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);
359 An C<isl_val> represents an integer value, a rational value
360 or one of three special values, infinity, negative infinity and NaN.
361 Some predefined values can be created using the following functions.
364 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
365 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
366 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
367 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
368 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
369 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
371 Specific integer values can be created using the following functions.
374 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
376 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
378 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
379 size_t n, size_t size, const void *chunks);
381 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
382 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
383 The least significant digit is assumed to be stored first.
385 Value objects can be copied and freed using the following functions.
388 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
389 void *isl_val_free(__isl_take isl_val *v);
391 They can be inspected using the following functions.
394 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
395 long isl_val_get_num_si(__isl_keep isl_val *v);
396 long isl_val_get_den_si(__isl_keep isl_val *v);
397 double isl_val_get_d(__isl_keep isl_val *v);
398 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
400 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
401 size_t size, void *chunks);
403 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
404 of C<size> bytes needed to store the absolute value of the
406 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
407 which is assumed to have been preallocated by the caller.
408 The least significant digit is stored first.
409 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
410 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
411 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
413 An C<isl_val> can be modified using the following function.
416 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
419 The following unary properties are defined on C<isl_val>s.
422 int isl_val_sgn(__isl_keep isl_val *v);
423 int isl_val_is_zero(__isl_keep isl_val *v);
424 int isl_val_is_one(__isl_keep isl_val *v);
425 int isl_val_is_negone(__isl_keep isl_val *v);
426 int isl_val_is_nonneg(__isl_keep isl_val *v);
427 int isl_val_is_nonpos(__isl_keep isl_val *v);
428 int isl_val_is_pos(__isl_keep isl_val *v);
429 int isl_val_is_neg(__isl_keep isl_val *v);
430 int isl_val_is_int(__isl_keep isl_val *v);
431 int isl_val_is_rat(__isl_keep isl_val *v);
432 int isl_val_is_nan(__isl_keep isl_val *v);
433 int isl_val_is_infty(__isl_keep isl_val *v);
434 int isl_val_is_neginfty(__isl_keep isl_val *v);
436 Note that the sign of NaN is undefined.
438 The following binary properties are defined on pairs of C<isl_val>s.
441 int isl_val_lt(__isl_keep isl_val *v1,
442 __isl_keep isl_val *v2);
443 int isl_val_le(__isl_keep isl_val *v1,
444 __isl_keep isl_val *v2);
445 int isl_val_gt(__isl_keep isl_val *v1,
446 __isl_keep isl_val *v2);
447 int isl_val_ge(__isl_keep isl_val *v1,
448 __isl_keep isl_val *v2);
449 int isl_val_eq(__isl_keep isl_val *v1,
450 __isl_keep isl_val *v2);
451 int isl_val_ne(__isl_keep isl_val *v1,
452 __isl_keep isl_val *v2);
454 For integer C<isl_val>s we additionally have the following binary property.
457 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
458 __isl_keep isl_val *v2);
460 An C<isl_val> can also be compared to an integer using the following
461 function. The result is undefined for NaN.
464 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
466 The following unary operations are available on C<isl_val>s.
469 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
470 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
471 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
472 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
473 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
475 The following binary operations are available on C<isl_val>s.
478 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
479 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
480 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
481 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
482 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
483 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
484 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
485 __isl_take isl_val *v2);
486 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
487 __isl_take isl_val *v2);
488 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
489 __isl_take isl_val *v2);
490 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
492 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
493 __isl_take isl_val *v2);
494 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
496 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
497 __isl_take isl_val *v2);
498 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
500 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
501 __isl_take isl_val *v2);
503 On integer values, we additionally have the following operations.
506 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
507 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
508 __isl_take isl_val *v2);
509 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
510 __isl_take isl_val *v2);
511 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
512 __isl_take isl_val *v2, __isl_give isl_val **x,
513 __isl_give isl_val **y);
515 The function C<isl_val_gcdext> returns the greatest common divisor g
516 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
517 that C<*x> * C<v1> + C<*y> * C<v2> = g.
519 A value can be read from input using
522 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
525 A value can be printed using
528 __isl_give isl_printer *isl_printer_print_val(
529 __isl_take isl_printer *p, __isl_keep isl_val *v);
531 =head3 GMP specific functions
533 These functions are only available if C<isl> has been compiled with C<GMP>
536 Specific integer and rational values can be created from C<GMP> values using
537 the following functions.
539 #include <isl/val_gmp.h>
540 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
542 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
543 const mpz_t n, const mpz_t d);
545 The numerator and denominator of a rational value can be extracted as
546 C<GMP> values using the following functions.
548 #include <isl/val_gmp.h>
549 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
550 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
552 =head2 Sets and Relations
554 C<isl> uses six types of objects for representing sets and relations,
555 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
556 C<isl_union_set> and C<isl_union_map>.
557 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
558 can be described as a conjunction of affine constraints, while
559 C<isl_set> and C<isl_map> represent unions of
560 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
561 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
562 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
563 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
564 where spaces are considered different if they have a different number
565 of dimensions and/or different names (see L<"Spaces">).
566 The difference between sets and relations (maps) is that sets have
567 one set of variables, while relations have two sets of variables,
568 input variables and output variables.
570 =head2 Memory Management
572 Since a high-level operation on sets and/or relations usually involves
573 several substeps and since the user is usually not interested in
574 the intermediate results, most functions that return a new object
575 will also release all the objects passed as arguments.
576 If the user still wants to use one or more of these arguments
577 after the function call, she should pass along a copy of the
578 object rather than the object itself.
579 The user is then responsible for making sure that the original
580 object gets used somewhere else or is explicitly freed.
582 The arguments and return values of all documented functions are
583 annotated to make clear which arguments are released and which
584 arguments are preserved. In particular, the following annotations
591 C<__isl_give> means that a new object is returned.
592 The user should make sure that the returned pointer is
593 used exactly once as a value for an C<__isl_take> argument.
594 In between, it can be used as a value for as many
595 C<__isl_keep> arguments as the user likes.
596 There is one exception, and that is the case where the
597 pointer returned is C<NULL>. Is this case, the user
598 is free to use it as an C<__isl_take> argument or not.
602 C<__isl_take> means that the object the argument points to
603 is taken over by the function and may no longer be used
604 by the user as an argument to any other function.
605 The pointer value must be one returned by a function
606 returning an C<__isl_give> pointer.
607 If the user passes in a C<NULL> value, then this will
608 be treated as an error in the sense that the function will
609 not perform its usual operation. However, it will still
610 make sure that all the other C<__isl_take> arguments
615 C<__isl_keep> means that the function will only use the object
616 temporarily. After the function has finished, the user
617 can still use it as an argument to other functions.
618 A C<NULL> value will be treated in the same way as
619 a C<NULL> value for an C<__isl_take> argument.
623 =head2 Error Handling
625 C<isl> supports different ways to react in case a runtime error is triggered.
626 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
627 with two maps that have incompatible spaces. There are three possible ways
628 to react on error: to warn, to continue or to abort.
630 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
631 the last error in the corresponding C<isl_ctx> and the function in which the
632 error was triggered returns C<NULL>. An error does not corrupt internal state,
633 such that isl can continue to be used. C<isl> also provides functions to
634 read the last error and to reset the memory that stores the last error. The
635 last error is only stored for information purposes. Its presence does not
636 change the behavior of C<isl>. Hence, resetting an error is not required to
637 continue to use isl, but only to observe new errors.
640 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
641 void isl_ctx_reset_error(isl_ctx *ctx);
643 Another option is to continue on error. This is similar to warn on error mode,
644 except that C<isl> does not print any warning. This allows a program to
645 implement its own error reporting.
647 The last option is to directly abort the execution of the program from within
648 the isl library. This makes it obviously impossible to recover from an error,
649 but it allows to directly spot the error location. By aborting on error,
650 debuggers break at the location the error occurred and can provide a stack
651 trace. Other tools that automatically provide stack traces on abort or that do
652 not want to continue execution after an error was triggered may also prefer to
655 The on error behavior of isl can be specified by calling
656 C<isl_options_set_on_error> or by setting the command line option
657 C<--isl-on-error>. Valid arguments for the function call are
658 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
659 choices for the command line option are C<warn>, C<continue> and C<abort>.
660 It is also possible to query the current error mode.
662 #include <isl/options.h>
663 int isl_options_set_on_error(isl_ctx *ctx, int val);
664 int isl_options_get_on_error(isl_ctx *ctx);
668 Identifiers are used to identify both individual dimensions
669 and tuples of dimensions. They consist of an optional name and an optional
670 user pointer. The name and the user pointer cannot both be C<NULL>, however.
671 Identifiers with the same name but different pointer values
672 are considered to be distinct.
673 Similarly, identifiers with different names but the same pointer value
674 are also considered to be distinct.
675 Equal identifiers are represented using the same object.
676 Pairs of identifiers can therefore be tested for equality using the
678 Identifiers can be constructed, copied, freed, inspected and printed
679 using the following functions.
682 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
683 __isl_keep const char *name, void *user);
684 __isl_give isl_id *isl_id_set_free_user(
685 __isl_take isl_id *id,
686 __isl_give void (*free_user)(void *user));
687 __isl_give isl_id *isl_id_copy(isl_id *id);
688 void *isl_id_free(__isl_take isl_id *id);
690 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
691 void *isl_id_get_user(__isl_keep isl_id *id);
692 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
694 __isl_give isl_printer *isl_printer_print_id(
695 __isl_take isl_printer *p, __isl_keep isl_id *id);
697 The callback set by C<isl_id_set_free_user> is called on the user
698 pointer when the last reference to the C<isl_id> is freed.
699 Note that C<isl_id_get_name> returns a pointer to some internal
700 data structure, so the result can only be used while the
701 corresponding C<isl_id> is alive.
705 Whenever a new set, relation or similiar object is created from scratch,
706 the space in which it lives needs to be specified using an C<isl_space>.
707 Each space involves zero or more parameters and zero, one or two
708 tuples of set or input/output dimensions. The parameters and dimensions
709 are identified by an C<isl_dim_type> and a position.
710 The type C<isl_dim_param> refers to parameters,
711 the type C<isl_dim_set> refers to set dimensions (for spaces
712 with a single tuple of dimensions) and the types C<isl_dim_in>
713 and C<isl_dim_out> refer to input and output dimensions
714 (for spaces with two tuples of dimensions).
715 Local spaces (see L</"Local Spaces">) also contain dimensions
716 of type C<isl_dim_div>.
717 Note that parameters are only identified by their position within
718 a given object. Across different objects, parameters are (usually)
719 identified by their names or identifiers. Only unnamed parameters
720 are identified by their positions across objects. The use of unnamed
721 parameters is discouraged.
723 #include <isl/space.h>
724 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
725 unsigned nparam, unsigned n_in, unsigned n_out);
726 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
728 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
729 unsigned nparam, unsigned dim);
730 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
731 void *isl_space_free(__isl_take isl_space *space);
732 unsigned isl_space_dim(__isl_keep isl_space *space,
733 enum isl_dim_type type);
735 The space used for creating a parameter domain
736 needs to be created using C<isl_space_params_alloc>.
737 For other sets, the space
738 needs to be created using C<isl_space_set_alloc>, while
739 for a relation, the space
740 needs to be created using C<isl_space_alloc>.
741 C<isl_space_dim> can be used
742 to find out the number of dimensions of each type in
743 a space, where type may be
744 C<isl_dim_param>, C<isl_dim_in> (only for relations),
745 C<isl_dim_out> (only for relations), C<isl_dim_set>
746 (only for sets) or C<isl_dim_all>.
748 To check whether a given space is that of a set or a map
749 or whether it is a parameter space, use these functions:
751 #include <isl/space.h>
752 int isl_space_is_params(__isl_keep isl_space *space);
753 int isl_space_is_set(__isl_keep isl_space *space);
754 int isl_space_is_map(__isl_keep isl_space *space);
756 Spaces can be compared using the following functions:
758 #include <isl/space.h>
759 int isl_space_is_equal(__isl_keep isl_space *space1,
760 __isl_keep isl_space *space2);
761 int isl_space_is_domain(__isl_keep isl_space *space1,
762 __isl_keep isl_space *space2);
763 int isl_space_is_range(__isl_keep isl_space *space1,
764 __isl_keep isl_space *space2);
766 C<isl_space_is_domain> checks whether the first argument is equal
767 to the domain of the second argument. This requires in particular that
768 the first argument is a set space and that the second argument
771 It is often useful to create objects that live in the
772 same space as some other object. This can be accomplished
773 by creating the new objects
774 (see L</"Creating New Sets and Relations"> or
775 L</"Creating New (Piecewise) Quasipolynomials">) based on the space
776 of the original object.
779 __isl_give isl_space *isl_basic_set_get_space(
780 __isl_keep isl_basic_set *bset);
781 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
783 #include <isl/union_set.h>
784 __isl_give isl_space *isl_union_set_get_space(
785 __isl_keep isl_union_set *uset);
788 __isl_give isl_space *isl_basic_map_get_space(
789 __isl_keep isl_basic_map *bmap);
790 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
792 #include <isl/union_map.h>
793 __isl_give isl_space *isl_union_map_get_space(
794 __isl_keep isl_union_map *umap);
796 #include <isl/constraint.h>
797 __isl_give isl_space *isl_constraint_get_space(
798 __isl_keep isl_constraint *constraint);
800 #include <isl/polynomial.h>
801 __isl_give isl_space *isl_qpolynomial_get_domain_space(
802 __isl_keep isl_qpolynomial *qp);
803 __isl_give isl_space *isl_qpolynomial_get_space(
804 __isl_keep isl_qpolynomial *qp);
805 __isl_give isl_space *isl_qpolynomial_fold_get_space(
806 __isl_keep isl_qpolynomial_fold *fold);
807 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
808 __isl_keep isl_pw_qpolynomial *pwqp);
809 __isl_give isl_space *isl_pw_qpolynomial_get_space(
810 __isl_keep isl_pw_qpolynomial *pwqp);
811 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
812 __isl_keep isl_pw_qpolynomial_fold *pwf);
813 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
814 __isl_keep isl_pw_qpolynomial_fold *pwf);
815 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
816 __isl_keep isl_union_pw_qpolynomial *upwqp);
817 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
818 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
821 __isl_give isl_space *isl_multi_val_get_space(
822 __isl_keep isl_multi_val *mv);
825 __isl_give isl_space *isl_aff_get_domain_space(
826 __isl_keep isl_aff *aff);
827 __isl_give isl_space *isl_aff_get_space(
828 __isl_keep isl_aff *aff);
829 __isl_give isl_space *isl_pw_aff_get_domain_space(
830 __isl_keep isl_pw_aff *pwaff);
831 __isl_give isl_space *isl_pw_aff_get_space(
832 __isl_keep isl_pw_aff *pwaff);
833 __isl_give isl_space *isl_multi_aff_get_domain_space(
834 __isl_keep isl_multi_aff *maff);
835 __isl_give isl_space *isl_multi_aff_get_space(
836 __isl_keep isl_multi_aff *maff);
837 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
838 __isl_keep isl_pw_multi_aff *pma);
839 __isl_give isl_space *isl_pw_multi_aff_get_space(
840 __isl_keep isl_pw_multi_aff *pma);
841 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
842 __isl_keep isl_union_pw_multi_aff *upma);
843 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
844 __isl_keep isl_multi_pw_aff *mpa);
845 __isl_give isl_space *isl_multi_pw_aff_get_space(
846 __isl_keep isl_multi_pw_aff *mpa);
848 #include <isl/point.h>
849 __isl_give isl_space *isl_point_get_space(
850 __isl_keep isl_point *pnt);
852 The identifiers or names of the individual dimensions may be set or read off
853 using the following functions.
855 #include <isl/space.h>
856 __isl_give isl_space *isl_space_set_dim_id(
857 __isl_take isl_space *space,
858 enum isl_dim_type type, unsigned pos,
859 __isl_take isl_id *id);
860 int isl_space_has_dim_id(__isl_keep isl_space *space,
861 enum isl_dim_type type, unsigned pos);
862 __isl_give isl_id *isl_space_get_dim_id(
863 __isl_keep isl_space *space,
864 enum isl_dim_type type, unsigned pos);
865 __isl_give isl_space *isl_space_set_dim_name(
866 __isl_take isl_space *space,
867 enum isl_dim_type type, unsigned pos,
868 __isl_keep const char *name);
869 int isl_space_has_dim_name(__isl_keep isl_space *space,
870 enum isl_dim_type type, unsigned pos);
871 __isl_keep const char *isl_space_get_dim_name(
872 __isl_keep isl_space *space,
873 enum isl_dim_type type, unsigned pos);
875 Note that C<isl_space_get_name> returns a pointer to some internal
876 data structure, so the result can only be used while the
877 corresponding C<isl_space> is alive.
878 Also note that every function that operates on two sets or relations
879 requires that both arguments have the same parameters. This also
880 means that if one of the arguments has named parameters, then the
881 other needs to have named parameters too and the names need to match.
882 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
883 arguments may have different parameters (as long as they are named),
884 in which case the result will have as parameters the union of the parameters of
887 Given the identifier or name of a dimension (typically a parameter),
888 its position can be obtained from the following function.
890 #include <isl/space.h>
891 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
892 enum isl_dim_type type, __isl_keep isl_id *id);
893 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
894 enum isl_dim_type type, const char *name);
896 The identifiers or names of entire spaces may be set or read off
897 using the following functions.
899 #include <isl/space.h>
900 __isl_give isl_space *isl_space_set_tuple_id(
901 __isl_take isl_space *space,
902 enum isl_dim_type type, __isl_take isl_id *id);
903 __isl_give isl_space *isl_space_reset_tuple_id(
904 __isl_take isl_space *space, enum isl_dim_type type);
905 int isl_space_has_tuple_id(__isl_keep isl_space *space,
906 enum isl_dim_type type);
907 __isl_give isl_id *isl_space_get_tuple_id(
908 __isl_keep isl_space *space, enum isl_dim_type type);
909 __isl_give isl_space *isl_space_set_tuple_name(
910 __isl_take isl_space *space,
911 enum isl_dim_type type, const char *s);
912 int isl_space_has_tuple_name(__isl_keep isl_space *space,
913 enum isl_dim_type type);
914 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
915 enum isl_dim_type type);
917 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
918 or C<isl_dim_set>. As with C<isl_space_get_name>,
919 the C<isl_space_get_tuple_name> function returns a pointer to some internal
921 Binary operations require the corresponding spaces of their arguments
922 to have the same name.
924 To keep the names of all parameters and tuples, but reset the user pointers
925 of all the corresponding identifiers, use the following function.
927 __isl_give isl_space *isl_space_reset_user(
928 __isl_take isl_space *space);
930 Spaces can be nested. In particular, the domain of a set or
931 the domain or range of a relation can be a nested relation.
932 This process is also called I<wrapping>.
933 The functions for detecting, constructing and deconstructing
934 such nested spaces can be found in the wrapping properties
935 of L</"Unary Properties">, the wrapping operations
936 of L</"Unary Operations"> and the Cartesian product operations
937 of L</"Basic Operations">.
939 Spaces can be created from other spaces
940 using the following functions.
942 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
943 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
944 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
945 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
946 __isl_give isl_space *isl_space_domain_map(
947 __isl_take isl_space *space);
948 __isl_give isl_space *isl_space_range_map(
949 __isl_take isl_space *space);
950 __isl_give isl_space *isl_space_params(
951 __isl_take isl_space *space);
952 __isl_give isl_space *isl_space_set_from_params(
953 __isl_take isl_space *space);
954 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
955 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
956 __isl_take isl_space *right);
957 __isl_give isl_space *isl_space_align_params(
958 __isl_take isl_space *space1, __isl_take isl_space *space2)
959 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
960 enum isl_dim_type type, unsigned pos, unsigned n);
961 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
962 enum isl_dim_type type, unsigned n);
963 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
964 enum isl_dim_type type, unsigned first, unsigned n);
965 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
966 enum isl_dim_type dst_type, unsigned dst_pos,
967 enum isl_dim_type src_type, unsigned src_pos,
969 __isl_give isl_space *isl_space_map_from_set(
970 __isl_take isl_space *space);
971 __isl_give isl_space *isl_space_map_from_domain_and_range(
972 __isl_take isl_space *domain,
973 __isl_take isl_space *range);
974 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
975 __isl_give isl_space *isl_space_curry(
976 __isl_take isl_space *space);
977 __isl_give isl_space *isl_space_uncurry(
978 __isl_take isl_space *space);
980 Note that if dimensions are added or removed from a space, then
981 the name and the internal structure are lost.
985 A local space is essentially a space with
986 zero or more existentially quantified variables.
987 The local space of a (constraint of a) basic set or relation can be obtained
988 using the following functions.
990 #include <isl/constraint.h>
991 __isl_give isl_local_space *isl_constraint_get_local_space(
992 __isl_keep isl_constraint *constraint);
995 __isl_give isl_local_space *isl_basic_set_get_local_space(
996 __isl_keep isl_basic_set *bset);
999 __isl_give isl_local_space *isl_basic_map_get_local_space(
1000 __isl_keep isl_basic_map *bmap);
1002 A new local space can be created from a space using
1004 #include <isl/local_space.h>
1005 __isl_give isl_local_space *isl_local_space_from_space(
1006 __isl_take isl_space *space);
1008 They can be inspected, modified, copied and freed using the following functions.
1010 #include <isl/local_space.h>
1011 isl_ctx *isl_local_space_get_ctx(
1012 __isl_keep isl_local_space *ls);
1013 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1014 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1015 enum isl_dim_type type);
1016 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1017 __isl_take isl_local_space *ls,
1018 enum isl_dim_type type, __isl_take isl_id *id);
1019 int isl_local_space_has_dim_id(
1020 __isl_keep isl_local_space *ls,
1021 enum isl_dim_type type, unsigned pos);
1022 __isl_give isl_id *isl_local_space_get_dim_id(
1023 __isl_keep isl_local_space *ls,
1024 enum isl_dim_type type, unsigned pos);
1025 int isl_local_space_has_dim_name(
1026 __isl_keep isl_local_space *ls,
1027 enum isl_dim_type type, unsigned pos)
1028 const char *isl_local_space_get_dim_name(
1029 __isl_keep isl_local_space *ls,
1030 enum isl_dim_type type, unsigned pos);
1031 __isl_give isl_local_space *isl_local_space_set_dim_name(
1032 __isl_take isl_local_space *ls,
1033 enum isl_dim_type type, unsigned pos, const char *s);
1034 __isl_give isl_local_space *isl_local_space_set_dim_id(
1035 __isl_take isl_local_space *ls,
1036 enum isl_dim_type type, unsigned pos,
1037 __isl_take isl_id *id);
1038 __isl_give isl_space *isl_local_space_get_space(
1039 __isl_keep isl_local_space *ls);
1040 __isl_give isl_aff *isl_local_space_get_div(
1041 __isl_keep isl_local_space *ls, int pos);
1042 __isl_give isl_local_space *isl_local_space_copy(
1043 __isl_keep isl_local_space *ls);
1044 void *isl_local_space_free(__isl_take isl_local_space *ls);
1046 Note that C<isl_local_space_get_div> can only be used on local spaces
1049 Two local spaces can be compared using
1051 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1052 __isl_keep isl_local_space *ls2);
1054 Local spaces can be created from other local spaces
1055 using the functions described in L</"Unary Operations">
1056 and L</"Binary Operations">.
1058 =head2 Input and Output
1060 C<isl> supports its own input/output format, which is similar
1061 to the C<Omega> format, but also supports the C<PolyLib> format
1064 =head3 C<isl> format
1066 The C<isl> format is similar to that of C<Omega>, but has a different
1067 syntax for describing the parameters and allows for the definition
1068 of an existentially quantified variable as the integer division
1069 of an affine expression.
1070 For example, the set of integers C<i> between C<0> and C<n>
1071 such that C<i % 10 <= 6> can be described as
1073 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1076 A set or relation can have several disjuncts, separated
1077 by the keyword C<or>. Each disjunct is either a conjunction
1078 of constraints or a projection (C<exists>) of a conjunction
1079 of constraints. The constraints are separated by the keyword
1082 =head3 C<PolyLib> format
1084 If the represented set is a union, then the first line
1085 contains a single number representing the number of disjuncts.
1086 Otherwise, a line containing the number C<1> is optional.
1088 Each disjunct is represented by a matrix of constraints.
1089 The first line contains two numbers representing
1090 the number of rows and columns,
1091 where the number of rows is equal to the number of constraints
1092 and the number of columns is equal to two plus the number of variables.
1093 The following lines contain the actual rows of the constraint matrix.
1094 In each row, the first column indicates whether the constraint
1095 is an equality (C<0>) or inequality (C<1>). The final column
1096 corresponds to the constant term.
1098 If the set is parametric, then the coefficients of the parameters
1099 appear in the last columns before the constant column.
1100 The coefficients of any existentially quantified variables appear
1101 between those of the set variables and those of the parameters.
1103 =head3 Extended C<PolyLib> format
1105 The extended C<PolyLib> format is nearly identical to the
1106 C<PolyLib> format. The only difference is that the line
1107 containing the number of rows and columns of a constraint matrix
1108 also contains four additional numbers:
1109 the number of output dimensions, the number of input dimensions,
1110 the number of local dimensions (i.e., the number of existentially
1111 quantified variables) and the number of parameters.
1112 For sets, the number of ``output'' dimensions is equal
1113 to the number of set dimensions, while the number of ``input''
1118 #include <isl/set.h>
1119 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1120 isl_ctx *ctx, FILE *input);
1121 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1122 isl_ctx *ctx, const char *str);
1123 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1125 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1128 #include <isl/map.h>
1129 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1130 isl_ctx *ctx, FILE *input);
1131 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1132 isl_ctx *ctx, const char *str);
1133 __isl_give isl_map *isl_map_read_from_file(
1134 isl_ctx *ctx, FILE *input);
1135 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1138 #include <isl/union_set.h>
1139 __isl_give isl_union_set *isl_union_set_read_from_file(
1140 isl_ctx *ctx, FILE *input);
1141 __isl_give isl_union_set *isl_union_set_read_from_str(
1142 isl_ctx *ctx, const char *str);
1144 #include <isl/union_map.h>
1145 __isl_give isl_union_map *isl_union_map_read_from_file(
1146 isl_ctx *ctx, FILE *input);
1147 __isl_give isl_union_map *isl_union_map_read_from_str(
1148 isl_ctx *ctx, const char *str);
1150 The input format is autodetected and may be either the C<PolyLib> format
1151 or the C<isl> format.
1155 Before anything can be printed, an C<isl_printer> needs to
1158 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1160 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1161 void *isl_printer_free(__isl_take isl_printer *printer);
1162 __isl_give char *isl_printer_get_str(
1163 __isl_keep isl_printer *printer);
1165 The printer can be inspected using the following functions.
1167 FILE *isl_printer_get_file(
1168 __isl_keep isl_printer *printer);
1169 int isl_printer_get_output_format(
1170 __isl_keep isl_printer *p);
1172 The behavior of the printer can be modified in various ways
1174 __isl_give isl_printer *isl_printer_set_output_format(
1175 __isl_take isl_printer *p, int output_format);
1176 __isl_give isl_printer *isl_printer_set_indent(
1177 __isl_take isl_printer *p, int indent);
1178 __isl_give isl_printer *isl_printer_indent(
1179 __isl_take isl_printer *p, int indent);
1180 __isl_give isl_printer *isl_printer_set_prefix(
1181 __isl_take isl_printer *p, const char *prefix);
1182 __isl_give isl_printer *isl_printer_set_suffix(
1183 __isl_take isl_printer *p, const char *suffix);
1185 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1186 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1187 and defaults to C<ISL_FORMAT_ISL>.
1188 Each line in the output is indented by C<indent> (set by
1189 C<isl_printer_set_indent>) spaces
1190 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1191 In the C<PolyLib> format output,
1192 the coefficients of the existentially quantified variables
1193 appear between those of the set variables and those
1195 The function C<isl_printer_indent> increases the indentation
1196 by the specified amount (which may be negative).
1198 To actually print something, use
1200 #include <isl/printer.h>
1201 __isl_give isl_printer *isl_printer_print_double(
1202 __isl_take isl_printer *p, double d);
1204 #include <isl/set.h>
1205 __isl_give isl_printer *isl_printer_print_basic_set(
1206 __isl_take isl_printer *printer,
1207 __isl_keep isl_basic_set *bset);
1208 __isl_give isl_printer *isl_printer_print_set(
1209 __isl_take isl_printer *printer,
1210 __isl_keep isl_set *set);
1212 #include <isl/map.h>
1213 __isl_give isl_printer *isl_printer_print_basic_map(
1214 __isl_take isl_printer *printer,
1215 __isl_keep isl_basic_map *bmap);
1216 __isl_give isl_printer *isl_printer_print_map(
1217 __isl_take isl_printer *printer,
1218 __isl_keep isl_map *map);
1220 #include <isl/union_set.h>
1221 __isl_give isl_printer *isl_printer_print_union_set(
1222 __isl_take isl_printer *p,
1223 __isl_keep isl_union_set *uset);
1225 #include <isl/union_map.h>
1226 __isl_give isl_printer *isl_printer_print_union_map(
1227 __isl_take isl_printer *p,
1228 __isl_keep isl_union_map *umap);
1230 When called on a file printer, the following function flushes
1231 the file. When called on a string printer, the buffer is cleared.
1233 __isl_give isl_printer *isl_printer_flush(
1234 __isl_take isl_printer *p);
1236 =head2 Creating New Sets and Relations
1238 C<isl> has functions for creating some standard sets and relations.
1242 =item * Empty sets and relations
1244 __isl_give isl_basic_set *isl_basic_set_empty(
1245 __isl_take isl_space *space);
1246 __isl_give isl_basic_map *isl_basic_map_empty(
1247 __isl_take isl_space *space);
1248 __isl_give isl_set *isl_set_empty(
1249 __isl_take isl_space *space);
1250 __isl_give isl_map *isl_map_empty(
1251 __isl_take isl_space *space);
1252 __isl_give isl_union_set *isl_union_set_empty(
1253 __isl_take isl_space *space);
1254 __isl_give isl_union_map *isl_union_map_empty(
1255 __isl_take isl_space *space);
1257 For C<isl_union_set>s and C<isl_union_map>s, the space
1258 is only used to specify the parameters.
1260 =item * Universe sets and relations
1262 __isl_give isl_basic_set *isl_basic_set_universe(
1263 __isl_take isl_space *space);
1264 __isl_give isl_basic_map *isl_basic_map_universe(
1265 __isl_take isl_space *space);
1266 __isl_give isl_set *isl_set_universe(
1267 __isl_take isl_space *space);
1268 __isl_give isl_map *isl_map_universe(
1269 __isl_take isl_space *space);
1270 __isl_give isl_union_set *isl_union_set_universe(
1271 __isl_take isl_union_set *uset);
1272 __isl_give isl_union_map *isl_union_map_universe(
1273 __isl_take isl_union_map *umap);
1275 The sets and relations constructed by the functions above
1276 contain all integer values, while those constructed by the
1277 functions below only contain non-negative values.
1279 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1280 __isl_take isl_space *space);
1281 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1282 __isl_take isl_space *space);
1283 __isl_give isl_set *isl_set_nat_universe(
1284 __isl_take isl_space *space);
1285 __isl_give isl_map *isl_map_nat_universe(
1286 __isl_take isl_space *space);
1288 =item * Identity relations
1290 __isl_give isl_basic_map *isl_basic_map_identity(
1291 __isl_take isl_space *space);
1292 __isl_give isl_map *isl_map_identity(
1293 __isl_take isl_space *space);
1295 The number of input and output dimensions in C<space> needs
1298 =item * Lexicographic order
1300 __isl_give isl_map *isl_map_lex_lt(
1301 __isl_take isl_space *set_space);
1302 __isl_give isl_map *isl_map_lex_le(
1303 __isl_take isl_space *set_space);
1304 __isl_give isl_map *isl_map_lex_gt(
1305 __isl_take isl_space *set_space);
1306 __isl_give isl_map *isl_map_lex_ge(
1307 __isl_take isl_space *set_space);
1308 __isl_give isl_map *isl_map_lex_lt_first(
1309 __isl_take isl_space *space, unsigned n);
1310 __isl_give isl_map *isl_map_lex_le_first(
1311 __isl_take isl_space *space, unsigned n);
1312 __isl_give isl_map *isl_map_lex_gt_first(
1313 __isl_take isl_space *space, unsigned n);
1314 __isl_give isl_map *isl_map_lex_ge_first(
1315 __isl_take isl_space *space, unsigned n);
1317 The first four functions take a space for a B<set>
1318 and return relations that express that the elements in the domain
1319 are lexicographically less
1320 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1321 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1322 than the elements in the range.
1323 The last four functions take a space for a map
1324 and return relations that express that the first C<n> dimensions
1325 in the domain are lexicographically less
1326 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1327 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1328 than the first C<n> dimensions in the range.
1332 A basic set or relation can be converted to a set or relation
1333 using the following functions.
1335 __isl_give isl_set *isl_set_from_basic_set(
1336 __isl_take isl_basic_set *bset);
1337 __isl_give isl_map *isl_map_from_basic_map(
1338 __isl_take isl_basic_map *bmap);
1340 Sets and relations can be converted to union sets and relations
1341 using the following functions.
1343 __isl_give isl_union_set *isl_union_set_from_basic_set(
1344 __isl_take isl_basic_set *bset);
1345 __isl_give isl_union_map *isl_union_map_from_basic_map(
1346 __isl_take isl_basic_map *bmap);
1347 __isl_give isl_union_set *isl_union_set_from_set(
1348 __isl_take isl_set *set);
1349 __isl_give isl_union_map *isl_union_map_from_map(
1350 __isl_take isl_map *map);
1352 The inverse conversions below can only be used if the input
1353 union set or relation is known to contain elements in exactly one
1356 __isl_give isl_set *isl_set_from_union_set(
1357 __isl_take isl_union_set *uset);
1358 __isl_give isl_map *isl_map_from_union_map(
1359 __isl_take isl_union_map *umap);
1361 A zero-dimensional (basic) set can be constructed on a given parameter domain
1362 using the following function.
1364 __isl_give isl_basic_set *isl_basic_set_from_params(
1365 __isl_take isl_basic_set *bset);
1366 __isl_give isl_set *isl_set_from_params(
1367 __isl_take isl_set *set);
1369 Sets and relations can be copied and freed again using the following
1372 __isl_give isl_basic_set *isl_basic_set_copy(
1373 __isl_keep isl_basic_set *bset);
1374 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1375 __isl_give isl_union_set *isl_union_set_copy(
1376 __isl_keep isl_union_set *uset);
1377 __isl_give isl_basic_map *isl_basic_map_copy(
1378 __isl_keep isl_basic_map *bmap);
1379 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1380 __isl_give isl_union_map *isl_union_map_copy(
1381 __isl_keep isl_union_map *umap);
1382 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1383 void *isl_set_free(__isl_take isl_set *set);
1384 void *isl_union_set_free(__isl_take isl_union_set *uset);
1385 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1386 void *isl_map_free(__isl_take isl_map *map);
1387 void *isl_union_map_free(__isl_take isl_union_map *umap);
1389 Other sets and relations can be constructed by starting
1390 from a universe set or relation, adding equality and/or
1391 inequality constraints and then projecting out the
1392 existentially quantified variables, if any.
1393 Constraints can be constructed, manipulated and
1394 added to (or removed from) (basic) sets and relations
1395 using the following functions.
1397 #include <isl/constraint.h>
1398 __isl_give isl_constraint *isl_equality_alloc(
1399 __isl_take isl_local_space *ls);
1400 __isl_give isl_constraint *isl_inequality_alloc(
1401 __isl_take isl_local_space *ls);
1402 __isl_give isl_constraint *isl_constraint_set_constant_si(
1403 __isl_take isl_constraint *constraint, int v);
1404 __isl_give isl_constraint *isl_constraint_set_constant_val(
1405 __isl_take isl_constraint *constraint,
1406 __isl_take isl_val *v);
1407 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1408 __isl_take isl_constraint *constraint,
1409 enum isl_dim_type type, int pos, int v);
1410 __isl_give isl_constraint *
1411 isl_constraint_set_coefficient_val(
1412 __isl_take isl_constraint *constraint,
1413 enum isl_dim_type type, int pos,
1414 __isl_take isl_val *v);
1415 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1416 __isl_take isl_basic_map *bmap,
1417 __isl_take isl_constraint *constraint);
1418 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1419 __isl_take isl_basic_set *bset,
1420 __isl_take isl_constraint *constraint);
1421 __isl_give isl_map *isl_map_add_constraint(
1422 __isl_take isl_map *map,
1423 __isl_take isl_constraint *constraint);
1424 __isl_give isl_set *isl_set_add_constraint(
1425 __isl_take isl_set *set,
1426 __isl_take isl_constraint *constraint);
1427 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1428 __isl_take isl_basic_set *bset,
1429 __isl_take isl_constraint *constraint);
1431 For example, to create a set containing the even integers
1432 between 10 and 42, you would use the following code.
1435 isl_local_space *ls;
1437 isl_basic_set *bset;
1439 space = isl_space_set_alloc(ctx, 0, 2);
1440 bset = isl_basic_set_universe(isl_space_copy(space));
1441 ls = isl_local_space_from_space(space);
1443 c = isl_equality_alloc(isl_local_space_copy(ls));
1444 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1445 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1446 bset = isl_basic_set_add_constraint(bset, c);
1448 c = isl_inequality_alloc(isl_local_space_copy(ls));
1449 c = isl_constraint_set_constant_si(c, -10);
1450 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1451 bset = isl_basic_set_add_constraint(bset, c);
1453 c = isl_inequality_alloc(ls);
1454 c = isl_constraint_set_constant_si(c, 42);
1455 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1456 bset = isl_basic_set_add_constraint(bset, c);
1458 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1462 isl_basic_set *bset;
1463 bset = isl_basic_set_read_from_str(ctx,
1464 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1466 A basic set or relation can also be constructed from two matrices
1467 describing the equalities and the inequalities.
1469 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1470 __isl_take isl_space *space,
1471 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1472 enum isl_dim_type c1,
1473 enum isl_dim_type c2, enum isl_dim_type c3,
1474 enum isl_dim_type c4);
1475 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1476 __isl_take isl_space *space,
1477 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1478 enum isl_dim_type c1,
1479 enum isl_dim_type c2, enum isl_dim_type c3,
1480 enum isl_dim_type c4, enum isl_dim_type c5);
1482 The C<isl_dim_type> arguments indicate the order in which
1483 different kinds of variables appear in the input matrices
1484 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1485 C<isl_dim_set> and C<isl_dim_div> for sets and
1486 of C<isl_dim_cst>, C<isl_dim_param>,
1487 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1489 A (basic or union) set or relation can also be constructed from a
1490 (union) (piecewise) (multiple) affine expression
1491 or a list of affine expressions
1492 (See L<"Piecewise Quasi Affine Expressions"> and
1493 L<"Piecewise Multiple Quasi Affine Expressions">).
1495 __isl_give isl_basic_map *isl_basic_map_from_aff(
1496 __isl_take isl_aff *aff);
1497 __isl_give isl_map *isl_map_from_aff(
1498 __isl_take isl_aff *aff);
1499 __isl_give isl_set *isl_set_from_pw_aff(
1500 __isl_take isl_pw_aff *pwaff);
1501 __isl_give isl_map *isl_map_from_pw_aff(
1502 __isl_take isl_pw_aff *pwaff);
1503 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1504 __isl_take isl_space *domain_space,
1505 __isl_take isl_aff_list *list);
1506 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1507 __isl_take isl_multi_aff *maff)
1508 __isl_give isl_map *isl_map_from_multi_aff(
1509 __isl_take isl_multi_aff *maff)
1510 __isl_give isl_set *isl_set_from_pw_multi_aff(
1511 __isl_take isl_pw_multi_aff *pma);
1512 __isl_give isl_map *isl_map_from_pw_multi_aff(
1513 __isl_take isl_pw_multi_aff *pma);
1514 __isl_give isl_set *isl_set_from_multi_pw_aff(
1515 __isl_take isl_multi_pw_aff *mpa);
1516 __isl_give isl_map *isl_map_from_multi_pw_aff(
1517 __isl_take isl_multi_pw_aff *mpa);
1518 __isl_give isl_union_map *
1519 isl_union_map_from_union_pw_multi_aff(
1520 __isl_take isl_union_pw_multi_aff *upma);
1522 The C<domain_space> argument describes the domain of the resulting
1523 basic relation. It is required because the C<list> may consist
1524 of zero affine expressions.
1526 =head2 Inspecting Sets and Relations
1528 Usually, the user should not have to care about the actual constraints
1529 of the sets and maps, but should instead apply the abstract operations
1530 explained in the following sections.
1531 Occasionally, however, it may be required to inspect the individual
1532 coefficients of the constraints. This section explains how to do so.
1533 In these cases, it may also be useful to have C<isl> compute
1534 an explicit representation of the existentially quantified variables.
1536 __isl_give isl_set *isl_set_compute_divs(
1537 __isl_take isl_set *set);
1538 __isl_give isl_map *isl_map_compute_divs(
1539 __isl_take isl_map *map);
1540 __isl_give isl_union_set *isl_union_set_compute_divs(
1541 __isl_take isl_union_set *uset);
1542 __isl_give isl_union_map *isl_union_map_compute_divs(
1543 __isl_take isl_union_map *umap);
1545 This explicit representation defines the existentially quantified
1546 variables as integer divisions of the other variables, possibly
1547 including earlier existentially quantified variables.
1548 An explicitly represented existentially quantified variable therefore
1549 has a unique value when the values of the other variables are known.
1550 If, furthermore, the same existentials, i.e., existentials
1551 with the same explicit representations, should appear in the
1552 same order in each of the disjuncts of a set or map, then the user should call
1553 either of the following functions.
1555 __isl_give isl_set *isl_set_align_divs(
1556 __isl_take isl_set *set);
1557 __isl_give isl_map *isl_map_align_divs(
1558 __isl_take isl_map *map);
1560 Alternatively, the existentially quantified variables can be removed
1561 using the following functions, which compute an overapproximation.
1563 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1564 __isl_take isl_basic_set *bset);
1565 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1566 __isl_take isl_basic_map *bmap);
1567 __isl_give isl_set *isl_set_remove_divs(
1568 __isl_take isl_set *set);
1569 __isl_give isl_map *isl_map_remove_divs(
1570 __isl_take isl_map *map);
1572 It is also possible to only remove those divs that are defined
1573 in terms of a given range of dimensions or only those for which
1574 no explicit representation is known.
1576 __isl_give isl_basic_set *
1577 isl_basic_set_remove_divs_involving_dims(
1578 __isl_take isl_basic_set *bset,
1579 enum isl_dim_type type,
1580 unsigned first, unsigned n);
1581 __isl_give isl_basic_map *
1582 isl_basic_map_remove_divs_involving_dims(
1583 __isl_take isl_basic_map *bmap,
1584 enum isl_dim_type type,
1585 unsigned first, unsigned n);
1586 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1587 __isl_take isl_set *set, enum isl_dim_type type,
1588 unsigned first, unsigned n);
1589 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1590 __isl_take isl_map *map, enum isl_dim_type type,
1591 unsigned first, unsigned n);
1593 __isl_give isl_basic_set *
1594 isl_basic_set_remove_unknown_divs(
1595 __isl_take isl_basic_set *bset);
1596 __isl_give isl_set *isl_set_remove_unknown_divs(
1597 __isl_take isl_set *set);
1598 __isl_give isl_map *isl_map_remove_unknown_divs(
1599 __isl_take isl_map *map);
1601 To iterate over all the sets or maps in a union set or map, use
1603 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1604 int (*fn)(__isl_take isl_set *set, void *user),
1606 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1607 int (*fn)(__isl_take isl_map *map, void *user),
1610 The number of sets or maps in a union set or map can be obtained
1613 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1614 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1616 To extract the set or map in a given space from a union, use
1618 __isl_give isl_set *isl_union_set_extract_set(
1619 __isl_keep isl_union_set *uset,
1620 __isl_take isl_space *space);
1621 __isl_give isl_map *isl_union_map_extract_map(
1622 __isl_keep isl_union_map *umap,
1623 __isl_take isl_space *space);
1625 To iterate over all the basic sets or maps in a set or map, use
1627 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1628 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1630 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1631 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1634 The callback function C<fn> should return 0 if successful and
1635 -1 if an error occurs. In the latter case, or if any other error
1636 occurs, the above functions will return -1.
1638 It should be noted that C<isl> does not guarantee that
1639 the basic sets or maps passed to C<fn> are disjoint.
1640 If this is required, then the user should call one of
1641 the following functions first.
1643 __isl_give isl_set *isl_set_make_disjoint(
1644 __isl_take isl_set *set);
1645 __isl_give isl_map *isl_map_make_disjoint(
1646 __isl_take isl_map *map);
1648 The number of basic sets in a set can be obtained
1651 int isl_set_n_basic_set(__isl_keep isl_set *set);
1653 To iterate over the constraints of a basic set or map, use
1655 #include <isl/constraint.h>
1657 int isl_basic_set_n_constraint(
1658 __isl_keep isl_basic_set *bset);
1659 int isl_basic_set_foreach_constraint(
1660 __isl_keep isl_basic_set *bset,
1661 int (*fn)(__isl_take isl_constraint *c, void *user),
1663 int isl_basic_map_foreach_constraint(
1664 __isl_keep isl_basic_map *bmap,
1665 int (*fn)(__isl_take isl_constraint *c, void *user),
1667 void *isl_constraint_free(__isl_take isl_constraint *c);
1669 Again, the callback function C<fn> should return 0 if successful and
1670 -1 if an error occurs. In the latter case, or if any other error
1671 occurs, the above functions will return -1.
1672 The constraint C<c> represents either an equality or an inequality.
1673 Use the following function to find out whether a constraint
1674 represents an equality. If not, it represents an inequality.
1676 int isl_constraint_is_equality(
1677 __isl_keep isl_constraint *constraint);
1679 The coefficients of the constraints can be inspected using
1680 the following functions.
1682 int isl_constraint_is_lower_bound(
1683 __isl_keep isl_constraint *constraint,
1684 enum isl_dim_type type, unsigned pos);
1685 int isl_constraint_is_upper_bound(
1686 __isl_keep isl_constraint *constraint,
1687 enum isl_dim_type type, unsigned pos);
1688 __isl_give isl_val *isl_constraint_get_constant_val(
1689 __isl_keep isl_constraint *constraint);
1690 __isl_give isl_val *isl_constraint_get_coefficient_val(
1691 __isl_keep isl_constraint *constraint,
1692 enum isl_dim_type type, int pos);
1693 int isl_constraint_involves_dims(
1694 __isl_keep isl_constraint *constraint,
1695 enum isl_dim_type type, unsigned first, unsigned n);
1697 The explicit representations of the existentially quantified
1698 variables can be inspected using the following function.
1699 Note that the user is only allowed to use this function
1700 if the inspected set or map is the result of a call
1701 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1702 The existentially quantified variable is equal to the floor
1703 of the returned affine expression. The affine expression
1704 itself can be inspected using the functions in
1705 L<"Piecewise Quasi Affine Expressions">.
1707 __isl_give isl_aff *isl_constraint_get_div(
1708 __isl_keep isl_constraint *constraint, int pos);
1710 To obtain the constraints of a basic set or map in matrix
1711 form, use the following functions.
1713 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1714 __isl_keep isl_basic_set *bset,
1715 enum isl_dim_type c1, enum isl_dim_type c2,
1716 enum isl_dim_type c3, enum isl_dim_type c4);
1717 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1718 __isl_keep isl_basic_set *bset,
1719 enum isl_dim_type c1, enum isl_dim_type c2,
1720 enum isl_dim_type c3, enum isl_dim_type c4);
1721 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1722 __isl_keep isl_basic_map *bmap,
1723 enum isl_dim_type c1,
1724 enum isl_dim_type c2, enum isl_dim_type c3,
1725 enum isl_dim_type c4, enum isl_dim_type c5);
1726 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1727 __isl_keep isl_basic_map *bmap,
1728 enum isl_dim_type c1,
1729 enum isl_dim_type c2, enum isl_dim_type c3,
1730 enum isl_dim_type c4, enum isl_dim_type c5);
1732 The C<isl_dim_type> arguments dictate the order in which
1733 different kinds of variables appear in the resulting matrix
1734 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1735 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1737 The number of parameters, input, output or set dimensions can
1738 be obtained using the following functions.
1740 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1741 enum isl_dim_type type);
1742 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1743 enum isl_dim_type type);
1744 unsigned isl_set_dim(__isl_keep isl_set *set,
1745 enum isl_dim_type type);
1746 unsigned isl_map_dim(__isl_keep isl_map *map,
1747 enum isl_dim_type type);
1749 To check whether the description of a set or relation depends
1750 on one or more given dimensions, it is not necessary to iterate over all
1751 constraints. Instead the following functions can be used.
1753 int isl_basic_set_involves_dims(
1754 __isl_keep isl_basic_set *bset,
1755 enum isl_dim_type type, unsigned first, unsigned n);
1756 int isl_set_involves_dims(__isl_keep isl_set *set,
1757 enum isl_dim_type type, unsigned first, unsigned n);
1758 int isl_basic_map_involves_dims(
1759 __isl_keep isl_basic_map *bmap,
1760 enum isl_dim_type type, unsigned first, unsigned n);
1761 int isl_map_involves_dims(__isl_keep isl_map *map,
1762 enum isl_dim_type type, unsigned first, unsigned n);
1764 Similarly, the following functions can be used to check whether
1765 a given dimension is involved in any lower or upper bound.
1767 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1768 enum isl_dim_type type, unsigned pos);
1769 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1770 enum isl_dim_type type, unsigned pos);
1772 Note that these functions return true even if there is a bound on
1773 the dimension on only some of the basic sets of C<set>.
1774 To check if they have a bound for all of the basic sets in C<set>,
1775 use the following functions instead.
1777 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1778 enum isl_dim_type type, unsigned pos);
1779 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1780 enum isl_dim_type type, unsigned pos);
1782 The identifiers or names of the domain and range spaces of a set
1783 or relation can be read off or set using the following functions.
1785 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1786 __isl_take isl_basic_set *bset,
1787 __isl_take isl_id *id);
1788 __isl_give isl_set *isl_set_set_tuple_id(
1789 __isl_take isl_set *set, __isl_take isl_id *id);
1790 __isl_give isl_set *isl_set_reset_tuple_id(
1791 __isl_take isl_set *set);
1792 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1793 __isl_give isl_id *isl_set_get_tuple_id(
1794 __isl_keep isl_set *set);
1795 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1796 __isl_take isl_basic_map *bmap,
1797 enum isl_dim_type type, __isl_take isl_id *id);
1798 __isl_give isl_map *isl_map_set_tuple_id(
1799 __isl_take isl_map *map, enum isl_dim_type type,
1800 __isl_take isl_id *id);
1801 __isl_give isl_map *isl_map_reset_tuple_id(
1802 __isl_take isl_map *map, enum isl_dim_type type);
1803 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1804 enum isl_dim_type type);
1805 __isl_give isl_id *isl_map_get_tuple_id(
1806 __isl_keep isl_map *map, enum isl_dim_type type);
1808 const char *isl_basic_set_get_tuple_name(
1809 __isl_keep isl_basic_set *bset);
1810 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1811 __isl_take isl_basic_set *set, const char *s);
1812 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1813 const char *isl_set_get_tuple_name(
1814 __isl_keep isl_set *set);
1815 const char *isl_basic_map_get_tuple_name(
1816 __isl_keep isl_basic_map *bmap,
1817 enum isl_dim_type type);
1818 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1819 __isl_take isl_basic_map *bmap,
1820 enum isl_dim_type type, const char *s);
1821 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1822 enum isl_dim_type type);
1823 const char *isl_map_get_tuple_name(
1824 __isl_keep isl_map *map,
1825 enum isl_dim_type type);
1827 As with C<isl_space_get_tuple_name>, the value returned points to
1828 an internal data structure.
1829 The identifiers, positions or names of individual dimensions can be
1830 read off using the following functions.
1832 __isl_give isl_id *isl_basic_set_get_dim_id(
1833 __isl_keep isl_basic_set *bset,
1834 enum isl_dim_type type, unsigned pos);
1835 __isl_give isl_set *isl_set_set_dim_id(
1836 __isl_take isl_set *set, enum isl_dim_type type,
1837 unsigned pos, __isl_take isl_id *id);
1838 int isl_set_has_dim_id(__isl_keep isl_set *set,
1839 enum isl_dim_type type, unsigned pos);
1840 __isl_give isl_id *isl_set_get_dim_id(
1841 __isl_keep isl_set *set, enum isl_dim_type type,
1843 int isl_basic_map_has_dim_id(
1844 __isl_keep isl_basic_map *bmap,
1845 enum isl_dim_type type, unsigned pos);
1846 __isl_give isl_map *isl_map_set_dim_id(
1847 __isl_take isl_map *map, enum isl_dim_type type,
1848 unsigned pos, __isl_take isl_id *id);
1849 int isl_map_has_dim_id(__isl_keep isl_map *map,
1850 enum isl_dim_type type, unsigned pos);
1851 __isl_give isl_id *isl_map_get_dim_id(
1852 __isl_keep isl_map *map, enum isl_dim_type type,
1855 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1856 enum isl_dim_type type, __isl_keep isl_id *id);
1857 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1858 enum isl_dim_type type, __isl_keep isl_id *id);
1859 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1860 enum isl_dim_type type, const char *name);
1861 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1862 enum isl_dim_type type, const char *name);
1864 const char *isl_constraint_get_dim_name(
1865 __isl_keep isl_constraint *constraint,
1866 enum isl_dim_type type, unsigned pos);
1867 const char *isl_basic_set_get_dim_name(
1868 __isl_keep isl_basic_set *bset,
1869 enum isl_dim_type type, unsigned pos);
1870 int isl_set_has_dim_name(__isl_keep isl_set *set,
1871 enum isl_dim_type type, unsigned pos);
1872 const char *isl_set_get_dim_name(
1873 __isl_keep isl_set *set,
1874 enum isl_dim_type type, unsigned pos);
1875 const char *isl_basic_map_get_dim_name(
1876 __isl_keep isl_basic_map *bmap,
1877 enum isl_dim_type type, unsigned pos);
1878 int isl_map_has_dim_name(__isl_keep isl_map *map,
1879 enum isl_dim_type type, unsigned pos);
1880 const char *isl_map_get_dim_name(
1881 __isl_keep isl_map *map,
1882 enum isl_dim_type type, unsigned pos);
1884 These functions are mostly useful to obtain the identifiers, positions
1885 or names of the parameters. Identifiers of individual dimensions are
1886 essentially only useful for printing. They are ignored by all other
1887 operations and may not be preserved across those operations.
1889 The user pointers on all parameters and tuples can be reset
1890 using the following functions.
1892 #include <isl/set.h>
1893 __isl_give isl_set *isl_set_reset_user(
1894 __isl_take isl_set *set);
1895 #include <isl/map.h>
1896 __isl_give isl_map *isl_map_reset_user(
1897 __isl_take isl_map *map);
1898 #include <isl/union_set.h>
1899 __isl_give isl_union_set *isl_union_set_reset_user(
1900 __isl_take isl_union_set *uset);
1901 #include <isl/union_map.h>
1902 __isl_give isl_union_map *isl_union_map_reset_user(
1903 __isl_take isl_union_map *umap);
1907 =head3 Unary Properties
1913 The following functions test whether the given set or relation
1914 contains any integer points. The ``plain'' variants do not perform
1915 any computations, but simply check if the given set or relation
1916 is already known to be empty.
1918 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1919 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1920 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1921 int isl_set_is_empty(__isl_keep isl_set *set);
1922 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1923 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1924 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1925 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1926 int isl_map_is_empty(__isl_keep isl_map *map);
1927 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1929 =item * Universality
1931 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1932 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1933 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1935 =item * Single-valuedness
1937 int isl_basic_map_is_single_valued(
1938 __isl_keep isl_basic_map *bmap);
1939 int isl_map_plain_is_single_valued(
1940 __isl_keep isl_map *map);
1941 int isl_map_is_single_valued(__isl_keep isl_map *map);
1942 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1946 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1947 int isl_map_is_injective(__isl_keep isl_map *map);
1948 int isl_union_map_plain_is_injective(
1949 __isl_keep isl_union_map *umap);
1950 int isl_union_map_is_injective(
1951 __isl_keep isl_union_map *umap);
1955 int isl_map_is_bijective(__isl_keep isl_map *map);
1956 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1960 __isl_give isl_val *
1961 isl_basic_map_plain_get_val_if_fixed(
1962 __isl_keep isl_basic_map *bmap,
1963 enum isl_dim_type type, unsigned pos);
1964 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
1965 __isl_keep isl_set *set,
1966 enum isl_dim_type type, unsigned pos);
1967 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
1968 __isl_keep isl_map *map,
1969 enum isl_dim_type type, unsigned pos);
1971 If the set or relation obviously lies on a hyperplane where the given dimension
1972 has a fixed value, then return that value.
1973 Otherwise return NaN.
1977 int isl_set_dim_residue_class_val(
1978 __isl_keep isl_set *set,
1979 int pos, __isl_give isl_val **modulo,
1980 __isl_give isl_val **residue);
1982 Check if the values of the given set dimension are equal to a fixed
1983 value modulo some integer value. If so, assign the modulo to C<*modulo>
1984 and the fixed value to C<*residue>. If the given dimension attains only
1985 a single value, then assign C<0> to C<*modulo> and the fixed value to
1987 If the dimension does not attain only a single value and if no modulo
1988 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
1992 To check whether a set is a parameter domain, use this function:
1994 int isl_set_is_params(__isl_keep isl_set *set);
1995 int isl_union_set_is_params(
1996 __isl_keep isl_union_set *uset);
2000 The following functions check whether the space of the given
2001 (basic) set or relation range is a wrapped relation.
2003 #include <isl/space.h>
2004 int isl_space_is_wrapping(
2005 __isl_keep isl_space *space);
2006 int isl_space_domain_is_wrapping(
2007 __isl_keep isl_space *space);
2008 int isl_space_range_is_wrapping(
2009 __isl_keep isl_space *space);
2011 #include <isl/set.h>
2012 int isl_basic_set_is_wrapping(
2013 __isl_keep isl_basic_set *bset);
2014 int isl_set_is_wrapping(__isl_keep isl_set *set);
2016 #include <isl/map.h>
2017 int isl_map_domain_is_wrapping(
2018 __isl_keep isl_map *map);
2019 int isl_map_range_is_wrapping(
2020 __isl_keep isl_map *map);
2022 The input to C<isl_space_is_wrapping> should
2023 be the space of a set, while that of
2024 C<isl_space_domain_is_wrapping> and
2025 C<isl_space_range_is_wrapping> should be the space of a relation.
2027 =item * Internal Product
2029 int isl_basic_map_can_zip(
2030 __isl_keep isl_basic_map *bmap);
2031 int isl_map_can_zip(__isl_keep isl_map *map);
2033 Check whether the product of domain and range of the given relation
2035 i.e., whether both domain and range are nested relations.
2039 int isl_basic_map_can_curry(
2040 __isl_keep isl_basic_map *bmap);
2041 int isl_map_can_curry(__isl_keep isl_map *map);
2043 Check whether the domain of the (basic) relation is a wrapped relation.
2045 int isl_basic_map_can_uncurry(
2046 __isl_keep isl_basic_map *bmap);
2047 int isl_map_can_uncurry(__isl_keep isl_map *map);
2049 Check whether the range of the (basic) relation is a wrapped relation.
2053 =head3 Binary Properties
2059 int isl_basic_set_plain_is_equal(
2060 __isl_keep isl_basic_set *bset1,
2061 __isl_keep isl_basic_set *bset2);
2062 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2063 __isl_keep isl_set *set2);
2064 int isl_set_is_equal(__isl_keep isl_set *set1,
2065 __isl_keep isl_set *set2);
2066 int isl_union_set_is_equal(
2067 __isl_keep isl_union_set *uset1,
2068 __isl_keep isl_union_set *uset2);
2069 int isl_basic_map_is_equal(
2070 __isl_keep isl_basic_map *bmap1,
2071 __isl_keep isl_basic_map *bmap2);
2072 int isl_map_is_equal(__isl_keep isl_map *map1,
2073 __isl_keep isl_map *map2);
2074 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2075 __isl_keep isl_map *map2);
2076 int isl_union_map_is_equal(
2077 __isl_keep isl_union_map *umap1,
2078 __isl_keep isl_union_map *umap2);
2080 =item * Disjointness
2082 int isl_basic_set_is_disjoint(
2083 __isl_keep isl_basic_set *bset1,
2084 __isl_keep isl_basic_set *bset2);
2085 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2086 __isl_keep isl_set *set2);
2087 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2088 __isl_keep isl_set *set2);
2089 int isl_basic_map_is_disjoint(
2090 __isl_keep isl_basic_map *bmap1,
2091 __isl_keep isl_basic_map *bmap2);
2092 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2093 __isl_keep isl_map *map2);
2097 int isl_basic_set_is_subset(
2098 __isl_keep isl_basic_set *bset1,
2099 __isl_keep isl_basic_set *bset2);
2100 int isl_set_is_subset(__isl_keep isl_set *set1,
2101 __isl_keep isl_set *set2);
2102 int isl_set_is_strict_subset(
2103 __isl_keep isl_set *set1,
2104 __isl_keep isl_set *set2);
2105 int isl_union_set_is_subset(
2106 __isl_keep isl_union_set *uset1,
2107 __isl_keep isl_union_set *uset2);
2108 int isl_union_set_is_strict_subset(
2109 __isl_keep isl_union_set *uset1,
2110 __isl_keep isl_union_set *uset2);
2111 int isl_basic_map_is_subset(
2112 __isl_keep isl_basic_map *bmap1,
2113 __isl_keep isl_basic_map *bmap2);
2114 int isl_basic_map_is_strict_subset(
2115 __isl_keep isl_basic_map *bmap1,
2116 __isl_keep isl_basic_map *bmap2);
2117 int isl_map_is_subset(
2118 __isl_keep isl_map *map1,
2119 __isl_keep isl_map *map2);
2120 int isl_map_is_strict_subset(
2121 __isl_keep isl_map *map1,
2122 __isl_keep isl_map *map2);
2123 int isl_union_map_is_subset(
2124 __isl_keep isl_union_map *umap1,
2125 __isl_keep isl_union_map *umap2);
2126 int isl_union_map_is_strict_subset(
2127 __isl_keep isl_union_map *umap1,
2128 __isl_keep isl_union_map *umap2);
2130 Check whether the first argument is a (strict) subset of the
2135 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2136 __isl_keep isl_set *set2);
2138 This function is useful for sorting C<isl_set>s.
2139 The order depends on the internal representation of the inputs.
2140 The order is fixed over different calls to the function (assuming
2141 the internal representation of the inputs has not changed), but may
2142 change over different versions of C<isl>.
2146 =head2 Unary Operations
2152 __isl_give isl_set *isl_set_complement(
2153 __isl_take isl_set *set);
2154 __isl_give isl_map *isl_map_complement(
2155 __isl_take isl_map *map);
2159 __isl_give isl_basic_map *isl_basic_map_reverse(
2160 __isl_take isl_basic_map *bmap);
2161 __isl_give isl_map *isl_map_reverse(
2162 __isl_take isl_map *map);
2163 __isl_give isl_union_map *isl_union_map_reverse(
2164 __isl_take isl_union_map *umap);
2168 #include <isl/local_space.h>
2169 __isl_give isl_local_space *isl_local_space_domain(
2170 __isl_take isl_local_space *ls);
2171 __isl_give isl_local_space *isl_local_space_range(
2172 __isl_take isl_local_space *ls);
2174 #include <isl/set.h>
2175 __isl_give isl_basic_set *isl_basic_set_project_out(
2176 __isl_take isl_basic_set *bset,
2177 enum isl_dim_type type, unsigned first, unsigned n);
2178 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2179 enum isl_dim_type type, unsigned first, unsigned n);
2180 __isl_give isl_basic_set *isl_basic_set_params(
2181 __isl_take isl_basic_set *bset);
2182 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2184 #include <isl/map.h>
2185 __isl_give isl_basic_map *isl_basic_map_project_out(
2186 __isl_take isl_basic_map *bmap,
2187 enum isl_dim_type type, unsigned first, unsigned n);
2188 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2189 enum isl_dim_type type, unsigned first, unsigned n);
2190 __isl_give isl_basic_set *isl_basic_map_domain(
2191 __isl_take isl_basic_map *bmap);
2192 __isl_give isl_basic_set *isl_basic_map_range(
2193 __isl_take isl_basic_map *bmap);
2194 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2195 __isl_give isl_set *isl_map_domain(
2196 __isl_take isl_map *bmap);
2197 __isl_give isl_set *isl_map_range(
2198 __isl_take isl_map *map);
2200 #include <isl/union_set.h>
2201 __isl_give isl_set *isl_union_set_params(
2202 __isl_take isl_union_set *uset);
2204 #include <isl/union_map.h>
2205 __isl_give isl_set *isl_union_map_params(
2206 __isl_take isl_union_map *umap);
2207 __isl_give isl_union_set *isl_union_map_domain(
2208 __isl_take isl_union_map *umap);
2209 __isl_give isl_union_set *isl_union_map_range(
2210 __isl_take isl_union_map *umap);
2212 #include <isl/map.h>
2213 __isl_give isl_basic_map *isl_basic_map_domain_map(
2214 __isl_take isl_basic_map *bmap);
2215 __isl_give isl_basic_map *isl_basic_map_range_map(
2216 __isl_take isl_basic_map *bmap);
2217 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2218 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2220 #include <isl/union_map.h>
2221 __isl_give isl_union_map *isl_union_map_domain_map(
2222 __isl_take isl_union_map *umap);
2223 __isl_give isl_union_map *isl_union_map_range_map(
2224 __isl_take isl_union_map *umap);
2226 The functions above construct a (basic, regular or union) relation
2227 that maps (a wrapped version of) the input relation to its domain or range.
2231 __isl_give isl_basic_set *isl_basic_set_eliminate(
2232 __isl_take isl_basic_set *bset,
2233 enum isl_dim_type type,
2234 unsigned first, unsigned n);
2235 __isl_give isl_set *isl_set_eliminate(
2236 __isl_take isl_set *set, enum isl_dim_type type,
2237 unsigned first, unsigned n);
2238 __isl_give isl_basic_map *isl_basic_map_eliminate(
2239 __isl_take isl_basic_map *bmap,
2240 enum isl_dim_type type,
2241 unsigned first, unsigned n);
2242 __isl_give isl_map *isl_map_eliminate(
2243 __isl_take isl_map *map, enum isl_dim_type type,
2244 unsigned first, unsigned n);
2246 Eliminate the coefficients for the given dimensions from the constraints,
2247 without removing the dimensions.
2249 =item * Constructing a relation from a set
2251 #include <isl/local_space.h>
2252 __isl_give isl_local_space *isl_local_space_from_domain(
2253 __isl_take isl_local_space *ls);
2255 #include <isl/map.h>
2256 __isl_give isl_map *isl_map_from_domain(
2257 __isl_take isl_set *set);
2258 __isl_give isl_map *isl_map_from_range(
2259 __isl_take isl_set *set);
2261 Create a relation with the given set as domain or range.
2262 The range or domain of the created relation is a zero-dimensional
2263 flat anonymous space.
2267 __isl_give isl_basic_set *isl_basic_set_fix_si(
2268 __isl_take isl_basic_set *bset,
2269 enum isl_dim_type type, unsigned pos, int value);
2270 __isl_give isl_basic_set *isl_basic_set_fix_val(
2271 __isl_take isl_basic_set *bset,
2272 enum isl_dim_type type, unsigned pos,
2273 __isl_take isl_val *v);
2274 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2275 enum isl_dim_type type, unsigned pos, int value);
2276 __isl_give isl_set *isl_set_fix_val(
2277 __isl_take isl_set *set,
2278 enum isl_dim_type type, unsigned pos,
2279 __isl_take isl_val *v);
2280 __isl_give isl_basic_map *isl_basic_map_fix_si(
2281 __isl_take isl_basic_map *bmap,
2282 enum isl_dim_type type, unsigned pos, int value);
2283 __isl_give isl_basic_map *isl_basic_map_fix_val(
2284 __isl_take isl_basic_map *bmap,
2285 enum isl_dim_type type, unsigned pos,
2286 __isl_take isl_val *v);
2287 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2288 enum isl_dim_type type, unsigned pos, int value);
2289 __isl_give isl_map *isl_map_fix_val(
2290 __isl_take isl_map *map,
2291 enum isl_dim_type type, unsigned pos,
2292 __isl_take isl_val *v);
2294 Intersect the set or relation with the hyperplane where the given
2295 dimension has the fixed given value.
2297 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2298 __isl_take isl_basic_map *bmap,
2299 enum isl_dim_type type, unsigned pos, int value);
2300 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2301 __isl_take isl_basic_map *bmap,
2302 enum isl_dim_type type, unsigned pos, int value);
2303 __isl_give isl_set *isl_set_lower_bound_si(
2304 __isl_take isl_set *set,
2305 enum isl_dim_type type, unsigned pos, int value);
2306 __isl_give isl_set *isl_set_lower_bound_val(
2307 __isl_take isl_set *set,
2308 enum isl_dim_type type, unsigned pos,
2309 __isl_take isl_val *value);
2310 __isl_give isl_map *isl_map_lower_bound_si(
2311 __isl_take isl_map *map,
2312 enum isl_dim_type type, unsigned pos, int value);
2313 __isl_give isl_set *isl_set_upper_bound_si(
2314 __isl_take isl_set *set,
2315 enum isl_dim_type type, unsigned pos, int value);
2316 __isl_give isl_set *isl_set_upper_bound_val(
2317 __isl_take isl_set *set,
2318 enum isl_dim_type type, unsigned pos,
2319 __isl_take isl_val *value);
2320 __isl_give isl_map *isl_map_upper_bound_si(
2321 __isl_take isl_map *map,
2322 enum isl_dim_type type, unsigned pos, int value);
2324 Intersect the set or relation with the half-space where the given
2325 dimension has a value bounded by the fixed given integer value.
2327 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2328 enum isl_dim_type type1, int pos1,
2329 enum isl_dim_type type2, int pos2);
2330 __isl_give isl_basic_map *isl_basic_map_equate(
2331 __isl_take isl_basic_map *bmap,
2332 enum isl_dim_type type1, int pos1,
2333 enum isl_dim_type type2, int pos2);
2334 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2335 enum isl_dim_type type1, int pos1,
2336 enum isl_dim_type type2, int pos2);
2338 Intersect the set or relation with the hyperplane where the given
2339 dimensions are equal to each other.
2341 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2342 enum isl_dim_type type1, int pos1,
2343 enum isl_dim_type type2, int pos2);
2345 Intersect the relation with the hyperplane where the given
2346 dimensions have opposite values.
2348 __isl_give isl_map *isl_map_order_le(
2349 __isl_take isl_map *map,
2350 enum isl_dim_type type1, int pos1,
2351 enum isl_dim_type type2, int pos2);
2352 __isl_give isl_basic_map *isl_basic_map_order_ge(
2353 __isl_take isl_basic_map *bmap,
2354 enum isl_dim_type type1, int pos1,
2355 enum isl_dim_type type2, int pos2);
2356 __isl_give isl_map *isl_map_order_ge(
2357 __isl_take isl_map *map,
2358 enum isl_dim_type type1, int pos1,
2359 enum isl_dim_type type2, int pos2);
2360 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2361 enum isl_dim_type type1, int pos1,
2362 enum isl_dim_type type2, int pos2);
2363 __isl_give isl_basic_map *isl_basic_map_order_gt(
2364 __isl_take isl_basic_map *bmap,
2365 enum isl_dim_type type1, int pos1,
2366 enum isl_dim_type type2, int pos2);
2367 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2368 enum isl_dim_type type1, int pos1,
2369 enum isl_dim_type type2, int pos2);
2371 Intersect the relation with the half-space where the given
2372 dimensions satisfy the given ordering.
2376 __isl_give isl_map *isl_set_identity(
2377 __isl_take isl_set *set);
2378 __isl_give isl_union_map *isl_union_set_identity(
2379 __isl_take isl_union_set *uset);
2381 Construct an identity relation on the given (union) set.
2385 __isl_give isl_basic_set *isl_basic_map_deltas(
2386 __isl_take isl_basic_map *bmap);
2387 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2388 __isl_give isl_union_set *isl_union_map_deltas(
2389 __isl_take isl_union_map *umap);
2391 These functions return a (basic) set containing the differences
2392 between image elements and corresponding domain elements in the input.
2394 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2395 __isl_take isl_basic_map *bmap);
2396 __isl_give isl_map *isl_map_deltas_map(
2397 __isl_take isl_map *map);
2398 __isl_give isl_union_map *isl_union_map_deltas_map(
2399 __isl_take isl_union_map *umap);
2401 The functions above construct a (basic, regular or union) relation
2402 that maps (a wrapped version of) the input relation to its delta set.
2406 Simplify the representation of a set or relation by trying
2407 to combine pairs of basic sets or relations into a single
2408 basic set or relation.
2410 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2411 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2412 __isl_give isl_union_set *isl_union_set_coalesce(
2413 __isl_take isl_union_set *uset);
2414 __isl_give isl_union_map *isl_union_map_coalesce(
2415 __isl_take isl_union_map *umap);
2417 One of the methods for combining pairs of basic sets or relations
2418 can result in coefficients that are much larger than those that appear
2419 in the constraints of the input. By default, the coefficients are
2420 not allowed to grow larger, but this can be changed by unsetting
2421 the following option.
2423 int isl_options_set_coalesce_bounded_wrapping(
2424 isl_ctx *ctx, int val);
2425 int isl_options_get_coalesce_bounded_wrapping(
2428 =item * Detecting equalities
2430 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2431 __isl_take isl_basic_set *bset);
2432 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2433 __isl_take isl_basic_map *bmap);
2434 __isl_give isl_set *isl_set_detect_equalities(
2435 __isl_take isl_set *set);
2436 __isl_give isl_map *isl_map_detect_equalities(
2437 __isl_take isl_map *map);
2438 __isl_give isl_union_set *isl_union_set_detect_equalities(
2439 __isl_take isl_union_set *uset);
2440 __isl_give isl_union_map *isl_union_map_detect_equalities(
2441 __isl_take isl_union_map *umap);
2443 Simplify the representation of a set or relation by detecting implicit
2446 =item * Removing redundant constraints
2448 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2449 __isl_take isl_basic_set *bset);
2450 __isl_give isl_set *isl_set_remove_redundancies(
2451 __isl_take isl_set *set);
2452 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2453 __isl_take isl_basic_map *bmap);
2454 __isl_give isl_map *isl_map_remove_redundancies(
2455 __isl_take isl_map *map);
2459 __isl_give isl_basic_set *isl_set_convex_hull(
2460 __isl_take isl_set *set);
2461 __isl_give isl_basic_map *isl_map_convex_hull(
2462 __isl_take isl_map *map);
2464 If the input set or relation has any existentially quantified
2465 variables, then the result of these operations is currently undefined.
2469 __isl_give isl_basic_set *
2470 isl_set_unshifted_simple_hull(
2471 __isl_take isl_set *set);
2472 __isl_give isl_basic_map *
2473 isl_map_unshifted_simple_hull(
2474 __isl_take isl_map *map);
2475 __isl_give isl_basic_set *isl_set_simple_hull(
2476 __isl_take isl_set *set);
2477 __isl_give isl_basic_map *isl_map_simple_hull(
2478 __isl_take isl_map *map);
2479 __isl_give isl_union_map *isl_union_map_simple_hull(
2480 __isl_take isl_union_map *umap);
2482 These functions compute a single basic set or relation
2483 that contains the whole input set or relation.
2484 In particular, the output is described by translates
2485 of the constraints describing the basic sets or relations in the input.
2486 In case of C<isl_set_unshifted_simple_hull>, only the original
2487 constraints are used, without any translation.
2491 (See \autoref{s:simple hull}.)
2497 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2498 __isl_take isl_basic_set *bset);
2499 __isl_give isl_basic_set *isl_set_affine_hull(
2500 __isl_take isl_set *set);
2501 __isl_give isl_union_set *isl_union_set_affine_hull(
2502 __isl_take isl_union_set *uset);
2503 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2504 __isl_take isl_basic_map *bmap);
2505 __isl_give isl_basic_map *isl_map_affine_hull(
2506 __isl_take isl_map *map);
2507 __isl_give isl_union_map *isl_union_map_affine_hull(
2508 __isl_take isl_union_map *umap);
2510 In case of union sets and relations, the affine hull is computed
2513 =item * Polyhedral hull
2515 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2516 __isl_take isl_set *set);
2517 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2518 __isl_take isl_map *map);
2519 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2520 __isl_take isl_union_set *uset);
2521 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2522 __isl_take isl_union_map *umap);
2524 These functions compute a single basic set or relation
2525 not involving any existentially quantified variables
2526 that contains the whole input set or relation.
2527 In case of union sets and relations, the polyhedral hull is computed
2530 =item * Other approximations
2532 __isl_give isl_basic_set *
2533 isl_basic_set_drop_constraints_involving_dims(
2534 __isl_take isl_basic_set *bset,
2535 enum isl_dim_type type,
2536 unsigned first, unsigned n);
2537 __isl_give isl_basic_map *
2538 isl_basic_map_drop_constraints_involving_dims(
2539 __isl_take isl_basic_map *bmap,
2540 enum isl_dim_type type,
2541 unsigned first, unsigned n);
2542 __isl_give isl_basic_set *
2543 isl_basic_set_drop_constraints_not_involving_dims(
2544 __isl_take isl_basic_set *bset,
2545 enum isl_dim_type type,
2546 unsigned first, unsigned n);
2547 __isl_give isl_set *
2548 isl_set_drop_constraints_involving_dims(
2549 __isl_take isl_set *set,
2550 enum isl_dim_type type,
2551 unsigned first, unsigned n);
2552 __isl_give isl_map *
2553 isl_map_drop_constraints_involving_dims(
2554 __isl_take isl_map *map,
2555 enum isl_dim_type type,
2556 unsigned first, unsigned n);
2558 These functions drop any constraints (not) involving the specified dimensions.
2559 Note that the result depends on the representation of the input.
2563 __isl_give isl_basic_set *isl_basic_set_sample(
2564 __isl_take isl_basic_set *bset);
2565 __isl_give isl_basic_set *isl_set_sample(
2566 __isl_take isl_set *set);
2567 __isl_give isl_basic_map *isl_basic_map_sample(
2568 __isl_take isl_basic_map *bmap);
2569 __isl_give isl_basic_map *isl_map_sample(
2570 __isl_take isl_map *map);
2572 If the input (basic) set or relation is non-empty, then return
2573 a singleton subset of the input. Otherwise, return an empty set.
2575 =item * Optimization
2577 #include <isl/ilp.h>
2578 __isl_give isl_val *isl_basic_set_max_val(
2579 __isl_keep isl_basic_set *bset,
2580 __isl_keep isl_aff *obj);
2581 __isl_give isl_val *isl_set_min_val(
2582 __isl_keep isl_set *set,
2583 __isl_keep isl_aff *obj);
2584 __isl_give isl_val *isl_set_max_val(
2585 __isl_keep isl_set *set,
2586 __isl_keep isl_aff *obj);
2588 Compute the minimum or maximum of the integer affine expression C<obj>
2589 over the points in C<set>, returning the result in C<opt>.
2590 The result is C<NULL> in case of an error, the optimal value in case
2591 there is one, negative infinity or infinity if the problem is unbounded and
2592 NaN if the problem is empty.
2594 =item * Parametric optimization
2596 __isl_give isl_pw_aff *isl_set_dim_min(
2597 __isl_take isl_set *set, int pos);
2598 __isl_give isl_pw_aff *isl_set_dim_max(
2599 __isl_take isl_set *set, int pos);
2600 __isl_give isl_pw_aff *isl_map_dim_max(
2601 __isl_take isl_map *map, int pos);
2603 Compute the minimum or maximum of the given set or output dimension
2604 as a function of the parameters (and input dimensions), but independently
2605 of the other set or output dimensions.
2606 For lexicographic optimization, see L<"Lexicographic Optimization">.
2610 The following functions compute either the set of (rational) coefficient
2611 values of valid constraints for the given set or the set of (rational)
2612 values satisfying the constraints with coefficients from the given set.
2613 Internally, these two sets of functions perform essentially the
2614 same operations, except that the set of coefficients is assumed to
2615 be a cone, while the set of values may be any polyhedron.
2616 The current implementation is based on the Farkas lemma and
2617 Fourier-Motzkin elimination, but this may change or be made optional
2618 in future. In particular, future implementations may use different
2619 dualization algorithms or skip the elimination step.
2621 __isl_give isl_basic_set *isl_basic_set_coefficients(
2622 __isl_take isl_basic_set *bset);
2623 __isl_give isl_basic_set *isl_set_coefficients(
2624 __isl_take isl_set *set);
2625 __isl_give isl_union_set *isl_union_set_coefficients(
2626 __isl_take isl_union_set *bset);
2627 __isl_give isl_basic_set *isl_basic_set_solutions(
2628 __isl_take isl_basic_set *bset);
2629 __isl_give isl_basic_set *isl_set_solutions(
2630 __isl_take isl_set *set);
2631 __isl_give isl_union_set *isl_union_set_solutions(
2632 __isl_take isl_union_set *bset);
2636 __isl_give isl_map *isl_map_fixed_power_val(
2637 __isl_take isl_map *map,
2638 __isl_take isl_val *exp);
2639 __isl_give isl_union_map *
2640 isl_union_map_fixed_power_val(
2641 __isl_take isl_union_map *umap,
2642 __isl_take isl_val *exp);
2644 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2645 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2646 of C<map> is computed.
2648 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2650 __isl_give isl_union_map *isl_union_map_power(
2651 __isl_take isl_union_map *umap, int *exact);
2653 Compute a parametric representation for all positive powers I<k> of C<map>.
2654 The result maps I<k> to a nested relation corresponding to the
2655 I<k>th power of C<map>.
2656 The result may be an overapproximation. If the result is known to be exact,
2657 then C<*exact> is set to C<1>.
2659 =item * Transitive closure
2661 __isl_give isl_map *isl_map_transitive_closure(
2662 __isl_take isl_map *map, int *exact);
2663 __isl_give isl_union_map *isl_union_map_transitive_closure(
2664 __isl_take isl_union_map *umap, int *exact);
2666 Compute the transitive closure of C<map>.
2667 The result may be an overapproximation. If the result is known to be exact,
2668 then C<*exact> is set to C<1>.
2670 =item * Reaching path lengths
2672 __isl_give isl_map *isl_map_reaching_path_lengths(
2673 __isl_take isl_map *map, int *exact);
2675 Compute a relation that maps each element in the range of C<map>
2676 to the lengths of all paths composed of edges in C<map> that
2677 end up in the given element.
2678 The result may be an overapproximation. If the result is known to be exact,
2679 then C<*exact> is set to C<1>.
2680 To compute the I<maximal> path length, the resulting relation
2681 should be postprocessed by C<isl_map_lexmax>.
2682 In particular, if the input relation is a dependence relation
2683 (mapping sources to sinks), then the maximal path length corresponds
2684 to the free schedule.
2685 Note, however, that C<isl_map_lexmax> expects the maximum to be
2686 finite, so if the path lengths are unbounded (possibly due to
2687 the overapproximation), then you will get an error message.
2691 #include <isl/space.h>
2692 __isl_give isl_space *isl_space_wrap(
2693 __isl_take isl_space *space);
2694 __isl_give isl_space *isl_space_unwrap(
2695 __isl_take isl_space *space);
2697 #include <isl/set.h>
2698 __isl_give isl_basic_map *isl_basic_set_unwrap(
2699 __isl_take isl_basic_set *bset);
2700 __isl_give isl_map *isl_set_unwrap(
2701 __isl_take isl_set *set);
2703 #include <isl/map.h>
2704 __isl_give isl_basic_set *isl_basic_map_wrap(
2705 __isl_take isl_basic_map *bmap);
2706 __isl_give isl_set *isl_map_wrap(
2707 __isl_take isl_map *map);
2709 #include <isl/union_set.h>
2710 __isl_give isl_union_map *isl_union_set_unwrap(
2711 __isl_take isl_union_set *uset);
2713 #include <isl/union_map.h>
2714 __isl_give isl_union_set *isl_union_map_wrap(
2715 __isl_take isl_union_map *umap);
2717 The input to C<isl_space_unwrap> should
2718 be the space of a set, while that of
2719 C<isl_space_wrap> should be the space of a relation.
2720 Conversely, the output of C<isl_space_unwrap> is the space
2721 of a relation, while that of C<isl_space_wrap> is the space of a set.
2725 Remove any internal structure of domain (and range) of the given
2726 set or relation. If there is any such internal structure in the input,
2727 then the name of the space is also removed.
2729 #include <isl/local_space.h>
2730 __isl_give isl_local_space *
2731 isl_local_space_flatten_domain(
2732 __isl_take isl_local_space *ls);
2733 __isl_give isl_local_space *
2734 isl_local_space_flatten_range(
2735 __isl_take isl_local_space *ls);
2737 #include <isl/set.h>
2738 __isl_give isl_basic_set *isl_basic_set_flatten(
2739 __isl_take isl_basic_set *bset);
2740 __isl_give isl_set *isl_set_flatten(
2741 __isl_take isl_set *set);
2743 #include <isl/map.h>
2744 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2745 __isl_take isl_basic_map *bmap);
2746 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2747 __isl_take isl_basic_map *bmap);
2748 __isl_give isl_map *isl_map_flatten_range(
2749 __isl_take isl_map *map);
2750 __isl_give isl_map *isl_map_flatten_domain(
2751 __isl_take isl_map *map);
2752 __isl_give isl_basic_map *isl_basic_map_flatten(
2753 __isl_take isl_basic_map *bmap);
2754 __isl_give isl_map *isl_map_flatten(
2755 __isl_take isl_map *map);
2757 #include <isl/map.h>
2758 __isl_give isl_map *isl_set_flatten_map(
2759 __isl_take isl_set *set);
2761 The function above constructs a relation
2762 that maps the input set to a flattened version of the set.
2766 Lift the input set to a space with extra dimensions corresponding
2767 to the existentially quantified variables in the input.
2768 In particular, the result lives in a wrapped map where the domain
2769 is the original space and the range corresponds to the original
2770 existentially quantified variables.
2772 __isl_give isl_basic_set *isl_basic_set_lift(
2773 __isl_take isl_basic_set *bset);
2774 __isl_give isl_set *isl_set_lift(
2775 __isl_take isl_set *set);
2776 __isl_give isl_union_set *isl_union_set_lift(
2777 __isl_take isl_union_set *uset);
2779 Given a local space that contains the existentially quantified
2780 variables of a set, a basic relation that, when applied to
2781 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2782 can be constructed using the following function.
2784 #include <isl/local_space.h>
2785 __isl_give isl_basic_map *isl_local_space_lifting(
2786 __isl_take isl_local_space *ls);
2788 =item * Internal Product
2790 __isl_give isl_basic_map *isl_basic_map_zip(
2791 __isl_take isl_basic_map *bmap);
2792 __isl_give isl_map *isl_map_zip(
2793 __isl_take isl_map *map);
2794 __isl_give isl_union_map *isl_union_map_zip(
2795 __isl_take isl_union_map *umap);
2797 Given a relation with nested relations for domain and range,
2798 interchange the range of the domain with the domain of the range.
2802 __isl_give isl_basic_map *isl_basic_map_curry(
2803 __isl_take isl_basic_map *bmap);
2804 __isl_give isl_basic_map *isl_basic_map_uncurry(
2805 __isl_take isl_basic_map *bmap);
2806 __isl_give isl_map *isl_map_curry(
2807 __isl_take isl_map *map);
2808 __isl_give isl_map *isl_map_uncurry(
2809 __isl_take isl_map *map);
2810 __isl_give isl_union_map *isl_union_map_curry(
2811 __isl_take isl_union_map *umap);
2812 __isl_give isl_union_map *isl_union_map_uncurry(
2813 __isl_take isl_union_map *umap);
2815 Given a relation with a nested relation for domain,
2816 the C<curry> functions
2817 move the range of the nested relation out of the domain
2818 and use it as the domain of a nested relation in the range,
2819 with the original range as range of this nested relation.
2820 The C<uncurry> functions perform the inverse operation.
2822 =item * Aligning parameters
2824 __isl_give isl_basic_set *isl_basic_set_align_params(
2825 __isl_take isl_basic_set *bset,
2826 __isl_take isl_space *model);
2827 __isl_give isl_set *isl_set_align_params(
2828 __isl_take isl_set *set,
2829 __isl_take isl_space *model);
2830 __isl_give isl_basic_map *isl_basic_map_align_params(
2831 __isl_take isl_basic_map *bmap,
2832 __isl_take isl_space *model);
2833 __isl_give isl_map *isl_map_align_params(
2834 __isl_take isl_map *map,
2835 __isl_take isl_space *model);
2837 Change the order of the parameters of the given set or relation
2838 such that the first parameters match those of C<model>.
2839 This may involve the introduction of extra parameters.
2840 All parameters need to be named.
2842 =item * Dimension manipulation
2844 #include <isl/local_space.h>
2845 __isl_give isl_local_space *isl_local_space_add_dims(
2846 __isl_take isl_local_space *ls,
2847 enum isl_dim_type type, unsigned n);
2848 __isl_give isl_local_space *isl_local_space_insert_dims(
2849 __isl_take isl_local_space *ls,
2850 enum isl_dim_type type, unsigned first, unsigned n);
2851 __isl_give isl_local_space *isl_local_space_drop_dims(
2852 __isl_take isl_local_space *ls,
2853 enum isl_dim_type type, unsigned first, unsigned n);
2855 #include <isl/set.h>
2856 __isl_give isl_basic_set *isl_basic_set_add_dims(
2857 __isl_take isl_basic_set *bset,
2858 enum isl_dim_type type, unsigned n);
2859 __isl_give isl_set *isl_set_add_dims(
2860 __isl_take isl_set *set,
2861 enum isl_dim_type type, unsigned n);
2862 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2863 __isl_take isl_basic_set *bset,
2864 enum isl_dim_type type, unsigned pos,
2866 __isl_give isl_set *isl_set_insert_dims(
2867 __isl_take isl_set *set,
2868 enum isl_dim_type type, unsigned pos, unsigned n);
2869 __isl_give isl_basic_set *isl_basic_set_move_dims(
2870 __isl_take isl_basic_set *bset,
2871 enum isl_dim_type dst_type, unsigned dst_pos,
2872 enum isl_dim_type src_type, unsigned src_pos,
2874 __isl_give isl_set *isl_set_move_dims(
2875 __isl_take isl_set *set,
2876 enum isl_dim_type dst_type, unsigned dst_pos,
2877 enum isl_dim_type src_type, unsigned src_pos,
2880 #include <isl/map.h>
2881 __isl_give isl_map *isl_map_add_dims(
2882 __isl_take isl_map *map,
2883 enum isl_dim_type type, unsigned n);
2884 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2885 __isl_take isl_basic_map *bmap,
2886 enum isl_dim_type type, unsigned pos,
2888 __isl_give isl_map *isl_map_insert_dims(
2889 __isl_take isl_map *map,
2890 enum isl_dim_type type, unsigned pos, unsigned n);
2891 __isl_give isl_basic_map *isl_basic_map_move_dims(
2892 __isl_take isl_basic_map *bmap,
2893 enum isl_dim_type dst_type, unsigned dst_pos,
2894 enum isl_dim_type src_type, unsigned src_pos,
2896 __isl_give isl_map *isl_map_move_dims(
2897 __isl_take isl_map *map,
2898 enum isl_dim_type dst_type, unsigned dst_pos,
2899 enum isl_dim_type src_type, unsigned src_pos,
2902 It is usually not advisable to directly change the (input or output)
2903 space of a set or a relation as this removes the name and the internal
2904 structure of the space. However, the above functions can be useful
2905 to add new parameters, assuming
2906 C<isl_set_align_params> and C<isl_map_align_params>
2911 =head2 Binary Operations
2913 The two arguments of a binary operation not only need to live
2914 in the same C<isl_ctx>, they currently also need to have
2915 the same (number of) parameters.
2917 =head3 Basic Operations
2921 =item * Intersection
2923 #include <isl/local_space.h>
2924 __isl_give isl_local_space *isl_local_space_intersect(
2925 __isl_take isl_local_space *ls1,
2926 __isl_take isl_local_space *ls2);
2928 #include <isl/set.h>
2929 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2930 __isl_take isl_basic_set *bset1,
2931 __isl_take isl_basic_set *bset2);
2932 __isl_give isl_basic_set *isl_basic_set_intersect(
2933 __isl_take isl_basic_set *bset1,
2934 __isl_take isl_basic_set *bset2);
2935 __isl_give isl_set *isl_set_intersect_params(
2936 __isl_take isl_set *set,
2937 __isl_take isl_set *params);
2938 __isl_give isl_set *isl_set_intersect(
2939 __isl_take isl_set *set1,
2940 __isl_take isl_set *set2);
2942 #include <isl/map.h>
2943 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2944 __isl_take isl_basic_map *bmap,
2945 __isl_take isl_basic_set *bset);
2946 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2947 __isl_take isl_basic_map *bmap,
2948 __isl_take isl_basic_set *bset);
2949 __isl_give isl_basic_map *isl_basic_map_intersect(
2950 __isl_take isl_basic_map *bmap1,
2951 __isl_take isl_basic_map *bmap2);
2952 __isl_give isl_map *isl_map_intersect_params(
2953 __isl_take isl_map *map,
2954 __isl_take isl_set *params);
2955 __isl_give isl_map *isl_map_intersect_domain(
2956 __isl_take isl_map *map,
2957 __isl_take isl_set *set);
2958 __isl_give isl_map *isl_map_intersect_range(
2959 __isl_take isl_map *map,
2960 __isl_take isl_set *set);
2961 __isl_give isl_map *isl_map_intersect(
2962 __isl_take isl_map *map1,
2963 __isl_take isl_map *map2);
2965 #include <isl/union_set.h>
2966 __isl_give isl_union_set *isl_union_set_intersect_params(
2967 __isl_take isl_union_set *uset,
2968 __isl_take isl_set *set);
2969 __isl_give isl_union_set *isl_union_set_intersect(
2970 __isl_take isl_union_set *uset1,
2971 __isl_take isl_union_set *uset2);
2973 #include <isl/union_map.h>
2974 __isl_give isl_union_map *isl_union_map_intersect_params(
2975 __isl_take isl_union_map *umap,
2976 __isl_take isl_set *set);
2977 __isl_give isl_union_map *isl_union_map_intersect_domain(
2978 __isl_take isl_union_map *umap,
2979 __isl_take isl_union_set *uset);
2980 __isl_give isl_union_map *isl_union_map_intersect_range(
2981 __isl_take isl_union_map *umap,
2982 __isl_take isl_union_set *uset);
2983 __isl_give isl_union_map *isl_union_map_intersect(
2984 __isl_take isl_union_map *umap1,
2985 __isl_take isl_union_map *umap2);
2987 The second argument to the C<_params> functions needs to be
2988 a parametric (basic) set. For the other functions, a parametric set
2989 for either argument is only allowed if the other argument is
2990 a parametric set as well.
2994 __isl_give isl_set *isl_basic_set_union(
2995 __isl_take isl_basic_set *bset1,
2996 __isl_take isl_basic_set *bset2);
2997 __isl_give isl_map *isl_basic_map_union(
2998 __isl_take isl_basic_map *bmap1,
2999 __isl_take isl_basic_map *bmap2);
3000 __isl_give isl_set *isl_set_union(
3001 __isl_take isl_set *set1,
3002 __isl_take isl_set *set2);
3003 __isl_give isl_map *isl_map_union(
3004 __isl_take isl_map *map1,
3005 __isl_take isl_map *map2);
3006 __isl_give isl_union_set *isl_union_set_union(
3007 __isl_take isl_union_set *uset1,
3008 __isl_take isl_union_set *uset2);
3009 __isl_give isl_union_map *isl_union_map_union(
3010 __isl_take isl_union_map *umap1,
3011 __isl_take isl_union_map *umap2);
3013 =item * Set difference
3015 __isl_give isl_set *isl_set_subtract(
3016 __isl_take isl_set *set1,
3017 __isl_take isl_set *set2);
3018 __isl_give isl_map *isl_map_subtract(
3019 __isl_take isl_map *map1,
3020 __isl_take isl_map *map2);
3021 __isl_give isl_map *isl_map_subtract_domain(
3022 __isl_take isl_map *map,
3023 __isl_take isl_set *dom);
3024 __isl_give isl_map *isl_map_subtract_range(
3025 __isl_take isl_map *map,
3026 __isl_take isl_set *dom);
3027 __isl_give isl_union_set *isl_union_set_subtract(
3028 __isl_take isl_union_set *uset1,
3029 __isl_take isl_union_set *uset2);
3030 __isl_give isl_union_map *isl_union_map_subtract(
3031 __isl_take isl_union_map *umap1,
3032 __isl_take isl_union_map *umap2);
3033 __isl_give isl_union_map *isl_union_map_subtract_domain(
3034 __isl_take isl_union_map *umap,
3035 __isl_take isl_union_set *dom);
3036 __isl_give isl_union_map *isl_union_map_subtract_range(
3037 __isl_take isl_union_map *umap,
3038 __isl_take isl_union_set *dom);
3042 __isl_give isl_basic_set *isl_basic_set_apply(
3043 __isl_take isl_basic_set *bset,
3044 __isl_take isl_basic_map *bmap);
3045 __isl_give isl_set *isl_set_apply(
3046 __isl_take isl_set *set,
3047 __isl_take isl_map *map);
3048 __isl_give isl_union_set *isl_union_set_apply(
3049 __isl_take isl_union_set *uset,
3050 __isl_take isl_union_map *umap);
3051 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3052 __isl_take isl_basic_map *bmap1,
3053 __isl_take isl_basic_map *bmap2);
3054 __isl_give isl_basic_map *isl_basic_map_apply_range(
3055 __isl_take isl_basic_map *bmap1,
3056 __isl_take isl_basic_map *bmap2);
3057 __isl_give isl_map *isl_map_apply_domain(
3058 __isl_take isl_map *map1,
3059 __isl_take isl_map *map2);
3060 __isl_give isl_union_map *isl_union_map_apply_domain(
3061 __isl_take isl_union_map *umap1,
3062 __isl_take isl_union_map *umap2);
3063 __isl_give isl_map *isl_map_apply_range(
3064 __isl_take isl_map *map1,
3065 __isl_take isl_map *map2);
3066 __isl_give isl_union_map *isl_union_map_apply_range(
3067 __isl_take isl_union_map *umap1,
3068 __isl_take isl_union_map *umap2);
3072 #include <isl/set.h>
3073 __isl_give isl_basic_set *
3074 isl_basic_set_preimage_multi_aff(
3075 __isl_take isl_basic_set *bset,
3076 __isl_take isl_multi_aff *ma);
3077 __isl_give isl_set *isl_set_preimage_multi_aff(
3078 __isl_take isl_set *set,
3079 __isl_take isl_multi_aff *ma);
3080 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3081 __isl_take isl_set *set,
3082 __isl_take isl_pw_multi_aff *pma);
3083 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
3084 __isl_take isl_set *set,
3085 __isl_take isl_multi_pw_aff *mpa);
3087 #include <isl/union_set.h>
3088 __isl_give isl_union_set *
3089 isl_union_set_preimage_multi_aff(
3090 __isl_take isl_union_set *uset,
3091 __isl_take isl_multi_aff *ma);
3092 __isl_give isl_union_set *
3093 isl_union_set_preimage_pw_multi_aff(
3094 __isl_take isl_union_set *uset,
3095 __isl_take isl_pw_multi_aff *pma);
3096 __isl_give isl_union_set *
3097 isl_union_set_preimage_union_pw_multi_aff(
3098 __isl_take isl_union_set *uset,
3099 __isl_take isl_union_pw_multi_aff *upma);
3101 #include <isl/map.h>
3102 __isl_give isl_basic_map *
3103 isl_basic_map_preimage_domain_multi_aff(
3104 __isl_take isl_basic_map *bmap,
3105 __isl_take isl_multi_aff *ma);
3106 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3107 __isl_take isl_map *map,
3108 __isl_take isl_multi_aff *ma);
3109 __isl_give isl_map *isl_map_preimage_range_multi_aff(
3110 __isl_take isl_map *map,
3111 __isl_take isl_multi_aff *ma);
3112 __isl_give isl_map *
3113 isl_map_preimage_domain_pw_multi_aff(
3114 __isl_take isl_map *map,
3115 __isl_take isl_pw_multi_aff *pma);
3116 __isl_give isl_map *
3117 isl_map_preimage_range_pw_multi_aff(
3118 __isl_take isl_map *map,
3119 __isl_take isl_pw_multi_aff *pma);
3120 __isl_give isl_map *
3121 isl_map_preimage_domain_multi_pw_aff(
3122 __isl_take isl_map *map,
3123 __isl_take isl_multi_pw_aff *mpa);
3124 __isl_give isl_basic_map *
3125 isl_basic_map_preimage_range_multi_aff(
3126 __isl_take isl_basic_map *bmap,
3127 __isl_take isl_multi_aff *ma);
3129 #include <isl/union_map.h>
3130 __isl_give isl_union_map *
3131 isl_union_map_preimage_domain_multi_aff(
3132 __isl_take isl_union_map *umap,
3133 __isl_take isl_multi_aff *ma);
3134 __isl_give isl_union_map *
3135 isl_union_map_preimage_range_multi_aff(
3136 __isl_take isl_union_map *umap,
3137 __isl_take isl_multi_aff *ma);
3138 __isl_give isl_union_map *
3139 isl_union_map_preimage_domain_pw_multi_aff(
3140 __isl_take isl_union_map *umap,
3141 __isl_take isl_pw_multi_aff *pma);
3142 __isl_give isl_union_map *
3143 isl_union_map_preimage_range_pw_multi_aff(
3144 __isl_take isl_union_map *umap,
3145 __isl_take isl_pw_multi_aff *pma);
3146 __isl_give isl_union_map *
3147 isl_union_map_preimage_domain_union_pw_multi_aff(
3148 __isl_take isl_union_map *umap,
3149 __isl_take isl_union_pw_multi_aff *upma);
3150 __isl_give isl_union_map *
3151 isl_union_map_preimage_range_union_pw_multi_aff(
3152 __isl_take isl_union_map *umap,
3153 __isl_take isl_union_pw_multi_aff *upma);
3155 These functions compute the preimage of the given set or map domain/range under
3156 the given function. In other words, the expression is plugged
3157 into the set description or into the domain/range of the map.
3158 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3159 L</"Piecewise Multiple Quasi Affine Expressions">.
3161 =item * Cartesian Product
3163 #include <isl/space.h>
3164 __isl_give isl_space *isl_space_product(
3165 __isl_take isl_space *space1,
3166 __isl_take isl_space *space2);
3167 __isl_give isl_space *isl_space_domain_product(
3168 __isl_take isl_space *space1,
3169 __isl_take isl_space *space2);
3170 __isl_give isl_space *isl_space_range_product(
3171 __isl_take isl_space *space1,
3172 __isl_take isl_space *space2);
3175 C<isl_space_product>, C<isl_space_domain_product>
3176 and C<isl_space_range_product> take pairs or relation spaces and
3177 produce a single relations space, where either the domain, the range
3178 or both domain and range are wrapped spaces of relations between
3179 the domains and/or ranges of the input spaces.
3180 If the product is only constructed over the domain or the range
3181 then the ranges or the domains of the inputs should be the same.
3183 #include <isl/set.h>
3184 __isl_give isl_set *isl_set_product(
3185 __isl_take isl_set *set1,
3186 __isl_take isl_set *set2);
3188 #include <isl/map.h>
3189 __isl_give isl_basic_map *isl_basic_map_domain_product(
3190 __isl_take isl_basic_map *bmap1,
3191 __isl_take isl_basic_map *bmap2);
3192 __isl_give isl_basic_map *isl_basic_map_range_product(
3193 __isl_take isl_basic_map *bmap1,
3194 __isl_take isl_basic_map *bmap2);
3195 __isl_give isl_basic_map *isl_basic_map_product(
3196 __isl_take isl_basic_map *bmap1,
3197 __isl_take isl_basic_map *bmap2);
3198 __isl_give isl_map *isl_map_domain_product(
3199 __isl_take isl_map *map1,
3200 __isl_take isl_map *map2);
3201 __isl_give isl_map *isl_map_range_product(
3202 __isl_take isl_map *map1,
3203 __isl_take isl_map *map2);
3204 __isl_give isl_map *isl_map_product(
3205 __isl_take isl_map *map1,
3206 __isl_take isl_map *map2);
3208 #include <isl/union_set.h>
3209 __isl_give isl_union_set *isl_union_set_product(
3210 __isl_take isl_union_set *uset1,
3211 __isl_take isl_union_set *uset2);
3213 #include <isl/union_map.h>
3214 __isl_give isl_union_map *isl_union_map_domain_product(
3215 __isl_take isl_union_map *umap1,
3216 __isl_take isl_union_map *umap2);
3217 __isl_give isl_union_map *isl_union_map_range_product(
3218 __isl_take isl_union_map *umap1,
3219 __isl_take isl_union_map *umap2);
3220 __isl_give isl_union_map *isl_union_map_product(
3221 __isl_take isl_union_map *umap1,
3222 __isl_take isl_union_map *umap2);
3224 The above functions compute the cross product of the given
3225 sets or relations. The domains and ranges of the results
3226 are wrapped maps between domains and ranges of the inputs.
3227 To obtain a ``flat'' product, use the following functions
3230 __isl_give isl_basic_set *isl_basic_set_flat_product(
3231 __isl_take isl_basic_set *bset1,
3232 __isl_take isl_basic_set *bset2);
3233 __isl_give isl_set *isl_set_flat_product(
3234 __isl_take isl_set *set1,
3235 __isl_take isl_set *set2);
3236 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3237 __isl_take isl_basic_map *bmap1,
3238 __isl_take isl_basic_map *bmap2);
3239 __isl_give isl_map *isl_map_flat_domain_product(
3240 __isl_take isl_map *map1,
3241 __isl_take isl_map *map2);
3242 __isl_give isl_map *isl_map_flat_range_product(
3243 __isl_take isl_map *map1,
3244 __isl_take isl_map *map2);
3245 __isl_give isl_union_map *isl_union_map_flat_range_product(
3246 __isl_take isl_union_map *umap1,
3247 __isl_take isl_union_map *umap2);
3248 __isl_give isl_basic_map *isl_basic_map_flat_product(
3249 __isl_take isl_basic_map *bmap1,
3250 __isl_take isl_basic_map *bmap2);
3251 __isl_give isl_map *isl_map_flat_product(
3252 __isl_take isl_map *map1,
3253 __isl_take isl_map *map2);
3255 #include <isl/space.h>
3256 __isl_give isl_space *isl_space_domain_factor_domain(
3257 __isl_take isl_space *space);
3258 __isl_give isl_space *isl_space_range_factor_domain(
3259 __isl_take isl_space *space);
3260 __isl_give isl_space *isl_space_range_factor_range(
3261 __isl_take isl_space *space);
3263 The functions C<isl_space_range_factor_domain> and
3264 C<isl_space_range_factor_range> extract the two arguments from
3265 the result of a call to C<isl_space_range_product>.
3267 The arguments of a call to C<isl_map_range_product> can be extracted
3268 from the result using the following two functions.
3270 #include <isl/map.h>
3271 __isl_give isl_map *isl_map_range_factor_domain(
3272 __isl_take isl_map *map);
3273 __isl_give isl_map *isl_map_range_factor_range(
3274 __isl_take isl_map *map);
3276 =item * Simplification
3278 __isl_give isl_basic_set *isl_basic_set_gist(
3279 __isl_take isl_basic_set *bset,
3280 __isl_take isl_basic_set *context);
3281 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3282 __isl_take isl_set *context);
3283 __isl_give isl_set *isl_set_gist_params(
3284 __isl_take isl_set *set,
3285 __isl_take isl_set *context);
3286 __isl_give isl_union_set *isl_union_set_gist(
3287 __isl_take isl_union_set *uset,
3288 __isl_take isl_union_set *context);
3289 __isl_give isl_union_set *isl_union_set_gist_params(
3290 __isl_take isl_union_set *uset,
3291 __isl_take isl_set *set);
3292 __isl_give isl_basic_map *isl_basic_map_gist(
3293 __isl_take isl_basic_map *bmap,
3294 __isl_take isl_basic_map *context);
3295 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3296 __isl_take isl_map *context);
3297 __isl_give isl_map *isl_map_gist_params(
3298 __isl_take isl_map *map,
3299 __isl_take isl_set *context);
3300 __isl_give isl_map *isl_map_gist_domain(
3301 __isl_take isl_map *map,
3302 __isl_take isl_set *context);
3303 __isl_give isl_map *isl_map_gist_range(
3304 __isl_take isl_map *map,
3305 __isl_take isl_set *context);
3306 __isl_give isl_union_map *isl_union_map_gist(
3307 __isl_take isl_union_map *umap,
3308 __isl_take isl_union_map *context);
3309 __isl_give isl_union_map *isl_union_map_gist_params(
3310 __isl_take isl_union_map *umap,
3311 __isl_take isl_set *set);
3312 __isl_give isl_union_map *isl_union_map_gist_domain(
3313 __isl_take isl_union_map *umap,
3314 __isl_take isl_union_set *uset);
3315 __isl_give isl_union_map *isl_union_map_gist_range(
3316 __isl_take isl_union_map *umap,
3317 __isl_take isl_union_set *uset);
3319 The gist operation returns a set or relation that has the
3320 same intersection with the context as the input set or relation.
3321 Any implicit equality in the intersection is made explicit in the result,
3322 while all inequalities that are redundant with respect to the intersection
3324 In case of union sets and relations, the gist operation is performed
3329 =head3 Lexicographic Optimization
3331 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3332 the following functions
3333 compute a set that contains the lexicographic minimum or maximum
3334 of the elements in C<set> (or C<bset>) for those values of the parameters
3335 that satisfy C<dom>.
3336 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3337 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3339 In other words, the union of the parameter values
3340 for which the result is non-empty and of C<*empty>
3343 __isl_give isl_set *isl_basic_set_partial_lexmin(
3344 __isl_take isl_basic_set *bset,
3345 __isl_take isl_basic_set *dom,
3346 __isl_give isl_set **empty);
3347 __isl_give isl_set *isl_basic_set_partial_lexmax(
3348 __isl_take isl_basic_set *bset,
3349 __isl_take isl_basic_set *dom,
3350 __isl_give isl_set **empty);
3351 __isl_give isl_set *isl_set_partial_lexmin(
3352 __isl_take isl_set *set, __isl_take isl_set *dom,
3353 __isl_give isl_set **empty);
3354 __isl_give isl_set *isl_set_partial_lexmax(
3355 __isl_take isl_set *set, __isl_take isl_set *dom,
3356 __isl_give isl_set **empty);
3358 Given a (basic) set C<set> (or C<bset>), the following functions simply
3359 return a set containing the lexicographic minimum or maximum
3360 of the elements in C<set> (or C<bset>).
3361 In case of union sets, the optimum is computed per space.
3363 __isl_give isl_set *isl_basic_set_lexmin(
3364 __isl_take isl_basic_set *bset);
3365 __isl_give isl_set *isl_basic_set_lexmax(
3366 __isl_take isl_basic_set *bset);
3367 __isl_give isl_set *isl_set_lexmin(
3368 __isl_take isl_set *set);
3369 __isl_give isl_set *isl_set_lexmax(
3370 __isl_take isl_set *set);
3371 __isl_give isl_union_set *isl_union_set_lexmin(
3372 __isl_take isl_union_set *uset);
3373 __isl_give isl_union_set *isl_union_set_lexmax(
3374 __isl_take isl_union_set *uset);
3376 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3377 the following functions
3378 compute a relation that maps each element of C<dom>
3379 to the single lexicographic minimum or maximum
3380 of the elements that are associated to that same
3381 element in C<map> (or C<bmap>).
3382 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3383 that contains the elements in C<dom> that do not map
3384 to any elements in C<map> (or C<bmap>).
3385 In other words, the union of the domain of the result and of C<*empty>
3388 __isl_give isl_map *isl_basic_map_partial_lexmax(
3389 __isl_take isl_basic_map *bmap,
3390 __isl_take isl_basic_set *dom,
3391 __isl_give isl_set **empty);
3392 __isl_give isl_map *isl_basic_map_partial_lexmin(
3393 __isl_take isl_basic_map *bmap,
3394 __isl_take isl_basic_set *dom,
3395 __isl_give isl_set **empty);
3396 __isl_give isl_map *isl_map_partial_lexmax(
3397 __isl_take isl_map *map, __isl_take isl_set *dom,
3398 __isl_give isl_set **empty);
3399 __isl_give isl_map *isl_map_partial_lexmin(
3400 __isl_take isl_map *map, __isl_take isl_set *dom,
3401 __isl_give isl_set **empty);
3403 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3404 return a map mapping each element in the domain of
3405 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3406 of all elements associated to that element.
3407 In case of union relations, the optimum is computed per space.
3409 __isl_give isl_map *isl_basic_map_lexmin(
3410 __isl_take isl_basic_map *bmap);
3411 __isl_give isl_map *isl_basic_map_lexmax(
3412 __isl_take isl_basic_map *bmap);
3413 __isl_give isl_map *isl_map_lexmin(
3414 __isl_take isl_map *map);
3415 __isl_give isl_map *isl_map_lexmax(
3416 __isl_take isl_map *map);
3417 __isl_give isl_union_map *isl_union_map_lexmin(
3418 __isl_take isl_union_map *umap);
3419 __isl_give isl_union_map *isl_union_map_lexmax(
3420 __isl_take isl_union_map *umap);
3422 The following functions return their result in the form of
3423 a piecewise multi-affine expression
3424 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3425 but are otherwise equivalent to the corresponding functions
3426 returning a basic set or relation.
3428 __isl_give isl_pw_multi_aff *
3429 isl_basic_map_lexmin_pw_multi_aff(
3430 __isl_take isl_basic_map *bmap);
3431 __isl_give isl_pw_multi_aff *
3432 isl_basic_set_partial_lexmin_pw_multi_aff(
3433 __isl_take isl_basic_set *bset,
3434 __isl_take isl_basic_set *dom,
3435 __isl_give isl_set **empty);
3436 __isl_give isl_pw_multi_aff *
3437 isl_basic_set_partial_lexmax_pw_multi_aff(
3438 __isl_take isl_basic_set *bset,
3439 __isl_take isl_basic_set *dom,
3440 __isl_give isl_set **empty);
3441 __isl_give isl_pw_multi_aff *
3442 isl_basic_map_partial_lexmin_pw_multi_aff(
3443 __isl_take isl_basic_map *bmap,
3444 __isl_take isl_basic_set *dom,
3445 __isl_give isl_set **empty);
3446 __isl_give isl_pw_multi_aff *
3447 isl_basic_map_partial_lexmax_pw_multi_aff(
3448 __isl_take isl_basic_map *bmap,
3449 __isl_take isl_basic_set *dom,
3450 __isl_give isl_set **empty);
3451 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3452 __isl_take isl_set *set);
3453 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3454 __isl_take isl_set *set);
3455 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3456 __isl_take isl_map *map);
3457 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3458 __isl_take isl_map *map);
3462 Lists are defined over several element types, including
3463 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3464 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3465 Here we take lists of C<isl_set>s as an example.
3466 Lists can be created, copied, modified and freed using the following functions.
3468 #include <isl/list.h>
3469 __isl_give isl_set_list *isl_set_list_from_set(
3470 __isl_take isl_set *el);
3471 __isl_give isl_set_list *isl_set_list_alloc(
3472 isl_ctx *ctx, int n);
3473 __isl_give isl_set_list *isl_set_list_copy(
3474 __isl_keep isl_set_list *list);
3475 __isl_give isl_set_list *isl_set_list_insert(
3476 __isl_take isl_set_list *list, unsigned pos,
3477 __isl_take isl_set *el);
3478 __isl_give isl_set_list *isl_set_list_add(
3479 __isl_take isl_set_list *list,
3480 __isl_take isl_set *el);
3481 __isl_give isl_set_list *isl_set_list_drop(
3482 __isl_take isl_set_list *list,
3483 unsigned first, unsigned n);
3484 __isl_give isl_set_list *isl_set_list_set_set(
3485 __isl_take isl_set_list *list, int index,
3486 __isl_take isl_set *set);
3487 __isl_give isl_set_list *isl_set_list_concat(
3488 __isl_take isl_set_list *list1,
3489 __isl_take isl_set_list *list2);
3490 __isl_give isl_set_list *isl_set_list_sort(
3491 __isl_take isl_set_list *list,
3492 int (*cmp)(__isl_keep isl_set *a,
3493 __isl_keep isl_set *b, void *user),
3495 void *isl_set_list_free(__isl_take isl_set_list *list);
3497 C<isl_set_list_alloc> creates an empty list with a capacity for
3498 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3501 Lists can be inspected using the following functions.
3503 #include <isl/list.h>
3504 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3505 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3506 __isl_give isl_set *isl_set_list_get_set(
3507 __isl_keep isl_set_list *list, int index);
3508 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3509 int (*fn)(__isl_take isl_set *el, void *user),
3511 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3512 int (*follows)(__isl_keep isl_set *a,
3513 __isl_keep isl_set *b, void *user),
3515 int (*fn)(__isl_take isl_set *el, void *user),
3518 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3519 strongly connected components of the graph with as vertices the elements
3520 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3521 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3522 should return C<-1> on error.
3524 Lists can be printed using
3526 #include <isl/list.h>
3527 __isl_give isl_printer *isl_printer_print_set_list(
3528 __isl_take isl_printer *p,
3529 __isl_keep isl_set_list *list);
3531 =head2 Associative arrays
3533 Associative arrays map isl objects of a specific type to isl objects
3534 of some (other) specific type. They are defined for several pairs
3535 of types, including (C<isl_map>, C<isl_basic_set>),
3536 (C<isl_id>, C<isl_ast_expr>) and.
3537 (C<isl_id>, C<isl_pw_aff>).
3538 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3541 Associative arrays can be created, copied and freed using
3542 the following functions.
3544 #include <isl/id_to_ast_expr.h>
3545 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3546 isl_ctx *ctx, int min_size);
3547 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3548 __isl_keep id_to_ast_expr *id2expr);
3549 void *isl_id_to_ast_expr_free(
3550 __isl_take id_to_ast_expr *id2expr);
3552 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3553 to specify the expected size of the associative array.
3554 The associative array will be grown automatically as needed.
3556 Associative arrays can be inspected using the following functions.
3558 #include <isl/id_to_ast_expr.h>
3559 isl_ctx *isl_id_to_ast_expr_get_ctx(
3560 __isl_keep id_to_ast_expr *id2expr);
3561 int isl_id_to_ast_expr_has(
3562 __isl_keep id_to_ast_expr *id2expr,
3563 __isl_keep isl_id *key);
3564 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3565 __isl_keep id_to_ast_expr *id2expr,
3566 __isl_take isl_id *key);
3567 int isl_id_to_ast_expr_foreach(
3568 __isl_keep id_to_ast_expr *id2expr,
3569 int (*fn)(__isl_take isl_id *key,
3570 __isl_take isl_ast_expr *val, void *user),
3573 They can be modified using the following function.
3575 #include <isl/id_to_ast_expr.h>
3576 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3577 __isl_take id_to_ast_expr *id2expr,
3578 __isl_take isl_id *key,
3579 __isl_take isl_ast_expr *val);
3580 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
3581 __isl_take id_to_ast_expr *id2expr,
3582 __isl_take isl_id *key);
3584 Associative arrays can be printed using the following function.
3586 #include <isl/id_to_ast_expr.h>
3587 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3588 __isl_take isl_printer *p,
3589 __isl_keep id_to_ast_expr *id2expr);
3591 =head2 Multiple Values
3593 An C<isl_multi_val> object represents a sequence of zero or more values,
3594 living in a set space.
3596 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3597 using the following function
3599 #include <isl/val.h>
3600 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3601 __isl_take isl_space *space,
3602 __isl_take isl_val_list *list);
3604 The zero multiple value (with value zero for each set dimension)
3605 can be created using the following function.
3607 #include <isl/val.h>
3608 __isl_give isl_multi_val *isl_multi_val_zero(
3609 __isl_take isl_space *space);
3611 Multiple values can be copied and freed using
3613 #include <isl/val.h>
3614 __isl_give isl_multi_val *isl_multi_val_copy(
3615 __isl_keep isl_multi_val *mv);
3616 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3618 They can be inspected using
3620 #include <isl/val.h>
3621 isl_ctx *isl_multi_val_get_ctx(
3622 __isl_keep isl_multi_val *mv);
3623 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3624 enum isl_dim_type type);
3625 __isl_give isl_val *isl_multi_val_get_val(
3626 __isl_keep isl_multi_val *mv, int pos);
3627 int isl_multi_val_find_dim_by_id(
3628 __isl_keep isl_multi_val *mv,
3629 enum isl_dim_type type, __isl_keep isl_id *id);
3630 __isl_give isl_id *isl_multi_val_get_dim_id(
3631 __isl_keep isl_multi_val *mv,
3632 enum isl_dim_type type, unsigned pos);
3633 const char *isl_multi_val_get_tuple_name(
3634 __isl_keep isl_multi_val *mv,
3635 enum isl_dim_type type);
3636 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3637 enum isl_dim_type type);
3638 __isl_give isl_id *isl_multi_val_get_tuple_id(
3639 __isl_keep isl_multi_val *mv,
3640 enum isl_dim_type type);
3641 int isl_multi_val_range_is_wrapping(
3642 __isl_keep isl_multi_val *mv);
3644 They can be modified using
3646 #include <isl/val.h>
3647 __isl_give isl_multi_val *isl_multi_val_set_val(
3648 __isl_take isl_multi_val *mv, int pos,
3649 __isl_take isl_val *val);
3650 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3651 __isl_take isl_multi_val *mv,
3652 enum isl_dim_type type, unsigned pos, const char *s);
3653 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3654 __isl_take isl_multi_val *mv,
3655 enum isl_dim_type type, unsigned pos,
3656 __isl_take isl_id *id);
3657 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3658 __isl_take isl_multi_val *mv,
3659 enum isl_dim_type type, const char *s);
3660 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3661 __isl_take isl_multi_val *mv,
3662 enum isl_dim_type type, __isl_take isl_id *id);
3663 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3664 __isl_take isl_multi_val *mv,
3665 enum isl_dim_type type);
3666 __isl_give isl_multi_val *isl_multi_val_reset_user(
3667 __isl_take isl_multi_val *mv);
3669 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3670 __isl_take isl_multi_val *mv,
3671 enum isl_dim_type type, unsigned first, unsigned n);
3672 __isl_give isl_multi_val *isl_multi_val_add_dims(
3673 __isl_take isl_multi_val *mv,
3674 enum isl_dim_type type, unsigned n);
3675 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3676 __isl_take isl_multi_val *mv,
3677 enum isl_dim_type type, unsigned first, unsigned n);
3681 #include <isl/val.h>
3682 __isl_give isl_multi_val *isl_multi_val_align_params(
3683 __isl_take isl_multi_val *mv,
3684 __isl_take isl_space *model);
3685 __isl_give isl_multi_val *isl_multi_val_from_range(
3686 __isl_take isl_multi_val *mv);
3687 __isl_give isl_multi_val *isl_multi_val_range_splice(
3688 __isl_take isl_multi_val *mv1, unsigned pos,
3689 __isl_take isl_multi_val *mv2);
3690 __isl_give isl_multi_val *isl_multi_val_range_product(
3691 __isl_take isl_multi_val *mv1,
3692 __isl_take isl_multi_val *mv2);
3693 __isl_give isl_multi_val *
3694 isl_multi_val_range_factor_domain(
3695 __isl_take isl_multi_val *mv);
3696 __isl_give isl_multi_val *
3697 isl_multi_val_range_factor_range(
3698 __isl_take isl_multi_val *mv);
3699 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3700 __isl_take isl_multi_val *mv1,
3701 __isl_take isl_multi_aff *mv2);
3702 __isl_give isl_multi_val *isl_multi_val_product(
3703 __isl_take isl_multi_val *mv1,
3704 __isl_take isl_multi_val *mv2);
3705 __isl_give isl_multi_val *isl_multi_val_add_val(
3706 __isl_take isl_multi_val *mv,
3707 __isl_take isl_val *v);
3708 __isl_give isl_multi_val *isl_multi_val_mod_val(
3709 __isl_take isl_multi_val *mv,
3710 __isl_take isl_val *v);
3711 __isl_give isl_multi_val *isl_multi_val_scale_val(
3712 __isl_take isl_multi_val *mv,
3713 __isl_take isl_val *v);
3714 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3715 __isl_take isl_multi_val *mv1,
3716 __isl_take isl_multi_val *mv2);
3717 __isl_give isl_multi_val *
3718 isl_multi_val_scale_down_multi_val(
3719 __isl_take isl_multi_val *mv1,
3720 __isl_take isl_multi_val *mv2);
3722 A multiple value can be printed using
3724 __isl_give isl_printer *isl_printer_print_multi_val(
3725 __isl_take isl_printer *p,
3726 __isl_keep isl_multi_val *mv);
3730 Vectors can be created, copied and freed using the following functions.
3732 #include <isl/vec.h>
3733 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3735 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3736 void *isl_vec_free(__isl_take isl_vec *vec);
3738 Note that the elements of a newly created vector may have arbitrary values.
3739 The elements can be changed and inspected using the following functions.
3741 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3742 int isl_vec_size(__isl_keep isl_vec *vec);
3743 __isl_give isl_val *isl_vec_get_element_val(
3744 __isl_keep isl_vec *vec, int pos);
3745 __isl_give isl_vec *isl_vec_set_element_si(
3746 __isl_take isl_vec *vec, int pos, int v);
3747 __isl_give isl_vec *isl_vec_set_element_val(
3748 __isl_take isl_vec *vec, int pos,
3749 __isl_take isl_val *v);
3750 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3752 __isl_give isl_vec *isl_vec_set_val(
3753 __isl_take isl_vec *vec, __isl_take isl_val *v);
3754 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3755 __isl_keep isl_vec *vec2, int pos);
3757 C<isl_vec_get_element> will return a negative value if anything went wrong.
3758 In that case, the value of C<*v> is undefined.
3760 The following function can be used to concatenate two vectors.
3762 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3763 __isl_take isl_vec *vec2);
3767 Matrices can be created, copied and freed using the following functions.
3769 #include <isl/mat.h>
3770 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3771 unsigned n_row, unsigned n_col);
3772 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3773 void *isl_mat_free(__isl_take isl_mat *mat);
3775 Note that the elements of a newly created matrix may have arbitrary values.
3776 The elements can be changed and inspected using the following functions.
3778 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3779 int isl_mat_rows(__isl_keep isl_mat *mat);
3780 int isl_mat_cols(__isl_keep isl_mat *mat);
3781 __isl_give isl_val *isl_mat_get_element_val(
3782 __isl_keep isl_mat *mat, int row, int col);
3783 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3784 int row, int col, int v);
3785 __isl_give isl_mat *isl_mat_set_element_val(
3786 __isl_take isl_mat *mat, int row, int col,
3787 __isl_take isl_val *v);
3789 C<isl_mat_get_element> will return a negative value if anything went wrong.
3790 In that case, the value of C<*v> is undefined.
3792 The following function can be used to compute the (right) inverse
3793 of a matrix, i.e., a matrix such that the product of the original
3794 and the inverse (in that order) is a multiple of the identity matrix.
3795 The input matrix is assumed to be of full row-rank.
3797 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3799 The following function can be used to compute the (right) kernel
3800 (or null space) of a matrix, i.e., a matrix such that the product of
3801 the original and the kernel (in that order) is the zero matrix.
3803 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3805 =head2 Piecewise Quasi Affine Expressions
3807 The zero quasi affine expression or the quasi affine expression
3808 that is equal to a given value or
3809 a specified dimension on a given domain can be created using
3811 __isl_give isl_aff *isl_aff_zero_on_domain(
3812 __isl_take isl_local_space *ls);
3813 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3814 __isl_take isl_local_space *ls);
3815 __isl_give isl_aff *isl_aff_val_on_domain(
3816 __isl_take isl_local_space *ls,
3817 __isl_take isl_val *val);
3818 __isl_give isl_aff *isl_aff_var_on_domain(
3819 __isl_take isl_local_space *ls,
3820 enum isl_dim_type type, unsigned pos);
3821 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3822 __isl_take isl_local_space *ls,
3823 enum isl_dim_type type, unsigned pos);
3825 Note that the space in which the resulting objects live is a map space
3826 with the given space as domain and a one-dimensional range.
3828 An empty piecewise quasi affine expression (one with no cells)
3829 or a piecewise quasi affine expression with a single cell can
3830 be created using the following functions.
3832 #include <isl/aff.h>
3833 __isl_give isl_pw_aff *isl_pw_aff_empty(
3834 __isl_take isl_space *space);
3835 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3836 __isl_take isl_set *set, __isl_take isl_aff *aff);
3837 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3838 __isl_take isl_aff *aff);
3840 A piecewise quasi affine expression that is equal to 1 on a set
3841 and 0 outside the set can be created using the following function.
3843 #include <isl/aff.h>
3844 __isl_give isl_pw_aff *isl_set_indicator_function(
3845 __isl_take isl_set *set);
3847 Quasi affine expressions can be copied and freed using
3849 #include <isl/aff.h>
3850 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3851 void *isl_aff_free(__isl_take isl_aff *aff);
3853 __isl_give isl_pw_aff *isl_pw_aff_copy(
3854 __isl_keep isl_pw_aff *pwaff);
3855 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3857 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3858 using the following function. The constraint is required to have
3859 a non-zero coefficient for the specified dimension.
3861 #include <isl/constraint.h>
3862 __isl_give isl_aff *isl_constraint_get_bound(
3863 __isl_keep isl_constraint *constraint,
3864 enum isl_dim_type type, int pos);
3866 The entire affine expression of the constraint can also be extracted
3867 using the following function.
3869 #include <isl/constraint.h>
3870 __isl_give isl_aff *isl_constraint_get_aff(
3871 __isl_keep isl_constraint *constraint);
3873 Conversely, an equality constraint equating
3874 the affine expression to zero or an inequality constraint enforcing
3875 the affine expression to be non-negative, can be constructed using
3877 __isl_give isl_constraint *isl_equality_from_aff(
3878 __isl_take isl_aff *aff);
3879 __isl_give isl_constraint *isl_inequality_from_aff(
3880 __isl_take isl_aff *aff);
3882 The expression can be inspected using
3884 #include <isl/aff.h>
3885 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3886 int isl_aff_dim(__isl_keep isl_aff *aff,
3887 enum isl_dim_type type);
3888 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3889 __isl_keep isl_aff *aff);
3890 __isl_give isl_local_space *isl_aff_get_local_space(
3891 __isl_keep isl_aff *aff);
3892 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3893 enum isl_dim_type type, unsigned pos);
3894 const char *isl_pw_aff_get_dim_name(
3895 __isl_keep isl_pw_aff *pa,
3896 enum isl_dim_type type, unsigned pos);
3897 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3898 enum isl_dim_type type, unsigned pos);
3899 __isl_give isl_id *isl_pw_aff_get_dim_id(
3900 __isl_keep isl_pw_aff *pa,
3901 enum isl_dim_type type, unsigned pos);
3902 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
3903 enum isl_dim_type type);
3904 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3905 __isl_keep isl_pw_aff *pa,
3906 enum isl_dim_type type);
3907 __isl_give isl_val *isl_aff_get_constant_val(
3908 __isl_keep isl_aff *aff);
3909 __isl_give isl_val *isl_aff_get_coefficient_val(
3910 __isl_keep isl_aff *aff,
3911 enum isl_dim_type type, int pos);
3912 __isl_give isl_val *isl_aff_get_denominator_val(
3913 __isl_keep isl_aff *aff);
3914 __isl_give isl_aff *isl_aff_get_div(
3915 __isl_keep isl_aff *aff, int pos);
3917 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3918 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3919 int (*fn)(__isl_take isl_set *set,
3920 __isl_take isl_aff *aff,
3921 void *user), void *user);
3923 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3924 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3926 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3927 enum isl_dim_type type, unsigned first, unsigned n);
3928 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3929 enum isl_dim_type type, unsigned first, unsigned n);
3931 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3932 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3933 enum isl_dim_type type);
3934 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3936 It can be modified using
3938 #include <isl/aff.h>
3939 __isl_give isl_aff *isl_aff_set_tuple_id(
3940 __isl_take isl_aff *aff,
3941 enum isl_dim_type type, __isl_take isl_id *id);
3942 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3943 __isl_take isl_pw_aff *pwaff,
3944 enum isl_dim_type type, __isl_take isl_id *id);
3945 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
3946 __isl_take isl_pw_aff *pa,
3947 enum isl_dim_type type);
3948 __isl_give isl_aff *isl_aff_set_dim_name(
3949 __isl_take isl_aff *aff, enum isl_dim_type type,
3950 unsigned pos, const char *s);
3951 __isl_give isl_aff *isl_aff_set_dim_id(
3952 __isl_take isl_aff *aff, enum isl_dim_type type,
3953 unsigned pos, __isl_take isl_id *id);
3954 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3955 __isl_take isl_pw_aff *pma,
3956 enum isl_dim_type type, unsigned pos,
3957 __isl_take isl_id *id);
3958 __isl_give isl_aff *isl_aff_set_constant_si(
3959 __isl_take isl_aff *aff, int v);
3960 __isl_give isl_aff *isl_aff_set_constant_val(
3961 __isl_take isl_aff *aff, __isl_take isl_val *v);
3962 __isl_give isl_aff *isl_aff_set_coefficient_si(
3963 __isl_take isl_aff *aff,
3964 enum isl_dim_type type, int pos, int v);
3965 __isl_give isl_aff *isl_aff_set_coefficient_val(
3966 __isl_take isl_aff *aff,
3967 enum isl_dim_type type, int pos,
3968 __isl_take isl_val *v);
3970 __isl_give isl_aff *isl_aff_add_constant_si(
3971 __isl_take isl_aff *aff, int v);
3972 __isl_give isl_aff *isl_aff_add_constant_val(
3973 __isl_take isl_aff *aff, __isl_take isl_val *v);
3974 __isl_give isl_aff *isl_aff_add_constant_num_si(
3975 __isl_take isl_aff *aff, int v);
3976 __isl_give isl_aff *isl_aff_add_coefficient_si(
3977 __isl_take isl_aff *aff,
3978 enum isl_dim_type type, int pos, int v);
3979 __isl_give isl_aff *isl_aff_add_coefficient_val(
3980 __isl_take isl_aff *aff,
3981 enum isl_dim_type type, int pos,
3982 __isl_take isl_val *v);
3984 __isl_give isl_aff *isl_aff_insert_dims(
3985 __isl_take isl_aff *aff,
3986 enum isl_dim_type type, unsigned first, unsigned n);
3987 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3988 __isl_take isl_pw_aff *pwaff,
3989 enum isl_dim_type type, unsigned first, unsigned n);
3990 __isl_give isl_aff *isl_aff_add_dims(
3991 __isl_take isl_aff *aff,
3992 enum isl_dim_type type, unsigned n);
3993 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3994 __isl_take isl_pw_aff *pwaff,
3995 enum isl_dim_type type, unsigned n);
3996 __isl_give isl_aff *isl_aff_drop_dims(
3997 __isl_take isl_aff *aff,
3998 enum isl_dim_type type, unsigned first, unsigned n);
3999 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
4000 __isl_take isl_pw_aff *pwaff,
4001 enum isl_dim_type type, unsigned first, unsigned n);
4002 __isl_give isl_aff *isl_aff_move_dims(
4003 __isl_take isl_aff *aff,
4004 enum isl_dim_type dst_type, unsigned dst_pos,
4005 enum isl_dim_type src_type, unsigned src_pos,
4007 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
4008 __isl_take isl_pw_aff *pa,
4009 enum isl_dim_type dst_type, unsigned dst_pos,
4010 enum isl_dim_type src_type, unsigned src_pos,
4013 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
4014 set the I<numerator> of the constant or coefficient, while
4015 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
4016 the constant or coefficient as a whole.
4017 The C<add_constant> and C<add_coefficient> functions add an integer
4018 or rational value to
4019 the possibly rational constant or coefficient.
4020 The C<add_constant_num> functions add an integer value to
4023 To check whether an affine expressions is obviously zero
4024 or (obviously) equal to some other affine expression, use
4026 #include <isl/aff.h>
4027 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
4028 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
4029 __isl_keep isl_aff *aff2);
4030 int isl_pw_aff_plain_is_equal(
4031 __isl_keep isl_pw_aff *pwaff1,
4032 __isl_keep isl_pw_aff *pwaff2);
4033 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
4034 __isl_keep isl_pw_aff *pa2);
4038 #include <isl/aff.h>
4039 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
4040 __isl_take isl_aff *aff2);
4041 __isl_give isl_pw_aff *isl_pw_aff_add(
4042 __isl_take isl_pw_aff *pwaff1,
4043 __isl_take isl_pw_aff *pwaff2);
4044 __isl_give isl_pw_aff *isl_pw_aff_min(
4045 __isl_take isl_pw_aff *pwaff1,
4046 __isl_take isl_pw_aff *pwaff2);
4047 __isl_give isl_pw_aff *isl_pw_aff_max(
4048 __isl_take isl_pw_aff *pwaff1,
4049 __isl_take isl_pw_aff *pwaff2);
4050 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
4051 __isl_take isl_aff *aff2);
4052 __isl_give isl_pw_aff *isl_pw_aff_sub(
4053 __isl_take isl_pw_aff *pwaff1,
4054 __isl_take isl_pw_aff *pwaff2);
4055 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
4056 __isl_give isl_pw_aff *isl_pw_aff_neg(
4057 __isl_take isl_pw_aff *pwaff);
4058 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
4059 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4060 __isl_take isl_pw_aff *pwaff);
4061 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
4062 __isl_give isl_pw_aff *isl_pw_aff_floor(
4063 __isl_take isl_pw_aff *pwaff);
4064 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
4065 __isl_take isl_val *mod);
4066 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
4067 __isl_take isl_pw_aff *pa,
4068 __isl_take isl_val *mod);
4069 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
4070 __isl_take isl_val *v);
4071 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
4072 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
4073 __isl_give isl_aff *isl_aff_scale_down_ui(
4074 __isl_take isl_aff *aff, unsigned f);
4075 __isl_give isl_aff *isl_aff_scale_down_val(
4076 __isl_take isl_aff *aff, __isl_take isl_val *v);
4077 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
4078 __isl_take isl_pw_aff *pa,
4079 __isl_take isl_val *f);
4081 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4082 __isl_take isl_pw_aff_list *list);
4083 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4084 __isl_take isl_pw_aff_list *list);
4086 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4087 __isl_take isl_pw_aff *pwqp);
4089 __isl_give isl_aff *isl_aff_align_params(
4090 __isl_take isl_aff *aff,
4091 __isl_take isl_space *model);
4092 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4093 __isl_take isl_pw_aff *pwaff,
4094 __isl_take isl_space *model);
4096 __isl_give isl_aff *isl_aff_project_domain_on_params(
4097 __isl_take isl_aff *aff);
4098 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4099 __isl_take isl_pw_aff *pwa);
4101 __isl_give isl_aff *isl_aff_gist_params(
4102 __isl_take isl_aff *aff,
4103 __isl_take isl_set *context);
4104 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
4105 __isl_take isl_set *context);
4106 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
4107 __isl_take isl_pw_aff *pwaff,
4108 __isl_take isl_set *context);
4109 __isl_give isl_pw_aff *isl_pw_aff_gist(
4110 __isl_take isl_pw_aff *pwaff,
4111 __isl_take isl_set *context);
4113 __isl_give isl_set *isl_pw_aff_domain(
4114 __isl_take isl_pw_aff *pwaff);
4115 __isl_give isl_set *isl_pw_aff_params(
4116 __isl_take isl_pw_aff *pwa);
4117 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4118 __isl_take isl_pw_aff *pa,
4119 __isl_take isl_set *set);
4120 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4121 __isl_take isl_pw_aff *pa,
4122 __isl_take isl_set *set);
4124 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
4125 __isl_take isl_aff *aff2);
4126 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
4127 __isl_take isl_aff *aff2);
4128 __isl_give isl_pw_aff *isl_pw_aff_mul(
4129 __isl_take isl_pw_aff *pwaff1,
4130 __isl_take isl_pw_aff *pwaff2);
4131 __isl_give isl_pw_aff *isl_pw_aff_div(
4132 __isl_take isl_pw_aff *pa1,
4133 __isl_take isl_pw_aff *pa2);
4134 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
4135 __isl_take isl_pw_aff *pa1,
4136 __isl_take isl_pw_aff *pa2);
4137 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
4138 __isl_take isl_pw_aff *pa1,
4139 __isl_take isl_pw_aff *pa2);
4141 When multiplying two affine expressions, at least one of the two needs
4142 to be a constant. Similarly, when dividing an affine expression by another,
4143 the second expression needs to be a constant.
4144 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
4145 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
4148 #include <isl/aff.h>
4149 __isl_give isl_aff *isl_aff_pullback_aff(
4150 __isl_take isl_aff *aff1,
4151 __isl_take isl_aff *aff2);
4152 __isl_give isl_aff *isl_aff_pullback_multi_aff(
4153 __isl_take isl_aff *aff,
4154 __isl_take isl_multi_aff *ma);
4155 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
4156 __isl_take isl_pw_aff *pa,
4157 __isl_take isl_multi_aff *ma);
4158 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
4159 __isl_take isl_pw_aff *pa,
4160 __isl_take isl_pw_multi_aff *pma);
4161 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
4162 __isl_take isl_pw_aff *pa,
4163 __isl_take isl_multi_pw_aff *mpa);
4165 These functions precompose the input expression by the given
4166 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
4167 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
4168 into the (piecewise) affine expression.
4169 Objects of type C<isl_multi_aff> are described in
4170 L</"Piecewise Multiple Quasi Affine Expressions">.
4172 #include <isl/aff.h>
4173 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4174 __isl_take isl_aff *aff);
4175 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4176 __isl_take isl_aff *aff);
4177 __isl_give isl_basic_set *isl_aff_le_basic_set(
4178 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4179 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4180 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4181 __isl_give isl_set *isl_pw_aff_eq_set(
4182 __isl_take isl_pw_aff *pwaff1,
4183 __isl_take isl_pw_aff *pwaff2);
4184 __isl_give isl_set *isl_pw_aff_ne_set(
4185 __isl_take isl_pw_aff *pwaff1,
4186 __isl_take isl_pw_aff *pwaff2);
4187 __isl_give isl_set *isl_pw_aff_le_set(
4188 __isl_take isl_pw_aff *pwaff1,
4189 __isl_take isl_pw_aff *pwaff2);
4190 __isl_give isl_set *isl_pw_aff_lt_set(
4191 __isl_take isl_pw_aff *pwaff1,
4192 __isl_take isl_pw_aff *pwaff2);
4193 __isl_give isl_set *isl_pw_aff_ge_set(
4194 __isl_take isl_pw_aff *pwaff1,
4195 __isl_take isl_pw_aff *pwaff2);
4196 __isl_give isl_set *isl_pw_aff_gt_set(
4197 __isl_take isl_pw_aff *pwaff1,
4198 __isl_take isl_pw_aff *pwaff2);
4200 __isl_give isl_set *isl_pw_aff_list_eq_set(
4201 __isl_take isl_pw_aff_list *list1,
4202 __isl_take isl_pw_aff_list *list2);
4203 __isl_give isl_set *isl_pw_aff_list_ne_set(
4204 __isl_take isl_pw_aff_list *list1,
4205 __isl_take isl_pw_aff_list *list2);
4206 __isl_give isl_set *isl_pw_aff_list_le_set(
4207 __isl_take isl_pw_aff_list *list1,
4208 __isl_take isl_pw_aff_list *list2);
4209 __isl_give isl_set *isl_pw_aff_list_lt_set(
4210 __isl_take isl_pw_aff_list *list1,
4211 __isl_take isl_pw_aff_list *list2);
4212 __isl_give isl_set *isl_pw_aff_list_ge_set(
4213 __isl_take isl_pw_aff_list *list1,
4214 __isl_take isl_pw_aff_list *list2);
4215 __isl_give isl_set *isl_pw_aff_list_gt_set(
4216 __isl_take isl_pw_aff_list *list1,
4217 __isl_take isl_pw_aff_list *list2);
4219 The function C<isl_aff_neg_basic_set> returns a basic set
4220 containing those elements in the domain space
4221 of C<aff> where C<aff> is negative.
4222 The function C<isl_aff_ge_basic_set> returns a basic set
4223 containing those elements in the shared space
4224 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4225 The function C<isl_pw_aff_ge_set> returns a set
4226 containing those elements in the shared domain
4227 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4228 The functions operating on C<isl_pw_aff_list> apply the corresponding
4229 C<isl_pw_aff> function to each pair of elements in the two lists.
4231 #include <isl/aff.h>
4232 __isl_give isl_set *isl_pw_aff_nonneg_set(
4233 __isl_take isl_pw_aff *pwaff);
4234 __isl_give isl_set *isl_pw_aff_zero_set(
4235 __isl_take isl_pw_aff *pwaff);
4236 __isl_give isl_set *isl_pw_aff_non_zero_set(
4237 __isl_take isl_pw_aff *pwaff);
4239 The function C<isl_pw_aff_nonneg_set> returns a set
4240 containing those elements in the domain
4241 of C<pwaff> where C<pwaff> is non-negative.
4243 #include <isl/aff.h>
4244 __isl_give isl_pw_aff *isl_pw_aff_cond(
4245 __isl_take isl_pw_aff *cond,
4246 __isl_take isl_pw_aff *pwaff_true,
4247 __isl_take isl_pw_aff *pwaff_false);
4249 The function C<isl_pw_aff_cond> performs a conditional operator
4250 and returns an expression that is equal to C<pwaff_true>
4251 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4252 where C<cond> is zero.
4254 #include <isl/aff.h>
4255 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4256 __isl_take isl_pw_aff *pwaff1,
4257 __isl_take isl_pw_aff *pwaff2);
4258 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4259 __isl_take isl_pw_aff *pwaff1,
4260 __isl_take isl_pw_aff *pwaff2);
4261 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4262 __isl_take isl_pw_aff *pwaff1,
4263 __isl_take isl_pw_aff *pwaff2);
4265 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4266 expression with a domain that is the union of those of C<pwaff1> and
4267 C<pwaff2> and such that on each cell, the quasi-affine expression is
4268 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4269 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4270 associated expression is the defined one.
4272 An expression can be read from input using
4274 #include <isl/aff.h>
4275 __isl_give isl_aff *isl_aff_read_from_str(
4276 isl_ctx *ctx, const char *str);
4277 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4278 isl_ctx *ctx, const char *str);
4280 An expression can be printed using
4282 #include <isl/aff.h>
4283 __isl_give isl_printer *isl_printer_print_aff(
4284 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4286 __isl_give isl_printer *isl_printer_print_pw_aff(
4287 __isl_take isl_printer *p,
4288 __isl_keep isl_pw_aff *pwaff);
4290 =head2 Piecewise Multiple Quasi Affine Expressions
4292 An C<isl_multi_aff> object represents a sequence of
4293 zero or more affine expressions, all defined on the same domain space.
4294 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4295 zero or more piecewise affine expressions.
4297 An C<isl_multi_aff> can be constructed from a single
4298 C<isl_aff> or an C<isl_aff_list> using the
4299 following functions. Similarly for C<isl_multi_pw_aff>
4300 and C<isl_pw_multi_aff>.
4302 #include <isl/aff.h>
4303 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4304 __isl_take isl_aff *aff);
4305 __isl_give isl_multi_pw_aff *
4306 isl_multi_pw_aff_from_multi_aff(
4307 __isl_take isl_multi_aff *ma);
4308 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4309 __isl_take isl_pw_aff *pa);
4310 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4311 __isl_take isl_pw_aff *pa);
4312 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4313 __isl_take isl_space *space,
4314 __isl_take isl_aff_list *list);
4316 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4317 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4318 Note however that the domain
4319 of the result is the intersection of the domains of the input.
4320 The reverse conversion is exact.
4322 #include <isl/aff.h>
4323 __isl_give isl_pw_multi_aff *
4324 isl_pw_multi_aff_from_multi_pw_aff(
4325 __isl_take isl_multi_pw_aff *mpa);
4326 __isl_give isl_multi_pw_aff *
4327 isl_multi_pw_aff_from_pw_multi_aff(
4328 __isl_take isl_pw_multi_aff *pma);
4330 An empty piecewise multiple quasi affine expression (one with no cells),
4331 the zero piecewise multiple quasi affine expression (with value zero
4332 for each output dimension),
4333 a piecewise multiple quasi affine expression with a single cell (with
4334 either a universe or a specified domain) or
4335 a zero-dimensional piecewise multiple quasi affine expression
4337 can be created using the following functions.
4339 #include <isl/aff.h>
4340 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4341 __isl_take isl_space *space);
4342 __isl_give isl_multi_aff *isl_multi_aff_zero(
4343 __isl_take isl_space *space);
4344 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4345 __isl_take isl_space *space);
4346 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4347 __isl_take isl_space *space);
4348 __isl_give isl_multi_aff *isl_multi_aff_identity(
4349 __isl_take isl_space *space);
4350 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4351 __isl_take isl_space *space);
4352 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4353 __isl_take isl_space *space);
4354 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4355 __isl_take isl_space *space);
4356 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4357 __isl_take isl_space *space);
4358 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4359 __isl_take isl_space *space,
4360 enum isl_dim_type type,
4361 unsigned first, unsigned n);
4362 __isl_give isl_pw_multi_aff *
4363 isl_pw_multi_aff_project_out_map(
4364 __isl_take isl_space *space,
4365 enum isl_dim_type type,
4366 unsigned first, unsigned n);
4367 __isl_give isl_pw_multi_aff *
4368 isl_pw_multi_aff_from_multi_aff(
4369 __isl_take isl_multi_aff *ma);
4370 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4371 __isl_take isl_set *set,
4372 __isl_take isl_multi_aff *maff);
4373 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4374 __isl_take isl_set *set);
4376 __isl_give isl_union_pw_multi_aff *
4377 isl_union_pw_multi_aff_empty(
4378 __isl_take isl_space *space);
4379 __isl_give isl_union_pw_multi_aff *
4380 isl_union_pw_multi_aff_add_pw_multi_aff(
4381 __isl_take isl_union_pw_multi_aff *upma,
4382 __isl_take isl_pw_multi_aff *pma);
4383 __isl_give isl_union_pw_multi_aff *
4384 isl_union_pw_multi_aff_from_domain(
4385 __isl_take isl_union_set *uset);
4387 A piecewise multiple quasi affine expression can also be initialized
4388 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4389 and the C<isl_map> is single-valued.
4390 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4391 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4393 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4394 __isl_take isl_set *set);
4395 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4396 __isl_take isl_map *map);
4398 __isl_give isl_union_pw_multi_aff *
4399 isl_union_pw_multi_aff_from_union_set(
4400 __isl_take isl_union_set *uset);
4401 __isl_give isl_union_pw_multi_aff *
4402 isl_union_pw_multi_aff_from_union_map(
4403 __isl_take isl_union_map *umap);
4405 Multiple quasi affine expressions can be copied and freed using
4407 #include <isl/aff.h>
4408 __isl_give isl_multi_aff *isl_multi_aff_copy(
4409 __isl_keep isl_multi_aff *maff);
4410 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4412 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4413 __isl_keep isl_pw_multi_aff *pma);
4414 void *isl_pw_multi_aff_free(
4415 __isl_take isl_pw_multi_aff *pma);
4417 __isl_give isl_union_pw_multi_aff *
4418 isl_union_pw_multi_aff_copy(
4419 __isl_keep isl_union_pw_multi_aff *upma);
4420 void *isl_union_pw_multi_aff_free(
4421 __isl_take isl_union_pw_multi_aff *upma);
4423 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4424 __isl_keep isl_multi_pw_aff *mpa);
4425 void *isl_multi_pw_aff_free(
4426 __isl_take isl_multi_pw_aff *mpa);
4428 The expression can be inspected using
4430 #include <isl/aff.h>
4431 isl_ctx *isl_multi_aff_get_ctx(
4432 __isl_keep isl_multi_aff *maff);
4433 isl_ctx *isl_pw_multi_aff_get_ctx(
4434 __isl_keep isl_pw_multi_aff *pma);
4435 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4436 __isl_keep isl_union_pw_multi_aff *upma);
4437 isl_ctx *isl_multi_pw_aff_get_ctx(
4438 __isl_keep isl_multi_pw_aff *mpa);
4440 int isl_multi_aff_involves_dims(
4441 __isl_keep isl_multi_aff *ma,
4442 enum isl_dim_type type, unsigned first, unsigned n);
4443 int isl_multi_pw_aff_involves_dims(
4444 __isl_keep isl_multi_pw_aff *mpa,
4445 enum isl_dim_type type, unsigned first, unsigned n);
4447 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4448 enum isl_dim_type type);
4449 unsigned isl_pw_multi_aff_dim(
4450 __isl_keep isl_pw_multi_aff *pma,
4451 enum isl_dim_type type);
4452 unsigned isl_multi_pw_aff_dim(
4453 __isl_keep isl_multi_pw_aff *mpa,
4454 enum isl_dim_type type);
4455 __isl_give isl_aff *isl_multi_aff_get_aff(
4456 __isl_keep isl_multi_aff *multi, int pos);
4457 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4458 __isl_keep isl_pw_multi_aff *pma, int pos);
4459 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4460 __isl_keep isl_multi_pw_aff *mpa, int pos);
4461 int isl_multi_aff_find_dim_by_id(
4462 __isl_keep isl_multi_aff *ma,
4463 enum isl_dim_type type, __isl_keep isl_id *id);
4464 int isl_multi_pw_aff_find_dim_by_id(
4465 __isl_keep isl_multi_pw_aff *mpa,
4466 enum isl_dim_type type, __isl_keep isl_id *id);
4467 const char *isl_pw_multi_aff_get_dim_name(
4468 __isl_keep isl_pw_multi_aff *pma,
4469 enum isl_dim_type type, unsigned pos);
4470 __isl_give isl_id *isl_multi_aff_get_dim_id(
4471 __isl_keep isl_multi_aff *ma,
4472 enum isl_dim_type type, unsigned pos);
4473 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4474 __isl_keep isl_pw_multi_aff *pma,
4475 enum isl_dim_type type, unsigned pos);
4476 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4477 __isl_keep isl_multi_pw_aff *mpa,
4478 enum isl_dim_type type, unsigned pos);
4479 const char *isl_multi_aff_get_tuple_name(
4480 __isl_keep isl_multi_aff *multi,
4481 enum isl_dim_type type);
4482 int isl_pw_multi_aff_has_tuple_name(
4483 __isl_keep isl_pw_multi_aff *pma,
4484 enum isl_dim_type type);
4485 const char *isl_pw_multi_aff_get_tuple_name(
4486 __isl_keep isl_pw_multi_aff *pma,
4487 enum isl_dim_type type);
4488 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4489 enum isl_dim_type type);
4490 int isl_pw_multi_aff_has_tuple_id(
4491 __isl_keep isl_pw_multi_aff *pma,
4492 enum isl_dim_type type);
4493 int isl_multi_pw_aff_has_tuple_id(
4494 __isl_keep isl_multi_pw_aff *mpa,
4495 enum isl_dim_type type);
4496 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4497 __isl_keep isl_multi_aff *ma,
4498 enum isl_dim_type type);
4499 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4500 __isl_keep isl_pw_multi_aff *pma,
4501 enum isl_dim_type type);
4502 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4503 __isl_keep isl_multi_pw_aff *mpa,
4504 enum isl_dim_type type);
4505 int isl_multi_aff_range_is_wrapping(
4506 __isl_keep isl_multi_aff *ma);
4507 int isl_multi_pw_aff_range_is_wrapping(
4508 __isl_keep isl_multi_pw_aff *mpa);
4510 int isl_pw_multi_aff_foreach_piece(
4511 __isl_keep isl_pw_multi_aff *pma,
4512 int (*fn)(__isl_take isl_set *set,
4513 __isl_take isl_multi_aff *maff,
4514 void *user), void *user);
4516 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4517 __isl_keep isl_union_pw_multi_aff *upma,
4518 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4519 void *user), void *user);
4521 It can be modified using
4523 #include <isl/aff.h>
4524 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4525 __isl_take isl_multi_aff *multi, int pos,
4526 __isl_take isl_aff *aff);
4527 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4528 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4529 __isl_take isl_pw_aff *pa);
4530 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4531 __isl_take isl_multi_aff *maff,
4532 enum isl_dim_type type, unsigned pos, const char *s);
4533 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4534 __isl_take isl_multi_aff *maff,
4535 enum isl_dim_type type, unsigned pos,
4536 __isl_take isl_id *id);
4537 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4538 __isl_take isl_multi_aff *maff,
4539 enum isl_dim_type type, const char *s);
4540 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4541 __isl_take isl_multi_aff *maff,
4542 enum isl_dim_type type, __isl_take isl_id *id);
4543 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4544 __isl_take isl_pw_multi_aff *pma,
4545 enum isl_dim_type type, __isl_take isl_id *id);
4546 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4547 __isl_take isl_multi_aff *ma,
4548 enum isl_dim_type type);
4549 __isl_give isl_multi_pw_aff *
4550 isl_multi_pw_aff_reset_tuple_id(
4551 __isl_take isl_multi_pw_aff *mpa,
4552 enum isl_dim_type type);
4553 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4554 __isl_take isl_multi_aff *ma);
4555 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4556 __isl_take isl_multi_pw_aff *mpa);
4558 __isl_give isl_multi_pw_aff *
4559 isl_multi_pw_aff_set_dim_name(
4560 __isl_take isl_multi_pw_aff *mpa,
4561 enum isl_dim_type type, unsigned pos, const char *s);
4562 __isl_give isl_multi_pw_aff *
4563 isl_multi_pw_aff_set_dim_id(
4564 __isl_take isl_multi_pw_aff *mpa,
4565 enum isl_dim_type type, unsigned pos,
4566 __isl_take isl_id *id);
4567 __isl_give isl_multi_pw_aff *
4568 isl_multi_pw_aff_set_tuple_name(
4569 __isl_take isl_multi_pw_aff *mpa,
4570 enum isl_dim_type type, const char *s);
4572 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4573 __isl_take isl_multi_aff *ma);
4575 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4576 __isl_take isl_multi_aff *ma,
4577 enum isl_dim_type type, unsigned first, unsigned n);
4578 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4579 __isl_take isl_multi_aff *ma,
4580 enum isl_dim_type type, unsigned n);
4581 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4582 __isl_take isl_multi_aff *maff,
4583 enum isl_dim_type type, unsigned first, unsigned n);
4584 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4585 __isl_take isl_pw_multi_aff *pma,
4586 enum isl_dim_type type, unsigned first, unsigned n);
4588 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4589 __isl_take isl_multi_pw_aff *mpa,
4590 enum isl_dim_type type, unsigned first, unsigned n);
4591 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4592 __isl_take isl_multi_pw_aff *mpa,
4593 enum isl_dim_type type, unsigned n);
4594 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4595 __isl_take isl_multi_pw_aff *pma,
4596 enum isl_dim_type dst_type, unsigned dst_pos,
4597 enum isl_dim_type src_type, unsigned src_pos,
4600 To check whether two multiple affine expressions are
4601 (obviously) equal to each other, use
4603 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4604 __isl_keep isl_multi_aff *maff2);
4605 int isl_pw_multi_aff_plain_is_equal(
4606 __isl_keep isl_pw_multi_aff *pma1,
4607 __isl_keep isl_pw_multi_aff *pma2);
4608 int isl_multi_pw_aff_plain_is_equal(
4609 __isl_keep isl_multi_pw_aff *mpa1,
4610 __isl_keep isl_multi_pw_aff *mpa2);
4611 int isl_multi_pw_aff_is_equal(
4612 __isl_keep isl_multi_pw_aff *mpa1,
4613 __isl_keep isl_multi_pw_aff *mpa2);
4617 #include <isl/aff.h>
4618 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4619 __isl_take isl_pw_multi_aff *pma1,
4620 __isl_take isl_pw_multi_aff *pma2);
4621 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4622 __isl_take isl_pw_multi_aff *pma1,
4623 __isl_take isl_pw_multi_aff *pma2);
4624 __isl_give isl_multi_aff *isl_multi_aff_add(
4625 __isl_take isl_multi_aff *maff1,
4626 __isl_take isl_multi_aff *maff2);
4627 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4628 __isl_take isl_pw_multi_aff *pma1,
4629 __isl_take isl_pw_multi_aff *pma2);
4630 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4631 __isl_take isl_union_pw_multi_aff *upma1,
4632 __isl_take isl_union_pw_multi_aff *upma2);
4633 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4634 __isl_take isl_pw_multi_aff *pma1,
4635 __isl_take isl_pw_multi_aff *pma2);
4636 __isl_give isl_multi_aff *isl_multi_aff_sub(
4637 __isl_take isl_multi_aff *ma1,
4638 __isl_take isl_multi_aff *ma2);
4639 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4640 __isl_take isl_pw_multi_aff *pma1,
4641 __isl_take isl_pw_multi_aff *pma2);
4642 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4643 __isl_take isl_union_pw_multi_aff *upma1,
4644 __isl_take isl_union_pw_multi_aff *upma2);
4646 C<isl_multi_aff_sub> subtracts the second argument from the first.
4648 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4649 __isl_take isl_multi_aff *ma,
4650 __isl_take isl_val *v);
4651 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4652 __isl_take isl_pw_multi_aff *pma,
4653 __isl_take isl_val *v);
4654 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4655 __isl_take isl_multi_pw_aff *mpa,
4656 __isl_take isl_val *v);
4657 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4658 __isl_take isl_multi_aff *ma,
4659 __isl_take isl_multi_val *mv);
4660 __isl_give isl_pw_multi_aff *
4661 isl_pw_multi_aff_scale_multi_val(
4662 __isl_take isl_pw_multi_aff *pma,
4663 __isl_take isl_multi_val *mv);
4664 __isl_give isl_multi_pw_aff *
4665 isl_multi_pw_aff_scale_multi_val(
4666 __isl_take isl_multi_pw_aff *mpa,
4667 __isl_take isl_multi_val *mv);
4668 __isl_give isl_union_pw_multi_aff *
4669 isl_union_pw_multi_aff_scale_multi_val(
4670 __isl_take isl_union_pw_multi_aff *upma,
4671 __isl_take isl_multi_val *mv);
4672 __isl_give isl_multi_aff *
4673 isl_multi_aff_scale_down_multi_val(
4674 __isl_take isl_multi_aff *ma,
4675 __isl_take isl_multi_val *mv);
4676 __isl_give isl_multi_pw_aff *
4677 isl_multi_pw_aff_scale_down_multi_val(
4678 __isl_take isl_multi_pw_aff *mpa,
4679 __isl_take isl_multi_val *mv);
4681 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4682 by the corresponding elements of C<mv>.
4684 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4685 __isl_take isl_pw_multi_aff *pma,
4686 enum isl_dim_type type, unsigned pos, int value);
4687 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4688 __isl_take isl_pw_multi_aff *pma,
4689 __isl_take isl_set *set);
4690 __isl_give isl_set *isl_multi_pw_aff_domain(
4691 __isl_take isl_multi_pw_aff *mpa);
4692 __isl_give isl_multi_pw_aff *
4693 isl_multi_pw_aff_intersect_params(
4694 __isl_take isl_multi_pw_aff *mpa,
4695 __isl_take isl_set *set);
4696 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4697 __isl_take isl_pw_multi_aff *pma,
4698 __isl_take isl_set *set);
4699 __isl_give isl_multi_pw_aff *
4700 isl_multi_pw_aff_intersect_domain(
4701 __isl_take isl_multi_pw_aff *mpa,
4702 __isl_take isl_set *domain);
4703 __isl_give isl_union_pw_multi_aff *
4704 isl_union_pw_multi_aff_intersect_domain(
4705 __isl_take isl_union_pw_multi_aff *upma,
4706 __isl_take isl_union_set *uset);
4707 __isl_give isl_multi_aff *isl_multi_aff_lift(
4708 __isl_take isl_multi_aff *maff,
4709 __isl_give isl_local_space **ls);
4710 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4711 __isl_take isl_pw_multi_aff *pma);
4712 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4713 __isl_take isl_multi_pw_aff *mpa);
4714 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4715 __isl_take isl_multi_aff *multi,
4716 __isl_take isl_space *model);
4717 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4718 __isl_take isl_pw_multi_aff *pma,
4719 __isl_take isl_space *model);
4720 __isl_give isl_pw_multi_aff *
4721 isl_pw_multi_aff_project_domain_on_params(
4722 __isl_take isl_pw_multi_aff *pma);
4723 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4724 __isl_take isl_multi_aff *maff,
4725 __isl_take isl_set *context);
4726 __isl_give isl_multi_aff *isl_multi_aff_gist(
4727 __isl_take isl_multi_aff *maff,
4728 __isl_take isl_set *context);
4729 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4730 __isl_take isl_pw_multi_aff *pma,
4731 __isl_take isl_set *set);
4732 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4733 __isl_take isl_pw_multi_aff *pma,
4734 __isl_take isl_set *set);
4735 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4736 __isl_take isl_multi_pw_aff *mpa,
4737 __isl_take isl_set *set);
4738 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4739 __isl_take isl_multi_pw_aff *mpa,
4740 __isl_take isl_set *set);
4741 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4742 __isl_take isl_multi_aff *ma);
4743 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4744 __isl_take isl_multi_pw_aff *mpa);
4745 __isl_give isl_set *isl_pw_multi_aff_domain(
4746 __isl_take isl_pw_multi_aff *pma);
4747 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4748 __isl_take isl_union_pw_multi_aff *upma);
4749 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4750 __isl_take isl_multi_aff *ma1, unsigned pos,
4751 __isl_take isl_multi_aff *ma2);
4752 __isl_give isl_multi_aff *isl_multi_aff_splice(
4753 __isl_take isl_multi_aff *ma1,
4754 unsigned in_pos, unsigned out_pos,
4755 __isl_take isl_multi_aff *ma2);
4756 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4757 __isl_take isl_multi_aff *ma1,
4758 __isl_take isl_multi_aff *ma2);
4759 __isl_give isl_multi_aff *
4760 isl_multi_aff_range_factor_domain(
4761 __isl_take isl_multi_aff *ma);
4762 __isl_give isl_multi_aff *
4763 isl_multi_aff_range_factor_range(
4764 __isl_take isl_multi_aff *ma);
4765 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4766 __isl_take isl_multi_aff *ma1,
4767 __isl_take isl_multi_aff *ma2);
4768 __isl_give isl_multi_aff *isl_multi_aff_product(
4769 __isl_take isl_multi_aff *ma1,
4770 __isl_take isl_multi_aff *ma2);
4771 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4772 __isl_take isl_multi_pw_aff *mpa1,
4773 __isl_take isl_multi_pw_aff *mpa2);
4774 __isl_give isl_pw_multi_aff *
4775 isl_pw_multi_aff_range_product(
4776 __isl_take isl_pw_multi_aff *pma1,
4777 __isl_take isl_pw_multi_aff *pma2);
4778 __isl_give isl_multi_pw_aff *
4779 isl_multi_pw_aff_range_factor_domain(
4780 __isl_take isl_multi_pw_aff *mpa);
4781 __isl_give isl_multi_pw_aff *
4782 isl_multi_pw_aff_range_factor_range(
4783 __isl_take isl_multi_pw_aff *mpa);
4784 __isl_give isl_pw_multi_aff *
4785 isl_pw_multi_aff_flat_range_product(
4786 __isl_take isl_pw_multi_aff *pma1,
4787 __isl_take isl_pw_multi_aff *pma2);
4788 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4789 __isl_take isl_pw_multi_aff *pma1,
4790 __isl_take isl_pw_multi_aff *pma2);
4791 __isl_give isl_union_pw_multi_aff *
4792 isl_union_pw_multi_aff_flat_range_product(
4793 __isl_take isl_union_pw_multi_aff *upma1,
4794 __isl_take isl_union_pw_multi_aff *upma2);
4795 __isl_give isl_multi_pw_aff *
4796 isl_multi_pw_aff_range_splice(
4797 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4798 __isl_take isl_multi_pw_aff *mpa2);
4799 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4800 __isl_take isl_multi_pw_aff *mpa1,
4801 unsigned in_pos, unsigned out_pos,
4802 __isl_take isl_multi_pw_aff *mpa2);
4803 __isl_give isl_multi_pw_aff *
4804 isl_multi_pw_aff_range_product(
4805 __isl_take isl_multi_pw_aff *mpa1,
4806 __isl_take isl_multi_pw_aff *mpa2);
4807 __isl_give isl_multi_pw_aff *
4808 isl_multi_pw_aff_flat_range_product(
4809 __isl_take isl_multi_pw_aff *mpa1,
4810 __isl_take isl_multi_pw_aff *mpa2);
4812 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4813 then it is assigned the local space that lies at the basis of
4814 the lifting applied.
4816 #include <isl/aff.h>
4817 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4818 __isl_take isl_multi_aff *ma1,
4819 __isl_take isl_multi_aff *ma2);
4820 __isl_give isl_pw_multi_aff *
4821 isl_pw_multi_aff_pullback_multi_aff(
4822 __isl_take isl_pw_multi_aff *pma,
4823 __isl_take isl_multi_aff *ma);
4824 __isl_give isl_multi_pw_aff *
4825 isl_multi_pw_aff_pullback_multi_aff(
4826 __isl_take isl_multi_pw_aff *mpa,
4827 __isl_take isl_multi_aff *ma);
4828 __isl_give isl_pw_multi_aff *
4829 isl_pw_multi_aff_pullback_pw_multi_aff(
4830 __isl_take isl_pw_multi_aff *pma1,
4831 __isl_take isl_pw_multi_aff *pma2);
4832 __isl_give isl_multi_pw_aff *
4833 isl_multi_pw_aff_pullback_pw_multi_aff(
4834 __isl_take isl_multi_pw_aff *mpa,
4835 __isl_take isl_pw_multi_aff *pma);
4836 __isl_give isl_multi_pw_aff *
4837 isl_multi_pw_aff_pullback_multi_pw_aff(
4838 __isl_take isl_multi_pw_aff *mpa1,
4839 __isl_take isl_multi_pw_aff *mpa2);
4841 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4842 In other words, C<ma2> is plugged
4845 __isl_give isl_set *isl_multi_aff_lex_le_set(
4846 __isl_take isl_multi_aff *ma1,
4847 __isl_take isl_multi_aff *ma2);
4848 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4849 __isl_take isl_multi_aff *ma1,
4850 __isl_take isl_multi_aff *ma2);
4852 The function C<isl_multi_aff_lex_le_set> returns a set
4853 containing those elements in the shared domain space
4854 where C<ma1> is lexicographically smaller than or
4857 An expression can be read from input using
4859 #include <isl/aff.h>
4860 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4861 isl_ctx *ctx, const char *str);
4862 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4863 isl_ctx *ctx, const char *str);
4864 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4865 isl_ctx *ctx, const char *str);
4866 __isl_give isl_union_pw_multi_aff *
4867 isl_union_pw_multi_aff_read_from_str(
4868 isl_ctx *ctx, const char *str);
4870 An expression can be printed using
4872 #include <isl/aff.h>
4873 __isl_give isl_printer *isl_printer_print_multi_aff(
4874 __isl_take isl_printer *p,
4875 __isl_keep isl_multi_aff *maff);
4876 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4877 __isl_take isl_printer *p,
4878 __isl_keep isl_pw_multi_aff *pma);
4879 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4880 __isl_take isl_printer *p,
4881 __isl_keep isl_union_pw_multi_aff *upma);
4882 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4883 __isl_take isl_printer *p,
4884 __isl_keep isl_multi_pw_aff *mpa);
4888 Points are elements of a set. They can be used to construct
4889 simple sets (boxes) or they can be used to represent the
4890 individual elements of a set.
4891 The zero point (the origin) can be created using
4893 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4895 The coordinates of a point can be inspected, set and changed
4898 __isl_give isl_val *isl_point_get_coordinate_val(
4899 __isl_keep isl_point *pnt,
4900 enum isl_dim_type type, int pos);
4901 __isl_give isl_point *isl_point_set_coordinate_val(
4902 __isl_take isl_point *pnt,
4903 enum isl_dim_type type, int pos,
4904 __isl_take isl_val *v);
4906 __isl_give isl_point *isl_point_add_ui(
4907 __isl_take isl_point *pnt,
4908 enum isl_dim_type type, int pos, unsigned val);
4909 __isl_give isl_point *isl_point_sub_ui(
4910 __isl_take isl_point *pnt,
4911 enum isl_dim_type type, int pos, unsigned val);
4913 Other properties can be obtained using
4915 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4917 Points can be copied or freed using
4919 __isl_give isl_point *isl_point_copy(
4920 __isl_keep isl_point *pnt);
4921 void isl_point_free(__isl_take isl_point *pnt);
4923 A singleton set can be created from a point using
4925 __isl_give isl_basic_set *isl_basic_set_from_point(
4926 __isl_take isl_point *pnt);
4927 __isl_give isl_set *isl_set_from_point(
4928 __isl_take isl_point *pnt);
4930 and a box can be created from two opposite extremal points using
4932 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4933 __isl_take isl_point *pnt1,
4934 __isl_take isl_point *pnt2);
4935 __isl_give isl_set *isl_set_box_from_points(
4936 __isl_take isl_point *pnt1,
4937 __isl_take isl_point *pnt2);
4939 All elements of a B<bounded> (union) set can be enumerated using
4940 the following functions.
4942 int isl_set_foreach_point(__isl_keep isl_set *set,
4943 int (*fn)(__isl_take isl_point *pnt, void *user),
4945 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4946 int (*fn)(__isl_take isl_point *pnt, void *user),
4949 The function C<fn> is called for each integer point in
4950 C<set> with as second argument the last argument of
4951 the C<isl_set_foreach_point> call. The function C<fn>
4952 should return C<0> on success and C<-1> on failure.
4953 In the latter case, C<isl_set_foreach_point> will stop
4954 enumerating and return C<-1> as well.
4955 If the enumeration is performed successfully and to completion,
4956 then C<isl_set_foreach_point> returns C<0>.
4958 To obtain a single point of a (basic) set, use
4960 __isl_give isl_point *isl_basic_set_sample_point(
4961 __isl_take isl_basic_set *bset);
4962 __isl_give isl_point *isl_set_sample_point(
4963 __isl_take isl_set *set);
4965 If C<set> does not contain any (integer) points, then the
4966 resulting point will be ``void'', a property that can be
4969 int isl_point_is_void(__isl_keep isl_point *pnt);
4971 =head2 Piecewise Quasipolynomials
4973 A piecewise quasipolynomial is a particular kind of function that maps
4974 a parametric point to a rational value.
4975 More specifically, a quasipolynomial is a polynomial expression in greatest
4976 integer parts of affine expressions of parameters and variables.
4977 A piecewise quasipolynomial is a subdivision of a given parametric
4978 domain into disjoint cells with a quasipolynomial associated to
4979 each cell. The value of the piecewise quasipolynomial at a given
4980 point is the value of the quasipolynomial associated to the cell
4981 that contains the point. Outside of the union of cells,
4982 the value is assumed to be zero.
4983 For example, the piecewise quasipolynomial
4985 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4987 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4988 A given piecewise quasipolynomial has a fixed domain dimension.
4989 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4990 defined over different domains.
4991 Piecewise quasipolynomials are mainly used by the C<barvinok>
4992 library for representing the number of elements in a parametric set or map.
4993 For example, the piecewise quasipolynomial above represents
4994 the number of points in the map
4996 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4998 =head3 Input and Output
5000 Piecewise quasipolynomials can be read from input using
5002 __isl_give isl_union_pw_qpolynomial *
5003 isl_union_pw_qpolynomial_read_from_str(
5004 isl_ctx *ctx, const char *str);
5006 Quasipolynomials and piecewise quasipolynomials can be printed
5007 using the following functions.
5009 __isl_give isl_printer *isl_printer_print_qpolynomial(
5010 __isl_take isl_printer *p,
5011 __isl_keep isl_qpolynomial *qp);
5013 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
5014 __isl_take isl_printer *p,
5015 __isl_keep isl_pw_qpolynomial *pwqp);
5017 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
5018 __isl_take isl_printer *p,
5019 __isl_keep isl_union_pw_qpolynomial *upwqp);
5021 The output format of the printer
5022 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5023 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
5025 In case of printing in C<ISL_FORMAT_C>, the user may want
5026 to set the names of all dimensions
5028 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
5029 __isl_take isl_qpolynomial *qp,
5030 enum isl_dim_type type, unsigned pos,
5032 __isl_give isl_pw_qpolynomial *
5033 isl_pw_qpolynomial_set_dim_name(
5034 __isl_take isl_pw_qpolynomial *pwqp,
5035 enum isl_dim_type type, unsigned pos,
5038 =head3 Creating New (Piecewise) Quasipolynomials
5040 Some simple quasipolynomials can be created using the following functions.
5041 More complicated quasipolynomials can be created by applying
5042 operations such as addition and multiplication
5043 on the resulting quasipolynomials
5045 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
5046 __isl_take isl_space *domain);
5047 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
5048 __isl_take isl_space *domain);
5049 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
5050 __isl_take isl_space *domain);
5051 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
5052 __isl_take isl_space *domain);
5053 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
5054 __isl_take isl_space *domain);
5055 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
5056 __isl_take isl_space *domain,
5057 __isl_take isl_val *val);
5058 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
5059 __isl_take isl_space *domain,
5060 enum isl_dim_type type, unsigned pos);
5061 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
5062 __isl_take isl_aff *aff);
5064 Note that the space in which a quasipolynomial lives is a map space
5065 with a one-dimensional range. The C<domain> argument in some of
5066 the functions above corresponds to the domain of this map space.
5068 The zero piecewise quasipolynomial or a piecewise quasipolynomial
5069 with a single cell can be created using the following functions.
5070 Multiple of these single cell piecewise quasipolynomials can
5071 be combined to create more complicated piecewise quasipolynomials.
5073 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
5074 __isl_take isl_space *space);
5075 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
5076 __isl_take isl_set *set,
5077 __isl_take isl_qpolynomial *qp);
5078 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
5079 __isl_take isl_qpolynomial *qp);
5080 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
5081 __isl_take isl_pw_aff *pwaff);
5083 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
5084 __isl_take isl_space *space);
5085 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
5086 __isl_take isl_pw_qpolynomial *pwqp);
5087 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
5088 __isl_take isl_union_pw_qpolynomial *upwqp,
5089 __isl_take isl_pw_qpolynomial *pwqp);
5091 Quasipolynomials can be copied and freed again using the following
5094 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
5095 __isl_keep isl_qpolynomial *qp);
5096 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
5098 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
5099 __isl_keep isl_pw_qpolynomial *pwqp);
5100 void *isl_pw_qpolynomial_free(
5101 __isl_take isl_pw_qpolynomial *pwqp);
5103 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
5104 __isl_keep isl_union_pw_qpolynomial *upwqp);
5105 void *isl_union_pw_qpolynomial_free(
5106 __isl_take isl_union_pw_qpolynomial *upwqp);
5108 =head3 Inspecting (Piecewise) Quasipolynomials
5110 To iterate over all piecewise quasipolynomials in a union
5111 piecewise quasipolynomial, use the following function
5113 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
5114 __isl_keep isl_union_pw_qpolynomial *upwqp,
5115 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
5118 To extract the piecewise quasipolynomial in a given space from a union, use
5120 __isl_give isl_pw_qpolynomial *
5121 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
5122 __isl_keep isl_union_pw_qpolynomial *upwqp,
5123 __isl_take isl_space *space);
5125 To iterate over the cells in a piecewise quasipolynomial,
5126 use either of the following two functions
5128 int isl_pw_qpolynomial_foreach_piece(
5129 __isl_keep isl_pw_qpolynomial *pwqp,
5130 int (*fn)(__isl_take isl_set *set,
5131 __isl_take isl_qpolynomial *qp,
5132 void *user), void *user);
5133 int isl_pw_qpolynomial_foreach_lifted_piece(
5134 __isl_keep isl_pw_qpolynomial *pwqp,
5135 int (*fn)(__isl_take isl_set *set,
5136 __isl_take isl_qpolynomial *qp,
5137 void *user), void *user);
5139 As usual, the function C<fn> should return C<0> on success
5140 and C<-1> on failure. The difference between
5141 C<isl_pw_qpolynomial_foreach_piece> and
5142 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
5143 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
5144 compute unique representations for all existentially quantified
5145 variables and then turn these existentially quantified variables
5146 into extra set variables, adapting the associated quasipolynomial
5147 accordingly. This means that the C<set> passed to C<fn>
5148 will not have any existentially quantified variables, but that
5149 the dimensions of the sets may be different for different
5150 invocations of C<fn>.
5152 The constant term of a quasipolynomial can be extracted using
5154 __isl_give isl_val *isl_qpolynomial_get_constant_val(
5155 __isl_keep isl_qpolynomial *qp);
5157 To iterate over all terms in a quasipolynomial,
5160 int isl_qpolynomial_foreach_term(
5161 __isl_keep isl_qpolynomial *qp,
5162 int (*fn)(__isl_take isl_term *term,
5163 void *user), void *user);
5165 The terms themselves can be inspected and freed using
5168 unsigned isl_term_dim(__isl_keep isl_term *term,
5169 enum isl_dim_type type);
5170 __isl_give isl_val *isl_term_get_coefficient_val(
5171 __isl_keep isl_term *term);
5172 int isl_term_get_exp(__isl_keep isl_term *term,
5173 enum isl_dim_type type, unsigned pos);
5174 __isl_give isl_aff *isl_term_get_div(
5175 __isl_keep isl_term *term, unsigned pos);
5176 void isl_term_free(__isl_take isl_term *term);
5178 Each term is a product of parameters, set variables and
5179 integer divisions. The function C<isl_term_get_exp>
5180 returns the exponent of a given dimensions in the given term.
5182 =head3 Properties of (Piecewise) Quasipolynomials
5184 To check whether two union piecewise quasipolynomials are
5185 obviously equal, use
5187 int isl_union_pw_qpolynomial_plain_is_equal(
5188 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5189 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5191 =head3 Operations on (Piecewise) Quasipolynomials
5193 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5194 __isl_take isl_qpolynomial *qp,
5195 __isl_take isl_val *v);
5196 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5197 __isl_take isl_qpolynomial *qp);
5198 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5199 __isl_take isl_qpolynomial *qp1,
5200 __isl_take isl_qpolynomial *qp2);
5201 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5202 __isl_take isl_qpolynomial *qp1,
5203 __isl_take isl_qpolynomial *qp2);
5204 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5205 __isl_take isl_qpolynomial *qp1,
5206 __isl_take isl_qpolynomial *qp2);
5207 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5208 __isl_take isl_qpolynomial *qp, unsigned exponent);
5210 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5211 __isl_take isl_pw_qpolynomial *pwqp,
5212 enum isl_dim_type type, unsigned n,
5213 __isl_take isl_val *v);
5214 __isl_give isl_pw_qpolynomial *
5215 isl_pw_qpolynomial_scale_val(
5216 __isl_take isl_pw_qpolynomial *pwqp,
5217 __isl_take isl_val *v);
5218 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5219 __isl_take isl_pw_qpolynomial *pwqp1,
5220 __isl_take isl_pw_qpolynomial *pwqp2);
5221 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5222 __isl_take isl_pw_qpolynomial *pwqp1,
5223 __isl_take isl_pw_qpolynomial *pwqp2);
5224 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5225 __isl_take isl_pw_qpolynomial *pwqp1,
5226 __isl_take isl_pw_qpolynomial *pwqp2);
5227 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5228 __isl_take isl_pw_qpolynomial *pwqp);
5229 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5230 __isl_take isl_pw_qpolynomial *pwqp1,
5231 __isl_take isl_pw_qpolynomial *pwqp2);
5232 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5233 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5235 __isl_give isl_union_pw_qpolynomial *
5236 isl_union_pw_qpolynomial_scale_val(
5237 __isl_take isl_union_pw_qpolynomial *upwqp,
5238 __isl_take isl_val *v);
5239 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5240 __isl_take isl_union_pw_qpolynomial *upwqp1,
5241 __isl_take isl_union_pw_qpolynomial *upwqp2);
5242 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5243 __isl_take isl_union_pw_qpolynomial *upwqp1,
5244 __isl_take isl_union_pw_qpolynomial *upwqp2);
5245 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5246 __isl_take isl_union_pw_qpolynomial *upwqp1,
5247 __isl_take isl_union_pw_qpolynomial *upwqp2);
5249 __isl_give isl_val *isl_pw_qpolynomial_eval(
5250 __isl_take isl_pw_qpolynomial *pwqp,
5251 __isl_take isl_point *pnt);
5253 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5254 __isl_take isl_union_pw_qpolynomial *upwqp,
5255 __isl_take isl_point *pnt);
5257 __isl_give isl_set *isl_pw_qpolynomial_domain(
5258 __isl_take isl_pw_qpolynomial *pwqp);
5259 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5260 __isl_take isl_pw_qpolynomial *pwpq,
5261 __isl_take isl_set *set);
5262 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5263 __isl_take isl_pw_qpolynomial *pwpq,
5264 __isl_take isl_set *set);
5266 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5267 __isl_take isl_union_pw_qpolynomial *upwqp);
5268 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5269 __isl_take isl_union_pw_qpolynomial *upwpq,
5270 __isl_take isl_union_set *uset);
5271 __isl_give isl_union_pw_qpolynomial *
5272 isl_union_pw_qpolynomial_intersect_params(
5273 __isl_take isl_union_pw_qpolynomial *upwpq,
5274 __isl_take isl_set *set);
5276 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5277 __isl_take isl_qpolynomial *qp,
5278 __isl_take isl_space *model);
5280 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5281 __isl_take isl_qpolynomial *qp);
5282 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5283 __isl_take isl_pw_qpolynomial *pwqp);
5285 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5286 __isl_take isl_union_pw_qpolynomial *upwqp);
5288 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5289 __isl_take isl_qpolynomial *qp,
5290 __isl_take isl_set *context);
5291 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5292 __isl_take isl_qpolynomial *qp,
5293 __isl_take isl_set *context);
5295 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5296 __isl_take isl_pw_qpolynomial *pwqp,
5297 __isl_take isl_set *context);
5298 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5299 __isl_take isl_pw_qpolynomial *pwqp,
5300 __isl_take isl_set *context);
5302 __isl_give isl_union_pw_qpolynomial *
5303 isl_union_pw_qpolynomial_gist_params(
5304 __isl_take isl_union_pw_qpolynomial *upwqp,
5305 __isl_take isl_set *context);
5306 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5307 __isl_take isl_union_pw_qpolynomial *upwqp,
5308 __isl_take isl_union_set *context);
5310 The gist operation applies the gist operation to each of
5311 the cells in the domain of the input piecewise quasipolynomial.
5312 The context is also exploited
5313 to simplify the quasipolynomials associated to each cell.
5315 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5316 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5317 __isl_give isl_union_pw_qpolynomial *
5318 isl_union_pw_qpolynomial_to_polynomial(
5319 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5321 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5322 the polynomial will be an overapproximation. If C<sign> is negative,
5323 it will be an underapproximation. If C<sign> is zero, the approximation
5324 will lie somewhere in between.
5326 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5328 A piecewise quasipolynomial reduction is a piecewise
5329 reduction (or fold) of quasipolynomials.
5330 In particular, the reduction can be maximum or a minimum.
5331 The objects are mainly used to represent the result of
5332 an upper or lower bound on a quasipolynomial over its domain,
5333 i.e., as the result of the following function.
5335 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5336 __isl_take isl_pw_qpolynomial *pwqp,
5337 enum isl_fold type, int *tight);
5339 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5340 __isl_take isl_union_pw_qpolynomial *upwqp,
5341 enum isl_fold type, int *tight);
5343 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5344 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5345 is the returned bound is known be tight, i.e., for each value
5346 of the parameters there is at least
5347 one element in the domain that reaches the bound.
5348 If the domain of C<pwqp> is not wrapping, then the bound is computed
5349 over all elements in that domain and the result has a purely parametric
5350 domain. If the domain of C<pwqp> is wrapping, then the bound is
5351 computed over the range of the wrapped relation. The domain of the
5352 wrapped relation becomes the domain of the result.
5354 A (piecewise) quasipolynomial reduction can be copied or freed using the
5355 following functions.
5357 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5358 __isl_keep isl_qpolynomial_fold *fold);
5359 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5360 __isl_keep isl_pw_qpolynomial_fold *pwf);
5361 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5362 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5363 void isl_qpolynomial_fold_free(
5364 __isl_take isl_qpolynomial_fold *fold);
5365 void *isl_pw_qpolynomial_fold_free(
5366 __isl_take isl_pw_qpolynomial_fold *pwf);
5367 void *isl_union_pw_qpolynomial_fold_free(
5368 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5370 =head3 Printing Piecewise Quasipolynomial Reductions
5372 Piecewise quasipolynomial reductions can be printed
5373 using the following function.
5375 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5376 __isl_take isl_printer *p,
5377 __isl_keep isl_pw_qpolynomial_fold *pwf);
5378 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5379 __isl_take isl_printer *p,
5380 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5382 For C<isl_printer_print_pw_qpolynomial_fold>,
5383 output format of the printer
5384 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5385 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5386 output format of the printer
5387 needs to be set to C<ISL_FORMAT_ISL>.
5388 In case of printing in C<ISL_FORMAT_C>, the user may want
5389 to set the names of all dimensions
5391 __isl_give isl_pw_qpolynomial_fold *
5392 isl_pw_qpolynomial_fold_set_dim_name(
5393 __isl_take isl_pw_qpolynomial_fold *pwf,
5394 enum isl_dim_type type, unsigned pos,
5397 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5399 To iterate over all piecewise quasipolynomial reductions in a union
5400 piecewise quasipolynomial reduction, use the following function
5402 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5403 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5404 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5405 void *user), void *user);
5407 To iterate over the cells in a piecewise quasipolynomial reduction,
5408 use either of the following two functions
5410 int isl_pw_qpolynomial_fold_foreach_piece(
5411 __isl_keep isl_pw_qpolynomial_fold *pwf,
5412 int (*fn)(__isl_take isl_set *set,
5413 __isl_take isl_qpolynomial_fold *fold,
5414 void *user), void *user);
5415 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5416 __isl_keep isl_pw_qpolynomial_fold *pwf,
5417 int (*fn)(__isl_take isl_set *set,
5418 __isl_take isl_qpolynomial_fold *fold,
5419 void *user), void *user);
5421 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5422 of the difference between these two functions.
5424 To iterate over all quasipolynomials in a reduction, use
5426 int isl_qpolynomial_fold_foreach_qpolynomial(
5427 __isl_keep isl_qpolynomial_fold *fold,
5428 int (*fn)(__isl_take isl_qpolynomial *qp,
5429 void *user), void *user);
5431 =head3 Properties of Piecewise Quasipolynomial Reductions
5433 To check whether two union piecewise quasipolynomial reductions are
5434 obviously equal, use
5436 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5437 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5438 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5440 =head3 Operations on Piecewise Quasipolynomial Reductions
5442 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5443 __isl_take isl_qpolynomial_fold *fold,
5444 __isl_take isl_val *v);
5445 __isl_give isl_pw_qpolynomial_fold *
5446 isl_pw_qpolynomial_fold_scale_val(
5447 __isl_take isl_pw_qpolynomial_fold *pwf,
5448 __isl_take isl_val *v);
5449 __isl_give isl_union_pw_qpolynomial_fold *
5450 isl_union_pw_qpolynomial_fold_scale_val(
5451 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5452 __isl_take isl_val *v);
5454 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5455 __isl_take isl_pw_qpolynomial_fold *pwf1,
5456 __isl_take isl_pw_qpolynomial_fold *pwf2);
5458 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5459 __isl_take isl_pw_qpolynomial_fold *pwf1,
5460 __isl_take isl_pw_qpolynomial_fold *pwf2);
5462 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5463 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5464 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5466 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5467 __isl_take isl_pw_qpolynomial_fold *pwf,
5468 __isl_take isl_point *pnt);
5470 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5471 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5472 __isl_take isl_point *pnt);
5474 __isl_give isl_pw_qpolynomial_fold *
5475 isl_pw_qpolynomial_fold_intersect_params(
5476 __isl_take isl_pw_qpolynomial_fold *pwf,
5477 __isl_take isl_set *set);
5479 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5480 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5481 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5482 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5483 __isl_take isl_union_set *uset);
5484 __isl_give isl_union_pw_qpolynomial_fold *
5485 isl_union_pw_qpolynomial_fold_intersect_params(
5486 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5487 __isl_take isl_set *set);
5489 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5490 __isl_take isl_pw_qpolynomial_fold *pwf);
5492 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5493 __isl_take isl_pw_qpolynomial_fold *pwf);
5495 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5496 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5498 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5499 __isl_take isl_qpolynomial_fold *fold,
5500 __isl_take isl_set *context);
5501 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5502 __isl_take isl_qpolynomial_fold *fold,
5503 __isl_take isl_set *context);
5505 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5506 __isl_take isl_pw_qpolynomial_fold *pwf,
5507 __isl_take isl_set *context);
5508 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5509 __isl_take isl_pw_qpolynomial_fold *pwf,
5510 __isl_take isl_set *context);
5512 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5513 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5514 __isl_take isl_union_set *context);
5515 __isl_give isl_union_pw_qpolynomial_fold *
5516 isl_union_pw_qpolynomial_fold_gist_params(
5517 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5518 __isl_take isl_set *context);
5520 The gist operation applies the gist operation to each of
5521 the cells in the domain of the input piecewise quasipolynomial reduction.
5522 In future, the operation will also exploit the context
5523 to simplify the quasipolynomial reductions associated to each cell.
5525 __isl_give isl_pw_qpolynomial_fold *
5526 isl_set_apply_pw_qpolynomial_fold(
5527 __isl_take isl_set *set,
5528 __isl_take isl_pw_qpolynomial_fold *pwf,
5530 __isl_give isl_pw_qpolynomial_fold *
5531 isl_map_apply_pw_qpolynomial_fold(
5532 __isl_take isl_map *map,
5533 __isl_take isl_pw_qpolynomial_fold *pwf,
5535 __isl_give isl_union_pw_qpolynomial_fold *
5536 isl_union_set_apply_union_pw_qpolynomial_fold(
5537 __isl_take isl_union_set *uset,
5538 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5540 __isl_give isl_union_pw_qpolynomial_fold *
5541 isl_union_map_apply_union_pw_qpolynomial_fold(
5542 __isl_take isl_union_map *umap,
5543 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5546 The functions taking a map
5547 compose the given map with the given piecewise quasipolynomial reduction.
5548 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5549 over all elements in the intersection of the range of the map
5550 and the domain of the piecewise quasipolynomial reduction
5551 as a function of an element in the domain of the map.
5552 The functions taking a set compute a bound over all elements in the
5553 intersection of the set and the domain of the
5554 piecewise quasipolynomial reduction.
5556 =head2 Parametric Vertex Enumeration
5558 The parametric vertex enumeration described in this section
5559 is mainly intended to be used internally and by the C<barvinok>
5562 #include <isl/vertices.h>
5563 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5564 __isl_keep isl_basic_set *bset);
5566 The function C<isl_basic_set_compute_vertices> performs the
5567 actual computation of the parametric vertices and the chamber
5568 decomposition and store the result in an C<isl_vertices> object.
5569 This information can be queried by either iterating over all
5570 the vertices or iterating over all the chambers or cells
5571 and then iterating over all vertices that are active on the chamber.
5573 int isl_vertices_foreach_vertex(
5574 __isl_keep isl_vertices *vertices,
5575 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5578 int isl_vertices_foreach_cell(
5579 __isl_keep isl_vertices *vertices,
5580 int (*fn)(__isl_take isl_cell *cell, void *user),
5582 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5583 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5586 Other operations that can be performed on an C<isl_vertices> object are
5589 isl_ctx *isl_vertices_get_ctx(
5590 __isl_keep isl_vertices *vertices);
5591 int isl_vertices_get_n_vertices(
5592 __isl_keep isl_vertices *vertices);
5593 void isl_vertices_free(__isl_take isl_vertices *vertices);
5595 Vertices can be inspected and destroyed using the following functions.
5597 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5598 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5599 __isl_give isl_basic_set *isl_vertex_get_domain(
5600 __isl_keep isl_vertex *vertex);
5601 __isl_give isl_basic_set *isl_vertex_get_expr(
5602 __isl_keep isl_vertex *vertex);
5603 void isl_vertex_free(__isl_take isl_vertex *vertex);
5605 C<isl_vertex_get_expr> returns a singleton parametric set describing
5606 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5608 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5609 B<rational> basic sets, so they should mainly be used for inspection
5610 and should not be mixed with integer sets.
5612 Chambers can be inspected and destroyed using the following functions.
5614 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5615 __isl_give isl_basic_set *isl_cell_get_domain(
5616 __isl_keep isl_cell *cell);
5617 void isl_cell_free(__isl_take isl_cell *cell);
5619 =head1 Polyhedral Compilation Library
5621 This section collects functionality in C<isl> that has been specifically
5622 designed for use during polyhedral compilation.
5624 =head2 Dependence Analysis
5626 C<isl> contains specialized functionality for performing
5627 array dataflow analysis. That is, given a I<sink> access relation
5628 and a collection of possible I<source> access relations,
5629 C<isl> can compute relations that describe
5630 for each iteration of the sink access, which iteration
5631 of which of the source access relations was the last
5632 to access the same data element before the given iteration
5634 The resulting dependence relations map source iterations
5635 to the corresponding sink iterations.
5636 To compute standard flow dependences, the sink should be
5637 a read, while the sources should be writes.
5638 If any of the source accesses are marked as being I<may>
5639 accesses, then there will be a dependence from the last
5640 I<must> access B<and> from any I<may> access that follows
5641 this last I<must> access.
5642 In particular, if I<all> sources are I<may> accesses,
5643 then memory based dependence analysis is performed.
5644 If, on the other hand, all sources are I<must> accesses,
5645 then value based dependence analysis is performed.
5647 #include <isl/flow.h>
5649 typedef int (*isl_access_level_before)(void *first, void *second);
5651 __isl_give isl_access_info *isl_access_info_alloc(
5652 __isl_take isl_map *sink,
5653 void *sink_user, isl_access_level_before fn,
5655 __isl_give isl_access_info *isl_access_info_add_source(
5656 __isl_take isl_access_info *acc,
5657 __isl_take isl_map *source, int must,
5659 void *isl_access_info_free(__isl_take isl_access_info *acc);
5661 __isl_give isl_flow *isl_access_info_compute_flow(
5662 __isl_take isl_access_info *acc);
5664 int isl_flow_foreach(__isl_keep isl_flow *deps,
5665 int (*fn)(__isl_take isl_map *dep, int must,
5666 void *dep_user, void *user),
5668 __isl_give isl_map *isl_flow_get_no_source(
5669 __isl_keep isl_flow *deps, int must);
5670 void isl_flow_free(__isl_take isl_flow *deps);
5672 The function C<isl_access_info_compute_flow> performs the actual
5673 dependence analysis. The other functions are used to construct
5674 the input for this function or to read off the output.
5676 The input is collected in an C<isl_access_info>, which can
5677 be created through a call to C<isl_access_info_alloc>.
5678 The arguments to this functions are the sink access relation
5679 C<sink>, a token C<sink_user> used to identify the sink
5680 access to the user, a callback function for specifying the
5681 relative order of source and sink accesses, and the number
5682 of source access relations that will be added.
5683 The callback function has type C<int (*)(void *first, void *second)>.
5684 The function is called with two user supplied tokens identifying
5685 either a source or the sink and it should return the shared nesting
5686 level and the relative order of the two accesses.
5687 In particular, let I<n> be the number of loops shared by
5688 the two accesses. If C<first> precedes C<second> textually,
5689 then the function should return I<2 * n + 1>; otherwise,
5690 it should return I<2 * n>.
5691 The sources can be added to the C<isl_access_info> by performing
5692 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5693 C<must> indicates whether the source is a I<must> access
5694 or a I<may> access. Note that a multi-valued access relation
5695 should only be marked I<must> if every iteration in the domain
5696 of the relation accesses I<all> elements in its image.
5697 The C<source_user> token is again used to identify
5698 the source access. The range of the source access relation
5699 C<source> should have the same dimension as the range
5700 of the sink access relation.
5701 The C<isl_access_info_free> function should usually not be
5702 called explicitly, because it is called implicitly by
5703 C<isl_access_info_compute_flow>.
5705 The result of the dependence analysis is collected in an
5706 C<isl_flow>. There may be elements of
5707 the sink access for which no preceding source access could be
5708 found or for which all preceding sources are I<may> accesses.
5709 The relations containing these elements can be obtained through
5710 calls to C<isl_flow_get_no_source>, the first with C<must> set
5711 and the second with C<must> unset.
5712 In the case of standard flow dependence analysis,
5713 with the sink a read and the sources I<must> writes,
5714 the first relation corresponds to the reads from uninitialized
5715 array elements and the second relation is empty.
5716 The actual flow dependences can be extracted using
5717 C<isl_flow_foreach>. This function will call the user-specified
5718 callback function C<fn> for each B<non-empty> dependence between
5719 a source and the sink. The callback function is called
5720 with four arguments, the actual flow dependence relation
5721 mapping source iterations to sink iterations, a boolean that
5722 indicates whether it is a I<must> or I<may> dependence, a token
5723 identifying the source and an additional C<void *> with value
5724 equal to the third argument of the C<isl_flow_foreach> call.
5725 A dependence is marked I<must> if it originates from a I<must>
5726 source and if it is not followed by any I<may> sources.
5728 After finishing with an C<isl_flow>, the user should call
5729 C<isl_flow_free> to free all associated memory.
5731 A higher-level interface to dependence analysis is provided
5732 by the following function.
5734 #include <isl/flow.h>
5736 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5737 __isl_take isl_union_map *must_source,
5738 __isl_take isl_union_map *may_source,
5739 __isl_take isl_union_map *schedule,
5740 __isl_give isl_union_map **must_dep,
5741 __isl_give isl_union_map **may_dep,
5742 __isl_give isl_union_map **must_no_source,
5743 __isl_give isl_union_map **may_no_source);
5745 The arrays are identified by the tuple names of the ranges
5746 of the accesses. The iteration domains by the tuple names
5747 of the domains of the accesses and of the schedule.
5748 The relative order of the iteration domains is given by the
5749 schedule. The relations returned through C<must_no_source>
5750 and C<may_no_source> are subsets of C<sink>.
5751 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5752 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5753 any of the other arguments is treated as an error.
5755 =head3 Interaction with Dependence Analysis
5757 During the dependence analysis, we frequently need to perform
5758 the following operation. Given a relation between sink iterations
5759 and potential source iterations from a particular source domain,
5760 what is the last potential source iteration corresponding to each
5761 sink iteration. It can sometimes be convenient to adjust
5762 the set of potential source iterations before or after each such operation.
5763 The prototypical example is fuzzy array dataflow analysis,
5764 where we need to analyze if, based on data-dependent constraints,
5765 the sink iteration can ever be executed without one or more of
5766 the corresponding potential source iterations being executed.
5767 If so, we can introduce extra parameters and select an unknown
5768 but fixed source iteration from the potential source iterations.
5769 To be able to perform such manipulations, C<isl> provides the following
5772 #include <isl/flow.h>
5774 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5775 __isl_keep isl_map *source_map,
5776 __isl_keep isl_set *sink, void *source_user,
5778 __isl_give isl_access_info *isl_access_info_set_restrict(
5779 __isl_take isl_access_info *acc,
5780 isl_access_restrict fn, void *user);
5782 The function C<isl_access_info_set_restrict> should be called
5783 before calling C<isl_access_info_compute_flow> and registers a callback function
5784 that will be called any time C<isl> is about to compute the last
5785 potential source. The first argument is the (reverse) proto-dependence,
5786 mapping sink iterations to potential source iterations.
5787 The second argument represents the sink iterations for which
5788 we want to compute the last source iteration.
5789 The third argument is the token corresponding to the source
5790 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5791 The callback is expected to return a restriction on either the input or
5792 the output of the operation computing the last potential source.
5793 If the input needs to be restricted then restrictions are needed
5794 for both the source and the sink iterations. The sink iterations
5795 and the potential source iterations will be intersected with these sets.
5796 If the output needs to be restricted then only a restriction on the source
5797 iterations is required.
5798 If any error occurs, the callback should return C<NULL>.
5799 An C<isl_restriction> object can be created, freed and inspected
5800 using the following functions.
5802 #include <isl/flow.h>
5804 __isl_give isl_restriction *isl_restriction_input(
5805 __isl_take isl_set *source_restr,
5806 __isl_take isl_set *sink_restr);
5807 __isl_give isl_restriction *isl_restriction_output(
5808 __isl_take isl_set *source_restr);
5809 __isl_give isl_restriction *isl_restriction_none(
5810 __isl_take isl_map *source_map);
5811 __isl_give isl_restriction *isl_restriction_empty(
5812 __isl_take isl_map *source_map);
5813 void *isl_restriction_free(
5814 __isl_take isl_restriction *restr);
5815 isl_ctx *isl_restriction_get_ctx(
5816 __isl_keep isl_restriction *restr);
5818 C<isl_restriction_none> and C<isl_restriction_empty> are special
5819 cases of C<isl_restriction_input>. C<isl_restriction_none>
5820 is essentially equivalent to
5822 isl_restriction_input(isl_set_universe(
5823 isl_space_range(isl_map_get_space(source_map))),
5825 isl_space_domain(isl_map_get_space(source_map))));
5827 whereas C<isl_restriction_empty> is essentially equivalent to
5829 isl_restriction_input(isl_set_empty(
5830 isl_space_range(isl_map_get_space(source_map))),
5832 isl_space_domain(isl_map_get_space(source_map))));
5836 B<The functionality described in this section is fairly new
5837 and may be subject to change.>
5839 #include <isl/schedule.h>
5840 __isl_give isl_schedule *
5841 isl_schedule_constraints_compute_schedule(
5842 __isl_take isl_schedule_constraints *sc);
5843 void *isl_schedule_free(__isl_take isl_schedule *sched);
5845 The function C<isl_schedule_constraints_compute_schedule> can be
5846 used to compute a schedule that satisfy the given schedule constraints.
5847 These schedule constraints include the iteration domain for which
5848 a schedule should be computed and dependences between pairs of
5849 iterations. In particular, these dependences include
5850 I<validity> dependences and I<proximity> dependences.
5851 By default, the algorithm used to construct the schedule is similar
5852 to that of C<Pluto>.
5853 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5855 The generated schedule respects all validity dependences.
5856 That is, all dependence distances over these dependences in the
5857 scheduled space are lexicographically positive.
5858 The default algorithm tries to ensure that the dependence distances
5859 over coincidence constraints are zero and to minimize the
5860 dependence distances over proximity dependences.
5861 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5862 for groups of domains where the dependence distances over validity
5863 dependences have only non-negative values.
5864 When using Feautrier's algorithm, the coincidence and proximity constraints
5865 are only taken into account during the extension to a
5866 full-dimensional schedule.
5868 An C<isl_schedule_constraints> object can be constructed
5869 and manipulated using the following functions.
5871 #include <isl/schedule.h>
5872 __isl_give isl_schedule_constraints *
5873 isl_schedule_constraints_copy(
5874 __isl_keep isl_schedule_constraints *sc);
5875 __isl_give isl_schedule_constraints *
5876 isl_schedule_constraints_on_domain(
5877 __isl_take isl_union_set *domain);
5878 isl_ctx *isl_schedule_constraints_get_ctx(
5879 __isl_keep isl_schedule_constraints *sc);
5880 __isl_give isl_schedule_constraints *
5881 isl_schedule_constraints_set_validity(
5882 __isl_take isl_schedule_constraints *sc,
5883 __isl_take isl_union_map *validity);
5884 __isl_give isl_schedule_constraints *
5885 isl_schedule_constraints_set_coincidence(
5886 __isl_take isl_schedule_constraints *sc,
5887 __isl_take isl_union_map *coincidence);
5888 __isl_give isl_schedule_constraints *
5889 isl_schedule_constraints_set_proximity(
5890 __isl_take isl_schedule_constraints *sc,
5891 __isl_take isl_union_map *proximity);
5892 __isl_give isl_schedule_constraints *
5893 isl_schedule_constraints_set_conditional_validity(
5894 __isl_take isl_schedule_constraints *sc,
5895 __isl_take isl_union_map *condition,
5896 __isl_take isl_union_map *validity);
5897 void *isl_schedule_constraints_free(
5898 __isl_take isl_schedule_constraints *sc);
5900 The initial C<isl_schedule_constraints> object created by
5901 C<isl_schedule_constraints_on_domain> does not impose any constraints.
5902 That is, it has an empty set of dependences.
5903 The function C<isl_schedule_constraints_set_validity> replaces the
5904 validity dependences, mapping domain elements I<i> to domain
5905 elements that should be scheduled after I<i>.
5906 The function C<isl_schedule_constraints_set_coincidence> replaces the
5907 coincidence dependences, mapping domain elements I<i> to domain
5908 elements that should be scheduled together with I<I>, if possible.
5909 The function C<isl_schedule_constraints_set_proximity> replaces the
5910 proximity dependences, mapping domain elements I<i> to domain
5911 elements that should be scheduled either before I<I>
5912 or as early as possible after I<i>.
5914 The function C<isl_schedule_constraints_set_conditional_validity>
5915 replaces the conditional validity constraints.
5916 A conditional validity constraint is only imposed when any of the corresponding
5917 conditions is satisfied, i.e., when any of them is non-zero.
5918 That is, the scheduler ensures that within each band if the dependence
5919 distances over the condition constraints are not all zero
5920 then all corresponding conditional validity constraints are respected.
5921 A conditional validity constraint corresponds to a condition
5922 if the two are adjacent, i.e., if the domain of one relation intersect
5923 the range of the other relation.
5924 The typical use case of conditional validity constraints is
5925 to allow order constraints between live ranges to be violated
5926 as long as the live ranges themselves are local to the band.
5927 To allow more fine-grained control over which conditions correspond
5928 to which conditional validity constraints, the domains and ranges
5929 of these relations may include I<tags>. That is, the domains and
5930 ranges of those relation may themselves be wrapped relations
5931 where the iteration domain appears in the domain of those wrapped relations
5932 and the range of the wrapped relations can be arbitrarily chosen
5933 by the user. Conditions and conditional validity constraints are only
5934 considere adjacent to each other if the entire wrapped relation matches.
5935 In particular, a relation with a tag will never be considered adjacent
5936 to a relation without a tag.
5938 The following function computes a schedule directly from
5939 an iteration domain and validity and proximity dependences
5940 and is implemented in terms of the functions described above.
5941 The use of C<isl_union_set_compute_schedule> is discouraged.
5943 #include <isl/schedule.h>
5944 __isl_give isl_schedule *isl_union_set_compute_schedule(
5945 __isl_take isl_union_set *domain,
5946 __isl_take isl_union_map *validity,
5947 __isl_take isl_union_map *proximity);
5949 A mapping from the domains to the scheduled space can be obtained
5950 from an C<isl_schedule> using the following function.
5952 __isl_give isl_union_map *isl_schedule_get_map(
5953 __isl_keep isl_schedule *sched);
5955 A representation of the schedule can be printed using
5957 __isl_give isl_printer *isl_printer_print_schedule(
5958 __isl_take isl_printer *p,
5959 __isl_keep isl_schedule *schedule);
5961 A representation of the schedule as a forest of bands can be obtained
5962 using the following function.
5964 __isl_give isl_band_list *isl_schedule_get_band_forest(
5965 __isl_keep isl_schedule *schedule);
5967 The individual bands can be visited in depth-first post-order
5968 using the following function.
5970 #include <isl/schedule.h>
5971 int isl_schedule_foreach_band(
5972 __isl_keep isl_schedule *sched,
5973 int (*fn)(__isl_keep isl_band *band, void *user),
5976 The list can be manipulated as explained in L<"Lists">.
5977 The bands inside the list can be copied and freed using the following
5980 #include <isl/band.h>
5981 __isl_give isl_band *isl_band_copy(
5982 __isl_keep isl_band *band);
5983 void *isl_band_free(__isl_take isl_band *band);
5985 Each band contains zero or more scheduling dimensions.
5986 These are referred to as the members of the band.
5987 The section of the schedule that corresponds to the band is
5988 referred to as the partial schedule of the band.
5989 For those nodes that participate in a band, the outer scheduling
5990 dimensions form the prefix schedule, while the inner scheduling
5991 dimensions form the suffix schedule.
5992 That is, if we take a cut of the band forest, then the union of
5993 the concatenations of the prefix, partial and suffix schedules of
5994 each band in the cut is equal to the entire schedule (modulo
5995 some possible padding at the end with zero scheduling dimensions).
5996 The properties of a band can be inspected using the following functions.
5998 #include <isl/band.h>
5999 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
6001 int isl_band_has_children(__isl_keep isl_band *band);
6002 __isl_give isl_band_list *isl_band_get_children(
6003 __isl_keep isl_band *band);
6005 __isl_give isl_union_map *isl_band_get_prefix_schedule(
6006 __isl_keep isl_band *band);
6007 __isl_give isl_union_map *isl_band_get_partial_schedule(
6008 __isl_keep isl_band *band);
6009 __isl_give isl_union_map *isl_band_get_suffix_schedule(
6010 __isl_keep isl_band *band);
6012 int isl_band_n_member(__isl_keep isl_band *band);
6013 int isl_band_member_is_coincident(
6014 __isl_keep isl_band *band, int pos);
6016 int isl_band_list_foreach_band(
6017 __isl_keep isl_band_list *list,
6018 int (*fn)(__isl_keep isl_band *band, void *user),
6021 Note that a scheduling dimension is considered to be ``coincident''
6022 if it satisfies the coincidence constraints within its band.
6023 That is, if the dependence distances of the coincidence
6024 constraints are all zero in that direction (for fixed
6025 iterations of outer bands).
6026 Like C<isl_schedule_foreach_band>,
6027 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
6028 in depth-first post-order.
6030 A band can be tiled using the following function.
6032 #include <isl/band.h>
6033 int isl_band_tile(__isl_keep isl_band *band,
6034 __isl_take isl_vec *sizes);
6036 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
6038 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
6039 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
6041 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
6043 The C<isl_band_tile> function tiles the band using the given tile sizes
6044 inside its schedule.
6045 A new child band is created to represent the point loops and it is
6046 inserted between the modified band and its children.
6047 The C<tile_scale_tile_loops> option specifies whether the tile
6048 loops iterators should be scaled by the tile sizes.
6049 If the C<tile_shift_point_loops> option is set, then the point loops
6050 are shifted to start at zero.
6052 A band can be split into two nested bands using the following function.
6054 int isl_band_split(__isl_keep isl_band *band, int pos);
6056 The resulting outer band contains the first C<pos> dimensions of C<band>
6057 while the inner band contains the remaining dimensions.
6059 A representation of the band can be printed using
6061 #include <isl/band.h>
6062 __isl_give isl_printer *isl_printer_print_band(
6063 __isl_take isl_printer *p,
6064 __isl_keep isl_band *band);
6068 #include <isl/schedule.h>
6069 int isl_options_set_schedule_max_coefficient(
6070 isl_ctx *ctx, int val);
6071 int isl_options_get_schedule_max_coefficient(
6073 int isl_options_set_schedule_max_constant_term(
6074 isl_ctx *ctx, int val);
6075 int isl_options_get_schedule_max_constant_term(
6077 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
6078 int isl_options_get_schedule_fuse(isl_ctx *ctx);
6079 int isl_options_set_schedule_maximize_band_depth(
6080 isl_ctx *ctx, int val);
6081 int isl_options_get_schedule_maximize_band_depth(
6083 int isl_options_set_schedule_outer_coincidence(
6084 isl_ctx *ctx, int val);
6085 int isl_options_get_schedule_outer_coincidence(
6087 int isl_options_set_schedule_split_scaled(
6088 isl_ctx *ctx, int val);
6089 int isl_options_get_schedule_split_scaled(
6091 int isl_options_set_schedule_algorithm(
6092 isl_ctx *ctx, int val);
6093 int isl_options_get_schedule_algorithm(
6095 int isl_options_set_schedule_separate_components(
6096 isl_ctx *ctx, int val);
6097 int isl_options_get_schedule_separate_components(
6102 =item * schedule_max_coefficient
6104 This option enforces that the coefficients for variable and parameter
6105 dimensions in the calculated schedule are not larger than the specified value.
6106 This option can significantly increase the speed of the scheduling calculation
6107 and may also prevent fusing of unrelated dimensions. A value of -1 means that
6108 this option does not introduce bounds on the variable or parameter
6111 =item * schedule_max_constant_term
6113 This option enforces that the constant coefficients in the calculated schedule
6114 are not larger than the maximal constant term. This option can significantly
6115 increase the speed of the scheduling calculation and may also prevent fusing of
6116 unrelated dimensions. A value of -1 means that this option does not introduce
6117 bounds on the constant coefficients.
6119 =item * schedule_fuse
6121 This option controls the level of fusion.
6122 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6123 resulting schedule will be distributed as much as possible.
6124 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6125 try to fuse loops in the resulting schedule.
6127 =item * schedule_maximize_band_depth
6129 If this option is set, we do not split bands at the point
6130 where we detect splitting is necessary. Instead, we
6131 backtrack and split bands as early as possible. This
6132 reduces the number of splits and maximizes the width of
6133 the bands. Wider bands give more possibilities for tiling.
6134 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6135 then bands will be split as early as possible, even if there is no need.
6136 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6138 =item * schedule_outer_coincidence
6140 If this option is set, then we try to construct schedules
6141 where the outermost scheduling dimension in each band
6142 satisfies the coincidence constraints.
6144 =item * schedule_split_scaled
6146 If this option is set, then we try to construct schedules in which the
6147 constant term is split off from the linear part if the linear parts of
6148 the scheduling rows for all nodes in the graphs have a common non-trivial
6150 The constant term is then placed in a separate band and the linear
6153 =item * schedule_algorithm
6155 Selects the scheduling algorithm to be used.
6156 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6157 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6159 =item * schedule_separate_components
6161 If at any point the dependence graph contains any (weakly connected) components,
6162 then these components are scheduled separately.
6163 If this option is not set, then some iterations of the domains
6164 in these components may be scheduled together.
6165 If this option is set, then the components are given consecutive
6170 =head2 AST Generation
6172 This section describes the C<isl> functionality for generating
6173 ASTs that visit all the elements
6174 in a domain in an order specified by a schedule.
6175 In particular, given a C<isl_union_map>, an AST is generated
6176 that visits all the elements in the domain of the C<isl_union_map>
6177 according to the lexicographic order of the corresponding image
6178 element(s). If the range of the C<isl_union_map> consists of
6179 elements in more than one space, then each of these spaces is handled
6180 separately in an arbitrary order.
6181 It should be noted that the image elements only specify the I<order>
6182 in which the corresponding domain elements should be visited.
6183 No direct relation between the image elements and the loop iterators
6184 in the generated AST should be assumed.
6186 Each AST is generated within a build. The initial build
6187 simply specifies the constraints on the parameters (if any)
6188 and can be created, inspected, copied and freed using the following functions.
6190 #include <isl/ast_build.h>
6191 __isl_give isl_ast_build *isl_ast_build_from_context(
6192 __isl_take isl_set *set);
6193 isl_ctx *isl_ast_build_get_ctx(
6194 __isl_keep isl_ast_build *build);
6195 __isl_give isl_ast_build *isl_ast_build_copy(
6196 __isl_keep isl_ast_build *build);
6197 void *isl_ast_build_free(
6198 __isl_take isl_ast_build *build);
6200 The C<set> argument is usually a parameter set with zero or more parameters.
6201 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6202 and L</"Fine-grained Control over AST Generation">.
6203 Finally, the AST itself can be constructed using the following
6206 #include <isl/ast_build.h>
6207 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6208 __isl_keep isl_ast_build *build,
6209 __isl_take isl_union_map *schedule);
6211 =head3 Inspecting the AST
6213 The basic properties of an AST node can be obtained as follows.
6215 #include <isl/ast.h>
6216 isl_ctx *isl_ast_node_get_ctx(
6217 __isl_keep isl_ast_node *node);
6218 enum isl_ast_node_type isl_ast_node_get_type(
6219 __isl_keep isl_ast_node *node);
6221 The type of an AST node is one of
6222 C<isl_ast_node_for>,
6224 C<isl_ast_node_block> or
6225 C<isl_ast_node_user>.
6226 An C<isl_ast_node_for> represents a for node.
6227 An C<isl_ast_node_if> represents an if node.
6228 An C<isl_ast_node_block> represents a compound node.
6229 An C<isl_ast_node_user> represents an expression statement.
6230 An expression statement typically corresponds to a domain element, i.e.,
6231 one of the elements that is visited by the AST.
6233 Each type of node has its own additional properties.
6235 #include <isl/ast.h>
6236 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6237 __isl_keep isl_ast_node *node);
6238 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6239 __isl_keep isl_ast_node *node);
6240 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6241 __isl_keep isl_ast_node *node);
6242 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6243 __isl_keep isl_ast_node *node);
6244 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6245 __isl_keep isl_ast_node *node);
6246 int isl_ast_node_for_is_degenerate(
6247 __isl_keep isl_ast_node *node);
6249 An C<isl_ast_for> is considered degenerate if it is known to execute
6252 #include <isl/ast.h>
6253 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6254 __isl_keep isl_ast_node *node);
6255 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6256 __isl_keep isl_ast_node *node);
6257 int isl_ast_node_if_has_else(
6258 __isl_keep isl_ast_node *node);
6259 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6260 __isl_keep isl_ast_node *node);
6262 __isl_give isl_ast_node_list *
6263 isl_ast_node_block_get_children(
6264 __isl_keep isl_ast_node *node);
6266 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6267 __isl_keep isl_ast_node *node);
6269 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6270 the following functions.
6272 #include <isl/ast.h>
6273 isl_ctx *isl_ast_expr_get_ctx(
6274 __isl_keep isl_ast_expr *expr);
6275 enum isl_ast_expr_type isl_ast_expr_get_type(
6276 __isl_keep isl_ast_expr *expr);
6278 The type of an AST expression is one of
6280 C<isl_ast_expr_id> or
6281 C<isl_ast_expr_int>.
6282 An C<isl_ast_expr_op> represents the result of an operation.
6283 An C<isl_ast_expr_id> represents an identifier.
6284 An C<isl_ast_expr_int> represents an integer value.
6286 Each type of expression has its own additional properties.
6288 #include <isl/ast.h>
6289 enum isl_ast_op_type isl_ast_expr_get_op_type(
6290 __isl_keep isl_ast_expr *expr);
6291 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6292 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6293 __isl_keep isl_ast_expr *expr, int pos);
6294 int isl_ast_node_foreach_ast_op_type(
6295 __isl_keep isl_ast_node *node,
6296 int (*fn)(enum isl_ast_op_type type, void *user),
6299 C<isl_ast_expr_get_op_type> returns the type of the operation
6300 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6301 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6303 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6304 C<isl_ast_op_type> that appears in C<node>.
6305 The operation type is one of the following.
6309 =item C<isl_ast_op_and>
6311 Logical I<and> of two arguments.
6312 Both arguments can be evaluated.
6314 =item C<isl_ast_op_and_then>
6316 Logical I<and> of two arguments.
6317 The second argument can only be evaluated if the first evaluates to true.
6319 =item C<isl_ast_op_or>
6321 Logical I<or> of two arguments.
6322 Both arguments can be evaluated.
6324 =item C<isl_ast_op_or_else>
6326 Logical I<or> of two arguments.
6327 The second argument can only be evaluated if the first evaluates to false.
6329 =item C<isl_ast_op_max>
6331 Maximum of two or more arguments.
6333 =item C<isl_ast_op_min>
6335 Minimum of two or more arguments.
6337 =item C<isl_ast_op_minus>
6341 =item C<isl_ast_op_add>
6343 Sum of two arguments.
6345 =item C<isl_ast_op_sub>
6347 Difference of two arguments.
6349 =item C<isl_ast_op_mul>
6351 Product of two arguments.
6353 =item C<isl_ast_op_div>
6355 Exact division. That is, the result is known to be an integer.
6357 =item C<isl_ast_op_fdiv_q>
6359 Result of integer division, rounded towards negative
6362 =item C<isl_ast_op_pdiv_q>
6364 Result of integer division, where dividend is known to be non-negative.
6366 =item C<isl_ast_op_pdiv_r>
6368 Remainder of integer division, where dividend is known to be non-negative.
6370 =item C<isl_ast_op_cond>
6372 Conditional operator defined on three arguments.
6373 If the first argument evaluates to true, then the result
6374 is equal to the second argument. Otherwise, the result
6375 is equal to the third argument.
6376 The second and third argument may only be evaluated if
6377 the first argument evaluates to true and false, respectively.
6378 Corresponds to C<a ? b : c> in C.
6380 =item C<isl_ast_op_select>
6382 Conditional operator defined on three arguments.
6383 If the first argument evaluates to true, then the result
6384 is equal to the second argument. Otherwise, the result
6385 is equal to the third argument.
6386 The second and third argument may be evaluated independently
6387 of the value of the first argument.
6388 Corresponds to C<a * b + (1 - a) * c> in C.
6390 =item C<isl_ast_op_eq>
6394 =item C<isl_ast_op_le>
6396 Less than or equal relation.
6398 =item C<isl_ast_op_lt>
6402 =item C<isl_ast_op_ge>
6404 Greater than or equal relation.
6406 =item C<isl_ast_op_gt>
6408 Greater than relation.
6410 =item C<isl_ast_op_call>
6413 The number of arguments of the C<isl_ast_expr> is one more than
6414 the number of arguments in the function call, the first argument
6415 representing the function being called.
6417 =item C<isl_ast_op_access>
6420 The number of arguments of the C<isl_ast_expr> is one more than
6421 the number of index expressions in the array access, the first argument
6422 representing the array being accessed.
6424 =item C<isl_ast_op_member>
6427 This operation has two arguments, a structure and the name of
6428 the member of the structure being accessed.
6432 #include <isl/ast.h>
6433 __isl_give isl_id *isl_ast_expr_get_id(
6434 __isl_keep isl_ast_expr *expr);
6436 Return the identifier represented by the AST expression.
6438 #include <isl/ast.h>
6439 __isl_give isl_val *isl_ast_expr_get_val(
6440 __isl_keep isl_ast_expr *expr);
6442 Return the integer represented by the AST expression.
6444 =head3 Properties of ASTs
6446 #include <isl/ast.h>
6447 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6448 __isl_keep isl_ast_expr *expr2);
6450 Check if two C<isl_ast_expr>s are equal to each other.
6452 =head3 Manipulating and printing the AST
6454 AST nodes can be copied and freed using the following functions.
6456 #include <isl/ast.h>
6457 __isl_give isl_ast_node *isl_ast_node_copy(
6458 __isl_keep isl_ast_node *node);
6459 void *isl_ast_node_free(__isl_take isl_ast_node *node);
6461 AST expressions can be copied and freed using the following functions.
6463 #include <isl/ast.h>
6464 __isl_give isl_ast_expr *isl_ast_expr_copy(
6465 __isl_keep isl_ast_expr *expr);
6466 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
6468 New AST expressions can be created either directly or within
6469 the context of an C<isl_ast_build>.
6471 #include <isl/ast.h>
6472 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6473 __isl_take isl_val *v);
6474 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6475 __isl_take isl_id *id);
6476 __isl_give isl_ast_expr *isl_ast_expr_neg(
6477 __isl_take isl_ast_expr *expr);
6478 __isl_give isl_ast_expr *isl_ast_expr_add(
6479 __isl_take isl_ast_expr *expr1,
6480 __isl_take isl_ast_expr *expr2);
6481 __isl_give isl_ast_expr *isl_ast_expr_sub(
6482 __isl_take isl_ast_expr *expr1,
6483 __isl_take isl_ast_expr *expr2);
6484 __isl_give isl_ast_expr *isl_ast_expr_mul(
6485 __isl_take isl_ast_expr *expr1,
6486 __isl_take isl_ast_expr *expr2);
6487 __isl_give isl_ast_expr *isl_ast_expr_div(
6488 __isl_take isl_ast_expr *expr1,
6489 __isl_take isl_ast_expr *expr2);
6490 __isl_give isl_ast_expr *isl_ast_expr_and(
6491 __isl_take isl_ast_expr *expr1,
6492 __isl_take isl_ast_expr *expr2)
6493 __isl_give isl_ast_expr *isl_ast_expr_or(
6494 __isl_take isl_ast_expr *expr1,
6495 __isl_take isl_ast_expr *expr2)
6496 __isl_give isl_ast_expr *isl_ast_expr_access(
6497 __isl_take isl_ast_expr *array,
6498 __isl_take isl_ast_expr_list *indices);
6500 #include <isl/ast_build.h>
6501 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6502 __isl_keep isl_ast_build *build,
6503 __isl_take isl_pw_aff *pa);
6504 __isl_give isl_ast_expr *
6505 isl_ast_build_access_from_pw_multi_aff(
6506 __isl_keep isl_ast_build *build,
6507 __isl_take isl_pw_multi_aff *pma);
6508 __isl_give isl_ast_expr *
6509 isl_ast_build_access_from_multi_pw_aff(
6510 __isl_keep isl_ast_build *build,
6511 __isl_take isl_multi_pw_aff *mpa);
6512 __isl_give isl_ast_expr *
6513 isl_ast_build_call_from_pw_multi_aff(
6514 __isl_keep isl_ast_build *build,
6515 __isl_take isl_pw_multi_aff *pma);
6516 __isl_give isl_ast_expr *
6517 isl_ast_build_call_from_multi_pw_aff(
6518 __isl_keep isl_ast_build *build,
6519 __isl_take isl_multi_pw_aff *mpa);
6521 The domains of C<pa>, C<mpa> and C<pma> should correspond
6522 to the schedule space of C<build>.
6523 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6524 the function being called.
6525 If the accessed space is a nested relation, then it is taken
6526 to represent an access of the member specified by the range
6527 of this nested relation of the structure specified by the domain
6528 of the nested relation.
6530 The following functions can be used to modify an C<isl_ast_expr>.
6532 #include <isl/ast.h>
6533 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6534 __isl_take isl_ast_expr *expr, int pos,
6535 __isl_take isl_ast_expr *arg);
6537 Replace the argument of C<expr> at position C<pos> by C<arg>.
6539 #include <isl/ast.h>
6540 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6541 __isl_take isl_ast_expr *expr,
6542 __isl_take isl_id_to_ast_expr *id2expr);
6544 The function C<isl_ast_expr_substitute_ids> replaces the
6545 subexpressions of C<expr> of type C<isl_ast_expr_id>
6546 by the corresponding expression in C<id2expr>, if there is any.
6549 User specified data can be attached to an C<isl_ast_node> and obtained
6550 from the same C<isl_ast_node> using the following functions.
6552 #include <isl/ast.h>
6553 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6554 __isl_take isl_ast_node *node,
6555 __isl_take isl_id *annotation);
6556 __isl_give isl_id *isl_ast_node_get_annotation(
6557 __isl_keep isl_ast_node *node);
6559 Basic printing can be performed using the following functions.
6561 #include <isl/ast.h>
6562 __isl_give isl_printer *isl_printer_print_ast_expr(
6563 __isl_take isl_printer *p,
6564 __isl_keep isl_ast_expr *expr);
6565 __isl_give isl_printer *isl_printer_print_ast_node(
6566 __isl_take isl_printer *p,
6567 __isl_keep isl_ast_node *node);
6569 More advanced printing can be performed using the following functions.
6571 #include <isl/ast.h>
6572 __isl_give isl_printer *isl_ast_op_type_print_macro(
6573 enum isl_ast_op_type type,
6574 __isl_take isl_printer *p);
6575 __isl_give isl_printer *isl_ast_node_print_macros(
6576 __isl_keep isl_ast_node *node,
6577 __isl_take isl_printer *p);
6578 __isl_give isl_printer *isl_ast_node_print(
6579 __isl_keep isl_ast_node *node,
6580 __isl_take isl_printer *p,
6581 __isl_take isl_ast_print_options *options);
6582 __isl_give isl_printer *isl_ast_node_for_print(
6583 __isl_keep isl_ast_node *node,
6584 __isl_take isl_printer *p,
6585 __isl_take isl_ast_print_options *options);
6586 __isl_give isl_printer *isl_ast_node_if_print(
6587 __isl_keep isl_ast_node *node,
6588 __isl_take isl_printer *p,
6589 __isl_take isl_ast_print_options *options);
6591 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6592 C<isl> may print out an AST that makes use of macros such
6593 as C<floord>, C<min> and C<max>.
6594 C<isl_ast_op_type_print_macro> prints out the macro
6595 corresponding to a specific C<isl_ast_op_type>.
6596 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6597 for expressions where these macros would be used and prints
6598 out the required macro definitions.
6599 Essentially, C<isl_ast_node_print_macros> calls
6600 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6601 as function argument.
6602 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6603 C<isl_ast_node_if_print> print an C<isl_ast_node>
6604 in C<ISL_FORMAT_C>, but allow for some extra control
6605 through an C<isl_ast_print_options> object.
6606 This object can be created using the following functions.
6608 #include <isl/ast.h>
6609 __isl_give isl_ast_print_options *
6610 isl_ast_print_options_alloc(isl_ctx *ctx);
6611 __isl_give isl_ast_print_options *
6612 isl_ast_print_options_copy(
6613 __isl_keep isl_ast_print_options *options);
6614 void *isl_ast_print_options_free(
6615 __isl_take isl_ast_print_options *options);
6617 __isl_give isl_ast_print_options *
6618 isl_ast_print_options_set_print_user(
6619 __isl_take isl_ast_print_options *options,
6620 __isl_give isl_printer *(*print_user)(
6621 __isl_take isl_printer *p,
6622 __isl_take isl_ast_print_options *options,
6623 __isl_keep isl_ast_node *node, void *user),
6625 __isl_give isl_ast_print_options *
6626 isl_ast_print_options_set_print_for(
6627 __isl_take isl_ast_print_options *options,
6628 __isl_give isl_printer *(*print_for)(
6629 __isl_take isl_printer *p,
6630 __isl_take isl_ast_print_options *options,
6631 __isl_keep isl_ast_node *node, void *user),
6634 The callback set by C<isl_ast_print_options_set_print_user>
6635 is called whenever a node of type C<isl_ast_node_user> needs to
6637 The callback set by C<isl_ast_print_options_set_print_for>
6638 is called whenever a node of type C<isl_ast_node_for> needs to
6640 Note that C<isl_ast_node_for_print> will I<not> call the
6641 callback set by C<isl_ast_print_options_set_print_for> on the node
6642 on which C<isl_ast_node_for_print> is called, but only on nested
6643 nodes of type C<isl_ast_node_for>. It is therefore safe to
6644 call C<isl_ast_node_for_print> from within the callback set by
6645 C<isl_ast_print_options_set_print_for>.
6647 The following option determines the type to be used for iterators
6648 while printing the AST.
6650 int isl_options_set_ast_iterator_type(
6651 isl_ctx *ctx, const char *val);
6652 const char *isl_options_get_ast_iterator_type(
6657 #include <isl/ast_build.h>
6658 int isl_options_set_ast_build_atomic_upper_bound(
6659 isl_ctx *ctx, int val);
6660 int isl_options_get_ast_build_atomic_upper_bound(
6662 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6664 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6665 int isl_options_set_ast_build_exploit_nested_bounds(
6666 isl_ctx *ctx, int val);
6667 int isl_options_get_ast_build_exploit_nested_bounds(
6669 int isl_options_set_ast_build_group_coscheduled(
6670 isl_ctx *ctx, int val);
6671 int isl_options_get_ast_build_group_coscheduled(
6673 int isl_options_set_ast_build_scale_strides(
6674 isl_ctx *ctx, int val);
6675 int isl_options_get_ast_build_scale_strides(
6677 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6679 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6680 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6682 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6686 =item * ast_build_atomic_upper_bound
6688 Generate loop upper bounds that consist of the current loop iterator,
6689 an operator and an expression not involving the iterator.
6690 If this option is not set, then the current loop iterator may appear
6691 several times in the upper bound.
6692 For example, when this option is turned off, AST generation
6695 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6699 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6702 When the option is turned on, the following AST is generated
6704 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6707 =item * ast_build_prefer_pdiv
6709 If this option is turned off, then the AST generation will
6710 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6711 operators, but no C<isl_ast_op_pdiv_q> or
6712 C<isl_ast_op_pdiv_r> operators.
6713 If this options is turned on, then C<isl> will try to convert
6714 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6715 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6717 =item * ast_build_exploit_nested_bounds
6719 Simplify conditions based on bounds of nested for loops.
6720 In particular, remove conditions that are implied by the fact
6721 that one or more nested loops have at least one iteration,
6722 meaning that the upper bound is at least as large as the lower bound.
6723 For example, when this option is turned off, AST generation
6726 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6732 for (int c0 = 0; c0 <= N; c0 += 1)
6733 for (int c1 = 0; c1 <= M; c1 += 1)
6736 When the option is turned on, the following AST is generated
6738 for (int c0 = 0; c0 <= N; c0 += 1)
6739 for (int c1 = 0; c1 <= M; c1 += 1)
6742 =item * ast_build_group_coscheduled
6744 If two domain elements are assigned the same schedule point, then
6745 they may be executed in any order and they may even appear in different
6746 loops. If this options is set, then the AST generator will make
6747 sure that coscheduled domain elements do not appear in separate parts
6748 of the AST. This is useful in case of nested AST generation
6749 if the outer AST generation is given only part of a schedule
6750 and the inner AST generation should handle the domains that are
6751 coscheduled by this initial part of the schedule together.
6752 For example if an AST is generated for a schedule
6754 { A[i] -> [0]; B[i] -> [0] }
6756 then the C<isl_ast_build_set_create_leaf> callback described
6757 below may get called twice, once for each domain.
6758 Setting this option ensures that the callback is only called once
6759 on both domains together.
6761 =item * ast_build_separation_bounds
6763 This option specifies which bounds to use during separation.
6764 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6765 then all (possibly implicit) bounds on the current dimension will
6766 be used during separation.
6767 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6768 then only those bounds that are explicitly available will
6769 be used during separation.
6771 =item * ast_build_scale_strides
6773 This option specifies whether the AST generator is allowed
6774 to scale down iterators of strided loops.
6776 =item * ast_build_allow_else
6778 This option specifies whether the AST generator is allowed
6779 to construct if statements with else branches.
6781 =item * ast_build_allow_or
6783 This option specifies whether the AST generator is allowed
6784 to construct if conditions with disjunctions.
6788 =head3 Fine-grained Control over AST Generation
6790 Besides specifying the constraints on the parameters,
6791 an C<isl_ast_build> object can be used to control
6792 various aspects of the AST generation process.
6793 The most prominent way of control is through ``options'',
6794 which can be set using the following function.
6796 #include <isl/ast_build.h>
6797 __isl_give isl_ast_build *
6798 isl_ast_build_set_options(
6799 __isl_take isl_ast_build *control,
6800 __isl_take isl_union_map *options);
6802 The options are encoded in an <isl_union_map>.
6803 The domain of this union relation refers to the schedule domain,
6804 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6805 In the case of nested AST generation (see L</"Nested AST Generation">),
6806 the domain of C<options> should refer to the extra piece of the schedule.
6807 That is, it should be equal to the range of the wrapped relation in the
6808 range of the schedule.
6809 The range of the options can consist of elements in one or more spaces,
6810 the names of which determine the effect of the option.
6811 The values of the range typically also refer to the schedule dimension
6812 to which the option applies. In case of nested AST generation
6813 (see L</"Nested AST Generation">), these values refer to the position
6814 of the schedule dimension within the innermost AST generation.
6815 The constraints on the domain elements of
6816 the option should only refer to this dimension and earlier dimensions.
6817 We consider the following spaces.
6821 =item C<separation_class>
6823 This space is a wrapped relation between two one dimensional spaces.
6824 The input space represents the schedule dimension to which the option
6825 applies and the output space represents the separation class.
6826 While constructing a loop corresponding to the specified schedule
6827 dimension(s), the AST generator will try to generate separate loops
6828 for domain elements that are assigned different classes.
6829 If only some of the elements are assigned a class, then those elements
6830 that are not assigned any class will be treated as belonging to a class
6831 that is separate from the explicitly assigned classes.
6832 The typical use case for this option is to separate full tiles from
6834 The other options, described below, are applied after the separation
6837 As an example, consider the separation into full and partial tiles
6838 of a tiling of a triangular domain.
6839 Take, for example, the domain
6841 { A[i,j] : 0 <= i,j and i + j <= 100 }
6843 and a tiling into tiles of 10 by 10. The input to the AST generator
6844 is then the schedule
6846 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6849 Without any options, the following AST is generated
6851 for (int c0 = 0; c0 <= 10; c0 += 1)
6852 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6853 for (int c2 = 10 * c0;
6854 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6856 for (int c3 = 10 * c1;
6857 c3 <= min(10 * c1 + 9, -c2 + 100);
6861 Separation into full and partial tiles can be obtained by assigning
6862 a class, say C<0>, to the full tiles. The full tiles are represented by those
6863 values of the first and second schedule dimensions for which there are
6864 values of the third and fourth dimensions to cover an entire tile.
6865 That is, we need to specify the following option
6867 { [a,b,c,d] -> separation_class[[0]->[0]] :
6868 exists b': 0 <= 10a,10b' and
6869 10a+9+10b'+9 <= 100;
6870 [a,b,c,d] -> separation_class[[1]->[0]] :
6871 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6875 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6876 a >= 0 and b >= 0 and b <= 8 - a;
6877 [a, b, c, d] -> separation_class[[0] -> [0]] :
6880 With this option, the generated AST is as follows
6883 for (int c0 = 0; c0 <= 8; c0 += 1) {
6884 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6885 for (int c2 = 10 * c0;
6886 c2 <= 10 * c0 + 9; c2 += 1)
6887 for (int c3 = 10 * c1;
6888 c3 <= 10 * c1 + 9; c3 += 1)
6890 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6891 for (int c2 = 10 * c0;
6892 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6894 for (int c3 = 10 * c1;
6895 c3 <= min(-c2 + 100, 10 * c1 + 9);
6899 for (int c0 = 9; c0 <= 10; c0 += 1)
6900 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6901 for (int c2 = 10 * c0;
6902 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6904 for (int c3 = 10 * c1;
6905 c3 <= min(10 * c1 + 9, -c2 + 100);
6912 This is a single-dimensional space representing the schedule dimension(s)
6913 to which ``separation'' should be applied. Separation tries to split
6914 a loop into several pieces if this can avoid the generation of guards
6916 See also the C<atomic> option.
6920 This is a single-dimensional space representing the schedule dimension(s)
6921 for which the domains should be considered ``atomic''. That is, the
6922 AST generator will make sure that any given domain space will only appear
6923 in a single loop at the specified level.
6925 Consider the following schedule
6927 { a[i] -> [i] : 0 <= i < 10;
6928 b[i] -> [i+1] : 0 <= i < 10 }
6930 If the following option is specified
6932 { [i] -> separate[x] }
6934 then the following AST will be generated
6938 for (int c0 = 1; c0 <= 9; c0 += 1) {
6945 If, on the other hand, the following option is specified
6947 { [i] -> atomic[x] }
6949 then the following AST will be generated
6951 for (int c0 = 0; c0 <= 10; c0 += 1) {
6958 If neither C<atomic> nor C<separate> is specified, then the AST generator
6959 may produce either of these two results or some intermediate form.
6963 This is a single-dimensional space representing the schedule dimension(s)
6964 that should be I<completely> unrolled.
6965 To obtain a partial unrolling, the user should apply an additional
6966 strip-mining to the schedule and fully unroll the inner loop.
6970 Additional control is available through the following functions.
6972 #include <isl/ast_build.h>
6973 __isl_give isl_ast_build *
6974 isl_ast_build_set_iterators(
6975 __isl_take isl_ast_build *control,
6976 __isl_take isl_id_list *iterators);
6978 The function C<isl_ast_build_set_iterators> allows the user to
6979 specify a list of iterator C<isl_id>s to be used as iterators.
6980 If the input schedule is injective, then
6981 the number of elements in this list should be as large as the dimension
6982 of the schedule space, but no direct correspondence should be assumed
6983 between dimensions and elements.
6984 If the input schedule is not injective, then an additional number
6985 of C<isl_id>s equal to the largest dimension of the input domains
6987 If the number of provided C<isl_id>s is insufficient, then additional
6988 names are automatically generated.
6990 #include <isl/ast_build.h>
6991 __isl_give isl_ast_build *
6992 isl_ast_build_set_create_leaf(
6993 __isl_take isl_ast_build *control,
6994 __isl_give isl_ast_node *(*fn)(
6995 __isl_take isl_ast_build *build,
6996 void *user), void *user);
6999 C<isl_ast_build_set_create_leaf> function allows for the
7000 specification of a callback that should be called whenever the AST
7001 generator arrives at an element of the schedule domain.
7002 The callback should return an AST node that should be inserted
7003 at the corresponding position of the AST. The default action (when
7004 the callback is not set) is to continue generating parts of the AST to scan
7005 all the domain elements associated to the schedule domain element
7006 and to insert user nodes, ``calling'' the domain element, for each of them.
7007 The C<build> argument contains the current state of the C<isl_ast_build>.
7008 To ease nested AST generation (see L</"Nested AST Generation">),
7009 all control information that is
7010 specific to the current AST generation such as the options and
7011 the callbacks has been removed from this C<isl_ast_build>.
7012 The callback would typically return the result of a nested
7014 user defined node created using the following function.
7016 #include <isl/ast.h>
7017 __isl_give isl_ast_node *isl_ast_node_alloc_user(
7018 __isl_take isl_ast_expr *expr);
7020 #include <isl/ast_build.h>
7021 __isl_give isl_ast_build *
7022 isl_ast_build_set_at_each_domain(
7023 __isl_take isl_ast_build *build,
7024 __isl_give isl_ast_node *(*fn)(
7025 __isl_take isl_ast_node *node,
7026 __isl_keep isl_ast_build *build,
7027 void *user), void *user);
7028 __isl_give isl_ast_build *
7029 isl_ast_build_set_before_each_for(
7030 __isl_take isl_ast_build *build,
7031 __isl_give isl_id *(*fn)(
7032 __isl_keep isl_ast_build *build,
7033 void *user), void *user);
7034 __isl_give isl_ast_build *
7035 isl_ast_build_set_after_each_for(
7036 __isl_take isl_ast_build *build,
7037 __isl_give isl_ast_node *(*fn)(
7038 __isl_take isl_ast_node *node,
7039 __isl_keep isl_ast_build *build,
7040 void *user), void *user);
7042 The callback set by C<isl_ast_build_set_at_each_domain> will
7043 be called for each domain AST node.
7044 The callbacks set by C<isl_ast_build_set_before_each_for>
7045 and C<isl_ast_build_set_after_each_for> will be called
7046 for each for AST node. The first will be called in depth-first
7047 pre-order, while the second will be called in depth-first post-order.
7048 Since C<isl_ast_build_set_before_each_for> is called before the for
7049 node is actually constructed, it is only passed an C<isl_ast_build>.
7050 The returned C<isl_id> will be added as an annotation (using
7051 C<isl_ast_node_set_annotation>) to the constructed for node.
7052 In particular, if the user has also specified an C<after_each_for>
7053 callback, then the annotation can be retrieved from the node passed to
7054 that callback using C<isl_ast_node_get_annotation>.
7055 All callbacks should C<NULL> on failure.
7056 The given C<isl_ast_build> can be used to create new
7057 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
7058 or C<isl_ast_build_call_from_pw_multi_aff>.
7060 =head3 Nested AST Generation
7062 C<isl> allows the user to create an AST within the context
7063 of another AST. These nested ASTs are created using the
7064 same C<isl_ast_build_ast_from_schedule> function that is used to create the
7065 outer AST. The C<build> argument should be an C<isl_ast_build>
7066 passed to a callback set by
7067 C<isl_ast_build_set_create_leaf>.
7068 The space of the range of the C<schedule> argument should refer
7069 to this build. In particular, the space should be a wrapped
7070 relation and the domain of this wrapped relation should be the
7071 same as that of the range of the schedule returned by
7072 C<isl_ast_build_get_schedule> below.
7073 In practice, the new schedule is typically
7074 created by calling C<isl_union_map_range_product> on the old schedule
7075 and some extra piece of the schedule.
7076 The space of the schedule domain is also available from
7077 the C<isl_ast_build>.
7079 #include <isl/ast_build.h>
7080 __isl_give isl_union_map *isl_ast_build_get_schedule(
7081 __isl_keep isl_ast_build *build);
7082 __isl_give isl_space *isl_ast_build_get_schedule_space(
7083 __isl_keep isl_ast_build *build);
7084 __isl_give isl_ast_build *isl_ast_build_restrict(
7085 __isl_take isl_ast_build *build,
7086 __isl_take isl_set *set);
7088 The C<isl_ast_build_get_schedule> function returns a (partial)
7089 schedule for the domains elements for which part of the AST still needs to
7090 be generated in the current build.
7091 In particular, the domain elements are mapped to those iterations of the loops
7092 enclosing the current point of the AST generation inside which
7093 the domain elements are executed.
7094 No direct correspondence between
7095 the input schedule and this schedule should be assumed.
7096 The space obtained from C<isl_ast_build_get_schedule_space> can be used
7097 to create a set for C<isl_ast_build_restrict> to intersect
7098 with the current build. In particular, the set passed to
7099 C<isl_ast_build_restrict> can have additional parameters.
7100 The ids of the set dimensions in the space returned by
7101 C<isl_ast_build_get_schedule_space> correspond to the
7102 iterators of the already generated loops.
7103 The user should not rely on the ids of the output dimensions
7104 of the relations in the union relation returned by
7105 C<isl_ast_build_get_schedule> having any particular value.
7109 Although C<isl> is mainly meant to be used as a library,
7110 it also contains some basic applications that use some
7111 of the functionality of C<isl>.
7112 The input may be specified in either the L<isl format>
7113 or the L<PolyLib format>.
7115 =head2 C<isl_polyhedron_sample>
7117 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7118 an integer element of the polyhedron, if there is any.
7119 The first column in the output is the denominator and is always
7120 equal to 1. If the polyhedron contains no integer points,
7121 then a vector of length zero is printed.
7125 C<isl_pip> takes the same input as the C<example> program
7126 from the C<piplib> distribution, i.e., a set of constraints
7127 on the parameters, a line containing only -1 and finally a set
7128 of constraints on a parametric polyhedron.
7129 The coefficients of the parameters appear in the last columns
7130 (but before the final constant column).
7131 The output is the lexicographic minimum of the parametric polyhedron.
7132 As C<isl> currently does not have its own output format, the output
7133 is just a dump of the internal state.
7135 =head2 C<isl_polyhedron_minimize>
7137 C<isl_polyhedron_minimize> computes the minimum of some linear
7138 or affine objective function over the integer points in a polyhedron.
7139 If an affine objective function
7140 is given, then the constant should appear in the last column.
7142 =head2 C<isl_polytope_scan>
7144 Given a polytope, C<isl_polytope_scan> prints
7145 all integer points in the polytope.
7147 =head2 C<isl_codegen>
7149 Given a schedule, a context set and an options relation,
7150 C<isl_codegen> prints out an AST that scans the domain elements
7151 of the schedule in the order of their image(s) taking into account
7152 the constraints in the context set.