP> can be built from
278 source, available from L<http://gmplib.org/>.
282 C<isl> uses the standard C<autoconf> C<configure> script.
287 optionally followed by some configure options.
288 A complete list of options can be obtained by running
292 Below we discuss some of the more common options.
298 Installation prefix for C<isl>
300 =item C<--with-gmp-prefix>
302 Installation prefix for C<GMP> (architecture-independent files).
304 =item C<--with-gmp-exec-prefix>
306 Installation prefix for C<GMP> (architecture-dependent files).
314 =item 4 Install (optional)
320 =head1 Integer Set Library
322 =head2 Initialization
324 All manipulations of integer sets and relations occur within
325 the context of an C<isl_ctx>.
326 A given C<isl_ctx> can only be used within a single thread.
327 All arguments of a function are required to have been allocated
328 within the same context.
329 There are currently no functions available for moving an object
330 from one C<isl_ctx> to another C<isl_ctx>. This means that
331 there is currently no way of safely moving an object from one
332 thread to another, unless the whole C<isl_ctx> is moved.
334 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
335 freed using C<isl_ctx_free>.
336 All objects allocated within an C<isl_ctx> should be freed
337 before the C<isl_ctx> itself is freed.
339 isl_ctx *isl_ctx_alloc();
340 void isl_ctx_free(isl_ctx *ctx);
342 The user can impose a bound on the number of low-level I<operations>
343 that can be performed by an C<isl_ctx>. This bound can be set and
344 retrieved using the following functions. A bound of zero means that
345 no bound is imposed. The number of operations performed can be
346 reset using C<isl_ctx_reset_operations>. Note that the number
347 of low-level operations needed to perform a high-level computation
348 may differ significantly across different versions
349 of C<isl>, but it should be the same across different platforms
350 for the same version of C<isl>.
352 void isl_ctx_set_max_operations(isl_ctx *ctx,
353 unsigned long max_operations);
354 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
355 void isl_ctx_reset_operations(isl_ctx *ctx);
357 =head2 Memory Management
359 Since a high-level operation on isl objects usually involves
360 several substeps and since the user is usually not interested in
361 the intermediate results, most functions that return a new object
362 will also release all the objects passed as arguments.
363 If the user still wants to use one or more of these arguments
364 after the function call, she should pass along a copy of the
365 object rather than the object itself.
366 The user is then responsible for making sure that the original
367 object gets used somewhere else or is explicitly freed.
369 The arguments and return values of all documented functions are
370 annotated to make clear which arguments are released and which
371 arguments are preserved. In particular, the following annotations
378 C<__isl_give> means that a new object is returned.
379 The user should make sure that the returned pointer is
380 used exactly once as a value for an C<__isl_take> argument.
381 In between, it can be used as a value for as many
382 C<__isl_keep> arguments as the user likes.
383 There is one exception, and that is the case where the
384 pointer returned is C<NULL>. Is this case, the user
385 is free to use it as an C<__isl_take> argument or not.
389 C<__isl_null> means that a C<NULL> value is returned.
393 C<__isl_take> means that the object the argument points to
394 is taken over by the function and may no longer be used
395 by the user as an argument to any other function.
396 The pointer value must be one returned by a function
397 returning an C<__isl_give> pointer.
398 If the user passes in a C<NULL> value, then this will
399 be treated as an error in the sense that the function will
400 not perform its usual operation. However, it will still
401 make sure that all the other C<__isl_take> arguments
406 C<__isl_keep> means that the function will only use the object
407 temporarily. After the function has finished, the user
408 can still use it as an argument to other functions.
409 A C<NULL> value will be treated in the same way as
410 a C<NULL> value for an C<__isl_take> argument.
416 An C<isl_val> represents an integer value, a rational value
417 or one of three special values, infinity, negative infinity and NaN.
418 Some predefined values can be created using the following functions.
421 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
422 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
423 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
424 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
425 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
426 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
428 Specific integer values can be created using the following functions.
431 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
433 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
435 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
436 size_t n, size_t size, const void *chunks);
438 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
439 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
440 The least significant digit is assumed to be stored first.
442 Value objects can be copied and freed using the following functions.
445 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
446 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
448 They can be inspected using the following functions.
451 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
452 long isl_val_get_num_si(__isl_keep isl_val *v);
453 long isl_val_get_den_si(__isl_keep isl_val *v);
454 double isl_val_get_d(__isl_keep isl_val *v);
455 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
457 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
458 size_t size, void *chunks);
460 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
461 of C<size> bytes needed to store the absolute value of the
463 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
464 which is assumed to have been preallocated by the caller.
465 The least significant digit is stored first.
466 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
467 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
468 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
470 An C<isl_val> can be modified using the following function.
473 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
476 The following unary properties are defined on C<isl_val>s.
479 int isl_val_sgn(__isl_keep isl_val *v);
480 int isl_val_is_zero(__isl_keep isl_val *v);
481 int isl_val_is_one(__isl_keep isl_val *v);
482 int isl_val_is_negone(__isl_keep isl_val *v);
483 int isl_val_is_nonneg(__isl_keep isl_val *v);
484 int isl_val_is_nonpos(__isl_keep isl_val *v);
485 int isl_val_is_pos(__isl_keep isl_val *v);
486 int isl_val_is_neg(__isl_keep isl_val *v);
487 int isl_val_is_int(__isl_keep isl_val *v);
488 int isl_val_is_rat(__isl_keep isl_val *v);
489 int isl_val_is_nan(__isl_keep isl_val *v);
490 int isl_val_is_infty(__isl_keep isl_val *v);
491 int isl_val_is_neginfty(__isl_keep isl_val *v);
493 Note that the sign of NaN is undefined.
495 The following binary properties are defined on pairs of C<isl_val>s.
498 int isl_val_lt(__isl_keep isl_val *v1,
499 __isl_keep isl_val *v2);
500 int isl_val_le(__isl_keep isl_val *v1,
501 __isl_keep isl_val *v2);
502 int isl_val_gt(__isl_keep isl_val *v1,
503 __isl_keep isl_val *v2);
504 int isl_val_ge(__isl_keep isl_val *v1,
505 __isl_keep isl_val *v2);
506 int isl_val_eq(__isl_keep isl_val *v1,
507 __isl_keep isl_val *v2);
508 int isl_val_ne(__isl_keep isl_val *v1,
509 __isl_keep isl_val *v2);
511 For integer C<isl_val>s we additionally have the following binary property.
514 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
515 __isl_keep isl_val *v2);
517 An C<isl_val> can also be compared to an integer using the following
518 function. The result is undefined for NaN.
521 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
523 The following unary operations are available on C<isl_val>s.
526 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
527 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
528 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
529 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
530 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
532 The following binary operations are available on C<isl_val>s.
535 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
536 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
537 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
538 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
539 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
540 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
541 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
542 __isl_take isl_val *v2);
543 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
544 __isl_take isl_val *v2);
545 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
546 __isl_take isl_val *v2);
547 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
549 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
550 __isl_take isl_val *v2);
551 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
553 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
554 __isl_take isl_val *v2);
555 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
557 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
558 __isl_take isl_val *v2);
560 On integer values, we additionally have the following operations.
563 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
564 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
565 __isl_take isl_val *v2);
566 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
567 __isl_take isl_val *v2);
568 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
569 __isl_take isl_val *v2, __isl_give isl_val **x,
570 __isl_give isl_val **y);
572 The function C<isl_val_gcdext> returns the greatest common divisor g
573 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
574 that C<*x> * C<v1> + C<*y> * C<v2> = g.
576 A value can be read from input using
579 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
582 A value can be printed using
585 __isl_give isl_printer *isl_printer_print_val(
586 __isl_take isl_printer *p, __isl_keep isl_val *v);
588 =head3 GMP specific functions
590 These functions are only available if C<isl> has been compiled with C<GMP>
593 Specific integer and rational values can be created from C<GMP> values using
594 the following functions.
596 #include <isl/val_gmp.h>
597 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
599 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
600 const mpz_t n, const mpz_t d);
602 The numerator and denominator of a rational value can be extracted as
603 C<GMP> values using the following functions.
605 #include <isl/val_gmp.h>
606 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
607 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
609 =head2 Sets and Relations
611 C<isl> uses six types of objects for representing sets and relations,
612 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
613 C<isl_union_set> and C<isl_union_map>.
614 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
615 can be described as a conjunction of affine constraints, while
616 C<isl_set> and C<isl_map> represent unions of
617 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
618 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
619 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
620 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
621 where spaces are considered different if they have a different number
622 of dimensions and/or different names (see L<"Spaces">).
623 The difference between sets and relations (maps) is that sets have
624 one set of variables, while relations have two sets of variables,
625 input variables and output variables.
627 =head2 Error Handling
629 C<isl> supports different ways to react in case a runtime error is triggered.
630 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
631 with two maps that have incompatible spaces. There are three possible ways
632 to react on error: to warn, to continue or to abort.
634 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
635 the last error in the corresponding C<isl_ctx> and the function in which the
636 error was triggered returns C<NULL>. An error does not corrupt internal state,
637 such that isl can continue to be used. C<isl> also provides functions to
638 read the last error and to reset the memory that stores the last error. The
639 last error is only stored for information purposes. Its presence does not
640 change the behavior of C<isl>. Hence, resetting an error is not required to
641 continue to use isl, but only to observe new errors.
644 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
645 void isl_ctx_reset_error(isl_ctx *ctx);
647 Another option is to continue on error. This is similar to warn on error mode,
648 except that C<isl> does not print any warning. This allows a program to
649 implement its own error reporting.
651 The last option is to directly abort the execution of the program from within
652 the isl library. This makes it obviously impossible to recover from an error,
653 but it allows to directly spot the error location. By aborting on error,
654 debuggers break at the location the error occurred and can provide a stack
655 trace. Other tools that automatically provide stack traces on abort or that do
656 not want to continue execution after an error was triggered may also prefer to
659 The on error behavior of isl can be specified by calling
660 C<isl_options_set_on_error> or by setting the command line option
661 C<--isl-on-error>. Valid arguments for the function call are
662 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
663 choices for the command line option are C<warn>, C<continue> and C<abort>.
664 It is also possible to query the current error mode.
666 #include <isl/options.h>
667 int isl_options_set_on_error(isl_ctx *ctx, int val);
668 int isl_options_get_on_error(isl_ctx *ctx);
672 Identifiers are used to identify both individual dimensions
673 and tuples of dimensions. They consist of an optional name and an optional
674 user pointer. The name and the user pointer cannot both be C<NULL>, however.
675 Identifiers with the same name but different pointer values
676 are considered to be distinct.
677 Similarly, identifiers with different names but the same pointer value
678 are also considered to be distinct.
679 Equal identifiers are represented using the same object.
680 Pairs of identifiers can therefore be tested for equality using the
682 Identifiers can be constructed, copied, freed, inspected and printed
683 using the following functions.
686 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
687 __isl_keep const char *name, void *user);
688 __isl_give isl_id *isl_id_set_free_user(
689 __isl_take isl_id *id,
690 __isl_give void (*free_user)(void *user));
691 __isl_give isl_id *isl_id_copy(isl_id *id);
692 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
694 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
695 void *isl_id_get_user(__isl_keep isl_id *id);
696 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
698 __isl_give isl_printer *isl_printer_print_id(
699 __isl_take isl_printer *p, __isl_keep isl_id *id);
701 The callback set by C<isl_id_set_free_user> is called on the user
702 pointer when the last reference to the C<isl_id> is freed.
703 Note that C<isl_id_get_name> returns a pointer to some internal
704 data structure, so the result can only be used while the
705 corresponding C<isl_id> is alive.
709 Whenever a new set, relation or similiar object is created from scratch,
710 the space in which it lives needs to be specified using an C<isl_space>.
711 Each space involves zero or more parameters and zero, one or two
712 tuples of set or input/output dimensions. The parameters and dimensions
713 are identified by an C<isl_dim_type> and a position.
714 The type C<isl_dim_param> refers to parameters,
715 the type C<isl_dim_set> refers to set dimensions (for spaces
716 with a single tuple of dimensions) and the types C<isl_dim_in>
717 and C<isl_dim_out> refer to input and output dimensions
718 (for spaces with two tuples of dimensions).
719 Local spaces (see L</"Local Spaces">) also contain dimensions
720 of type C<isl_dim_div>.
721 Note that parameters are only identified by their position within
722 a given object. Across different objects, parameters are (usually)
723 identified by their names or identifiers. Only unnamed parameters
724 are identified by their positions across objects. The use of unnamed
725 parameters is discouraged.
727 #include <isl/space.h>
728 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
729 unsigned nparam, unsigned n_in, unsigned n_out);
730 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
732 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
733 unsigned nparam, unsigned dim);
734 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
735 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
736 unsigned isl_space_dim(__isl_keep isl_space *space,
737 enum isl_dim_type type);
739 The space used for creating a parameter domain
740 needs to be created using C<isl_space_params_alloc>.
741 For other sets, the space
742 needs to be created using C<isl_space_set_alloc>, while
743 for a relation, the space
744 needs to be created using C<isl_space_alloc>.
745 C<isl_space_dim> can be used
746 to find out the number of dimensions of each type in
747 a space, where type may be
748 C<isl_dim_param>, C<isl_dim_in> (only for relations),
749 C<isl_dim_out> (only for relations), C<isl_dim_set>
750 (only for sets) or C<isl_dim_all>.
752 To check whether a given space is that of a set or a map
753 or whether it is a parameter space, use these functions:
755 #include <isl/space.h>
756 int isl_space_is_params(__isl_keep isl_space *space);
757 int isl_space_is_set(__isl_keep isl_space *space);
758 int isl_space_is_map(__isl_keep isl_space *space);
760 Spaces can be compared using the following functions:
762 #include <isl/space.h>
763 int isl_space_is_equal(__isl_keep isl_space *space1,
764 __isl_keep isl_space *space2);
765 int isl_space_is_domain(__isl_keep isl_space *space1,
766 __isl_keep isl_space *space2);
767 int isl_space_is_range(__isl_keep isl_space *space1,
768 __isl_keep isl_space *space2);
770 C<isl_space_is_domain> checks whether the first argument is equal
771 to the domain of the second argument. This requires in particular that
772 the first argument is a set space and that the second argument
775 It is often useful to create objects that live in the
776 same space as some other object. This can be accomplished
777 by creating the new objects
778 (see L</"Creating New Sets and Relations"> or
779 L</"Creating New (Piecewise) Quasipolynomials">) based on the space
780 of the original object.
783 __isl_give isl_space *isl_basic_set_get_space(
784 __isl_keep isl_basic_set *bset);
785 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
787 #include <isl/union_set.h>
788 __isl_give isl_space *isl_union_set_get_space(
789 __isl_keep isl_union_set *uset);
792 __isl_give isl_space *isl_basic_map_get_space(
793 __isl_keep isl_basic_map *bmap);
794 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
796 #include <isl/union_map.h>
797 __isl_give isl_space *isl_union_map_get_space(
798 __isl_keep isl_union_map *umap);
800 #include <isl/constraint.h>
801 __isl_give isl_space *isl_constraint_get_space(
802 __isl_keep isl_constraint *constraint);
804 #include <isl/polynomial.h>
805 __isl_give isl_space *isl_qpolynomial_get_domain_space(
806 __isl_keep isl_qpolynomial *qp);
807 __isl_give isl_space *isl_qpolynomial_get_space(
808 __isl_keep isl_qpolynomial *qp);
809 __isl_give isl_space *isl_qpolynomial_fold_get_space(
810 __isl_keep isl_qpolynomial_fold *fold);
811 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
812 __isl_keep isl_pw_qpolynomial *pwqp);
813 __isl_give isl_space *isl_pw_qpolynomial_get_space(
814 __isl_keep isl_pw_qpolynomial *pwqp);
815 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
816 __isl_keep isl_pw_qpolynomial_fold *pwf);
817 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
818 __isl_keep isl_pw_qpolynomial_fold *pwf);
819 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
820 __isl_keep isl_union_pw_qpolynomial *upwqp);
821 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
822 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
825 __isl_give isl_space *isl_multi_val_get_space(
826 __isl_keep isl_multi_val *mv);
829 __isl_give isl_space *isl_aff_get_domain_space(
830 __isl_keep isl_aff *aff);
831 __isl_give isl_space *isl_aff_get_space(
832 __isl_keep isl_aff *aff);
833 __isl_give isl_space *isl_pw_aff_get_domain_space(
834 __isl_keep isl_pw_aff *pwaff);
835 __isl_give isl_space *isl_pw_aff_get_space(
836 __isl_keep isl_pw_aff *pwaff);
837 __isl_give isl_space *isl_multi_aff_get_domain_space(
838 __isl_keep isl_multi_aff *maff);
839 __isl_give isl_space *isl_multi_aff_get_space(
840 __isl_keep isl_multi_aff *maff);
841 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
842 __isl_keep isl_pw_multi_aff *pma);
843 __isl_give isl_space *isl_pw_multi_aff_get_space(
844 __isl_keep isl_pw_multi_aff *pma);
845 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
846 __isl_keep isl_union_pw_multi_aff *upma);
847 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
848 __isl_keep isl_multi_pw_aff *mpa);
849 __isl_give isl_space *isl_multi_pw_aff_get_space(
850 __isl_keep isl_multi_pw_aff *mpa);
852 #include <isl/point.h>
853 __isl_give isl_space *isl_point_get_space(
854 __isl_keep isl_point *pnt);
856 The identifiers or names of the individual dimensions may be set or read off
857 using the following functions.
859 #include <isl/space.h>
860 __isl_give isl_space *isl_space_set_dim_id(
861 __isl_take isl_space *space,
862 enum isl_dim_type type, unsigned pos,
863 __isl_take isl_id *id);
864 int isl_space_has_dim_id(__isl_keep isl_space *space,
865 enum isl_dim_type type, unsigned pos);
866 __isl_give isl_id *isl_space_get_dim_id(
867 __isl_keep isl_space *space,
868 enum isl_dim_type type, unsigned pos);
869 __isl_give isl_space *isl_space_set_dim_name(
870 __isl_take isl_space *space,
871 enum isl_dim_type type, unsigned pos,
872 __isl_keep const char *name);
873 int isl_space_has_dim_name(__isl_keep isl_space *space,
874 enum isl_dim_type type, unsigned pos);
875 __isl_keep const char *isl_space_get_dim_name(
876 __isl_keep isl_space *space,
877 enum isl_dim_type type, unsigned pos);
879 Note that C<isl_space_get_name> returns a pointer to some internal
880 data structure, so the result can only be used while the
881 corresponding C<isl_space> is alive.
882 Also note that every function that operates on two sets or relations
883 requires that both arguments have the same parameters. This also
884 means that if one of the arguments has named parameters, then the
885 other needs to have named parameters too and the names need to match.
886 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
887 arguments may have different parameters (as long as they are named),
888 in which case the result will have as parameters the union of the parameters of
891 Given the identifier or name of a dimension (typically a parameter),
892 its position can be obtained from the following function.
894 #include <isl/space.h>
895 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
896 enum isl_dim_type type, __isl_keep isl_id *id);
897 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
898 enum isl_dim_type type, const char *name);
900 The identifiers or names of entire spaces may be set or read off
901 using the following functions.
903 #include <isl/space.h>
904 __isl_give isl_space *isl_space_set_tuple_id(
905 __isl_take isl_space *space,
906 enum isl_dim_type type, __isl_take isl_id *id);
907 __isl_give isl_space *isl_space_reset_tuple_id(
908 __isl_take isl_space *space, enum isl_dim_type type);
909 int isl_space_has_tuple_id(__isl_keep isl_space *space,
910 enum isl_dim_type type);
911 __isl_give isl_id *isl_space_get_tuple_id(
912 __isl_keep isl_space *space, enum isl_dim_type type);
913 __isl_give isl_space *isl_space_set_tuple_name(
914 __isl_take isl_space *space,
915 enum isl_dim_type type, const char *s);
916 int isl_space_has_tuple_name(__isl_keep isl_space *space,
917 enum isl_dim_type type);
918 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
919 enum isl_dim_type type);
921 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
922 or C<isl_dim_set>. As with C<isl_space_get_name>,
923 the C<isl_space_get_tuple_name> function returns a pointer to some internal
925 Binary operations require the corresponding spaces of their arguments
926 to have the same name.
928 To keep the names of all parameters and tuples, but reset the user pointers
929 of all the corresponding identifiers, use the following function.
931 __isl_give isl_space *isl_space_reset_user(
932 __isl_take isl_space *space);
934 Spaces can be nested. In particular, the domain of a set or
935 the domain or range of a relation can be a nested relation.
936 This process is also called I<wrapping>.
937 The functions for detecting, constructing and deconstructing
938 such nested spaces can be found in the wrapping properties
939 of L</"Unary Properties">, the wrapping operations
940 of L</"Unary Operations"> and the Cartesian product operations
941 of L</"Basic Operations">.
943 Spaces can be created from other spaces
944 using the following functions.
946 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
947 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
948 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
949 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
950 __isl_give isl_space *isl_space_domain_map(
951 __isl_take isl_space *space);
952 __isl_give isl_space *isl_space_range_map(
953 __isl_take isl_space *space);
954 __isl_give isl_space *isl_space_params(
955 __isl_take isl_space *space);
956 __isl_give isl_space *isl_space_set_from_params(
957 __isl_take isl_space *space);
958 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
959 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
960 __isl_take isl_space *right);
961 __isl_give isl_space *isl_space_align_params(
962 __isl_take isl_space *space1, __isl_take isl_space *space2)
963 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
964 enum isl_dim_type type, unsigned pos, unsigned n);
965 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
966 enum isl_dim_type type, unsigned n);
967 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
968 enum isl_dim_type type, unsigned first, unsigned n);
969 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
970 enum isl_dim_type dst_type, unsigned dst_pos,
971 enum isl_dim_type src_type, unsigned src_pos,
973 __isl_give isl_space *isl_space_map_from_set(
974 __isl_take isl_space *space);
975 __isl_give isl_space *isl_space_map_from_domain_and_range(
976 __isl_take isl_space *domain,
977 __isl_take isl_space *range);
978 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
979 __isl_give isl_space *isl_space_curry(
980 __isl_take isl_space *space);
981 __isl_give isl_space *isl_space_uncurry(
982 __isl_take isl_space *space);
984 Note that if dimensions are added or removed from a space, then
985 the name and the internal structure are lost.
989 A local space is essentially a space with
990 zero or more existentially quantified variables.
991 The local space of a (constraint of a) basic set or relation can be obtained
992 using the following functions.
994 #include <isl/constraint.h>
995 __isl_give isl_local_space *isl_constraint_get_local_space(
996 __isl_keep isl_constraint *constraint);
999 __isl_give isl_local_space *isl_basic_set_get_local_space(
1000 __isl_keep isl_basic_set *bset);
1002 #include <isl/map.h>
1003 __isl_give isl_local_space *isl_basic_map_get_local_space(
1004 __isl_keep isl_basic_map *bmap);
1006 A new local space can be created from a space using
1008 #include <isl/local_space.h>
1009 __isl_give isl_local_space *isl_local_space_from_space(
1010 __isl_take isl_space *space);
1012 They can be inspected, modified, copied and freed using the following functions.
1014 #include <isl/local_space.h>
1015 isl_ctx *isl_local_space_get_ctx(
1016 __isl_keep isl_local_space *ls);
1017 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1018 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1019 enum isl_dim_type type);
1020 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1021 __isl_take isl_local_space *ls,
1022 enum isl_dim_type type, __isl_take isl_id *id);
1023 int isl_local_space_has_dim_id(
1024 __isl_keep isl_local_space *ls,
1025 enum isl_dim_type type, unsigned pos);
1026 __isl_give isl_id *isl_local_space_get_dim_id(
1027 __isl_keep isl_local_space *ls,
1028 enum isl_dim_type type, unsigned pos);
1029 int isl_local_space_has_dim_name(
1030 __isl_keep isl_local_space *ls,
1031 enum isl_dim_type type, unsigned pos)
1032 const char *isl_local_space_get_dim_name(
1033 __isl_keep isl_local_space *ls,
1034 enum isl_dim_type type, unsigned pos);
1035 __isl_give isl_local_space *isl_local_space_set_dim_name(
1036 __isl_take isl_local_space *ls,
1037 enum isl_dim_type type, unsigned pos, const char *s);
1038 __isl_give isl_local_space *isl_local_space_set_dim_id(
1039 __isl_take isl_local_space *ls,
1040 enum isl_dim_type type, unsigned pos,
1041 __isl_take isl_id *id);
1042 __isl_give isl_space *isl_local_space_get_space(
1043 __isl_keep isl_local_space *ls);
1044 __isl_give isl_aff *isl_local_space_get_div(
1045 __isl_keep isl_local_space *ls, int pos);
1046 __isl_give isl_local_space *isl_local_space_copy(
1047 __isl_keep isl_local_space *ls);
1048 __isl_null isl_local_space *isl_local_space_free(
1049 __isl_take isl_local_space *ls);
1051 Note that C<isl_local_space_get_div> can only be used on local spaces
1054 Two local spaces can be compared using
1056 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1057 __isl_keep isl_local_space *ls2);
1059 Local spaces can be created from other local spaces
1060 using the functions described in L</"Unary Operations">
1061 and L</"Binary Operations">.
1063 =head2 Input and Output
1065 C<isl> supports its own input/output format, which is similar
1066 to the C<Omega> format, but also supports the C<PolyLib> format
1069 =head3 C<isl> format
1071 The C<isl> format is similar to that of C<Omega>, but has a different
1072 syntax for describing the parameters and allows for the definition
1073 of an existentially quantified variable as the integer division
1074 of an affine expression.
1075 For example, the set of integers C<i> between C<0> and C<n>
1076 such that C<i % 10 <= 6> can be described as
1078 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1081 A set or relation can have several disjuncts, separated
1082 by the keyword C<or>. Each disjunct is either a conjunction
1083 of constraints or a projection (C<exists>) of a conjunction
1084 of constraints. The constraints are separated by the keyword
1087 =head3 C<PolyLib> format
1089 If the represented set is a union, then the first line
1090 contains a single number representing the number of disjuncts.
1091 Otherwise, a line containing the number C<1> is optional.
1093 Each disjunct is represented by a matrix of constraints.
1094 The first line contains two numbers representing
1095 the number of rows and columns,
1096 where the number of rows is equal to the number of constraints
1097 and the number of columns is equal to two plus the number of variables.
1098 The following lines contain the actual rows of the constraint matrix.
1099 In each row, the first column indicates whether the constraint
1100 is an equality (C<0>) or inequality (C<1>). The final column
1101 corresponds to the constant term.
1103 If the set is parametric, then the coefficients of the parameters
1104 appear in the last columns before the constant column.
1105 The coefficients of any existentially quantified variables appear
1106 between those of the set variables and those of the parameters.
1108 =head3 Extended C<PolyLib> format
1110 The extended C<PolyLib> format is nearly identical to the
1111 C<PolyLib> format. The only difference is that the line
1112 containing the number of rows and columns of a constraint matrix
1113 also contains four additional numbers:
1114 the number of output dimensions, the number of input dimensions,
1115 the number of local dimensions (i.e., the number of existentially
1116 quantified variables) and the number of parameters.
1117 For sets, the number of ``output'' dimensions is equal
1118 to the number of set dimensions, while the number of ``input''
1123 #include <isl/set.h>
1124 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1125 isl_ctx *ctx, FILE *input);
1126 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1127 isl_ctx *ctx, const char *str);
1128 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1130 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1133 #include <isl/map.h>
1134 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1135 isl_ctx *ctx, FILE *input);
1136 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1137 isl_ctx *ctx, const char *str);
1138 __isl_give isl_map *isl_map_read_from_file(
1139 isl_ctx *ctx, FILE *input);
1140 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1143 #include <isl/union_set.h>
1144 __isl_give isl_union_set *isl_union_set_read_from_file(
1145 isl_ctx *ctx, FILE *input);
1146 __isl_give isl_union_set *isl_union_set_read_from_str(
1147 isl_ctx *ctx, const char *str);
1149 #include <isl/union_map.h>
1150 __isl_give isl_union_map *isl_union_map_read_from_file(
1151 isl_ctx *ctx, FILE *input);
1152 __isl_give isl_union_map *isl_union_map_read_from_str(
1153 isl_ctx *ctx, const char *str);
1155 The input format is autodetected and may be either the C<PolyLib> format
1156 or the C<isl> format.
1160 Before anything can be printed, an C<isl_printer> needs to
1163 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1165 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1166 __isl_null isl_printer *isl_printer_free(
1167 __isl_take isl_printer *printer);
1168 __isl_give char *isl_printer_get_str(
1169 __isl_keep isl_printer *printer);
1171 The printer can be inspected using the following functions.
1173 FILE *isl_printer_get_file(
1174 __isl_keep isl_printer *printer);
1175 int isl_printer_get_output_format(
1176 __isl_keep isl_printer *p);
1178 The behavior of the printer can be modified in various ways
1180 __isl_give isl_printer *isl_printer_set_output_format(
1181 __isl_take isl_printer *p, int output_format);
1182 __isl_give isl_printer *isl_printer_set_indent(
1183 __isl_take isl_printer *p, int indent);
1184 __isl_give isl_printer *isl_printer_indent(
1185 __isl_take isl_printer *p, int indent);
1186 __isl_give isl_printer *isl_printer_set_prefix(
1187 __isl_take isl_printer *p, const char *prefix);
1188 __isl_give isl_printer *isl_printer_set_suffix(
1189 __isl_take isl_printer *p, const char *suffix);
1191 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1192 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1193 and defaults to C<ISL_FORMAT_ISL>.
1194 Each line in the output is indented by C<indent> (set by
1195 C<isl_printer_set_indent>) spaces
1196 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1197 In the C<PolyLib> format output,
1198 the coefficients of the existentially quantified variables
1199 appear between those of the set variables and those
1201 The function C<isl_printer_indent> increases the indentation
1202 by the specified amount (which may be negative).
1204 To actually print something, use
1206 #include <isl/printer.h>
1207 __isl_give isl_printer *isl_printer_print_double(
1208 __isl_take isl_printer *p, double d);
1210 #include <isl/set.h>
1211 __isl_give isl_printer *isl_printer_print_basic_set(
1212 __isl_take isl_printer *printer,
1213 __isl_keep isl_basic_set *bset);
1214 __isl_give isl_printer *isl_printer_print_set(
1215 __isl_take isl_printer *printer,
1216 __isl_keep isl_set *set);
1218 #include <isl/map.h>
1219 __isl_give isl_printer *isl_printer_print_basic_map(
1220 __isl_take isl_printer *printer,
1221 __isl_keep isl_basic_map *bmap);
1222 __isl_give isl_printer *isl_printer_print_map(
1223 __isl_take isl_printer *printer,
1224 __isl_keep isl_map *map);
1226 #include <isl/union_set.h>
1227 __isl_give isl_printer *isl_printer_print_union_set(
1228 __isl_take isl_printer *p,
1229 __isl_keep isl_union_set *uset);
1231 #include <isl/union_map.h>
1232 __isl_give isl_printer *isl_printer_print_union_map(
1233 __isl_take isl_printer *p,
1234 __isl_keep isl_union_map *umap);
1236 When called on a file printer, the following function flushes
1237 the file. When called on a string printer, the buffer is cleared.
1239 __isl_give isl_printer *isl_printer_flush(
1240 __isl_take isl_printer *p);
1242 =head2 Creating New Sets and Relations
1244 C<isl> has functions for creating some standard sets and relations.
1248 =item * Empty sets and relations
1250 __isl_give isl_basic_set *isl_basic_set_empty(
1251 __isl_take isl_space *space);
1252 __isl_give isl_basic_map *isl_basic_map_empty(
1253 __isl_take isl_space *space);
1254 __isl_give isl_set *isl_set_empty(
1255 __isl_take isl_space *space);
1256 __isl_give isl_map *isl_map_empty(
1257 __isl_take isl_space *space);
1258 __isl_give isl_union_set *isl_union_set_empty(
1259 __isl_take isl_space *space);
1260 __isl_give isl_union_map *isl_union_map_empty(
1261 __isl_take isl_space *space);
1263 For C<isl_union_set>s and C<isl_union_map>s, the space
1264 is only used to specify the parameters.
1266 =item * Universe sets and relations
1268 __isl_give isl_basic_set *isl_basic_set_universe(
1269 __isl_take isl_space *space);
1270 __isl_give isl_basic_map *isl_basic_map_universe(
1271 __isl_take isl_space *space);
1272 __isl_give isl_set *isl_set_universe(
1273 __isl_take isl_space *space);
1274 __isl_give isl_map *isl_map_universe(
1275 __isl_take isl_space *space);
1276 __isl_give isl_union_set *isl_union_set_universe(
1277 __isl_take isl_union_set *uset);
1278 __isl_give isl_union_map *isl_union_map_universe(
1279 __isl_take isl_union_map *umap);
1281 The sets and relations constructed by the functions above
1282 contain all integer values, while those constructed by the
1283 functions below only contain non-negative values.
1285 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1286 __isl_take isl_space *space);
1287 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1288 __isl_take isl_space *space);
1289 __isl_give isl_set *isl_set_nat_universe(
1290 __isl_take isl_space *space);
1291 __isl_give isl_map *isl_map_nat_universe(
1292 __isl_take isl_space *space);
1294 =item * Identity relations
1296 __isl_give isl_basic_map *isl_basic_map_identity(
1297 __isl_take isl_space *space);
1298 __isl_give isl_map *isl_map_identity(
1299 __isl_take isl_space *space);
1301 The number of input and output dimensions in C<space> needs
1304 =item * Lexicographic order
1306 __isl_give isl_map *isl_map_lex_lt(
1307 __isl_take isl_space *set_space);
1308 __isl_give isl_map *isl_map_lex_le(
1309 __isl_take isl_space *set_space);
1310 __isl_give isl_map *isl_map_lex_gt(
1311 __isl_take isl_space *set_space);
1312 __isl_give isl_map *isl_map_lex_ge(
1313 __isl_take isl_space *set_space);
1314 __isl_give isl_map *isl_map_lex_lt_first(
1315 __isl_take isl_space *space, unsigned n);
1316 __isl_give isl_map *isl_map_lex_le_first(
1317 __isl_take isl_space *space, unsigned n);
1318 __isl_give isl_map *isl_map_lex_gt_first(
1319 __isl_take isl_space *space, unsigned n);
1320 __isl_give isl_map *isl_map_lex_ge_first(
1321 __isl_take isl_space *space, unsigned n);
1323 The first four functions take a space for a B<set>
1324 and return relations that express that the elements in the domain
1325 are lexicographically less
1326 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1327 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1328 than the elements in the range.
1329 The last four functions take a space for a map
1330 and return relations that express that the first C<n> dimensions
1331 in the domain are lexicographically less
1332 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1333 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1334 than the first C<n> dimensions in the range.
1338 A basic set or relation can be converted to a set or relation
1339 using the following functions.
1341 __isl_give isl_set *isl_set_from_basic_set(
1342 __isl_take isl_basic_set *bset);
1343 __isl_give isl_map *isl_map_from_basic_map(
1344 __isl_take isl_basic_map *bmap);
1346 Sets and relations can be converted to union sets and relations
1347 using the following functions.
1349 __isl_give isl_union_set *isl_union_set_from_basic_set(
1350 __isl_take isl_basic_set *bset);
1351 __isl_give isl_union_map *isl_union_map_from_basic_map(
1352 __isl_take isl_basic_map *bmap);
1353 __isl_give isl_union_set *isl_union_set_from_set(
1354 __isl_take isl_set *set);
1355 __isl_give isl_union_map *isl_union_map_from_map(
1356 __isl_take isl_map *map);
1358 The inverse conversions below can only be used if the input
1359 union set or relation is known to contain elements in exactly one
1362 __isl_give isl_set *isl_set_from_union_set(
1363 __isl_take isl_union_set *uset);
1364 __isl_give isl_map *isl_map_from_union_map(
1365 __isl_take isl_union_map *umap);
1367 A zero-dimensional (basic) set can be constructed on a given parameter domain
1368 using the following function.
1370 __isl_give isl_basic_set *isl_basic_set_from_params(
1371 __isl_take isl_basic_set *bset);
1372 __isl_give isl_set *isl_set_from_params(
1373 __isl_take isl_set *set);
1375 Sets and relations can be copied and freed again using the following
1378 __isl_give isl_basic_set *isl_basic_set_copy(
1379 __isl_keep isl_basic_set *bset);
1380 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1381 __isl_give isl_union_set *isl_union_set_copy(
1382 __isl_keep isl_union_set *uset);
1383 __isl_give isl_basic_map *isl_basic_map_copy(
1384 __isl_keep isl_basic_map *bmap);
1385 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1386 __isl_give isl_union_map *isl_union_map_copy(
1387 __isl_keep isl_union_map *umap);
1388 __isl_null isl_basic_set *isl_basic_set_free(
1389 __isl_take isl_basic_set *bset);
1390 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1391 __isl_null isl_union_set *isl_union_set_free(
1392 __isl_take isl_union_set *uset);
1393 __isl_null isl_basic_map *isl_basic_map_free(
1394 __isl_take isl_basic_map *bmap);
1395 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1396 __isl_null isl_union_map *isl_union_map_free(
1397 __isl_take isl_union_map *umap);
1399 Other sets and relations can be constructed by starting
1400 from a universe set or relation, adding equality and/or
1401 inequality constraints and then projecting out the
1402 existentially quantified variables, if any.
1403 Constraints can be constructed, manipulated and
1404 added to (or removed from) (basic) sets and relations
1405 using the following functions.
1407 #include <isl/constraint.h>
1408 __isl_give isl_constraint *isl_equality_alloc(
1409 __isl_take isl_local_space *ls);
1410 __isl_give isl_constraint *isl_inequality_alloc(
1411 __isl_take isl_local_space *ls);
1412 __isl_give isl_constraint *isl_constraint_set_constant_si(
1413 __isl_take isl_constraint *constraint, int v);
1414 __isl_give isl_constraint *isl_constraint_set_constant_val(
1415 __isl_take isl_constraint *constraint,
1416 __isl_take isl_val *v);
1417 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1418 __isl_take isl_constraint *constraint,
1419 enum isl_dim_type type, int pos, int v);
1420 __isl_give isl_constraint *
1421 isl_constraint_set_coefficient_val(
1422 __isl_take isl_constraint *constraint,
1423 enum isl_dim_type type, int pos,
1424 __isl_take isl_val *v);
1425 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1426 __isl_take isl_basic_map *bmap,
1427 __isl_take isl_constraint *constraint);
1428 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1429 __isl_take isl_basic_set *bset,
1430 __isl_take isl_constraint *constraint);
1431 __isl_give isl_map *isl_map_add_constraint(
1432 __isl_take isl_map *map,
1433 __isl_take isl_constraint *constraint);
1434 __isl_give isl_set *isl_set_add_constraint(
1435 __isl_take isl_set *set,
1436 __isl_take isl_constraint *constraint);
1437 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1438 __isl_take isl_basic_set *bset,
1439 __isl_take isl_constraint *constraint);
1441 For example, to create a set containing the even integers
1442 between 10 and 42, you would use the following code.
1445 isl_local_space *ls;
1447 isl_basic_set *bset;
1449 space = isl_space_set_alloc(ctx, 0, 2);
1450 bset = isl_basic_set_universe(isl_space_copy(space));
1451 ls = isl_local_space_from_space(space);
1453 c = isl_equality_alloc(isl_local_space_copy(ls));
1454 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1455 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1456 bset = isl_basic_set_add_constraint(bset, c);
1458 c = isl_inequality_alloc(isl_local_space_copy(ls));
1459 c = isl_constraint_set_constant_si(c, -10);
1460 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1461 bset = isl_basic_set_add_constraint(bset, c);
1463 c = isl_inequality_alloc(ls);
1464 c = isl_constraint_set_constant_si(c, 42);
1465 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1466 bset = isl_basic_set_add_constraint(bset, c);
1468 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1472 isl_basic_set *bset;
1473 bset = isl_basic_set_read_from_str(ctx,
1474 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1476 A basic set or relation can also be constructed from two matrices
1477 describing the equalities and the inequalities.
1479 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1480 __isl_take isl_space *space,
1481 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1482 enum isl_dim_type c1,
1483 enum isl_dim_type c2, enum isl_dim_type c3,
1484 enum isl_dim_type c4);
1485 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1486 __isl_take isl_space *space,
1487 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1488 enum isl_dim_type c1,
1489 enum isl_dim_type c2, enum isl_dim_type c3,
1490 enum isl_dim_type c4, enum isl_dim_type c5);
1492 The C<isl_dim_type> arguments indicate the order in which
1493 different kinds of variables appear in the input matrices
1494 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1495 C<isl_dim_set> and C<isl_dim_div> for sets and
1496 of C<isl_dim_cst>, C<isl_dim_param>,
1497 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1499 A (basic or union) set or relation can also be constructed from a
1500 (union) (piecewise) (multiple) affine expression
1501 or a list of affine expressions
1502 (See L<"Piecewise Quasi Affine Expressions"> and
1503 L<"Piecewise Multiple Quasi Affine Expressions">).
1505 __isl_give isl_basic_map *isl_basic_map_from_aff(
1506 __isl_take isl_aff *aff);
1507 __isl_give isl_map *isl_map_from_aff(
1508 __isl_take isl_aff *aff);
1509 __isl_give isl_set *isl_set_from_pw_aff(
1510 __isl_take isl_pw_aff *pwaff);
1511 __isl_give isl_map *isl_map_from_pw_aff(
1512 __isl_take isl_pw_aff *pwaff);
1513 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1514 __isl_take isl_space *domain_space,
1515 __isl_take isl_aff_list *list);
1516 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1517 __isl_take isl_multi_aff *maff)
1518 __isl_give isl_map *isl_map_from_multi_aff(
1519 __isl_take isl_multi_aff *maff)
1520 __isl_give isl_set *isl_set_from_pw_multi_aff(
1521 __isl_take isl_pw_multi_aff *pma);
1522 __isl_give isl_map *isl_map_from_pw_multi_aff(
1523 __isl_take isl_pw_multi_aff *pma);
1524 __isl_give isl_set *isl_set_from_multi_pw_aff(
1525 __isl_take isl_multi_pw_aff *mpa);
1526 __isl_give isl_map *isl_map_from_multi_pw_aff(
1527 __isl_take isl_multi_pw_aff *mpa);
1528 __isl_give isl_union_map *
1529 isl_union_map_from_union_pw_multi_aff(
1530 __isl_take isl_union_pw_multi_aff *upma);
1532 The C<domain_space> argument describes the domain of the resulting
1533 basic relation. It is required because the C<list> may consist
1534 of zero affine expressions.
1536 =head2 Inspecting Sets and Relations
1538 Usually, the user should not have to care about the actual constraints
1539 of the sets and maps, but should instead apply the abstract operations
1540 explained in the following sections.
1541 Occasionally, however, it may be required to inspect the individual
1542 coefficients of the constraints. This section explains how to do so.
1543 In these cases, it may also be useful to have C<isl> compute
1544 an explicit representation of the existentially quantified variables.
1546 __isl_give isl_set *isl_set_compute_divs(
1547 __isl_take isl_set *set);
1548 __isl_give isl_map *isl_map_compute_divs(
1549 __isl_take isl_map *map);
1550 __isl_give isl_union_set *isl_union_set_compute_divs(
1551 __isl_take isl_union_set *uset);
1552 __isl_give isl_union_map *isl_union_map_compute_divs(
1553 __isl_take isl_union_map *umap);
1555 This explicit representation defines the existentially quantified
1556 variables as integer divisions of the other variables, possibly
1557 including earlier existentially quantified variables.
1558 An explicitly represented existentially quantified variable therefore
1559 has a unique value when the values of the other variables are known.
1560 If, furthermore, the same existentials, i.e., existentials
1561 with the same explicit representations, should appear in the
1562 same order in each of the disjuncts of a set or map, then the user should call
1563 either of the following functions.
1565 __isl_give isl_set *isl_set_align_divs(
1566 __isl_take isl_set *set);
1567 __isl_give isl_map *isl_map_align_divs(
1568 __isl_take isl_map *map);
1570 Alternatively, the existentially quantified variables can be removed
1571 using the following functions, which compute an overapproximation.
1573 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1574 __isl_take isl_basic_set *bset);
1575 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1576 __isl_take isl_basic_map *bmap);
1577 __isl_give isl_set *isl_set_remove_divs(
1578 __isl_take isl_set *set);
1579 __isl_give isl_map *isl_map_remove_divs(
1580 __isl_take isl_map *map);
1582 It is also possible to only remove those divs that are defined
1583 in terms of a given range of dimensions or only those for which
1584 no explicit representation is known.
1586 __isl_give isl_basic_set *
1587 isl_basic_set_remove_divs_involving_dims(
1588 __isl_take isl_basic_set *bset,
1589 enum isl_dim_type type,
1590 unsigned first, unsigned n);
1591 __isl_give isl_basic_map *
1592 isl_basic_map_remove_divs_involving_dims(
1593 __isl_take isl_basic_map *bmap,
1594 enum isl_dim_type type,
1595 unsigned first, unsigned n);
1596 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1597 __isl_take isl_set *set, enum isl_dim_type type,
1598 unsigned first, unsigned n);
1599 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1600 __isl_take isl_map *map, enum isl_dim_type type,
1601 unsigned first, unsigned n);
1603 __isl_give isl_basic_set *
1604 isl_basic_set_remove_unknown_divs(
1605 __isl_take isl_basic_set *bset);
1606 __isl_give isl_set *isl_set_remove_unknown_divs(
1607 __isl_take isl_set *set);
1608 __isl_give isl_map *isl_map_remove_unknown_divs(
1609 __isl_take isl_map *map);
1611 To iterate over all the sets or maps in a union set or map, use
1613 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1614 int (*fn)(__isl_take isl_set *set, void *user),
1616 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1617 int (*fn)(__isl_take isl_map *map, void *user),
1620 The number of sets or maps in a union set or map can be obtained
1623 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1624 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1626 To extract the set or map in a given space from a union, use
1628 __isl_give isl_set *isl_union_set_extract_set(
1629 __isl_keep isl_union_set *uset,
1630 __isl_take isl_space *space);
1631 __isl_give isl_map *isl_union_map_extract_map(
1632 __isl_keep isl_union_map *umap,
1633 __isl_take isl_space *space);
1635 To iterate over all the basic sets or maps in a set or map, use
1637 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1638 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1640 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1641 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1644 The callback function C<fn> should return 0 if successful and
1645 -1 if an error occurs. In the latter case, or if any other error
1646 occurs, the above functions will return -1.
1648 It should be noted that C<isl> does not guarantee that
1649 the basic sets or maps passed to C<fn> are disjoint.
1650 If this is required, then the user should call one of
1651 the following functions first.
1653 __isl_give isl_set *isl_set_make_disjoint(
1654 __isl_take isl_set *set);
1655 __isl_give isl_map *isl_map_make_disjoint(
1656 __isl_take isl_map *map);
1658 The number of basic sets in a set can be obtained
1661 int isl_set_n_basic_set(__isl_keep isl_set *set);
1663 To iterate over the constraints of a basic set or map, use
1665 #include <isl/constraint.h>
1667 int isl_basic_set_n_constraint(
1668 __isl_keep isl_basic_set *bset);
1669 int isl_basic_set_foreach_constraint(
1670 __isl_keep isl_basic_set *bset,
1671 int (*fn)(__isl_take isl_constraint *c, void *user),
1673 int isl_basic_map_foreach_constraint(
1674 __isl_keep isl_basic_map *bmap,
1675 int (*fn)(__isl_take isl_constraint *c, void *user),
1677 __isl_null isl_constraint *isl_constraint_free(
1678 __isl_take isl_constraint *c);
1680 Again, the callback function C<fn> should return 0 if successful and
1681 -1 if an error occurs. In the latter case, or if any other error
1682 occurs, the above functions will return -1.
1683 The constraint C<c> represents either an equality or an inequality.
1684 Use the following function to find out whether a constraint
1685 represents an equality. If not, it represents an inequality.
1687 int isl_constraint_is_equality(
1688 __isl_keep isl_constraint *constraint);
1690 The coefficients of the constraints can be inspected using
1691 the following functions.
1693 int isl_constraint_is_lower_bound(
1694 __isl_keep isl_constraint *constraint,
1695 enum isl_dim_type type, unsigned pos);
1696 int isl_constraint_is_upper_bound(
1697 __isl_keep isl_constraint *constraint,
1698 enum isl_dim_type type, unsigned pos);
1699 __isl_give isl_val *isl_constraint_get_constant_val(
1700 __isl_keep isl_constraint *constraint);
1701 __isl_give isl_val *isl_constraint_get_coefficient_val(
1702 __isl_keep isl_constraint *constraint,
1703 enum isl_dim_type type, int pos);
1704 int isl_constraint_involves_dims(
1705 __isl_keep isl_constraint *constraint,
1706 enum isl_dim_type type, unsigned first, unsigned n);
1708 The explicit representations of the existentially quantified
1709 variables can be inspected using the following function.
1710 Note that the user is only allowed to use this function
1711 if the inspected set or map is the result of a call
1712 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1713 The existentially quantified variable is equal to the floor
1714 of the returned affine expression. The affine expression
1715 itself can be inspected using the functions in
1716 L<"Piecewise Quasi Affine Expressions">.
1718 __isl_give isl_aff *isl_constraint_get_div(
1719 __isl_keep isl_constraint *constraint, int pos);
1721 To obtain the constraints of a basic set or map in matrix
1722 form, use the following functions.
1724 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1725 __isl_keep isl_basic_set *bset,
1726 enum isl_dim_type c1, enum isl_dim_type c2,
1727 enum isl_dim_type c3, enum isl_dim_type c4);
1728 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1729 __isl_keep isl_basic_set *bset,
1730 enum isl_dim_type c1, enum isl_dim_type c2,
1731 enum isl_dim_type c3, enum isl_dim_type c4);
1732 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1733 __isl_keep isl_basic_map *bmap,
1734 enum isl_dim_type c1,
1735 enum isl_dim_type c2, enum isl_dim_type c3,
1736 enum isl_dim_type c4, enum isl_dim_type c5);
1737 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1738 __isl_keep isl_basic_map *bmap,
1739 enum isl_dim_type c1,
1740 enum isl_dim_type c2, enum isl_dim_type c3,
1741 enum isl_dim_type c4, enum isl_dim_type c5);
1743 The C<isl_dim_type> arguments dictate the order in which
1744 different kinds of variables appear in the resulting matrix
1745 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1746 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1748 The number of parameters, input, output or set dimensions can
1749 be obtained using the following functions.
1751 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1752 enum isl_dim_type type);
1753 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1754 enum isl_dim_type type);
1755 unsigned isl_set_dim(__isl_keep isl_set *set,
1756 enum isl_dim_type type);
1757 unsigned isl_map_dim(__isl_keep isl_map *map,
1758 enum isl_dim_type type);
1760 To check whether the description of a set or relation depends
1761 on one or more given dimensions, it is not necessary to iterate over all
1762 constraints. Instead the following functions can be used.
1764 int isl_basic_set_involves_dims(
1765 __isl_keep isl_basic_set *bset,
1766 enum isl_dim_type type, unsigned first, unsigned n);
1767 int isl_set_involves_dims(__isl_keep isl_set *set,
1768 enum isl_dim_type type, unsigned first, unsigned n);
1769 int isl_basic_map_involves_dims(
1770 __isl_keep isl_basic_map *bmap,
1771 enum isl_dim_type type, unsigned first, unsigned n);
1772 int isl_map_involves_dims(__isl_keep isl_map *map,
1773 enum isl_dim_type type, unsigned first, unsigned n);
1775 Similarly, the following functions can be used to check whether
1776 a given dimension is involved in any lower or upper bound.
1778 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1779 enum isl_dim_type type, unsigned pos);
1780 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1781 enum isl_dim_type type, unsigned pos);
1783 Note that these functions return true even if there is a bound on
1784 the dimension on only some of the basic sets of C<set>.
1785 To check if they have a bound for all of the basic sets in C<set>,
1786 use the following functions instead.
1788 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1789 enum isl_dim_type type, unsigned pos);
1790 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1791 enum isl_dim_type type, unsigned pos);
1793 The identifiers or names of the domain and range spaces of a set
1794 or relation can be read off or set using the following functions.
1796 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1797 __isl_take isl_basic_set *bset,
1798 __isl_take isl_id *id);
1799 __isl_give isl_set *isl_set_set_tuple_id(
1800 __isl_take isl_set *set, __isl_take isl_id *id);
1801 __isl_give isl_set *isl_set_reset_tuple_id(
1802 __isl_take isl_set *set);
1803 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1804 __isl_give isl_id *isl_set_get_tuple_id(
1805 __isl_keep isl_set *set);
1806 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1807 __isl_take isl_basic_map *bmap,
1808 enum isl_dim_type type, __isl_take isl_id *id);
1809 __isl_give isl_map *isl_map_set_tuple_id(
1810 __isl_take isl_map *map, enum isl_dim_type type,
1811 __isl_take isl_id *id);
1812 __isl_give isl_map *isl_map_reset_tuple_id(
1813 __isl_take isl_map *map, enum isl_dim_type type);
1814 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1815 enum isl_dim_type type);
1816 __isl_give isl_id *isl_map_get_tuple_id(
1817 __isl_keep isl_map *map, enum isl_dim_type type);
1819 const char *isl_basic_set_get_tuple_name(
1820 __isl_keep isl_basic_set *bset);
1821 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1822 __isl_take isl_basic_set *set, const char *s);
1823 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1824 const char *isl_set_get_tuple_name(
1825 __isl_keep isl_set *set);
1826 const char *isl_basic_map_get_tuple_name(
1827 __isl_keep isl_basic_map *bmap,
1828 enum isl_dim_type type);
1829 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1830 __isl_take isl_basic_map *bmap,
1831 enum isl_dim_type type, const char *s);
1832 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1833 enum isl_dim_type type);
1834 const char *isl_map_get_tuple_name(
1835 __isl_keep isl_map *map,
1836 enum isl_dim_type type);
1838 As with C<isl_space_get_tuple_name>, the value returned points to
1839 an internal data structure.
1840 The identifiers, positions or names of individual dimensions can be
1841 read off using the following functions.
1843 __isl_give isl_id *isl_basic_set_get_dim_id(
1844 __isl_keep isl_basic_set *bset,
1845 enum isl_dim_type type, unsigned pos);
1846 __isl_give isl_set *isl_set_set_dim_id(
1847 __isl_take isl_set *set, enum isl_dim_type type,
1848 unsigned pos, __isl_take isl_id *id);
1849 int isl_set_has_dim_id(__isl_keep isl_set *set,
1850 enum isl_dim_type type, unsigned pos);
1851 __isl_give isl_id *isl_set_get_dim_id(
1852 __isl_keep isl_set *set, enum isl_dim_type type,
1854 int isl_basic_map_has_dim_id(
1855 __isl_keep isl_basic_map *bmap,
1856 enum isl_dim_type type, unsigned pos);
1857 __isl_give isl_map *isl_map_set_dim_id(
1858 __isl_take isl_map *map, enum isl_dim_type type,
1859 unsigned pos, __isl_take isl_id *id);
1860 int isl_map_has_dim_id(__isl_keep isl_map *map,
1861 enum isl_dim_type type, unsigned pos);
1862 __isl_give isl_id *isl_map_get_dim_id(
1863 __isl_keep isl_map *map, enum isl_dim_type type,
1866 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1867 enum isl_dim_type type, __isl_keep isl_id *id);
1868 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1869 enum isl_dim_type type, __isl_keep isl_id *id);
1870 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1871 enum isl_dim_type type, const char *name);
1872 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1873 enum isl_dim_type type, const char *name);
1875 const char *isl_constraint_get_dim_name(
1876 __isl_keep isl_constraint *constraint,
1877 enum isl_dim_type type, unsigned pos);
1878 const char *isl_basic_set_get_dim_name(
1879 __isl_keep isl_basic_set *bset,
1880 enum isl_dim_type type, unsigned pos);
1881 int isl_set_has_dim_name(__isl_keep isl_set *set,
1882 enum isl_dim_type type, unsigned pos);
1883 const char *isl_set_get_dim_name(
1884 __isl_keep isl_set *set,
1885 enum isl_dim_type type, unsigned pos);
1886 const char *isl_basic_map_get_dim_name(
1887 __isl_keep isl_basic_map *bmap,
1888 enum isl_dim_type type, unsigned pos);
1889 int isl_map_has_dim_name(__isl_keep isl_map *map,
1890 enum isl_dim_type type, unsigned pos);
1891 const char *isl_map_get_dim_name(
1892 __isl_keep isl_map *map,
1893 enum isl_dim_type type, unsigned pos);
1895 These functions are mostly useful to obtain the identifiers, positions
1896 or names of the parameters. Identifiers of individual dimensions are
1897 essentially only useful for printing. They are ignored by all other
1898 operations and may not be preserved across those operations.
1900 The user pointers on all parameters and tuples can be reset
1901 using the following functions.
1903 #include <isl/set.h>
1904 __isl_give isl_set *isl_set_reset_user(
1905 __isl_take isl_set *set);
1906 #include <isl/map.h>
1907 __isl_give isl_map *isl_map_reset_user(
1908 __isl_take isl_map *map);
1909 #include <isl/union_set.h>
1910 __isl_give isl_union_set *isl_union_set_reset_user(
1911 __isl_take isl_union_set *uset);
1912 #include <isl/union_map.h>
1913 __isl_give isl_union_map *isl_union_map_reset_user(
1914 __isl_take isl_union_map *umap);
1918 =head3 Unary Properties
1924 The following functions test whether the given set or relation
1925 contains any integer points. The ``plain'' variants do not perform
1926 any computations, but simply check if the given set or relation
1927 is already known to be empty.
1929 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1930 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1931 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1932 int isl_set_is_empty(__isl_keep isl_set *set);
1933 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1934 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1935 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1936 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1937 int isl_map_is_empty(__isl_keep isl_map *map);
1938 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1940 =item * Universality
1942 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1943 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1944 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1946 =item * Single-valuedness
1948 int isl_basic_map_is_single_valued(
1949 __isl_keep isl_basic_map *bmap);
1950 int isl_map_plain_is_single_valued(
1951 __isl_keep isl_map *map);
1952 int isl_map_is_single_valued(__isl_keep isl_map *map);
1953 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1957 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1958 int isl_map_is_injective(__isl_keep isl_map *map);
1959 int isl_union_map_plain_is_injective(
1960 __isl_keep isl_union_map *umap);
1961 int isl_union_map_is_injective(
1962 __isl_keep isl_union_map *umap);
1966 int isl_map_is_bijective(__isl_keep isl_map *map);
1967 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1971 __isl_give isl_val *
1972 isl_basic_map_plain_get_val_if_fixed(
1973 __isl_keep isl_basic_map *bmap,
1974 enum isl_dim_type type, unsigned pos);
1975 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
1976 __isl_keep isl_set *set,
1977 enum isl_dim_type type, unsigned pos);
1978 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
1979 __isl_keep isl_map *map,
1980 enum isl_dim_type type, unsigned pos);
1982 If the set or relation obviously lies on a hyperplane where the given dimension
1983 has a fixed value, then return that value.
1984 Otherwise return NaN.
1988 int isl_set_dim_residue_class_val(
1989 __isl_keep isl_set *set,
1990 int pos, __isl_give isl_val **modulo,
1991 __isl_give isl_val **residue);
1993 Check if the values of the given set dimension are equal to a fixed
1994 value modulo some integer value. If so, assign the modulo to C<*modulo>
1995 and the fixed value to C<*residue>. If the given dimension attains only
1996 a single value, then assign C<0> to C<*modulo> and the fixed value to
1998 If the dimension does not attain only a single value and if no modulo
1999 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
2003 To check whether a set is a parameter domain, use this function:
2005 int isl_set_is_params(__isl_keep isl_set *set);
2006 int isl_union_set_is_params(
2007 __isl_keep isl_union_set *uset);
2011 The following functions check whether the space of the given
2012 (basic) set or relation range is a wrapped relation.
2014 #include <isl/space.h>
2015 int isl_space_is_wrapping(
2016 __isl_keep isl_space *space);
2017 int isl_space_domain_is_wrapping(
2018 __isl_keep isl_space *space);
2019 int isl_space_range_is_wrapping(
2020 __isl_keep isl_space *space);
2022 #include <isl/set.h>
2023 int isl_basic_set_is_wrapping(
2024 __isl_keep isl_basic_set *bset);
2025 int isl_set_is_wrapping(__isl_keep isl_set *set);
2027 #include <isl/map.h>
2028 int isl_map_domain_is_wrapping(
2029 __isl_keep isl_map *map);
2030 int isl_map_range_is_wrapping(
2031 __isl_keep isl_map *map);
2033 The input to C<isl_space_is_wrapping> should
2034 be the space of a set, while that of
2035 C<isl_space_domain_is_wrapping> and
2036 C<isl_space_range_is_wrapping> should be the space of a relation.
2038 =item * Internal Product
2040 int isl_basic_map_can_zip(
2041 __isl_keep isl_basic_map *bmap);
2042 int isl_map_can_zip(__isl_keep isl_map *map);
2044 Check whether the product of domain and range of the given relation
2046 i.e., whether both domain and range are nested relations.
2050 int isl_basic_map_can_curry(
2051 __isl_keep isl_basic_map *bmap);
2052 int isl_map_can_curry(__isl_keep isl_map *map);
2054 Check whether the domain of the (basic) relation is a wrapped relation.
2056 int isl_basic_map_can_uncurry(
2057 __isl_keep isl_basic_map *bmap);
2058 int isl_map_can_uncurry(__isl_keep isl_map *map);
2060 Check whether the range of the (basic) relation is a wrapped relation.
2064 =head3 Binary Properties
2070 int isl_basic_set_plain_is_equal(
2071 __isl_keep isl_basic_set *bset1,
2072 __isl_keep isl_basic_set *bset2);
2073 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2074 __isl_keep isl_set *set2);
2075 int isl_set_is_equal(__isl_keep isl_set *set1,
2076 __isl_keep isl_set *set2);
2077 int isl_union_set_is_equal(
2078 __isl_keep isl_union_set *uset1,
2079 __isl_keep isl_union_set *uset2);
2080 int isl_basic_map_is_equal(
2081 __isl_keep isl_basic_map *bmap1,
2082 __isl_keep isl_basic_map *bmap2);
2083 int isl_map_is_equal(__isl_keep isl_map *map1,
2084 __isl_keep isl_map *map2);
2085 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2086 __isl_keep isl_map *map2);
2087 int isl_union_map_is_equal(
2088 __isl_keep isl_union_map *umap1,
2089 __isl_keep isl_union_map *umap2);
2091 =item * Disjointness
2093 int isl_basic_set_is_disjoint(
2094 __isl_keep isl_basic_set *bset1,
2095 __isl_keep isl_basic_set *bset2);
2096 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2097 __isl_keep isl_set *set2);
2098 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2099 __isl_keep isl_set *set2);
2100 int isl_basic_map_is_disjoint(
2101 __isl_keep isl_basic_map *bmap1,
2102 __isl_keep isl_basic_map *bmap2);
2103 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2104 __isl_keep isl_map *map2);
2108 int isl_basic_set_is_subset(
2109 __isl_keep isl_basic_set *bset1,
2110 __isl_keep isl_basic_set *bset2);
2111 int isl_set_is_subset(__isl_keep isl_set *set1,
2112 __isl_keep isl_set *set2);
2113 int isl_set_is_strict_subset(
2114 __isl_keep isl_set *set1,
2115 __isl_keep isl_set *set2);
2116 int isl_union_set_is_subset(
2117 __isl_keep isl_union_set *uset1,
2118 __isl_keep isl_union_set *uset2);
2119 int isl_union_set_is_strict_subset(
2120 __isl_keep isl_union_set *uset1,
2121 __isl_keep isl_union_set *uset2);
2122 int isl_basic_map_is_subset(
2123 __isl_keep isl_basic_map *bmap1,
2124 __isl_keep isl_basic_map *bmap2);
2125 int isl_basic_map_is_strict_subset(
2126 __isl_keep isl_basic_map *bmap1,
2127 __isl_keep isl_basic_map *bmap2);
2128 int isl_map_is_subset(
2129 __isl_keep isl_map *map1,
2130 __isl_keep isl_map *map2);
2131 int isl_map_is_strict_subset(
2132 __isl_keep isl_map *map1,
2133 __isl_keep isl_map *map2);
2134 int isl_union_map_is_subset(
2135 __isl_keep isl_union_map *umap1,
2136 __isl_keep isl_union_map *umap2);
2137 int isl_union_map_is_strict_subset(
2138 __isl_keep isl_union_map *umap1,
2139 __isl_keep isl_union_map *umap2);
2141 Check whether the first argument is a (strict) subset of the
2146 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2147 __isl_keep isl_set *set2);
2149 This function is useful for sorting C<isl_set>s.
2150 The order depends on the internal representation of the inputs.
2151 The order is fixed over different calls to the function (assuming
2152 the internal representation of the inputs has not changed), but may
2153 change over different versions of C<isl>.
2157 =head2 Unary Operations
2163 __isl_give isl_set *isl_set_complement(
2164 __isl_take isl_set *set);
2165 __isl_give isl_map *isl_map_complement(
2166 __isl_take isl_map *map);
2170 __isl_give isl_basic_map *isl_basic_map_reverse(
2171 __isl_take isl_basic_map *bmap);
2172 __isl_give isl_map *isl_map_reverse(
2173 __isl_take isl_map *map);
2174 __isl_give isl_union_map *isl_union_map_reverse(
2175 __isl_take isl_union_map *umap);
2179 #include <isl/local_space.h>
2180 __isl_give isl_local_space *isl_local_space_domain(
2181 __isl_take isl_local_space *ls);
2182 __isl_give isl_local_space *isl_local_space_range(
2183 __isl_take isl_local_space *ls);
2185 #include <isl/set.h>
2186 __isl_give isl_basic_set *isl_basic_set_project_out(
2187 __isl_take isl_basic_set *bset,
2188 enum isl_dim_type type, unsigned first, unsigned n);
2189 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2190 enum isl_dim_type type, unsigned first, unsigned n);
2191 __isl_give isl_basic_set *isl_basic_set_params(
2192 __isl_take isl_basic_set *bset);
2193 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2195 #include <isl/map.h>
2196 __isl_give isl_basic_map *isl_basic_map_project_out(
2197 __isl_take isl_basic_map *bmap,
2198 enum isl_dim_type type, unsigned first, unsigned n);
2199 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2200 enum isl_dim_type type, unsigned first, unsigned n);
2201 __isl_give isl_basic_set *isl_basic_map_domain(
2202 __isl_take isl_basic_map *bmap);
2203 __isl_give isl_basic_set *isl_basic_map_range(
2204 __isl_take isl_basic_map *bmap);
2205 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2206 __isl_give isl_set *isl_map_domain(
2207 __isl_take isl_map *bmap);
2208 __isl_give isl_set *isl_map_range(
2209 __isl_take isl_map *map);
2211 #include <isl/union_set.h>
2212 __isl_give isl_set *isl_union_set_params(
2213 __isl_take isl_union_set *uset);
2215 #include <isl/union_map.h>
2216 __isl_give isl_set *isl_union_map_params(
2217 __isl_take isl_union_map *umap);
2218 __isl_give isl_union_set *isl_union_map_domain(
2219 __isl_take isl_union_map *umap);
2220 __isl_give isl_union_set *isl_union_map_range(
2221 __isl_take isl_union_map *umap);
2223 #include <isl/map.h>
2224 __isl_give isl_basic_map *isl_basic_map_domain_map(
2225 __isl_take isl_basic_map *bmap);
2226 __isl_give isl_basic_map *isl_basic_map_range_map(
2227 __isl_take isl_basic_map *bmap);
2228 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2229 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2231 #include <isl/union_map.h>
2232 __isl_give isl_union_map *isl_union_map_domain_map(
2233 __isl_take isl_union_map *umap);
2234 __isl_give isl_union_map *isl_union_map_range_map(
2235 __isl_take isl_union_map *umap);
2237 The functions above construct a (basic, regular or union) relation
2238 that maps (a wrapped version of) the input relation to its domain or range.
2242 __isl_give isl_basic_set *isl_basic_set_eliminate(
2243 __isl_take isl_basic_set *bset,
2244 enum isl_dim_type type,
2245 unsigned first, unsigned n);
2246 __isl_give isl_set *isl_set_eliminate(
2247 __isl_take isl_set *set, enum isl_dim_type type,
2248 unsigned first, unsigned n);
2249 __isl_give isl_basic_map *isl_basic_map_eliminate(
2250 __isl_take isl_basic_map *bmap,
2251 enum isl_dim_type type,
2252 unsigned first, unsigned n);
2253 __isl_give isl_map *isl_map_eliminate(
2254 __isl_take isl_map *map, enum isl_dim_type type,
2255 unsigned first, unsigned n);
2257 Eliminate the coefficients for the given dimensions from the constraints,
2258 without removing the dimensions.
2260 =item * Constructing a relation from a set
2262 #include <isl/local_space.h>
2263 __isl_give isl_local_space *isl_local_space_from_domain(
2264 __isl_take isl_local_space *ls);
2266 #include <isl/map.h>
2267 __isl_give isl_map *isl_map_from_domain(
2268 __isl_take isl_set *set);
2269 __isl_give isl_map *isl_map_from_range(
2270 __isl_take isl_set *set);
2272 Create a relation with the given set as domain or range.
2273 The range or domain of the created relation is a zero-dimensional
2274 flat anonymous space.
2278 __isl_give isl_basic_set *isl_basic_set_fix_si(
2279 __isl_take isl_basic_set *bset,
2280 enum isl_dim_type type, unsigned pos, int value);
2281 __isl_give isl_basic_set *isl_basic_set_fix_val(
2282 __isl_take isl_basic_set *bset,
2283 enum isl_dim_type type, unsigned pos,
2284 __isl_take isl_val *v);
2285 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2286 enum isl_dim_type type, unsigned pos, int value);
2287 __isl_give isl_set *isl_set_fix_val(
2288 __isl_take isl_set *set,
2289 enum isl_dim_type type, unsigned pos,
2290 __isl_take isl_val *v);
2291 __isl_give isl_basic_map *isl_basic_map_fix_si(
2292 __isl_take isl_basic_map *bmap,
2293 enum isl_dim_type type, unsigned pos, int value);
2294 __isl_give isl_basic_map *isl_basic_map_fix_val(
2295 __isl_take isl_basic_map *bmap,
2296 enum isl_dim_type type, unsigned pos,
2297 __isl_take isl_val *v);
2298 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2299 enum isl_dim_type type, unsigned pos, int value);
2300 __isl_give isl_map *isl_map_fix_val(
2301 __isl_take isl_map *map,
2302 enum isl_dim_type type, unsigned pos,
2303 __isl_take isl_val *v);
2305 Intersect the set or relation with the hyperplane where the given
2306 dimension has the fixed given value.
2308 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2309 __isl_take isl_basic_map *bmap,
2310 enum isl_dim_type type, unsigned pos, int value);
2311 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2312 __isl_take isl_basic_map *bmap,
2313 enum isl_dim_type type, unsigned pos, int value);
2314 __isl_give isl_set *isl_set_lower_bound_si(
2315 __isl_take isl_set *set,
2316 enum isl_dim_type type, unsigned pos, int value);
2317 __isl_give isl_set *isl_set_lower_bound_val(
2318 __isl_take isl_set *set,
2319 enum isl_dim_type type, unsigned pos,
2320 __isl_take isl_val *value);
2321 __isl_give isl_map *isl_map_lower_bound_si(
2322 __isl_take isl_map *map,
2323 enum isl_dim_type type, unsigned pos, int value);
2324 __isl_give isl_set *isl_set_upper_bound_si(
2325 __isl_take isl_set *set,
2326 enum isl_dim_type type, unsigned pos, int value);
2327 __isl_give isl_set *isl_set_upper_bound_val(
2328 __isl_take isl_set *set,
2329 enum isl_dim_type type, unsigned pos,
2330 __isl_take isl_val *value);
2331 __isl_give isl_map *isl_map_upper_bound_si(
2332 __isl_take isl_map *map,
2333 enum isl_dim_type type, unsigned pos, int value);
2335 Intersect the set or relation with the half-space where the given
2336 dimension has a value bounded by the fixed given integer value.
2338 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2339 enum isl_dim_type type1, int pos1,
2340 enum isl_dim_type type2, int pos2);
2341 __isl_give isl_basic_map *isl_basic_map_equate(
2342 __isl_take isl_basic_map *bmap,
2343 enum isl_dim_type type1, int pos1,
2344 enum isl_dim_type type2, int pos2);
2345 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2346 enum isl_dim_type type1, int pos1,
2347 enum isl_dim_type type2, int pos2);
2349 Intersect the set or relation with the hyperplane where the given
2350 dimensions are equal to each other.
2352 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2353 enum isl_dim_type type1, int pos1,
2354 enum isl_dim_type type2, int pos2);
2356 Intersect the relation with the hyperplane where the given
2357 dimensions have opposite values.
2359 __isl_give isl_map *isl_map_order_le(
2360 __isl_take isl_map *map,
2361 enum isl_dim_type type1, int pos1,
2362 enum isl_dim_type type2, int pos2);
2363 __isl_give isl_basic_map *isl_basic_map_order_ge(
2364 __isl_take isl_basic_map *bmap,
2365 enum isl_dim_type type1, int pos1,
2366 enum isl_dim_type type2, int pos2);
2367 __isl_give isl_map *isl_map_order_ge(
2368 __isl_take isl_map *map,
2369 enum isl_dim_type type1, int pos1,
2370 enum isl_dim_type type2, int pos2);
2371 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2372 enum isl_dim_type type1, int pos1,
2373 enum isl_dim_type type2, int pos2);
2374 __isl_give isl_basic_map *isl_basic_map_order_gt(
2375 __isl_take isl_basic_map *bmap,
2376 enum isl_dim_type type1, int pos1,
2377 enum isl_dim_type type2, int pos2);
2378 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2379 enum isl_dim_type type1, int pos1,
2380 enum isl_dim_type type2, int pos2);
2382 Intersect the relation with the half-space where the given
2383 dimensions satisfy the given ordering.
2387 __isl_give isl_map *isl_set_identity(
2388 __isl_take isl_set *set);
2389 __isl_give isl_union_map *isl_union_set_identity(
2390 __isl_take isl_union_set *uset);
2392 Construct an identity relation on the given (union) set.
2396 __isl_give isl_basic_set *isl_basic_map_deltas(
2397 __isl_take isl_basic_map *bmap);
2398 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2399 __isl_give isl_union_set *isl_union_map_deltas(
2400 __isl_take isl_union_map *umap);
2402 These functions return a (basic) set containing the differences
2403 between image elements and corresponding domain elements in the input.
2405 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2406 __isl_take isl_basic_map *bmap);
2407 __isl_give isl_map *isl_map_deltas_map(
2408 __isl_take isl_map *map);
2409 __isl_give isl_union_map *isl_union_map_deltas_map(
2410 __isl_take isl_union_map *umap);
2412 The functions above construct a (basic, regular or union) relation
2413 that maps (a wrapped version of) the input relation to its delta set.
2417 Simplify the representation of a set or relation by trying
2418 to combine pairs of basic sets or relations into a single
2419 basic set or relation.
2421 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2422 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2423 __isl_give isl_union_set *isl_union_set_coalesce(
2424 __isl_take isl_union_set *uset);
2425 __isl_give isl_union_map *isl_union_map_coalesce(
2426 __isl_take isl_union_map *umap);
2428 One of the methods for combining pairs of basic sets or relations
2429 can result in coefficients that are much larger than those that appear
2430 in the constraints of the input. By default, the coefficients are
2431 not allowed to grow larger, but this can be changed by unsetting
2432 the following option.
2434 int isl_options_set_coalesce_bounded_wrapping(
2435 isl_ctx *ctx, int val);
2436 int isl_options_get_coalesce_bounded_wrapping(
2439 =item * Detecting equalities
2441 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2442 __isl_take isl_basic_set *bset);
2443 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2444 __isl_take isl_basic_map *bmap);
2445 __isl_give isl_set *isl_set_detect_equalities(
2446 __isl_take isl_set *set);
2447 __isl_give isl_map *isl_map_detect_equalities(
2448 __isl_take isl_map *map);
2449 __isl_give isl_union_set *isl_union_set_detect_equalities(
2450 __isl_take isl_union_set *uset);
2451 __isl_give isl_union_map *isl_union_map_detect_equalities(
2452 __isl_take isl_union_map *umap);
2454 Simplify the representation of a set or relation by detecting implicit
2457 =item * Removing redundant constraints
2459 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2460 __isl_take isl_basic_set *bset);
2461 __isl_give isl_set *isl_set_remove_redundancies(
2462 __isl_take isl_set *set);
2463 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2464 __isl_take isl_basic_map *bmap);
2465 __isl_give isl_map *isl_map_remove_redundancies(
2466 __isl_take isl_map *map);
2470 __isl_give isl_basic_set *isl_set_convex_hull(
2471 __isl_take isl_set *set);
2472 __isl_give isl_basic_map *isl_map_convex_hull(
2473 __isl_take isl_map *map);
2475 If the input set or relation has any existentially quantified
2476 variables, then the result of these operations is currently undefined.
2480 __isl_give isl_basic_set *
2481 isl_set_unshifted_simple_hull(
2482 __isl_take isl_set *set);
2483 __isl_give isl_basic_map *
2484 isl_map_unshifted_simple_hull(
2485 __isl_take isl_map *map);
2486 __isl_give isl_basic_set *isl_set_simple_hull(
2487 __isl_take isl_set *set);
2488 __isl_give isl_basic_map *isl_map_simple_hull(
2489 __isl_take isl_map *map);
2490 __isl_give isl_union_map *isl_union_map_simple_hull(
2491 __isl_take isl_union_map *umap);
2493 These functions compute a single basic set or relation
2494 that contains the whole input set or relation.
2495 In particular, the output is described by translates
2496 of the constraints describing the basic sets or relations in the input.
2497 In case of C<isl_set_unshifted_simple_hull>, only the original
2498 constraints are used, without any translation.
2502 (See \autoref{s:simple hull}.)
2508 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2509 __isl_take isl_basic_set *bset);
2510 __isl_give isl_basic_set *isl_set_affine_hull(
2511 __isl_take isl_set *set);
2512 __isl_give isl_union_set *isl_union_set_affine_hull(
2513 __isl_take isl_union_set *uset);
2514 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2515 __isl_take isl_basic_map *bmap);
2516 __isl_give isl_basic_map *isl_map_affine_hull(
2517 __isl_take isl_map *map);
2518 __isl_give isl_union_map *isl_union_map_affine_hull(
2519 __isl_take isl_union_map *umap);
2521 In case of union sets and relations, the affine hull is computed
2524 =item * Polyhedral hull
2526 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2527 __isl_take isl_set *set);
2528 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2529 __isl_take isl_map *map);
2530 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2531 __isl_take isl_union_set *uset);
2532 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2533 __isl_take isl_union_map *umap);
2535 These functions compute a single basic set or relation
2536 not involving any existentially quantified variables
2537 that contains the whole input set or relation.
2538 In case of union sets and relations, the polyhedral hull is computed
2541 =item * Other approximations
2543 __isl_give isl_basic_set *
2544 isl_basic_set_drop_constraints_involving_dims(
2545 __isl_take isl_basic_set *bset,
2546 enum isl_dim_type type,
2547 unsigned first, unsigned n);
2548 __isl_give isl_basic_map *
2549 isl_basic_map_drop_constraints_involving_dims(
2550 __isl_take isl_basic_map *bmap,
2551 enum isl_dim_type type,
2552 unsigned first, unsigned n);
2553 __isl_give isl_basic_set *
2554 isl_basic_set_drop_constraints_not_involving_dims(
2555 __isl_take isl_basic_set *bset,
2556 enum isl_dim_type type,
2557 unsigned first, unsigned n);
2558 __isl_give isl_set *
2559 isl_set_drop_constraints_involving_dims(
2560 __isl_take isl_set *set,
2561 enum isl_dim_type type,
2562 unsigned first, unsigned n);
2563 __isl_give isl_map *
2564 isl_map_drop_constraints_involving_dims(
2565 __isl_take isl_map *map,
2566 enum isl_dim_type type,
2567 unsigned first, unsigned n);
2569 These functions drop any constraints (not) involving the specified dimensions.
2570 Note that the result depends on the representation of the input.
2574 __isl_give isl_basic_set *isl_basic_set_sample(
2575 __isl_take isl_basic_set *bset);
2576 __isl_give isl_basic_set *isl_set_sample(
2577 __isl_take isl_set *set);
2578 __isl_give isl_basic_map *isl_basic_map_sample(
2579 __isl_take isl_basic_map *bmap);
2580 __isl_give isl_basic_map *isl_map_sample(
2581 __isl_take isl_map *map);
2583 If the input (basic) set or relation is non-empty, then return
2584 a singleton subset of the input. Otherwise, return an empty set.
2586 =item * Optimization
2588 #include <isl/ilp.h>
2589 __isl_give isl_val *isl_basic_set_max_val(
2590 __isl_keep isl_basic_set *bset,
2591 __isl_keep isl_aff *obj);
2592 __isl_give isl_val *isl_set_min_val(
2593 __isl_keep isl_set *set,
2594 __isl_keep isl_aff *obj);
2595 __isl_give isl_val *isl_set_max_val(
2596 __isl_keep isl_set *set,
2597 __isl_keep isl_aff *obj);
2599 Compute the minimum or maximum of the integer affine expression C<obj>
2600 over the points in C<set>, returning the result in C<opt>.
2601 The result is C<NULL> in case of an error, the optimal value in case
2602 there is one, negative infinity or infinity if the problem is unbounded and
2603 NaN if the problem is empty.
2605 =item * Parametric optimization
2607 __isl_give isl_pw_aff *isl_set_dim_min(
2608 __isl_take isl_set *set, int pos);
2609 __isl_give isl_pw_aff *isl_set_dim_max(
2610 __isl_take isl_set *set, int pos);
2611 __isl_give isl_pw_aff *isl_map_dim_max(
2612 __isl_take isl_map *map, int pos);
2614 Compute the minimum or maximum of the given set or output dimension
2615 as a function of the parameters (and input dimensions), but independently
2616 of the other set or output dimensions.
2617 For lexicographic optimization, see L<"Lexicographic Optimization">.
2621 The following functions compute either the set of (rational) coefficient
2622 values of valid constraints for the given set or the set of (rational)
2623 values satisfying the constraints with coefficients from the given set.
2624 Internally, these two sets of functions perform essentially the
2625 same operations, except that the set of coefficients is assumed to
2626 be a cone, while the set of values may be any polyhedron.
2627 The current implementation is based on the Farkas lemma and
2628 Fourier-Motzkin elimination, but this may change or be made optional
2629 in future. In particular, future implementations may use different
2630 dualization algorithms or skip the elimination step.
2632 __isl_give isl_basic_set *isl_basic_set_coefficients(
2633 __isl_take isl_basic_set *bset);
2634 __isl_give isl_basic_set *isl_set_coefficients(
2635 __isl_take isl_set *set);
2636 __isl_give isl_union_set *isl_union_set_coefficients(
2637 __isl_take isl_union_set *bset);
2638 __isl_give isl_basic_set *isl_basic_set_solutions(
2639 __isl_take isl_basic_set *bset);
2640 __isl_give isl_basic_set *isl_set_solutions(
2641 __isl_take isl_set *set);
2642 __isl_give isl_union_set *isl_union_set_solutions(
2643 __isl_take isl_union_set *bset);
2647 __isl_give isl_map *isl_map_fixed_power_val(
2648 __isl_take isl_map *map,
2649 __isl_take isl_val *exp);
2650 __isl_give isl_union_map *
2651 isl_union_map_fixed_power_val(
2652 __isl_take isl_union_map *umap,
2653 __isl_take isl_val *exp);
2655 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2656 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2657 of C<map> is computed.
2659 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2661 __isl_give isl_union_map *isl_union_map_power(
2662 __isl_take isl_union_map *umap, int *exact);
2664 Compute a parametric representation for all positive powers I<k> of C<map>.
2665 The result maps I<k> to a nested relation corresponding to the
2666 I<k>th power of C<map>.
2667 The result may be an overapproximation. If the result is known to be exact,
2668 then C<*exact> is set to C<1>.
2670 =item * Transitive closure
2672 __isl_give isl_map *isl_map_transitive_closure(
2673 __isl_take isl_map *map, int *exact);
2674 __isl_give isl_union_map *isl_union_map_transitive_closure(
2675 __isl_take isl_union_map *umap, int *exact);
2677 Compute the transitive closure of C<map>.
2678 The result may be an overapproximation. If the result is known to be exact,
2679 then C<*exact> is set to C<1>.
2681 =item * Reaching path lengths
2683 __isl_give isl_map *isl_map_reaching_path_lengths(
2684 __isl_take isl_map *map, int *exact);
2686 Compute a relation that maps each element in the range of C<map>
2687 to the lengths of all paths composed of edges in C<map> that
2688 end up in the given element.
2689 The result may be an overapproximation. If the result is known to be exact,
2690 then C<*exact> is set to C<1>.
2691 To compute the I<maximal> path length, the resulting relation
2692 should be postprocessed by C<isl_map_lexmax>.
2693 In particular, if the input relation is a dependence relation
2694 (mapping sources to sinks), then the maximal path length corresponds
2695 to the free schedule.
2696 Note, however, that C<isl_map_lexmax> expects the maximum to be
2697 finite, so if the path lengths are unbounded (possibly due to
2698 the overapproximation), then you will get an error message.
2702 #include <isl/space.h>
2703 __isl_give isl_space *isl_space_wrap(
2704 __isl_take isl_space *space);
2705 __isl_give isl_space *isl_space_unwrap(
2706 __isl_take isl_space *space);
2708 #include <isl/set.h>
2709 __isl_give isl_basic_map *isl_basic_set_unwrap(
2710 __isl_take isl_basic_set *bset);
2711 __isl_give isl_map *isl_set_unwrap(
2712 __isl_take isl_set *set);
2714 #include <isl/map.h>
2715 __isl_give isl_basic_set *isl_basic_map_wrap(
2716 __isl_take isl_basic_map *bmap);
2717 __isl_give isl_set *isl_map_wrap(
2718 __isl_take isl_map *map);
2720 #include <isl/union_set.h>
2721 __isl_give isl_union_map *isl_union_set_unwrap(
2722 __isl_take isl_union_set *uset);
2724 #include <isl/union_map.h>
2725 __isl_give isl_union_set *isl_union_map_wrap(
2726 __isl_take isl_union_map *umap);
2728 The input to C<isl_space_unwrap> should
2729 be the space of a set, while that of
2730 C<isl_space_wrap> should be the space of a relation.
2731 Conversely, the output of C<isl_space_unwrap> is the space
2732 of a relation, while that of C<isl_space_wrap> is the space of a set.
2736 Remove any internal structure of domain (and range) of the given
2737 set or relation. If there is any such internal structure in the input,
2738 then the name of the space is also removed.
2740 #include <isl/local_space.h>
2741 __isl_give isl_local_space *
2742 isl_local_space_flatten_domain(
2743 __isl_take isl_local_space *ls);
2744 __isl_give isl_local_space *
2745 isl_local_space_flatten_range(
2746 __isl_take isl_local_space *ls);
2748 #include <isl/set.h>
2749 __isl_give isl_basic_set *isl_basic_set_flatten(
2750 __isl_take isl_basic_set *bset);
2751 __isl_give isl_set *isl_set_flatten(
2752 __isl_take isl_set *set);
2754 #include <isl/map.h>
2755 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2756 __isl_take isl_basic_map *bmap);
2757 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2758 __isl_take isl_basic_map *bmap);
2759 __isl_give isl_map *isl_map_flatten_range(
2760 __isl_take isl_map *map);
2761 __isl_give isl_map *isl_map_flatten_domain(
2762 __isl_take isl_map *map);
2763 __isl_give isl_basic_map *isl_basic_map_flatten(
2764 __isl_take isl_basic_map *bmap);
2765 __isl_give isl_map *isl_map_flatten(
2766 __isl_take isl_map *map);
2768 #include <isl/map.h>
2769 __isl_give isl_map *isl_set_flatten_map(
2770 __isl_take isl_set *set);
2772 The function above constructs a relation
2773 that maps the input set to a flattened version of the set.
2777 Lift the input set to a space with extra dimensions corresponding
2778 to the existentially quantified variables in the input.
2779 In particular, the result lives in a wrapped map where the domain
2780 is the original space and the range corresponds to the original
2781 existentially quantified variables.
2783 __isl_give isl_basic_set *isl_basic_set_lift(
2784 __isl_take isl_basic_set *bset);
2785 __isl_give isl_set *isl_set_lift(
2786 __isl_take isl_set *set);
2787 __isl_give isl_union_set *isl_union_set_lift(
2788 __isl_take isl_union_set *uset);
2790 Given a local space that contains the existentially quantified
2791 variables of a set, a basic relation that, when applied to
2792 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2793 can be constructed using the following function.
2795 #include <isl/local_space.h>
2796 __isl_give isl_basic_map *isl_local_space_lifting(
2797 __isl_take isl_local_space *ls);
2799 =item * Internal Product
2801 __isl_give isl_basic_map *isl_basic_map_zip(
2802 __isl_take isl_basic_map *bmap);
2803 __isl_give isl_map *isl_map_zip(
2804 __isl_take isl_map *map);
2805 __isl_give isl_union_map *isl_union_map_zip(
2806 __isl_take isl_union_map *umap);
2808 Given a relation with nested relations for domain and range,
2809 interchange the range of the domain with the domain of the range.
2813 __isl_give isl_basic_map *isl_basic_map_curry(
2814 __isl_take isl_basic_map *bmap);
2815 __isl_give isl_basic_map *isl_basic_map_uncurry(
2816 __isl_take isl_basic_map *bmap);
2817 __isl_give isl_map *isl_map_curry(
2818 __isl_take isl_map *map);
2819 __isl_give isl_map *isl_map_uncurry(
2820 __isl_take isl_map *map);
2821 __isl_give isl_union_map *isl_union_map_curry(
2822 __isl_take isl_union_map *umap);
2823 __isl_give isl_union_map *isl_union_map_uncurry(
2824 __isl_take isl_union_map *umap);
2826 Given a relation with a nested relation for domain,
2827 the C<curry> functions
2828 move the range of the nested relation out of the domain
2829 and use it as the domain of a nested relation in the range,
2830 with the original range as range of this nested relation.
2831 The C<uncurry> functions perform the inverse operation.
2833 =item * Aligning parameters
2835 __isl_give isl_basic_set *isl_basic_set_align_params(
2836 __isl_take isl_basic_set *bset,
2837 __isl_take isl_space *model);
2838 __isl_give isl_set *isl_set_align_params(
2839 __isl_take isl_set *set,
2840 __isl_take isl_space *model);
2841 __isl_give isl_basic_map *isl_basic_map_align_params(
2842 __isl_take isl_basic_map *bmap,
2843 __isl_take isl_space *model);
2844 __isl_give isl_map *isl_map_align_params(
2845 __isl_take isl_map *map,
2846 __isl_take isl_space *model);
2848 Change the order of the parameters of the given set or relation
2849 such that the first parameters match those of C<model>.
2850 This may involve the introduction of extra parameters.
2851 All parameters need to be named.
2853 =item * Dimension manipulation
2855 #include <isl/local_space.h>
2856 __isl_give isl_local_space *isl_local_space_add_dims(
2857 __isl_take isl_local_space *ls,
2858 enum isl_dim_type type, unsigned n);
2859 __isl_give isl_local_space *isl_local_space_insert_dims(
2860 __isl_take isl_local_space *ls,
2861 enum isl_dim_type type, unsigned first, unsigned n);
2862 __isl_give isl_local_space *isl_local_space_drop_dims(
2863 __isl_take isl_local_space *ls,
2864 enum isl_dim_type type, unsigned first, unsigned n);
2866 #include <isl/set.h>
2867 __isl_give isl_basic_set *isl_basic_set_add_dims(
2868 __isl_take isl_basic_set *bset,
2869 enum isl_dim_type type, unsigned n);
2870 __isl_give isl_set *isl_set_add_dims(
2871 __isl_take isl_set *set,
2872 enum isl_dim_type type, unsigned n);
2873 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2874 __isl_take isl_basic_set *bset,
2875 enum isl_dim_type type, unsigned pos,
2877 __isl_give isl_set *isl_set_insert_dims(
2878 __isl_take isl_set *set,
2879 enum isl_dim_type type, unsigned pos, unsigned n);
2880 __isl_give isl_basic_set *isl_basic_set_move_dims(
2881 __isl_take isl_basic_set *bset,
2882 enum isl_dim_type dst_type, unsigned dst_pos,
2883 enum isl_dim_type src_type, unsigned src_pos,
2885 __isl_give isl_set *isl_set_move_dims(
2886 __isl_take isl_set *set,
2887 enum isl_dim_type dst_type, unsigned dst_pos,
2888 enum isl_dim_type src_type, unsigned src_pos,
2891 #include <isl/map.h>
2892 __isl_give isl_map *isl_map_add_dims(
2893 __isl_take isl_map *map,
2894 enum isl_dim_type type, unsigned n);
2895 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2896 __isl_take isl_basic_map *bmap,
2897 enum isl_dim_type type, unsigned pos,
2899 __isl_give isl_map *isl_map_insert_dims(
2900 __isl_take isl_map *map,
2901 enum isl_dim_type type, unsigned pos, unsigned n);
2902 __isl_give isl_basic_map *isl_basic_map_move_dims(
2903 __isl_take isl_basic_map *bmap,
2904 enum isl_dim_type dst_type, unsigned dst_pos,
2905 enum isl_dim_type src_type, unsigned src_pos,
2907 __isl_give isl_map *isl_map_move_dims(
2908 __isl_take isl_map *map,
2909 enum isl_dim_type dst_type, unsigned dst_pos,
2910 enum isl_dim_type src_type, unsigned src_pos,
2913 It is usually not advisable to directly change the (input or output)
2914 space of a set or a relation as this removes the name and the internal
2915 structure of the space. However, the above functions can be useful
2916 to add new parameters, assuming
2917 C<isl_set_align_params> and C<isl_map_align_params>
2922 =head2 Binary Operations
2924 The two arguments of a binary operation not only need to live
2925 in the same C<isl_ctx>, they currently also need to have
2926 the same (number of) parameters.
2928 =head3 Basic Operations
2932 =item * Intersection
2934 #include <isl/local_space.h>
2935 __isl_give isl_local_space *isl_local_space_intersect(
2936 __isl_take isl_local_space *ls1,
2937 __isl_take isl_local_space *ls2);
2939 #include <isl/set.h>
2940 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2941 __isl_take isl_basic_set *bset1,
2942 __isl_take isl_basic_set *bset2);
2943 __isl_give isl_basic_set *isl_basic_set_intersect(
2944 __isl_take isl_basic_set *bset1,
2945 __isl_take isl_basic_set *bset2);
2946 __isl_give isl_set *isl_set_intersect_params(
2947 __isl_take isl_set *set,
2948 __isl_take isl_set *params);
2949 __isl_give isl_set *isl_set_intersect(
2950 __isl_take isl_set *set1,
2951 __isl_take isl_set *set2);
2953 #include <isl/map.h>
2954 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2955 __isl_take isl_basic_map *bmap,
2956 __isl_take isl_basic_set *bset);
2957 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2958 __isl_take isl_basic_map *bmap,
2959 __isl_take isl_basic_set *bset);
2960 __isl_give isl_basic_map *isl_basic_map_intersect(
2961 __isl_take isl_basic_map *bmap1,
2962 __isl_take isl_basic_map *bmap2);
2963 __isl_give isl_map *isl_map_intersect_params(
2964 __isl_take isl_map *map,
2965 __isl_take isl_set *params);
2966 __isl_give isl_map *isl_map_intersect_domain(
2967 __isl_take isl_map *map,
2968 __isl_take isl_set *set);
2969 __isl_give isl_map *isl_map_intersect_range(
2970 __isl_take isl_map *map,
2971 __isl_take isl_set *set);
2972 __isl_give isl_map *isl_map_intersect(
2973 __isl_take isl_map *map1,
2974 __isl_take isl_map *map2);
2976 #include <isl/union_set.h>
2977 __isl_give isl_union_set *isl_union_set_intersect_params(
2978 __isl_take isl_union_set *uset,
2979 __isl_take isl_set *set);
2980 __isl_give isl_union_set *isl_union_set_intersect(
2981 __isl_take isl_union_set *uset1,
2982 __isl_take isl_union_set *uset2);
2984 #include <isl/union_map.h>
2985 __isl_give isl_union_map *isl_union_map_intersect_params(
2986 __isl_take isl_union_map *umap,
2987 __isl_take isl_set *set);
2988 __isl_give isl_union_map *isl_union_map_intersect_domain(
2989 __isl_take isl_union_map *umap,
2990 __isl_take isl_union_set *uset);
2991 __isl_give isl_union_map *isl_union_map_intersect_range(
2992 __isl_take isl_union_map *umap,
2993 __isl_take isl_union_set *uset);
2994 __isl_give isl_union_map *isl_union_map_intersect(
2995 __isl_take isl_union_map *umap1,
2996 __isl_take isl_union_map *umap2);
2998 The second argument to the C<_params> functions needs to be
2999 a parametric (basic) set. For the other functions, a parametric set
3000 for either argument is only allowed if the other argument is
3001 a parametric set as well.
3005 __isl_give isl_set *isl_basic_set_union(
3006 __isl_take isl_basic_set *bset1,
3007 __isl_take isl_basic_set *bset2);
3008 __isl_give isl_map *isl_basic_map_union(
3009 __isl_take isl_basic_map *bmap1,
3010 __isl_take isl_basic_map *bmap2);
3011 __isl_give isl_set *isl_set_union(
3012 __isl_take isl_set *set1,
3013 __isl_take isl_set *set2);
3014 __isl_give isl_map *isl_map_union(
3015 __isl_take isl_map *map1,
3016 __isl_take isl_map *map2);
3017 __isl_give isl_union_set *isl_union_set_union(
3018 __isl_take isl_union_set *uset1,
3019 __isl_take isl_union_set *uset2);
3020 __isl_give isl_union_map *isl_union_map_union(
3021 __isl_take isl_union_map *umap1,
3022 __isl_take isl_union_map *umap2);
3024 =item * Set difference
3026 __isl_give isl_set *isl_set_subtract(
3027 __isl_take isl_set *set1,
3028 __isl_take isl_set *set2);
3029 __isl_give isl_map *isl_map_subtract(
3030 __isl_take isl_map *map1,
3031 __isl_take isl_map *map2);
3032 __isl_give isl_map *isl_map_subtract_domain(
3033 __isl_take isl_map *map,
3034 __isl_take isl_set *dom);
3035 __isl_give isl_map *isl_map_subtract_range(
3036 __isl_take isl_map *map,
3037 __isl_take isl_set *dom);
3038 __isl_give isl_union_set *isl_union_set_subtract(
3039 __isl_take isl_union_set *uset1,
3040 __isl_take isl_union_set *uset2);
3041 __isl_give isl_union_map *isl_union_map_subtract(
3042 __isl_take isl_union_map *umap1,
3043 __isl_take isl_union_map *umap2);
3044 __isl_give isl_union_map *isl_union_map_subtract_domain(
3045 __isl_take isl_union_map *umap,
3046 __isl_take isl_union_set *dom);
3047 __isl_give isl_union_map *isl_union_map_subtract_range(
3048 __isl_take isl_union_map *umap,
3049 __isl_take isl_union_set *dom);
3053 __isl_give isl_basic_set *isl_basic_set_apply(
3054 __isl_take isl_basic_set *bset,
3055 __isl_take isl_basic_map *bmap);
3056 __isl_give isl_set *isl_set_apply(
3057 __isl_take isl_set *set,
3058 __isl_take isl_map *map);
3059 __isl_give isl_union_set *isl_union_set_apply(
3060 __isl_take isl_union_set *uset,
3061 __isl_take isl_union_map *umap);
3062 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3063 __isl_take isl_basic_map *bmap1,
3064 __isl_take isl_basic_map *bmap2);
3065 __isl_give isl_basic_map *isl_basic_map_apply_range(
3066 __isl_take isl_basic_map *bmap1,
3067 __isl_take isl_basic_map *bmap2);
3068 __isl_give isl_map *isl_map_apply_domain(
3069 __isl_take isl_map *map1,
3070 __isl_take isl_map *map2);
3071 __isl_give isl_union_map *isl_union_map_apply_domain(
3072 __isl_take isl_union_map *umap1,
3073 __isl_take isl_union_map *umap2);
3074 __isl_give isl_map *isl_map_apply_range(
3075 __isl_take isl_map *map1,
3076 __isl_take isl_map *map2);
3077 __isl_give isl_union_map *isl_union_map_apply_range(
3078 __isl_take isl_union_map *umap1,
3079 __isl_take isl_union_map *umap2);
3083 #include <isl/set.h>
3084 __isl_give isl_basic_set *
3085 isl_basic_set_preimage_multi_aff(
3086 __isl_take isl_basic_set *bset,
3087 __isl_take isl_multi_aff *ma);
3088 __isl_give isl_set *isl_set_preimage_multi_aff(
3089 __isl_take isl_set *set,
3090 __isl_take isl_multi_aff *ma);
3091 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3092 __isl_take isl_set *set,
3093 __isl_take isl_pw_multi_aff *pma);
3094 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
3095 __isl_take isl_set *set,
3096 __isl_take isl_multi_pw_aff *mpa);
3098 #include <isl/union_set.h>
3099 __isl_give isl_union_set *
3100 isl_union_set_preimage_multi_aff(
3101 __isl_take isl_union_set *uset,
3102 __isl_take isl_multi_aff *ma);
3103 __isl_give isl_union_set *
3104 isl_union_set_preimage_pw_multi_aff(
3105 __isl_take isl_union_set *uset,
3106 __isl_take isl_pw_multi_aff *pma);
3107 __isl_give isl_union_set *
3108 isl_union_set_preimage_union_pw_multi_aff(
3109 __isl_take isl_union_set *uset,
3110 __isl_take isl_union_pw_multi_aff *upma);
3112 #include <isl/map.h>
3113 __isl_give isl_basic_map *
3114 isl_basic_map_preimage_domain_multi_aff(
3115 __isl_take isl_basic_map *bmap,
3116 __isl_take isl_multi_aff *ma);
3117 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3118 __isl_take isl_map *map,
3119 __isl_take isl_multi_aff *ma);
3120 __isl_give isl_map *isl_map_preimage_range_multi_aff(
3121 __isl_take isl_map *map,
3122 __isl_take isl_multi_aff *ma);
3123 __isl_give isl_map *
3124 isl_map_preimage_domain_pw_multi_aff(
3125 __isl_take isl_map *map,
3126 __isl_take isl_pw_multi_aff *pma);
3127 __isl_give isl_map *
3128 isl_map_preimage_range_pw_multi_aff(
3129 __isl_take isl_map *map,
3130 __isl_take isl_pw_multi_aff *pma);
3131 __isl_give isl_map *
3132 isl_map_preimage_domain_multi_pw_aff(
3133 __isl_take isl_map *map,
3134 __isl_take isl_multi_pw_aff *mpa);
3135 __isl_give isl_basic_map *
3136 isl_basic_map_preimage_range_multi_aff(
3137 __isl_take isl_basic_map *bmap,
3138 __isl_take isl_multi_aff *ma);
3140 #include <isl/union_map.h>
3141 __isl_give isl_union_map *
3142 isl_union_map_preimage_domain_multi_aff(
3143 __isl_take isl_union_map *umap,
3144 __isl_take isl_multi_aff *ma);
3145 __isl_give isl_union_map *
3146 isl_union_map_preimage_range_multi_aff(
3147 __isl_take isl_union_map *umap,
3148 __isl_take isl_multi_aff *ma);
3149 __isl_give isl_union_map *
3150 isl_union_map_preimage_domain_pw_multi_aff(
3151 __isl_take isl_union_map *umap,
3152 __isl_take isl_pw_multi_aff *pma);
3153 __isl_give isl_union_map *
3154 isl_union_map_preimage_range_pw_multi_aff(
3155 __isl_take isl_union_map *umap,
3156 __isl_take isl_pw_multi_aff *pma);
3157 __isl_give isl_union_map *
3158 isl_union_map_preimage_domain_union_pw_multi_aff(
3159 __isl_take isl_union_map *umap,
3160 __isl_take isl_union_pw_multi_aff *upma);
3161 __isl_give isl_union_map *
3162 isl_union_map_preimage_range_union_pw_multi_aff(
3163 __isl_take isl_union_map *umap,
3164 __isl_take isl_union_pw_multi_aff *upma);
3166 These functions compute the preimage of the given set or map domain/range under
3167 the given function. In other words, the expression is plugged
3168 into the set description or into the domain/range of the map.
3169 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3170 L</"Piecewise Multiple Quasi Affine Expressions">.
3172 =item * Cartesian Product
3174 #include <isl/space.h>
3175 __isl_give isl_space *isl_space_product(
3176 __isl_take isl_space *space1,
3177 __isl_take isl_space *space2);
3178 __isl_give isl_space *isl_space_domain_product(
3179 __isl_take isl_space *space1,
3180 __isl_take isl_space *space2);
3181 __isl_give isl_space *isl_space_range_product(
3182 __isl_take isl_space *space1,
3183 __isl_take isl_space *space2);
3186 C<isl_space_product>, C<isl_space_domain_product>
3187 and C<isl_space_range_product> take pairs or relation spaces and
3188 produce a single relations space, where either the domain, the range
3189 or both domain and range are wrapped spaces of relations between
3190 the domains and/or ranges of the input spaces.
3191 If the product is only constructed over the domain or the range
3192 then the ranges or the domains of the inputs should be the same.
3194 #include <isl/set.h>
3195 __isl_give isl_set *isl_set_product(
3196 __isl_take isl_set *set1,
3197 __isl_take isl_set *set2);
3199 #include <isl/map.h>
3200 __isl_give isl_basic_map *isl_basic_map_domain_product(
3201 __isl_take isl_basic_map *bmap1,
3202 __isl_take isl_basic_map *bmap2);
3203 __isl_give isl_basic_map *isl_basic_map_range_product(
3204 __isl_take isl_basic_map *bmap1,
3205 __isl_take isl_basic_map *bmap2);
3206 __isl_give isl_basic_map *isl_basic_map_product(
3207 __isl_take isl_basic_map *bmap1,
3208 __isl_take isl_basic_map *bmap2);
3209 __isl_give isl_map *isl_map_domain_product(
3210 __isl_take isl_map *map1,
3211 __isl_take isl_map *map2);
3212 __isl_give isl_map *isl_map_range_product(
3213 __isl_take isl_map *map1,
3214 __isl_take isl_map *map2);
3215 __isl_give isl_map *isl_map_product(
3216 __isl_take isl_map *map1,
3217 __isl_take isl_map *map2);
3219 #include <isl/union_set.h>
3220 __isl_give isl_union_set *isl_union_set_product(
3221 __isl_take isl_union_set *uset1,
3222 __isl_take isl_union_set *uset2);
3224 #include <isl/union_map.h>
3225 __isl_give isl_union_map *isl_union_map_domain_product(
3226 __isl_take isl_union_map *umap1,
3227 __isl_take isl_union_map *umap2);
3228 __isl_give isl_union_map *isl_union_map_range_product(
3229 __isl_take isl_union_map *umap1,
3230 __isl_take isl_union_map *umap2);
3231 __isl_give isl_union_map *isl_union_map_product(
3232 __isl_take isl_union_map *umap1,
3233 __isl_take isl_union_map *umap2);
3235 The above functions compute the cross product of the given
3236 sets or relations. The domains and ranges of the results
3237 are wrapped maps between domains and ranges of the inputs.
3238 To obtain a ``flat'' product, use the following functions
3241 __isl_give isl_basic_set *isl_basic_set_flat_product(
3242 __isl_take isl_basic_set *bset1,
3243 __isl_take isl_basic_set *bset2);
3244 __isl_give isl_set *isl_set_flat_product(
3245 __isl_take isl_set *set1,
3246 __isl_take isl_set *set2);
3247 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3248 __isl_take isl_basic_map *bmap1,
3249 __isl_take isl_basic_map *bmap2);
3250 __isl_give isl_map *isl_map_flat_domain_product(
3251 __isl_take isl_map *map1,
3252 __isl_take isl_map *map2);
3253 __isl_give isl_map *isl_map_flat_range_product(
3254 __isl_take isl_map *map1,
3255 __isl_take isl_map *map2);
3256 __isl_give isl_union_map *isl_union_map_flat_range_product(
3257 __isl_take isl_union_map *umap1,
3258 __isl_take isl_union_map *umap2);
3259 __isl_give isl_basic_map *isl_basic_map_flat_product(
3260 __isl_take isl_basic_map *bmap1,
3261 __isl_take isl_basic_map *bmap2);
3262 __isl_give isl_map *isl_map_flat_product(
3263 __isl_take isl_map *map1,
3264 __isl_take isl_map *map2);
3266 #include <isl/space.h>
3267 __isl_give isl_space *isl_space_domain_factor_domain(
3268 __isl_take isl_space *space);
3269 __isl_give isl_space *isl_space_range_factor_domain(
3270 __isl_take isl_space *space);
3271 __isl_give isl_space *isl_space_range_factor_range(
3272 __isl_take isl_space *space);
3274 The functions C<isl_space_range_factor_domain> and
3275 C<isl_space_range_factor_range> extract the two arguments from
3276 the result of a call to C<isl_space_range_product>.
3278 The arguments of a call to C<isl_map_range_product> can be extracted
3279 from the result using the following two functions.
3281 #include <isl/map.h>
3282 __isl_give isl_map *isl_map_range_factor_domain(
3283 __isl_take isl_map *map);
3284 __isl_give isl_map *isl_map_range_factor_range(
3285 __isl_take isl_map *map);
3287 =item * Simplification
3289 __isl_give isl_basic_set *isl_basic_set_gist(
3290 __isl_take isl_basic_set *bset,
3291 __isl_take isl_basic_set *context);
3292 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3293 __isl_take isl_set *context);
3294 __isl_give isl_set *isl_set_gist_params(
3295 __isl_take isl_set *set,
3296 __isl_take isl_set *context);
3297 __isl_give isl_union_set *isl_union_set_gist(
3298 __isl_take isl_union_set *uset,
3299 __isl_take isl_union_set *context);
3300 __isl_give isl_union_set *isl_union_set_gist_params(
3301 __isl_take isl_union_set *uset,
3302 __isl_take isl_set *set);
3303 __isl_give isl_basic_map *isl_basic_map_gist(
3304 __isl_take isl_basic_map *bmap,
3305 __isl_take isl_basic_map *context);
3306 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3307 __isl_take isl_map *context);
3308 __isl_give isl_map *isl_map_gist_params(
3309 __isl_take isl_map *map,
3310 __isl_take isl_set *context);
3311 __isl_give isl_map *isl_map_gist_domain(
3312 __isl_take isl_map *map,
3313 __isl_take isl_set *context);
3314 __isl_give isl_map *isl_map_gist_range(
3315 __isl_take isl_map *map,
3316 __isl_take isl_set *context);
3317 __isl_give isl_union_map *isl_union_map_gist(
3318 __isl_take isl_union_map *umap,
3319 __isl_take isl_union_map *context);
3320 __isl_give isl_union_map *isl_union_map_gist_params(
3321 __isl_take isl_union_map *umap,
3322 __isl_take isl_set *set);
3323 __isl_give isl_union_map *isl_union_map_gist_domain(
3324 __isl_take isl_union_map *umap,
3325 __isl_take isl_union_set *uset);
3326 __isl_give isl_union_map *isl_union_map_gist_range(
3327 __isl_take isl_union_map *umap,
3328 __isl_take isl_union_set *uset);
3330 The gist operation returns a set or relation that has the
3331 same intersection with the context as the input set or relation.
3332 Any implicit equality in the intersection is made explicit in the result,
3333 while all inequalities that are redundant with respect to the intersection
3335 In case of union sets and relations, the gist operation is performed
3340 =head3 Lexicographic Optimization
3342 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3343 the following functions
3344 compute a set that contains the lexicographic minimum or maximum
3345 of the elements in C<set> (or C<bset>) for those values of the parameters
3346 that satisfy C<dom>.
3347 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3348 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3350 In other words, the union of the parameter values
3351 for which the result is non-empty and of C<*empty>
3354 __isl_give isl_set *isl_basic_set_partial_lexmin(
3355 __isl_take isl_basic_set *bset,
3356 __isl_take isl_basic_set *dom,
3357 __isl_give isl_set **empty);
3358 __isl_give isl_set *isl_basic_set_partial_lexmax(
3359 __isl_take isl_basic_set *bset,
3360 __isl_take isl_basic_set *dom,
3361 __isl_give isl_set **empty);
3362 __isl_give isl_set *isl_set_partial_lexmin(
3363 __isl_take isl_set *set, __isl_take isl_set *dom,
3364 __isl_give isl_set **empty);
3365 __isl_give isl_set *isl_set_partial_lexmax(
3366 __isl_take isl_set *set, __isl_take isl_set *dom,
3367 __isl_give isl_set **empty);
3369 Given a (basic) set C<set> (or C<bset>), the following functions simply
3370 return a set containing the lexicographic minimum or maximum
3371 of the elements in C<set> (or C<bset>).
3372 In case of union sets, the optimum is computed per space.
3374 __isl_give isl_set *isl_basic_set_lexmin(
3375 __isl_take isl_basic_set *bset);
3376 __isl_give isl_set *isl_basic_set_lexmax(
3377 __isl_take isl_basic_set *bset);
3378 __isl_give isl_set *isl_set_lexmin(
3379 __isl_take isl_set *set);
3380 __isl_give isl_set *isl_set_lexmax(
3381 __isl_take isl_set *set);
3382 __isl_give isl_union_set *isl_union_set_lexmin(
3383 __isl_take isl_union_set *uset);
3384 __isl_give isl_union_set *isl_union_set_lexmax(
3385 __isl_take isl_union_set *uset);
3387 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3388 the following functions
3389 compute a relation that maps each element of C<dom>
3390 to the single lexicographic minimum or maximum
3391 of the elements that are associated to that same
3392 element in C<map> (or C<bmap>).
3393 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3394 that contains the elements in C<dom> that do not map
3395 to any elements in C<map> (or C<bmap>).
3396 In other words, the union of the domain of the result and of C<*empty>
3399 __isl_give isl_map *isl_basic_map_partial_lexmax(
3400 __isl_take isl_basic_map *bmap,
3401 __isl_take isl_basic_set *dom,
3402 __isl_give isl_set **empty);
3403 __isl_give isl_map *isl_basic_map_partial_lexmin(
3404 __isl_take isl_basic_map *bmap,
3405 __isl_take isl_basic_set *dom,
3406 __isl_give isl_set **empty);
3407 __isl_give isl_map *isl_map_partial_lexmax(
3408 __isl_take isl_map *map, __isl_take isl_set *dom,
3409 __isl_give isl_set **empty);
3410 __isl_give isl_map *isl_map_partial_lexmin(
3411 __isl_take isl_map *map, __isl_take isl_set *dom,
3412 __isl_give isl_set **empty);
3414 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3415 return a map mapping each element in the domain of
3416 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3417 of all elements associated to that element.
3418 In case of union relations, the optimum is computed per space.
3420 __isl_give isl_map *isl_basic_map_lexmin(
3421 __isl_take isl_basic_map *bmap);
3422 __isl_give isl_map *isl_basic_map_lexmax(
3423 __isl_take isl_basic_map *bmap);
3424 __isl_give isl_map *isl_map_lexmin(
3425 __isl_take isl_map *map);
3426 __isl_give isl_map *isl_map_lexmax(
3427 __isl_take isl_map *map);
3428 __isl_give isl_union_map *isl_union_map_lexmin(
3429 __isl_take isl_union_map *umap);
3430 __isl_give isl_union_map *isl_union_map_lexmax(
3431 __isl_take isl_union_map *umap);
3433 The following functions return their result in the form of
3434 a piecewise multi-affine expression
3435 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3436 but are otherwise equivalent to the corresponding functions
3437 returning a basic set or relation.
3439 __isl_give isl_pw_multi_aff *
3440 isl_basic_map_lexmin_pw_multi_aff(
3441 __isl_take isl_basic_map *bmap);
3442 __isl_give isl_pw_multi_aff *
3443 isl_basic_set_partial_lexmin_pw_multi_aff(
3444 __isl_take isl_basic_set *bset,
3445 __isl_take isl_basic_set *dom,
3446 __isl_give isl_set **empty);
3447 __isl_give isl_pw_multi_aff *
3448 isl_basic_set_partial_lexmax_pw_multi_aff(
3449 __isl_take isl_basic_set *bset,
3450 __isl_take isl_basic_set *dom,
3451 __isl_give isl_set **empty);
3452 __isl_give isl_pw_multi_aff *
3453 isl_basic_map_partial_lexmin_pw_multi_aff(
3454 __isl_take isl_basic_map *bmap,
3455 __isl_take isl_basic_set *dom,
3456 __isl_give isl_set **empty);
3457 __isl_give isl_pw_multi_aff *
3458 isl_basic_map_partial_lexmax_pw_multi_aff(
3459 __isl_take isl_basic_map *bmap,
3460 __isl_take isl_basic_set *dom,
3461 __isl_give isl_set **empty);
3462 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3463 __isl_take isl_set *set);
3464 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3465 __isl_take isl_set *set);
3466 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3467 __isl_take isl_map *map);
3468 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3469 __isl_take isl_map *map);
3473 Lists are defined over several element types, including
3474 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3475 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3476 Here we take lists of C<isl_set>s as an example.
3477 Lists can be created, copied, modified and freed using the following functions.
3479 #include <isl/list.h>
3480 __isl_give isl_set_list *isl_set_list_from_set(
3481 __isl_take isl_set *el);
3482 __isl_give isl_set_list *isl_set_list_alloc(
3483 isl_ctx *ctx, int n);
3484 __isl_give isl_set_list *isl_set_list_copy(
3485 __isl_keep isl_set_list *list);
3486 __isl_give isl_set_list *isl_set_list_insert(
3487 __isl_take isl_set_list *list, unsigned pos,
3488 __isl_take isl_set *el);
3489 __isl_give isl_set_list *isl_set_list_add(
3490 __isl_take isl_set_list *list,
3491 __isl_take isl_set *el);
3492 __isl_give isl_set_list *isl_set_list_drop(
3493 __isl_take isl_set_list *list,
3494 unsigned first, unsigned n);
3495 __isl_give isl_set_list *isl_set_list_set_set(
3496 __isl_take isl_set_list *list, int index,
3497 __isl_take isl_set *set);
3498 __isl_give isl_set_list *isl_set_list_concat(
3499 __isl_take isl_set_list *list1,
3500 __isl_take isl_set_list *list2);
3501 __isl_give isl_set_list *isl_set_list_sort(
3502 __isl_take isl_set_list *list,
3503 int (*cmp)(__isl_keep isl_set *a,
3504 __isl_keep isl_set *b, void *user),
3506 __isl_null isl_set_list *isl_set_list_free(
3507 __isl_take isl_set_list *list);
3509 C<isl_set_list_alloc> creates an empty list with a capacity for
3510 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3513 Lists can be inspected using the following functions.
3515 #include <isl/list.h>
3516 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3517 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3518 __isl_give isl_set *isl_set_list_get_set(
3519 __isl_keep isl_set_list *list, int index);
3520 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3521 int (*fn)(__isl_take isl_set *el, void *user),
3523 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3524 int (*follows)(__isl_keep isl_set *a,
3525 __isl_keep isl_set *b, void *user),
3527 int (*fn)(__isl_take isl_set *el, void *user),
3530 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3531 strongly connected components of the graph with as vertices the elements
3532 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3533 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3534 should return C<-1> on error.
3536 Lists can be printed using
3538 #include <isl/list.h>
3539 __isl_give isl_printer *isl_printer_print_set_list(
3540 __isl_take isl_printer *p,
3541 __isl_keep isl_set_list *list);
3543 =head2 Associative arrays
3545 Associative arrays map isl objects of a specific type to isl objects
3546 of some (other) specific type. They are defined for several pairs
3547 of types, including (C<isl_map>, C<isl_basic_set>),
3548 (C<isl_id>, C<isl_ast_expr>) and.
3549 (C<isl_id>, C<isl_pw_aff>).
3550 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3553 Associative arrays can be created, copied and freed using
3554 the following functions.
3556 #include <isl/id_to_ast_expr.h>
3557 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3558 isl_ctx *ctx, int min_size);
3559 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3560 __isl_keep id_to_ast_expr *id2expr);
3561 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
3562 __isl_take id_to_ast_expr *id2expr);
3564 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3565 to specify the expected size of the associative array.
3566 The associative array will be grown automatically as needed.
3568 Associative arrays can be inspected using the following functions.
3570 #include <isl/id_to_ast_expr.h>
3571 isl_ctx *isl_id_to_ast_expr_get_ctx(
3572 __isl_keep id_to_ast_expr *id2expr);
3573 int isl_id_to_ast_expr_has(
3574 __isl_keep id_to_ast_expr *id2expr,
3575 __isl_keep isl_id *key);
3576 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3577 __isl_keep id_to_ast_expr *id2expr,
3578 __isl_take isl_id *key);
3579 int isl_id_to_ast_expr_foreach(
3580 __isl_keep id_to_ast_expr *id2expr,
3581 int (*fn)(__isl_take isl_id *key,
3582 __isl_take isl_ast_expr *val, void *user),
3585 They can be modified using the following function.
3587 #include <isl/id_to_ast_expr.h>
3588 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3589 __isl_take id_to_ast_expr *id2expr,
3590 __isl_take isl_id *key,
3591 __isl_take isl_ast_expr *val);
3592 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
3593 __isl_take id_to_ast_expr *id2expr,
3594 __isl_take isl_id *key);
3596 Associative arrays can be printed using the following function.
3598 #include <isl/id_to_ast_expr.h>
3599 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3600 __isl_take isl_printer *p,
3601 __isl_keep id_to_ast_expr *id2expr);
3603 =head2 Multiple Values
3605 An C<isl_multi_val> object represents a sequence of zero or more values,
3606 living in a set space.
3608 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3609 using the following function
3611 #include <isl/val.h>
3612 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3613 __isl_take isl_space *space,
3614 __isl_take isl_val_list *list);
3616 The zero multiple value (with value zero for each set dimension)
3617 can be created using the following function.
3619 #include <isl/val.h>
3620 __isl_give isl_multi_val *isl_multi_val_zero(
3621 __isl_take isl_space *space);
3623 Multiple values can be copied and freed using
3625 #include <isl/val.h>
3626 __isl_give isl_multi_val *isl_multi_val_copy(
3627 __isl_keep isl_multi_val *mv);
3628 __isl_null isl_multi_val *isl_multi_val_free(
3629 __isl_take isl_multi_val *mv);
3631 They can be inspected using
3633 #include <isl/val.h>
3634 isl_ctx *isl_multi_val_get_ctx(
3635 __isl_keep isl_multi_val *mv);
3636 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3637 enum isl_dim_type type);
3638 __isl_give isl_val *isl_multi_val_get_val(
3639 __isl_keep isl_multi_val *mv, int pos);
3640 int isl_multi_val_find_dim_by_id(
3641 __isl_keep isl_multi_val *mv,
3642 enum isl_dim_type type, __isl_keep isl_id *id);
3643 __isl_give isl_id *isl_multi_val_get_dim_id(
3644 __isl_keep isl_multi_val *mv,
3645 enum isl_dim_type type, unsigned pos);
3646 const char *isl_multi_val_get_tuple_name(
3647 __isl_keep isl_multi_val *mv,
3648 enum isl_dim_type type);
3649 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3650 enum isl_dim_type type);
3651 __isl_give isl_id *isl_multi_val_get_tuple_id(
3652 __isl_keep isl_multi_val *mv,
3653 enum isl_dim_type type);
3654 int isl_multi_val_range_is_wrapping(
3655 __isl_keep isl_multi_val *mv);
3657 They can be modified using
3659 #include <isl/val.h>
3660 __isl_give isl_multi_val *isl_multi_val_set_val(
3661 __isl_take isl_multi_val *mv, int pos,
3662 __isl_take isl_val *val);
3663 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3664 __isl_take isl_multi_val *mv,
3665 enum isl_dim_type type, unsigned pos, const char *s);
3666 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3667 __isl_take isl_multi_val *mv,
3668 enum isl_dim_type type, unsigned pos,
3669 __isl_take isl_id *id);
3670 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3671 __isl_take isl_multi_val *mv,
3672 enum isl_dim_type type, const char *s);
3673 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3674 __isl_take isl_multi_val *mv,
3675 enum isl_dim_type type, __isl_take isl_id *id);
3676 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3677 __isl_take isl_multi_val *mv,
3678 enum isl_dim_type type);
3679 __isl_give isl_multi_val *isl_multi_val_reset_user(
3680 __isl_take isl_multi_val *mv);
3682 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3683 __isl_take isl_multi_val *mv,
3684 enum isl_dim_type type, unsigned first, unsigned n);
3685 __isl_give isl_multi_val *isl_multi_val_add_dims(
3686 __isl_take isl_multi_val *mv,
3687 enum isl_dim_type type, unsigned n);
3688 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3689 __isl_take isl_multi_val *mv,
3690 enum isl_dim_type type, unsigned first, unsigned n);
3694 #include <isl/val.h>
3695 __isl_give isl_multi_val *isl_multi_val_align_params(
3696 __isl_take isl_multi_val *mv,
3697 __isl_take isl_space *model);
3698 __isl_give isl_multi_val *isl_multi_val_from_range(
3699 __isl_take isl_multi_val *mv);
3700 __isl_give isl_multi_val *isl_multi_val_range_splice(
3701 __isl_take isl_multi_val *mv1, unsigned pos,
3702 __isl_take isl_multi_val *mv2);
3703 __isl_give isl_multi_val *isl_multi_val_range_product(
3704 __isl_take isl_multi_val *mv1,
3705 __isl_take isl_multi_val *mv2);
3706 __isl_give isl_multi_val *
3707 isl_multi_val_range_factor_domain(
3708 __isl_take isl_multi_val *mv);
3709 __isl_give isl_multi_val *
3710 isl_multi_val_range_factor_range(
3711 __isl_take isl_multi_val *mv);
3712 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3713 __isl_take isl_multi_val *mv1,
3714 __isl_take isl_multi_aff *mv2);
3715 __isl_give isl_multi_val *isl_multi_val_product(
3716 __isl_take isl_multi_val *mv1,
3717 __isl_take isl_multi_val *mv2);
3718 __isl_give isl_multi_val *isl_multi_val_add_val(
3719 __isl_take isl_multi_val *mv,
3720 __isl_take isl_val *v);
3721 __isl_give isl_multi_val *isl_multi_val_mod_val(
3722 __isl_take isl_multi_val *mv,
3723 __isl_take isl_val *v);
3724 __isl_give isl_multi_val *isl_multi_val_scale_val(
3725 __isl_take isl_multi_val *mv,
3726 __isl_take isl_val *v);
3727 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3728 __isl_take isl_multi_val *mv1,
3729 __isl_take isl_multi_val *mv2);
3730 __isl_give isl_multi_val *
3731 isl_multi_val_scale_down_multi_val(
3732 __isl_take isl_multi_val *mv1,
3733 __isl_take isl_multi_val *mv2);
3735 A multiple value can be printed using
3737 __isl_give isl_printer *isl_printer_print_multi_val(
3738 __isl_take isl_printer *p,
3739 __isl_keep isl_multi_val *mv);
3743 Vectors can be created, copied and freed using the following functions.
3745 #include <isl/vec.h>
3746 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3748 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3749 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
3751 Note that the elements of a newly created vector may have arbitrary values.
3752 The elements can be changed and inspected using the following functions.
3754 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3755 int isl_vec_size(__isl_keep isl_vec *vec);
3756 __isl_give isl_val *isl_vec_get_element_val(
3757 __isl_keep isl_vec *vec, int pos);
3758 __isl_give isl_vec *isl_vec_set_element_si(
3759 __isl_take isl_vec *vec, int pos, int v);
3760 __isl_give isl_vec *isl_vec_set_element_val(
3761 __isl_take isl_vec *vec, int pos,
3762 __isl_take isl_val *v);
3763 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3765 __isl_give isl_vec *isl_vec_set_val(
3766 __isl_take isl_vec *vec, __isl_take isl_val *v);
3767 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3768 __isl_keep isl_vec *vec2, int pos);
3770 C<isl_vec_get_element> will return a negative value if anything went wrong.
3771 In that case, the value of C<*v> is undefined.
3773 The following function can be used to concatenate two vectors.
3775 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3776 __isl_take isl_vec *vec2);
3780 Matrices can be created, copied and freed using the following functions.
3782 #include <isl/mat.h>
3783 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3784 unsigned n_row, unsigned n_col);
3785 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3786 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
3788 Note that the elements of a newly created matrix may have arbitrary values.
3789 The elements can be changed and inspected using the following functions.
3791 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3792 int isl_mat_rows(__isl_keep isl_mat *mat);
3793 int isl_mat_cols(__isl_keep isl_mat *mat);
3794 __isl_give isl_val *isl_mat_get_element_val(
3795 __isl_keep isl_mat *mat, int row, int col);
3796 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3797 int row, int col, int v);
3798 __isl_give isl_mat *isl_mat_set_element_val(
3799 __isl_take isl_mat *mat, int row, int col,
3800 __isl_take isl_val *v);
3802 C<isl_mat_get_element> will return a negative value if anything went wrong.
3803 In that case, the value of C<*v> is undefined.
3805 The following function can be used to compute the (right) inverse
3806 of a matrix, i.e., a matrix such that the product of the original
3807 and the inverse (in that order) is a multiple of the identity matrix.
3808 The input matrix is assumed to be of full row-rank.
3810 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3812 The following function can be used to compute the (right) kernel
3813 (or null space) of a matrix, i.e., a matrix such that the product of
3814 the original and the kernel (in that order) is the zero matrix.
3816 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3818 =head2 Piecewise Quasi Affine Expressions
3820 The zero quasi affine expression or the quasi affine expression
3821 that is equal to a given value or
3822 a specified dimension on a given domain can be created using
3824 __isl_give isl_aff *isl_aff_zero_on_domain(
3825 __isl_take isl_local_space *ls);
3826 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3827 __isl_take isl_local_space *ls);
3828 __isl_give isl_aff *isl_aff_val_on_domain(
3829 __isl_take isl_local_space *ls,
3830 __isl_take isl_val *val);
3831 __isl_give isl_aff *isl_aff_var_on_domain(
3832 __isl_take isl_local_space *ls,
3833 enum isl_dim_type type, unsigned pos);
3834 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3835 __isl_take isl_local_space *ls,
3836 enum isl_dim_type type, unsigned pos);
3838 Note that the space in which the resulting objects live is a map space
3839 with the given space as domain and a one-dimensional range.
3841 An empty piecewise quasi affine expression (one with no cells)
3842 or a piecewise quasi affine expression with a single cell can
3843 be created using the following functions.
3845 #include <isl/aff.h>
3846 __isl_give isl_pw_aff *isl_pw_aff_empty(
3847 __isl_take isl_space *space);
3848 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3849 __isl_take isl_set *set, __isl_take isl_aff *aff);
3850 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3851 __isl_take isl_aff *aff);
3853 A piecewise quasi affine expression that is equal to 1 on a set
3854 and 0 outside the set can be created using the following function.
3856 #include <isl/aff.h>
3857 __isl_give isl_pw_aff *isl_set_indicator_function(
3858 __isl_take isl_set *set);
3860 Quasi affine expressions can be copied and freed using
3862 #include <isl/aff.h>
3863 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3864 __isl_null isl_aff *isl_aff_free(__isl_take isl_aff *aff);
3866 __isl_give isl_pw_aff *isl_pw_aff_copy(
3867 __isl_keep isl_pw_aff *pwaff);
3868 __isl_null isl_pw_aff *isl_pw_aff_free(
3869 __isl_take isl_pw_aff *pwaff);
3871 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3872 using the following function. The constraint is required to have
3873 a non-zero coefficient for the specified dimension.
3875 #include <isl/constraint.h>
3876 __isl_give isl_aff *isl_constraint_get_bound(
3877 __isl_keep isl_constraint *constraint,
3878 enum isl_dim_type type, int pos);
3880 The entire affine expression of the constraint can also be extracted
3881 using the following function.
3883 #include <isl/constraint.h>
3884 __isl_give isl_aff *isl_constraint_get_aff(
3885 __isl_keep isl_constraint *constraint);
3887 Conversely, an equality constraint equating
3888 the affine expression to zero or an inequality constraint enforcing
3889 the affine expression to be non-negative, can be constructed using
3891 __isl_give isl_constraint *isl_equality_from_aff(
3892 __isl_take isl_aff *aff);
3893 __isl_give isl_constraint *isl_inequality_from_aff(
3894 __isl_take isl_aff *aff);
3896 The expression can be inspected using
3898 #include <isl/aff.h>
3899 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3900 int isl_aff_dim(__isl_keep isl_aff *aff,
3901 enum isl_dim_type type);
3902 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3903 __isl_keep isl_aff *aff);
3904 __isl_give isl_local_space *isl_aff_get_local_space(
3905 __isl_keep isl_aff *aff);
3906 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3907 enum isl_dim_type type, unsigned pos);
3908 const char *isl_pw_aff_get_dim_name(
3909 __isl_keep isl_pw_aff *pa,
3910 enum isl_dim_type type, unsigned pos);
3911 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3912 enum isl_dim_type type, unsigned pos);
3913 __isl_give isl_id *isl_pw_aff_get_dim_id(
3914 __isl_keep isl_pw_aff *pa,
3915 enum isl_dim_type type, unsigned pos);
3916 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
3917 enum isl_dim_type type);
3918 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3919 __isl_keep isl_pw_aff *pa,
3920 enum isl_dim_type type);
3921 __isl_give isl_val *isl_aff_get_constant_val(
3922 __isl_keep isl_aff *aff);
3923 __isl_give isl_val *isl_aff_get_coefficient_val(
3924 __isl_keep isl_aff *aff,
3925 enum isl_dim_type type, int pos);
3926 __isl_give isl_val *isl_aff_get_denominator_val(
3927 __isl_keep isl_aff *aff);
3928 __isl_give isl_aff *isl_aff_get_div(
3929 __isl_keep isl_aff *aff, int pos);
3931 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3932 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3933 int (*fn)(__isl_take isl_set *set,
3934 __isl_take isl_aff *aff,
3935 void *user), void *user);
3937 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3938 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3940 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3941 enum isl_dim_type type, unsigned first, unsigned n);
3942 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3943 enum isl_dim_type type, unsigned first, unsigned n);
3945 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3946 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3947 enum isl_dim_type type);
3948 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3950 It can be modified using
3952 #include <isl/aff.h>
3953 __isl_give isl_aff *isl_aff_set_tuple_id(
3954 __isl_take isl_aff *aff,
3955 enum isl_dim_type type, __isl_take isl_id *id);
3956 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3957 __isl_take isl_pw_aff *pwaff,
3958 enum isl_dim_type type, __isl_take isl_id *id);
3959 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
3960 __isl_take isl_pw_aff *pa,
3961 enum isl_dim_type type);
3962 __isl_give isl_aff *isl_aff_set_dim_name(
3963 __isl_take isl_aff *aff, enum isl_dim_type type,
3964 unsigned pos, const char *s);
3965 __isl_give isl_aff *isl_aff_set_dim_id(
3966 __isl_take isl_aff *aff, enum isl_dim_type type,
3967 unsigned pos, __isl_take isl_id *id);
3968 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3969 __isl_take isl_pw_aff *pma,
3970 enum isl_dim_type type, unsigned pos,
3971 __isl_take isl_id *id);
3972 __isl_give isl_aff *isl_aff_set_constant_si(
3973 __isl_take isl_aff *aff, int v);
3974 __isl_give isl_aff *isl_aff_set_constant_val(
3975 __isl_take isl_aff *aff, __isl_take isl_val *v);
3976 __isl_give isl_aff *isl_aff_set_coefficient_si(
3977 __isl_take isl_aff *aff,
3978 enum isl_dim_type type, int pos, int v);
3979 __isl_give isl_aff *isl_aff_set_coefficient_val(
3980 __isl_take isl_aff *aff,
3981 enum isl_dim_type type, int pos,
3982 __isl_take isl_val *v);
3984 __isl_give isl_aff *isl_aff_add_constant_si(
3985 __isl_take isl_aff *aff, int v);
3986 __isl_give isl_aff *isl_aff_add_constant_val(
3987 __isl_take isl_aff *aff, __isl_take isl_val *v);
3988 __isl_give isl_aff *isl_aff_add_constant_num_si(
3989 __isl_take isl_aff *aff, int v);
3990 __isl_give isl_aff *isl_aff_add_coefficient_si(
3991 __isl_take isl_aff *aff,
3992 enum isl_dim_type type, int pos, int v);
3993 __isl_give isl_aff *isl_aff_add_coefficient_val(
3994 __isl_take isl_aff *aff,
3995 enum isl_dim_type type, int pos,
3996 __isl_take isl_val *v);
3998 __isl_give isl_aff *isl_aff_insert_dims(
3999 __isl_take isl_aff *aff,
4000 enum isl_dim_type type, unsigned first, unsigned n);
4001 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
4002 __isl_take isl_pw_aff *pwaff,
4003 enum isl_dim_type type, unsigned first, unsigned n);
4004 __isl_give isl_aff *isl_aff_add_dims(
4005 __isl_take isl_aff *aff,
4006 enum isl_dim_type type, unsigned n);
4007 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
4008 __isl_take isl_pw_aff *pwaff,
4009 enum isl_dim_type type, unsigned n);
4010 __isl_give isl_aff *isl_aff_drop_dims(
4011 __isl_take isl_aff *aff,
4012 enum isl_dim_type type, unsigned first, unsigned n);
4013 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
4014 __isl_take isl_pw_aff *pwaff,
4015 enum isl_dim_type type, unsigned first, unsigned n);
4016 __isl_give isl_aff *isl_aff_move_dims(
4017 __isl_take isl_aff *aff,
4018 enum isl_dim_type dst_type, unsigned dst_pos,
4019 enum isl_dim_type src_type, unsigned src_pos,
4021 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
4022 __isl_take isl_pw_aff *pa,
4023 enum isl_dim_type dst_type, unsigned dst_pos,
4024 enum isl_dim_type src_type, unsigned src_pos,
4027 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
4028 set the I<numerator> of the constant or coefficient, while
4029 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
4030 the constant or coefficient as a whole.
4031 The C<add_constant> and C<add_coefficient> functions add an integer
4032 or rational value to
4033 the possibly rational constant or coefficient.
4034 The C<add_constant_num> functions add an integer value to
4037 To check whether an affine expressions is obviously zero
4038 or (obviously) equal to some other affine expression, use
4040 #include <isl/aff.h>
4041 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
4042 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
4043 __isl_keep isl_aff *aff2);
4044 int isl_pw_aff_plain_is_equal(
4045 __isl_keep isl_pw_aff *pwaff1,
4046 __isl_keep isl_pw_aff *pwaff2);
4047 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
4048 __isl_keep isl_pw_aff *pa2);
4049 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4050 __isl_keep isl_pw_aff *pa2);
4052 The function C<isl_pw_aff_plain_cmp> can be used to sort
4053 C<isl_pw_aff>s. The order is not strictly defined.
4054 The current order sorts expressions that only involve
4055 earlier dimensions before those that involve later dimensions.
4059 #include <isl/aff.h>
4060 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
4061 __isl_take isl_aff *aff2);
4062 __isl_give isl_pw_aff *isl_pw_aff_add(
4063 __isl_take isl_pw_aff *pwaff1,
4064 __isl_take isl_pw_aff *pwaff2);
4065 __isl_give isl_pw_aff *isl_pw_aff_min(
4066 __isl_take isl_pw_aff *pwaff1,
4067 __isl_take isl_pw_aff *pwaff2);
4068 __isl_give isl_pw_aff *isl_pw_aff_max(
4069 __isl_take isl_pw_aff *pwaff1,
4070 __isl_take isl_pw_aff *pwaff2);
4071 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
4072 __isl_take isl_aff *aff2);
4073 __isl_give isl_pw_aff *isl_pw_aff_sub(
4074 __isl_take isl_pw_aff *pwaff1,
4075 __isl_take isl_pw_aff *pwaff2);
4076 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
4077 __isl_give isl_pw_aff *isl_pw_aff_neg(
4078 __isl_take isl_pw_aff *pwaff);
4079 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
4080 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4081 __isl_take isl_pw_aff *pwaff);
4082 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
4083 __isl_give isl_pw_aff *isl_pw_aff_floor(
4084 __isl_take isl_pw_aff *pwaff);
4085 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
4086 __isl_take isl_val *mod);
4087 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
4088 __isl_take isl_pw_aff *pa,
4089 __isl_take isl_val *mod);
4090 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
4091 __isl_take isl_val *v);
4092 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
4093 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
4094 __isl_give isl_aff *isl_aff_scale_down_ui(
4095 __isl_take isl_aff *aff, unsigned f);
4096 __isl_give isl_aff *isl_aff_scale_down_val(
4097 __isl_take isl_aff *aff, __isl_take isl_val *v);
4098 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
4099 __isl_take isl_pw_aff *pa,
4100 __isl_take isl_val *f);
4102 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4103 __isl_take isl_pw_aff_list *list);
4104 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4105 __isl_take isl_pw_aff_list *list);
4107 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4108 __isl_take isl_pw_aff *pwqp);
4110 __isl_give isl_aff *isl_aff_align_params(
4111 __isl_take isl_aff *aff,
4112 __isl_take isl_space *model);
4113 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4114 __isl_take isl_pw_aff *pwaff,
4115 __isl_take isl_space *model);
4117 __isl_give isl_aff *isl_aff_project_domain_on_params(
4118 __isl_take isl_aff *aff);
4119 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4120 __isl_take isl_pw_aff *pwa);
4122 __isl_give isl_aff *isl_aff_gist_params(
4123 __isl_take isl_aff *aff,
4124 __isl_take isl_set *context);
4125 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
4126 __isl_take isl_set *context);
4127 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
4128 __isl_take isl_pw_aff *pwaff,
4129 __isl_take isl_set *context);
4130 __isl_give isl_pw_aff *isl_pw_aff_gist(
4131 __isl_take isl_pw_aff *pwaff,
4132 __isl_take isl_set *context);
4134 __isl_give isl_set *isl_pw_aff_domain(
4135 __isl_take isl_pw_aff *pwaff);
4136 __isl_give isl_set *isl_pw_aff_params(
4137 __isl_take isl_pw_aff *pwa);
4138 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4139 __isl_take isl_pw_aff *pa,
4140 __isl_take isl_set *set);
4141 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4142 __isl_take isl_pw_aff *pa,
4143 __isl_take isl_set *set);
4145 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
4146 __isl_take isl_aff *aff2);
4147 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
4148 __isl_take isl_aff *aff2);
4149 __isl_give isl_pw_aff *isl_pw_aff_mul(
4150 __isl_take isl_pw_aff *pwaff1,
4151 __isl_take isl_pw_aff *pwaff2);
4152 __isl_give isl_pw_aff *isl_pw_aff_div(
4153 __isl_take isl_pw_aff *pa1,
4154 __isl_take isl_pw_aff *pa2);
4155 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
4156 __isl_take isl_pw_aff *pa1,
4157 __isl_take isl_pw_aff *pa2);
4158 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
4159 __isl_take isl_pw_aff *pa1,
4160 __isl_take isl_pw_aff *pa2);
4162 When multiplying two affine expressions, at least one of the two needs
4163 to be a constant. Similarly, when dividing an affine expression by another,
4164 the second expression needs to be a constant.
4165 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
4166 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
4169 #include <isl/aff.h>
4170 __isl_give isl_aff *isl_aff_pullback_aff(
4171 __isl_take isl_aff *aff1,
4172 __isl_take isl_aff *aff2);
4173 __isl_give isl_aff *isl_aff_pullback_multi_aff(
4174 __isl_take isl_aff *aff,
4175 __isl_take isl_multi_aff *ma);
4176 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
4177 __isl_take isl_pw_aff *pa,
4178 __isl_take isl_multi_aff *ma);
4179 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
4180 __isl_take isl_pw_aff *pa,
4181 __isl_take isl_pw_multi_aff *pma);
4182 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
4183 __isl_take isl_pw_aff *pa,
4184 __isl_take isl_multi_pw_aff *mpa);
4186 These functions precompose the input expression by the given
4187 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
4188 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
4189 into the (piecewise) affine expression.
4190 Objects of type C<isl_multi_aff> are described in
4191 L</"Piecewise Multiple Quasi Affine Expressions">.
4193 #include <isl/aff.h>
4194 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4195 __isl_take isl_aff *aff);
4196 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4197 __isl_take isl_aff *aff);
4198 __isl_give isl_basic_set *isl_aff_le_basic_set(
4199 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4200 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4201 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4202 __isl_give isl_set *isl_pw_aff_eq_set(
4203 __isl_take isl_pw_aff *pwaff1,
4204 __isl_take isl_pw_aff *pwaff2);
4205 __isl_give isl_set *isl_pw_aff_ne_set(
4206 __isl_take isl_pw_aff *pwaff1,
4207 __isl_take isl_pw_aff *pwaff2);
4208 __isl_give isl_set *isl_pw_aff_le_set(
4209 __isl_take isl_pw_aff *pwaff1,
4210 __isl_take isl_pw_aff *pwaff2);
4211 __isl_give isl_set *isl_pw_aff_lt_set(
4212 __isl_take isl_pw_aff *pwaff1,
4213 __isl_take isl_pw_aff *pwaff2);
4214 __isl_give isl_set *isl_pw_aff_ge_set(
4215 __isl_take isl_pw_aff *pwaff1,
4216 __isl_take isl_pw_aff *pwaff2);
4217 __isl_give isl_set *isl_pw_aff_gt_set(
4218 __isl_take isl_pw_aff *pwaff1,
4219 __isl_take isl_pw_aff *pwaff2);
4221 __isl_give isl_set *isl_pw_aff_list_eq_set(
4222 __isl_take isl_pw_aff_list *list1,
4223 __isl_take isl_pw_aff_list *list2);
4224 __isl_give isl_set *isl_pw_aff_list_ne_set(
4225 __isl_take isl_pw_aff_list *list1,
4226 __isl_take isl_pw_aff_list *list2);
4227 __isl_give isl_set *isl_pw_aff_list_le_set(
4228 __isl_take isl_pw_aff_list *list1,
4229 __isl_take isl_pw_aff_list *list2);
4230 __isl_give isl_set *isl_pw_aff_list_lt_set(
4231 __isl_take isl_pw_aff_list *list1,
4232 __isl_take isl_pw_aff_list *list2);
4233 __isl_give isl_set *isl_pw_aff_list_ge_set(
4234 __isl_take isl_pw_aff_list *list1,
4235 __isl_take isl_pw_aff_list *list2);
4236 __isl_give isl_set *isl_pw_aff_list_gt_set(
4237 __isl_take isl_pw_aff_list *list1,
4238 __isl_take isl_pw_aff_list *list2);
4240 The function C<isl_aff_neg_basic_set> returns a basic set
4241 containing those elements in the domain space
4242 of C<aff> where C<aff> is negative.
4243 The function C<isl_aff_ge_basic_set> returns a basic set
4244 containing those elements in the shared space
4245 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4246 The function C<isl_pw_aff_ge_set> returns a set
4247 containing those elements in the shared domain
4248 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4249 The functions operating on C<isl_pw_aff_list> apply the corresponding
4250 C<isl_pw_aff> function to each pair of elements in the two lists.
4252 #include <isl/aff.h>
4253 __isl_give isl_set *isl_pw_aff_nonneg_set(
4254 __isl_take isl_pw_aff *pwaff);
4255 __isl_give isl_set *isl_pw_aff_zero_set(
4256 __isl_take isl_pw_aff *pwaff);
4257 __isl_give isl_set *isl_pw_aff_non_zero_set(
4258 __isl_take isl_pw_aff *pwaff);
4260 The function C<isl_pw_aff_nonneg_set> returns a set
4261 containing those elements in the domain
4262 of C<pwaff> where C<pwaff> is non-negative.
4264 #include <isl/aff.h>
4265 __isl_give isl_pw_aff *isl_pw_aff_cond(
4266 __isl_take isl_pw_aff *cond,
4267 __isl_take isl_pw_aff *pwaff_true,
4268 __isl_take isl_pw_aff *pwaff_false);
4270 The function C<isl_pw_aff_cond> performs a conditional operator
4271 and returns an expression that is equal to C<pwaff_true>
4272 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4273 where C<cond> is zero.
4275 #include <isl/aff.h>
4276 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4277 __isl_take isl_pw_aff *pwaff1,
4278 __isl_take isl_pw_aff *pwaff2);
4279 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4280 __isl_take isl_pw_aff *pwaff1,
4281 __isl_take isl_pw_aff *pwaff2);
4282 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4283 __isl_take isl_pw_aff *pwaff1,
4284 __isl_take isl_pw_aff *pwaff2);
4286 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4287 expression with a domain that is the union of those of C<pwaff1> and
4288 C<pwaff2> and such that on each cell, the quasi-affine expression is
4289 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4290 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4291 associated expression is the defined one.
4293 An expression can be read from input using
4295 #include <isl/aff.h>
4296 __isl_give isl_aff *isl_aff_read_from_str(
4297 isl_ctx *ctx, const char *str);
4298 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4299 isl_ctx *ctx, const char *str);
4301 An expression can be printed using
4303 #include <isl/aff.h>
4304 __isl_give isl_printer *isl_printer_print_aff(
4305 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4307 __isl_give isl_printer *isl_printer_print_pw_aff(
4308 __isl_take isl_printer *p,
4309 __isl_keep isl_pw_aff *pwaff);
4311 =head2 Piecewise Multiple Quasi Affine Expressions
4313 An C<isl_multi_aff> object represents a sequence of
4314 zero or more affine expressions, all defined on the same domain space.
4315 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4316 zero or more piecewise affine expressions.
4318 An C<isl_multi_aff> can be constructed from a single
4319 C<isl_aff> or an C<isl_aff_list> using the
4320 following functions. Similarly for C<isl_multi_pw_aff>
4321 and C<isl_pw_multi_aff>.
4323 #include <isl/aff.h>
4324 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4325 __isl_take isl_aff *aff);
4326 __isl_give isl_multi_pw_aff *
4327 isl_multi_pw_aff_from_multi_aff(
4328 __isl_take isl_multi_aff *ma);
4329 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4330 __isl_take isl_pw_aff *pa);
4331 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4332 __isl_take isl_pw_aff *pa);
4333 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4334 __isl_take isl_space *space,
4335 __isl_take isl_aff_list *list);
4337 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4338 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4339 Note however that the domain
4340 of the result is the intersection of the domains of the input.
4341 The reverse conversion is exact.
4343 #include <isl/aff.h>
4344 __isl_give isl_pw_multi_aff *
4345 isl_pw_multi_aff_from_multi_pw_aff(
4346 __isl_take isl_multi_pw_aff *mpa);
4347 __isl_give isl_multi_pw_aff *
4348 isl_multi_pw_aff_from_pw_multi_aff(
4349 __isl_take isl_pw_multi_aff *pma);
4351 An empty piecewise multiple quasi affine expression (one with no cells),
4352 the zero piecewise multiple quasi affine expression (with value zero
4353 for each output dimension),
4354 a piecewise multiple quasi affine expression with a single cell (with
4355 either a universe or a specified domain) or
4356 a zero-dimensional piecewise multiple quasi affine expression
4358 can be created using the following functions.
4360 #include <isl/aff.h>
4361 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4362 __isl_take isl_space *space);
4363 __isl_give isl_multi_aff *isl_multi_aff_zero(
4364 __isl_take isl_space *space);
4365 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4366 __isl_take isl_space *space);
4367 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4368 __isl_take isl_space *space);
4369 __isl_give isl_multi_aff *isl_multi_aff_identity(
4370 __isl_take isl_space *space);
4371 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4372 __isl_take isl_space *space);
4373 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4374 __isl_take isl_space *space);
4375 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4376 __isl_take isl_space *space);
4377 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4378 __isl_take isl_space *space);
4379 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4380 __isl_take isl_space *space,
4381 enum isl_dim_type type,
4382 unsigned first, unsigned n);
4383 __isl_give isl_pw_multi_aff *
4384 isl_pw_multi_aff_project_out_map(
4385 __isl_take isl_space *space,
4386 enum isl_dim_type type,
4387 unsigned first, unsigned n);
4388 __isl_give isl_pw_multi_aff *
4389 isl_pw_multi_aff_from_multi_aff(
4390 __isl_take isl_multi_aff *ma);
4391 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4392 __isl_take isl_set *set,
4393 __isl_take isl_multi_aff *maff);
4394 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4395 __isl_take isl_set *set);
4397 __isl_give isl_union_pw_multi_aff *
4398 isl_union_pw_multi_aff_empty(
4399 __isl_take isl_space *space);
4400 __isl_give isl_union_pw_multi_aff *
4401 isl_union_pw_multi_aff_add_pw_multi_aff(
4402 __isl_take isl_union_pw_multi_aff *upma,
4403 __isl_take isl_pw_multi_aff *pma);
4404 __isl_give isl_union_pw_multi_aff *
4405 isl_union_pw_multi_aff_from_domain(
4406 __isl_take isl_union_set *uset);
4408 A piecewise multiple quasi affine expression can also be initialized
4409 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4410 and the C<isl_map> is single-valued.
4411 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4412 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4414 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4415 __isl_take isl_set *set);
4416 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4417 __isl_take isl_map *map);
4419 __isl_give isl_union_pw_multi_aff *
4420 isl_union_pw_multi_aff_from_union_set(
4421 __isl_take isl_union_set *uset);
4422 __isl_give isl_union_pw_multi_aff *
4423 isl_union_pw_multi_aff_from_union_map(
4424 __isl_take isl_union_map *umap);
4426 Multiple quasi affine expressions can be copied and freed using
4428 #include <isl/aff.h>
4429 __isl_give isl_multi_aff *isl_multi_aff_copy(
4430 __isl_keep isl_multi_aff *maff);
4431 __isl_null isl_multi_aff *isl_multi_aff_free(
4432 __isl_take isl_multi_aff *maff);
4434 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4435 __isl_keep isl_pw_multi_aff *pma);
4436 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
4437 __isl_take isl_pw_multi_aff *pma);
4439 __isl_give isl_union_pw_multi_aff *
4440 isl_union_pw_multi_aff_copy(
4441 __isl_keep isl_union_pw_multi_aff *upma);
4442 __isl_null isl_union_pw_multi_aff *
4443 isl_union_pw_multi_aff_free(
4444 __isl_take isl_union_pw_multi_aff *upma);
4446 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4447 __isl_keep isl_multi_pw_aff *mpa);
4448 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
4449 __isl_take isl_multi_pw_aff *mpa);
4451 The expression can be inspected using
4453 #include <isl/aff.h>
4454 isl_ctx *isl_multi_aff_get_ctx(
4455 __isl_keep isl_multi_aff *maff);
4456 isl_ctx *isl_pw_multi_aff_get_ctx(
4457 __isl_keep isl_pw_multi_aff *pma);
4458 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4459 __isl_keep isl_union_pw_multi_aff *upma);
4460 isl_ctx *isl_multi_pw_aff_get_ctx(
4461 __isl_keep isl_multi_pw_aff *mpa);
4463 int isl_multi_aff_involves_dims(
4464 __isl_keep isl_multi_aff *ma,
4465 enum isl_dim_type type, unsigned first, unsigned n);
4466 int isl_multi_pw_aff_involves_dims(
4467 __isl_keep isl_multi_pw_aff *mpa,
4468 enum isl_dim_type type, unsigned first, unsigned n);
4470 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4471 enum isl_dim_type type);
4472 unsigned isl_pw_multi_aff_dim(
4473 __isl_keep isl_pw_multi_aff *pma,
4474 enum isl_dim_type type);
4475 unsigned isl_multi_pw_aff_dim(
4476 __isl_keep isl_multi_pw_aff *mpa,
4477 enum isl_dim_type type);
4478 __isl_give isl_aff *isl_multi_aff_get_aff(
4479 __isl_keep isl_multi_aff *multi, int pos);
4480 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4481 __isl_keep isl_pw_multi_aff *pma, int pos);
4482 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4483 __isl_keep isl_multi_pw_aff *mpa, int pos);
4484 int isl_multi_aff_find_dim_by_id(
4485 __isl_keep isl_multi_aff *ma,
4486 enum isl_dim_type type, __isl_keep isl_id *id);
4487 int isl_multi_pw_aff_find_dim_by_id(
4488 __isl_keep isl_multi_pw_aff *mpa,
4489 enum isl_dim_type type, __isl_keep isl_id *id);
4490 const char *isl_pw_multi_aff_get_dim_name(
4491 __isl_keep isl_pw_multi_aff *pma,
4492 enum isl_dim_type type, unsigned pos);
4493 __isl_give isl_id *isl_multi_aff_get_dim_id(
4494 __isl_keep isl_multi_aff *ma,
4495 enum isl_dim_type type, unsigned pos);
4496 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4497 __isl_keep isl_pw_multi_aff *pma,
4498 enum isl_dim_type type, unsigned pos);
4499 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4500 __isl_keep isl_multi_pw_aff *mpa,
4501 enum isl_dim_type type, unsigned pos);
4502 const char *isl_multi_aff_get_tuple_name(
4503 __isl_keep isl_multi_aff *multi,
4504 enum isl_dim_type type);
4505 int isl_pw_multi_aff_has_tuple_name(
4506 __isl_keep isl_pw_multi_aff *pma,
4507 enum isl_dim_type type);
4508 const char *isl_pw_multi_aff_get_tuple_name(
4509 __isl_keep isl_pw_multi_aff *pma,
4510 enum isl_dim_type type);
4511 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4512 enum isl_dim_type type);
4513 int isl_pw_multi_aff_has_tuple_id(
4514 __isl_keep isl_pw_multi_aff *pma,
4515 enum isl_dim_type type);
4516 int isl_multi_pw_aff_has_tuple_id(
4517 __isl_keep isl_multi_pw_aff *mpa,
4518 enum isl_dim_type type);
4519 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4520 __isl_keep isl_multi_aff *ma,
4521 enum isl_dim_type type);
4522 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4523 __isl_keep isl_pw_multi_aff *pma,
4524 enum isl_dim_type type);
4525 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4526 __isl_keep isl_multi_pw_aff *mpa,
4527 enum isl_dim_type type);
4528 int isl_multi_aff_range_is_wrapping(
4529 __isl_keep isl_multi_aff *ma);
4530 int isl_multi_pw_aff_range_is_wrapping(
4531 __isl_keep isl_multi_pw_aff *mpa);
4533 int isl_pw_multi_aff_foreach_piece(
4534 __isl_keep isl_pw_multi_aff *pma,
4535 int (*fn)(__isl_take isl_set *set,
4536 __isl_take isl_multi_aff *maff,
4537 void *user), void *user);
4539 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4540 __isl_keep isl_union_pw_multi_aff *upma,
4541 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4542 void *user), void *user);
4544 It can be modified using
4546 #include <isl/aff.h>
4547 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4548 __isl_take isl_multi_aff *multi, int pos,
4549 __isl_take isl_aff *aff);
4550 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4551 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4552 __isl_take isl_pw_aff *pa);
4553 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4554 __isl_take isl_multi_aff *maff,
4555 enum isl_dim_type type, unsigned pos, const char *s);
4556 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4557 __isl_take isl_multi_aff *maff,
4558 enum isl_dim_type type, unsigned pos,
4559 __isl_take isl_id *id);
4560 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4561 __isl_take isl_multi_aff *maff,
4562 enum isl_dim_type type, const char *s);
4563 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4564 __isl_take isl_multi_aff *maff,
4565 enum isl_dim_type type, __isl_take isl_id *id);
4566 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4567 __isl_take isl_pw_multi_aff *pma,
4568 enum isl_dim_type type, __isl_take isl_id *id);
4569 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4570 __isl_take isl_multi_aff *ma,
4571 enum isl_dim_type type);
4572 __isl_give isl_multi_pw_aff *
4573 isl_multi_pw_aff_reset_tuple_id(
4574 __isl_take isl_multi_pw_aff *mpa,
4575 enum isl_dim_type type);
4576 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4577 __isl_take isl_multi_aff *ma);
4578 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4579 __isl_take isl_multi_pw_aff *mpa);
4581 __isl_give isl_multi_pw_aff *
4582 isl_multi_pw_aff_set_dim_name(
4583 __isl_take isl_multi_pw_aff *mpa,
4584 enum isl_dim_type type, unsigned pos, const char *s);
4585 __isl_give isl_multi_pw_aff *
4586 isl_multi_pw_aff_set_dim_id(
4587 __isl_take isl_multi_pw_aff *mpa,
4588 enum isl_dim_type type, unsigned pos,
4589 __isl_take isl_id *id);
4590 __isl_give isl_multi_pw_aff *
4591 isl_multi_pw_aff_set_tuple_name(
4592 __isl_take isl_multi_pw_aff *mpa,
4593 enum isl_dim_type type, const char *s);
4595 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4596 __isl_take isl_multi_aff *ma);
4598 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4599 __isl_take isl_multi_aff *ma,
4600 enum isl_dim_type type, unsigned first, unsigned n);
4601 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4602 __isl_take isl_multi_aff *ma,
4603 enum isl_dim_type type, unsigned n);
4604 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4605 __isl_take isl_multi_aff *maff,
4606 enum isl_dim_type type, unsigned first, unsigned n);
4607 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4608 __isl_take isl_pw_multi_aff *pma,
4609 enum isl_dim_type type, unsigned first, unsigned n);
4611 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4612 __isl_take isl_multi_pw_aff *mpa,
4613 enum isl_dim_type type, unsigned first, unsigned n);
4614 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4615 __isl_take isl_multi_pw_aff *mpa,
4616 enum isl_dim_type type, unsigned n);
4617 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4618 __isl_take isl_multi_pw_aff *pma,
4619 enum isl_dim_type dst_type, unsigned dst_pos,
4620 enum isl_dim_type src_type, unsigned src_pos,
4623 To check whether two multiple affine expressions are
4624 (obviously) equal to each other, use
4626 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4627 __isl_keep isl_multi_aff *maff2);
4628 int isl_pw_multi_aff_plain_is_equal(
4629 __isl_keep isl_pw_multi_aff *pma1,
4630 __isl_keep isl_pw_multi_aff *pma2);
4631 int isl_multi_pw_aff_plain_is_equal(
4632 __isl_keep isl_multi_pw_aff *mpa1,
4633 __isl_keep isl_multi_pw_aff *mpa2);
4634 int isl_multi_pw_aff_is_equal(
4635 __isl_keep isl_multi_pw_aff *mpa1,
4636 __isl_keep isl_multi_pw_aff *mpa2);
4640 #include <isl/aff.h>
4641 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4642 __isl_take isl_pw_multi_aff *pma1,
4643 __isl_take isl_pw_multi_aff *pma2);
4644 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4645 __isl_take isl_pw_multi_aff *pma1,
4646 __isl_take isl_pw_multi_aff *pma2);
4647 __isl_give isl_multi_aff *isl_multi_aff_add(
4648 __isl_take isl_multi_aff *maff1,
4649 __isl_take isl_multi_aff *maff2);
4650 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4651 __isl_take isl_pw_multi_aff *pma1,
4652 __isl_take isl_pw_multi_aff *pma2);
4653 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4654 __isl_take isl_union_pw_multi_aff *upma1,
4655 __isl_take isl_union_pw_multi_aff *upma2);
4656 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4657 __isl_take isl_pw_multi_aff *pma1,
4658 __isl_take isl_pw_multi_aff *pma2);
4659 __isl_give isl_multi_aff *isl_multi_aff_sub(
4660 __isl_take isl_multi_aff *ma1,
4661 __isl_take isl_multi_aff *ma2);
4662 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4663 __isl_take isl_pw_multi_aff *pma1,
4664 __isl_take isl_pw_multi_aff *pma2);
4665 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4666 __isl_take isl_union_pw_multi_aff *upma1,
4667 __isl_take isl_union_pw_multi_aff *upma2);
4669 C<isl_multi_aff_sub> subtracts the second argument from the first.
4671 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4672 __isl_take isl_multi_aff *ma,
4673 __isl_take isl_val *v);
4674 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4675 __isl_take isl_pw_multi_aff *pma,
4676 __isl_take isl_val *v);
4677 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4678 __isl_take isl_multi_pw_aff *mpa,
4679 __isl_take isl_val *v);
4680 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4681 __isl_take isl_multi_aff *ma,
4682 __isl_take isl_multi_val *mv);
4683 __isl_give isl_pw_multi_aff *
4684 isl_pw_multi_aff_scale_multi_val(
4685 __isl_take isl_pw_multi_aff *pma,
4686 __isl_take isl_multi_val *mv);
4687 __isl_give isl_multi_pw_aff *
4688 isl_multi_pw_aff_scale_multi_val(
4689 __isl_take isl_multi_pw_aff *mpa,
4690 __isl_take isl_multi_val *mv);
4691 __isl_give isl_union_pw_multi_aff *
4692 isl_union_pw_multi_aff_scale_multi_val(
4693 __isl_take isl_union_pw_multi_aff *upma,
4694 __isl_take isl_multi_val *mv);
4695 __isl_give isl_multi_aff *
4696 isl_multi_aff_scale_down_multi_val(
4697 __isl_take isl_multi_aff *ma,
4698 __isl_take isl_multi_val *mv);
4699 __isl_give isl_multi_pw_aff *
4700 isl_multi_pw_aff_scale_down_multi_val(
4701 __isl_take isl_multi_pw_aff *mpa,
4702 __isl_take isl_multi_val *mv);
4704 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4705 by the corresponding elements of C<mv>.
4707 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4708 __isl_take isl_pw_multi_aff *pma,
4709 enum isl_dim_type type, unsigned pos, int value);
4710 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4711 __isl_take isl_pw_multi_aff *pma,
4712 __isl_take isl_set *set);
4713 __isl_give isl_set *isl_multi_pw_aff_domain(
4714 __isl_take isl_multi_pw_aff *mpa);
4715 __isl_give isl_multi_pw_aff *
4716 isl_multi_pw_aff_intersect_params(
4717 __isl_take isl_multi_pw_aff *mpa,
4718 __isl_take isl_set *set);
4719 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4720 __isl_take isl_pw_multi_aff *pma,
4721 __isl_take isl_set *set);
4722 __isl_give isl_multi_pw_aff *
4723 isl_multi_pw_aff_intersect_domain(
4724 __isl_take isl_multi_pw_aff *mpa,
4725 __isl_take isl_set *domain);
4726 __isl_give isl_union_pw_multi_aff *
4727 isl_union_pw_multi_aff_intersect_domain(
4728 __isl_take isl_union_pw_multi_aff *upma,
4729 __isl_take isl_union_set *uset);
4730 __isl_give isl_multi_aff *isl_multi_aff_lift(
4731 __isl_take isl_multi_aff *maff,
4732 __isl_give isl_local_space **ls);
4733 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4734 __isl_take isl_pw_multi_aff *pma);
4735 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4736 __isl_take isl_multi_pw_aff *mpa);
4737 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4738 __isl_take isl_multi_aff *multi,
4739 __isl_take isl_space *model);
4740 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4741 __isl_take isl_pw_multi_aff *pma,
4742 __isl_take isl_space *model);
4743 __isl_give isl_union_pw_multi_aff *
4744 isl_union_pw_multi_aff_align_params(
4745 __isl_take isl_union_pw_multi_aff *upma,
4746 __isl_take isl_space *model);
4747 __isl_give isl_pw_multi_aff *
4748 isl_pw_multi_aff_project_domain_on_params(
4749 __isl_take isl_pw_multi_aff *pma);
4750 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4751 __isl_take isl_multi_aff *maff,
4752 __isl_take isl_set *context);
4753 __isl_give isl_multi_aff *isl_multi_aff_gist(
4754 __isl_take isl_multi_aff *maff,
4755 __isl_take isl_set *context);
4756 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4757 __isl_take isl_pw_multi_aff *pma,
4758 __isl_take isl_set *set);
4759 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4760 __isl_take isl_pw_multi_aff *pma,
4761 __isl_take isl_set *set);
4762 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4763 __isl_take isl_multi_pw_aff *mpa,
4764 __isl_take isl_set *set);
4765 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4766 __isl_take isl_multi_pw_aff *mpa,
4767 __isl_take isl_set *set);
4768 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4769 __isl_take isl_multi_aff *ma);
4770 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4771 __isl_take isl_multi_pw_aff *mpa);
4772 __isl_give isl_set *isl_pw_multi_aff_domain(
4773 __isl_take isl_pw_multi_aff *pma);
4774 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4775 __isl_take isl_union_pw_multi_aff *upma);
4776 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4777 __isl_take isl_multi_aff *ma1, unsigned pos,
4778 __isl_take isl_multi_aff *ma2);
4779 __isl_give isl_multi_aff *isl_multi_aff_splice(
4780 __isl_take isl_multi_aff *ma1,
4781 unsigned in_pos, unsigned out_pos,
4782 __isl_take isl_multi_aff *ma2);
4783 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4784 __isl_take isl_multi_aff *ma1,
4785 __isl_take isl_multi_aff *ma2);
4786 __isl_give isl_multi_aff *
4787 isl_multi_aff_range_factor_domain(
4788 __isl_take isl_multi_aff *ma);
4789 __isl_give isl_multi_aff *
4790 isl_multi_aff_range_factor_range(
4791 __isl_take isl_multi_aff *ma);
4792 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4793 __isl_take isl_multi_aff *ma1,
4794 __isl_take isl_multi_aff *ma2);
4795 __isl_give isl_multi_aff *isl_multi_aff_product(
4796 __isl_take isl_multi_aff *ma1,
4797 __isl_take isl_multi_aff *ma2);
4798 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4799 __isl_take isl_multi_pw_aff *mpa1,
4800 __isl_take isl_multi_pw_aff *mpa2);
4801 __isl_give isl_pw_multi_aff *
4802 isl_pw_multi_aff_range_product(
4803 __isl_take isl_pw_multi_aff *pma1,
4804 __isl_take isl_pw_multi_aff *pma2);
4805 __isl_give isl_multi_pw_aff *
4806 isl_multi_pw_aff_range_factor_domain(
4807 __isl_take isl_multi_pw_aff *mpa);
4808 __isl_give isl_multi_pw_aff *
4809 isl_multi_pw_aff_range_factor_range(
4810 __isl_take isl_multi_pw_aff *mpa);
4811 __isl_give isl_pw_multi_aff *
4812 isl_pw_multi_aff_flat_range_product(
4813 __isl_take isl_pw_multi_aff *pma1,
4814 __isl_take isl_pw_multi_aff *pma2);
4815 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4816 __isl_take isl_pw_multi_aff *pma1,
4817 __isl_take isl_pw_multi_aff *pma2);
4818 __isl_give isl_union_pw_multi_aff *
4819 isl_union_pw_multi_aff_flat_range_product(
4820 __isl_take isl_union_pw_multi_aff *upma1,
4821 __isl_take isl_union_pw_multi_aff *upma2);
4822 __isl_give isl_multi_pw_aff *
4823 isl_multi_pw_aff_range_splice(
4824 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4825 __isl_take isl_multi_pw_aff *mpa2);
4826 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4827 __isl_take isl_multi_pw_aff *mpa1,
4828 unsigned in_pos, unsigned out_pos,
4829 __isl_take isl_multi_pw_aff *mpa2);
4830 __isl_give isl_multi_pw_aff *
4831 isl_multi_pw_aff_range_product(
4832 __isl_take isl_multi_pw_aff *mpa1,
4833 __isl_take isl_multi_pw_aff *mpa2);
4834 __isl_give isl_multi_pw_aff *
4835 isl_multi_pw_aff_flat_range_product(
4836 __isl_take isl_multi_pw_aff *mpa1,
4837 __isl_take isl_multi_pw_aff *mpa2);
4839 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4840 then it is assigned the local space that lies at the basis of
4841 the lifting applied.
4843 #include <isl/aff.h>
4844 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4845 __isl_take isl_multi_aff *ma1,
4846 __isl_take isl_multi_aff *ma2);
4847 __isl_give isl_pw_multi_aff *
4848 isl_pw_multi_aff_pullback_multi_aff(
4849 __isl_take isl_pw_multi_aff *pma,
4850 __isl_take isl_multi_aff *ma);
4851 __isl_give isl_multi_pw_aff *
4852 isl_multi_pw_aff_pullback_multi_aff(
4853 __isl_take isl_multi_pw_aff *mpa,
4854 __isl_take isl_multi_aff *ma);
4855 __isl_give isl_pw_multi_aff *
4856 isl_pw_multi_aff_pullback_pw_multi_aff(
4857 __isl_take isl_pw_multi_aff *pma1,
4858 __isl_take isl_pw_multi_aff *pma2);
4859 __isl_give isl_multi_pw_aff *
4860 isl_multi_pw_aff_pullback_pw_multi_aff(
4861 __isl_take isl_multi_pw_aff *mpa,
4862 __isl_take isl_pw_multi_aff *pma);
4863 __isl_give isl_multi_pw_aff *
4864 isl_multi_pw_aff_pullback_multi_pw_aff(
4865 __isl_take isl_multi_pw_aff *mpa1,
4866 __isl_take isl_multi_pw_aff *mpa2);
4868 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4869 In other words, C<ma2> is plugged
4872 __isl_give isl_set *isl_multi_aff_lex_le_set(
4873 __isl_take isl_multi_aff *ma1,
4874 __isl_take isl_multi_aff *ma2);
4875 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4876 __isl_take isl_multi_aff *ma1,
4877 __isl_take isl_multi_aff *ma2);
4879 The function C<isl_multi_aff_lex_le_set> returns a set
4880 containing those elements in the shared domain space
4881 where C<ma1> is lexicographically smaller than or
4884 An expression can be read from input using
4886 #include <isl/aff.h>
4887 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4888 isl_ctx *ctx, const char *str);
4889 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4890 isl_ctx *ctx, const char *str);
4891 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4892 isl_ctx *ctx, const char *str);
4893 __isl_give isl_union_pw_multi_aff *
4894 isl_union_pw_multi_aff_read_from_str(
4895 isl_ctx *ctx, const char *str);
4897 An expression can be printed using
4899 #include <isl/aff.h>
4900 __isl_give isl_printer *isl_printer_print_multi_aff(
4901 __isl_take isl_printer *p,
4902 __isl_keep isl_multi_aff *maff);
4903 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4904 __isl_take isl_printer *p,
4905 __isl_keep isl_pw_multi_aff *pma);
4906 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4907 __isl_take isl_printer *p,
4908 __isl_keep isl_union_pw_multi_aff *upma);
4909 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4910 __isl_take isl_printer *p,
4911 __isl_keep isl_multi_pw_aff *mpa);
4915 Points are elements of a set. They can be used to construct
4916 simple sets (boxes) or they can be used to represent the
4917 individual elements of a set.
4918 The zero point (the origin) can be created using
4920 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4922 The coordinates of a point can be inspected, set and changed
4925 __isl_give isl_val *isl_point_get_coordinate_val(
4926 __isl_keep isl_point *pnt,
4927 enum isl_dim_type type, int pos);
4928 __isl_give isl_point *isl_point_set_coordinate_val(
4929 __isl_take isl_point *pnt,
4930 enum isl_dim_type type, int pos,
4931 __isl_take isl_val *v);
4933 __isl_give isl_point *isl_point_add_ui(
4934 __isl_take isl_point *pnt,
4935 enum isl_dim_type type, int pos, unsigned val);
4936 __isl_give isl_point *isl_point_sub_ui(
4937 __isl_take isl_point *pnt,
4938 enum isl_dim_type type, int pos, unsigned val);
4940 Other properties can be obtained using
4942 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4944 Points can be copied or freed using
4946 __isl_give isl_point *isl_point_copy(
4947 __isl_keep isl_point *pnt);
4948 void isl_point_free(__isl_take isl_point *pnt);
4950 A singleton set can be created from a point using
4952 __isl_give isl_basic_set *isl_basic_set_from_point(
4953 __isl_take isl_point *pnt);
4954 __isl_give isl_set *isl_set_from_point(
4955 __isl_take isl_point *pnt);
4957 and a box can be created from two opposite extremal points using
4959 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4960 __isl_take isl_point *pnt1,
4961 __isl_take isl_point *pnt2);
4962 __isl_give isl_set *isl_set_box_from_points(
4963 __isl_take isl_point *pnt1,
4964 __isl_take isl_point *pnt2);
4966 All elements of a B<bounded> (union) set can be enumerated using
4967 the following functions.
4969 int isl_set_foreach_point(__isl_keep isl_set *set,
4970 int (*fn)(__isl_take isl_point *pnt, void *user),
4972 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4973 int (*fn)(__isl_take isl_point *pnt, void *user),
4976 The function C<fn> is called for each integer point in
4977 C<set> with as second argument the last argument of
4978 the C<isl_set_foreach_point> call. The function C<fn>
4979 should return C<0> on success and C<-1> on failure.
4980 In the latter case, C<isl_set_foreach_point> will stop
4981 enumerating and return C<-1> as well.
4982 If the enumeration is performed successfully and to completion,
4983 then C<isl_set_foreach_point> returns C<0>.
4985 To obtain a single point of a (basic) set, use
4987 __isl_give isl_point *isl_basic_set_sample_point(
4988 __isl_take isl_basic_set *bset);
4989 __isl_give isl_point *isl_set_sample_point(
4990 __isl_take isl_set *set);
4992 If C<set> does not contain any (integer) points, then the
4993 resulting point will be ``void'', a property that can be
4996 int isl_point_is_void(__isl_keep isl_point *pnt);
4998 =head2 Piecewise Quasipolynomials
5000 A piecewise quasipolynomial is a particular kind of function that maps
5001 a parametric point to a rational value.
5002 More specifically, a quasipolynomial is a polynomial expression in greatest
5003 integer parts of affine expressions of parameters and variables.
5004 A piecewise quasipolynomial is a subdivision of a given parametric
5005 domain into disjoint cells with a quasipolynomial associated to
5006 each cell. The value of the piecewise quasipolynomial at a given
5007 point is the value of the quasipolynomial associated to the cell
5008 that contains the point. Outside of the union of cells,
5009 the value is assumed to be zero.
5010 For example, the piecewise quasipolynomial
5012 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
5014 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
5015 A given piecewise quasipolynomial has a fixed domain dimension.
5016 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
5017 defined over different domains.
5018 Piecewise quasipolynomials are mainly used by the C<barvinok>
5019 library for representing the number of elements in a parametric set or map.
5020 For example, the piecewise quasipolynomial above represents
5021 the number of points in the map
5023 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
5025 =head3 Input and Output
5027 Piecewise quasipolynomials can be read from input using
5029 __isl_give isl_union_pw_qpolynomial *
5030 isl_union_pw_qpolynomial_read_from_str(
5031 isl_ctx *ctx, const char *str);
5033 Quasipolynomials and piecewise quasipolynomials can be printed
5034 using the following functions.
5036 __isl_give isl_printer *isl_printer_print_qpolynomial(
5037 __isl_take isl_printer *p,
5038 __isl_keep isl_qpolynomial *qp);
5040 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
5041 __isl_take isl_printer *p,
5042 __isl_keep isl_pw_qpolynomial *pwqp);
5044 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
5045 __isl_take isl_printer *p,
5046 __isl_keep isl_union_pw_qpolynomial *upwqp);
5048 The output format of the printer
5049 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5050 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
5052 In case of printing in C<ISL_FORMAT_C>, the user may want
5053 to set the names of all dimensions
5055 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
5056 __isl_take isl_qpolynomial *qp,
5057 enum isl_dim_type type, unsigned pos,
5059 __isl_give isl_pw_qpolynomial *
5060 isl_pw_qpolynomial_set_dim_name(
5061 __isl_take isl_pw_qpolynomial *pwqp,
5062 enum isl_dim_type type, unsigned pos,
5065 =head3 Creating New (Piecewise) Quasipolynomials
5067 Some simple quasipolynomials can be created using the following functions.
5068 More complicated quasipolynomials can be created by applying
5069 operations such as addition and multiplication
5070 on the resulting quasipolynomials
5072 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
5073 __isl_take isl_space *domain);
5074 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
5075 __isl_take isl_space *domain);
5076 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
5077 __isl_take isl_space *domain);
5078 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
5079 __isl_take isl_space *domain);
5080 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
5081 __isl_take isl_space *domain);
5082 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
5083 __isl_take isl_space *domain,
5084 __isl_take isl_val *val);
5085 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
5086 __isl_take isl_space *domain,
5087 enum isl_dim_type type, unsigned pos);
5088 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
5089 __isl_take isl_aff *aff);
5091 Note that the space in which a quasipolynomial lives is a map space
5092 with a one-dimensional range. The C<domain> argument in some of
5093 the functions above corresponds to the domain of this map space.
5095 The zero piecewise quasipolynomial or a piecewise quasipolynomial
5096 with a single cell can be created using the following functions.
5097 Multiple of these single cell piecewise quasipolynomials can
5098 be combined to create more complicated piecewise quasipolynomials.
5100 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
5101 __isl_take isl_space *space);
5102 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
5103 __isl_take isl_set *set,
5104 __isl_take isl_qpolynomial *qp);
5105 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
5106 __isl_take isl_qpolynomial *qp);
5107 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
5108 __isl_take isl_pw_aff *pwaff);
5110 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
5111 __isl_take isl_space *space);
5112 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
5113 __isl_take isl_pw_qpolynomial *pwqp);
5114 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
5115 __isl_take isl_union_pw_qpolynomial *upwqp,
5116 __isl_take isl_pw_qpolynomial *pwqp);
5118 Quasipolynomials can be copied and freed again using the following
5121 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
5122 __isl_keep isl_qpolynomial *qp);
5123 __isl_null isl_qpolynomial *isl_qpolynomial_free(
5124 __isl_take isl_qpolynomial *qp);
5126 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
5127 __isl_keep isl_pw_qpolynomial *pwqp);
5128 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
5129 __isl_take isl_pw_qpolynomial *pwqp);
5131 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
5132 __isl_keep isl_union_pw_qpolynomial *upwqp);
5133 __isl_null isl_union_pw_qpolynomial *
5134 isl_union_pw_qpolynomial_free(
5135 __isl_take isl_union_pw_qpolynomial *upwqp);
5137 =head3 Inspecting (Piecewise) Quasipolynomials
5139 To iterate over all piecewise quasipolynomials in a union
5140 piecewise quasipolynomial, use the following function
5142 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
5143 __isl_keep isl_union_pw_qpolynomial *upwqp,
5144 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
5147 To extract the piecewise quasipolynomial in a given space from a union, use
5149 __isl_give isl_pw_qpolynomial *
5150 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
5151 __isl_keep isl_union_pw_qpolynomial *upwqp,
5152 __isl_take isl_space *space);
5154 To iterate over the cells in a piecewise quasipolynomial,
5155 use either of the following two functions
5157 int isl_pw_qpolynomial_foreach_piece(
5158 __isl_keep isl_pw_qpolynomial *pwqp,
5159 int (*fn)(__isl_take isl_set *set,
5160 __isl_take isl_qpolynomial *qp,
5161 void *user), void *user);
5162 int isl_pw_qpolynomial_foreach_lifted_piece(
5163 __isl_keep isl_pw_qpolynomial *pwqp,
5164 int (*fn)(__isl_take isl_set *set,
5165 __isl_take isl_qpolynomial *qp,
5166 void *user), void *user);
5168 As usual, the function C<fn> should return C<0> on success
5169 and C<-1> on failure. The difference between
5170 C<isl_pw_qpolynomial_foreach_piece> and
5171 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
5172 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
5173 compute unique representations for all existentially quantified
5174 variables and then turn these existentially quantified variables
5175 into extra set variables, adapting the associated quasipolynomial
5176 accordingly. This means that the C<set> passed to C<fn>
5177 will not have any existentially quantified variables, but that
5178 the dimensions of the sets may be different for different
5179 invocations of C<fn>.
5181 The constant term of a quasipolynomial can be extracted using
5183 __isl_give isl_val *isl_qpolynomial_get_constant_val(
5184 __isl_keep isl_qpolynomial *qp);
5186 To iterate over all terms in a quasipolynomial,
5189 int isl_qpolynomial_foreach_term(
5190 __isl_keep isl_qpolynomial *qp,
5191 int (*fn)(__isl_take isl_term *term,
5192 void *user), void *user);
5194 The terms themselves can be inspected and freed using
5197 unsigned isl_term_dim(__isl_keep isl_term *term,
5198 enum isl_dim_type type);
5199 __isl_give isl_val *isl_term_get_coefficient_val(
5200 __isl_keep isl_term *term);
5201 int isl_term_get_exp(__isl_keep isl_term *term,
5202 enum isl_dim_type type, unsigned pos);
5203 __isl_give isl_aff *isl_term_get_div(
5204 __isl_keep isl_term *term, unsigned pos);
5205 void isl_term_free(__isl_take isl_term *term);
5207 Each term is a product of parameters, set variables and
5208 integer divisions. The function C<isl_term_get_exp>
5209 returns the exponent of a given dimensions in the given term.
5211 =head3 Properties of (Piecewise) Quasipolynomials
5213 To check whether two union piecewise quasipolynomials are
5214 obviously equal, use
5216 int isl_union_pw_qpolynomial_plain_is_equal(
5217 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5218 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5220 =head3 Operations on (Piecewise) Quasipolynomials
5222 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5223 __isl_take isl_qpolynomial *qp,
5224 __isl_take isl_val *v);
5225 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5226 __isl_take isl_qpolynomial *qp);
5227 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5228 __isl_take isl_qpolynomial *qp1,
5229 __isl_take isl_qpolynomial *qp2);
5230 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5231 __isl_take isl_qpolynomial *qp1,
5232 __isl_take isl_qpolynomial *qp2);
5233 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5234 __isl_take isl_qpolynomial *qp1,
5235 __isl_take isl_qpolynomial *qp2);
5236 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5237 __isl_take isl_qpolynomial *qp, unsigned exponent);
5239 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5240 __isl_take isl_pw_qpolynomial *pwqp,
5241 enum isl_dim_type type, unsigned n,
5242 __isl_take isl_val *v);
5243 __isl_give isl_pw_qpolynomial *
5244 isl_pw_qpolynomial_scale_val(
5245 __isl_take isl_pw_qpolynomial *pwqp,
5246 __isl_take isl_val *v);
5247 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5248 __isl_take isl_pw_qpolynomial *pwqp1,
5249 __isl_take isl_pw_qpolynomial *pwqp2);
5250 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5251 __isl_take isl_pw_qpolynomial *pwqp1,
5252 __isl_take isl_pw_qpolynomial *pwqp2);
5253 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5254 __isl_take isl_pw_qpolynomial *pwqp1,
5255 __isl_take isl_pw_qpolynomial *pwqp2);
5256 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5257 __isl_take isl_pw_qpolynomial *pwqp);
5258 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5259 __isl_take isl_pw_qpolynomial *pwqp1,
5260 __isl_take isl_pw_qpolynomial *pwqp2);
5261 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5262 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5264 __isl_give isl_union_pw_qpolynomial *
5265 isl_union_pw_qpolynomial_scale_val(
5266 __isl_take isl_union_pw_qpolynomial *upwqp,
5267 __isl_take isl_val *v);
5268 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5269 __isl_take isl_union_pw_qpolynomial *upwqp1,
5270 __isl_take isl_union_pw_qpolynomial *upwqp2);
5271 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5272 __isl_take isl_union_pw_qpolynomial *upwqp1,
5273 __isl_take isl_union_pw_qpolynomial *upwqp2);
5274 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5275 __isl_take isl_union_pw_qpolynomial *upwqp1,
5276 __isl_take isl_union_pw_qpolynomial *upwqp2);
5278 __isl_give isl_val *isl_pw_qpolynomial_eval(
5279 __isl_take isl_pw_qpolynomial *pwqp,
5280 __isl_take isl_point *pnt);
5282 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5283 __isl_take isl_union_pw_qpolynomial *upwqp,
5284 __isl_take isl_point *pnt);
5286 __isl_give isl_set *isl_pw_qpolynomial_domain(
5287 __isl_take isl_pw_qpolynomial *pwqp);
5288 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5289 __isl_take isl_pw_qpolynomial *pwpq,
5290 __isl_take isl_set *set);
5291 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5292 __isl_take isl_pw_qpolynomial *pwpq,
5293 __isl_take isl_set *set);
5295 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5296 __isl_take isl_union_pw_qpolynomial *upwqp);
5297 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5298 __isl_take isl_union_pw_qpolynomial *upwpq,
5299 __isl_take isl_union_set *uset);
5300 __isl_give isl_union_pw_qpolynomial *
5301 isl_union_pw_qpolynomial_intersect_params(
5302 __isl_take isl_union_pw_qpolynomial *upwpq,
5303 __isl_take isl_set *set);
5305 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5306 __isl_take isl_qpolynomial *qp,
5307 __isl_take isl_space *model);
5309 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5310 __isl_take isl_qpolynomial *qp);
5311 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5312 __isl_take isl_pw_qpolynomial *pwqp);
5314 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5315 __isl_take isl_union_pw_qpolynomial *upwqp);
5317 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5318 __isl_take isl_qpolynomial *qp,
5319 __isl_take isl_set *context);
5320 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5321 __isl_take isl_qpolynomial *qp,
5322 __isl_take isl_set *context);
5324 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5325 __isl_take isl_pw_qpolynomial *pwqp,
5326 __isl_take isl_set *context);
5327 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5328 __isl_take isl_pw_qpolynomial *pwqp,
5329 __isl_take isl_set *context);
5331 __isl_give isl_union_pw_qpolynomial *
5332 isl_union_pw_qpolynomial_gist_params(
5333 __isl_take isl_union_pw_qpolynomial *upwqp,
5334 __isl_take isl_set *context);
5335 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5336 __isl_take isl_union_pw_qpolynomial *upwqp,
5337 __isl_take isl_union_set *context);
5339 The gist operation applies the gist operation to each of
5340 the cells in the domain of the input piecewise quasipolynomial.
5341 The context is also exploited
5342 to simplify the quasipolynomials associated to each cell.
5344 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5345 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5346 __isl_give isl_union_pw_qpolynomial *
5347 isl_union_pw_qpolynomial_to_polynomial(
5348 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5350 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5351 the polynomial will be an overapproximation. If C<sign> is negative,
5352 it will be an underapproximation. If C<sign> is zero, the approximation
5353 will lie somewhere in between.
5355 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5357 A piecewise quasipolynomial reduction is a piecewise
5358 reduction (or fold) of quasipolynomials.
5359 In particular, the reduction can be maximum or a minimum.
5360 The objects are mainly used to represent the result of
5361 an upper or lower bound on a quasipolynomial over its domain,
5362 i.e., as the result of the following function.
5364 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5365 __isl_take isl_pw_qpolynomial *pwqp,
5366 enum isl_fold type, int *tight);
5368 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5369 __isl_take isl_union_pw_qpolynomial *upwqp,
5370 enum isl_fold type, int *tight);
5372 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5373 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5374 is the returned bound is known be tight, i.e., for each value
5375 of the parameters there is at least
5376 one element in the domain that reaches the bound.
5377 If the domain of C<pwqp> is not wrapping, then the bound is computed
5378 over all elements in that domain and the result has a purely parametric
5379 domain. If the domain of C<pwqp> is wrapping, then the bound is
5380 computed over the range of the wrapped relation. The domain of the
5381 wrapped relation becomes the domain of the result.
5383 A (piecewise) quasipolynomial reduction can be copied or freed using the
5384 following functions.
5386 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5387 __isl_keep isl_qpolynomial_fold *fold);
5388 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5389 __isl_keep isl_pw_qpolynomial_fold *pwf);
5390 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5391 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5392 void isl_qpolynomial_fold_free(
5393 __isl_take isl_qpolynomial_fold *fold);
5394 __isl_null isl_pw_qpolynomial_fold *
5395 isl_pw_qpolynomial_fold_free(
5396 __isl_take isl_pw_qpolynomial_fold *pwf);
5397 __isl_null isl_union_pw_qpolynomial_fold *
5398 isl_union_pw_qpolynomial_fold_free(
5399 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5401 =head3 Printing Piecewise Quasipolynomial Reductions
5403 Piecewise quasipolynomial reductions can be printed
5404 using the following function.
5406 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5407 __isl_take isl_printer *p,
5408 __isl_keep isl_pw_qpolynomial_fold *pwf);
5409 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5410 __isl_take isl_printer *p,
5411 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5413 For C<isl_printer_print_pw_qpolynomial_fold>,
5414 output format of the printer
5415 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5416 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5417 output format of the printer
5418 needs to be set to C<ISL_FORMAT_ISL>.
5419 In case of printing in C<ISL_FORMAT_C>, the user may want
5420 to set the names of all dimensions
5422 __isl_give isl_pw_qpolynomial_fold *
5423 isl_pw_qpolynomial_fold_set_dim_name(
5424 __isl_take isl_pw_qpolynomial_fold *pwf,
5425 enum isl_dim_type type, unsigned pos,
5428 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5430 To iterate over all piecewise quasipolynomial reductions in a union
5431 piecewise quasipolynomial reduction, use the following function
5433 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5434 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5435 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5436 void *user), void *user);
5438 To iterate over the cells in a piecewise quasipolynomial reduction,
5439 use either of the following two functions
5441 int isl_pw_qpolynomial_fold_foreach_piece(
5442 __isl_keep isl_pw_qpolynomial_fold *pwf,
5443 int (*fn)(__isl_take isl_set *set,
5444 __isl_take isl_qpolynomial_fold *fold,
5445 void *user), void *user);
5446 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5447 __isl_keep isl_pw_qpolynomial_fold *pwf,
5448 int (*fn)(__isl_take isl_set *set,
5449 __isl_take isl_qpolynomial_fold *fold,
5450 void *user), void *user);
5452 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5453 of the difference between these two functions.
5455 To iterate over all quasipolynomials in a reduction, use
5457 int isl_qpolynomial_fold_foreach_qpolynomial(
5458 __isl_keep isl_qpolynomial_fold *fold,
5459 int (*fn)(__isl_take isl_qpolynomial *qp,
5460 void *user), void *user);
5462 =head3 Properties of Piecewise Quasipolynomial Reductions
5464 To check whether two union piecewise quasipolynomial reductions are
5465 obviously equal, use
5467 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5468 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5469 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5471 =head3 Operations on Piecewise Quasipolynomial Reductions
5473 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5474 __isl_take isl_qpolynomial_fold *fold,
5475 __isl_take isl_val *v);
5476 __isl_give isl_pw_qpolynomial_fold *
5477 isl_pw_qpolynomial_fold_scale_val(
5478 __isl_take isl_pw_qpolynomial_fold *pwf,
5479 __isl_take isl_val *v);
5480 __isl_give isl_union_pw_qpolynomial_fold *
5481 isl_union_pw_qpolynomial_fold_scale_val(
5482 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5483 __isl_take isl_val *v);
5485 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5486 __isl_take isl_pw_qpolynomial_fold *pwf1,
5487 __isl_take isl_pw_qpolynomial_fold *pwf2);
5489 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5490 __isl_take isl_pw_qpolynomial_fold *pwf1,
5491 __isl_take isl_pw_qpolynomial_fold *pwf2);
5493 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5494 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5495 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5497 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5498 __isl_take isl_pw_qpolynomial_fold *pwf,
5499 __isl_take isl_point *pnt);
5501 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5502 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5503 __isl_take isl_point *pnt);
5505 __isl_give isl_pw_qpolynomial_fold *
5506 isl_pw_qpolynomial_fold_intersect_params(
5507 __isl_take isl_pw_qpolynomial_fold *pwf,
5508 __isl_take isl_set *set);
5510 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5511 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5512 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5513 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5514 __isl_take isl_union_set *uset);
5515 __isl_give isl_union_pw_qpolynomial_fold *
5516 isl_union_pw_qpolynomial_fold_intersect_params(
5517 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5518 __isl_take isl_set *set);
5520 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5521 __isl_take isl_pw_qpolynomial_fold *pwf);
5523 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5524 __isl_take isl_pw_qpolynomial_fold *pwf);
5526 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5527 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5529 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5530 __isl_take isl_qpolynomial_fold *fold,
5531 __isl_take isl_set *context);
5532 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5533 __isl_take isl_qpolynomial_fold *fold,
5534 __isl_take isl_set *context);
5536 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5537 __isl_take isl_pw_qpolynomial_fold *pwf,
5538 __isl_take isl_set *context);
5539 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5540 __isl_take isl_pw_qpolynomial_fold *pwf,
5541 __isl_take isl_set *context);
5543 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5544 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5545 __isl_take isl_union_set *context);
5546 __isl_give isl_union_pw_qpolynomial_fold *
5547 isl_union_pw_qpolynomial_fold_gist_params(
5548 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5549 __isl_take isl_set *context);
5551 The gist operation applies the gist operation to each of
5552 the cells in the domain of the input piecewise quasipolynomial reduction.
5553 In future, the operation will also exploit the context
5554 to simplify the quasipolynomial reductions associated to each cell.
5556 __isl_give isl_pw_qpolynomial_fold *
5557 isl_set_apply_pw_qpolynomial_fold(
5558 __isl_take isl_set *set,
5559 __isl_take isl_pw_qpolynomial_fold *pwf,
5561 __isl_give isl_pw_qpolynomial_fold *
5562 isl_map_apply_pw_qpolynomial_fold(
5563 __isl_take isl_map *map,
5564 __isl_take isl_pw_qpolynomial_fold *pwf,
5566 __isl_give isl_union_pw_qpolynomial_fold *
5567 isl_union_set_apply_union_pw_qpolynomial_fold(
5568 __isl_take isl_union_set *uset,
5569 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5571 __isl_give isl_union_pw_qpolynomial_fold *
5572 isl_union_map_apply_union_pw_qpolynomial_fold(
5573 __isl_take isl_union_map *umap,
5574 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5577 The functions taking a map
5578 compose the given map with the given piecewise quasipolynomial reduction.
5579 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5580 over all elements in the intersection of the range of the map
5581 and the domain of the piecewise quasipolynomial reduction
5582 as a function of an element in the domain of the map.
5583 The functions taking a set compute a bound over all elements in the
5584 intersection of the set and the domain of the
5585 piecewise quasipolynomial reduction.
5587 =head2 Parametric Vertex Enumeration
5589 The parametric vertex enumeration described in this section
5590 is mainly intended to be used internally and by the C<barvinok>
5593 #include <isl/vertices.h>
5594 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5595 __isl_keep isl_basic_set *bset);
5597 The function C<isl_basic_set_compute_vertices> performs the
5598 actual computation of the parametric vertices and the chamber
5599 decomposition and store the result in an C<isl_vertices> object.
5600 This information can be queried by either iterating over all
5601 the vertices or iterating over all the chambers or cells
5602 and then iterating over all vertices that are active on the chamber.
5604 int isl_vertices_foreach_vertex(
5605 __isl_keep isl_vertices *vertices,
5606 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5609 int isl_vertices_foreach_cell(
5610 __isl_keep isl_vertices *vertices,
5611 int (*fn)(__isl_take isl_cell *cell, void *user),
5613 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5614 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5617 Other operations that can be performed on an C<isl_vertices> object are
5620 isl_ctx *isl_vertices_get_ctx(
5621 __isl_keep isl_vertices *vertices);
5622 int isl_vertices_get_n_vertices(
5623 __isl_keep isl_vertices *vertices);
5624 void isl_vertices_free(__isl_take isl_vertices *vertices);
5626 Vertices can be inspected and destroyed using the following functions.
5628 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5629 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5630 __isl_give isl_basic_set *isl_vertex_get_domain(
5631 __isl_keep isl_vertex *vertex);
5632 __isl_give isl_basic_set *isl_vertex_get_expr(
5633 __isl_keep isl_vertex *vertex);
5634 void isl_vertex_free(__isl_take isl_vertex *vertex);
5636 C<isl_vertex_get_expr> returns a singleton parametric set describing
5637 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5639 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5640 B<rational> basic sets, so they should mainly be used for inspection
5641 and should not be mixed with integer sets.
5643 Chambers can be inspected and destroyed using the following functions.
5645 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5646 __isl_give isl_basic_set *isl_cell_get_domain(
5647 __isl_keep isl_cell *cell);
5648 void isl_cell_free(__isl_take isl_cell *cell);
5650 =head1 Polyhedral Compilation Library
5652 This section collects functionality in C<isl> that has been specifically
5653 designed for use during polyhedral compilation.
5655 =head2 Dependence Analysis
5657 C<isl> contains specialized functionality for performing
5658 array dataflow analysis. That is, given a I<sink> access relation
5659 and a collection of possible I<source> access relations,
5660 C<isl> can compute relations that describe
5661 for each iteration of the sink access, which iteration
5662 of which of the source access relations was the last
5663 to access the same data element before the given iteration
5665 The resulting dependence relations map source iterations
5666 to the corresponding sink iterations.
5667 To compute standard flow dependences, the sink should be
5668 a read, while the sources should be writes.
5669 If any of the source accesses are marked as being I<may>
5670 accesses, then there will be a dependence from the last
5671 I<must> access B<and> from any I<may> access that follows
5672 this last I<must> access.
5673 In particular, if I<all> sources are I<may> accesses,
5674 then memory based dependence analysis is performed.
5675 If, on the other hand, all sources are I<must> accesses,
5676 then value based dependence analysis is performed.
5678 #include <isl/flow.h>
5680 typedef int (*isl_access_level_before)(void *first, void *second);
5682 __isl_give isl_access_info *isl_access_info_alloc(
5683 __isl_take isl_map *sink,
5684 void *sink_user, isl_access_level_before fn,
5686 __isl_give isl_access_info *isl_access_info_add_source(
5687 __isl_take isl_access_info *acc,
5688 __isl_take isl_map *source, int must,
5690 __isl_null isl_access_info *isl_access_info_free(
5691 __isl_take isl_access_info *acc);
5693 __isl_give isl_flow *isl_access_info_compute_flow(
5694 __isl_take isl_access_info *acc);
5696 int isl_flow_foreach(__isl_keep isl_flow *deps,
5697 int (*fn)(__isl_take isl_map *dep, int must,
5698 void *dep_user, void *user),
5700 __isl_give isl_map *isl_flow_get_no_source(
5701 __isl_keep isl_flow *deps, int must);
5702 void isl_flow_free(__isl_take isl_flow *deps);
5704 The function C<isl_access_info_compute_flow> performs the actual
5705 dependence analysis. The other functions are used to construct
5706 the input for this function or to read off the output.
5708 The input is collected in an C<isl_access_info>, which can
5709 be created through a call to C<isl_access_info_alloc>.
5710 The arguments to this functions are the sink access relation
5711 C<sink>, a token C<sink_user> used to identify the sink
5712 access to the user, a callback function for specifying the
5713 relative order of source and sink accesses, and the number
5714 of source access relations that will be added.
5715 The callback function has type C<int (*)(void *first, void *second)>.
5716 The function is called with two user supplied tokens identifying
5717 either a source or the sink and it should return the shared nesting
5718 level and the relative order of the two accesses.
5719 In particular, let I<n> be the number of loops shared by
5720 the two accesses. If C<first> precedes C<second> textually,
5721 then the function should return I<2 * n + 1>; otherwise,
5722 it should return I<2 * n>.
5723 The sources can be added to the C<isl_access_info> by performing
5724 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5725 C<must> indicates whether the source is a I<must> access
5726 or a I<may> access. Note that a multi-valued access relation
5727 should only be marked I<must> if every iteration in the domain
5728 of the relation accesses I<all> elements in its image.
5729 The C<source_user> token is again used to identify
5730 the source access. The range of the source access relation
5731 C<source> should have the same dimension as the range
5732 of the sink access relation.
5733 The C<isl_access_info_free> function should usually not be
5734 called explicitly, because it is called implicitly by
5735 C<isl_access_info_compute_flow>.
5737 The result of the dependence analysis is collected in an
5738 C<isl_flow>. There may be elements of
5739 the sink access for which no preceding source access could be
5740 found or for which all preceding sources are I<may> accesses.
5741 The relations containing these elements can be obtained through
5742 calls to C<isl_flow_get_no_source>, the first with C<must> set
5743 and the second with C<must> unset.
5744 In the case of standard flow dependence analysis,
5745 with the sink a read and the sources I<must> writes,
5746 the first relation corresponds to the reads from uninitialized
5747 array elements and the second relation is empty.
5748 The actual flow dependences can be extracted using
5749 C<isl_flow_foreach>. This function will call the user-specified
5750 callback function C<fn> for each B<non-empty> dependence between
5751 a source and the sink. The callback function is called
5752 with four arguments, the actual flow dependence relation
5753 mapping source iterations to sink iterations, a boolean that
5754 indicates whether it is a I<must> or I<may> dependence, a token
5755 identifying the source and an additional C<void *> with value
5756 equal to the third argument of the C<isl_flow_foreach> call.
5757 A dependence is marked I<must> if it originates from a I<must>
5758 source and if it is not followed by any I<may> sources.
5760 After finishing with an C<isl_flow>, the user should call
5761 C<isl_flow_free> to free all associated memory.
5763 A higher-level interface to dependence analysis is provided
5764 by the following function.
5766 #include <isl/flow.h>
5768 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5769 __isl_take isl_union_map *must_source,
5770 __isl_take isl_union_map *may_source,
5771 __isl_take isl_union_map *schedule,
5772 __isl_give isl_union_map **must_dep,
5773 __isl_give isl_union_map **may_dep,
5774 __isl_give isl_union_map **must_no_source,
5775 __isl_give isl_union_map **may_no_source);
5777 The arrays are identified by the tuple names of the ranges
5778 of the accesses. The iteration domains by the tuple names
5779 of the domains of the accesses and of the schedule.
5780 The relative order of the iteration domains is given by the
5781 schedule. The relations returned through C<must_no_source>
5782 and C<may_no_source> are subsets of C<sink>.
5783 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5784 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5785 any of the other arguments is treated as an error.
5787 =head3 Interaction with Dependence Analysis
5789 During the dependence analysis, we frequently need to perform
5790 the following operation. Given a relation between sink iterations
5791 and potential source iterations from a particular source domain,
5792 what is the last potential source iteration corresponding to each
5793 sink iteration. It can sometimes be convenient to adjust
5794 the set of potential source iterations before or after each such operation.
5795 The prototypical example is fuzzy array dataflow analysis,
5796 where we need to analyze if, based on data-dependent constraints,
5797 the sink iteration can ever be executed without one or more of
5798 the corresponding potential source iterations being executed.
5799 If so, we can introduce extra parameters and select an unknown
5800 but fixed source iteration from the potential source iterations.
5801 To be able to perform such manipulations, C<isl> provides the following
5804 #include <isl/flow.h>
5806 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5807 __isl_keep isl_map *source_map,
5808 __isl_keep isl_set *sink, void *source_user,
5810 __isl_give isl_access_info *isl_access_info_set_restrict(
5811 __isl_take isl_access_info *acc,
5812 isl_access_restrict fn, void *user);
5814 The function C<isl_access_info_set_restrict> should be called
5815 before calling C<isl_access_info_compute_flow> and registers a callback function
5816 that will be called any time C<isl> is about to compute the last
5817 potential source. The first argument is the (reverse) proto-dependence,
5818 mapping sink iterations to potential source iterations.
5819 The second argument represents the sink iterations for which
5820 we want to compute the last source iteration.
5821 The third argument is the token corresponding to the source
5822 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5823 The callback is expected to return a restriction on either the input or
5824 the output of the operation computing the last potential source.
5825 If the input needs to be restricted then restrictions are needed
5826 for both the source and the sink iterations. The sink iterations
5827 and the potential source iterations will be intersected with these sets.
5828 If the output needs to be restricted then only a restriction on the source
5829 iterations is required.
5830 If any error occurs, the callback should return C<NULL>.
5831 An C<isl_restriction> object can be created, freed and inspected
5832 using the following functions.
5834 #include <isl/flow.h>
5836 __isl_give isl_restriction *isl_restriction_input(
5837 __isl_take isl_set *source_restr,
5838 __isl_take isl_set *sink_restr);
5839 __isl_give isl_restriction *isl_restriction_output(
5840 __isl_take isl_set *source_restr);
5841 __isl_give isl_restriction *isl_restriction_none(
5842 __isl_take isl_map *source_map);
5843 __isl_give isl_restriction *isl_restriction_empty(
5844 __isl_take isl_map *source_map);
5845 __isl_null isl_restriction *isl_restriction_free(
5846 __isl_take isl_restriction *restr);
5847 isl_ctx *isl_restriction_get_ctx(
5848 __isl_keep isl_restriction *restr);
5850 C<isl_restriction_none> and C<isl_restriction_empty> are special
5851 cases of C<isl_restriction_input>. C<isl_restriction_none>
5852 is essentially equivalent to
5854 isl_restriction_input(isl_set_universe(
5855 isl_space_range(isl_map_get_space(source_map))),
5857 isl_space_domain(isl_map_get_space(source_map))));
5859 whereas C<isl_restriction_empty> is essentially equivalent to
5861 isl_restriction_input(isl_set_empty(
5862 isl_space_range(isl_map_get_space(source_map))),
5864 isl_space_domain(isl_map_get_space(source_map))));
5868 B<The functionality described in this section is fairly new
5869 and may be subject to change.>
5871 #include <isl/schedule.h>
5872 __isl_give isl_schedule *
5873 isl_schedule_constraints_compute_schedule(
5874 __isl_take isl_schedule_constraints *sc);
5875 __isl_null isl_schedule *isl_schedule_free(
5876 __isl_take isl_schedule *sched);
5878 The function C<isl_schedule_constraints_compute_schedule> can be
5879 used to compute a schedule that satisfy the given schedule constraints.
5880 These schedule constraints include the iteration domain for which
5881 a schedule should be computed and dependences between pairs of
5882 iterations. In particular, these dependences include
5883 I<validity> dependences and I<proximity> dependences.
5884 By default, the algorithm used to construct the schedule is similar
5885 to that of C<Pluto>.
5886 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5888 The generated schedule respects all validity dependences.
5889 That is, all dependence distances over these dependences in the
5890 scheduled space are lexicographically positive.
5891 The default algorithm tries to ensure that the dependence distances
5892 over coincidence constraints are zero and to minimize the
5893 dependence distances over proximity dependences.
5894 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5895 for groups of domains where the dependence distances over validity
5896 dependences have only non-negative values.
5897 When using Feautrier's algorithm, the coincidence and proximity constraints
5898 are only taken into account during the extension to a
5899 full-dimensional schedule.
5901 An C<isl_schedule_constraints> object can be constructed
5902 and manipulated using the following functions.
5904 #include <isl/schedule.h>
5905 __isl_give isl_schedule_constraints *
5906 isl_schedule_constraints_copy(
5907 __isl_keep isl_schedule_constraints *sc);
5908 __isl_give isl_schedule_constraints *
5909 isl_schedule_constraints_on_domain(
5910 __isl_take isl_union_set *domain);
5911 isl_ctx *isl_schedule_constraints_get_ctx(
5912 __isl_keep isl_schedule_constraints *sc);
5913 __isl_give isl_schedule_constraints *
5914 isl_schedule_constraints_set_validity(
5915 __isl_take isl_schedule_constraints *sc,
5916 __isl_take isl_union_map *validity);
5917 __isl_give isl_schedule_constraints *
5918 isl_schedule_constraints_set_coincidence(
5919 __isl_take isl_schedule_constraints *sc,
5920 __isl_take isl_union_map *coincidence);
5921 __isl_give isl_schedule_constraints *
5922 isl_schedule_constraints_set_proximity(
5923 __isl_take isl_schedule_constraints *sc,
5924 __isl_take isl_union_map *proximity);
5925 __isl_give isl_schedule_constraints *
5926 isl_schedule_constraints_set_conditional_validity(
5927 __isl_take isl_schedule_constraints *sc,
5928 __isl_take isl_union_map *condition,
5929 __isl_take isl_union_map *validity);
5930 __isl_null isl_schedule_constraints *
5931 isl_schedule_constraints_free(
5932 __isl_take isl_schedule_constraints *sc);
5934 The initial C<isl_schedule_constraints> object created by
5935 C<isl_schedule_constraints_on_domain> does not impose any constraints.
5936 That is, it has an empty set of dependences.
5937 The function C<isl_schedule_constraints_set_validity> replaces the
5938 validity dependences, mapping domain elements I<i> to domain
5939 elements that should be scheduled after I<i>.
5940 The function C<isl_schedule_constraints_set_coincidence> replaces the
5941 coincidence dependences, mapping domain elements I<i> to domain
5942 elements that should be scheduled together with I<I>, if possible.
5943 The function C<isl_schedule_constraints_set_proximity> replaces the
5944 proximity dependences, mapping domain elements I<i> to domain
5945 elements that should be scheduled either before I<I>
5946 or as early as possible after I<i>.
5948 The function C<isl_schedule_constraints_set_conditional_validity>
5949 replaces the conditional validity constraints.
5950 A conditional validity constraint is only imposed when any of the corresponding
5951 conditions is satisfied, i.e., when any of them is non-zero.
5952 That is, the scheduler ensures that within each band if the dependence
5953 distances over the condition constraints are not all zero
5954 then all corresponding conditional validity constraints are respected.
5955 A conditional validity constraint corresponds to a condition
5956 if the two are adjacent, i.e., if the domain of one relation intersect
5957 the range of the other relation.
5958 The typical use case of conditional validity constraints is
5959 to allow order constraints between live ranges to be violated
5960 as long as the live ranges themselves are local to the band.
5961 To allow more fine-grained control over which conditions correspond
5962 to which conditional validity constraints, the domains and ranges
5963 of these relations may include I<tags>. That is, the domains and
5964 ranges of those relation may themselves be wrapped relations
5965 where the iteration domain appears in the domain of those wrapped relations
5966 and the range of the wrapped relations can be arbitrarily chosen
5967 by the user. Conditions and conditional validity constraints are only
5968 considere adjacent to each other if the entire wrapped relation matches.
5969 In particular, a relation with a tag will never be considered adjacent
5970 to a relation without a tag.
5972 The following function computes a schedule directly from
5973 an iteration domain and validity and proximity dependences
5974 and is implemented in terms of the functions described above.
5975 The use of C<isl_union_set_compute_schedule> is discouraged.
5977 #include <isl/schedule.h>
5978 __isl_give isl_schedule *isl_union_set_compute_schedule(
5979 __isl_take isl_union_set *domain,
5980 __isl_take isl_union_map *validity,
5981 __isl_take isl_union_map *proximity);
5983 A mapping from the domains to the scheduled space can be obtained
5984 from an C<isl_schedule> using the following function.
5986 __isl_give isl_union_map *isl_schedule_get_map(
5987 __isl_keep isl_schedule *sched);
5989 A representation of the schedule can be printed using
5991 __isl_give isl_printer *isl_printer_print_schedule(
5992 __isl_take isl_printer *p,
5993 __isl_keep isl_schedule *schedule);
5995 A representation of the schedule as a forest of bands can be obtained
5996 using the following function.
5998 __isl_give isl_band_list *isl_schedule_get_band_forest(
5999 __isl_keep isl_schedule *schedule);
6001 The individual bands can be visited in depth-first post-order
6002 using the following function.
6004 #include <isl/schedule.h>
6005 int isl_schedule_foreach_band(
6006 __isl_keep isl_schedule *sched,
6007 int (*fn)(__isl_keep isl_band *band, void *user),
6010 The list can be manipulated as explained in L<"Lists">.
6011 The bands inside the list can be copied and freed using the following
6014 #include <isl/band.h>
6015 __isl_give isl_band *isl_band_copy(
6016 __isl_keep isl_band *band);
6017 __isl_null isl_band *isl_band_free(
6018 __isl_take isl_band *band);
6020 Each band contains zero or more scheduling dimensions.
6021 These are referred to as the members of the band.
6022 The section of the schedule that corresponds to the band is
6023 referred to as the partial schedule of the band.
6024 For those nodes that participate in a band, the outer scheduling
6025 dimensions form the prefix schedule, while the inner scheduling
6026 dimensions form the suffix schedule.
6027 That is, if we take a cut of the band forest, then the union of
6028 the concatenations of the prefix, partial and suffix schedules of
6029 each band in the cut is equal to the entire schedule (modulo
6030 some possible padding at the end with zero scheduling dimensions).
6031 The properties of a band can be inspected using the following functions.
6033 #include <isl/band.h>
6034 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
6036 int isl_band_has_children(__isl_keep isl_band *band);
6037 __isl_give isl_band_list *isl_band_get_children(
6038 __isl_keep isl_band *band);
6040 __isl_give isl_union_map *isl_band_get_prefix_schedule(
6041 __isl_keep isl_band *band);
6042 __isl_give isl_union_map *isl_band_get_partial_schedule(
6043 __isl_keep isl_band *band);
6044 __isl_give isl_union_map *isl_band_get_suffix_schedule(
6045 __isl_keep isl_band *band);
6047 int isl_band_n_member(__isl_keep isl_band *band);
6048 int isl_band_member_is_coincident(
6049 __isl_keep isl_band *band, int pos);
6051 int isl_band_list_foreach_band(
6052 __isl_keep isl_band_list *list,
6053 int (*fn)(__isl_keep isl_band *band, void *user),
6056 Note that a scheduling dimension is considered to be ``coincident''
6057 if it satisfies the coincidence constraints within its band.
6058 That is, if the dependence distances of the coincidence
6059 constraints are all zero in that direction (for fixed
6060 iterations of outer bands).
6061 Like C<isl_schedule_foreach_band>,
6062 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
6063 in depth-first post-order.
6065 A band can be tiled using the following function.
6067 #include <isl/band.h>
6068 int isl_band_tile(__isl_keep isl_band *band,
6069 __isl_take isl_vec *sizes);
6071 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
6073 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
6074 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
6076 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
6078 The C<isl_band_tile> function tiles the band using the given tile sizes
6079 inside its schedule.
6080 A new child band is created to represent the point loops and it is
6081 inserted between the modified band and its children.
6082 The C<tile_scale_tile_loops> option specifies whether the tile
6083 loops iterators should be scaled by the tile sizes.
6084 If the C<tile_shift_point_loops> option is set, then the point loops
6085 are shifted to start at zero.
6087 A band can be split into two nested bands using the following function.
6089 int isl_band_split(__isl_keep isl_band *band, int pos);
6091 The resulting outer band contains the first C<pos> dimensions of C<band>
6092 while the inner band contains the remaining dimensions.
6094 A representation of the band can be printed using
6096 #include <isl/band.h>
6097 __isl_give isl_printer *isl_printer_print_band(
6098 __isl_take isl_printer *p,
6099 __isl_keep isl_band *band);
6103 #include <isl/schedule.h>
6104 int isl_options_set_schedule_max_coefficient(
6105 isl_ctx *ctx, int val);
6106 int isl_options_get_schedule_max_coefficient(
6108 int isl_options_set_schedule_max_constant_term(
6109 isl_ctx *ctx, int val);
6110 int isl_options_get_schedule_max_constant_term(
6112 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
6113 int isl_options_get_schedule_fuse(isl_ctx *ctx);
6114 int isl_options_set_schedule_maximize_band_depth(
6115 isl_ctx *ctx, int val);
6116 int isl_options_get_schedule_maximize_band_depth(
6118 int isl_options_set_schedule_outer_coincidence(
6119 isl_ctx *ctx, int val);
6120 int isl_options_get_schedule_outer_coincidence(
6122 int isl_options_set_schedule_split_scaled(
6123 isl_ctx *ctx, int val);
6124 int isl_options_get_schedule_split_scaled(
6126 int isl_options_set_schedule_algorithm(
6127 isl_ctx *ctx, int val);
6128 int isl_options_get_schedule_algorithm(
6130 int isl_options_set_schedule_separate_components(
6131 isl_ctx *ctx, int val);
6132 int isl_options_get_schedule_separate_components(
6137 =item * schedule_max_coefficient
6139 This option enforces that the coefficients for variable and parameter
6140 dimensions in the calculated schedule are not larger than the specified value.
6141 This option can significantly increase the speed of the scheduling calculation
6142 and may also prevent fusing of unrelated dimensions. A value of -1 means that
6143 this option does not introduce bounds on the variable or parameter
6146 =item * schedule_max_constant_term
6148 This option enforces that the constant coefficients in the calculated schedule
6149 are not larger than the maximal constant term. This option can significantly
6150 increase the speed of the scheduling calculation and may also prevent fusing of
6151 unrelated dimensions. A value of -1 means that this option does not introduce
6152 bounds on the constant coefficients.
6154 =item * schedule_fuse
6156 This option controls the level of fusion.
6157 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6158 resulting schedule will be distributed as much as possible.
6159 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6160 try to fuse loops in the resulting schedule.
6162 =item * schedule_maximize_band_depth
6164 If this option is set, we do not split bands at the point
6165 where we detect splitting is necessary. Instead, we
6166 backtrack and split bands as early as possible. This
6167 reduces the number of splits and maximizes the width of
6168 the bands. Wider bands give more possibilities for tiling.
6169 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6170 then bands will be split as early as possible, even if there is no need.
6171 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6173 =item * schedule_outer_coincidence
6175 If this option is set, then we try to construct schedules
6176 where the outermost scheduling dimension in each band
6177 satisfies the coincidence constraints.
6179 =item * schedule_split_scaled
6181 If this option is set, then we try to construct schedules in which the
6182 constant term is split off from the linear part if the linear parts of
6183 the scheduling rows for all nodes in the graphs have a common non-trivial
6185 The constant term is then placed in a separate band and the linear
6188 =item * schedule_algorithm
6190 Selects the scheduling algorithm to be used.
6191 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6192 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6194 =item * schedule_separate_components
6196 If at any point the dependence graph contains any (weakly connected) components,
6197 then these components are scheduled separately.
6198 If this option is not set, then some iterations of the domains
6199 in these components may be scheduled together.
6200 If this option is set, then the components are given consecutive
6205 =head2 AST Generation
6207 This section describes the C<isl> functionality for generating
6208 ASTs that visit all the elements
6209 in a domain in an order specified by a schedule.
6210 In particular, given a C<isl_union_map>, an AST is generated
6211 that visits all the elements in the domain of the C<isl_union_map>
6212 according to the lexicographic order of the corresponding image
6213 element(s). If the range of the C<isl_union_map> consists of
6214 elements in more than one space, then each of these spaces is handled
6215 separately in an arbitrary order.
6216 It should be noted that the image elements only specify the I<order>
6217 in which the corresponding domain elements should be visited.
6218 No direct relation between the image elements and the loop iterators
6219 in the generated AST should be assumed.
6221 Each AST is generated within a build. The initial build
6222 simply specifies the constraints on the parameters (if any)
6223 and can be created, inspected, copied and freed using the following functions.
6225 #include <isl/ast_build.h>
6226 __isl_give isl_ast_build *isl_ast_build_from_context(
6227 __isl_take isl_set *set);
6228 isl_ctx *isl_ast_build_get_ctx(
6229 __isl_keep isl_ast_build *build);
6230 __isl_give isl_ast_build *isl_ast_build_copy(
6231 __isl_keep isl_ast_build *build);
6232 __isl_null isl_ast_build *isl_ast_build_free(
6233 __isl_take isl_ast_build *build);
6235 The C<set> argument is usually a parameter set with zero or more parameters.
6236 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6237 and L</"Fine-grained Control over AST Generation">.
6238 Finally, the AST itself can be constructed using the following
6241 #include <isl/ast_build.h>
6242 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6243 __isl_keep isl_ast_build *build,
6244 __isl_take isl_union_map *schedule);
6246 =head3 Inspecting the AST
6248 The basic properties of an AST node can be obtained as follows.
6250 #include <isl/ast.h>
6251 isl_ctx *isl_ast_node_get_ctx(
6252 __isl_keep isl_ast_node *node);
6253 enum isl_ast_node_type isl_ast_node_get_type(
6254 __isl_keep isl_ast_node *node);
6256 The type of an AST node is one of
6257 C<isl_ast_node_for>,
6259 C<isl_ast_node_block> or
6260 C<isl_ast_node_user>.
6261 An C<isl_ast_node_for> represents a for node.
6262 An C<isl_ast_node_if> represents an if node.
6263 An C<isl_ast_node_block> represents a compound node.
6264 An C<isl_ast_node_user> represents an expression statement.
6265 An expression statement typically corresponds to a domain element, i.e.,
6266 one of the elements that is visited by the AST.
6268 Each type of node has its own additional properties.
6270 #include <isl/ast.h>
6271 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6272 __isl_keep isl_ast_node *node);
6273 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6274 __isl_keep isl_ast_node *node);
6275 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6276 __isl_keep isl_ast_node *node);
6277 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6278 __isl_keep isl_ast_node *node);
6279 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6280 __isl_keep isl_ast_node *node);
6281 int isl_ast_node_for_is_degenerate(
6282 __isl_keep isl_ast_node *node);
6284 An C<isl_ast_for> is considered degenerate if it is known to execute
6287 #include <isl/ast.h>
6288 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6289 __isl_keep isl_ast_node *node);
6290 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6291 __isl_keep isl_ast_node *node);
6292 int isl_ast_node_if_has_else(
6293 __isl_keep isl_ast_node *node);
6294 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6295 __isl_keep isl_ast_node *node);
6297 __isl_give isl_ast_node_list *
6298 isl_ast_node_block_get_children(
6299 __isl_keep isl_ast_node *node);
6301 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6302 __isl_keep isl_ast_node *node);
6304 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6305 the following functions.
6307 #include <isl/ast.h>
6308 isl_ctx *isl_ast_expr_get_ctx(
6309 __isl_keep isl_ast_expr *expr);
6310 enum isl_ast_expr_type isl_ast_expr_get_type(
6311 __isl_keep isl_ast_expr *expr);
6313 The type of an AST expression is one of
6315 C<isl_ast_expr_id> or
6316 C<isl_ast_expr_int>.
6317 An C<isl_ast_expr_op> represents the result of an operation.
6318 An C<isl_ast_expr_id> represents an identifier.
6319 An C<isl_ast_expr_int> represents an integer value.
6321 Each type of expression has its own additional properties.
6323 #include <isl/ast.h>
6324 enum isl_ast_op_type isl_ast_expr_get_op_type(
6325 __isl_keep isl_ast_expr *expr);
6326 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6327 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6328 __isl_keep isl_ast_expr *expr, int pos);
6329 int isl_ast_node_foreach_ast_op_type(
6330 __isl_keep isl_ast_node *node,
6331 int (*fn)(enum isl_ast_op_type type, void *user),
6334 C<isl_ast_expr_get_op_type> returns the type of the operation
6335 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6336 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6338 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6339 C<isl_ast_op_type> that appears in C<node>.
6340 The operation type is one of the following.
6344 =item C<isl_ast_op_and>
6346 Logical I<and> of two arguments.
6347 Both arguments can be evaluated.
6349 =item C<isl_ast_op_and_then>
6351 Logical I<and> of two arguments.
6352 The second argument can only be evaluated if the first evaluates to true.
6354 =item C<isl_ast_op_or>
6356 Logical I<or> of two arguments.
6357 Both arguments can be evaluated.
6359 =item C<isl_ast_op_or_else>
6361 Logical I<or> of two arguments.
6362 The second argument can only be evaluated if the first evaluates to false.
6364 =item C<isl_ast_op_max>
6366 Maximum of two or more arguments.
6368 =item C<isl_ast_op_min>
6370 Minimum of two or more arguments.
6372 =item C<isl_ast_op_minus>
6376 =item C<isl_ast_op_add>
6378 Sum of two arguments.
6380 =item C<isl_ast_op_sub>
6382 Difference of two arguments.
6384 =item C<isl_ast_op_mul>
6386 Product of two arguments.
6388 =item C<isl_ast_op_div>
6390 Exact division. That is, the result is known to be an integer.
6392 =item C<isl_ast_op_fdiv_q>
6394 Result of integer division, rounded towards negative
6397 =item C<isl_ast_op_pdiv_q>
6399 Result of integer division, where dividend is known to be non-negative.
6401 =item C<isl_ast_op_pdiv_r>
6403 Remainder of integer division, where dividend is known to be non-negative.
6405 =item C<isl_ast_op_cond>
6407 Conditional operator defined on three arguments.
6408 If the first argument evaluates to true, then the result
6409 is equal to the second argument. Otherwise, the result
6410 is equal to the third argument.
6411 The second and third argument may only be evaluated if
6412 the first argument evaluates to true and false, respectively.
6413 Corresponds to C<a ? b : c> in C.
6415 =item C<isl_ast_op_select>
6417 Conditional operator defined on three arguments.
6418 If the first argument evaluates to true, then the result
6419 is equal to the second argument. Otherwise, the result
6420 is equal to the third argument.
6421 The second and third argument may be evaluated independently
6422 of the value of the first argument.
6423 Corresponds to C<a * b + (1 - a) * c> in C.
6425 =item C<isl_ast_op_eq>
6429 =item C<isl_ast_op_le>
6431 Less than or equal relation.
6433 =item C<isl_ast_op_lt>
6437 =item C<isl_ast_op_ge>
6439 Greater than or equal relation.
6441 =item C<isl_ast_op_gt>
6443 Greater than relation.
6445 =item C<isl_ast_op_call>
6448 The number of arguments of the C<isl_ast_expr> is one more than
6449 the number of arguments in the function call, the first argument
6450 representing the function being called.
6452 =item C<isl_ast_op_access>
6455 The number of arguments of the C<isl_ast_expr> is one more than
6456 the number of index expressions in the array access, the first argument
6457 representing the array being accessed.
6459 =item C<isl_ast_op_member>
6462 This operation has two arguments, a structure and the name of
6463 the member of the structure being accessed.
6467 #include <isl/ast.h>
6468 __isl_give isl_id *isl_ast_expr_get_id(
6469 __isl_keep isl_ast_expr *expr);
6471 Return the identifier represented by the AST expression.
6473 #include <isl/ast.h>
6474 __isl_give isl_val *isl_ast_expr_get_val(
6475 __isl_keep isl_ast_expr *expr);
6477 Return the integer represented by the AST expression.
6479 =head3 Properties of ASTs
6481 #include <isl/ast.h>
6482 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6483 __isl_keep isl_ast_expr *expr2);
6485 Check if two C<isl_ast_expr>s are equal to each other.
6487 =head3 Manipulating and printing the AST
6489 AST nodes can be copied and freed using the following functions.
6491 #include <isl/ast.h>
6492 __isl_give isl_ast_node *isl_ast_node_copy(
6493 __isl_keep isl_ast_node *node);
6494 __isl_null isl_ast_node *isl_ast_node_free(
6495 __isl_take isl_ast_node *node);
6497 AST expressions can be copied and freed using the following functions.
6499 #include <isl/ast.h>
6500 __isl_give isl_ast_expr *isl_ast_expr_copy(
6501 __isl_keep isl_ast_expr *expr);
6502 __isl_null isl_ast_expr *isl_ast_expr_free(
6503 __isl_take isl_ast_expr *expr);
6505 New AST expressions can be created either directly or within
6506 the context of an C<isl_ast_build>.
6508 #include <isl/ast.h>
6509 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6510 __isl_take isl_val *v);
6511 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6512 __isl_take isl_id *id);
6513 __isl_give isl_ast_expr *isl_ast_expr_neg(
6514 __isl_take isl_ast_expr *expr);
6515 __isl_give isl_ast_expr *isl_ast_expr_add(
6516 __isl_take isl_ast_expr *expr1,
6517 __isl_take isl_ast_expr *expr2);
6518 __isl_give isl_ast_expr *isl_ast_expr_sub(
6519 __isl_take isl_ast_expr *expr1,
6520 __isl_take isl_ast_expr *expr2);
6521 __isl_give isl_ast_expr *isl_ast_expr_mul(
6522 __isl_take isl_ast_expr *expr1,
6523 __isl_take isl_ast_expr *expr2);
6524 __isl_give isl_ast_expr *isl_ast_expr_div(
6525 __isl_take isl_ast_expr *expr1,
6526 __isl_take isl_ast_expr *expr2);
6527 __isl_give isl_ast_expr *isl_ast_expr_and(
6528 __isl_take isl_ast_expr *expr1,
6529 __isl_take isl_ast_expr *expr2)
6530 __isl_give isl_ast_expr *isl_ast_expr_or(
6531 __isl_take isl_ast_expr *expr1,
6532 __isl_take isl_ast_expr *expr2)
6533 __isl_give isl_ast_expr *isl_ast_expr_access(
6534 __isl_take isl_ast_expr *array,
6535 __isl_take isl_ast_expr_list *indices);
6537 #include <isl/ast_build.h>
6538 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6539 __isl_keep isl_ast_build *build,
6540 __isl_take isl_pw_aff *pa);
6541 __isl_give isl_ast_expr *
6542 isl_ast_build_access_from_pw_multi_aff(
6543 __isl_keep isl_ast_build *build,
6544 __isl_take isl_pw_multi_aff *pma);
6545 __isl_give isl_ast_expr *
6546 isl_ast_build_access_from_multi_pw_aff(
6547 __isl_keep isl_ast_build *build,
6548 __isl_take isl_multi_pw_aff *mpa);
6549 __isl_give isl_ast_expr *
6550 isl_ast_build_call_from_pw_multi_aff(
6551 __isl_keep isl_ast_build *build,
6552 __isl_take isl_pw_multi_aff *pma);
6553 __isl_give isl_ast_expr *
6554 isl_ast_build_call_from_multi_pw_aff(
6555 __isl_keep isl_ast_build *build,
6556 __isl_take isl_multi_pw_aff *mpa);
6558 The domains of C<pa>, C<mpa> and C<pma> should correspond
6559 to the schedule space of C<build>.
6560 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6561 the function being called.
6562 If the accessed space is a nested relation, then it is taken
6563 to represent an access of the member specified by the range
6564 of this nested relation of the structure specified by the domain
6565 of the nested relation.
6567 The following functions can be used to modify an C<isl_ast_expr>.
6569 #include <isl/ast.h>
6570 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6571 __isl_take isl_ast_expr *expr, int pos,
6572 __isl_take isl_ast_expr *arg);
6574 Replace the argument of C<expr> at position C<pos> by C<arg>.
6576 #include <isl/ast.h>
6577 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6578 __isl_take isl_ast_expr *expr,
6579 __isl_take isl_id_to_ast_expr *id2expr);
6581 The function C<isl_ast_expr_substitute_ids> replaces the
6582 subexpressions of C<expr> of type C<isl_ast_expr_id>
6583 by the corresponding expression in C<id2expr>, if there is any.
6586 User specified data can be attached to an C<isl_ast_node> and obtained
6587 from the same C<isl_ast_node> using the following functions.
6589 #include <isl/ast.h>
6590 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6591 __isl_take isl_ast_node *node,
6592 __isl_take isl_id *annotation);
6593 __isl_give isl_id *isl_ast_node_get_annotation(
6594 __isl_keep isl_ast_node *node);
6596 Basic printing can be performed using the following functions.
6598 #include <isl/ast.h>
6599 __isl_give isl_printer *isl_printer_print_ast_expr(
6600 __isl_take isl_printer *p,
6601 __isl_keep isl_ast_expr *expr);
6602 __isl_give isl_printer *isl_printer_print_ast_node(
6603 __isl_take isl_printer *p,
6604 __isl_keep isl_ast_node *node);
6606 More advanced printing can be performed using the following functions.
6608 #include <isl/ast.h>
6609 __isl_give isl_printer *isl_ast_op_type_print_macro(
6610 enum isl_ast_op_type type,
6611 __isl_take isl_printer *p);
6612 __isl_give isl_printer *isl_ast_node_print_macros(
6613 __isl_keep isl_ast_node *node,
6614 __isl_take isl_printer *p);
6615 __isl_give isl_printer *isl_ast_node_print(
6616 __isl_keep isl_ast_node *node,
6617 __isl_take isl_printer *p,
6618 __isl_take isl_ast_print_options *options);
6619 __isl_give isl_printer *isl_ast_node_for_print(
6620 __isl_keep isl_ast_node *node,
6621 __isl_take isl_printer *p,
6622 __isl_take isl_ast_print_options *options);
6623 __isl_give isl_printer *isl_ast_node_if_print(
6624 __isl_keep isl_ast_node *node,
6625 __isl_take isl_printer *p,
6626 __isl_take isl_ast_print_options *options);
6628 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6629 C<isl> may print out an AST that makes use of macros such
6630 as C<floord>, C<min> and C<max>.
6631 C<isl_ast_op_type_print_macro> prints out the macro
6632 corresponding to a specific C<isl_ast_op_type>.
6633 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6634 for expressions where these macros would be used and prints
6635 out the required macro definitions.
6636 Essentially, C<isl_ast_node_print_macros> calls
6637 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6638 as function argument.
6639 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6640 C<isl_ast_node_if_print> print an C<isl_ast_node>
6641 in C<ISL_FORMAT_C>, but allow for some extra control
6642 through an C<isl_ast_print_options> object.
6643 This object can be created using the following functions.
6645 #include <isl/ast.h>
6646 __isl_give isl_ast_print_options *
6647 isl_ast_print_options_alloc(isl_ctx *ctx);
6648 __isl_give isl_ast_print_options *
6649 isl_ast_print_options_copy(
6650 __isl_keep isl_ast_print_options *options);
6651 __isl_null isl_ast_print_options *
6652 isl_ast_print_options_free(
6653 __isl_take isl_ast_print_options *options);
6655 __isl_give isl_ast_print_options *
6656 isl_ast_print_options_set_print_user(
6657 __isl_take isl_ast_print_options *options,
6658 __isl_give isl_printer *(*print_user)(
6659 __isl_take isl_printer *p,
6660 __isl_take isl_ast_print_options *options,
6661 __isl_keep isl_ast_node *node, void *user),
6663 __isl_give isl_ast_print_options *
6664 isl_ast_print_options_set_print_for(
6665 __isl_take isl_ast_print_options *options,
6666 __isl_give isl_printer *(*print_for)(
6667 __isl_take isl_printer *p,
6668 __isl_take isl_ast_print_options *options,
6669 __isl_keep isl_ast_node *node, void *user),
6672 The callback set by C<isl_ast_print_options_set_print_user>
6673 is called whenever a node of type C<isl_ast_node_user> needs to
6675 The callback set by C<isl_ast_print_options_set_print_for>
6676 is called whenever a node of type C<isl_ast_node_for> needs to
6678 Note that C<isl_ast_node_for_print> will I<not> call the
6679 callback set by C<isl_ast_print_options_set_print_for> on the node
6680 on which C<isl_ast_node_for_print> is called, but only on nested
6681 nodes of type C<isl_ast_node_for>. It is therefore safe to
6682 call C<isl_ast_node_for_print> from within the callback set by
6683 C<isl_ast_print_options_set_print_for>.
6685 The following option determines the type to be used for iterators
6686 while printing the AST.
6688 int isl_options_set_ast_iterator_type(
6689 isl_ctx *ctx, const char *val);
6690 const char *isl_options_get_ast_iterator_type(
6695 #include <isl/ast_build.h>
6696 int isl_options_set_ast_build_atomic_upper_bound(
6697 isl_ctx *ctx, int val);
6698 int isl_options_get_ast_build_atomic_upper_bound(
6700 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6702 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6703 int isl_options_set_ast_build_exploit_nested_bounds(
6704 isl_ctx *ctx, int val);
6705 int isl_options_get_ast_build_exploit_nested_bounds(
6707 int isl_options_set_ast_build_group_coscheduled(
6708 isl_ctx *ctx, int val);
6709 int isl_options_get_ast_build_group_coscheduled(
6711 int isl_options_set_ast_build_scale_strides(
6712 isl_ctx *ctx, int val);
6713 int isl_options_get_ast_build_scale_strides(
6715 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6717 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6718 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6720 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6724 =item * ast_build_atomic_upper_bound
6726 Generate loop upper bounds that consist of the current loop iterator,
6727 an operator and an expression not involving the iterator.
6728 If this option is not set, then the current loop iterator may appear
6729 several times in the upper bound.
6730 For example, when this option is turned off, AST generation
6733 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6737 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6740 When the option is turned on, the following AST is generated
6742 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6745 =item * ast_build_prefer_pdiv
6747 If this option is turned off, then the AST generation will
6748 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6749 operators, but no C<isl_ast_op_pdiv_q> or
6750 C<isl_ast_op_pdiv_r> operators.
6751 If this options is turned on, then C<isl> will try to convert
6752 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6753 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6755 =item * ast_build_exploit_nested_bounds
6757 Simplify conditions based on bounds of nested for loops.
6758 In particular, remove conditions that are implied by the fact
6759 that one or more nested loops have at least one iteration,
6760 meaning that the upper bound is at least as large as the lower bound.
6761 For example, when this option is turned off, AST generation
6764 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6770 for (int c0 = 0; c0 <= N; c0 += 1)
6771 for (int c1 = 0; c1 <= M; c1 += 1)
6774 When the option is turned on, the following AST is generated
6776 for (int c0 = 0; c0 <= N; c0 += 1)
6777 for (int c1 = 0; c1 <= M; c1 += 1)
6780 =item * ast_build_group_coscheduled
6782 If two domain elements are assigned the same schedule point, then
6783 they may be executed in any order and they may even appear in different
6784 loops. If this options is set, then the AST generator will make
6785 sure that coscheduled domain elements do not appear in separate parts
6786 of the AST. This is useful in case of nested AST generation
6787 if the outer AST generation is given only part of a schedule
6788 and the inner AST generation should handle the domains that are
6789 coscheduled by this initial part of the schedule together.
6790 For example if an AST is generated for a schedule
6792 { A[i] -> [0]; B[i] -> [0] }
6794 then the C<isl_ast_build_set_create_leaf> callback described
6795 below may get called twice, once for each domain.
6796 Setting this option ensures that the callback is only called once
6797 on both domains together.
6799 =item * ast_build_separation_bounds
6801 This option specifies which bounds to use during separation.
6802 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6803 then all (possibly implicit) bounds on the current dimension will
6804 be used during separation.
6805 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6806 then only those bounds that are explicitly available will
6807 be used during separation.
6809 =item * ast_build_scale_strides
6811 This option specifies whether the AST generator is allowed
6812 to scale down iterators of strided loops.
6814 =item * ast_build_allow_else
6816 This option specifies whether the AST generator is allowed
6817 to construct if statements with else branches.
6819 =item * ast_build_allow_or
6821 This option specifies whether the AST generator is allowed
6822 to construct if conditions with disjunctions.
6826 =head3 Fine-grained Control over AST Generation
6828 Besides specifying the constraints on the parameters,
6829 an C<isl_ast_build> object can be used to control
6830 various aspects of the AST generation process.
6831 The most prominent way of control is through ``options'',
6832 which can be set using the following function.
6834 #include <isl/ast_build.h>
6835 __isl_give isl_ast_build *
6836 isl_ast_build_set_options(
6837 __isl_take isl_ast_build *control,
6838 __isl_take isl_union_map *options);
6840 The options are encoded in an <isl_union_map>.
6841 The domain of this union relation refers to the schedule domain,
6842 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6843 In the case of nested AST generation (see L</"Nested AST Generation">),
6844 the domain of C<options> should refer to the extra piece of the schedule.
6845 That is, it should be equal to the range of the wrapped relation in the
6846 range of the schedule.
6847 The range of the options can consist of elements in one or more spaces,
6848 the names of which determine the effect of the option.
6849 The values of the range typically also refer to the schedule dimension
6850 to which the option applies. In case of nested AST generation
6851 (see L</"Nested AST Generation">), these values refer to the position
6852 of the schedule dimension within the innermost AST generation.
6853 The constraints on the domain elements of
6854 the option should only refer to this dimension and earlier dimensions.
6855 We consider the following spaces.
6859 =item C<separation_class>
6861 This space is a wrapped relation between two one dimensional spaces.
6862 The input space represents the schedule dimension to which the option
6863 applies and the output space represents the separation class.
6864 While constructing a loop corresponding to the specified schedule
6865 dimension(s), the AST generator will try to generate separate loops
6866 for domain elements that are assigned different classes.
6867 If only some of the elements are assigned a class, then those elements
6868 that are not assigned any class will be treated as belonging to a class
6869 that is separate from the explicitly assigned classes.
6870 The typical use case for this option is to separate full tiles from
6872 The other options, described below, are applied after the separation
6875 As an example, consider the separation into full and partial tiles
6876 of a tiling of a triangular domain.
6877 Take, for example, the domain
6879 { A[i,j] : 0 <= i,j and i + j <= 100 }
6881 and a tiling into tiles of 10 by 10. The input to the AST generator
6882 is then the schedule
6884 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6887 Without any options, the following AST is generated
6889 for (int c0 = 0; c0 <= 10; c0 += 1)
6890 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6891 for (int c2 = 10 * c0;
6892 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6894 for (int c3 = 10 * c1;
6895 c3 <= min(10 * c1 + 9, -c2 + 100);
6899 Separation into full and partial tiles can be obtained by assigning
6900 a class, say C<0>, to the full tiles. The full tiles are represented by those
6901 values of the first and second schedule dimensions for which there are
6902 values of the third and fourth dimensions to cover an entire tile.
6903 That is, we need to specify the following option
6905 { [a,b,c,d] -> separation_class[[0]->[0]] :
6906 exists b': 0 <= 10a,10b' and
6907 10a+9+10b'+9 <= 100;
6908 [a,b,c,d] -> separation_class[[1]->[0]] :
6909 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6913 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6914 a >= 0 and b >= 0 and b <= 8 - a;
6915 [a, b, c, d] -> separation_class[[0] -> [0]] :
6918 With this option, the generated AST is as follows
6921 for (int c0 = 0; c0 <= 8; c0 += 1) {
6922 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6923 for (int c2 = 10 * c0;
6924 c2 <= 10 * c0 + 9; c2 += 1)
6925 for (int c3 = 10 * c1;
6926 c3 <= 10 * c1 + 9; c3 += 1)
6928 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6929 for (int c2 = 10 * c0;
6930 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6932 for (int c3 = 10 * c1;
6933 c3 <= min(-c2 + 100, 10 * c1 + 9);
6937 for (int c0 = 9; c0 <= 10; c0 += 1)
6938 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6939 for (int c2 = 10 * c0;
6940 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6942 for (int c3 = 10 * c1;
6943 c3 <= min(10 * c1 + 9, -c2 + 100);
6950 This is a single-dimensional space representing the schedule dimension(s)
6951 to which ``separation'' should be applied. Separation tries to split
6952 a loop into several pieces if this can avoid the generation of guards
6954 See also the C<atomic> option.
6958 This is a single-dimensional space representing the schedule dimension(s)
6959 for which the domains should be considered ``atomic''. That is, the
6960 AST generator will make sure that any given domain space will only appear
6961 in a single loop at the specified level.
6963 Consider the following schedule
6965 { a[i] -> [i] : 0 <= i < 10;
6966 b[i] -> [i+1] : 0 <= i < 10 }
6968 If the following option is specified
6970 { [i] -> separate[x] }
6972 then the following AST will be generated
6976 for (int c0 = 1; c0 <= 9; c0 += 1) {
6983 If, on the other hand, the following option is specified
6985 { [i] -> atomic[x] }
6987 then the following AST will be generated
6989 for (int c0 = 0; c0 <= 10; c0 += 1) {
6996 If neither C<atomic> nor C<separate> is specified, then the AST generator
6997 may produce either of these two results or some intermediate form.
7001 This is a single-dimensional space representing the schedule dimension(s)
7002 that should be I<completely> unrolled.
7003 To obtain a partial unrolling, the user should apply an additional
7004 strip-mining to the schedule and fully unroll the inner loop.
7008 Additional control is available through the following functions.
7010 #include <isl/ast_build.h>
7011 __isl_give isl_ast_build *
7012 isl_ast_build_set_iterators(
7013 __isl_take isl_ast_build *control,
7014 __isl_take isl_id_list *iterators);
7016 The function C<isl_ast_build_set_iterators> allows the user to
7017 specify a list of iterator C<isl_id>s to be used as iterators.
7018 If the input schedule is injective, then
7019 the number of elements in this list should be as large as the dimension
7020 of the schedule space, but no direct correspondence should be assumed
7021 between dimensions and elements.
7022 If the input schedule is not injective, then an additional number
7023 of C<isl_id>s equal to the largest dimension of the input domains
7025 If the number of provided C<isl_id>s is insufficient, then additional
7026 names are automatically generated.
7028 #include <isl/ast_build.h>
7029 __isl_give isl_ast_build *
7030 isl_ast_build_set_create_leaf(
7031 __isl_take isl_ast_build *control,
7032 __isl_give isl_ast_node *(*fn)(
7033 __isl_take isl_ast_build *build,
7034 void *user), void *user);
7037 C<isl_ast_build_set_create_leaf> function allows for the
7038 specification of a callback that should be called whenever the AST
7039 generator arrives at an element of the schedule domain.
7040 The callback should return an AST node that should be inserted
7041 at the corresponding position of the AST. The default action (when
7042 the callback is not set) is to continue generating parts of the AST to scan
7043 all the domain elements associated to the schedule domain element
7044 and to insert user nodes, ``calling'' the domain element, for each of them.
7045 The C<build> argument contains the current state of the C<isl_ast_build>.
7046 To ease nested AST generation (see L</"Nested AST Generation">),
7047 all control information that is
7048 specific to the current AST generation such as the options and
7049 the callbacks has been removed from this C<isl_ast_build>.
7050 The callback would typically return the result of a nested
7052 user defined node created using the following function.
7054 #include <isl/ast.h>
7055 __isl_give isl_ast_node *isl_ast_node_alloc_user(
7056 __isl_take isl_ast_expr *expr);
7058 #include <isl/ast_build.h>
7059 __isl_give isl_ast_build *
7060 isl_ast_build_set_at_each_domain(
7061 __isl_take isl_ast_build *build,
7062 __isl_give isl_ast_node *(*fn)(
7063 __isl_take isl_ast_node *node,
7064 __isl_keep isl_ast_build *build,
7065 void *user), void *user);
7066 __isl_give isl_ast_build *
7067 isl_ast_build_set_before_each_for(
7068 __isl_take isl_ast_build *build,
7069 __isl_give isl_id *(*fn)(
7070 __isl_keep isl_ast_build *build,
7071 void *user), void *user);
7072 __isl_give isl_ast_build *
7073 isl_ast_build_set_after_each_for(
7074 __isl_take isl_ast_build *build,
7075 __isl_give isl_ast_node *(*fn)(
7076 __isl_take isl_ast_node *node,
7077 __isl_keep isl_ast_build *build,
7078 void *user), void *user);
7080 The callback set by C<isl_ast_build_set_at_each_domain> will
7081 be called for each domain AST node.
7082 The callbacks set by C<isl_ast_build_set_before_each_for>
7083 and C<isl_ast_build_set_after_each_for> will be called
7084 for each for AST node. The first will be called in depth-first
7085 pre-order, while the second will be called in depth-first post-order.
7086 Since C<isl_ast_build_set_before_each_for> is called before the for
7087 node is actually constructed, it is only passed an C<isl_ast_build>.
7088 The returned C<isl_id> will be added as an annotation (using
7089 C<isl_ast_node_set_annotation>) to the constructed for node.
7090 In particular, if the user has also specified an C<after_each_for>
7091 callback, then the annotation can be retrieved from the node passed to
7092 that callback using C<isl_ast_node_get_annotation>.
7093 All callbacks should C<NULL> on failure.
7094 The given C<isl_ast_build> can be used to create new
7095 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
7096 or C<isl_ast_build_call_from_pw_multi_aff>.
7098 =head3 Nested AST Generation
7100 C<isl> allows the user to create an AST within the context
7101 of another AST. These nested ASTs are created using the
7102 same C<isl_ast_build_ast_from_schedule> function that is used to create the
7103 outer AST. The C<build> argument should be an C<isl_ast_build>
7104 passed to a callback set by
7105 C<isl_ast_build_set_create_leaf>.
7106 The space of the range of the C<schedule> argument should refer
7107 to this build. In particular, the space should be a wrapped
7108 relation and the domain of this wrapped relation should be the
7109 same as that of the range of the schedule returned by
7110 C<isl_ast_build_get_schedule> below.
7111 In practice, the new schedule is typically
7112 created by calling C<isl_union_map_range_product> on the old schedule
7113 and some extra piece of the schedule.
7114 The space of the schedule domain is also available from
7115 the C<isl_ast_build>.
7117 #include <isl/ast_build.h>
7118 __isl_give isl_union_map *isl_ast_build_get_schedule(
7119 __isl_keep isl_ast_build *build);
7120 __isl_give isl_space *isl_ast_build_get_schedule_space(
7121 __isl_keep isl_ast_build *build);
7122 __isl_give isl_ast_build *isl_ast_build_restrict(
7123 __isl_take isl_ast_build *build,
7124 __isl_take isl_set *set);
7126 The C<isl_ast_build_get_schedule> function returns a (partial)
7127 schedule for the domains elements for which part of the AST still needs to
7128 be generated in the current build.
7129 In particular, the domain elements are mapped to those iterations of the loops
7130 enclosing the current point of the AST generation inside which
7131 the domain elements are executed.
7132 No direct correspondence between
7133 the input schedule and this schedule should be assumed.
7134 The space obtained from C<isl_ast_build_get_schedule_space> can be used
7135 to create a set for C<isl_ast_build_restrict> to intersect
7136 with the current build. In particular, the set passed to
7137 C<isl_ast_build_restrict> can have additional parameters.
7138 The ids of the set dimensions in the space returned by
7139 C<isl_ast_build_get_schedule_space> correspond to the
7140 iterators of the already generated loops.
7141 The user should not rely on the ids of the output dimensions
7142 of the relations in the union relation returned by
7143 C<isl_ast_build_get_schedule> having any particular value.
7147 Although C<isl> is mainly meant to be used as a library,
7148 it also contains some basic applications that use some
7149 of the functionality of C<isl>.
7150 The input may be specified in either the L<isl format>
7151 or the L<PolyLib format>.
7153 =head2 C<isl_polyhedron_sample>
7155 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7156 an integer element of the polyhedron, if there is any.
7157 The first column in the output is the denominator and is always
7158 equal to 1. If the polyhedron contains no integer points,
7159 then a vector of length zero is printed.
7163 C<isl_pip> takes the same input as the C<example> program
7164 from the C<piplib> distribution, i.e., a set of constraints
7165 on the parameters, a line containing only -1 and finally a set
7166 of constraints on a parametric polyhedron.
7167 The coefficients of the parameters appear in the last columns
7168 (but before the final constant column).
7169 The output is the lexicographic minimum of the parametric polyhedron.
7170 As C<isl> currently does not have its own output format, the output
7171 is just a dump of the internal state.
7173 =head2 C<isl_polyhedron_minimize>
7175 C<isl_polyhedron_minimize> computes the minimum of some linear
7176 or affine objective function over the integer points in a polyhedron.
7177 If an affine objective function
7178 is given, then the constant should appear in the last column.
7180 =head2 C<isl_polytope_scan>
7182 Given a polytope, C<isl_polytope_scan> prints
7183 all integer points in the polytope.
7185 =head2 C<isl_codegen>
7187 Given a schedule, a context set and an options relation,
7188 C<isl_codegen> prints out an AST that scans the domain elements
7189 of the schedule in the order of their image(s) taking into account
7190 the constraints in the context set.