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_set_indent_prefix(
1185 __isl_take isl_printer *p, const char *prefix);
1186 __isl_give isl_printer *isl_printer_indent(
1187 __isl_take isl_printer *p, int indent);
1188 __isl_give isl_printer *isl_printer_set_prefix(
1189 __isl_take isl_printer *p, const char *prefix);
1190 __isl_give isl_printer *isl_printer_set_suffix(
1191 __isl_take isl_printer *p, const char *suffix);
1193 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1194 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1195 and defaults to C<ISL_FORMAT_ISL>.
1196 Each line in the output is prefixed by C<indent_prefix>,
1197 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
1198 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1199 In the C<PolyLib> format output,
1200 the coefficients of the existentially quantified variables
1201 appear between those of the set variables and those
1203 The function C<isl_printer_indent> increases the indentation
1204 by the specified amount (which may be negative).
1206 To actually print something, use
1208 #include <isl/printer.h>
1209 __isl_give isl_printer *isl_printer_print_double(
1210 __isl_take isl_printer *p, double d);
1212 #include <isl/set.h>
1213 __isl_give isl_printer *isl_printer_print_basic_set(
1214 __isl_take isl_printer *printer,
1215 __isl_keep isl_basic_set *bset);
1216 __isl_give isl_printer *isl_printer_print_set(
1217 __isl_take isl_printer *printer,
1218 __isl_keep isl_set *set);
1220 #include <isl/map.h>
1221 __isl_give isl_printer *isl_printer_print_basic_map(
1222 __isl_take isl_printer *printer,
1223 __isl_keep isl_basic_map *bmap);
1224 __isl_give isl_printer *isl_printer_print_map(
1225 __isl_take isl_printer *printer,
1226 __isl_keep isl_map *map);
1228 #include <isl/union_set.h>
1229 __isl_give isl_printer *isl_printer_print_union_set(
1230 __isl_take isl_printer *p,
1231 __isl_keep isl_union_set *uset);
1233 #include <isl/union_map.h>
1234 __isl_give isl_printer *isl_printer_print_union_map(
1235 __isl_take isl_printer *p,
1236 __isl_keep isl_union_map *umap);
1238 When called on a file printer, the following function flushes
1239 the file. When called on a string printer, the buffer is cleared.
1241 __isl_give isl_printer *isl_printer_flush(
1242 __isl_take isl_printer *p);
1244 =head2 Creating New Sets and Relations
1246 C<isl> has functions for creating some standard sets and relations.
1250 =item * Empty sets and relations
1252 __isl_give isl_basic_set *isl_basic_set_empty(
1253 __isl_take isl_space *space);
1254 __isl_give isl_basic_map *isl_basic_map_empty(
1255 __isl_take isl_space *space);
1256 __isl_give isl_set *isl_set_empty(
1257 __isl_take isl_space *space);
1258 __isl_give isl_map *isl_map_empty(
1259 __isl_take isl_space *space);
1260 __isl_give isl_union_set *isl_union_set_empty(
1261 __isl_take isl_space *space);
1262 __isl_give isl_union_map *isl_union_map_empty(
1263 __isl_take isl_space *space);
1265 For C<isl_union_set>s and C<isl_union_map>s, the space
1266 is only used to specify the parameters.
1268 =item * Universe sets and relations
1270 __isl_give isl_basic_set *isl_basic_set_universe(
1271 __isl_take isl_space *space);
1272 __isl_give isl_basic_map *isl_basic_map_universe(
1273 __isl_take isl_space *space);
1274 __isl_give isl_set *isl_set_universe(
1275 __isl_take isl_space *space);
1276 __isl_give isl_map *isl_map_universe(
1277 __isl_take isl_space *space);
1278 __isl_give isl_union_set *isl_union_set_universe(
1279 __isl_take isl_union_set *uset);
1280 __isl_give isl_union_map *isl_union_map_universe(
1281 __isl_take isl_union_map *umap);
1283 The sets and relations constructed by the functions above
1284 contain all integer values, while those constructed by the
1285 functions below only contain non-negative values.
1287 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1288 __isl_take isl_space *space);
1289 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1290 __isl_take isl_space *space);
1291 __isl_give isl_set *isl_set_nat_universe(
1292 __isl_take isl_space *space);
1293 __isl_give isl_map *isl_map_nat_universe(
1294 __isl_take isl_space *space);
1296 =item * Identity relations
1298 __isl_give isl_basic_map *isl_basic_map_identity(
1299 __isl_take isl_space *space);
1300 __isl_give isl_map *isl_map_identity(
1301 __isl_take isl_space *space);
1303 The number of input and output dimensions in C<space> needs
1306 =item * Lexicographic order
1308 __isl_give isl_map *isl_map_lex_lt(
1309 __isl_take isl_space *set_space);
1310 __isl_give isl_map *isl_map_lex_le(
1311 __isl_take isl_space *set_space);
1312 __isl_give isl_map *isl_map_lex_gt(
1313 __isl_take isl_space *set_space);
1314 __isl_give isl_map *isl_map_lex_ge(
1315 __isl_take isl_space *set_space);
1316 __isl_give isl_map *isl_map_lex_lt_first(
1317 __isl_take isl_space *space, unsigned n);
1318 __isl_give isl_map *isl_map_lex_le_first(
1319 __isl_take isl_space *space, unsigned n);
1320 __isl_give isl_map *isl_map_lex_gt_first(
1321 __isl_take isl_space *space, unsigned n);
1322 __isl_give isl_map *isl_map_lex_ge_first(
1323 __isl_take isl_space *space, unsigned n);
1325 The first four functions take a space for a B<set>
1326 and return relations that express that the elements in the domain
1327 are lexicographically less
1328 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1329 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1330 than the elements in the range.
1331 The last four functions take a space for a map
1332 and return relations that express that the first C<n> dimensions
1333 in the domain are lexicographically less
1334 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1335 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1336 than the first C<n> dimensions in the range.
1340 A basic set or relation can be converted to a set or relation
1341 using the following functions.
1343 __isl_give isl_set *isl_set_from_basic_set(
1344 __isl_take isl_basic_set *bset);
1345 __isl_give isl_map *isl_map_from_basic_map(
1346 __isl_take isl_basic_map *bmap);
1348 Sets and relations can be converted to union sets and relations
1349 using the following functions.
1351 __isl_give isl_union_set *isl_union_set_from_basic_set(
1352 __isl_take isl_basic_set *bset);
1353 __isl_give isl_union_map *isl_union_map_from_basic_map(
1354 __isl_take isl_basic_map *bmap);
1355 __isl_give isl_union_set *isl_union_set_from_set(
1356 __isl_take isl_set *set);
1357 __isl_give isl_union_map *isl_union_map_from_map(
1358 __isl_take isl_map *map);
1360 The inverse conversions below can only be used if the input
1361 union set or relation is known to contain elements in exactly one
1364 __isl_give isl_set *isl_set_from_union_set(
1365 __isl_take isl_union_set *uset);
1366 __isl_give isl_map *isl_map_from_union_map(
1367 __isl_take isl_union_map *umap);
1369 A zero-dimensional (basic) set can be constructed on a given parameter domain
1370 using the following function.
1372 __isl_give isl_basic_set *isl_basic_set_from_params(
1373 __isl_take isl_basic_set *bset);
1374 __isl_give isl_set *isl_set_from_params(
1375 __isl_take isl_set *set);
1377 Sets and relations can be copied and freed again using the following
1380 __isl_give isl_basic_set *isl_basic_set_copy(
1381 __isl_keep isl_basic_set *bset);
1382 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1383 __isl_give isl_union_set *isl_union_set_copy(
1384 __isl_keep isl_union_set *uset);
1385 __isl_give isl_basic_map *isl_basic_map_copy(
1386 __isl_keep isl_basic_map *bmap);
1387 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1388 __isl_give isl_union_map *isl_union_map_copy(
1389 __isl_keep isl_union_map *umap);
1390 __isl_null isl_basic_set *isl_basic_set_free(
1391 __isl_take isl_basic_set *bset);
1392 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1393 __isl_null isl_union_set *isl_union_set_free(
1394 __isl_take isl_union_set *uset);
1395 __isl_null isl_basic_map *isl_basic_map_free(
1396 __isl_take isl_basic_map *bmap);
1397 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1398 __isl_null isl_union_map *isl_union_map_free(
1399 __isl_take isl_union_map *umap);
1401 Other sets and relations can be constructed by starting
1402 from a universe set or relation, adding equality and/or
1403 inequality constraints and then projecting out the
1404 existentially quantified variables, if any.
1405 Constraints can be constructed, manipulated and
1406 added to (or removed from) (basic) sets and relations
1407 using the following functions.
1409 #include <isl/constraint.h>
1410 __isl_give isl_constraint *isl_equality_alloc(
1411 __isl_take isl_local_space *ls);
1412 __isl_give isl_constraint *isl_inequality_alloc(
1413 __isl_take isl_local_space *ls);
1414 __isl_give isl_constraint *isl_constraint_set_constant_si(
1415 __isl_take isl_constraint *constraint, int v);
1416 __isl_give isl_constraint *isl_constraint_set_constant_val(
1417 __isl_take isl_constraint *constraint,
1418 __isl_take isl_val *v);
1419 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1420 __isl_take isl_constraint *constraint,
1421 enum isl_dim_type type, int pos, int v);
1422 __isl_give isl_constraint *
1423 isl_constraint_set_coefficient_val(
1424 __isl_take isl_constraint *constraint,
1425 enum isl_dim_type type, int pos,
1426 __isl_take isl_val *v);
1427 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1428 __isl_take isl_basic_map *bmap,
1429 __isl_take isl_constraint *constraint);
1430 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1431 __isl_take isl_basic_set *bset,
1432 __isl_take isl_constraint *constraint);
1433 __isl_give isl_map *isl_map_add_constraint(
1434 __isl_take isl_map *map,
1435 __isl_take isl_constraint *constraint);
1436 __isl_give isl_set *isl_set_add_constraint(
1437 __isl_take isl_set *set,
1438 __isl_take isl_constraint *constraint);
1439 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1440 __isl_take isl_basic_set *bset,
1441 __isl_take isl_constraint *constraint);
1443 For example, to create a set containing the even integers
1444 between 10 and 42, you would use the following code.
1447 isl_local_space *ls;
1449 isl_basic_set *bset;
1451 space = isl_space_set_alloc(ctx, 0, 2);
1452 bset = isl_basic_set_universe(isl_space_copy(space));
1453 ls = isl_local_space_from_space(space);
1455 c = isl_equality_alloc(isl_local_space_copy(ls));
1456 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1457 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1458 bset = isl_basic_set_add_constraint(bset, c);
1460 c = isl_inequality_alloc(isl_local_space_copy(ls));
1461 c = isl_constraint_set_constant_si(c, -10);
1462 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1463 bset = isl_basic_set_add_constraint(bset, c);
1465 c = isl_inequality_alloc(ls);
1466 c = isl_constraint_set_constant_si(c, 42);
1467 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1468 bset = isl_basic_set_add_constraint(bset, c);
1470 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1474 isl_basic_set *bset;
1475 bset = isl_basic_set_read_from_str(ctx,
1476 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1478 A basic set or relation can also be constructed from two matrices
1479 describing the equalities and the inequalities.
1481 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1482 __isl_take isl_space *space,
1483 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1484 enum isl_dim_type c1,
1485 enum isl_dim_type c2, enum isl_dim_type c3,
1486 enum isl_dim_type c4);
1487 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1488 __isl_take isl_space *space,
1489 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1490 enum isl_dim_type c1,
1491 enum isl_dim_type c2, enum isl_dim_type c3,
1492 enum isl_dim_type c4, enum isl_dim_type c5);
1494 The C<isl_dim_type> arguments indicate the order in which
1495 different kinds of variables appear in the input matrices
1496 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1497 C<isl_dim_set> and C<isl_dim_div> for sets and
1498 of C<isl_dim_cst>, C<isl_dim_param>,
1499 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1501 A (basic or union) set or relation can also be constructed from a
1502 (union) (piecewise) (multiple) affine expression
1503 or a list of affine expressions
1504 (See L<"Piecewise Quasi Affine Expressions"> and
1505 L<"Piecewise Multiple Quasi Affine Expressions">).
1507 __isl_give isl_basic_map *isl_basic_map_from_aff(
1508 __isl_take isl_aff *aff);
1509 __isl_give isl_map *isl_map_from_aff(
1510 __isl_take isl_aff *aff);
1511 __isl_give isl_set *isl_set_from_pw_aff(
1512 __isl_take isl_pw_aff *pwaff);
1513 __isl_give isl_map *isl_map_from_pw_aff(
1514 __isl_take isl_pw_aff *pwaff);
1515 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1516 __isl_take isl_space *domain_space,
1517 __isl_take isl_aff_list *list);
1518 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1519 __isl_take isl_multi_aff *maff)
1520 __isl_give isl_map *isl_map_from_multi_aff(
1521 __isl_take isl_multi_aff *maff)
1522 __isl_give isl_set *isl_set_from_pw_multi_aff(
1523 __isl_take isl_pw_multi_aff *pma);
1524 __isl_give isl_map *isl_map_from_pw_multi_aff(
1525 __isl_take isl_pw_multi_aff *pma);
1526 __isl_give isl_set *isl_set_from_multi_pw_aff(
1527 __isl_take isl_multi_pw_aff *mpa);
1528 __isl_give isl_map *isl_map_from_multi_pw_aff(
1529 __isl_take isl_multi_pw_aff *mpa);
1530 __isl_give isl_union_map *
1531 isl_union_map_from_union_pw_multi_aff(
1532 __isl_take isl_union_pw_multi_aff *upma);
1534 The C<domain_space> argument describes the domain of the resulting
1535 basic relation. It is required because the C<list> may consist
1536 of zero affine expressions.
1538 =head2 Inspecting Sets and Relations
1540 Usually, the user should not have to care about the actual constraints
1541 of the sets and maps, but should instead apply the abstract operations
1542 explained in the following sections.
1543 Occasionally, however, it may be required to inspect the individual
1544 coefficients of the constraints. This section explains how to do so.
1545 In these cases, it may also be useful to have C<isl> compute
1546 an explicit representation of the existentially quantified variables.
1548 __isl_give isl_set *isl_set_compute_divs(
1549 __isl_take isl_set *set);
1550 __isl_give isl_map *isl_map_compute_divs(
1551 __isl_take isl_map *map);
1552 __isl_give isl_union_set *isl_union_set_compute_divs(
1553 __isl_take isl_union_set *uset);
1554 __isl_give isl_union_map *isl_union_map_compute_divs(
1555 __isl_take isl_union_map *umap);
1557 This explicit representation defines the existentially quantified
1558 variables as integer divisions of the other variables, possibly
1559 including earlier existentially quantified variables.
1560 An explicitly represented existentially quantified variable therefore
1561 has a unique value when the values of the other variables are known.
1562 If, furthermore, the same existentials, i.e., existentials
1563 with the same explicit representations, should appear in the
1564 same order in each of the disjuncts of a set or map, then the user should call
1565 either of the following functions.
1567 __isl_give isl_set *isl_set_align_divs(
1568 __isl_take isl_set *set);
1569 __isl_give isl_map *isl_map_align_divs(
1570 __isl_take isl_map *map);
1572 Alternatively, the existentially quantified variables can be removed
1573 using the following functions, which compute an overapproximation.
1575 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1576 __isl_take isl_basic_set *bset);
1577 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1578 __isl_take isl_basic_map *bmap);
1579 __isl_give isl_set *isl_set_remove_divs(
1580 __isl_take isl_set *set);
1581 __isl_give isl_map *isl_map_remove_divs(
1582 __isl_take isl_map *map);
1584 It is also possible to only remove those divs that are defined
1585 in terms of a given range of dimensions or only those for which
1586 no explicit representation is known.
1588 __isl_give isl_basic_set *
1589 isl_basic_set_remove_divs_involving_dims(
1590 __isl_take isl_basic_set *bset,
1591 enum isl_dim_type type,
1592 unsigned first, unsigned n);
1593 __isl_give isl_basic_map *
1594 isl_basic_map_remove_divs_involving_dims(
1595 __isl_take isl_basic_map *bmap,
1596 enum isl_dim_type type,
1597 unsigned first, unsigned n);
1598 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1599 __isl_take isl_set *set, enum isl_dim_type type,
1600 unsigned first, unsigned n);
1601 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1602 __isl_take isl_map *map, enum isl_dim_type type,
1603 unsigned first, unsigned n);
1605 __isl_give isl_basic_set *
1606 isl_basic_set_remove_unknown_divs(
1607 __isl_take isl_basic_set *bset);
1608 __isl_give isl_set *isl_set_remove_unknown_divs(
1609 __isl_take isl_set *set);
1610 __isl_give isl_map *isl_map_remove_unknown_divs(
1611 __isl_take isl_map *map);
1613 To iterate over all the sets or maps in a union set or map, use
1615 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1616 int (*fn)(__isl_take isl_set *set, void *user),
1618 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1619 int (*fn)(__isl_take isl_map *map, void *user),
1622 The number of sets or maps in a union set or map can be obtained
1625 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1626 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1628 To extract the set or map in a given space from a union, use
1630 __isl_give isl_set *isl_union_set_extract_set(
1631 __isl_keep isl_union_set *uset,
1632 __isl_take isl_space *space);
1633 __isl_give isl_map *isl_union_map_extract_map(
1634 __isl_keep isl_union_map *umap,
1635 __isl_take isl_space *space);
1637 To iterate over all the basic sets or maps in a set or map, use
1639 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1640 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1642 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1643 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1646 The callback function C<fn> should return 0 if successful and
1647 -1 if an error occurs. In the latter case, or if any other error
1648 occurs, the above functions will return -1.
1650 It should be noted that C<isl> does not guarantee that
1651 the basic sets or maps passed to C<fn> are disjoint.
1652 If this is required, then the user should call one of
1653 the following functions first.
1655 __isl_give isl_set *isl_set_make_disjoint(
1656 __isl_take isl_set *set);
1657 __isl_give isl_map *isl_map_make_disjoint(
1658 __isl_take isl_map *map);
1660 The number of basic sets in a set can be obtained
1663 int isl_set_n_basic_set(__isl_keep isl_set *set);
1665 To iterate over the constraints of a basic set or map, use
1667 #include <isl/constraint.h>
1669 int isl_basic_set_n_constraint(
1670 __isl_keep isl_basic_set *bset);
1671 int isl_basic_set_foreach_constraint(
1672 __isl_keep isl_basic_set *bset,
1673 int (*fn)(__isl_take isl_constraint *c, void *user),
1675 int isl_basic_map_foreach_constraint(
1676 __isl_keep isl_basic_map *bmap,
1677 int (*fn)(__isl_take isl_constraint *c, void *user),
1679 __isl_null isl_constraint *isl_constraint_free(
1680 __isl_take isl_constraint *c);
1682 Again, the callback function C<fn> should return 0 if successful and
1683 -1 if an error occurs. In the latter case, or if any other error
1684 occurs, the above functions will return -1.
1685 The constraint C<c> represents either an equality or an inequality.
1686 Use the following function to find out whether a constraint
1687 represents an equality. If not, it represents an inequality.
1689 int isl_constraint_is_equality(
1690 __isl_keep isl_constraint *constraint);
1692 The coefficients of the constraints can be inspected using
1693 the following functions.
1695 int isl_constraint_is_lower_bound(
1696 __isl_keep isl_constraint *constraint,
1697 enum isl_dim_type type, unsigned pos);
1698 int isl_constraint_is_upper_bound(
1699 __isl_keep isl_constraint *constraint,
1700 enum isl_dim_type type, unsigned pos);
1701 __isl_give isl_val *isl_constraint_get_constant_val(
1702 __isl_keep isl_constraint *constraint);
1703 __isl_give isl_val *isl_constraint_get_coefficient_val(
1704 __isl_keep isl_constraint *constraint,
1705 enum isl_dim_type type, int pos);
1706 int isl_constraint_involves_dims(
1707 __isl_keep isl_constraint *constraint,
1708 enum isl_dim_type type, unsigned first, unsigned n);
1710 The explicit representations of the existentially quantified
1711 variables can be inspected using the following function.
1712 Note that the user is only allowed to use this function
1713 if the inspected set or map is the result of a call
1714 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1715 The existentially quantified variable is equal to the floor
1716 of the returned affine expression. The affine expression
1717 itself can be inspected using the functions in
1718 L<"Piecewise Quasi Affine Expressions">.
1720 __isl_give isl_aff *isl_constraint_get_div(
1721 __isl_keep isl_constraint *constraint, int pos);
1723 To obtain the constraints of a basic set or map in matrix
1724 form, use the following functions.
1726 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1727 __isl_keep isl_basic_set *bset,
1728 enum isl_dim_type c1, enum isl_dim_type c2,
1729 enum isl_dim_type c3, enum isl_dim_type c4);
1730 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1731 __isl_keep isl_basic_set *bset,
1732 enum isl_dim_type c1, enum isl_dim_type c2,
1733 enum isl_dim_type c3, enum isl_dim_type c4);
1734 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1735 __isl_keep isl_basic_map *bmap,
1736 enum isl_dim_type c1,
1737 enum isl_dim_type c2, enum isl_dim_type c3,
1738 enum isl_dim_type c4, enum isl_dim_type c5);
1739 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1740 __isl_keep isl_basic_map *bmap,
1741 enum isl_dim_type c1,
1742 enum isl_dim_type c2, enum isl_dim_type c3,
1743 enum isl_dim_type c4, enum isl_dim_type c5);
1745 The C<isl_dim_type> arguments dictate the order in which
1746 different kinds of variables appear in the resulting matrix
1747 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1748 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1750 The number of parameters, input, output or set dimensions can
1751 be obtained using the following functions.
1753 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1754 enum isl_dim_type type);
1755 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1756 enum isl_dim_type type);
1757 unsigned isl_set_dim(__isl_keep isl_set *set,
1758 enum isl_dim_type type);
1759 unsigned isl_map_dim(__isl_keep isl_map *map,
1760 enum isl_dim_type type);
1762 To check whether the description of a set or relation depends
1763 on one or more given dimensions, it is not necessary to iterate over all
1764 constraints. Instead the following functions can be used.
1766 int isl_basic_set_involves_dims(
1767 __isl_keep isl_basic_set *bset,
1768 enum isl_dim_type type, unsigned first, unsigned n);
1769 int isl_set_involves_dims(__isl_keep isl_set *set,
1770 enum isl_dim_type type, unsigned first, unsigned n);
1771 int isl_basic_map_involves_dims(
1772 __isl_keep isl_basic_map *bmap,
1773 enum isl_dim_type type, unsigned first, unsigned n);
1774 int isl_map_involves_dims(__isl_keep isl_map *map,
1775 enum isl_dim_type type, unsigned first, unsigned n);
1777 Similarly, the following functions can be used to check whether
1778 a given dimension is involved in any lower or upper bound.
1780 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1781 enum isl_dim_type type, unsigned pos);
1782 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1783 enum isl_dim_type type, unsigned pos);
1785 Note that these functions return true even if there is a bound on
1786 the dimension on only some of the basic sets of C<set>.
1787 To check if they have a bound for all of the basic sets in C<set>,
1788 use the following functions instead.
1790 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1791 enum isl_dim_type type, unsigned pos);
1792 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1793 enum isl_dim_type type, unsigned pos);
1795 The identifiers or names of the domain and range spaces of a set
1796 or relation can be read off or set using the following functions.
1798 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1799 __isl_take isl_basic_set *bset,
1800 __isl_take isl_id *id);
1801 __isl_give isl_set *isl_set_set_tuple_id(
1802 __isl_take isl_set *set, __isl_take isl_id *id);
1803 __isl_give isl_set *isl_set_reset_tuple_id(
1804 __isl_take isl_set *set);
1805 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1806 __isl_give isl_id *isl_set_get_tuple_id(
1807 __isl_keep isl_set *set);
1808 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1809 __isl_take isl_basic_map *bmap,
1810 enum isl_dim_type type, __isl_take isl_id *id);
1811 __isl_give isl_map *isl_map_set_tuple_id(
1812 __isl_take isl_map *map, enum isl_dim_type type,
1813 __isl_take isl_id *id);
1814 __isl_give isl_map *isl_map_reset_tuple_id(
1815 __isl_take isl_map *map, enum isl_dim_type type);
1816 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1817 enum isl_dim_type type);
1818 __isl_give isl_id *isl_map_get_tuple_id(
1819 __isl_keep isl_map *map, enum isl_dim_type type);
1821 const char *isl_basic_set_get_tuple_name(
1822 __isl_keep isl_basic_set *bset);
1823 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1824 __isl_take isl_basic_set *set, const char *s);
1825 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1826 const char *isl_set_get_tuple_name(
1827 __isl_keep isl_set *set);
1828 const char *isl_basic_map_get_tuple_name(
1829 __isl_keep isl_basic_map *bmap,
1830 enum isl_dim_type type);
1831 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1832 __isl_take isl_basic_map *bmap,
1833 enum isl_dim_type type, const char *s);
1834 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1835 enum isl_dim_type type);
1836 const char *isl_map_get_tuple_name(
1837 __isl_keep isl_map *map,
1838 enum isl_dim_type type);
1840 As with C<isl_space_get_tuple_name>, the value returned points to
1841 an internal data structure.
1842 The identifiers, positions or names of individual dimensions can be
1843 read off using the following functions.
1845 __isl_give isl_id *isl_basic_set_get_dim_id(
1846 __isl_keep isl_basic_set *bset,
1847 enum isl_dim_type type, unsigned pos);
1848 __isl_give isl_set *isl_set_set_dim_id(
1849 __isl_take isl_set *set, enum isl_dim_type type,
1850 unsigned pos, __isl_take isl_id *id);
1851 int isl_set_has_dim_id(__isl_keep isl_set *set,
1852 enum isl_dim_type type, unsigned pos);
1853 __isl_give isl_id *isl_set_get_dim_id(
1854 __isl_keep isl_set *set, enum isl_dim_type type,
1856 int isl_basic_map_has_dim_id(
1857 __isl_keep isl_basic_map *bmap,
1858 enum isl_dim_type type, unsigned pos);
1859 __isl_give isl_map *isl_map_set_dim_id(
1860 __isl_take isl_map *map, enum isl_dim_type type,
1861 unsigned pos, __isl_take isl_id *id);
1862 int isl_map_has_dim_id(__isl_keep isl_map *map,
1863 enum isl_dim_type type, unsigned pos);
1864 __isl_give isl_id *isl_map_get_dim_id(
1865 __isl_keep isl_map *map, enum isl_dim_type type,
1868 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1869 enum isl_dim_type type, __isl_keep isl_id *id);
1870 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1871 enum isl_dim_type type, __isl_keep isl_id *id);
1872 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1873 enum isl_dim_type type, const char *name);
1874 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1875 enum isl_dim_type type, const char *name);
1877 const char *isl_constraint_get_dim_name(
1878 __isl_keep isl_constraint *constraint,
1879 enum isl_dim_type type, unsigned pos);
1880 const char *isl_basic_set_get_dim_name(
1881 __isl_keep isl_basic_set *bset,
1882 enum isl_dim_type type, unsigned pos);
1883 int isl_set_has_dim_name(__isl_keep isl_set *set,
1884 enum isl_dim_type type, unsigned pos);
1885 const char *isl_set_get_dim_name(
1886 __isl_keep isl_set *set,
1887 enum isl_dim_type type, unsigned pos);
1888 const char *isl_basic_map_get_dim_name(
1889 __isl_keep isl_basic_map *bmap,
1890 enum isl_dim_type type, unsigned pos);
1891 int isl_map_has_dim_name(__isl_keep isl_map *map,
1892 enum isl_dim_type type, unsigned pos);
1893 const char *isl_map_get_dim_name(
1894 __isl_keep isl_map *map,
1895 enum isl_dim_type type, unsigned pos);
1897 These functions are mostly useful to obtain the identifiers, positions
1898 or names of the parameters. Identifiers of individual dimensions are
1899 essentially only useful for printing. They are ignored by all other
1900 operations and may not be preserved across those operations.
1902 The user pointers on all parameters and tuples can be reset
1903 using the following functions.
1905 #include <isl/set.h>
1906 __isl_give isl_set *isl_set_reset_user(
1907 __isl_take isl_set *set);
1908 #include <isl/map.h>
1909 __isl_give isl_map *isl_map_reset_user(
1910 __isl_take isl_map *map);
1911 #include <isl/union_set.h>
1912 __isl_give isl_union_set *isl_union_set_reset_user(
1913 __isl_take isl_union_set *uset);
1914 #include <isl/union_map.h>
1915 __isl_give isl_union_map *isl_union_map_reset_user(
1916 __isl_take isl_union_map *umap);
1920 =head3 Unary Properties
1926 The following functions test whether the given set or relation
1927 contains any integer points. The ``plain'' variants do not perform
1928 any computations, but simply check if the given set or relation
1929 is already known to be empty.
1931 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1932 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1933 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1934 int isl_set_is_empty(__isl_keep isl_set *set);
1935 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1936 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1937 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1938 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1939 int isl_map_is_empty(__isl_keep isl_map *map);
1940 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1942 =item * Universality
1944 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1945 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1946 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1948 =item * Single-valuedness
1950 int isl_basic_map_is_single_valued(
1951 __isl_keep isl_basic_map *bmap);
1952 int isl_map_plain_is_single_valued(
1953 __isl_keep isl_map *map);
1954 int isl_map_is_single_valued(__isl_keep isl_map *map);
1955 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1959 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1960 int isl_map_is_injective(__isl_keep isl_map *map);
1961 int isl_union_map_plain_is_injective(
1962 __isl_keep isl_union_map *umap);
1963 int isl_union_map_is_injective(
1964 __isl_keep isl_union_map *umap);
1968 int isl_map_is_bijective(__isl_keep isl_map *map);
1969 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1973 __isl_give isl_val *
1974 isl_basic_map_plain_get_val_if_fixed(
1975 __isl_keep isl_basic_map *bmap,
1976 enum isl_dim_type type, unsigned pos);
1977 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
1978 __isl_keep isl_set *set,
1979 enum isl_dim_type type, unsigned pos);
1980 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
1981 __isl_keep isl_map *map,
1982 enum isl_dim_type type, unsigned pos);
1984 If the set or relation obviously lies on a hyperplane where the given dimension
1985 has a fixed value, then return that value.
1986 Otherwise return NaN.
1990 int isl_set_dim_residue_class_val(
1991 __isl_keep isl_set *set,
1992 int pos, __isl_give isl_val **modulo,
1993 __isl_give isl_val **residue);
1995 Check if the values of the given set dimension are equal to a fixed
1996 value modulo some integer value. If so, assign the modulo to C<*modulo>
1997 and the fixed value to C<*residue>. If the given dimension attains only
1998 a single value, then assign C<0> to C<*modulo> and the fixed value to
2000 If the dimension does not attain only a single value and if no modulo
2001 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
2005 To check whether a set is a parameter domain, use this function:
2007 int isl_set_is_params(__isl_keep isl_set *set);
2008 int isl_union_set_is_params(
2009 __isl_keep isl_union_set *uset);
2013 The following functions check whether the space of the given
2014 (basic) set or relation range is a wrapped relation.
2016 #include <isl/space.h>
2017 int isl_space_is_wrapping(
2018 __isl_keep isl_space *space);
2019 int isl_space_domain_is_wrapping(
2020 __isl_keep isl_space *space);
2021 int isl_space_range_is_wrapping(
2022 __isl_keep isl_space *space);
2024 #include <isl/set.h>
2025 int isl_basic_set_is_wrapping(
2026 __isl_keep isl_basic_set *bset);
2027 int isl_set_is_wrapping(__isl_keep isl_set *set);
2029 #include <isl/map.h>
2030 int isl_map_domain_is_wrapping(
2031 __isl_keep isl_map *map);
2032 int isl_map_range_is_wrapping(
2033 __isl_keep isl_map *map);
2035 The input to C<isl_space_is_wrapping> should
2036 be the space of a set, while that of
2037 C<isl_space_domain_is_wrapping> and
2038 C<isl_space_range_is_wrapping> should be the space of a relation.
2040 =item * Internal Product
2042 int isl_basic_map_can_zip(
2043 __isl_keep isl_basic_map *bmap);
2044 int isl_map_can_zip(__isl_keep isl_map *map);
2046 Check whether the product of domain and range of the given relation
2048 i.e., whether both domain and range are nested relations.
2052 int isl_basic_map_can_curry(
2053 __isl_keep isl_basic_map *bmap);
2054 int isl_map_can_curry(__isl_keep isl_map *map);
2056 Check whether the domain of the (basic) relation is a wrapped relation.
2058 int isl_basic_map_can_uncurry(
2059 __isl_keep isl_basic_map *bmap);
2060 int isl_map_can_uncurry(__isl_keep isl_map *map);
2062 Check whether the range of the (basic) relation is a wrapped relation.
2066 =head3 Binary Properties
2072 int isl_basic_set_plain_is_equal(
2073 __isl_keep isl_basic_set *bset1,
2074 __isl_keep isl_basic_set *bset2);
2075 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2076 __isl_keep isl_set *set2);
2077 int isl_set_is_equal(__isl_keep isl_set *set1,
2078 __isl_keep isl_set *set2);
2079 int isl_union_set_is_equal(
2080 __isl_keep isl_union_set *uset1,
2081 __isl_keep isl_union_set *uset2);
2082 int isl_basic_map_is_equal(
2083 __isl_keep isl_basic_map *bmap1,
2084 __isl_keep isl_basic_map *bmap2);
2085 int isl_map_is_equal(__isl_keep isl_map *map1,
2086 __isl_keep isl_map *map2);
2087 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2088 __isl_keep isl_map *map2);
2089 int isl_union_map_is_equal(
2090 __isl_keep isl_union_map *umap1,
2091 __isl_keep isl_union_map *umap2);
2093 =item * Disjointness
2095 int isl_basic_set_is_disjoint(
2096 __isl_keep isl_basic_set *bset1,
2097 __isl_keep isl_basic_set *bset2);
2098 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2099 __isl_keep isl_set *set2);
2100 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2101 __isl_keep isl_set *set2);
2102 int isl_basic_map_is_disjoint(
2103 __isl_keep isl_basic_map *bmap1,
2104 __isl_keep isl_basic_map *bmap2);
2105 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2106 __isl_keep isl_map *map2);
2110 int isl_basic_set_is_subset(
2111 __isl_keep isl_basic_set *bset1,
2112 __isl_keep isl_basic_set *bset2);
2113 int isl_set_is_subset(__isl_keep isl_set *set1,
2114 __isl_keep isl_set *set2);
2115 int isl_set_is_strict_subset(
2116 __isl_keep isl_set *set1,
2117 __isl_keep isl_set *set2);
2118 int isl_union_set_is_subset(
2119 __isl_keep isl_union_set *uset1,
2120 __isl_keep isl_union_set *uset2);
2121 int isl_union_set_is_strict_subset(
2122 __isl_keep isl_union_set *uset1,
2123 __isl_keep isl_union_set *uset2);
2124 int isl_basic_map_is_subset(
2125 __isl_keep isl_basic_map *bmap1,
2126 __isl_keep isl_basic_map *bmap2);
2127 int isl_basic_map_is_strict_subset(
2128 __isl_keep isl_basic_map *bmap1,
2129 __isl_keep isl_basic_map *bmap2);
2130 int isl_map_is_subset(
2131 __isl_keep isl_map *map1,
2132 __isl_keep isl_map *map2);
2133 int isl_map_is_strict_subset(
2134 __isl_keep isl_map *map1,
2135 __isl_keep isl_map *map2);
2136 int isl_union_map_is_subset(
2137 __isl_keep isl_union_map *umap1,
2138 __isl_keep isl_union_map *umap2);
2139 int isl_union_map_is_strict_subset(
2140 __isl_keep isl_union_map *umap1,
2141 __isl_keep isl_union_map *umap2);
2143 Check whether the first argument is a (strict) subset of the
2148 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2149 __isl_keep isl_set *set2);
2151 This function is useful for sorting C<isl_set>s.
2152 The order depends on the internal representation of the inputs.
2153 The order is fixed over different calls to the function (assuming
2154 the internal representation of the inputs has not changed), but may
2155 change over different versions of C<isl>.
2159 =head2 Unary Operations
2165 __isl_give isl_set *isl_set_complement(
2166 __isl_take isl_set *set);
2167 __isl_give isl_map *isl_map_complement(
2168 __isl_take isl_map *map);
2172 __isl_give isl_basic_map *isl_basic_map_reverse(
2173 __isl_take isl_basic_map *bmap);
2174 __isl_give isl_map *isl_map_reverse(
2175 __isl_take isl_map *map);
2176 __isl_give isl_union_map *isl_union_map_reverse(
2177 __isl_take isl_union_map *umap);
2181 #include <isl/local_space.h>
2182 __isl_give isl_local_space *isl_local_space_domain(
2183 __isl_take isl_local_space *ls);
2184 __isl_give isl_local_space *isl_local_space_range(
2185 __isl_take isl_local_space *ls);
2187 #include <isl/set.h>
2188 __isl_give isl_basic_set *isl_basic_set_project_out(
2189 __isl_take isl_basic_set *bset,
2190 enum isl_dim_type type, unsigned first, unsigned n);
2191 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2192 enum isl_dim_type type, unsigned first, unsigned n);
2193 __isl_give isl_basic_set *isl_basic_set_params(
2194 __isl_take isl_basic_set *bset);
2195 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2197 #include <isl/map.h>
2198 __isl_give isl_basic_map *isl_basic_map_project_out(
2199 __isl_take isl_basic_map *bmap,
2200 enum isl_dim_type type, unsigned first, unsigned n);
2201 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2202 enum isl_dim_type type, unsigned first, unsigned n);
2203 __isl_give isl_basic_set *isl_basic_map_domain(
2204 __isl_take isl_basic_map *bmap);
2205 __isl_give isl_basic_set *isl_basic_map_range(
2206 __isl_take isl_basic_map *bmap);
2207 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2208 __isl_give isl_set *isl_map_domain(
2209 __isl_take isl_map *bmap);
2210 __isl_give isl_set *isl_map_range(
2211 __isl_take isl_map *map);
2213 #include <isl/union_set.h>
2214 __isl_give isl_set *isl_union_set_params(
2215 __isl_take isl_union_set *uset);
2217 #include <isl/union_map.h>
2218 __isl_give isl_set *isl_union_map_params(
2219 __isl_take isl_union_map *umap);
2220 __isl_give isl_union_set *isl_union_map_domain(
2221 __isl_take isl_union_map *umap);
2222 __isl_give isl_union_set *isl_union_map_range(
2223 __isl_take isl_union_map *umap);
2225 #include <isl/map.h>
2226 __isl_give isl_basic_map *isl_basic_map_domain_map(
2227 __isl_take isl_basic_map *bmap);
2228 __isl_give isl_basic_map *isl_basic_map_range_map(
2229 __isl_take isl_basic_map *bmap);
2230 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2231 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2233 #include <isl/union_map.h>
2234 __isl_give isl_union_map *isl_union_map_domain_map(
2235 __isl_take isl_union_map *umap);
2236 __isl_give isl_union_map *isl_union_map_range_map(
2237 __isl_take isl_union_map *umap);
2239 The functions above construct a (basic, regular or union) relation
2240 that maps (a wrapped version of) the input relation to its domain or range.
2244 __isl_give isl_basic_set *isl_basic_set_eliminate(
2245 __isl_take isl_basic_set *bset,
2246 enum isl_dim_type type,
2247 unsigned first, unsigned n);
2248 __isl_give isl_set *isl_set_eliminate(
2249 __isl_take isl_set *set, enum isl_dim_type type,
2250 unsigned first, unsigned n);
2251 __isl_give isl_basic_map *isl_basic_map_eliminate(
2252 __isl_take isl_basic_map *bmap,
2253 enum isl_dim_type type,
2254 unsigned first, unsigned n);
2255 __isl_give isl_map *isl_map_eliminate(
2256 __isl_take isl_map *map, enum isl_dim_type type,
2257 unsigned first, unsigned n);
2259 Eliminate the coefficients for the given dimensions from the constraints,
2260 without removing the dimensions.
2262 =item * Constructing a relation from a set
2264 #include <isl/local_space.h>
2265 __isl_give isl_local_space *isl_local_space_from_domain(
2266 __isl_take isl_local_space *ls);
2268 #include <isl/map.h>
2269 __isl_give isl_map *isl_map_from_domain(
2270 __isl_take isl_set *set);
2271 __isl_give isl_map *isl_map_from_range(
2272 __isl_take isl_set *set);
2274 Create a relation with the given set as domain or range.
2275 The range or domain of the created relation is a zero-dimensional
2276 flat anonymous space.
2280 __isl_give isl_basic_set *isl_basic_set_fix_si(
2281 __isl_take isl_basic_set *bset,
2282 enum isl_dim_type type, unsigned pos, int value);
2283 __isl_give isl_basic_set *isl_basic_set_fix_val(
2284 __isl_take isl_basic_set *bset,
2285 enum isl_dim_type type, unsigned pos,
2286 __isl_take isl_val *v);
2287 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2288 enum isl_dim_type type, unsigned pos, int value);
2289 __isl_give isl_set *isl_set_fix_val(
2290 __isl_take isl_set *set,
2291 enum isl_dim_type type, unsigned pos,
2292 __isl_take isl_val *v);
2293 __isl_give isl_basic_map *isl_basic_map_fix_si(
2294 __isl_take isl_basic_map *bmap,
2295 enum isl_dim_type type, unsigned pos, int value);
2296 __isl_give isl_basic_map *isl_basic_map_fix_val(
2297 __isl_take isl_basic_map *bmap,
2298 enum isl_dim_type type, unsigned pos,
2299 __isl_take isl_val *v);
2300 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2301 enum isl_dim_type type, unsigned pos, int value);
2302 __isl_give isl_map *isl_map_fix_val(
2303 __isl_take isl_map *map,
2304 enum isl_dim_type type, unsigned pos,
2305 __isl_take isl_val *v);
2307 Intersect the set or relation with the hyperplane where the given
2308 dimension has the fixed given value.
2310 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2311 __isl_take isl_basic_map *bmap,
2312 enum isl_dim_type type, unsigned pos, int value);
2313 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2314 __isl_take isl_basic_map *bmap,
2315 enum isl_dim_type type, unsigned pos, int value);
2316 __isl_give isl_set *isl_set_lower_bound_si(
2317 __isl_take isl_set *set,
2318 enum isl_dim_type type, unsigned pos, int value);
2319 __isl_give isl_set *isl_set_lower_bound_val(
2320 __isl_take isl_set *set,
2321 enum isl_dim_type type, unsigned pos,
2322 __isl_take isl_val *value);
2323 __isl_give isl_map *isl_map_lower_bound_si(
2324 __isl_take isl_map *map,
2325 enum isl_dim_type type, unsigned pos, int value);
2326 __isl_give isl_set *isl_set_upper_bound_si(
2327 __isl_take isl_set *set,
2328 enum isl_dim_type type, unsigned pos, int value);
2329 __isl_give isl_set *isl_set_upper_bound_val(
2330 __isl_take isl_set *set,
2331 enum isl_dim_type type, unsigned pos,
2332 __isl_take isl_val *value);
2333 __isl_give isl_map *isl_map_upper_bound_si(
2334 __isl_take isl_map *map,
2335 enum isl_dim_type type, unsigned pos, int value);
2337 Intersect the set or relation with the half-space where the given
2338 dimension has a value bounded by the fixed given integer value.
2340 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2341 enum isl_dim_type type1, int pos1,
2342 enum isl_dim_type type2, int pos2);
2343 __isl_give isl_basic_map *isl_basic_map_equate(
2344 __isl_take isl_basic_map *bmap,
2345 enum isl_dim_type type1, int pos1,
2346 enum isl_dim_type type2, int pos2);
2347 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2348 enum isl_dim_type type1, int pos1,
2349 enum isl_dim_type type2, int pos2);
2351 Intersect the set or relation with the hyperplane where the given
2352 dimensions are equal to each other.
2354 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2355 enum isl_dim_type type1, int pos1,
2356 enum isl_dim_type type2, int pos2);
2358 Intersect the relation with the hyperplane where the given
2359 dimensions have opposite values.
2361 __isl_give isl_map *isl_map_order_le(
2362 __isl_take isl_map *map,
2363 enum isl_dim_type type1, int pos1,
2364 enum isl_dim_type type2, int pos2);
2365 __isl_give isl_basic_map *isl_basic_map_order_ge(
2366 __isl_take isl_basic_map *bmap,
2367 enum isl_dim_type type1, int pos1,
2368 enum isl_dim_type type2, int pos2);
2369 __isl_give isl_map *isl_map_order_ge(
2370 __isl_take isl_map *map,
2371 enum isl_dim_type type1, int pos1,
2372 enum isl_dim_type type2, int pos2);
2373 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2374 enum isl_dim_type type1, int pos1,
2375 enum isl_dim_type type2, int pos2);
2376 __isl_give isl_basic_map *isl_basic_map_order_gt(
2377 __isl_take isl_basic_map *bmap,
2378 enum isl_dim_type type1, int pos1,
2379 enum isl_dim_type type2, int pos2);
2380 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2381 enum isl_dim_type type1, int pos1,
2382 enum isl_dim_type type2, int pos2);
2384 Intersect the relation with the half-space where the given
2385 dimensions satisfy the given ordering.
2389 __isl_give isl_map *isl_set_identity(
2390 __isl_take isl_set *set);
2391 __isl_give isl_union_map *isl_union_set_identity(
2392 __isl_take isl_union_set *uset);
2394 Construct an identity relation on the given (union) set.
2398 __isl_give isl_basic_set *isl_basic_map_deltas(
2399 __isl_take isl_basic_map *bmap);
2400 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2401 __isl_give isl_union_set *isl_union_map_deltas(
2402 __isl_take isl_union_map *umap);
2404 These functions return a (basic) set containing the differences
2405 between image elements and corresponding domain elements in the input.
2407 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2408 __isl_take isl_basic_map *bmap);
2409 __isl_give isl_map *isl_map_deltas_map(
2410 __isl_take isl_map *map);
2411 __isl_give isl_union_map *isl_union_map_deltas_map(
2412 __isl_take isl_union_map *umap);
2414 The functions above construct a (basic, regular or union) relation
2415 that maps (a wrapped version of) the input relation to its delta set.
2419 Simplify the representation of a set or relation by trying
2420 to combine pairs of basic sets or relations into a single
2421 basic set or relation.
2423 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2424 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2425 __isl_give isl_union_set *isl_union_set_coalesce(
2426 __isl_take isl_union_set *uset);
2427 __isl_give isl_union_map *isl_union_map_coalesce(
2428 __isl_take isl_union_map *umap);
2430 One of the methods for combining pairs of basic sets or relations
2431 can result in coefficients that are much larger than those that appear
2432 in the constraints of the input. By default, the coefficients are
2433 not allowed to grow larger, but this can be changed by unsetting
2434 the following option.
2436 int isl_options_set_coalesce_bounded_wrapping(
2437 isl_ctx *ctx, int val);
2438 int isl_options_get_coalesce_bounded_wrapping(
2441 =item * Detecting equalities
2443 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2444 __isl_take isl_basic_set *bset);
2445 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2446 __isl_take isl_basic_map *bmap);
2447 __isl_give isl_set *isl_set_detect_equalities(
2448 __isl_take isl_set *set);
2449 __isl_give isl_map *isl_map_detect_equalities(
2450 __isl_take isl_map *map);
2451 __isl_give isl_union_set *isl_union_set_detect_equalities(
2452 __isl_take isl_union_set *uset);
2453 __isl_give isl_union_map *isl_union_map_detect_equalities(
2454 __isl_take isl_union_map *umap);
2456 Simplify the representation of a set or relation by detecting implicit
2459 =item * Removing redundant constraints
2461 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2462 __isl_take isl_basic_set *bset);
2463 __isl_give isl_set *isl_set_remove_redundancies(
2464 __isl_take isl_set *set);
2465 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2466 __isl_take isl_basic_map *bmap);
2467 __isl_give isl_map *isl_map_remove_redundancies(
2468 __isl_take isl_map *map);
2472 __isl_give isl_basic_set *isl_set_convex_hull(
2473 __isl_take isl_set *set);
2474 __isl_give isl_basic_map *isl_map_convex_hull(
2475 __isl_take isl_map *map);
2477 If the input set or relation has any existentially quantified
2478 variables, then the result of these operations is currently undefined.
2482 __isl_give isl_basic_set *
2483 isl_set_unshifted_simple_hull(
2484 __isl_take isl_set *set);
2485 __isl_give isl_basic_map *
2486 isl_map_unshifted_simple_hull(
2487 __isl_take isl_map *map);
2488 __isl_give isl_basic_set *isl_set_simple_hull(
2489 __isl_take isl_set *set);
2490 __isl_give isl_basic_map *isl_map_simple_hull(
2491 __isl_take isl_map *map);
2492 __isl_give isl_union_map *isl_union_map_simple_hull(
2493 __isl_take isl_union_map *umap);
2495 These functions compute a single basic set or relation
2496 that contains the whole input set or relation.
2497 In particular, the output is described by translates
2498 of the constraints describing the basic sets or relations in the input.
2499 In case of C<isl_set_unshifted_simple_hull>, only the original
2500 constraints are used, without any translation.
2504 (See \autoref{s:simple hull}.)
2510 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2511 __isl_take isl_basic_set *bset);
2512 __isl_give isl_basic_set *isl_set_affine_hull(
2513 __isl_take isl_set *set);
2514 __isl_give isl_union_set *isl_union_set_affine_hull(
2515 __isl_take isl_union_set *uset);
2516 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2517 __isl_take isl_basic_map *bmap);
2518 __isl_give isl_basic_map *isl_map_affine_hull(
2519 __isl_take isl_map *map);
2520 __isl_give isl_union_map *isl_union_map_affine_hull(
2521 __isl_take isl_union_map *umap);
2523 In case of union sets and relations, the affine hull is computed
2526 =item * Polyhedral hull
2528 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2529 __isl_take isl_set *set);
2530 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2531 __isl_take isl_map *map);
2532 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2533 __isl_take isl_union_set *uset);
2534 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2535 __isl_take isl_union_map *umap);
2537 These functions compute a single basic set or relation
2538 not involving any existentially quantified variables
2539 that contains the whole input set or relation.
2540 In case of union sets and relations, the polyhedral hull is computed
2543 =item * Other approximations
2545 __isl_give isl_basic_set *
2546 isl_basic_set_drop_constraints_involving_dims(
2547 __isl_take isl_basic_set *bset,
2548 enum isl_dim_type type,
2549 unsigned first, unsigned n);
2550 __isl_give isl_basic_map *
2551 isl_basic_map_drop_constraints_involving_dims(
2552 __isl_take isl_basic_map *bmap,
2553 enum isl_dim_type type,
2554 unsigned first, unsigned n);
2555 __isl_give isl_basic_set *
2556 isl_basic_set_drop_constraints_not_involving_dims(
2557 __isl_take isl_basic_set *bset,
2558 enum isl_dim_type type,
2559 unsigned first, unsigned n);
2560 __isl_give isl_set *
2561 isl_set_drop_constraints_involving_dims(
2562 __isl_take isl_set *set,
2563 enum isl_dim_type type,
2564 unsigned first, unsigned n);
2565 __isl_give isl_map *
2566 isl_map_drop_constraints_involving_dims(
2567 __isl_take isl_map *map,
2568 enum isl_dim_type type,
2569 unsigned first, unsigned n);
2571 These functions drop any constraints (not) involving the specified dimensions.
2572 Note that the result depends on the representation of the input.
2576 __isl_give isl_basic_set *isl_basic_set_sample(
2577 __isl_take isl_basic_set *bset);
2578 __isl_give isl_basic_set *isl_set_sample(
2579 __isl_take isl_set *set);
2580 __isl_give isl_basic_map *isl_basic_map_sample(
2581 __isl_take isl_basic_map *bmap);
2582 __isl_give isl_basic_map *isl_map_sample(
2583 __isl_take isl_map *map);
2585 If the input (basic) set or relation is non-empty, then return
2586 a singleton subset of the input. Otherwise, return an empty set.
2588 =item * Optimization
2590 #include <isl/ilp.h>
2591 __isl_give isl_val *isl_basic_set_max_val(
2592 __isl_keep isl_basic_set *bset,
2593 __isl_keep isl_aff *obj);
2594 __isl_give isl_val *isl_set_min_val(
2595 __isl_keep isl_set *set,
2596 __isl_keep isl_aff *obj);
2597 __isl_give isl_val *isl_set_max_val(
2598 __isl_keep isl_set *set,
2599 __isl_keep isl_aff *obj);
2601 Compute the minimum or maximum of the integer affine expression C<obj>
2602 over the points in C<set>, returning the result in C<opt>.
2603 The result is C<NULL> in case of an error, the optimal value in case
2604 there is one, negative infinity or infinity if the problem is unbounded and
2605 NaN if the problem is empty.
2607 =item * Parametric optimization
2609 __isl_give isl_pw_aff *isl_set_dim_min(
2610 __isl_take isl_set *set, int pos);
2611 __isl_give isl_pw_aff *isl_set_dim_max(
2612 __isl_take isl_set *set, int pos);
2613 __isl_give isl_pw_aff *isl_map_dim_max(
2614 __isl_take isl_map *map, int pos);
2616 Compute the minimum or maximum of the given set or output dimension
2617 as a function of the parameters (and input dimensions), but independently
2618 of the other set or output dimensions.
2619 For lexicographic optimization, see L<"Lexicographic Optimization">.
2623 The following functions compute either the set of (rational) coefficient
2624 values of valid constraints for the given set or the set of (rational)
2625 values satisfying the constraints with coefficients from the given set.
2626 Internally, these two sets of functions perform essentially the
2627 same operations, except that the set of coefficients is assumed to
2628 be a cone, while the set of values may be any polyhedron.
2629 The current implementation is based on the Farkas lemma and
2630 Fourier-Motzkin elimination, but this may change or be made optional
2631 in future. In particular, future implementations may use different
2632 dualization algorithms or skip the elimination step.
2634 __isl_give isl_basic_set *isl_basic_set_coefficients(
2635 __isl_take isl_basic_set *bset);
2636 __isl_give isl_basic_set *isl_set_coefficients(
2637 __isl_take isl_set *set);
2638 __isl_give isl_union_set *isl_union_set_coefficients(
2639 __isl_take isl_union_set *bset);
2640 __isl_give isl_basic_set *isl_basic_set_solutions(
2641 __isl_take isl_basic_set *bset);
2642 __isl_give isl_basic_set *isl_set_solutions(
2643 __isl_take isl_set *set);
2644 __isl_give isl_union_set *isl_union_set_solutions(
2645 __isl_take isl_union_set *bset);
2649 __isl_give isl_map *isl_map_fixed_power_val(
2650 __isl_take isl_map *map,
2651 __isl_take isl_val *exp);
2652 __isl_give isl_union_map *
2653 isl_union_map_fixed_power_val(
2654 __isl_take isl_union_map *umap,
2655 __isl_take isl_val *exp);
2657 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2658 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2659 of C<map> is computed.
2661 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2663 __isl_give isl_union_map *isl_union_map_power(
2664 __isl_take isl_union_map *umap, int *exact);
2666 Compute a parametric representation for all positive powers I<k> of C<map>.
2667 The result maps I<k> to a nested relation corresponding to the
2668 I<k>th power of C<map>.
2669 The result may be an overapproximation. If the result is known to be exact,
2670 then C<*exact> is set to C<1>.
2672 =item * Transitive closure
2674 __isl_give isl_map *isl_map_transitive_closure(
2675 __isl_take isl_map *map, int *exact);
2676 __isl_give isl_union_map *isl_union_map_transitive_closure(
2677 __isl_take isl_union_map *umap, int *exact);
2679 Compute the transitive closure of C<map>.
2680 The result may be an overapproximation. If the result is known to be exact,
2681 then C<*exact> is set to C<1>.
2683 =item * Reaching path lengths
2685 __isl_give isl_map *isl_map_reaching_path_lengths(
2686 __isl_take isl_map *map, int *exact);
2688 Compute a relation that maps each element in the range of C<map>
2689 to the lengths of all paths composed of edges in C<map> that
2690 end up in the given element.
2691 The result may be an overapproximation. If the result is known to be exact,
2692 then C<*exact> is set to C<1>.
2693 To compute the I<maximal> path length, the resulting relation
2694 should be postprocessed by C<isl_map_lexmax>.
2695 In particular, if the input relation is a dependence relation
2696 (mapping sources to sinks), then the maximal path length corresponds
2697 to the free schedule.
2698 Note, however, that C<isl_map_lexmax> expects the maximum to be
2699 finite, so if the path lengths are unbounded (possibly due to
2700 the overapproximation), then you will get an error message.
2704 #include <isl/space.h>
2705 __isl_give isl_space *isl_space_wrap(
2706 __isl_take isl_space *space);
2707 __isl_give isl_space *isl_space_unwrap(
2708 __isl_take isl_space *space);
2710 #include <isl/set.h>
2711 __isl_give isl_basic_map *isl_basic_set_unwrap(
2712 __isl_take isl_basic_set *bset);
2713 __isl_give isl_map *isl_set_unwrap(
2714 __isl_take isl_set *set);
2716 #include <isl/map.h>
2717 __isl_give isl_basic_set *isl_basic_map_wrap(
2718 __isl_take isl_basic_map *bmap);
2719 __isl_give isl_set *isl_map_wrap(
2720 __isl_take isl_map *map);
2722 #include <isl/union_set.h>
2723 __isl_give isl_union_map *isl_union_set_unwrap(
2724 __isl_take isl_union_set *uset);
2726 #include <isl/union_map.h>
2727 __isl_give isl_union_set *isl_union_map_wrap(
2728 __isl_take isl_union_map *umap);
2730 The input to C<isl_space_unwrap> should
2731 be the space of a set, while that of
2732 C<isl_space_wrap> should be the space of a relation.
2733 Conversely, the output of C<isl_space_unwrap> is the space
2734 of a relation, while that of C<isl_space_wrap> is the space of a set.
2738 Remove any internal structure of domain (and range) of the given
2739 set or relation. If there is any such internal structure in the input,
2740 then the name of the space is also removed.
2742 #include <isl/local_space.h>
2743 __isl_give isl_local_space *
2744 isl_local_space_flatten_domain(
2745 __isl_take isl_local_space *ls);
2746 __isl_give isl_local_space *
2747 isl_local_space_flatten_range(
2748 __isl_take isl_local_space *ls);
2750 #include <isl/set.h>
2751 __isl_give isl_basic_set *isl_basic_set_flatten(
2752 __isl_take isl_basic_set *bset);
2753 __isl_give isl_set *isl_set_flatten(
2754 __isl_take isl_set *set);
2756 #include <isl/map.h>
2757 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2758 __isl_take isl_basic_map *bmap);
2759 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2760 __isl_take isl_basic_map *bmap);
2761 __isl_give isl_map *isl_map_flatten_range(
2762 __isl_take isl_map *map);
2763 __isl_give isl_map *isl_map_flatten_domain(
2764 __isl_take isl_map *map);
2765 __isl_give isl_basic_map *isl_basic_map_flatten(
2766 __isl_take isl_basic_map *bmap);
2767 __isl_give isl_map *isl_map_flatten(
2768 __isl_take isl_map *map);
2770 #include <isl/map.h>
2771 __isl_give isl_map *isl_set_flatten_map(
2772 __isl_take isl_set *set);
2774 The function above constructs a relation
2775 that maps the input set to a flattened version of the set.
2779 Lift the input set to a space with extra dimensions corresponding
2780 to the existentially quantified variables in the input.
2781 In particular, the result lives in a wrapped map where the domain
2782 is the original space and the range corresponds to the original
2783 existentially quantified variables.
2785 __isl_give isl_basic_set *isl_basic_set_lift(
2786 __isl_take isl_basic_set *bset);
2787 __isl_give isl_set *isl_set_lift(
2788 __isl_take isl_set *set);
2789 __isl_give isl_union_set *isl_union_set_lift(
2790 __isl_take isl_union_set *uset);
2792 Given a local space that contains the existentially quantified
2793 variables of a set, a basic relation that, when applied to
2794 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2795 can be constructed using the following function.
2797 #include <isl/local_space.h>
2798 __isl_give isl_basic_map *isl_local_space_lifting(
2799 __isl_take isl_local_space *ls);
2801 =item * Internal Product
2803 __isl_give isl_basic_map *isl_basic_map_zip(
2804 __isl_take isl_basic_map *bmap);
2805 __isl_give isl_map *isl_map_zip(
2806 __isl_take isl_map *map);
2807 __isl_give isl_union_map *isl_union_map_zip(
2808 __isl_take isl_union_map *umap);
2810 Given a relation with nested relations for domain and range,
2811 interchange the range of the domain with the domain of the range.
2815 __isl_give isl_basic_map *isl_basic_map_curry(
2816 __isl_take isl_basic_map *bmap);
2817 __isl_give isl_basic_map *isl_basic_map_uncurry(
2818 __isl_take isl_basic_map *bmap);
2819 __isl_give isl_map *isl_map_curry(
2820 __isl_take isl_map *map);
2821 __isl_give isl_map *isl_map_uncurry(
2822 __isl_take isl_map *map);
2823 __isl_give isl_union_map *isl_union_map_curry(
2824 __isl_take isl_union_map *umap);
2825 __isl_give isl_union_map *isl_union_map_uncurry(
2826 __isl_take isl_union_map *umap);
2828 Given a relation with a nested relation for domain,
2829 the C<curry> functions
2830 move the range of the nested relation out of the domain
2831 and use it as the domain of a nested relation in the range,
2832 with the original range as range of this nested relation.
2833 The C<uncurry> functions perform the inverse operation.
2835 =item * Aligning parameters
2837 __isl_give isl_basic_set *isl_basic_set_align_params(
2838 __isl_take isl_basic_set *bset,
2839 __isl_take isl_space *model);
2840 __isl_give isl_set *isl_set_align_params(
2841 __isl_take isl_set *set,
2842 __isl_take isl_space *model);
2843 __isl_give isl_basic_map *isl_basic_map_align_params(
2844 __isl_take isl_basic_map *bmap,
2845 __isl_take isl_space *model);
2846 __isl_give isl_map *isl_map_align_params(
2847 __isl_take isl_map *map,
2848 __isl_take isl_space *model);
2850 Change the order of the parameters of the given set or relation
2851 such that the first parameters match those of C<model>.
2852 This may involve the introduction of extra parameters.
2853 All parameters need to be named.
2855 =item * Dimension manipulation
2857 #include <isl/local_space.h>
2858 __isl_give isl_local_space *isl_local_space_add_dims(
2859 __isl_take isl_local_space *ls,
2860 enum isl_dim_type type, unsigned n);
2861 __isl_give isl_local_space *isl_local_space_insert_dims(
2862 __isl_take isl_local_space *ls,
2863 enum isl_dim_type type, unsigned first, unsigned n);
2864 __isl_give isl_local_space *isl_local_space_drop_dims(
2865 __isl_take isl_local_space *ls,
2866 enum isl_dim_type type, unsigned first, unsigned n);
2868 #include <isl/set.h>
2869 __isl_give isl_basic_set *isl_basic_set_add_dims(
2870 __isl_take isl_basic_set *bset,
2871 enum isl_dim_type type, unsigned n);
2872 __isl_give isl_set *isl_set_add_dims(
2873 __isl_take isl_set *set,
2874 enum isl_dim_type type, unsigned n);
2875 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2876 __isl_take isl_basic_set *bset,
2877 enum isl_dim_type type, unsigned pos,
2879 __isl_give isl_set *isl_set_insert_dims(
2880 __isl_take isl_set *set,
2881 enum isl_dim_type type, unsigned pos, unsigned n);
2882 __isl_give isl_basic_set *isl_basic_set_move_dims(
2883 __isl_take isl_basic_set *bset,
2884 enum isl_dim_type dst_type, unsigned dst_pos,
2885 enum isl_dim_type src_type, unsigned src_pos,
2887 __isl_give isl_set *isl_set_move_dims(
2888 __isl_take isl_set *set,
2889 enum isl_dim_type dst_type, unsigned dst_pos,
2890 enum isl_dim_type src_type, unsigned src_pos,
2893 #include <isl/map.h>
2894 __isl_give isl_map *isl_map_add_dims(
2895 __isl_take isl_map *map,
2896 enum isl_dim_type type, unsigned n);
2897 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2898 __isl_take isl_basic_map *bmap,
2899 enum isl_dim_type type, unsigned pos,
2901 __isl_give isl_map *isl_map_insert_dims(
2902 __isl_take isl_map *map,
2903 enum isl_dim_type type, unsigned pos, unsigned n);
2904 __isl_give isl_basic_map *isl_basic_map_move_dims(
2905 __isl_take isl_basic_map *bmap,
2906 enum isl_dim_type dst_type, unsigned dst_pos,
2907 enum isl_dim_type src_type, unsigned src_pos,
2909 __isl_give isl_map *isl_map_move_dims(
2910 __isl_take isl_map *map,
2911 enum isl_dim_type dst_type, unsigned dst_pos,
2912 enum isl_dim_type src_type, unsigned src_pos,
2915 It is usually not advisable to directly change the (input or output)
2916 space of a set or a relation as this removes the name and the internal
2917 structure of the space. However, the above functions can be useful
2918 to add new parameters, assuming
2919 C<isl_set_align_params> and C<isl_map_align_params>
2924 =head2 Binary Operations
2926 The two arguments of a binary operation not only need to live
2927 in the same C<isl_ctx>, they currently also need to have
2928 the same (number of) parameters.
2930 =head3 Basic Operations
2934 =item * Intersection
2936 #include <isl/local_space.h>
2937 __isl_give isl_local_space *isl_local_space_intersect(
2938 __isl_take isl_local_space *ls1,
2939 __isl_take isl_local_space *ls2);
2941 #include <isl/set.h>
2942 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2943 __isl_take isl_basic_set *bset1,
2944 __isl_take isl_basic_set *bset2);
2945 __isl_give isl_basic_set *isl_basic_set_intersect(
2946 __isl_take isl_basic_set *bset1,
2947 __isl_take isl_basic_set *bset2);
2948 __isl_give isl_set *isl_set_intersect_params(
2949 __isl_take isl_set *set,
2950 __isl_take isl_set *params);
2951 __isl_give isl_set *isl_set_intersect(
2952 __isl_take isl_set *set1,
2953 __isl_take isl_set *set2);
2955 #include <isl/map.h>
2956 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2957 __isl_take isl_basic_map *bmap,
2958 __isl_take isl_basic_set *bset);
2959 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2960 __isl_take isl_basic_map *bmap,
2961 __isl_take isl_basic_set *bset);
2962 __isl_give isl_basic_map *isl_basic_map_intersect(
2963 __isl_take isl_basic_map *bmap1,
2964 __isl_take isl_basic_map *bmap2);
2965 __isl_give isl_map *isl_map_intersect_params(
2966 __isl_take isl_map *map,
2967 __isl_take isl_set *params);
2968 __isl_give isl_map *isl_map_intersect_domain(
2969 __isl_take isl_map *map,
2970 __isl_take isl_set *set);
2971 __isl_give isl_map *isl_map_intersect_range(
2972 __isl_take isl_map *map,
2973 __isl_take isl_set *set);
2974 __isl_give isl_map *isl_map_intersect(
2975 __isl_take isl_map *map1,
2976 __isl_take isl_map *map2);
2978 #include <isl/union_set.h>
2979 __isl_give isl_union_set *isl_union_set_intersect_params(
2980 __isl_take isl_union_set *uset,
2981 __isl_take isl_set *set);
2982 __isl_give isl_union_set *isl_union_set_intersect(
2983 __isl_take isl_union_set *uset1,
2984 __isl_take isl_union_set *uset2);
2986 #include <isl/union_map.h>
2987 __isl_give isl_union_map *isl_union_map_intersect_params(
2988 __isl_take isl_union_map *umap,
2989 __isl_take isl_set *set);
2990 __isl_give isl_union_map *isl_union_map_intersect_domain(
2991 __isl_take isl_union_map *umap,
2992 __isl_take isl_union_set *uset);
2993 __isl_give isl_union_map *isl_union_map_intersect_range(
2994 __isl_take isl_union_map *umap,
2995 __isl_take isl_union_set *uset);
2996 __isl_give isl_union_map *isl_union_map_intersect(
2997 __isl_take isl_union_map *umap1,
2998 __isl_take isl_union_map *umap2);
3000 The second argument to the C<_params> functions needs to be
3001 a parametric (basic) set. For the other functions, a parametric set
3002 for either argument is only allowed if the other argument is
3003 a parametric set as well.
3007 __isl_give isl_set *isl_basic_set_union(
3008 __isl_take isl_basic_set *bset1,
3009 __isl_take isl_basic_set *bset2);
3010 __isl_give isl_map *isl_basic_map_union(
3011 __isl_take isl_basic_map *bmap1,
3012 __isl_take isl_basic_map *bmap2);
3013 __isl_give isl_set *isl_set_union(
3014 __isl_take isl_set *set1,
3015 __isl_take isl_set *set2);
3016 __isl_give isl_map *isl_map_union(
3017 __isl_take isl_map *map1,
3018 __isl_take isl_map *map2);
3019 __isl_give isl_union_set *isl_union_set_union(
3020 __isl_take isl_union_set *uset1,
3021 __isl_take isl_union_set *uset2);
3022 __isl_give isl_union_map *isl_union_map_union(
3023 __isl_take isl_union_map *umap1,
3024 __isl_take isl_union_map *umap2);
3026 =item * Set difference
3028 __isl_give isl_set *isl_set_subtract(
3029 __isl_take isl_set *set1,
3030 __isl_take isl_set *set2);
3031 __isl_give isl_map *isl_map_subtract(
3032 __isl_take isl_map *map1,
3033 __isl_take isl_map *map2);
3034 __isl_give isl_map *isl_map_subtract_domain(
3035 __isl_take isl_map *map,
3036 __isl_take isl_set *dom);
3037 __isl_give isl_map *isl_map_subtract_range(
3038 __isl_take isl_map *map,
3039 __isl_take isl_set *dom);
3040 __isl_give isl_union_set *isl_union_set_subtract(
3041 __isl_take isl_union_set *uset1,
3042 __isl_take isl_union_set *uset2);
3043 __isl_give isl_union_map *isl_union_map_subtract(
3044 __isl_take isl_union_map *umap1,
3045 __isl_take isl_union_map *umap2);
3046 __isl_give isl_union_map *isl_union_map_subtract_domain(
3047 __isl_take isl_union_map *umap,
3048 __isl_take isl_union_set *dom);
3049 __isl_give isl_union_map *isl_union_map_subtract_range(
3050 __isl_take isl_union_map *umap,
3051 __isl_take isl_union_set *dom);
3055 __isl_give isl_basic_set *isl_basic_set_apply(
3056 __isl_take isl_basic_set *bset,
3057 __isl_take isl_basic_map *bmap);
3058 __isl_give isl_set *isl_set_apply(
3059 __isl_take isl_set *set,
3060 __isl_take isl_map *map);
3061 __isl_give isl_union_set *isl_union_set_apply(
3062 __isl_take isl_union_set *uset,
3063 __isl_take isl_union_map *umap);
3064 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3065 __isl_take isl_basic_map *bmap1,
3066 __isl_take isl_basic_map *bmap2);
3067 __isl_give isl_basic_map *isl_basic_map_apply_range(
3068 __isl_take isl_basic_map *bmap1,
3069 __isl_take isl_basic_map *bmap2);
3070 __isl_give isl_map *isl_map_apply_domain(
3071 __isl_take isl_map *map1,
3072 __isl_take isl_map *map2);
3073 __isl_give isl_union_map *isl_union_map_apply_domain(
3074 __isl_take isl_union_map *umap1,
3075 __isl_take isl_union_map *umap2);
3076 __isl_give isl_map *isl_map_apply_range(
3077 __isl_take isl_map *map1,
3078 __isl_take isl_map *map2);
3079 __isl_give isl_union_map *isl_union_map_apply_range(
3080 __isl_take isl_union_map *umap1,
3081 __isl_take isl_union_map *umap2);
3085 #include <isl/set.h>
3086 __isl_give isl_basic_set *
3087 isl_basic_set_preimage_multi_aff(
3088 __isl_take isl_basic_set *bset,
3089 __isl_take isl_multi_aff *ma);
3090 __isl_give isl_set *isl_set_preimage_multi_aff(
3091 __isl_take isl_set *set,
3092 __isl_take isl_multi_aff *ma);
3093 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3094 __isl_take isl_set *set,
3095 __isl_take isl_pw_multi_aff *pma);
3096 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
3097 __isl_take isl_set *set,
3098 __isl_take isl_multi_pw_aff *mpa);
3100 #include <isl/union_set.h>
3101 __isl_give isl_union_set *
3102 isl_union_set_preimage_multi_aff(
3103 __isl_take isl_union_set *uset,
3104 __isl_take isl_multi_aff *ma);
3105 __isl_give isl_union_set *
3106 isl_union_set_preimage_pw_multi_aff(
3107 __isl_take isl_union_set *uset,
3108 __isl_take isl_pw_multi_aff *pma);
3109 __isl_give isl_union_set *
3110 isl_union_set_preimage_union_pw_multi_aff(
3111 __isl_take isl_union_set *uset,
3112 __isl_take isl_union_pw_multi_aff *upma);
3114 #include <isl/map.h>
3115 __isl_give isl_basic_map *
3116 isl_basic_map_preimage_domain_multi_aff(
3117 __isl_take isl_basic_map *bmap,
3118 __isl_take isl_multi_aff *ma);
3119 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3120 __isl_take isl_map *map,
3121 __isl_take isl_multi_aff *ma);
3122 __isl_give isl_map *isl_map_preimage_range_multi_aff(
3123 __isl_take isl_map *map,
3124 __isl_take isl_multi_aff *ma);
3125 __isl_give isl_map *
3126 isl_map_preimage_domain_pw_multi_aff(
3127 __isl_take isl_map *map,
3128 __isl_take isl_pw_multi_aff *pma);
3129 __isl_give isl_map *
3130 isl_map_preimage_range_pw_multi_aff(
3131 __isl_take isl_map *map,
3132 __isl_take isl_pw_multi_aff *pma);
3133 __isl_give isl_map *
3134 isl_map_preimage_domain_multi_pw_aff(
3135 __isl_take isl_map *map,
3136 __isl_take isl_multi_pw_aff *mpa);
3137 __isl_give isl_basic_map *
3138 isl_basic_map_preimage_range_multi_aff(
3139 __isl_take isl_basic_map *bmap,
3140 __isl_take isl_multi_aff *ma);
3142 #include <isl/union_map.h>
3143 __isl_give isl_union_map *
3144 isl_union_map_preimage_domain_multi_aff(
3145 __isl_take isl_union_map *umap,
3146 __isl_take isl_multi_aff *ma);
3147 __isl_give isl_union_map *
3148 isl_union_map_preimage_range_multi_aff(
3149 __isl_take isl_union_map *umap,
3150 __isl_take isl_multi_aff *ma);
3151 __isl_give isl_union_map *
3152 isl_union_map_preimage_domain_pw_multi_aff(
3153 __isl_take isl_union_map *umap,
3154 __isl_take isl_pw_multi_aff *pma);
3155 __isl_give isl_union_map *
3156 isl_union_map_preimage_range_pw_multi_aff(
3157 __isl_take isl_union_map *umap,
3158 __isl_take isl_pw_multi_aff *pma);
3159 __isl_give isl_union_map *
3160 isl_union_map_preimage_domain_union_pw_multi_aff(
3161 __isl_take isl_union_map *umap,
3162 __isl_take isl_union_pw_multi_aff *upma);
3163 __isl_give isl_union_map *
3164 isl_union_map_preimage_range_union_pw_multi_aff(
3165 __isl_take isl_union_map *umap,
3166 __isl_take isl_union_pw_multi_aff *upma);
3168 These functions compute the preimage of the given set or map domain/range under
3169 the given function. In other words, the expression is plugged
3170 into the set description or into the domain/range of the map.
3171 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3172 L</"Piecewise Multiple Quasi Affine Expressions">.
3174 =item * Cartesian Product
3176 #include <isl/space.h>
3177 __isl_give isl_space *isl_space_product(
3178 __isl_take isl_space *space1,
3179 __isl_take isl_space *space2);
3180 __isl_give isl_space *isl_space_domain_product(
3181 __isl_take isl_space *space1,
3182 __isl_take isl_space *space2);
3183 __isl_give isl_space *isl_space_range_product(
3184 __isl_take isl_space *space1,
3185 __isl_take isl_space *space2);
3188 C<isl_space_product>, C<isl_space_domain_product>
3189 and C<isl_space_range_product> take pairs or relation spaces and
3190 produce a single relations space, where either the domain, the range
3191 or both domain and range are wrapped spaces of relations between
3192 the domains and/or ranges of the input spaces.
3193 If the product is only constructed over the domain or the range
3194 then the ranges or the domains of the inputs should be the same.
3196 #include <isl/set.h>
3197 __isl_give isl_set *isl_set_product(
3198 __isl_take isl_set *set1,
3199 __isl_take isl_set *set2);
3201 #include <isl/map.h>
3202 __isl_give isl_basic_map *isl_basic_map_domain_product(
3203 __isl_take isl_basic_map *bmap1,
3204 __isl_take isl_basic_map *bmap2);
3205 __isl_give isl_basic_map *isl_basic_map_range_product(
3206 __isl_take isl_basic_map *bmap1,
3207 __isl_take isl_basic_map *bmap2);
3208 __isl_give isl_basic_map *isl_basic_map_product(
3209 __isl_take isl_basic_map *bmap1,
3210 __isl_take isl_basic_map *bmap2);
3211 __isl_give isl_map *isl_map_domain_product(
3212 __isl_take isl_map *map1,
3213 __isl_take isl_map *map2);
3214 __isl_give isl_map *isl_map_range_product(
3215 __isl_take isl_map *map1,
3216 __isl_take isl_map *map2);
3217 __isl_give isl_map *isl_map_product(
3218 __isl_take isl_map *map1,
3219 __isl_take isl_map *map2);
3221 #include <isl/union_set.h>
3222 __isl_give isl_union_set *isl_union_set_product(
3223 __isl_take isl_union_set *uset1,
3224 __isl_take isl_union_set *uset2);
3226 #include <isl/union_map.h>
3227 __isl_give isl_union_map *isl_union_map_domain_product(
3228 __isl_take isl_union_map *umap1,
3229 __isl_take isl_union_map *umap2);
3230 __isl_give isl_union_map *isl_union_map_range_product(
3231 __isl_take isl_union_map *umap1,
3232 __isl_take isl_union_map *umap2);
3233 __isl_give isl_union_map *isl_union_map_product(
3234 __isl_take isl_union_map *umap1,
3235 __isl_take isl_union_map *umap2);
3237 The above functions compute the cross product of the given
3238 sets or relations. The domains and ranges of the results
3239 are wrapped maps between domains and ranges of the inputs.
3240 To obtain a ``flat'' product, use the following functions
3243 __isl_give isl_basic_set *isl_basic_set_flat_product(
3244 __isl_take isl_basic_set *bset1,
3245 __isl_take isl_basic_set *bset2);
3246 __isl_give isl_set *isl_set_flat_product(
3247 __isl_take isl_set *set1,
3248 __isl_take isl_set *set2);
3249 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3250 __isl_take isl_basic_map *bmap1,
3251 __isl_take isl_basic_map *bmap2);
3252 __isl_give isl_map *isl_map_flat_domain_product(
3253 __isl_take isl_map *map1,
3254 __isl_take isl_map *map2);
3255 __isl_give isl_map *isl_map_flat_range_product(
3256 __isl_take isl_map *map1,
3257 __isl_take isl_map *map2);
3258 __isl_give isl_union_map *isl_union_map_flat_range_product(
3259 __isl_take isl_union_map *umap1,
3260 __isl_take isl_union_map *umap2);
3261 __isl_give isl_basic_map *isl_basic_map_flat_product(
3262 __isl_take isl_basic_map *bmap1,
3263 __isl_take isl_basic_map *bmap2);
3264 __isl_give isl_map *isl_map_flat_product(
3265 __isl_take isl_map *map1,
3266 __isl_take isl_map *map2);
3268 #include <isl/space.h>
3269 __isl_give isl_space *isl_space_domain_factor_domain(
3270 __isl_take isl_space *space);
3271 __isl_give isl_space *isl_space_range_factor_domain(
3272 __isl_take isl_space *space);
3273 __isl_give isl_space *isl_space_range_factor_range(
3274 __isl_take isl_space *space);
3276 The functions C<isl_space_range_factor_domain> and
3277 C<isl_space_range_factor_range> extract the two arguments from
3278 the result of a call to C<isl_space_range_product>.
3280 The arguments of a call to C<isl_map_range_product> can be extracted
3281 from the result using the following two functions.
3283 #include <isl/map.h>
3284 __isl_give isl_map *isl_map_range_factor_domain(
3285 __isl_take isl_map *map);
3286 __isl_give isl_map *isl_map_range_factor_range(
3287 __isl_take isl_map *map);
3289 =item * Simplification
3291 __isl_give isl_basic_set *isl_basic_set_gist(
3292 __isl_take isl_basic_set *bset,
3293 __isl_take isl_basic_set *context);
3294 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3295 __isl_take isl_set *context);
3296 __isl_give isl_set *isl_set_gist_params(
3297 __isl_take isl_set *set,
3298 __isl_take isl_set *context);
3299 __isl_give isl_union_set *isl_union_set_gist(
3300 __isl_take isl_union_set *uset,
3301 __isl_take isl_union_set *context);
3302 __isl_give isl_union_set *isl_union_set_gist_params(
3303 __isl_take isl_union_set *uset,
3304 __isl_take isl_set *set);
3305 __isl_give isl_basic_map *isl_basic_map_gist(
3306 __isl_take isl_basic_map *bmap,
3307 __isl_take isl_basic_map *context);
3308 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3309 __isl_take isl_map *context);
3310 __isl_give isl_map *isl_map_gist_params(
3311 __isl_take isl_map *map,
3312 __isl_take isl_set *context);
3313 __isl_give isl_map *isl_map_gist_domain(
3314 __isl_take isl_map *map,
3315 __isl_take isl_set *context);
3316 __isl_give isl_map *isl_map_gist_range(
3317 __isl_take isl_map *map,
3318 __isl_take isl_set *context);
3319 __isl_give isl_union_map *isl_union_map_gist(
3320 __isl_take isl_union_map *umap,
3321 __isl_take isl_union_map *context);
3322 __isl_give isl_union_map *isl_union_map_gist_params(
3323 __isl_take isl_union_map *umap,
3324 __isl_take isl_set *set);
3325 __isl_give isl_union_map *isl_union_map_gist_domain(
3326 __isl_take isl_union_map *umap,
3327 __isl_take isl_union_set *uset);
3328 __isl_give isl_union_map *isl_union_map_gist_range(
3329 __isl_take isl_union_map *umap,
3330 __isl_take isl_union_set *uset);
3332 The gist operation returns a set or relation that has the
3333 same intersection with the context as the input set or relation.
3334 Any implicit equality in the intersection is made explicit in the result,
3335 while all inequalities that are redundant with respect to the intersection
3337 In case of union sets and relations, the gist operation is performed
3342 =head3 Lexicographic Optimization
3344 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3345 the following functions
3346 compute a set that contains the lexicographic minimum or maximum
3347 of the elements in C<set> (or C<bset>) for those values of the parameters
3348 that satisfy C<dom>.
3349 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3350 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3352 In other words, the union of the parameter values
3353 for which the result is non-empty and of C<*empty>
3356 __isl_give isl_set *isl_basic_set_partial_lexmin(
3357 __isl_take isl_basic_set *bset,
3358 __isl_take isl_basic_set *dom,
3359 __isl_give isl_set **empty);
3360 __isl_give isl_set *isl_basic_set_partial_lexmax(
3361 __isl_take isl_basic_set *bset,
3362 __isl_take isl_basic_set *dom,
3363 __isl_give isl_set **empty);
3364 __isl_give isl_set *isl_set_partial_lexmin(
3365 __isl_take isl_set *set, __isl_take isl_set *dom,
3366 __isl_give isl_set **empty);
3367 __isl_give isl_set *isl_set_partial_lexmax(
3368 __isl_take isl_set *set, __isl_take isl_set *dom,
3369 __isl_give isl_set **empty);
3371 Given a (basic) set C<set> (or C<bset>), the following functions simply
3372 return a set containing the lexicographic minimum or maximum
3373 of the elements in C<set> (or C<bset>).
3374 In case of union sets, the optimum is computed per space.
3376 __isl_give isl_set *isl_basic_set_lexmin(
3377 __isl_take isl_basic_set *bset);
3378 __isl_give isl_set *isl_basic_set_lexmax(
3379 __isl_take isl_basic_set *bset);
3380 __isl_give isl_set *isl_set_lexmin(
3381 __isl_take isl_set *set);
3382 __isl_give isl_set *isl_set_lexmax(
3383 __isl_take isl_set *set);
3384 __isl_give isl_union_set *isl_union_set_lexmin(
3385 __isl_take isl_union_set *uset);
3386 __isl_give isl_union_set *isl_union_set_lexmax(
3387 __isl_take isl_union_set *uset);
3389 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3390 the following functions
3391 compute a relation that maps each element of C<dom>
3392 to the single lexicographic minimum or maximum
3393 of the elements that are associated to that same
3394 element in C<map> (or C<bmap>).
3395 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3396 that contains the elements in C<dom> that do not map
3397 to any elements in C<map> (or C<bmap>).
3398 In other words, the union of the domain of the result and of C<*empty>
3401 __isl_give isl_map *isl_basic_map_partial_lexmax(
3402 __isl_take isl_basic_map *bmap,
3403 __isl_take isl_basic_set *dom,
3404 __isl_give isl_set **empty);
3405 __isl_give isl_map *isl_basic_map_partial_lexmin(
3406 __isl_take isl_basic_map *bmap,
3407 __isl_take isl_basic_set *dom,
3408 __isl_give isl_set **empty);
3409 __isl_give isl_map *isl_map_partial_lexmax(
3410 __isl_take isl_map *map, __isl_take isl_set *dom,
3411 __isl_give isl_set **empty);
3412 __isl_give isl_map *isl_map_partial_lexmin(
3413 __isl_take isl_map *map, __isl_take isl_set *dom,
3414 __isl_give isl_set **empty);
3416 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3417 return a map mapping each element in the domain of
3418 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3419 of all elements associated to that element.
3420 In case of union relations, the optimum is computed per space.
3422 __isl_give isl_map *isl_basic_map_lexmin(
3423 __isl_take isl_basic_map *bmap);
3424 __isl_give isl_map *isl_basic_map_lexmax(
3425 __isl_take isl_basic_map *bmap);
3426 __isl_give isl_map *isl_map_lexmin(
3427 __isl_take isl_map *map);
3428 __isl_give isl_map *isl_map_lexmax(
3429 __isl_take isl_map *map);
3430 __isl_give isl_union_map *isl_union_map_lexmin(
3431 __isl_take isl_union_map *umap);
3432 __isl_give isl_union_map *isl_union_map_lexmax(
3433 __isl_take isl_union_map *umap);
3435 The following functions return their result in the form of
3436 a piecewise multi-affine expression
3437 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3438 but are otherwise equivalent to the corresponding functions
3439 returning a basic set or relation.
3441 __isl_give isl_pw_multi_aff *
3442 isl_basic_map_lexmin_pw_multi_aff(
3443 __isl_take isl_basic_map *bmap);
3444 __isl_give isl_pw_multi_aff *
3445 isl_basic_set_partial_lexmin_pw_multi_aff(
3446 __isl_take isl_basic_set *bset,
3447 __isl_take isl_basic_set *dom,
3448 __isl_give isl_set **empty);
3449 __isl_give isl_pw_multi_aff *
3450 isl_basic_set_partial_lexmax_pw_multi_aff(
3451 __isl_take isl_basic_set *bset,
3452 __isl_take isl_basic_set *dom,
3453 __isl_give isl_set **empty);
3454 __isl_give isl_pw_multi_aff *
3455 isl_basic_map_partial_lexmin_pw_multi_aff(
3456 __isl_take isl_basic_map *bmap,
3457 __isl_take isl_basic_set *dom,
3458 __isl_give isl_set **empty);
3459 __isl_give isl_pw_multi_aff *
3460 isl_basic_map_partial_lexmax_pw_multi_aff(
3461 __isl_take isl_basic_map *bmap,
3462 __isl_take isl_basic_set *dom,
3463 __isl_give isl_set **empty);
3464 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3465 __isl_take isl_set *set);
3466 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3467 __isl_take isl_set *set);
3468 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3469 __isl_take isl_map *map);
3470 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3471 __isl_take isl_map *map);
3475 Lists are defined over several element types, including
3476 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3477 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3478 Here we take lists of C<isl_set>s as an example.
3479 Lists can be created, copied, modified and freed using the following functions.
3481 #include <isl/list.h>
3482 __isl_give isl_set_list *isl_set_list_from_set(
3483 __isl_take isl_set *el);
3484 __isl_give isl_set_list *isl_set_list_alloc(
3485 isl_ctx *ctx, int n);
3486 __isl_give isl_set_list *isl_set_list_copy(
3487 __isl_keep isl_set_list *list);
3488 __isl_give isl_set_list *isl_set_list_insert(
3489 __isl_take isl_set_list *list, unsigned pos,
3490 __isl_take isl_set *el);
3491 __isl_give isl_set_list *isl_set_list_add(
3492 __isl_take isl_set_list *list,
3493 __isl_take isl_set *el);
3494 __isl_give isl_set_list *isl_set_list_drop(
3495 __isl_take isl_set_list *list,
3496 unsigned first, unsigned n);
3497 __isl_give isl_set_list *isl_set_list_set_set(
3498 __isl_take isl_set_list *list, int index,
3499 __isl_take isl_set *set);
3500 __isl_give isl_set_list *isl_set_list_concat(
3501 __isl_take isl_set_list *list1,
3502 __isl_take isl_set_list *list2);
3503 __isl_give isl_set_list *isl_set_list_sort(
3504 __isl_take isl_set_list *list,
3505 int (*cmp)(__isl_keep isl_set *a,
3506 __isl_keep isl_set *b, void *user),
3508 __isl_null isl_set_list *isl_set_list_free(
3509 __isl_take isl_set_list *list);
3511 C<isl_set_list_alloc> creates an empty list with a capacity for
3512 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3515 Lists can be inspected using the following functions.
3517 #include <isl/list.h>
3518 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3519 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3520 __isl_give isl_set *isl_set_list_get_set(
3521 __isl_keep isl_set_list *list, int index);
3522 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3523 int (*fn)(__isl_take isl_set *el, void *user),
3525 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3526 int (*follows)(__isl_keep isl_set *a,
3527 __isl_keep isl_set *b, void *user),
3529 int (*fn)(__isl_take isl_set *el, void *user),
3532 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3533 strongly connected components of the graph with as vertices the elements
3534 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3535 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3536 should return C<-1> on error.
3538 Lists can be printed using
3540 #include <isl/list.h>
3541 __isl_give isl_printer *isl_printer_print_set_list(
3542 __isl_take isl_printer *p,
3543 __isl_keep isl_set_list *list);
3545 =head2 Associative arrays
3547 Associative arrays map isl objects of a specific type to isl objects
3548 of some (other) specific type. They are defined for several pairs
3549 of types, including (C<isl_map>, C<isl_basic_set>),
3550 (C<isl_id>, C<isl_ast_expr>) and.
3551 (C<isl_id>, C<isl_pw_aff>).
3552 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3555 Associative arrays can be created, copied and freed using
3556 the following functions.
3558 #include <isl/id_to_ast_expr.h>
3559 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3560 isl_ctx *ctx, int min_size);
3561 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3562 __isl_keep id_to_ast_expr *id2expr);
3563 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
3564 __isl_take id_to_ast_expr *id2expr);
3566 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3567 to specify the expected size of the associative array.
3568 The associative array will be grown automatically as needed.
3570 Associative arrays can be inspected using the following functions.
3572 #include <isl/id_to_ast_expr.h>
3573 isl_ctx *isl_id_to_ast_expr_get_ctx(
3574 __isl_keep id_to_ast_expr *id2expr);
3575 int isl_id_to_ast_expr_has(
3576 __isl_keep id_to_ast_expr *id2expr,
3577 __isl_keep isl_id *key);
3578 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3579 __isl_keep id_to_ast_expr *id2expr,
3580 __isl_take isl_id *key);
3581 int isl_id_to_ast_expr_foreach(
3582 __isl_keep id_to_ast_expr *id2expr,
3583 int (*fn)(__isl_take isl_id *key,
3584 __isl_take isl_ast_expr *val, void *user),
3587 They can be modified using the following function.
3589 #include <isl/id_to_ast_expr.h>
3590 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3591 __isl_take id_to_ast_expr *id2expr,
3592 __isl_take isl_id *key,
3593 __isl_take isl_ast_expr *val);
3594 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
3595 __isl_take id_to_ast_expr *id2expr,
3596 __isl_take isl_id *key);
3598 Associative arrays can be printed using the following function.
3600 #include <isl/id_to_ast_expr.h>
3601 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3602 __isl_take isl_printer *p,
3603 __isl_keep id_to_ast_expr *id2expr);
3605 =head2 Multiple Values
3607 An C<isl_multi_val> object represents a sequence of zero or more values,
3608 living in a set space.
3610 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3611 using the following function
3613 #include <isl/val.h>
3614 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3615 __isl_take isl_space *space,
3616 __isl_take isl_val_list *list);
3618 The zero multiple value (with value zero for each set dimension)
3619 can be created using the following function.
3621 #include <isl/val.h>
3622 __isl_give isl_multi_val *isl_multi_val_zero(
3623 __isl_take isl_space *space);
3625 Multiple values can be copied and freed using
3627 #include <isl/val.h>
3628 __isl_give isl_multi_val *isl_multi_val_copy(
3629 __isl_keep isl_multi_val *mv);
3630 __isl_null isl_multi_val *isl_multi_val_free(
3631 __isl_take isl_multi_val *mv);
3633 They can be inspected using
3635 #include <isl/val.h>
3636 isl_ctx *isl_multi_val_get_ctx(
3637 __isl_keep isl_multi_val *mv);
3638 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3639 enum isl_dim_type type);
3640 __isl_give isl_val *isl_multi_val_get_val(
3641 __isl_keep isl_multi_val *mv, int pos);
3642 int isl_multi_val_find_dim_by_id(
3643 __isl_keep isl_multi_val *mv,
3644 enum isl_dim_type type, __isl_keep isl_id *id);
3645 __isl_give isl_id *isl_multi_val_get_dim_id(
3646 __isl_keep isl_multi_val *mv,
3647 enum isl_dim_type type, unsigned pos);
3648 const char *isl_multi_val_get_tuple_name(
3649 __isl_keep isl_multi_val *mv,
3650 enum isl_dim_type type);
3651 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3652 enum isl_dim_type type);
3653 __isl_give isl_id *isl_multi_val_get_tuple_id(
3654 __isl_keep isl_multi_val *mv,
3655 enum isl_dim_type type);
3656 int isl_multi_val_range_is_wrapping(
3657 __isl_keep isl_multi_val *mv);
3659 They can be modified using
3661 #include <isl/val.h>
3662 __isl_give isl_multi_val *isl_multi_val_set_val(
3663 __isl_take isl_multi_val *mv, int pos,
3664 __isl_take isl_val *val);
3665 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3666 __isl_take isl_multi_val *mv,
3667 enum isl_dim_type type, unsigned pos, const char *s);
3668 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3669 __isl_take isl_multi_val *mv,
3670 enum isl_dim_type type, unsigned pos,
3671 __isl_take isl_id *id);
3672 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3673 __isl_take isl_multi_val *mv,
3674 enum isl_dim_type type, const char *s);
3675 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3676 __isl_take isl_multi_val *mv,
3677 enum isl_dim_type type, __isl_take isl_id *id);
3678 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3679 __isl_take isl_multi_val *mv,
3680 enum isl_dim_type type);
3681 __isl_give isl_multi_val *isl_multi_val_reset_user(
3682 __isl_take isl_multi_val *mv);
3684 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3685 __isl_take isl_multi_val *mv,
3686 enum isl_dim_type type, unsigned first, unsigned n);
3687 __isl_give isl_multi_val *isl_multi_val_add_dims(
3688 __isl_take isl_multi_val *mv,
3689 enum isl_dim_type type, unsigned n);
3690 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3691 __isl_take isl_multi_val *mv,
3692 enum isl_dim_type type, unsigned first, unsigned n);
3696 #include <isl/val.h>
3697 __isl_give isl_multi_val *isl_multi_val_align_params(
3698 __isl_take isl_multi_val *mv,
3699 __isl_take isl_space *model);
3700 __isl_give isl_multi_val *isl_multi_val_from_range(
3701 __isl_take isl_multi_val *mv);
3702 __isl_give isl_multi_val *isl_multi_val_range_splice(
3703 __isl_take isl_multi_val *mv1, unsigned pos,
3704 __isl_take isl_multi_val *mv2);
3705 __isl_give isl_multi_val *isl_multi_val_range_product(
3706 __isl_take isl_multi_val *mv1,
3707 __isl_take isl_multi_val *mv2);
3708 __isl_give isl_multi_val *
3709 isl_multi_val_range_factor_domain(
3710 __isl_take isl_multi_val *mv);
3711 __isl_give isl_multi_val *
3712 isl_multi_val_range_factor_range(
3713 __isl_take isl_multi_val *mv);
3714 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3715 __isl_take isl_multi_val *mv1,
3716 __isl_take isl_multi_aff *mv2);
3717 __isl_give isl_multi_val *isl_multi_val_product(
3718 __isl_take isl_multi_val *mv1,
3719 __isl_take isl_multi_val *mv2);
3720 __isl_give isl_multi_val *isl_multi_val_add_val(
3721 __isl_take isl_multi_val *mv,
3722 __isl_take isl_val *v);
3723 __isl_give isl_multi_val *isl_multi_val_mod_val(
3724 __isl_take isl_multi_val *mv,
3725 __isl_take isl_val *v);
3726 __isl_give isl_multi_val *isl_multi_val_scale_val(
3727 __isl_take isl_multi_val *mv,
3728 __isl_take isl_val *v);
3729 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3730 __isl_take isl_multi_val *mv1,
3731 __isl_take isl_multi_val *mv2);
3732 __isl_give isl_multi_val *
3733 isl_multi_val_scale_down_multi_val(
3734 __isl_take isl_multi_val *mv1,
3735 __isl_take isl_multi_val *mv2);
3737 A multiple value can be printed using
3739 __isl_give isl_printer *isl_printer_print_multi_val(
3740 __isl_take isl_printer *p,
3741 __isl_keep isl_multi_val *mv);
3745 Vectors can be created, copied and freed using the following functions.
3747 #include <isl/vec.h>
3748 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3750 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3751 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
3753 Note that the elements of a newly created vector may have arbitrary values.
3754 The elements can be changed and inspected using the following functions.
3756 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3757 int isl_vec_size(__isl_keep isl_vec *vec);
3758 __isl_give isl_val *isl_vec_get_element_val(
3759 __isl_keep isl_vec *vec, int pos);
3760 __isl_give isl_vec *isl_vec_set_element_si(
3761 __isl_take isl_vec *vec, int pos, int v);
3762 __isl_give isl_vec *isl_vec_set_element_val(
3763 __isl_take isl_vec *vec, int pos,
3764 __isl_take isl_val *v);
3765 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3767 __isl_give isl_vec *isl_vec_set_val(
3768 __isl_take isl_vec *vec, __isl_take isl_val *v);
3769 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3770 __isl_keep isl_vec *vec2, int pos);
3772 C<isl_vec_get_element> will return a negative value if anything went wrong.
3773 In that case, the value of C<*v> is undefined.
3775 The following function can be used to concatenate two vectors.
3777 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3778 __isl_take isl_vec *vec2);
3782 Matrices can be created, copied and freed using the following functions.
3784 #include <isl/mat.h>
3785 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3786 unsigned n_row, unsigned n_col);
3787 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3788 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
3790 Note that the elements of a newly created matrix may have arbitrary values.
3791 The elements can be changed and inspected using the following functions.
3793 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3794 int isl_mat_rows(__isl_keep isl_mat *mat);
3795 int isl_mat_cols(__isl_keep isl_mat *mat);
3796 __isl_give isl_val *isl_mat_get_element_val(
3797 __isl_keep isl_mat *mat, int row, int col);
3798 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3799 int row, int col, int v);
3800 __isl_give isl_mat *isl_mat_set_element_val(
3801 __isl_take isl_mat *mat, int row, int col,
3802 __isl_take isl_val *v);
3804 C<isl_mat_get_element> will return a negative value if anything went wrong.
3805 In that case, the value of C<*v> is undefined.
3807 The following function can be used to compute the (right) inverse
3808 of a matrix, i.e., a matrix such that the product of the original
3809 and the inverse (in that order) is a multiple of the identity matrix.
3810 The input matrix is assumed to be of full row-rank.
3812 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3814 The following function can be used to compute the (right) kernel
3815 (or null space) of a matrix, i.e., a matrix such that the product of
3816 the original and the kernel (in that order) is the zero matrix.
3818 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3820 =head2 Piecewise Quasi Affine Expressions
3822 The zero quasi affine expression or the quasi affine expression
3823 that is equal to a given value or
3824 a specified dimension on a given domain can be created using
3826 __isl_give isl_aff *isl_aff_zero_on_domain(
3827 __isl_take isl_local_space *ls);
3828 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3829 __isl_take isl_local_space *ls);
3830 __isl_give isl_aff *isl_aff_val_on_domain(
3831 __isl_take isl_local_space *ls,
3832 __isl_take isl_val *val);
3833 __isl_give isl_aff *isl_aff_var_on_domain(
3834 __isl_take isl_local_space *ls,
3835 enum isl_dim_type type, unsigned pos);
3836 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3837 __isl_take isl_local_space *ls,
3838 enum isl_dim_type type, unsigned pos);
3839 __isl_give isl_aff *isl_aff_nan_on_domain(
3840 __isl_take isl_local_space *ls);
3841 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3842 __isl_take isl_local_space *ls);
3844 Note that the space in which the resulting objects live is a map space
3845 with the given space as domain and a one-dimensional range.
3847 An empty piecewise quasi affine expression (one with no cells)
3848 or a piecewise quasi affine expression with a single cell can
3849 be created using the following functions.
3851 #include <isl/aff.h>
3852 __isl_give isl_pw_aff *isl_pw_aff_empty(
3853 __isl_take isl_space *space);
3854 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3855 __isl_take isl_set *set, __isl_take isl_aff *aff);
3856 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3857 __isl_take isl_aff *aff);
3859 A piecewise quasi affine expression that is equal to 1 on a set
3860 and 0 outside the set can be created using the following function.
3862 #include <isl/aff.h>
3863 __isl_give isl_pw_aff *isl_set_indicator_function(
3864 __isl_take isl_set *set);
3866 Quasi affine expressions can be copied and freed using
3868 #include <isl/aff.h>
3869 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3870 __isl_null isl_aff *isl_aff_free(__isl_take isl_aff *aff);
3872 __isl_give isl_pw_aff *isl_pw_aff_copy(
3873 __isl_keep isl_pw_aff *pwaff);
3874 __isl_null isl_pw_aff *isl_pw_aff_free(
3875 __isl_take isl_pw_aff *pwaff);
3877 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3878 using the following function. The constraint is required to have
3879 a non-zero coefficient for the specified dimension.
3881 #include <isl/constraint.h>
3882 __isl_give isl_aff *isl_constraint_get_bound(
3883 __isl_keep isl_constraint *constraint,
3884 enum isl_dim_type type, int pos);
3886 The entire affine expression of the constraint can also be extracted
3887 using the following function.
3889 #include <isl/constraint.h>
3890 __isl_give isl_aff *isl_constraint_get_aff(
3891 __isl_keep isl_constraint *constraint);
3893 Conversely, an equality constraint equating
3894 the affine expression to zero or an inequality constraint enforcing
3895 the affine expression to be non-negative, can be constructed using
3897 __isl_give isl_constraint *isl_equality_from_aff(
3898 __isl_take isl_aff *aff);
3899 __isl_give isl_constraint *isl_inequality_from_aff(
3900 __isl_take isl_aff *aff);
3902 The expression can be inspected using
3904 #include <isl/aff.h>
3905 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3906 int isl_aff_dim(__isl_keep isl_aff *aff,
3907 enum isl_dim_type type);
3908 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3909 __isl_keep isl_aff *aff);
3910 __isl_give isl_local_space *isl_aff_get_local_space(
3911 __isl_keep isl_aff *aff);
3912 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3913 enum isl_dim_type type, unsigned pos);
3914 const char *isl_pw_aff_get_dim_name(
3915 __isl_keep isl_pw_aff *pa,
3916 enum isl_dim_type type, unsigned pos);
3917 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3918 enum isl_dim_type type, unsigned pos);
3919 __isl_give isl_id *isl_pw_aff_get_dim_id(
3920 __isl_keep isl_pw_aff *pa,
3921 enum isl_dim_type type, unsigned pos);
3922 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
3923 enum isl_dim_type type);
3924 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3925 __isl_keep isl_pw_aff *pa,
3926 enum isl_dim_type type);
3927 __isl_give isl_val *isl_aff_get_constant_val(
3928 __isl_keep isl_aff *aff);
3929 __isl_give isl_val *isl_aff_get_coefficient_val(
3930 __isl_keep isl_aff *aff,
3931 enum isl_dim_type type, int pos);
3932 __isl_give isl_val *isl_aff_get_denominator_val(
3933 __isl_keep isl_aff *aff);
3934 __isl_give isl_aff *isl_aff_get_div(
3935 __isl_keep isl_aff *aff, int pos);
3937 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3938 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3939 int (*fn)(__isl_take isl_set *set,
3940 __isl_take isl_aff *aff,
3941 void *user), void *user);
3943 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3944 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3946 int isl_aff_is_nan(__isl_keep isl_aff *aff);
3947 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
3949 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3950 enum isl_dim_type type, unsigned first, unsigned n);
3951 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3952 enum isl_dim_type type, unsigned first, unsigned n);
3954 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3955 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3956 enum isl_dim_type type);
3957 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3959 It can be modified using
3961 #include <isl/aff.h>
3962 __isl_give isl_aff *isl_aff_set_tuple_id(
3963 __isl_take isl_aff *aff,
3964 enum isl_dim_type type, __isl_take isl_id *id);
3965 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3966 __isl_take isl_pw_aff *pwaff,
3967 enum isl_dim_type type, __isl_take isl_id *id);
3968 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
3969 __isl_take isl_pw_aff *pa,
3970 enum isl_dim_type type);
3971 __isl_give isl_aff *isl_aff_set_dim_name(
3972 __isl_take isl_aff *aff, enum isl_dim_type type,
3973 unsigned pos, const char *s);
3974 __isl_give isl_aff *isl_aff_set_dim_id(
3975 __isl_take isl_aff *aff, enum isl_dim_type type,
3976 unsigned pos, __isl_take isl_id *id);
3977 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3978 __isl_take isl_pw_aff *pma,
3979 enum isl_dim_type type, unsigned pos,
3980 __isl_take isl_id *id);
3981 __isl_give isl_aff *isl_aff_set_constant_si(
3982 __isl_take isl_aff *aff, int v);
3983 __isl_give isl_aff *isl_aff_set_constant_val(
3984 __isl_take isl_aff *aff, __isl_take isl_val *v);
3985 __isl_give isl_aff *isl_aff_set_coefficient_si(
3986 __isl_take isl_aff *aff,
3987 enum isl_dim_type type, int pos, int v);
3988 __isl_give isl_aff *isl_aff_set_coefficient_val(
3989 __isl_take isl_aff *aff,
3990 enum isl_dim_type type, int pos,
3991 __isl_take isl_val *v);
3993 __isl_give isl_aff *isl_aff_add_constant_si(
3994 __isl_take isl_aff *aff, int v);
3995 __isl_give isl_aff *isl_aff_add_constant_val(
3996 __isl_take isl_aff *aff, __isl_take isl_val *v);
3997 __isl_give isl_aff *isl_aff_add_constant_num_si(
3998 __isl_take isl_aff *aff, int v);
3999 __isl_give isl_aff *isl_aff_add_coefficient_si(
4000 __isl_take isl_aff *aff,
4001 enum isl_dim_type type, int pos, int v);
4002 __isl_give isl_aff *isl_aff_add_coefficient_val(
4003 __isl_take isl_aff *aff,
4004 enum isl_dim_type type, int pos,
4005 __isl_take isl_val *v);
4007 __isl_give isl_aff *isl_aff_insert_dims(
4008 __isl_take isl_aff *aff,
4009 enum isl_dim_type type, unsigned first, unsigned n);
4010 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
4011 __isl_take isl_pw_aff *pwaff,
4012 enum isl_dim_type type, unsigned first, unsigned n);
4013 __isl_give isl_aff *isl_aff_add_dims(
4014 __isl_take isl_aff *aff,
4015 enum isl_dim_type type, unsigned n);
4016 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
4017 __isl_take isl_pw_aff *pwaff,
4018 enum isl_dim_type type, unsigned n);
4019 __isl_give isl_aff *isl_aff_drop_dims(
4020 __isl_take isl_aff *aff,
4021 enum isl_dim_type type, unsigned first, unsigned n);
4022 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
4023 __isl_take isl_pw_aff *pwaff,
4024 enum isl_dim_type type, unsigned first, unsigned n);
4025 __isl_give isl_aff *isl_aff_move_dims(
4026 __isl_take isl_aff *aff,
4027 enum isl_dim_type dst_type, unsigned dst_pos,
4028 enum isl_dim_type src_type, unsigned src_pos,
4030 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
4031 __isl_take isl_pw_aff *pa,
4032 enum isl_dim_type dst_type, unsigned dst_pos,
4033 enum isl_dim_type src_type, unsigned src_pos,
4036 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
4037 set the I<numerator> of the constant or coefficient, while
4038 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
4039 the constant or coefficient as a whole.
4040 The C<add_constant> and C<add_coefficient> functions add an integer
4041 or rational value to
4042 the possibly rational constant or coefficient.
4043 The C<add_constant_num> functions add an integer value to
4046 To check whether an affine expressions is obviously zero
4047 or (obviously) equal to some other affine expression, use
4049 #include <isl/aff.h>
4050 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
4051 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
4052 __isl_keep isl_aff *aff2);
4053 int isl_pw_aff_plain_is_equal(
4054 __isl_keep isl_pw_aff *pwaff1,
4055 __isl_keep isl_pw_aff *pwaff2);
4056 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
4057 __isl_keep isl_pw_aff *pa2);
4058 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4059 __isl_keep isl_pw_aff *pa2);
4061 The function C<isl_pw_aff_plain_cmp> can be used to sort
4062 C<isl_pw_aff>s. The order is not strictly defined.
4063 The current order sorts expressions that only involve
4064 earlier dimensions before those that involve later dimensions.
4068 #include <isl/aff.h>
4069 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
4070 __isl_take isl_aff *aff2);
4071 __isl_give isl_pw_aff *isl_pw_aff_add(
4072 __isl_take isl_pw_aff *pwaff1,
4073 __isl_take isl_pw_aff *pwaff2);
4074 __isl_give isl_pw_aff *isl_pw_aff_min(
4075 __isl_take isl_pw_aff *pwaff1,
4076 __isl_take isl_pw_aff *pwaff2);
4077 __isl_give isl_pw_aff *isl_pw_aff_max(
4078 __isl_take isl_pw_aff *pwaff1,
4079 __isl_take isl_pw_aff *pwaff2);
4080 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
4081 __isl_take isl_aff *aff2);
4082 __isl_give isl_pw_aff *isl_pw_aff_sub(
4083 __isl_take isl_pw_aff *pwaff1,
4084 __isl_take isl_pw_aff *pwaff2);
4085 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
4086 __isl_give isl_pw_aff *isl_pw_aff_neg(
4087 __isl_take isl_pw_aff *pwaff);
4088 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
4089 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4090 __isl_take isl_pw_aff *pwaff);
4091 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
4092 __isl_give isl_pw_aff *isl_pw_aff_floor(
4093 __isl_take isl_pw_aff *pwaff);
4094 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
4095 __isl_take isl_val *mod);
4096 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
4097 __isl_take isl_pw_aff *pa,
4098 __isl_take isl_val *mod);
4099 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
4100 __isl_take isl_val *v);
4101 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
4102 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
4103 __isl_give isl_aff *isl_aff_scale_down_ui(
4104 __isl_take isl_aff *aff, unsigned f);
4105 __isl_give isl_aff *isl_aff_scale_down_val(
4106 __isl_take isl_aff *aff, __isl_take isl_val *v);
4107 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
4108 __isl_take isl_pw_aff *pa,
4109 __isl_take isl_val *f);
4111 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4112 __isl_take isl_pw_aff_list *list);
4113 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4114 __isl_take isl_pw_aff_list *list);
4116 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4117 __isl_take isl_pw_aff *pwqp);
4119 __isl_give isl_aff *isl_aff_align_params(
4120 __isl_take isl_aff *aff,
4121 __isl_take isl_space *model);
4122 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4123 __isl_take isl_pw_aff *pwaff,
4124 __isl_take isl_space *model);
4126 __isl_give isl_aff *isl_aff_project_domain_on_params(
4127 __isl_take isl_aff *aff);
4128 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4129 __isl_take isl_pw_aff *pwa);
4131 __isl_give isl_aff *isl_aff_gist_params(
4132 __isl_take isl_aff *aff,
4133 __isl_take isl_set *context);
4134 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
4135 __isl_take isl_set *context);
4136 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
4137 __isl_take isl_pw_aff *pwaff,
4138 __isl_take isl_set *context);
4139 __isl_give isl_pw_aff *isl_pw_aff_gist(
4140 __isl_take isl_pw_aff *pwaff,
4141 __isl_take isl_set *context);
4143 __isl_give isl_set *isl_pw_aff_domain(
4144 __isl_take isl_pw_aff *pwaff);
4145 __isl_give isl_set *isl_pw_aff_params(
4146 __isl_take isl_pw_aff *pwa);
4147 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4148 __isl_take isl_pw_aff *pa,
4149 __isl_take isl_set *set);
4150 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4151 __isl_take isl_pw_aff *pa,
4152 __isl_take isl_set *set);
4154 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
4155 __isl_take isl_aff *aff2);
4156 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
4157 __isl_take isl_aff *aff2);
4158 __isl_give isl_pw_aff *isl_pw_aff_mul(
4159 __isl_take isl_pw_aff *pwaff1,
4160 __isl_take isl_pw_aff *pwaff2);
4161 __isl_give isl_pw_aff *isl_pw_aff_div(
4162 __isl_take isl_pw_aff *pa1,
4163 __isl_take isl_pw_aff *pa2);
4164 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
4165 __isl_take isl_pw_aff *pa1,
4166 __isl_take isl_pw_aff *pa2);
4167 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
4168 __isl_take isl_pw_aff *pa1,
4169 __isl_take isl_pw_aff *pa2);
4171 When multiplying two affine expressions, at least one of the two needs
4172 to be a constant. Similarly, when dividing an affine expression by another,
4173 the second expression needs to be a constant.
4174 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
4175 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
4178 #include <isl/aff.h>
4179 __isl_give isl_aff *isl_aff_pullback_aff(
4180 __isl_take isl_aff *aff1,
4181 __isl_take isl_aff *aff2);
4182 __isl_give isl_aff *isl_aff_pullback_multi_aff(
4183 __isl_take isl_aff *aff,
4184 __isl_take isl_multi_aff *ma);
4185 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
4186 __isl_take isl_pw_aff *pa,
4187 __isl_take isl_multi_aff *ma);
4188 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
4189 __isl_take isl_pw_aff *pa,
4190 __isl_take isl_pw_multi_aff *pma);
4191 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
4192 __isl_take isl_pw_aff *pa,
4193 __isl_take isl_multi_pw_aff *mpa);
4195 These functions precompose the input expression by the given
4196 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
4197 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
4198 into the (piecewise) affine expression.
4199 Objects of type C<isl_multi_aff> are described in
4200 L</"Piecewise Multiple Quasi Affine Expressions">.
4202 #include <isl/aff.h>
4203 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4204 __isl_take isl_aff *aff);
4205 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4206 __isl_take isl_aff *aff);
4207 __isl_give isl_basic_set *isl_aff_le_basic_set(
4208 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4209 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4210 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4211 __isl_give isl_set *isl_pw_aff_eq_set(
4212 __isl_take isl_pw_aff *pwaff1,
4213 __isl_take isl_pw_aff *pwaff2);
4214 __isl_give isl_set *isl_pw_aff_ne_set(
4215 __isl_take isl_pw_aff *pwaff1,
4216 __isl_take isl_pw_aff *pwaff2);
4217 __isl_give isl_set *isl_pw_aff_le_set(
4218 __isl_take isl_pw_aff *pwaff1,
4219 __isl_take isl_pw_aff *pwaff2);
4220 __isl_give isl_set *isl_pw_aff_lt_set(
4221 __isl_take isl_pw_aff *pwaff1,
4222 __isl_take isl_pw_aff *pwaff2);
4223 __isl_give isl_set *isl_pw_aff_ge_set(
4224 __isl_take isl_pw_aff *pwaff1,
4225 __isl_take isl_pw_aff *pwaff2);
4226 __isl_give isl_set *isl_pw_aff_gt_set(
4227 __isl_take isl_pw_aff *pwaff1,
4228 __isl_take isl_pw_aff *pwaff2);
4230 __isl_give isl_set *isl_pw_aff_list_eq_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_ne_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_le_set(
4237 __isl_take isl_pw_aff_list *list1,
4238 __isl_take isl_pw_aff_list *list2);
4239 __isl_give isl_set *isl_pw_aff_list_lt_set(
4240 __isl_take isl_pw_aff_list *list1,
4241 __isl_take isl_pw_aff_list *list2);
4242 __isl_give isl_set *isl_pw_aff_list_ge_set(
4243 __isl_take isl_pw_aff_list *list1,
4244 __isl_take isl_pw_aff_list *list2);
4245 __isl_give isl_set *isl_pw_aff_list_gt_set(
4246 __isl_take isl_pw_aff_list *list1,
4247 __isl_take isl_pw_aff_list *list2);
4249 The function C<isl_aff_neg_basic_set> returns a basic set
4250 containing those elements in the domain space
4251 of C<aff> where C<aff> is negative.
4252 The function C<isl_aff_ge_basic_set> returns a basic set
4253 containing those elements in the shared space
4254 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4255 The function C<isl_pw_aff_ge_set> returns a set
4256 containing those elements in the shared domain
4257 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4258 The functions operating on C<isl_pw_aff_list> apply the corresponding
4259 C<isl_pw_aff> function to each pair of elements in the two lists.
4261 #include <isl/aff.h>
4262 __isl_give isl_set *isl_pw_aff_nonneg_set(
4263 __isl_take isl_pw_aff *pwaff);
4264 __isl_give isl_set *isl_pw_aff_zero_set(
4265 __isl_take isl_pw_aff *pwaff);
4266 __isl_give isl_set *isl_pw_aff_non_zero_set(
4267 __isl_take isl_pw_aff *pwaff);
4269 The function C<isl_pw_aff_nonneg_set> returns a set
4270 containing those elements in the domain
4271 of C<pwaff> where C<pwaff> is non-negative.
4273 #include <isl/aff.h>
4274 __isl_give isl_pw_aff *isl_pw_aff_cond(
4275 __isl_take isl_pw_aff *cond,
4276 __isl_take isl_pw_aff *pwaff_true,
4277 __isl_take isl_pw_aff *pwaff_false);
4279 The function C<isl_pw_aff_cond> performs a conditional operator
4280 and returns an expression that is equal to C<pwaff_true>
4281 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4282 where C<cond> is zero.
4284 #include <isl/aff.h>
4285 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4286 __isl_take isl_pw_aff *pwaff1,
4287 __isl_take isl_pw_aff *pwaff2);
4288 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4289 __isl_take isl_pw_aff *pwaff1,
4290 __isl_take isl_pw_aff *pwaff2);
4291 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4292 __isl_take isl_pw_aff *pwaff1,
4293 __isl_take isl_pw_aff *pwaff2);
4295 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4296 expression with a domain that is the union of those of C<pwaff1> and
4297 C<pwaff2> and such that on each cell, the quasi-affine expression is
4298 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4299 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4300 associated expression is the defined one.
4302 An expression can be read from input using
4304 #include <isl/aff.h>
4305 __isl_give isl_aff *isl_aff_read_from_str(
4306 isl_ctx *ctx, const char *str);
4307 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4308 isl_ctx *ctx, const char *str);
4310 An expression can be printed using
4312 #include <isl/aff.h>
4313 __isl_give isl_printer *isl_printer_print_aff(
4314 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4316 __isl_give isl_printer *isl_printer_print_pw_aff(
4317 __isl_take isl_printer *p,
4318 __isl_keep isl_pw_aff *pwaff);
4320 =head2 Piecewise Multiple Quasi Affine Expressions
4322 An C<isl_multi_aff> object represents a sequence of
4323 zero or more affine expressions, all defined on the same domain space.
4324 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4325 zero or more piecewise affine expressions.
4327 An C<isl_multi_aff> can be constructed from a single
4328 C<isl_aff> or an C<isl_aff_list> using the
4329 following functions. Similarly for C<isl_multi_pw_aff>
4330 and C<isl_pw_multi_aff>.
4332 #include <isl/aff.h>
4333 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4334 __isl_take isl_aff *aff);
4335 __isl_give isl_multi_pw_aff *
4336 isl_multi_pw_aff_from_multi_aff(
4337 __isl_take isl_multi_aff *ma);
4338 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4339 __isl_take isl_pw_aff *pa);
4340 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4341 __isl_take isl_pw_aff *pa);
4342 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4343 __isl_take isl_space *space,
4344 __isl_take isl_aff_list *list);
4346 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4347 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4348 Note however that the domain
4349 of the result is the intersection of the domains of the input.
4350 The reverse conversion is exact.
4352 #include <isl/aff.h>
4353 __isl_give isl_pw_multi_aff *
4354 isl_pw_multi_aff_from_multi_pw_aff(
4355 __isl_take isl_multi_pw_aff *mpa);
4356 __isl_give isl_multi_pw_aff *
4357 isl_multi_pw_aff_from_pw_multi_aff(
4358 __isl_take isl_pw_multi_aff *pma);
4360 An empty piecewise multiple quasi affine expression (one with no cells),
4361 the zero piecewise multiple quasi affine expression (with value zero
4362 for each output dimension),
4363 a piecewise multiple quasi affine expression with a single cell (with
4364 either a universe or a specified domain) or
4365 a zero-dimensional piecewise multiple quasi affine expression
4367 can be created using the following functions.
4369 #include <isl/aff.h>
4370 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4371 __isl_take isl_space *space);
4372 __isl_give isl_multi_aff *isl_multi_aff_zero(
4373 __isl_take isl_space *space);
4374 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4375 __isl_take isl_space *space);
4376 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4377 __isl_take isl_space *space);
4378 __isl_give isl_multi_aff *isl_multi_aff_identity(
4379 __isl_take isl_space *space);
4380 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4381 __isl_take isl_space *space);
4382 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4383 __isl_take isl_space *space);
4384 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4385 __isl_take isl_space *space);
4386 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4387 __isl_take isl_space *space);
4388 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4389 __isl_take isl_space *space,
4390 enum isl_dim_type type,
4391 unsigned first, unsigned n);
4392 __isl_give isl_pw_multi_aff *
4393 isl_pw_multi_aff_project_out_map(
4394 __isl_take isl_space *space,
4395 enum isl_dim_type type,
4396 unsigned first, unsigned n);
4397 __isl_give isl_pw_multi_aff *
4398 isl_pw_multi_aff_from_multi_aff(
4399 __isl_take isl_multi_aff *ma);
4400 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4401 __isl_take isl_set *set,
4402 __isl_take isl_multi_aff *maff);
4403 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4404 __isl_take isl_set *set);
4406 __isl_give isl_union_pw_multi_aff *
4407 isl_union_pw_multi_aff_empty(
4408 __isl_take isl_space *space);
4409 __isl_give isl_union_pw_multi_aff *
4410 isl_union_pw_multi_aff_add_pw_multi_aff(
4411 __isl_take isl_union_pw_multi_aff *upma,
4412 __isl_take isl_pw_multi_aff *pma);
4413 __isl_give isl_union_pw_multi_aff *
4414 isl_union_pw_multi_aff_from_domain(
4415 __isl_take isl_union_set *uset);
4417 A piecewise multiple quasi affine expression can also be initialized
4418 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4419 and the C<isl_map> is single-valued.
4420 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4421 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4423 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4424 __isl_take isl_set *set);
4425 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4426 __isl_take isl_map *map);
4428 __isl_give isl_union_pw_multi_aff *
4429 isl_union_pw_multi_aff_from_union_set(
4430 __isl_take isl_union_set *uset);
4431 __isl_give isl_union_pw_multi_aff *
4432 isl_union_pw_multi_aff_from_union_map(
4433 __isl_take isl_union_map *umap);
4435 Multiple quasi affine expressions can be copied and freed using
4437 #include <isl/aff.h>
4438 __isl_give isl_multi_aff *isl_multi_aff_copy(
4439 __isl_keep isl_multi_aff *maff);
4440 __isl_null isl_multi_aff *isl_multi_aff_free(
4441 __isl_take isl_multi_aff *maff);
4443 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4444 __isl_keep isl_pw_multi_aff *pma);
4445 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
4446 __isl_take isl_pw_multi_aff *pma);
4448 __isl_give isl_union_pw_multi_aff *
4449 isl_union_pw_multi_aff_copy(
4450 __isl_keep isl_union_pw_multi_aff *upma);
4451 __isl_null isl_union_pw_multi_aff *
4452 isl_union_pw_multi_aff_free(
4453 __isl_take isl_union_pw_multi_aff *upma);
4455 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4456 __isl_keep isl_multi_pw_aff *mpa);
4457 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
4458 __isl_take isl_multi_pw_aff *mpa);
4460 The expression can be inspected using
4462 #include <isl/aff.h>
4463 isl_ctx *isl_multi_aff_get_ctx(
4464 __isl_keep isl_multi_aff *maff);
4465 isl_ctx *isl_pw_multi_aff_get_ctx(
4466 __isl_keep isl_pw_multi_aff *pma);
4467 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4468 __isl_keep isl_union_pw_multi_aff *upma);
4469 isl_ctx *isl_multi_pw_aff_get_ctx(
4470 __isl_keep isl_multi_pw_aff *mpa);
4472 int isl_multi_aff_involves_dims(
4473 __isl_keep isl_multi_aff *ma,
4474 enum isl_dim_type type, unsigned first, unsigned n);
4475 int isl_multi_pw_aff_involves_dims(
4476 __isl_keep isl_multi_pw_aff *mpa,
4477 enum isl_dim_type type, unsigned first, unsigned n);
4479 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4480 enum isl_dim_type type);
4481 unsigned isl_pw_multi_aff_dim(
4482 __isl_keep isl_pw_multi_aff *pma,
4483 enum isl_dim_type type);
4484 unsigned isl_multi_pw_aff_dim(
4485 __isl_keep isl_multi_pw_aff *mpa,
4486 enum isl_dim_type type);
4487 __isl_give isl_aff *isl_multi_aff_get_aff(
4488 __isl_keep isl_multi_aff *multi, int pos);
4489 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4490 __isl_keep isl_pw_multi_aff *pma, int pos);
4491 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4492 __isl_keep isl_multi_pw_aff *mpa, int pos);
4493 int isl_multi_aff_find_dim_by_id(
4494 __isl_keep isl_multi_aff *ma,
4495 enum isl_dim_type type, __isl_keep isl_id *id);
4496 int isl_multi_pw_aff_find_dim_by_id(
4497 __isl_keep isl_multi_pw_aff *mpa,
4498 enum isl_dim_type type, __isl_keep isl_id *id);
4499 const char *isl_pw_multi_aff_get_dim_name(
4500 __isl_keep isl_pw_multi_aff *pma,
4501 enum isl_dim_type type, unsigned pos);
4502 __isl_give isl_id *isl_multi_aff_get_dim_id(
4503 __isl_keep isl_multi_aff *ma,
4504 enum isl_dim_type type, unsigned pos);
4505 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4506 __isl_keep isl_pw_multi_aff *pma,
4507 enum isl_dim_type type, unsigned pos);
4508 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4509 __isl_keep isl_multi_pw_aff *mpa,
4510 enum isl_dim_type type, unsigned pos);
4511 const char *isl_multi_aff_get_tuple_name(
4512 __isl_keep isl_multi_aff *multi,
4513 enum isl_dim_type type);
4514 int isl_pw_multi_aff_has_tuple_name(
4515 __isl_keep isl_pw_multi_aff *pma,
4516 enum isl_dim_type type);
4517 const char *isl_pw_multi_aff_get_tuple_name(
4518 __isl_keep isl_pw_multi_aff *pma,
4519 enum isl_dim_type type);
4520 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4521 enum isl_dim_type type);
4522 int isl_pw_multi_aff_has_tuple_id(
4523 __isl_keep isl_pw_multi_aff *pma,
4524 enum isl_dim_type type);
4525 int isl_multi_pw_aff_has_tuple_id(
4526 __isl_keep isl_multi_pw_aff *mpa,
4527 enum isl_dim_type type);
4528 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4529 __isl_keep isl_multi_aff *ma,
4530 enum isl_dim_type type);
4531 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4532 __isl_keep isl_pw_multi_aff *pma,
4533 enum isl_dim_type type);
4534 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4535 __isl_keep isl_multi_pw_aff *mpa,
4536 enum isl_dim_type type);
4537 int isl_multi_aff_range_is_wrapping(
4538 __isl_keep isl_multi_aff *ma);
4539 int isl_multi_pw_aff_range_is_wrapping(
4540 __isl_keep isl_multi_pw_aff *mpa);
4542 int isl_pw_multi_aff_foreach_piece(
4543 __isl_keep isl_pw_multi_aff *pma,
4544 int (*fn)(__isl_take isl_set *set,
4545 __isl_take isl_multi_aff *maff,
4546 void *user), void *user);
4548 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4549 __isl_keep isl_union_pw_multi_aff *upma,
4550 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4551 void *user), void *user);
4553 It can be modified using
4555 #include <isl/aff.h>
4556 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4557 __isl_take isl_multi_aff *multi, int pos,
4558 __isl_take isl_aff *aff);
4559 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4560 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4561 __isl_take isl_pw_aff *pa);
4562 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4563 __isl_take isl_multi_aff *maff,
4564 enum isl_dim_type type, unsigned pos, const char *s);
4565 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4566 __isl_take isl_multi_aff *maff,
4567 enum isl_dim_type type, unsigned pos,
4568 __isl_take isl_id *id);
4569 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4570 __isl_take isl_multi_aff *maff,
4571 enum isl_dim_type type, const char *s);
4572 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4573 __isl_take isl_multi_aff *maff,
4574 enum isl_dim_type type, __isl_take isl_id *id);
4575 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4576 __isl_take isl_pw_multi_aff *pma,
4577 enum isl_dim_type type, __isl_take isl_id *id);
4578 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4579 __isl_take isl_multi_aff *ma,
4580 enum isl_dim_type type);
4581 __isl_give isl_multi_pw_aff *
4582 isl_multi_pw_aff_reset_tuple_id(
4583 __isl_take isl_multi_pw_aff *mpa,
4584 enum isl_dim_type type);
4585 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4586 __isl_take isl_multi_aff *ma);
4587 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4588 __isl_take isl_multi_pw_aff *mpa);
4590 __isl_give isl_multi_pw_aff *
4591 isl_multi_pw_aff_set_dim_name(
4592 __isl_take isl_multi_pw_aff *mpa,
4593 enum isl_dim_type type, unsigned pos, const char *s);
4594 __isl_give isl_multi_pw_aff *
4595 isl_multi_pw_aff_set_dim_id(
4596 __isl_take isl_multi_pw_aff *mpa,
4597 enum isl_dim_type type, unsigned pos,
4598 __isl_take isl_id *id);
4599 __isl_give isl_multi_pw_aff *
4600 isl_multi_pw_aff_set_tuple_name(
4601 __isl_take isl_multi_pw_aff *mpa,
4602 enum isl_dim_type type, const char *s);
4604 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4605 __isl_take isl_multi_aff *ma);
4607 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4608 __isl_take isl_multi_aff *ma,
4609 enum isl_dim_type type, unsigned first, unsigned n);
4610 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4611 __isl_take isl_multi_aff *ma,
4612 enum isl_dim_type type, unsigned n);
4613 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4614 __isl_take isl_multi_aff *maff,
4615 enum isl_dim_type type, unsigned first, unsigned n);
4616 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4617 __isl_take isl_pw_multi_aff *pma,
4618 enum isl_dim_type type, unsigned first, unsigned n);
4620 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4621 __isl_take isl_multi_pw_aff *mpa,
4622 enum isl_dim_type type, unsigned first, unsigned n);
4623 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4624 __isl_take isl_multi_pw_aff *mpa,
4625 enum isl_dim_type type, unsigned n);
4626 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4627 __isl_take isl_multi_pw_aff *pma,
4628 enum isl_dim_type dst_type, unsigned dst_pos,
4629 enum isl_dim_type src_type, unsigned src_pos,
4632 To check whether two multiple affine expressions are
4633 (obviously) equal to each other, use
4635 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4636 __isl_keep isl_multi_aff *maff2);
4637 int isl_pw_multi_aff_plain_is_equal(
4638 __isl_keep isl_pw_multi_aff *pma1,
4639 __isl_keep isl_pw_multi_aff *pma2);
4640 int isl_multi_pw_aff_plain_is_equal(
4641 __isl_keep isl_multi_pw_aff *mpa1,
4642 __isl_keep isl_multi_pw_aff *mpa2);
4643 int isl_multi_pw_aff_is_equal(
4644 __isl_keep isl_multi_pw_aff *mpa1,
4645 __isl_keep isl_multi_pw_aff *mpa2);
4649 #include <isl/aff.h>
4650 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4651 __isl_take isl_pw_multi_aff *pma1,
4652 __isl_take isl_pw_multi_aff *pma2);
4653 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4654 __isl_take isl_pw_multi_aff *pma1,
4655 __isl_take isl_pw_multi_aff *pma2);
4656 __isl_give isl_multi_aff *isl_multi_aff_floor(
4657 __isl_take isl_multi_aff *ma);
4658 __isl_give isl_multi_aff *isl_multi_aff_add(
4659 __isl_take isl_multi_aff *maff1,
4660 __isl_take isl_multi_aff *maff2);
4661 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4662 __isl_take isl_pw_multi_aff *pma1,
4663 __isl_take isl_pw_multi_aff *pma2);
4664 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4665 __isl_take isl_union_pw_multi_aff *upma1,
4666 __isl_take isl_union_pw_multi_aff *upma2);
4667 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4668 __isl_take isl_pw_multi_aff *pma1,
4669 __isl_take isl_pw_multi_aff *pma2);
4670 __isl_give isl_multi_aff *isl_multi_aff_sub(
4671 __isl_take isl_multi_aff *ma1,
4672 __isl_take isl_multi_aff *ma2);
4673 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4674 __isl_take isl_pw_multi_aff *pma1,
4675 __isl_take isl_pw_multi_aff *pma2);
4676 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4677 __isl_take isl_union_pw_multi_aff *upma1,
4678 __isl_take isl_union_pw_multi_aff *upma2);
4680 C<isl_multi_aff_sub> subtracts the second argument from the first.
4682 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4683 __isl_take isl_multi_aff *ma,
4684 __isl_take isl_val *v);
4685 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4686 __isl_take isl_pw_multi_aff *pma,
4687 __isl_take isl_val *v);
4688 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4689 __isl_take isl_multi_pw_aff *mpa,
4690 __isl_take isl_val *v);
4691 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4692 __isl_take isl_multi_aff *ma,
4693 __isl_take isl_multi_val *mv);
4694 __isl_give isl_pw_multi_aff *
4695 isl_pw_multi_aff_scale_multi_val(
4696 __isl_take isl_pw_multi_aff *pma,
4697 __isl_take isl_multi_val *mv);
4698 __isl_give isl_multi_pw_aff *
4699 isl_multi_pw_aff_scale_multi_val(
4700 __isl_take isl_multi_pw_aff *mpa,
4701 __isl_take isl_multi_val *mv);
4702 __isl_give isl_union_pw_multi_aff *
4703 isl_union_pw_multi_aff_scale_multi_val(
4704 __isl_take isl_union_pw_multi_aff *upma,
4705 __isl_take isl_multi_val *mv);
4706 __isl_give isl_multi_aff *
4707 isl_multi_aff_scale_down_multi_val(
4708 __isl_take isl_multi_aff *ma,
4709 __isl_take isl_multi_val *mv);
4710 __isl_give isl_multi_pw_aff *
4711 isl_multi_pw_aff_scale_down_multi_val(
4712 __isl_take isl_multi_pw_aff *mpa,
4713 __isl_take isl_multi_val *mv);
4715 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4716 by the corresponding elements of C<mv>.
4718 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4719 __isl_take isl_pw_multi_aff *pma,
4720 enum isl_dim_type type, unsigned pos, int value);
4721 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4722 __isl_take isl_pw_multi_aff *pma,
4723 __isl_take isl_set *set);
4724 __isl_give isl_set *isl_multi_pw_aff_domain(
4725 __isl_take isl_multi_pw_aff *mpa);
4726 __isl_give isl_multi_pw_aff *
4727 isl_multi_pw_aff_intersect_params(
4728 __isl_take isl_multi_pw_aff *mpa,
4729 __isl_take isl_set *set);
4730 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4731 __isl_take isl_pw_multi_aff *pma,
4732 __isl_take isl_set *set);
4733 __isl_give isl_multi_pw_aff *
4734 isl_multi_pw_aff_intersect_domain(
4735 __isl_take isl_multi_pw_aff *mpa,
4736 __isl_take isl_set *domain);
4737 __isl_give isl_union_pw_multi_aff *
4738 isl_union_pw_multi_aff_intersect_domain(
4739 __isl_take isl_union_pw_multi_aff *upma,
4740 __isl_take isl_union_set *uset);
4741 __isl_give isl_multi_aff *isl_multi_aff_lift(
4742 __isl_take isl_multi_aff *maff,
4743 __isl_give isl_local_space **ls);
4744 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4745 __isl_take isl_pw_multi_aff *pma);
4746 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4747 __isl_take isl_multi_pw_aff *mpa);
4748 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4749 __isl_take isl_multi_aff *multi,
4750 __isl_take isl_space *model);
4751 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4752 __isl_take isl_pw_multi_aff *pma,
4753 __isl_take isl_space *model);
4754 __isl_give isl_union_pw_multi_aff *
4755 isl_union_pw_multi_aff_align_params(
4756 __isl_take isl_union_pw_multi_aff *upma,
4757 __isl_take isl_space *model);
4758 __isl_give isl_pw_multi_aff *
4759 isl_pw_multi_aff_project_domain_on_params(
4760 __isl_take isl_pw_multi_aff *pma);
4761 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4762 __isl_take isl_multi_aff *maff,
4763 __isl_take isl_set *context);
4764 __isl_give isl_multi_aff *isl_multi_aff_gist(
4765 __isl_take isl_multi_aff *maff,
4766 __isl_take isl_set *context);
4767 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4768 __isl_take isl_pw_multi_aff *pma,
4769 __isl_take isl_set *set);
4770 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4771 __isl_take isl_pw_multi_aff *pma,
4772 __isl_take isl_set *set);
4773 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4774 __isl_take isl_multi_pw_aff *mpa,
4775 __isl_take isl_set *set);
4776 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4777 __isl_take isl_multi_pw_aff *mpa,
4778 __isl_take isl_set *set);
4779 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4780 __isl_take isl_multi_aff *ma);
4781 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4782 __isl_take isl_multi_pw_aff *mpa);
4783 __isl_give isl_set *isl_pw_multi_aff_domain(
4784 __isl_take isl_pw_multi_aff *pma);
4785 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4786 __isl_take isl_union_pw_multi_aff *upma);
4787 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4788 __isl_take isl_multi_aff *ma1, unsigned pos,
4789 __isl_take isl_multi_aff *ma2);
4790 __isl_give isl_multi_aff *isl_multi_aff_splice(
4791 __isl_take isl_multi_aff *ma1,
4792 unsigned in_pos, unsigned out_pos,
4793 __isl_take isl_multi_aff *ma2);
4794 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4795 __isl_take isl_multi_aff *ma1,
4796 __isl_take isl_multi_aff *ma2);
4797 __isl_give isl_multi_aff *
4798 isl_multi_aff_range_factor_domain(
4799 __isl_take isl_multi_aff *ma);
4800 __isl_give isl_multi_aff *
4801 isl_multi_aff_range_factor_range(
4802 __isl_take isl_multi_aff *ma);
4803 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4804 __isl_take isl_multi_aff *ma1,
4805 __isl_take isl_multi_aff *ma2);
4806 __isl_give isl_multi_aff *isl_multi_aff_product(
4807 __isl_take isl_multi_aff *ma1,
4808 __isl_take isl_multi_aff *ma2);
4809 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4810 __isl_take isl_multi_pw_aff *mpa1,
4811 __isl_take isl_multi_pw_aff *mpa2);
4812 __isl_give isl_pw_multi_aff *
4813 isl_pw_multi_aff_range_product(
4814 __isl_take isl_pw_multi_aff *pma1,
4815 __isl_take isl_pw_multi_aff *pma2);
4816 __isl_give isl_multi_pw_aff *
4817 isl_multi_pw_aff_range_factor_domain(
4818 __isl_take isl_multi_pw_aff *mpa);
4819 __isl_give isl_multi_pw_aff *
4820 isl_multi_pw_aff_range_factor_range(
4821 __isl_take isl_multi_pw_aff *mpa);
4822 __isl_give isl_pw_multi_aff *
4823 isl_pw_multi_aff_flat_range_product(
4824 __isl_take isl_pw_multi_aff *pma1,
4825 __isl_take isl_pw_multi_aff *pma2);
4826 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4827 __isl_take isl_pw_multi_aff *pma1,
4828 __isl_take isl_pw_multi_aff *pma2);
4829 __isl_give isl_union_pw_multi_aff *
4830 isl_union_pw_multi_aff_flat_range_product(
4831 __isl_take isl_union_pw_multi_aff *upma1,
4832 __isl_take isl_union_pw_multi_aff *upma2);
4833 __isl_give isl_multi_pw_aff *
4834 isl_multi_pw_aff_range_splice(
4835 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4836 __isl_take isl_multi_pw_aff *mpa2);
4837 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4838 __isl_take isl_multi_pw_aff *mpa1,
4839 unsigned in_pos, unsigned out_pos,
4840 __isl_take isl_multi_pw_aff *mpa2);
4841 __isl_give isl_multi_pw_aff *
4842 isl_multi_pw_aff_range_product(
4843 __isl_take isl_multi_pw_aff *mpa1,
4844 __isl_take isl_multi_pw_aff *mpa2);
4845 __isl_give isl_multi_pw_aff *
4846 isl_multi_pw_aff_flat_range_product(
4847 __isl_take isl_multi_pw_aff *mpa1,
4848 __isl_take isl_multi_pw_aff *mpa2);
4850 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4851 then it is assigned the local space that lies at the basis of
4852 the lifting applied.
4854 #include <isl/aff.h>
4855 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4856 __isl_take isl_multi_aff *ma1,
4857 __isl_take isl_multi_aff *ma2);
4858 __isl_give isl_pw_multi_aff *
4859 isl_pw_multi_aff_pullback_multi_aff(
4860 __isl_take isl_pw_multi_aff *pma,
4861 __isl_take isl_multi_aff *ma);
4862 __isl_give isl_multi_pw_aff *
4863 isl_multi_pw_aff_pullback_multi_aff(
4864 __isl_take isl_multi_pw_aff *mpa,
4865 __isl_take isl_multi_aff *ma);
4866 __isl_give isl_pw_multi_aff *
4867 isl_pw_multi_aff_pullback_pw_multi_aff(
4868 __isl_take isl_pw_multi_aff *pma1,
4869 __isl_take isl_pw_multi_aff *pma2);
4870 __isl_give isl_multi_pw_aff *
4871 isl_multi_pw_aff_pullback_pw_multi_aff(
4872 __isl_take isl_multi_pw_aff *mpa,
4873 __isl_take isl_pw_multi_aff *pma);
4874 __isl_give isl_multi_pw_aff *
4875 isl_multi_pw_aff_pullback_multi_pw_aff(
4876 __isl_take isl_multi_pw_aff *mpa1,
4877 __isl_take isl_multi_pw_aff *mpa2);
4879 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4880 In other words, C<ma2> is plugged
4883 __isl_give isl_set *isl_multi_aff_lex_le_set(
4884 __isl_take isl_multi_aff *ma1,
4885 __isl_take isl_multi_aff *ma2);
4886 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4887 __isl_take isl_multi_aff *ma1,
4888 __isl_take isl_multi_aff *ma2);
4890 The function C<isl_multi_aff_lex_le_set> returns a set
4891 containing those elements in the shared domain space
4892 where C<ma1> is lexicographically smaller than or
4895 An expression can be read from input using
4897 #include <isl/aff.h>
4898 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4899 isl_ctx *ctx, const char *str);
4900 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4901 isl_ctx *ctx, const char *str);
4902 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4903 isl_ctx *ctx, const char *str);
4904 __isl_give isl_union_pw_multi_aff *
4905 isl_union_pw_multi_aff_read_from_str(
4906 isl_ctx *ctx, const char *str);
4908 An expression can be printed using
4910 #include <isl/aff.h>
4911 __isl_give isl_printer *isl_printer_print_multi_aff(
4912 __isl_take isl_printer *p,
4913 __isl_keep isl_multi_aff *maff);
4914 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4915 __isl_take isl_printer *p,
4916 __isl_keep isl_pw_multi_aff *pma);
4917 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4918 __isl_take isl_printer *p,
4919 __isl_keep isl_union_pw_multi_aff *upma);
4920 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4921 __isl_take isl_printer *p,
4922 __isl_keep isl_multi_pw_aff *mpa);
4926 Points are elements of a set. They can be used to construct
4927 simple sets (boxes) or they can be used to represent the
4928 individual elements of a set.
4929 The zero point (the origin) can be created using
4931 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4933 The coordinates of a point can be inspected, set and changed
4936 __isl_give isl_val *isl_point_get_coordinate_val(
4937 __isl_keep isl_point *pnt,
4938 enum isl_dim_type type, int pos);
4939 __isl_give isl_point *isl_point_set_coordinate_val(
4940 __isl_take isl_point *pnt,
4941 enum isl_dim_type type, int pos,
4942 __isl_take isl_val *v);
4944 __isl_give isl_point *isl_point_add_ui(
4945 __isl_take isl_point *pnt,
4946 enum isl_dim_type type, int pos, unsigned val);
4947 __isl_give isl_point *isl_point_sub_ui(
4948 __isl_take isl_point *pnt,
4949 enum isl_dim_type type, int pos, unsigned val);
4951 Other properties can be obtained using
4953 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4955 Points can be copied or freed using
4957 __isl_give isl_point *isl_point_copy(
4958 __isl_keep isl_point *pnt);
4959 void isl_point_free(__isl_take isl_point *pnt);
4961 A singleton set can be created from a point using
4963 __isl_give isl_basic_set *isl_basic_set_from_point(
4964 __isl_take isl_point *pnt);
4965 __isl_give isl_set *isl_set_from_point(
4966 __isl_take isl_point *pnt);
4968 and a box can be created from two opposite extremal points using
4970 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4971 __isl_take isl_point *pnt1,
4972 __isl_take isl_point *pnt2);
4973 __isl_give isl_set *isl_set_box_from_points(
4974 __isl_take isl_point *pnt1,
4975 __isl_take isl_point *pnt2);
4977 All elements of a B<bounded> (union) set can be enumerated using
4978 the following functions.
4980 int isl_set_foreach_point(__isl_keep isl_set *set,
4981 int (*fn)(__isl_take isl_point *pnt, void *user),
4983 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4984 int (*fn)(__isl_take isl_point *pnt, void *user),
4987 The function C<fn> is called for each integer point in
4988 C<set> with as second argument the last argument of
4989 the C<isl_set_foreach_point> call. The function C<fn>
4990 should return C<0> on success and C<-1> on failure.
4991 In the latter case, C<isl_set_foreach_point> will stop
4992 enumerating and return C<-1> as well.
4993 If the enumeration is performed successfully and to completion,
4994 then C<isl_set_foreach_point> returns C<0>.
4996 To obtain a single point of a (basic) set, use
4998 __isl_give isl_point *isl_basic_set_sample_point(
4999 __isl_take isl_basic_set *bset);
5000 __isl_give isl_point *isl_set_sample_point(
5001 __isl_take isl_set *set);
5003 If C<set> does not contain any (integer) points, then the
5004 resulting point will be ``void'', a property that can be
5007 int isl_point_is_void(__isl_keep isl_point *pnt);
5009 =head2 Piecewise Quasipolynomials
5011 A piecewise quasipolynomial is a particular kind of function that maps
5012 a parametric point to a rational value.
5013 More specifically, a quasipolynomial is a polynomial expression in greatest
5014 integer parts of affine expressions of parameters and variables.
5015 A piecewise quasipolynomial is a subdivision of a given parametric
5016 domain into disjoint cells with a quasipolynomial associated to
5017 each cell. The value of the piecewise quasipolynomial at a given
5018 point is the value of the quasipolynomial associated to the cell
5019 that contains the point. Outside of the union of cells,
5020 the value is assumed to be zero.
5021 For example, the piecewise quasipolynomial
5023 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
5025 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
5026 A given piecewise quasipolynomial has a fixed domain dimension.
5027 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
5028 defined over different domains.
5029 Piecewise quasipolynomials are mainly used by the C<barvinok>
5030 library for representing the number of elements in a parametric set or map.
5031 For example, the piecewise quasipolynomial above represents
5032 the number of points in the map
5034 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
5036 =head3 Input and Output
5038 Piecewise quasipolynomials can be read from input using
5040 __isl_give isl_union_pw_qpolynomial *
5041 isl_union_pw_qpolynomial_read_from_str(
5042 isl_ctx *ctx, const char *str);
5044 Quasipolynomials and piecewise quasipolynomials can be printed
5045 using the following functions.
5047 __isl_give isl_printer *isl_printer_print_qpolynomial(
5048 __isl_take isl_printer *p,
5049 __isl_keep isl_qpolynomial *qp);
5051 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
5052 __isl_take isl_printer *p,
5053 __isl_keep isl_pw_qpolynomial *pwqp);
5055 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
5056 __isl_take isl_printer *p,
5057 __isl_keep isl_union_pw_qpolynomial *upwqp);
5059 The output format of the printer
5060 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5061 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
5063 In case of printing in C<ISL_FORMAT_C>, the user may want
5064 to set the names of all dimensions
5066 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
5067 __isl_take isl_qpolynomial *qp,
5068 enum isl_dim_type type, unsigned pos,
5070 __isl_give isl_pw_qpolynomial *
5071 isl_pw_qpolynomial_set_dim_name(
5072 __isl_take isl_pw_qpolynomial *pwqp,
5073 enum isl_dim_type type, unsigned pos,
5076 =head3 Creating New (Piecewise) Quasipolynomials
5078 Some simple quasipolynomials can be created using the following functions.
5079 More complicated quasipolynomials can be created by applying
5080 operations such as addition and multiplication
5081 on the resulting quasipolynomials
5083 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
5084 __isl_take isl_space *domain);
5085 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
5086 __isl_take isl_space *domain);
5087 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
5088 __isl_take isl_space *domain);
5089 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
5090 __isl_take isl_space *domain);
5091 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
5092 __isl_take isl_space *domain);
5093 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
5094 __isl_take isl_space *domain,
5095 __isl_take isl_val *val);
5096 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
5097 __isl_take isl_space *domain,
5098 enum isl_dim_type type, unsigned pos);
5099 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
5100 __isl_take isl_aff *aff);
5102 Note that the space in which a quasipolynomial lives is a map space
5103 with a one-dimensional range. The C<domain> argument in some of
5104 the functions above corresponds to the domain of this map space.
5106 The zero piecewise quasipolynomial or a piecewise quasipolynomial
5107 with a single cell can be created using the following functions.
5108 Multiple of these single cell piecewise quasipolynomials can
5109 be combined to create more complicated piecewise quasipolynomials.
5111 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
5112 __isl_take isl_space *space);
5113 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
5114 __isl_take isl_set *set,
5115 __isl_take isl_qpolynomial *qp);
5116 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
5117 __isl_take isl_qpolynomial *qp);
5118 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
5119 __isl_take isl_pw_aff *pwaff);
5121 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
5122 __isl_take isl_space *space);
5123 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
5124 __isl_take isl_pw_qpolynomial *pwqp);
5125 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
5126 __isl_take isl_union_pw_qpolynomial *upwqp,
5127 __isl_take isl_pw_qpolynomial *pwqp);
5129 Quasipolynomials can be copied and freed again using the following
5132 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
5133 __isl_keep isl_qpolynomial *qp);
5134 __isl_null isl_qpolynomial *isl_qpolynomial_free(
5135 __isl_take isl_qpolynomial *qp);
5137 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
5138 __isl_keep isl_pw_qpolynomial *pwqp);
5139 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
5140 __isl_take isl_pw_qpolynomial *pwqp);
5142 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
5143 __isl_keep isl_union_pw_qpolynomial *upwqp);
5144 __isl_null isl_union_pw_qpolynomial *
5145 isl_union_pw_qpolynomial_free(
5146 __isl_take isl_union_pw_qpolynomial *upwqp);
5148 =head3 Inspecting (Piecewise) Quasipolynomials
5150 To iterate over all piecewise quasipolynomials in a union
5151 piecewise quasipolynomial, use the following function
5153 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
5154 __isl_keep isl_union_pw_qpolynomial *upwqp,
5155 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
5158 To extract the piecewise quasipolynomial in a given space from a union, use
5160 __isl_give isl_pw_qpolynomial *
5161 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
5162 __isl_keep isl_union_pw_qpolynomial *upwqp,
5163 __isl_take isl_space *space);
5165 To iterate over the cells in a piecewise quasipolynomial,
5166 use either of the following two functions
5168 int isl_pw_qpolynomial_foreach_piece(
5169 __isl_keep isl_pw_qpolynomial *pwqp,
5170 int (*fn)(__isl_take isl_set *set,
5171 __isl_take isl_qpolynomial *qp,
5172 void *user), void *user);
5173 int isl_pw_qpolynomial_foreach_lifted_piece(
5174 __isl_keep isl_pw_qpolynomial *pwqp,
5175 int (*fn)(__isl_take isl_set *set,
5176 __isl_take isl_qpolynomial *qp,
5177 void *user), void *user);
5179 As usual, the function C<fn> should return C<0> on success
5180 and C<-1> on failure. The difference between
5181 C<isl_pw_qpolynomial_foreach_piece> and
5182 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
5183 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
5184 compute unique representations for all existentially quantified
5185 variables and then turn these existentially quantified variables
5186 into extra set variables, adapting the associated quasipolynomial
5187 accordingly. This means that the C<set> passed to C<fn>
5188 will not have any existentially quantified variables, but that
5189 the dimensions of the sets may be different for different
5190 invocations of C<fn>.
5192 The constant term of a quasipolynomial can be extracted using
5194 __isl_give isl_val *isl_qpolynomial_get_constant_val(
5195 __isl_keep isl_qpolynomial *qp);
5197 To iterate over all terms in a quasipolynomial,
5200 int isl_qpolynomial_foreach_term(
5201 __isl_keep isl_qpolynomial *qp,
5202 int (*fn)(__isl_take isl_term *term,
5203 void *user), void *user);
5205 The terms themselves can be inspected and freed using
5208 unsigned isl_term_dim(__isl_keep isl_term *term,
5209 enum isl_dim_type type);
5210 __isl_give isl_val *isl_term_get_coefficient_val(
5211 __isl_keep isl_term *term);
5212 int isl_term_get_exp(__isl_keep isl_term *term,
5213 enum isl_dim_type type, unsigned pos);
5214 __isl_give isl_aff *isl_term_get_div(
5215 __isl_keep isl_term *term, unsigned pos);
5216 void isl_term_free(__isl_take isl_term *term);
5218 Each term is a product of parameters, set variables and
5219 integer divisions. The function C<isl_term_get_exp>
5220 returns the exponent of a given dimensions in the given term.
5222 =head3 Properties of (Piecewise) Quasipolynomials
5224 To check whether two union piecewise quasipolynomials are
5225 obviously equal, use
5227 int isl_union_pw_qpolynomial_plain_is_equal(
5228 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5229 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5231 =head3 Operations on (Piecewise) Quasipolynomials
5233 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5234 __isl_take isl_qpolynomial *qp,
5235 __isl_take isl_val *v);
5236 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5237 __isl_take isl_qpolynomial *qp);
5238 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5239 __isl_take isl_qpolynomial *qp1,
5240 __isl_take isl_qpolynomial *qp2);
5241 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5242 __isl_take isl_qpolynomial *qp1,
5243 __isl_take isl_qpolynomial *qp2);
5244 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5245 __isl_take isl_qpolynomial *qp1,
5246 __isl_take isl_qpolynomial *qp2);
5247 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5248 __isl_take isl_qpolynomial *qp, unsigned exponent);
5250 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5251 __isl_take isl_pw_qpolynomial *pwqp,
5252 enum isl_dim_type type, unsigned n,
5253 __isl_take isl_val *v);
5254 __isl_give isl_pw_qpolynomial *
5255 isl_pw_qpolynomial_scale_val(
5256 __isl_take isl_pw_qpolynomial *pwqp,
5257 __isl_take isl_val *v);
5258 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5259 __isl_take isl_pw_qpolynomial *pwqp1,
5260 __isl_take isl_pw_qpolynomial *pwqp2);
5261 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5262 __isl_take isl_pw_qpolynomial *pwqp1,
5263 __isl_take isl_pw_qpolynomial *pwqp2);
5264 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5265 __isl_take isl_pw_qpolynomial *pwqp1,
5266 __isl_take isl_pw_qpolynomial *pwqp2);
5267 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5268 __isl_take isl_pw_qpolynomial *pwqp);
5269 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5270 __isl_take isl_pw_qpolynomial *pwqp1,
5271 __isl_take isl_pw_qpolynomial *pwqp2);
5272 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5273 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5275 __isl_give isl_union_pw_qpolynomial *
5276 isl_union_pw_qpolynomial_scale_val(
5277 __isl_take isl_union_pw_qpolynomial *upwqp,
5278 __isl_take isl_val *v);
5279 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5280 __isl_take isl_union_pw_qpolynomial *upwqp1,
5281 __isl_take isl_union_pw_qpolynomial *upwqp2);
5282 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5283 __isl_take isl_union_pw_qpolynomial *upwqp1,
5284 __isl_take isl_union_pw_qpolynomial *upwqp2);
5285 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5286 __isl_take isl_union_pw_qpolynomial *upwqp1,
5287 __isl_take isl_union_pw_qpolynomial *upwqp2);
5289 __isl_give isl_val *isl_pw_qpolynomial_eval(
5290 __isl_take isl_pw_qpolynomial *pwqp,
5291 __isl_take isl_point *pnt);
5293 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5294 __isl_take isl_union_pw_qpolynomial *upwqp,
5295 __isl_take isl_point *pnt);
5297 __isl_give isl_set *isl_pw_qpolynomial_domain(
5298 __isl_take isl_pw_qpolynomial *pwqp);
5299 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5300 __isl_take isl_pw_qpolynomial *pwpq,
5301 __isl_take isl_set *set);
5302 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5303 __isl_take isl_pw_qpolynomial *pwpq,
5304 __isl_take isl_set *set);
5306 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5307 __isl_take isl_union_pw_qpolynomial *upwqp);
5308 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5309 __isl_take isl_union_pw_qpolynomial *upwpq,
5310 __isl_take isl_union_set *uset);
5311 __isl_give isl_union_pw_qpolynomial *
5312 isl_union_pw_qpolynomial_intersect_params(
5313 __isl_take isl_union_pw_qpolynomial *upwpq,
5314 __isl_take isl_set *set);
5316 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5317 __isl_take isl_qpolynomial *qp,
5318 __isl_take isl_space *model);
5320 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5321 __isl_take isl_qpolynomial *qp);
5322 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5323 __isl_take isl_pw_qpolynomial *pwqp);
5325 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5326 __isl_take isl_union_pw_qpolynomial *upwqp);
5328 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5329 __isl_take isl_qpolynomial *qp,
5330 __isl_take isl_set *context);
5331 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5332 __isl_take isl_qpolynomial *qp,
5333 __isl_take isl_set *context);
5335 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5336 __isl_take isl_pw_qpolynomial *pwqp,
5337 __isl_take isl_set *context);
5338 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5339 __isl_take isl_pw_qpolynomial *pwqp,
5340 __isl_take isl_set *context);
5342 __isl_give isl_union_pw_qpolynomial *
5343 isl_union_pw_qpolynomial_gist_params(
5344 __isl_take isl_union_pw_qpolynomial *upwqp,
5345 __isl_take isl_set *context);
5346 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5347 __isl_take isl_union_pw_qpolynomial *upwqp,
5348 __isl_take isl_union_set *context);
5350 The gist operation applies the gist operation to each of
5351 the cells in the domain of the input piecewise quasipolynomial.
5352 The context is also exploited
5353 to simplify the quasipolynomials associated to each cell.
5355 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5356 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5357 __isl_give isl_union_pw_qpolynomial *
5358 isl_union_pw_qpolynomial_to_polynomial(
5359 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5361 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5362 the polynomial will be an overapproximation. If C<sign> is negative,
5363 it will be an underapproximation. If C<sign> is zero, the approximation
5364 will lie somewhere in between.
5366 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5368 A piecewise quasipolynomial reduction is a piecewise
5369 reduction (or fold) of quasipolynomials.
5370 In particular, the reduction can be maximum or a minimum.
5371 The objects are mainly used to represent the result of
5372 an upper or lower bound on a quasipolynomial over its domain,
5373 i.e., as the result of the following function.
5375 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5376 __isl_take isl_pw_qpolynomial *pwqp,
5377 enum isl_fold type, int *tight);
5379 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5380 __isl_take isl_union_pw_qpolynomial *upwqp,
5381 enum isl_fold type, int *tight);
5383 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5384 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5385 is the returned bound is known be tight, i.e., for each value
5386 of the parameters there is at least
5387 one element in the domain that reaches the bound.
5388 If the domain of C<pwqp> is not wrapping, then the bound is computed
5389 over all elements in that domain and the result has a purely parametric
5390 domain. If the domain of C<pwqp> is wrapping, then the bound is
5391 computed over the range of the wrapped relation. The domain of the
5392 wrapped relation becomes the domain of the result.
5394 A (piecewise) quasipolynomial reduction can be copied or freed using the
5395 following functions.
5397 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5398 __isl_keep isl_qpolynomial_fold *fold);
5399 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5400 __isl_keep isl_pw_qpolynomial_fold *pwf);
5401 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5402 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5403 void isl_qpolynomial_fold_free(
5404 __isl_take isl_qpolynomial_fold *fold);
5405 __isl_null isl_pw_qpolynomial_fold *
5406 isl_pw_qpolynomial_fold_free(
5407 __isl_take isl_pw_qpolynomial_fold *pwf);
5408 __isl_null isl_union_pw_qpolynomial_fold *
5409 isl_union_pw_qpolynomial_fold_free(
5410 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5412 =head3 Printing Piecewise Quasipolynomial Reductions
5414 Piecewise quasipolynomial reductions can be printed
5415 using the following function.
5417 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5418 __isl_take isl_printer *p,
5419 __isl_keep isl_pw_qpolynomial_fold *pwf);
5420 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5421 __isl_take isl_printer *p,
5422 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5424 For C<isl_printer_print_pw_qpolynomial_fold>,
5425 output format of the printer
5426 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5427 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5428 output format of the printer
5429 needs to be set to C<ISL_FORMAT_ISL>.
5430 In case of printing in C<ISL_FORMAT_C>, the user may want
5431 to set the names of all dimensions
5433 __isl_give isl_pw_qpolynomial_fold *
5434 isl_pw_qpolynomial_fold_set_dim_name(
5435 __isl_take isl_pw_qpolynomial_fold *pwf,
5436 enum isl_dim_type type, unsigned pos,
5439 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5441 To iterate over all piecewise quasipolynomial reductions in a union
5442 piecewise quasipolynomial reduction, use the following function
5444 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5445 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5446 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5447 void *user), void *user);
5449 To iterate over the cells in a piecewise quasipolynomial reduction,
5450 use either of the following two functions
5452 int isl_pw_qpolynomial_fold_foreach_piece(
5453 __isl_keep isl_pw_qpolynomial_fold *pwf,
5454 int (*fn)(__isl_take isl_set *set,
5455 __isl_take isl_qpolynomial_fold *fold,
5456 void *user), void *user);
5457 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5458 __isl_keep isl_pw_qpolynomial_fold *pwf,
5459 int (*fn)(__isl_take isl_set *set,
5460 __isl_take isl_qpolynomial_fold *fold,
5461 void *user), void *user);
5463 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5464 of the difference between these two functions.
5466 To iterate over all quasipolynomials in a reduction, use
5468 int isl_qpolynomial_fold_foreach_qpolynomial(
5469 __isl_keep isl_qpolynomial_fold *fold,
5470 int (*fn)(__isl_take isl_qpolynomial *qp,
5471 void *user), void *user);
5473 =head3 Properties of Piecewise Quasipolynomial Reductions
5475 To check whether two union piecewise quasipolynomial reductions are
5476 obviously equal, use
5478 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5479 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5480 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5482 =head3 Operations on Piecewise Quasipolynomial Reductions
5484 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5485 __isl_take isl_qpolynomial_fold *fold,
5486 __isl_take isl_val *v);
5487 __isl_give isl_pw_qpolynomial_fold *
5488 isl_pw_qpolynomial_fold_scale_val(
5489 __isl_take isl_pw_qpolynomial_fold *pwf,
5490 __isl_take isl_val *v);
5491 __isl_give isl_union_pw_qpolynomial_fold *
5492 isl_union_pw_qpolynomial_fold_scale_val(
5493 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5494 __isl_take isl_val *v);
5496 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5497 __isl_take isl_pw_qpolynomial_fold *pwf1,
5498 __isl_take isl_pw_qpolynomial_fold *pwf2);
5500 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5501 __isl_take isl_pw_qpolynomial_fold *pwf1,
5502 __isl_take isl_pw_qpolynomial_fold *pwf2);
5504 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5505 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5506 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5508 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5509 __isl_take isl_pw_qpolynomial_fold *pwf,
5510 __isl_take isl_point *pnt);
5512 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5513 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5514 __isl_take isl_point *pnt);
5516 __isl_give isl_pw_qpolynomial_fold *
5517 isl_pw_qpolynomial_fold_intersect_params(
5518 __isl_take isl_pw_qpolynomial_fold *pwf,
5519 __isl_take isl_set *set);
5521 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5522 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5523 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5524 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5525 __isl_take isl_union_set *uset);
5526 __isl_give isl_union_pw_qpolynomial_fold *
5527 isl_union_pw_qpolynomial_fold_intersect_params(
5528 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5529 __isl_take isl_set *set);
5531 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5532 __isl_take isl_pw_qpolynomial_fold *pwf);
5534 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5535 __isl_take isl_pw_qpolynomial_fold *pwf);
5537 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5538 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5540 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5541 __isl_take isl_qpolynomial_fold *fold,
5542 __isl_take isl_set *context);
5543 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5544 __isl_take isl_qpolynomial_fold *fold,
5545 __isl_take isl_set *context);
5547 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5548 __isl_take isl_pw_qpolynomial_fold *pwf,
5549 __isl_take isl_set *context);
5550 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5551 __isl_take isl_pw_qpolynomial_fold *pwf,
5552 __isl_take isl_set *context);
5554 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5555 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5556 __isl_take isl_union_set *context);
5557 __isl_give isl_union_pw_qpolynomial_fold *
5558 isl_union_pw_qpolynomial_fold_gist_params(
5559 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5560 __isl_take isl_set *context);
5562 The gist operation applies the gist operation to each of
5563 the cells in the domain of the input piecewise quasipolynomial reduction.
5564 In future, the operation will also exploit the context
5565 to simplify the quasipolynomial reductions associated to each cell.
5567 __isl_give isl_pw_qpolynomial_fold *
5568 isl_set_apply_pw_qpolynomial_fold(
5569 __isl_take isl_set *set,
5570 __isl_take isl_pw_qpolynomial_fold *pwf,
5572 __isl_give isl_pw_qpolynomial_fold *
5573 isl_map_apply_pw_qpolynomial_fold(
5574 __isl_take isl_map *map,
5575 __isl_take isl_pw_qpolynomial_fold *pwf,
5577 __isl_give isl_union_pw_qpolynomial_fold *
5578 isl_union_set_apply_union_pw_qpolynomial_fold(
5579 __isl_take isl_union_set *uset,
5580 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5582 __isl_give isl_union_pw_qpolynomial_fold *
5583 isl_union_map_apply_union_pw_qpolynomial_fold(
5584 __isl_take isl_union_map *umap,
5585 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5588 The functions taking a map
5589 compose the given map with the given piecewise quasipolynomial reduction.
5590 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5591 over all elements in the intersection of the range of the map
5592 and the domain of the piecewise quasipolynomial reduction
5593 as a function of an element in the domain of the map.
5594 The functions taking a set compute a bound over all elements in the
5595 intersection of the set and the domain of the
5596 piecewise quasipolynomial reduction.
5598 =head2 Parametric Vertex Enumeration
5600 The parametric vertex enumeration described in this section
5601 is mainly intended to be used internally and by the C<barvinok>
5604 #include <isl/vertices.h>
5605 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5606 __isl_keep isl_basic_set *bset);
5608 The function C<isl_basic_set_compute_vertices> performs the
5609 actual computation of the parametric vertices and the chamber
5610 decomposition and store the result in an C<isl_vertices> object.
5611 This information can be queried by either iterating over all
5612 the vertices or iterating over all the chambers or cells
5613 and then iterating over all vertices that are active on the chamber.
5615 int isl_vertices_foreach_vertex(
5616 __isl_keep isl_vertices *vertices,
5617 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5620 int isl_vertices_foreach_cell(
5621 __isl_keep isl_vertices *vertices,
5622 int (*fn)(__isl_take isl_cell *cell, void *user),
5624 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5625 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5628 Other operations that can be performed on an C<isl_vertices> object are
5631 isl_ctx *isl_vertices_get_ctx(
5632 __isl_keep isl_vertices *vertices);
5633 int isl_vertices_get_n_vertices(
5634 __isl_keep isl_vertices *vertices);
5635 void isl_vertices_free(__isl_take isl_vertices *vertices);
5637 Vertices can be inspected and destroyed using the following functions.
5639 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5640 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5641 __isl_give isl_basic_set *isl_vertex_get_domain(
5642 __isl_keep isl_vertex *vertex);
5643 __isl_give isl_basic_set *isl_vertex_get_expr(
5644 __isl_keep isl_vertex *vertex);
5645 void isl_vertex_free(__isl_take isl_vertex *vertex);
5647 C<isl_vertex_get_expr> returns a singleton parametric set describing
5648 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5650 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5651 B<rational> basic sets, so they should mainly be used for inspection
5652 and should not be mixed with integer sets.
5654 Chambers can be inspected and destroyed using the following functions.
5656 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5657 __isl_give isl_basic_set *isl_cell_get_domain(
5658 __isl_keep isl_cell *cell);
5659 void isl_cell_free(__isl_take isl_cell *cell);
5661 =head1 Polyhedral Compilation Library
5663 This section collects functionality in C<isl> that has been specifically
5664 designed for use during polyhedral compilation.
5666 =head2 Dependence Analysis
5668 C<isl> contains specialized functionality for performing
5669 array dataflow analysis. That is, given a I<sink> access relation
5670 and a collection of possible I<source> access relations,
5671 C<isl> can compute relations that describe
5672 for each iteration of the sink access, which iteration
5673 of which of the source access relations was the last
5674 to access the same data element before the given iteration
5676 The resulting dependence relations map source iterations
5677 to the corresponding sink iterations.
5678 To compute standard flow dependences, the sink should be
5679 a read, while the sources should be writes.
5680 If any of the source accesses are marked as being I<may>
5681 accesses, then there will be a dependence from the last
5682 I<must> access B<and> from any I<may> access that follows
5683 this last I<must> access.
5684 In particular, if I<all> sources are I<may> accesses,
5685 then memory based dependence analysis is performed.
5686 If, on the other hand, all sources are I<must> accesses,
5687 then value based dependence analysis is performed.
5689 #include <isl/flow.h>
5691 typedef int (*isl_access_level_before)(void *first, void *second);
5693 __isl_give isl_access_info *isl_access_info_alloc(
5694 __isl_take isl_map *sink,
5695 void *sink_user, isl_access_level_before fn,
5697 __isl_give isl_access_info *isl_access_info_add_source(
5698 __isl_take isl_access_info *acc,
5699 __isl_take isl_map *source, int must,
5701 __isl_null isl_access_info *isl_access_info_free(
5702 __isl_take isl_access_info *acc);
5704 __isl_give isl_flow *isl_access_info_compute_flow(
5705 __isl_take isl_access_info *acc);
5707 int isl_flow_foreach(__isl_keep isl_flow *deps,
5708 int (*fn)(__isl_take isl_map *dep, int must,
5709 void *dep_user, void *user),
5711 __isl_give isl_map *isl_flow_get_no_source(
5712 __isl_keep isl_flow *deps, int must);
5713 void isl_flow_free(__isl_take isl_flow *deps);
5715 The function C<isl_access_info_compute_flow> performs the actual
5716 dependence analysis. The other functions are used to construct
5717 the input for this function or to read off the output.
5719 The input is collected in an C<isl_access_info>, which can
5720 be created through a call to C<isl_access_info_alloc>.
5721 The arguments to this functions are the sink access relation
5722 C<sink>, a token C<sink_user> used to identify the sink
5723 access to the user, a callback function for specifying the
5724 relative order of source and sink accesses, and the number
5725 of source access relations that will be added.
5726 The callback function has type C<int (*)(void *first, void *second)>.
5727 The function is called with two user supplied tokens identifying
5728 either a source or the sink and it should return the shared nesting
5729 level and the relative order of the two accesses.
5730 In particular, let I<n> be the number of loops shared by
5731 the two accesses. If C<first> precedes C<second> textually,
5732 then the function should return I<2 * n + 1>; otherwise,
5733 it should return I<2 * n>.
5734 The sources can be added to the C<isl_access_info> by performing
5735 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5736 C<must> indicates whether the source is a I<must> access
5737 or a I<may> access. Note that a multi-valued access relation
5738 should only be marked I<must> if every iteration in the domain
5739 of the relation accesses I<all> elements in its image.
5740 The C<source_user> token is again used to identify
5741 the source access. The range of the source access relation
5742 C<source> should have the same dimension as the range
5743 of the sink access relation.
5744 The C<isl_access_info_free> function should usually not be
5745 called explicitly, because it is called implicitly by
5746 C<isl_access_info_compute_flow>.
5748 The result of the dependence analysis is collected in an
5749 C<isl_flow>. There may be elements of
5750 the sink access for which no preceding source access could be
5751 found or for which all preceding sources are I<may> accesses.
5752 The relations containing these elements can be obtained through
5753 calls to C<isl_flow_get_no_source>, the first with C<must> set
5754 and the second with C<must> unset.
5755 In the case of standard flow dependence analysis,
5756 with the sink a read and the sources I<must> writes,
5757 the first relation corresponds to the reads from uninitialized
5758 array elements and the second relation is empty.
5759 The actual flow dependences can be extracted using
5760 C<isl_flow_foreach>. This function will call the user-specified
5761 callback function C<fn> for each B<non-empty> dependence between
5762 a source and the sink. The callback function is called
5763 with four arguments, the actual flow dependence relation
5764 mapping source iterations to sink iterations, a boolean that
5765 indicates whether it is a I<must> or I<may> dependence, a token
5766 identifying the source and an additional C<void *> with value
5767 equal to the third argument of the C<isl_flow_foreach> call.
5768 A dependence is marked I<must> if it originates from a I<must>
5769 source and if it is not followed by any I<may> sources.
5771 After finishing with an C<isl_flow>, the user should call
5772 C<isl_flow_free> to free all associated memory.
5774 A higher-level interface to dependence analysis is provided
5775 by the following function.
5777 #include <isl/flow.h>
5779 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5780 __isl_take isl_union_map *must_source,
5781 __isl_take isl_union_map *may_source,
5782 __isl_take isl_union_map *schedule,
5783 __isl_give isl_union_map **must_dep,
5784 __isl_give isl_union_map **may_dep,
5785 __isl_give isl_union_map **must_no_source,
5786 __isl_give isl_union_map **may_no_source);
5788 The arrays are identified by the tuple names of the ranges
5789 of the accesses. The iteration domains by the tuple names
5790 of the domains of the accesses and of the schedule.
5791 The relative order of the iteration domains is given by the
5792 schedule. The relations returned through C<must_no_source>
5793 and C<may_no_source> are subsets of C<sink>.
5794 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5795 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5796 any of the other arguments is treated as an error.
5798 =head3 Interaction with Dependence Analysis
5800 During the dependence analysis, we frequently need to perform
5801 the following operation. Given a relation between sink iterations
5802 and potential source iterations from a particular source domain,
5803 what is the last potential source iteration corresponding to each
5804 sink iteration. It can sometimes be convenient to adjust
5805 the set of potential source iterations before or after each such operation.
5806 The prototypical example is fuzzy array dataflow analysis,
5807 where we need to analyze if, based on data-dependent constraints,
5808 the sink iteration can ever be executed without one or more of
5809 the corresponding potential source iterations being executed.
5810 If so, we can introduce extra parameters and select an unknown
5811 but fixed source iteration from the potential source iterations.
5812 To be able to perform such manipulations, C<isl> provides the following
5815 #include <isl/flow.h>
5817 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5818 __isl_keep isl_map *source_map,
5819 __isl_keep isl_set *sink, void *source_user,
5821 __isl_give isl_access_info *isl_access_info_set_restrict(
5822 __isl_take isl_access_info *acc,
5823 isl_access_restrict fn, void *user);
5825 The function C<isl_access_info_set_restrict> should be called
5826 before calling C<isl_access_info_compute_flow> and registers a callback function
5827 that will be called any time C<isl> is about to compute the last
5828 potential source. The first argument is the (reverse) proto-dependence,
5829 mapping sink iterations to potential source iterations.
5830 The second argument represents the sink iterations for which
5831 we want to compute the last source iteration.
5832 The third argument is the token corresponding to the source
5833 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5834 The callback is expected to return a restriction on either the input or
5835 the output of the operation computing the last potential source.
5836 If the input needs to be restricted then restrictions are needed
5837 for both the source and the sink iterations. The sink iterations
5838 and the potential source iterations will be intersected with these sets.
5839 If the output needs to be restricted then only a restriction on the source
5840 iterations is required.
5841 If any error occurs, the callback should return C<NULL>.
5842 An C<isl_restriction> object can be created, freed and inspected
5843 using the following functions.
5845 #include <isl/flow.h>
5847 __isl_give isl_restriction *isl_restriction_input(
5848 __isl_take isl_set *source_restr,
5849 __isl_take isl_set *sink_restr);
5850 __isl_give isl_restriction *isl_restriction_output(
5851 __isl_take isl_set *source_restr);
5852 __isl_give isl_restriction *isl_restriction_none(
5853 __isl_take isl_map *source_map);
5854 __isl_give isl_restriction *isl_restriction_empty(
5855 __isl_take isl_map *source_map);
5856 __isl_null isl_restriction *isl_restriction_free(
5857 __isl_take isl_restriction *restr);
5858 isl_ctx *isl_restriction_get_ctx(
5859 __isl_keep isl_restriction *restr);
5861 C<isl_restriction_none> and C<isl_restriction_empty> are special
5862 cases of C<isl_restriction_input>. C<isl_restriction_none>
5863 is essentially equivalent to
5865 isl_restriction_input(isl_set_universe(
5866 isl_space_range(isl_map_get_space(source_map))),
5868 isl_space_domain(isl_map_get_space(source_map))));
5870 whereas C<isl_restriction_empty> is essentially equivalent to
5872 isl_restriction_input(isl_set_empty(
5873 isl_space_range(isl_map_get_space(source_map))),
5875 isl_space_domain(isl_map_get_space(source_map))));
5879 B<The functionality described in this section is fairly new
5880 and may be subject to change.>
5882 #include <isl/schedule.h>
5883 __isl_give isl_schedule *
5884 isl_schedule_constraints_compute_schedule(
5885 __isl_take isl_schedule_constraints *sc);
5886 __isl_null isl_schedule *isl_schedule_free(
5887 __isl_take isl_schedule *sched);
5889 The function C<isl_schedule_constraints_compute_schedule> can be
5890 used to compute a schedule that satisfy the given schedule constraints.
5891 These schedule constraints include the iteration domain for which
5892 a schedule should be computed and dependences between pairs of
5893 iterations. In particular, these dependences include
5894 I<validity> dependences and I<proximity> dependences.
5895 By default, the algorithm used to construct the schedule is similar
5896 to that of C<Pluto>.
5897 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5899 The generated schedule respects all validity dependences.
5900 That is, all dependence distances over these dependences in the
5901 scheduled space are lexicographically positive.
5902 The default algorithm tries to ensure that the dependence distances
5903 over coincidence constraints are zero and to minimize the
5904 dependence distances over proximity dependences.
5905 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5906 for groups of domains where the dependence distances over validity
5907 dependences have only non-negative values.
5908 When using Feautrier's algorithm, the coincidence and proximity constraints
5909 are only taken into account during the extension to a
5910 full-dimensional schedule.
5912 An C<isl_schedule_constraints> object can be constructed
5913 and manipulated using the following functions.
5915 #include <isl/schedule.h>
5916 __isl_give isl_schedule_constraints *
5917 isl_schedule_constraints_copy(
5918 __isl_keep isl_schedule_constraints *sc);
5919 __isl_give isl_schedule_constraints *
5920 isl_schedule_constraints_on_domain(
5921 __isl_take isl_union_set *domain);
5922 isl_ctx *isl_schedule_constraints_get_ctx(
5923 __isl_keep isl_schedule_constraints *sc);
5924 __isl_give isl_schedule_constraints *
5925 isl_schedule_constraints_set_validity(
5926 __isl_take isl_schedule_constraints *sc,
5927 __isl_take isl_union_map *validity);
5928 __isl_give isl_schedule_constraints *
5929 isl_schedule_constraints_set_coincidence(
5930 __isl_take isl_schedule_constraints *sc,
5931 __isl_take isl_union_map *coincidence);
5932 __isl_give isl_schedule_constraints *
5933 isl_schedule_constraints_set_proximity(
5934 __isl_take isl_schedule_constraints *sc,
5935 __isl_take isl_union_map *proximity);
5936 __isl_give isl_schedule_constraints *
5937 isl_schedule_constraints_set_conditional_validity(
5938 __isl_take isl_schedule_constraints *sc,
5939 __isl_take isl_union_map *condition,
5940 __isl_take isl_union_map *validity);
5941 __isl_null isl_schedule_constraints *
5942 isl_schedule_constraints_free(
5943 __isl_take isl_schedule_constraints *sc);
5945 The initial C<isl_schedule_constraints> object created by
5946 C<isl_schedule_constraints_on_domain> does not impose any constraints.
5947 That is, it has an empty set of dependences.
5948 The function C<isl_schedule_constraints_set_validity> replaces the
5949 validity dependences, mapping domain elements I<i> to domain
5950 elements that should be scheduled after I<i>.
5951 The function C<isl_schedule_constraints_set_coincidence> replaces the
5952 coincidence dependences, mapping domain elements I<i> to domain
5953 elements that should be scheduled together with I<I>, if possible.
5954 The function C<isl_schedule_constraints_set_proximity> replaces the
5955 proximity dependences, mapping domain elements I<i> to domain
5956 elements that should be scheduled either before I<I>
5957 or as early as possible after I<i>.
5959 The function C<isl_schedule_constraints_set_conditional_validity>
5960 replaces the conditional validity constraints.
5961 A conditional validity constraint is only imposed when any of the corresponding
5962 conditions is satisfied, i.e., when any of them is non-zero.
5963 That is, the scheduler ensures that within each band if the dependence
5964 distances over the condition constraints are not all zero
5965 then all corresponding conditional validity constraints are respected.
5966 A conditional validity constraint corresponds to a condition
5967 if the two are adjacent, i.e., if the domain of one relation intersect
5968 the range of the other relation.
5969 The typical use case of conditional validity constraints is
5970 to allow order constraints between live ranges to be violated
5971 as long as the live ranges themselves are local to the band.
5972 To allow more fine-grained control over which conditions correspond
5973 to which conditional validity constraints, the domains and ranges
5974 of these relations may include I<tags>. That is, the domains and
5975 ranges of those relation may themselves be wrapped relations
5976 where the iteration domain appears in the domain of those wrapped relations
5977 and the range of the wrapped relations can be arbitrarily chosen
5978 by the user. Conditions and conditional validity constraints are only
5979 considere adjacent to each other if the entire wrapped relation matches.
5980 In particular, a relation with a tag will never be considered adjacent
5981 to a relation without a tag.
5983 The following function computes a schedule directly from
5984 an iteration domain and validity and proximity dependences
5985 and is implemented in terms of the functions described above.
5986 The use of C<isl_union_set_compute_schedule> is discouraged.
5988 #include <isl/schedule.h>
5989 __isl_give isl_schedule *isl_union_set_compute_schedule(
5990 __isl_take isl_union_set *domain,
5991 __isl_take isl_union_map *validity,
5992 __isl_take isl_union_map *proximity);
5994 A mapping from the domains to the scheduled space can be obtained
5995 from an C<isl_schedule> using the following function.
5997 __isl_give isl_union_map *isl_schedule_get_map(
5998 __isl_keep isl_schedule *sched);
6000 A representation of the schedule can be printed using
6002 __isl_give isl_printer *isl_printer_print_schedule(
6003 __isl_take isl_printer *p,
6004 __isl_keep isl_schedule *schedule);
6006 A representation of the schedule as a forest of bands can be obtained
6007 using the following function.
6009 __isl_give isl_band_list *isl_schedule_get_band_forest(
6010 __isl_keep isl_schedule *schedule);
6012 The individual bands can be visited in depth-first post-order
6013 using the following function.
6015 #include <isl/schedule.h>
6016 int isl_schedule_foreach_band(
6017 __isl_keep isl_schedule *sched,
6018 int (*fn)(__isl_keep isl_band *band, void *user),
6021 The list can be manipulated as explained in L<"Lists">.
6022 The bands inside the list can be copied and freed using the following
6025 #include <isl/band.h>
6026 __isl_give isl_band *isl_band_copy(
6027 __isl_keep isl_band *band);
6028 __isl_null isl_band *isl_band_free(
6029 __isl_take isl_band *band);
6031 Each band contains zero or more scheduling dimensions.
6032 These are referred to as the members of the band.
6033 The section of the schedule that corresponds to the band is
6034 referred to as the partial schedule of the band.
6035 For those nodes that participate in a band, the outer scheduling
6036 dimensions form the prefix schedule, while the inner scheduling
6037 dimensions form the suffix schedule.
6038 That is, if we take a cut of the band forest, then the union of
6039 the concatenations of the prefix, partial and suffix schedules of
6040 each band in the cut is equal to the entire schedule (modulo
6041 some possible padding at the end with zero scheduling dimensions).
6042 The properties of a band can be inspected using the following functions.
6044 #include <isl/band.h>
6045 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
6047 int isl_band_has_children(__isl_keep isl_band *band);
6048 __isl_give isl_band_list *isl_band_get_children(
6049 __isl_keep isl_band *band);
6051 __isl_give isl_union_map *isl_band_get_prefix_schedule(
6052 __isl_keep isl_band *band);
6053 __isl_give isl_union_map *isl_band_get_partial_schedule(
6054 __isl_keep isl_band *band);
6055 __isl_give isl_union_map *isl_band_get_suffix_schedule(
6056 __isl_keep isl_band *band);
6058 int isl_band_n_member(__isl_keep isl_band *band);
6059 int isl_band_member_is_coincident(
6060 __isl_keep isl_band *band, int pos);
6062 int isl_band_list_foreach_band(
6063 __isl_keep isl_band_list *list,
6064 int (*fn)(__isl_keep isl_band *band, void *user),
6067 Note that a scheduling dimension is considered to be ``coincident''
6068 if it satisfies the coincidence constraints within its band.
6069 That is, if the dependence distances of the coincidence
6070 constraints are all zero in that direction (for fixed
6071 iterations of outer bands).
6072 Like C<isl_schedule_foreach_band>,
6073 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
6074 in depth-first post-order.
6076 A band can be tiled using the following function.
6078 #include <isl/band.h>
6079 int isl_band_tile(__isl_keep isl_band *band,
6080 __isl_take isl_vec *sizes);
6082 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
6084 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
6085 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
6087 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
6089 The C<isl_band_tile> function tiles the band using the given tile sizes
6090 inside its schedule.
6091 A new child band is created to represent the point loops and it is
6092 inserted between the modified band and its children.
6093 The C<tile_scale_tile_loops> option specifies whether the tile
6094 loops iterators should be scaled by the tile sizes.
6095 If the C<tile_shift_point_loops> option is set, then the point loops
6096 are shifted to start at zero.
6098 A band can be split into two nested bands using the following function.
6100 int isl_band_split(__isl_keep isl_band *band, int pos);
6102 The resulting outer band contains the first C<pos> dimensions of C<band>
6103 while the inner band contains the remaining dimensions.
6105 A representation of the band can be printed using
6107 #include <isl/band.h>
6108 __isl_give isl_printer *isl_printer_print_band(
6109 __isl_take isl_printer *p,
6110 __isl_keep isl_band *band);
6114 #include <isl/schedule.h>
6115 int isl_options_set_schedule_max_coefficient(
6116 isl_ctx *ctx, int val);
6117 int isl_options_get_schedule_max_coefficient(
6119 int isl_options_set_schedule_max_constant_term(
6120 isl_ctx *ctx, int val);
6121 int isl_options_get_schedule_max_constant_term(
6123 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
6124 int isl_options_get_schedule_fuse(isl_ctx *ctx);
6125 int isl_options_set_schedule_maximize_band_depth(
6126 isl_ctx *ctx, int val);
6127 int isl_options_get_schedule_maximize_band_depth(
6129 int isl_options_set_schedule_outer_coincidence(
6130 isl_ctx *ctx, int val);
6131 int isl_options_get_schedule_outer_coincidence(
6133 int isl_options_set_schedule_split_scaled(
6134 isl_ctx *ctx, int val);
6135 int isl_options_get_schedule_split_scaled(
6137 int isl_options_set_schedule_algorithm(
6138 isl_ctx *ctx, int val);
6139 int isl_options_get_schedule_algorithm(
6141 int isl_options_set_schedule_separate_components(
6142 isl_ctx *ctx, int val);
6143 int isl_options_get_schedule_separate_components(
6148 =item * schedule_max_coefficient
6150 This option enforces that the coefficients for variable and parameter
6151 dimensions in the calculated schedule are not larger than the specified value.
6152 This option can significantly increase the speed of the scheduling calculation
6153 and may also prevent fusing of unrelated dimensions. A value of -1 means that
6154 this option does not introduce bounds on the variable or parameter
6157 =item * schedule_max_constant_term
6159 This option enforces that the constant coefficients in the calculated schedule
6160 are not larger than the maximal constant term. This option can significantly
6161 increase the speed of the scheduling calculation and may also prevent fusing of
6162 unrelated dimensions. A value of -1 means that this option does not introduce
6163 bounds on the constant coefficients.
6165 =item * schedule_fuse
6167 This option controls the level of fusion.
6168 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6169 resulting schedule will be distributed as much as possible.
6170 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6171 try to fuse loops in the resulting schedule.
6173 =item * schedule_maximize_band_depth
6175 If this option is set, we do not split bands at the point
6176 where we detect splitting is necessary. Instead, we
6177 backtrack and split bands as early as possible. This
6178 reduces the number of splits and maximizes the width of
6179 the bands. Wider bands give more possibilities for tiling.
6180 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6181 then bands will be split as early as possible, even if there is no need.
6182 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6184 =item * schedule_outer_coincidence
6186 If this option is set, then we try to construct schedules
6187 where the outermost scheduling dimension in each band
6188 satisfies the coincidence constraints.
6190 =item * schedule_split_scaled
6192 If this option is set, then we try to construct schedules in which the
6193 constant term is split off from the linear part if the linear parts of
6194 the scheduling rows for all nodes in the graphs have a common non-trivial
6196 The constant term is then placed in a separate band and the linear
6199 =item * schedule_algorithm
6201 Selects the scheduling algorithm to be used.
6202 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6203 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6205 =item * schedule_separate_components
6207 If at any point the dependence graph contains any (weakly connected) components,
6208 then these components are scheduled separately.
6209 If this option is not set, then some iterations of the domains
6210 in these components may be scheduled together.
6211 If this option is set, then the components are given consecutive
6216 =head2 AST Generation
6218 This section describes the C<isl> functionality for generating
6219 ASTs that visit all the elements
6220 in a domain in an order specified by a schedule.
6221 In particular, given a C<isl_union_map>, an AST is generated
6222 that visits all the elements in the domain of the C<isl_union_map>
6223 according to the lexicographic order of the corresponding image
6224 element(s). If the range of the C<isl_union_map> consists of
6225 elements in more than one space, then each of these spaces is handled
6226 separately in an arbitrary order.
6227 It should be noted that the image elements only specify the I<order>
6228 in which the corresponding domain elements should be visited.
6229 No direct relation between the image elements and the loop iterators
6230 in the generated AST should be assumed.
6232 Each AST is generated within a build. The initial build
6233 simply specifies the constraints on the parameters (if any)
6234 and can be created, inspected, copied and freed using the following functions.
6236 #include <isl/ast_build.h>
6237 __isl_give isl_ast_build *isl_ast_build_from_context(
6238 __isl_take isl_set *set);
6239 isl_ctx *isl_ast_build_get_ctx(
6240 __isl_keep isl_ast_build *build);
6241 __isl_give isl_ast_build *isl_ast_build_copy(
6242 __isl_keep isl_ast_build *build);
6243 __isl_null isl_ast_build *isl_ast_build_free(
6244 __isl_take isl_ast_build *build);
6246 The C<set> argument is usually a parameter set with zero or more parameters.
6247 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6248 and L</"Fine-grained Control over AST Generation">.
6249 Finally, the AST itself can be constructed using the following
6252 #include <isl/ast_build.h>
6253 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6254 __isl_keep isl_ast_build *build,
6255 __isl_take isl_union_map *schedule);
6257 =head3 Inspecting the AST
6259 The basic properties of an AST node can be obtained as follows.
6261 #include <isl/ast.h>
6262 isl_ctx *isl_ast_node_get_ctx(
6263 __isl_keep isl_ast_node *node);
6264 enum isl_ast_node_type isl_ast_node_get_type(
6265 __isl_keep isl_ast_node *node);
6267 The type of an AST node is one of
6268 C<isl_ast_node_for>,
6270 C<isl_ast_node_block> or
6271 C<isl_ast_node_user>.
6272 An C<isl_ast_node_for> represents a for node.
6273 An C<isl_ast_node_if> represents an if node.
6274 An C<isl_ast_node_block> represents a compound node.
6275 An C<isl_ast_node_user> represents an expression statement.
6276 An expression statement typically corresponds to a domain element, i.e.,
6277 one of the elements that is visited by the AST.
6279 Each type of node has its own additional properties.
6281 #include <isl/ast.h>
6282 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6283 __isl_keep isl_ast_node *node);
6284 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6285 __isl_keep isl_ast_node *node);
6286 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6287 __isl_keep isl_ast_node *node);
6288 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6289 __isl_keep isl_ast_node *node);
6290 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6291 __isl_keep isl_ast_node *node);
6292 int isl_ast_node_for_is_degenerate(
6293 __isl_keep isl_ast_node *node);
6295 An C<isl_ast_for> is considered degenerate if it is known to execute
6298 #include <isl/ast.h>
6299 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6300 __isl_keep isl_ast_node *node);
6301 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6302 __isl_keep isl_ast_node *node);
6303 int isl_ast_node_if_has_else(
6304 __isl_keep isl_ast_node *node);
6305 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6306 __isl_keep isl_ast_node *node);
6308 __isl_give isl_ast_node_list *
6309 isl_ast_node_block_get_children(
6310 __isl_keep isl_ast_node *node);
6312 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6313 __isl_keep isl_ast_node *node);
6315 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6316 the following functions.
6318 #include <isl/ast.h>
6319 isl_ctx *isl_ast_expr_get_ctx(
6320 __isl_keep isl_ast_expr *expr);
6321 enum isl_ast_expr_type isl_ast_expr_get_type(
6322 __isl_keep isl_ast_expr *expr);
6324 The type of an AST expression is one of
6326 C<isl_ast_expr_id> or
6327 C<isl_ast_expr_int>.
6328 An C<isl_ast_expr_op> represents the result of an operation.
6329 An C<isl_ast_expr_id> represents an identifier.
6330 An C<isl_ast_expr_int> represents an integer value.
6332 Each type of expression has its own additional properties.
6334 #include <isl/ast.h>
6335 enum isl_ast_op_type isl_ast_expr_get_op_type(
6336 __isl_keep isl_ast_expr *expr);
6337 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6338 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6339 __isl_keep isl_ast_expr *expr, int pos);
6340 int isl_ast_node_foreach_ast_op_type(
6341 __isl_keep isl_ast_node *node,
6342 int (*fn)(enum isl_ast_op_type type, void *user),
6345 C<isl_ast_expr_get_op_type> returns the type of the operation
6346 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6347 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6349 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6350 C<isl_ast_op_type> that appears in C<node>.
6351 The operation type is one of the following.
6355 =item C<isl_ast_op_and>
6357 Logical I<and> of two arguments.
6358 Both arguments can be evaluated.
6360 =item C<isl_ast_op_and_then>
6362 Logical I<and> of two arguments.
6363 The second argument can only be evaluated if the first evaluates to true.
6365 =item C<isl_ast_op_or>
6367 Logical I<or> of two arguments.
6368 Both arguments can be evaluated.
6370 =item C<isl_ast_op_or_else>
6372 Logical I<or> of two arguments.
6373 The second argument can only be evaluated if the first evaluates to false.
6375 =item C<isl_ast_op_max>
6377 Maximum of two or more arguments.
6379 =item C<isl_ast_op_min>
6381 Minimum of two or more arguments.
6383 =item C<isl_ast_op_minus>
6387 =item C<isl_ast_op_add>
6389 Sum of two arguments.
6391 =item C<isl_ast_op_sub>
6393 Difference of two arguments.
6395 =item C<isl_ast_op_mul>
6397 Product of two arguments.
6399 =item C<isl_ast_op_div>
6401 Exact division. That is, the result is known to be an integer.
6403 =item C<isl_ast_op_fdiv_q>
6405 Result of integer division, rounded towards negative
6408 =item C<isl_ast_op_pdiv_q>
6410 Result of integer division, where dividend is known to be non-negative.
6412 =item C<isl_ast_op_pdiv_r>
6414 Remainder of integer division, where dividend is known to be non-negative.
6416 =item C<isl_ast_op_cond>
6418 Conditional operator defined on three arguments.
6419 If the first argument evaluates to true, then the result
6420 is equal to the second argument. Otherwise, the result
6421 is equal to the third argument.
6422 The second and third argument may only be evaluated if
6423 the first argument evaluates to true and false, respectively.
6424 Corresponds to C<a ? b : c> in C.
6426 =item C<isl_ast_op_select>
6428 Conditional operator defined on three arguments.
6429 If the first argument evaluates to true, then the result
6430 is equal to the second argument. Otherwise, the result
6431 is equal to the third argument.
6432 The second and third argument may be evaluated independently
6433 of the value of the first argument.
6434 Corresponds to C<a * b + (1 - a) * c> in C.
6436 =item C<isl_ast_op_eq>
6440 =item C<isl_ast_op_le>
6442 Less than or equal relation.
6444 =item C<isl_ast_op_lt>
6448 =item C<isl_ast_op_ge>
6450 Greater than or equal relation.
6452 =item C<isl_ast_op_gt>
6454 Greater than relation.
6456 =item C<isl_ast_op_call>
6459 The number of arguments of the C<isl_ast_expr> is one more than
6460 the number of arguments in the function call, the first argument
6461 representing the function being called.
6463 =item C<isl_ast_op_access>
6466 The number of arguments of the C<isl_ast_expr> is one more than
6467 the number of index expressions in the array access, the first argument
6468 representing the array being accessed.
6470 =item C<isl_ast_op_member>
6473 This operation has two arguments, a structure and the name of
6474 the member of the structure being accessed.
6478 #include <isl/ast.h>
6479 __isl_give isl_id *isl_ast_expr_get_id(
6480 __isl_keep isl_ast_expr *expr);
6482 Return the identifier represented by the AST expression.
6484 #include <isl/ast.h>
6485 __isl_give isl_val *isl_ast_expr_get_val(
6486 __isl_keep isl_ast_expr *expr);
6488 Return the integer represented by the AST expression.
6490 =head3 Properties of ASTs
6492 #include <isl/ast.h>
6493 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6494 __isl_keep isl_ast_expr *expr2);
6496 Check if two C<isl_ast_expr>s are equal to each other.
6498 =head3 Manipulating and printing the AST
6500 AST nodes can be copied and freed using the following functions.
6502 #include <isl/ast.h>
6503 __isl_give isl_ast_node *isl_ast_node_copy(
6504 __isl_keep isl_ast_node *node);
6505 __isl_null isl_ast_node *isl_ast_node_free(
6506 __isl_take isl_ast_node *node);
6508 AST expressions can be copied and freed using the following functions.
6510 #include <isl/ast.h>
6511 __isl_give isl_ast_expr *isl_ast_expr_copy(
6512 __isl_keep isl_ast_expr *expr);
6513 __isl_null isl_ast_expr *isl_ast_expr_free(
6514 __isl_take isl_ast_expr *expr);
6516 New AST expressions can be created either directly or within
6517 the context of an C<isl_ast_build>.
6519 #include <isl/ast.h>
6520 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6521 __isl_take isl_val *v);
6522 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6523 __isl_take isl_id *id);
6524 __isl_give isl_ast_expr *isl_ast_expr_neg(
6525 __isl_take isl_ast_expr *expr);
6526 __isl_give isl_ast_expr *isl_ast_expr_add(
6527 __isl_take isl_ast_expr *expr1,
6528 __isl_take isl_ast_expr *expr2);
6529 __isl_give isl_ast_expr *isl_ast_expr_sub(
6530 __isl_take isl_ast_expr *expr1,
6531 __isl_take isl_ast_expr *expr2);
6532 __isl_give isl_ast_expr *isl_ast_expr_mul(
6533 __isl_take isl_ast_expr *expr1,
6534 __isl_take isl_ast_expr *expr2);
6535 __isl_give isl_ast_expr *isl_ast_expr_div(
6536 __isl_take isl_ast_expr *expr1,
6537 __isl_take isl_ast_expr *expr2);
6538 __isl_give isl_ast_expr *isl_ast_expr_and(
6539 __isl_take isl_ast_expr *expr1,
6540 __isl_take isl_ast_expr *expr2)
6541 __isl_give isl_ast_expr *isl_ast_expr_or(
6542 __isl_take isl_ast_expr *expr1,
6543 __isl_take isl_ast_expr *expr2)
6544 __isl_give isl_ast_expr *isl_ast_expr_access(
6545 __isl_take isl_ast_expr *array,
6546 __isl_take isl_ast_expr_list *indices);
6548 #include <isl/ast_build.h>
6549 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6550 __isl_keep isl_ast_build *build,
6551 __isl_take isl_pw_aff *pa);
6552 __isl_give isl_ast_expr *
6553 isl_ast_build_access_from_pw_multi_aff(
6554 __isl_keep isl_ast_build *build,
6555 __isl_take isl_pw_multi_aff *pma);
6556 __isl_give isl_ast_expr *
6557 isl_ast_build_access_from_multi_pw_aff(
6558 __isl_keep isl_ast_build *build,
6559 __isl_take isl_multi_pw_aff *mpa);
6560 __isl_give isl_ast_expr *
6561 isl_ast_build_call_from_pw_multi_aff(
6562 __isl_keep isl_ast_build *build,
6563 __isl_take isl_pw_multi_aff *pma);
6564 __isl_give isl_ast_expr *
6565 isl_ast_build_call_from_multi_pw_aff(
6566 __isl_keep isl_ast_build *build,
6567 __isl_take isl_multi_pw_aff *mpa);
6569 The domains of C<pa>, C<mpa> and C<pma> should correspond
6570 to the schedule space of C<build>.
6571 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6572 the function being called.
6573 If the accessed space is a nested relation, then it is taken
6574 to represent an access of the member specified by the range
6575 of this nested relation of the structure specified by the domain
6576 of the nested relation.
6578 The following functions can be used to modify an C<isl_ast_expr>.
6580 #include <isl/ast.h>
6581 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6582 __isl_take isl_ast_expr *expr, int pos,
6583 __isl_take isl_ast_expr *arg);
6585 Replace the argument of C<expr> at position C<pos> by C<arg>.
6587 #include <isl/ast.h>
6588 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6589 __isl_take isl_ast_expr *expr,
6590 __isl_take isl_id_to_ast_expr *id2expr);
6592 The function C<isl_ast_expr_substitute_ids> replaces the
6593 subexpressions of C<expr> of type C<isl_ast_expr_id>
6594 by the corresponding expression in C<id2expr>, if there is any.
6597 User specified data can be attached to an C<isl_ast_node> and obtained
6598 from the same C<isl_ast_node> using the following functions.
6600 #include <isl/ast.h>
6601 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6602 __isl_take isl_ast_node *node,
6603 __isl_take isl_id *annotation);
6604 __isl_give isl_id *isl_ast_node_get_annotation(
6605 __isl_keep isl_ast_node *node);
6607 Basic printing can be performed using the following functions.
6609 #include <isl/ast.h>
6610 __isl_give isl_printer *isl_printer_print_ast_expr(
6611 __isl_take isl_printer *p,
6612 __isl_keep isl_ast_expr *expr);
6613 __isl_give isl_printer *isl_printer_print_ast_node(
6614 __isl_take isl_printer *p,
6615 __isl_keep isl_ast_node *node);
6617 More advanced printing can be performed using the following functions.
6619 #include <isl/ast.h>
6620 __isl_give isl_printer *isl_ast_op_type_print_macro(
6621 enum isl_ast_op_type type,
6622 __isl_take isl_printer *p);
6623 __isl_give isl_printer *isl_ast_node_print_macros(
6624 __isl_keep isl_ast_node *node,
6625 __isl_take isl_printer *p);
6626 __isl_give isl_printer *isl_ast_node_print(
6627 __isl_keep isl_ast_node *node,
6628 __isl_take isl_printer *p,
6629 __isl_take isl_ast_print_options *options);
6630 __isl_give isl_printer *isl_ast_node_for_print(
6631 __isl_keep isl_ast_node *node,
6632 __isl_take isl_printer *p,
6633 __isl_take isl_ast_print_options *options);
6634 __isl_give isl_printer *isl_ast_node_if_print(
6635 __isl_keep isl_ast_node *node,
6636 __isl_take isl_printer *p,
6637 __isl_take isl_ast_print_options *options);
6639 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6640 C<isl> may print out an AST that makes use of macros such
6641 as C<floord>, C<min> and C<max>.
6642 C<isl_ast_op_type_print_macro> prints out the macro
6643 corresponding to a specific C<isl_ast_op_type>.
6644 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6645 for expressions where these macros would be used and prints
6646 out the required macro definitions.
6647 Essentially, C<isl_ast_node_print_macros> calls
6648 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6649 as function argument.
6650 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6651 C<isl_ast_node_if_print> print an C<isl_ast_node>
6652 in C<ISL_FORMAT_C>, but allow for some extra control
6653 through an C<isl_ast_print_options> object.
6654 This object can be created using the following functions.
6656 #include <isl/ast.h>
6657 __isl_give isl_ast_print_options *
6658 isl_ast_print_options_alloc(isl_ctx *ctx);
6659 __isl_give isl_ast_print_options *
6660 isl_ast_print_options_copy(
6661 __isl_keep isl_ast_print_options *options);
6662 __isl_null isl_ast_print_options *
6663 isl_ast_print_options_free(
6664 __isl_take isl_ast_print_options *options);
6666 __isl_give isl_ast_print_options *
6667 isl_ast_print_options_set_print_user(
6668 __isl_take isl_ast_print_options *options,
6669 __isl_give isl_printer *(*print_user)(
6670 __isl_take isl_printer *p,
6671 __isl_take isl_ast_print_options *options,
6672 __isl_keep isl_ast_node *node, void *user),
6674 __isl_give isl_ast_print_options *
6675 isl_ast_print_options_set_print_for(
6676 __isl_take isl_ast_print_options *options,
6677 __isl_give isl_printer *(*print_for)(
6678 __isl_take isl_printer *p,
6679 __isl_take isl_ast_print_options *options,
6680 __isl_keep isl_ast_node *node, void *user),
6683 The callback set by C<isl_ast_print_options_set_print_user>
6684 is called whenever a node of type C<isl_ast_node_user> needs to
6686 The callback set by C<isl_ast_print_options_set_print_for>
6687 is called whenever a node of type C<isl_ast_node_for> needs to
6689 Note that C<isl_ast_node_for_print> will I<not> call the
6690 callback set by C<isl_ast_print_options_set_print_for> on the node
6691 on which C<isl_ast_node_for_print> is called, but only on nested
6692 nodes of type C<isl_ast_node_for>. It is therefore safe to
6693 call C<isl_ast_node_for_print> from within the callback set by
6694 C<isl_ast_print_options_set_print_for>.
6696 The following option determines the type to be used for iterators
6697 while printing the AST.
6699 int isl_options_set_ast_iterator_type(
6700 isl_ctx *ctx, const char *val);
6701 const char *isl_options_get_ast_iterator_type(
6706 #include <isl/ast_build.h>
6707 int isl_options_set_ast_build_atomic_upper_bound(
6708 isl_ctx *ctx, int val);
6709 int isl_options_get_ast_build_atomic_upper_bound(
6711 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6713 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6714 int isl_options_set_ast_build_exploit_nested_bounds(
6715 isl_ctx *ctx, int val);
6716 int isl_options_get_ast_build_exploit_nested_bounds(
6718 int isl_options_set_ast_build_group_coscheduled(
6719 isl_ctx *ctx, int val);
6720 int isl_options_get_ast_build_group_coscheduled(
6722 int isl_options_set_ast_build_scale_strides(
6723 isl_ctx *ctx, int val);
6724 int isl_options_get_ast_build_scale_strides(
6726 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6728 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6729 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6731 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6735 =item * ast_build_atomic_upper_bound
6737 Generate loop upper bounds that consist of the current loop iterator,
6738 an operator and an expression not involving the iterator.
6739 If this option is not set, then the current loop iterator may appear
6740 several times in the upper bound.
6741 For example, when this option is turned off, AST generation
6744 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6748 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6751 When the option is turned on, the following AST is generated
6753 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6756 =item * ast_build_prefer_pdiv
6758 If this option is turned off, then the AST generation will
6759 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6760 operators, but no C<isl_ast_op_pdiv_q> or
6761 C<isl_ast_op_pdiv_r> operators.
6762 If this options is turned on, then C<isl> will try to convert
6763 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6764 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6766 =item * ast_build_exploit_nested_bounds
6768 Simplify conditions based on bounds of nested for loops.
6769 In particular, remove conditions that are implied by the fact
6770 that one or more nested loops have at least one iteration,
6771 meaning that the upper bound is at least as large as the lower bound.
6772 For example, when this option is turned off, AST generation
6775 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6781 for (int c0 = 0; c0 <= N; c0 += 1)
6782 for (int c1 = 0; c1 <= M; c1 += 1)
6785 When the option is turned on, the following AST is generated
6787 for (int c0 = 0; c0 <= N; c0 += 1)
6788 for (int c1 = 0; c1 <= M; c1 += 1)
6791 =item * ast_build_group_coscheduled
6793 If two domain elements are assigned the same schedule point, then
6794 they may be executed in any order and they may even appear in different
6795 loops. If this options is set, then the AST generator will make
6796 sure that coscheduled domain elements do not appear in separate parts
6797 of the AST. This is useful in case of nested AST generation
6798 if the outer AST generation is given only part of a schedule
6799 and the inner AST generation should handle the domains that are
6800 coscheduled by this initial part of the schedule together.
6801 For example if an AST is generated for a schedule
6803 { A[i] -> [0]; B[i] -> [0] }
6805 then the C<isl_ast_build_set_create_leaf> callback described
6806 below may get called twice, once for each domain.
6807 Setting this option ensures that the callback is only called once
6808 on both domains together.
6810 =item * ast_build_separation_bounds
6812 This option specifies which bounds to use during separation.
6813 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6814 then all (possibly implicit) bounds on the current dimension will
6815 be used during separation.
6816 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6817 then only those bounds that are explicitly available will
6818 be used during separation.
6820 =item * ast_build_scale_strides
6822 This option specifies whether the AST generator is allowed
6823 to scale down iterators of strided loops.
6825 =item * ast_build_allow_else
6827 This option specifies whether the AST generator is allowed
6828 to construct if statements with else branches.
6830 =item * ast_build_allow_or
6832 This option specifies whether the AST generator is allowed
6833 to construct if conditions with disjunctions.
6837 =head3 Fine-grained Control over AST Generation
6839 Besides specifying the constraints on the parameters,
6840 an C<isl_ast_build> object can be used to control
6841 various aspects of the AST generation process.
6842 The most prominent way of control is through ``options'',
6843 which can be set using the following function.
6845 #include <isl/ast_build.h>
6846 __isl_give isl_ast_build *
6847 isl_ast_build_set_options(
6848 __isl_take isl_ast_build *control,
6849 __isl_take isl_union_map *options);
6851 The options are encoded in an <isl_union_map>.
6852 The domain of this union relation refers to the schedule domain,
6853 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6854 In the case of nested AST generation (see L</"Nested AST Generation">),
6855 the domain of C<options> should refer to the extra piece of the schedule.
6856 That is, it should be equal to the range of the wrapped relation in the
6857 range of the schedule.
6858 The range of the options can consist of elements in one or more spaces,
6859 the names of which determine the effect of the option.
6860 The values of the range typically also refer to the schedule dimension
6861 to which the option applies. In case of nested AST generation
6862 (see L</"Nested AST Generation">), these values refer to the position
6863 of the schedule dimension within the innermost AST generation.
6864 The constraints on the domain elements of
6865 the option should only refer to this dimension and earlier dimensions.
6866 We consider the following spaces.
6870 =item C<separation_class>
6872 This space is a wrapped relation between two one dimensional spaces.
6873 The input space represents the schedule dimension to which the option
6874 applies and the output space represents the separation class.
6875 While constructing a loop corresponding to the specified schedule
6876 dimension(s), the AST generator will try to generate separate loops
6877 for domain elements that are assigned different classes.
6878 If only some of the elements are assigned a class, then those elements
6879 that are not assigned any class will be treated as belonging to a class
6880 that is separate from the explicitly assigned classes.
6881 The typical use case for this option is to separate full tiles from
6883 The other options, described below, are applied after the separation
6886 As an example, consider the separation into full and partial tiles
6887 of a tiling of a triangular domain.
6888 Take, for example, the domain
6890 { A[i,j] : 0 <= i,j and i + j <= 100 }
6892 and a tiling into tiles of 10 by 10. The input to the AST generator
6893 is then the schedule
6895 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6898 Without any options, the following AST is generated
6900 for (int c0 = 0; c0 <= 10; c0 += 1)
6901 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6902 for (int c2 = 10 * c0;
6903 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6905 for (int c3 = 10 * c1;
6906 c3 <= min(10 * c1 + 9, -c2 + 100);
6910 Separation into full and partial tiles can be obtained by assigning
6911 a class, say C<0>, to the full tiles. The full tiles are represented by those
6912 values of the first and second schedule dimensions for which there are
6913 values of the third and fourth dimensions to cover an entire tile.
6914 That is, we need to specify the following option
6916 { [a,b,c,d] -> separation_class[[0]->[0]] :
6917 exists b': 0 <= 10a,10b' and
6918 10a+9+10b'+9 <= 100;
6919 [a,b,c,d] -> separation_class[[1]->[0]] :
6920 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6924 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6925 a >= 0 and b >= 0 and b <= 8 - a;
6926 [a, b, c, d] -> separation_class[[0] -> [0]] :
6929 With this option, the generated AST is as follows
6932 for (int c0 = 0; c0 <= 8; c0 += 1) {
6933 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6934 for (int c2 = 10 * c0;
6935 c2 <= 10 * c0 + 9; c2 += 1)
6936 for (int c3 = 10 * c1;
6937 c3 <= 10 * c1 + 9; c3 += 1)
6939 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6940 for (int c2 = 10 * c0;
6941 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6943 for (int c3 = 10 * c1;
6944 c3 <= min(-c2 + 100, 10 * c1 + 9);
6948 for (int c0 = 9; c0 <= 10; c0 += 1)
6949 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6950 for (int c2 = 10 * c0;
6951 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6953 for (int c3 = 10 * c1;
6954 c3 <= min(10 * c1 + 9, -c2 + 100);
6961 This is a single-dimensional space representing the schedule dimension(s)
6962 to which ``separation'' should be applied. Separation tries to split
6963 a loop into several pieces if this can avoid the generation of guards
6965 See also the C<atomic> option.
6969 This is a single-dimensional space representing the schedule dimension(s)
6970 for which the domains should be considered ``atomic''. That is, the
6971 AST generator will make sure that any given domain space will only appear
6972 in a single loop at the specified level.
6974 Consider the following schedule
6976 { a[i] -> [i] : 0 <= i < 10;
6977 b[i] -> [i+1] : 0 <= i < 10 }
6979 If the following option is specified
6981 { [i] -> separate[x] }
6983 then the following AST will be generated
6987 for (int c0 = 1; c0 <= 9; c0 += 1) {
6994 If, on the other hand, the following option is specified
6996 { [i] -> atomic[x] }
6998 then the following AST will be generated
7000 for (int c0 = 0; c0 <= 10; c0 += 1) {
7007 If neither C<atomic> nor C<separate> is specified, then the AST generator
7008 may produce either of these two results or some intermediate form.
7012 This is a single-dimensional space representing the schedule dimension(s)
7013 that should be I<completely> unrolled.
7014 To obtain a partial unrolling, the user should apply an additional
7015 strip-mining to the schedule and fully unroll the inner loop.
7019 Additional control is available through the following functions.
7021 #include <isl/ast_build.h>
7022 __isl_give isl_ast_build *
7023 isl_ast_build_set_iterators(
7024 __isl_take isl_ast_build *control,
7025 __isl_take isl_id_list *iterators);
7027 The function C<isl_ast_build_set_iterators> allows the user to
7028 specify a list of iterator C<isl_id>s to be used as iterators.
7029 If the input schedule is injective, then
7030 the number of elements in this list should be as large as the dimension
7031 of the schedule space, but no direct correspondence should be assumed
7032 between dimensions and elements.
7033 If the input schedule is not injective, then an additional number
7034 of C<isl_id>s equal to the largest dimension of the input domains
7036 If the number of provided C<isl_id>s is insufficient, then additional
7037 names are automatically generated.
7039 #include <isl/ast_build.h>
7040 __isl_give isl_ast_build *
7041 isl_ast_build_set_create_leaf(
7042 __isl_take isl_ast_build *control,
7043 __isl_give isl_ast_node *(*fn)(
7044 __isl_take isl_ast_build *build,
7045 void *user), void *user);
7048 C<isl_ast_build_set_create_leaf> function allows for the
7049 specification of a callback that should be called whenever the AST
7050 generator arrives at an element of the schedule domain.
7051 The callback should return an AST node that should be inserted
7052 at the corresponding position of the AST. The default action (when
7053 the callback is not set) is to continue generating parts of the AST to scan
7054 all the domain elements associated to the schedule domain element
7055 and to insert user nodes, ``calling'' the domain element, for each of them.
7056 The C<build> argument contains the current state of the C<isl_ast_build>.
7057 To ease nested AST generation (see L</"Nested AST Generation">),
7058 all control information that is
7059 specific to the current AST generation such as the options and
7060 the callbacks has been removed from this C<isl_ast_build>.
7061 The callback would typically return the result of a nested
7063 user defined node created using the following function.
7065 #include <isl/ast.h>
7066 __isl_give isl_ast_node *isl_ast_node_alloc_user(
7067 __isl_take isl_ast_expr *expr);
7069 #include <isl/ast_build.h>
7070 __isl_give isl_ast_build *
7071 isl_ast_build_set_at_each_domain(
7072 __isl_take isl_ast_build *build,
7073 __isl_give isl_ast_node *(*fn)(
7074 __isl_take isl_ast_node *node,
7075 __isl_keep isl_ast_build *build,
7076 void *user), void *user);
7077 __isl_give isl_ast_build *
7078 isl_ast_build_set_before_each_for(
7079 __isl_take isl_ast_build *build,
7080 __isl_give isl_id *(*fn)(
7081 __isl_keep isl_ast_build *build,
7082 void *user), void *user);
7083 __isl_give isl_ast_build *
7084 isl_ast_build_set_after_each_for(
7085 __isl_take isl_ast_build *build,
7086 __isl_give isl_ast_node *(*fn)(
7087 __isl_take isl_ast_node *node,
7088 __isl_keep isl_ast_build *build,
7089 void *user), void *user);
7091 The callback set by C<isl_ast_build_set_at_each_domain> will
7092 be called for each domain AST node.
7093 The callbacks set by C<isl_ast_build_set_before_each_for>
7094 and C<isl_ast_build_set_after_each_for> will be called
7095 for each for AST node. The first will be called in depth-first
7096 pre-order, while the second will be called in depth-first post-order.
7097 Since C<isl_ast_build_set_before_each_for> is called before the for
7098 node is actually constructed, it is only passed an C<isl_ast_build>.
7099 The returned C<isl_id> will be added as an annotation (using
7100 C<isl_ast_node_set_annotation>) to the constructed for node.
7101 In particular, if the user has also specified an C<after_each_for>
7102 callback, then the annotation can be retrieved from the node passed to
7103 that callback using C<isl_ast_node_get_annotation>.
7104 All callbacks should C<NULL> on failure.
7105 The given C<isl_ast_build> can be used to create new
7106 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
7107 or C<isl_ast_build_call_from_pw_multi_aff>.
7109 =head3 Nested AST Generation
7111 C<isl> allows the user to create an AST within the context
7112 of another AST. These nested ASTs are created using the
7113 same C<isl_ast_build_ast_from_schedule> function that is used to create the
7114 outer AST. The C<build> argument should be an C<isl_ast_build>
7115 passed to a callback set by
7116 C<isl_ast_build_set_create_leaf>.
7117 The space of the range of the C<schedule> argument should refer
7118 to this build. In particular, the space should be a wrapped
7119 relation and the domain of this wrapped relation should be the
7120 same as that of the range of the schedule returned by
7121 C<isl_ast_build_get_schedule> below.
7122 In practice, the new schedule is typically
7123 created by calling C<isl_union_map_range_product> on the old schedule
7124 and some extra piece of the schedule.
7125 The space of the schedule domain is also available from
7126 the C<isl_ast_build>.
7128 #include <isl/ast_build.h>
7129 __isl_give isl_union_map *isl_ast_build_get_schedule(
7130 __isl_keep isl_ast_build *build);
7131 __isl_give isl_space *isl_ast_build_get_schedule_space(
7132 __isl_keep isl_ast_build *build);
7133 __isl_give isl_ast_build *isl_ast_build_restrict(
7134 __isl_take isl_ast_build *build,
7135 __isl_take isl_set *set);
7137 The C<isl_ast_build_get_schedule> function returns a (partial)
7138 schedule for the domains elements for which part of the AST still needs to
7139 be generated in the current build.
7140 In particular, the domain elements are mapped to those iterations of the loops
7141 enclosing the current point of the AST generation inside which
7142 the domain elements are executed.
7143 No direct correspondence between
7144 the input schedule and this schedule should be assumed.
7145 The space obtained from C<isl_ast_build_get_schedule_space> can be used
7146 to create a set for C<isl_ast_build_restrict> to intersect
7147 with the current build. In particular, the set passed to
7148 C<isl_ast_build_restrict> can have additional parameters.
7149 The ids of the set dimensions in the space returned by
7150 C<isl_ast_build_get_schedule_space> correspond to the
7151 iterators of the already generated loops.
7152 The user should not rely on the ids of the output dimensions
7153 of the relations in the union relation returned by
7154 C<isl_ast_build_get_schedule> having any particular value.
7158 Although C<isl> is mainly meant to be used as a library,
7159 it also contains some basic applications that use some
7160 of the functionality of C<isl>.
7161 The input may be specified in either the L<isl format>
7162 or the L<PolyLib format>.
7164 =head2 C<isl_polyhedron_sample>
7166 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7167 an integer element of the polyhedron, if there is any.
7168 The first column in the output is the denominator and is always
7169 equal to 1. If the polyhedron contains no integer points,
7170 then a vector of length zero is printed.
7174 C<isl_pip> takes the same input as the C<example> program
7175 from the C<piplib> distribution, i.e., a set of constraints
7176 on the parameters, a line containing only -1 and finally a set
7177 of constraints on a parametric polyhedron.
7178 The coefficients of the parameters appear in the last columns
7179 (but before the final constant column).
7180 The output is the lexicographic minimum of the parametric polyhedron.
7181 As C<isl> currently does not have its own output format, the output
7182 is just a dump of the internal state.
7184 =head2 C<isl_polyhedron_minimize>
7186 C<isl_polyhedron_minimize> computes the minimum of some linear
7187 or affine objective function over the integer points in a polyhedron.
7188 If an affine objective function
7189 is given, then the constant should appear in the last column.
7191 =head2 C<isl_polytope_scan>
7193 Given a polytope, C<isl_polytope_scan> prints
7194 all integer points in the polytope.
7196 =head2 C<isl_codegen>
7198 Given a schedule, a context set and an options relation,
7199 C<isl_codegen> prints out an AST that scans the domain elements
7200 of the schedule in the order of their image(s) taking into account
7201 the constraints in the context set.