3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
184 =head3 Changes since isl-0.12
188 =item * C<isl_int> has been replaced by C<isl_val>.
189 Some of the old functions are still available in C<isl/deprecated/*.h>
190 but they will be removed in the future.
192 =item * The functions C<isl_pw_qpolynomial_eval>,
193 C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval>
194 and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return
195 an C<isl_val> instead of an C<isl_qpolynomial>.
197 =item * The function C<isl_band_member_is_zero_distance>
198 has been removed. Essentially the same functionality is available
199 through C<isl_band_member_is_coincident>, except that is requires
200 setting up coincidence constraints.
201 The option C<schedule_outer_zero_distance> has accordingly been
202 replaced by the option C<schedule_outer_coincidence>.
204 =item * The function C<isl_vertex_get_expr> has been changed
205 to return an C<isl_multi_aff> instead of a rational C<isl_basic_set>.
206 The function C<isl_vertex_get_domain> has been changed to return
207 a regular basic set, rather than a rational basic set.
213 C<isl> is released under the MIT license.
217 Permission is hereby granted, free of charge, to any person obtaining a copy of
218 this software and associated documentation files (the "Software"), to deal in
219 the Software without restriction, including without limitation the rights to
220 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
221 of the Software, and to permit persons to whom the Software is furnished to do
222 so, subject to the following conditions:
224 The above copyright notice and this permission notice shall be included in all
225 copies or substantial portions of the Software.
227 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
228 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
229 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
230 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
231 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
232 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
237 Note that C<isl> currently requires C<GMP>, which is released
238 under the GNU Lesser General Public License (LGPL). This means
239 that code linked against C<isl> is also linked against LGPL code.
243 The source of C<isl> can be obtained either as a tarball
244 or from the git repository. Both are available from
245 L<http://freshmeat.net/projects/isl/>.
246 The installation process depends on how you obtained
249 =head2 Installation from the git repository
253 =item 1 Clone or update the repository
255 The first time the source is obtained, you need to clone
258 git clone git://repo.or.cz/isl.git
260 To obtain updates, you need to pull in the latest changes
264 =item 2 Generate C<configure>
270 After performing the above steps, continue
271 with the L<Common installation instructions>.
273 =head2 Common installation instructions
277 =item 1 Obtain C<GMP>
279 Building C<isl> requires C<GMP>, including its headers files.
280 Your distribution may not provide these header files by default
281 and you may need to install a package called C<gmp-devel> or something
282 similar. Alternatively, C<GMP> can be built from
283 source, available from L<http://gmplib.org/>.
287 C<isl> uses the standard C<autoconf> C<configure> script.
292 optionally followed by some configure options.
293 A complete list of options can be obtained by running
297 Below we discuss some of the more common options.
303 Installation prefix for C<isl>
305 =item C<--with-gmp-prefix>
307 Installation prefix for C<GMP> (architecture-independent files).
309 =item C<--with-gmp-exec-prefix>
311 Installation prefix for C<GMP> (architecture-dependent files).
319 =item 4 Install (optional)
325 =head1 Integer Set Library
327 =head2 Initialization
329 All manipulations of integer sets and relations occur within
330 the context of an C<isl_ctx>.
331 A given C<isl_ctx> can only be used within a single thread.
332 All arguments of a function are required to have been allocated
333 within the same context.
334 There are currently no functions available for moving an object
335 from one C<isl_ctx> to another C<isl_ctx>. This means that
336 there is currently no way of safely moving an object from one
337 thread to another, unless the whole C<isl_ctx> is moved.
339 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
340 freed using C<isl_ctx_free>.
341 All objects allocated within an C<isl_ctx> should be freed
342 before the C<isl_ctx> itself is freed.
344 isl_ctx *isl_ctx_alloc();
345 void isl_ctx_free(isl_ctx *ctx);
347 The user can impose a bound on the number of low-level I<operations>
348 that can be performed by an C<isl_ctx>. This bound can be set and
349 retrieved using the following functions. A bound of zero means that
350 no bound is imposed. The number of operations performed can be
351 reset using C<isl_ctx_reset_operations>. Note that the number
352 of low-level operations needed to perform a high-level computation
353 may differ significantly across different versions
354 of C<isl>, but it should be the same across different platforms
355 for the same version of C<isl>.
357 void isl_ctx_set_max_operations(isl_ctx *ctx,
358 unsigned long max_operations);
359 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
360 void isl_ctx_reset_operations(isl_ctx *ctx);
362 =head2 Memory Management
364 Since a high-level operation on isl objects usually involves
365 several substeps and since the user is usually not interested in
366 the intermediate results, most functions that return a new object
367 will also release all the objects passed as arguments.
368 If the user still wants to use one or more of these arguments
369 after the function call, she should pass along a copy of the
370 object rather than the object itself.
371 The user is then responsible for making sure that the original
372 object gets used somewhere else or is explicitly freed.
374 The arguments and return values of all documented functions are
375 annotated to make clear which arguments are released and which
376 arguments are preserved. In particular, the following annotations
383 C<__isl_give> means that a new object is returned.
384 The user should make sure that the returned pointer is
385 used exactly once as a value for an C<__isl_take> argument.
386 In between, it can be used as a value for as many
387 C<__isl_keep> arguments as the user likes.
388 There is one exception, and that is the case where the
389 pointer returned is C<NULL>. Is this case, the user
390 is free to use it as an C<__isl_take> argument or not.
394 C<__isl_null> means that a C<NULL> value is returned.
398 C<__isl_take> means that the object the argument points to
399 is taken over by the function and may no longer be used
400 by the user as an argument to any other function.
401 The pointer value must be one returned by a function
402 returning an C<__isl_give> pointer.
403 If the user passes in a C<NULL> value, then this will
404 be treated as an error in the sense that the function will
405 not perform its usual operation. However, it will still
406 make sure that all the other C<__isl_take> arguments
411 C<__isl_keep> means that the function will only use the object
412 temporarily. After the function has finished, the user
413 can still use it as an argument to other functions.
414 A C<NULL> value will be treated in the same way as
415 a C<NULL> value for an C<__isl_take> argument.
421 An C<isl_val> represents an integer value, a rational value
422 or one of three special values, infinity, negative infinity and NaN.
423 Some predefined values can be created using the following functions.
426 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
427 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
428 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
429 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
430 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
431 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
433 Specific integer values can be created using the following functions.
436 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
438 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
440 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
441 size_t n, size_t size, const void *chunks);
443 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
444 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
445 The least significant digit is assumed to be stored first.
447 Value objects can be copied and freed using the following functions.
450 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
451 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
453 They can be inspected using the following functions.
456 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
457 long isl_val_get_num_si(__isl_keep isl_val *v);
458 long isl_val_get_den_si(__isl_keep isl_val *v);
459 double isl_val_get_d(__isl_keep isl_val *v);
460 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
462 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
463 size_t size, void *chunks);
465 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
466 of C<size> bytes needed to store the absolute value of the
468 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
469 which is assumed to have been preallocated by the caller.
470 The least significant digit is stored first.
471 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
472 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
473 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
475 An C<isl_val> can be modified using the following function.
478 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
481 The following unary properties are defined on C<isl_val>s.
484 int isl_val_sgn(__isl_keep isl_val *v);
485 int isl_val_is_zero(__isl_keep isl_val *v);
486 int isl_val_is_one(__isl_keep isl_val *v);
487 int isl_val_is_negone(__isl_keep isl_val *v);
488 int isl_val_is_nonneg(__isl_keep isl_val *v);
489 int isl_val_is_nonpos(__isl_keep isl_val *v);
490 int isl_val_is_pos(__isl_keep isl_val *v);
491 int isl_val_is_neg(__isl_keep isl_val *v);
492 int isl_val_is_int(__isl_keep isl_val *v);
493 int isl_val_is_rat(__isl_keep isl_val *v);
494 int isl_val_is_nan(__isl_keep isl_val *v);
495 int isl_val_is_infty(__isl_keep isl_val *v);
496 int isl_val_is_neginfty(__isl_keep isl_val *v);
498 Note that the sign of NaN is undefined.
500 The following binary properties are defined on pairs of C<isl_val>s.
503 int isl_val_lt(__isl_keep isl_val *v1,
504 __isl_keep isl_val *v2);
505 int isl_val_le(__isl_keep isl_val *v1,
506 __isl_keep isl_val *v2);
507 int isl_val_gt(__isl_keep isl_val *v1,
508 __isl_keep isl_val *v2);
509 int isl_val_ge(__isl_keep isl_val *v1,
510 __isl_keep isl_val *v2);
511 int isl_val_eq(__isl_keep isl_val *v1,
512 __isl_keep isl_val *v2);
513 int isl_val_ne(__isl_keep isl_val *v1,
514 __isl_keep isl_val *v2);
516 For integer C<isl_val>s we additionally have the following binary property.
519 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
520 __isl_keep isl_val *v2);
522 An C<isl_val> can also be compared to an integer using the following
523 function. The result is undefined for NaN.
526 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
528 The following unary operations are available on C<isl_val>s.
531 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
532 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
533 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
534 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
535 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
537 The following binary operations are available on C<isl_val>s.
540 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
541 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
542 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
543 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
544 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
545 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
546 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
547 __isl_take isl_val *v2);
548 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
549 __isl_take isl_val *v2);
550 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
551 __isl_take isl_val *v2);
552 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
554 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
555 __isl_take isl_val *v2);
556 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
558 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
559 __isl_take isl_val *v2);
560 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
562 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
563 __isl_take isl_val *v2);
565 On integer values, we additionally have the following operations.
568 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
569 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
570 __isl_take isl_val *v2);
571 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
572 __isl_take isl_val *v2);
573 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
574 __isl_take isl_val *v2, __isl_give isl_val **x,
575 __isl_give isl_val **y);
577 The function C<isl_val_gcdext> returns the greatest common divisor g
578 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
579 that C<*x> * C<v1> + C<*y> * C<v2> = g.
581 A value can be read from input using
584 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
587 A value can be printed using
590 __isl_give isl_printer *isl_printer_print_val(
591 __isl_take isl_printer *p, __isl_keep isl_val *v);
593 =head3 GMP specific functions
595 These functions are only available if C<isl> has been compiled with C<GMP>
598 Specific integer and rational values can be created from C<GMP> values using
599 the following functions.
601 #include <isl/val_gmp.h>
602 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
604 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
605 const mpz_t n, const mpz_t d);
607 The numerator and denominator of a rational value can be extracted as
608 C<GMP> values using the following functions.
610 #include <isl/val_gmp.h>
611 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
612 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
614 =head2 Sets and Relations
616 C<isl> uses six types of objects for representing sets and relations,
617 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
618 C<isl_union_set> and C<isl_union_map>.
619 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
620 can be described as a conjunction of affine constraints, while
621 C<isl_set> and C<isl_map> represent unions of
622 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
623 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
624 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
625 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
626 where spaces are considered different if they have a different number
627 of dimensions and/or different names (see L<"Spaces">).
628 The difference between sets and relations (maps) is that sets have
629 one set of variables, while relations have two sets of variables,
630 input variables and output variables.
632 =head2 Error Handling
634 C<isl> supports different ways to react in case a runtime error is triggered.
635 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
636 with two maps that have incompatible spaces. There are three possible ways
637 to react on error: to warn, to continue or to abort.
639 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
640 the last error in the corresponding C<isl_ctx> and the function in which the
641 error was triggered returns C<NULL>. An error does not corrupt internal state,
642 such that isl can continue to be used. C<isl> also provides functions to
643 read the last error and to reset the memory that stores the last error. The
644 last error is only stored for information purposes. Its presence does not
645 change the behavior of C<isl>. Hence, resetting an error is not required to
646 continue to use isl, but only to observe new errors.
649 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
650 void isl_ctx_reset_error(isl_ctx *ctx);
652 Another option is to continue on error. This is similar to warn on error mode,
653 except that C<isl> does not print any warning. This allows a program to
654 implement its own error reporting.
656 The last option is to directly abort the execution of the program from within
657 the isl library. This makes it obviously impossible to recover from an error,
658 but it allows to directly spot the error location. By aborting on error,
659 debuggers break at the location the error occurred and can provide a stack
660 trace. Other tools that automatically provide stack traces on abort or that do
661 not want to continue execution after an error was triggered may also prefer to
664 The on error behavior of isl can be specified by calling
665 C<isl_options_set_on_error> or by setting the command line option
666 C<--isl-on-error>. Valid arguments for the function call are
667 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
668 choices for the command line option are C<warn>, C<continue> and C<abort>.
669 It is also possible to query the current error mode.
671 #include <isl/options.h>
672 int isl_options_set_on_error(isl_ctx *ctx, int val);
673 int isl_options_get_on_error(isl_ctx *ctx);
677 Identifiers are used to identify both individual dimensions
678 and tuples of dimensions. They consist of an optional name and an optional
679 user pointer. The name and the user pointer cannot both be C<NULL>, however.
680 Identifiers with the same name but different pointer values
681 are considered to be distinct.
682 Similarly, identifiers with different names but the same pointer value
683 are also considered to be distinct.
684 Equal identifiers are represented using the same object.
685 Pairs of identifiers can therefore be tested for equality using the
687 Identifiers can be constructed, copied, freed, inspected and printed
688 using the following functions.
691 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
692 __isl_keep const char *name, void *user);
693 __isl_give isl_id *isl_id_set_free_user(
694 __isl_take isl_id *id,
695 __isl_give void (*free_user)(void *user));
696 __isl_give isl_id *isl_id_copy(isl_id *id);
697 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
699 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
700 void *isl_id_get_user(__isl_keep isl_id *id);
701 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
703 __isl_give isl_printer *isl_printer_print_id(
704 __isl_take isl_printer *p, __isl_keep isl_id *id);
706 The callback set by C<isl_id_set_free_user> is called on the user
707 pointer when the last reference to the C<isl_id> is freed.
708 Note that C<isl_id_get_name> returns a pointer to some internal
709 data structure, so the result can only be used while the
710 corresponding C<isl_id> is alive.
714 Whenever a new set, relation or similiar object is created from scratch,
715 the space in which it lives needs to be specified using an C<isl_space>.
716 Each space involves zero or more parameters and zero, one or two
717 tuples of set or input/output dimensions. The parameters and dimensions
718 are identified by an C<isl_dim_type> and a position.
719 The type C<isl_dim_param> refers to parameters,
720 the type C<isl_dim_set> refers to set dimensions (for spaces
721 with a single tuple of dimensions) and the types C<isl_dim_in>
722 and C<isl_dim_out> refer to input and output dimensions
723 (for spaces with two tuples of dimensions).
724 Local spaces (see L</"Local Spaces">) also contain dimensions
725 of type C<isl_dim_div>.
726 Note that parameters are only identified by their position within
727 a given object. Across different objects, parameters are (usually)
728 identified by their names or identifiers. Only unnamed parameters
729 are identified by their positions across objects. The use of unnamed
730 parameters is discouraged.
732 #include <isl/space.h>
733 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
734 unsigned nparam, unsigned n_in, unsigned n_out);
735 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
737 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
738 unsigned nparam, unsigned dim);
739 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
740 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
741 unsigned isl_space_dim(__isl_keep isl_space *space,
742 enum isl_dim_type type);
744 The space used for creating a parameter domain
745 needs to be created using C<isl_space_params_alloc>.
746 For other sets, the space
747 needs to be created using C<isl_space_set_alloc>, while
748 for a relation, the space
749 needs to be created using C<isl_space_alloc>.
750 C<isl_space_dim> can be used
751 to find out the number of dimensions of each type in
752 a space, where type may be
753 C<isl_dim_param>, C<isl_dim_in> (only for relations),
754 C<isl_dim_out> (only for relations), C<isl_dim_set>
755 (only for sets) or C<isl_dim_all>.
757 To check whether a given space is that of a set or a map
758 or whether it is a parameter space, use these functions:
760 #include <isl/space.h>
761 int isl_space_is_params(__isl_keep isl_space *space);
762 int isl_space_is_set(__isl_keep isl_space *space);
763 int isl_space_is_map(__isl_keep isl_space *space);
765 Spaces can be compared using the following functions:
767 #include <isl/space.h>
768 int isl_space_is_equal(__isl_keep isl_space *space1,
769 __isl_keep isl_space *space2);
770 int isl_space_is_domain(__isl_keep isl_space *space1,
771 __isl_keep isl_space *space2);
772 int isl_space_is_range(__isl_keep isl_space *space1,
773 __isl_keep isl_space *space2);
775 C<isl_space_is_domain> checks whether the first argument is equal
776 to the domain of the second argument. This requires in particular that
777 the first argument is a set space and that the second argument
780 It is often useful to create objects that live in the
781 same space as some other object. This can be accomplished
782 by creating the new objects
783 (see L</"Creating New Sets and Relations"> or
784 L</"Creating New (Piecewise) Quasipolynomials">) based on the space
785 of the original object.
788 __isl_give isl_space *isl_basic_set_get_space(
789 __isl_keep isl_basic_set *bset);
790 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
792 #include <isl/union_set.h>
793 __isl_give isl_space *isl_union_set_get_space(
794 __isl_keep isl_union_set *uset);
797 __isl_give isl_space *isl_basic_map_get_space(
798 __isl_keep isl_basic_map *bmap);
799 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
801 #include <isl/union_map.h>
802 __isl_give isl_space *isl_union_map_get_space(
803 __isl_keep isl_union_map *umap);
805 #include <isl/constraint.h>
806 __isl_give isl_space *isl_constraint_get_space(
807 __isl_keep isl_constraint *constraint);
809 #include <isl/polynomial.h>
810 __isl_give isl_space *isl_qpolynomial_get_domain_space(
811 __isl_keep isl_qpolynomial *qp);
812 __isl_give isl_space *isl_qpolynomial_get_space(
813 __isl_keep isl_qpolynomial *qp);
814 __isl_give isl_space *isl_qpolynomial_fold_get_space(
815 __isl_keep isl_qpolynomial_fold *fold);
816 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
817 __isl_keep isl_pw_qpolynomial *pwqp);
818 __isl_give isl_space *isl_pw_qpolynomial_get_space(
819 __isl_keep isl_pw_qpolynomial *pwqp);
820 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
821 __isl_keep isl_pw_qpolynomial_fold *pwf);
822 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
823 __isl_keep isl_pw_qpolynomial_fold *pwf);
824 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
825 __isl_keep isl_union_pw_qpolynomial *upwqp);
826 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
827 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
830 __isl_give isl_space *isl_multi_val_get_space(
831 __isl_keep isl_multi_val *mv);
834 __isl_give isl_space *isl_aff_get_domain_space(
835 __isl_keep isl_aff *aff);
836 __isl_give isl_space *isl_aff_get_space(
837 __isl_keep isl_aff *aff);
838 __isl_give isl_space *isl_pw_aff_get_domain_space(
839 __isl_keep isl_pw_aff *pwaff);
840 __isl_give isl_space *isl_pw_aff_get_space(
841 __isl_keep isl_pw_aff *pwaff);
842 __isl_give isl_space *isl_multi_aff_get_domain_space(
843 __isl_keep isl_multi_aff *maff);
844 __isl_give isl_space *isl_multi_aff_get_space(
845 __isl_keep isl_multi_aff *maff);
846 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
847 __isl_keep isl_pw_multi_aff *pma);
848 __isl_give isl_space *isl_pw_multi_aff_get_space(
849 __isl_keep isl_pw_multi_aff *pma);
850 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
851 __isl_keep isl_union_pw_multi_aff *upma);
852 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
853 __isl_keep isl_multi_pw_aff *mpa);
854 __isl_give isl_space *isl_multi_pw_aff_get_space(
855 __isl_keep isl_multi_pw_aff *mpa);
857 #include <isl/point.h>
858 __isl_give isl_space *isl_point_get_space(
859 __isl_keep isl_point *pnt);
861 The identifiers or names of the individual dimensions may be set or read off
862 using the following functions.
864 #include <isl/space.h>
865 __isl_give isl_space *isl_space_set_dim_id(
866 __isl_take isl_space *space,
867 enum isl_dim_type type, unsigned pos,
868 __isl_take isl_id *id);
869 int isl_space_has_dim_id(__isl_keep isl_space *space,
870 enum isl_dim_type type, unsigned pos);
871 __isl_give isl_id *isl_space_get_dim_id(
872 __isl_keep isl_space *space,
873 enum isl_dim_type type, unsigned pos);
874 __isl_give isl_space *isl_space_set_dim_name(
875 __isl_take isl_space *space,
876 enum isl_dim_type type, unsigned pos,
877 __isl_keep const char *name);
878 int isl_space_has_dim_name(__isl_keep isl_space *space,
879 enum isl_dim_type type, unsigned pos);
880 __isl_keep const char *isl_space_get_dim_name(
881 __isl_keep isl_space *space,
882 enum isl_dim_type type, unsigned pos);
884 Note that C<isl_space_get_name> returns a pointer to some internal
885 data structure, so the result can only be used while the
886 corresponding C<isl_space> is alive.
887 Also note that every function that operates on two sets or relations
888 requires that both arguments have the same parameters. This also
889 means that if one of the arguments has named parameters, then the
890 other needs to have named parameters too and the names need to match.
891 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
892 arguments may have different parameters (as long as they are named),
893 in which case the result will have as parameters the union of the parameters of
896 Given the identifier or name of a dimension (typically a parameter),
897 its position can be obtained from the following function.
899 #include <isl/space.h>
900 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
901 enum isl_dim_type type, __isl_keep isl_id *id);
902 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
903 enum isl_dim_type type, const char *name);
905 The identifiers or names of entire spaces may be set or read off
906 using the following functions.
908 #include <isl/space.h>
909 __isl_give isl_space *isl_space_set_tuple_id(
910 __isl_take isl_space *space,
911 enum isl_dim_type type, __isl_take isl_id *id);
912 __isl_give isl_space *isl_space_reset_tuple_id(
913 __isl_take isl_space *space, enum isl_dim_type type);
914 int isl_space_has_tuple_id(__isl_keep isl_space *space,
915 enum isl_dim_type type);
916 __isl_give isl_id *isl_space_get_tuple_id(
917 __isl_keep isl_space *space, enum isl_dim_type type);
918 __isl_give isl_space *isl_space_set_tuple_name(
919 __isl_take isl_space *space,
920 enum isl_dim_type type, const char *s);
921 int isl_space_has_tuple_name(__isl_keep isl_space *space,
922 enum isl_dim_type type);
923 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
924 enum isl_dim_type type);
926 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
927 or C<isl_dim_set>. As with C<isl_space_get_name>,
928 the C<isl_space_get_tuple_name> function returns a pointer to some internal
930 Binary operations require the corresponding spaces of their arguments
931 to have the same name.
933 To keep the names of all parameters and tuples, but reset the user pointers
934 of all the corresponding identifiers, use the following function.
936 __isl_give isl_space *isl_space_reset_user(
937 __isl_take isl_space *space);
939 Spaces can be nested. In particular, the domain of a set or
940 the domain or range of a relation can be a nested relation.
941 This process is also called I<wrapping>.
942 The functions for detecting, constructing and deconstructing
943 such nested spaces can be found in the wrapping properties
944 of L</"Unary Properties">, the wrapping operations
945 of L</"Unary Operations"> and the Cartesian product operations
946 of L</"Basic Operations">.
948 Spaces can be created from other spaces
949 using the following functions.
951 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
952 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
953 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
954 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
955 __isl_give isl_space *isl_space_domain_map(
956 __isl_take isl_space *space);
957 __isl_give isl_space *isl_space_range_map(
958 __isl_take isl_space *space);
959 __isl_give isl_space *isl_space_params(
960 __isl_take isl_space *space);
961 __isl_give isl_space *isl_space_set_from_params(
962 __isl_take isl_space *space);
963 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
964 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
965 __isl_take isl_space *right);
966 __isl_give isl_space *isl_space_align_params(
967 __isl_take isl_space *space1, __isl_take isl_space *space2)
968 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
969 enum isl_dim_type type, unsigned pos, unsigned n);
970 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
971 enum isl_dim_type type, unsigned n);
972 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
973 enum isl_dim_type type, unsigned first, unsigned n);
974 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
975 enum isl_dim_type dst_type, unsigned dst_pos,
976 enum isl_dim_type src_type, unsigned src_pos,
978 __isl_give isl_space *isl_space_map_from_set(
979 __isl_take isl_space *space);
980 __isl_give isl_space *isl_space_map_from_domain_and_range(
981 __isl_take isl_space *domain,
982 __isl_take isl_space *range);
983 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
984 __isl_give isl_space *isl_space_curry(
985 __isl_take isl_space *space);
986 __isl_give isl_space *isl_space_uncurry(
987 __isl_take isl_space *space);
989 Note that if dimensions are added or removed from a space, then
990 the name and the internal structure are lost.
994 A local space is essentially a space with
995 zero or more existentially quantified variables.
996 The local space of a (constraint of a) basic set or relation can be obtained
997 using the following functions.
999 #include <isl/constraint.h>
1000 __isl_give isl_local_space *isl_constraint_get_local_space(
1001 __isl_keep isl_constraint *constraint);
1003 #include <isl/set.h>
1004 __isl_give isl_local_space *isl_basic_set_get_local_space(
1005 __isl_keep isl_basic_set *bset);
1007 #include <isl/map.h>
1008 __isl_give isl_local_space *isl_basic_map_get_local_space(
1009 __isl_keep isl_basic_map *bmap);
1011 A new local space can be created from a space using
1013 #include <isl/local_space.h>
1014 __isl_give isl_local_space *isl_local_space_from_space(
1015 __isl_take isl_space *space);
1017 They can be inspected, modified, copied and freed using the following functions.
1019 #include <isl/local_space.h>
1020 isl_ctx *isl_local_space_get_ctx(
1021 __isl_keep isl_local_space *ls);
1022 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1023 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1024 enum isl_dim_type type);
1025 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1026 __isl_take isl_local_space *ls,
1027 enum isl_dim_type type, __isl_take isl_id *id);
1028 int isl_local_space_has_dim_id(
1029 __isl_keep isl_local_space *ls,
1030 enum isl_dim_type type, unsigned pos);
1031 __isl_give isl_id *isl_local_space_get_dim_id(
1032 __isl_keep isl_local_space *ls,
1033 enum isl_dim_type type, unsigned pos);
1034 int isl_local_space_has_dim_name(
1035 __isl_keep isl_local_space *ls,
1036 enum isl_dim_type type, unsigned pos)
1037 const char *isl_local_space_get_dim_name(
1038 __isl_keep isl_local_space *ls,
1039 enum isl_dim_type type, unsigned pos);
1040 __isl_give isl_local_space *isl_local_space_set_dim_name(
1041 __isl_take isl_local_space *ls,
1042 enum isl_dim_type type, unsigned pos, const char *s);
1043 __isl_give isl_local_space *isl_local_space_set_dim_id(
1044 __isl_take isl_local_space *ls,
1045 enum isl_dim_type type, unsigned pos,
1046 __isl_take isl_id *id);
1047 __isl_give isl_space *isl_local_space_get_space(
1048 __isl_keep isl_local_space *ls);
1049 __isl_give isl_aff *isl_local_space_get_div(
1050 __isl_keep isl_local_space *ls, int pos);
1051 __isl_give isl_local_space *isl_local_space_copy(
1052 __isl_keep isl_local_space *ls);
1053 __isl_null isl_local_space *isl_local_space_free(
1054 __isl_take isl_local_space *ls);
1056 Note that C<isl_local_space_get_div> can only be used on local spaces
1059 Two local spaces can be compared using
1061 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1062 __isl_keep isl_local_space *ls2);
1064 Local spaces can be created from other local spaces
1065 using the functions described in L</"Unary Operations">
1066 and L</"Binary Operations">.
1068 =head2 Input and Output
1070 C<isl> supports its own input/output format, which is similar
1071 to the C<Omega> format, but also supports the C<PolyLib> format
1074 =head3 C<isl> format
1076 The C<isl> format is similar to that of C<Omega>, but has a different
1077 syntax for describing the parameters and allows for the definition
1078 of an existentially quantified variable as the integer division
1079 of an affine expression.
1080 For example, the set of integers C<i> between C<0> and C<n>
1081 such that C<i % 10 <= 6> can be described as
1083 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1086 A set or relation can have several disjuncts, separated
1087 by the keyword C<or>. Each disjunct is either a conjunction
1088 of constraints or a projection (C<exists>) of a conjunction
1089 of constraints. The constraints are separated by the keyword
1092 =head3 C<PolyLib> format
1094 If the represented set is a union, then the first line
1095 contains a single number representing the number of disjuncts.
1096 Otherwise, a line containing the number C<1> is optional.
1098 Each disjunct is represented by a matrix of constraints.
1099 The first line contains two numbers representing
1100 the number of rows and columns,
1101 where the number of rows is equal to the number of constraints
1102 and the number of columns is equal to two plus the number of variables.
1103 The following lines contain the actual rows of the constraint matrix.
1104 In each row, the first column indicates whether the constraint
1105 is an equality (C<0>) or inequality (C<1>). The final column
1106 corresponds to the constant term.
1108 If the set is parametric, then the coefficients of the parameters
1109 appear in the last columns before the constant column.
1110 The coefficients of any existentially quantified variables appear
1111 between those of the set variables and those of the parameters.
1113 =head3 Extended C<PolyLib> format
1115 The extended C<PolyLib> format is nearly identical to the
1116 C<PolyLib> format. The only difference is that the line
1117 containing the number of rows and columns of a constraint matrix
1118 also contains four additional numbers:
1119 the number of output dimensions, the number of input dimensions,
1120 the number of local dimensions (i.e., the number of existentially
1121 quantified variables) and the number of parameters.
1122 For sets, the number of ``output'' dimensions is equal
1123 to the number of set dimensions, while the number of ``input''
1128 #include <isl/set.h>
1129 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1130 isl_ctx *ctx, FILE *input);
1131 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1132 isl_ctx *ctx, const char *str);
1133 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1135 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1138 #include <isl/map.h>
1139 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1140 isl_ctx *ctx, FILE *input);
1141 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1142 isl_ctx *ctx, const char *str);
1143 __isl_give isl_map *isl_map_read_from_file(
1144 isl_ctx *ctx, FILE *input);
1145 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1148 #include <isl/union_set.h>
1149 __isl_give isl_union_set *isl_union_set_read_from_file(
1150 isl_ctx *ctx, FILE *input);
1151 __isl_give isl_union_set *isl_union_set_read_from_str(
1152 isl_ctx *ctx, const char *str);
1154 #include <isl/union_map.h>
1155 __isl_give isl_union_map *isl_union_map_read_from_file(
1156 isl_ctx *ctx, FILE *input);
1157 __isl_give isl_union_map *isl_union_map_read_from_str(
1158 isl_ctx *ctx, const char *str);
1160 The input format is autodetected and may be either the C<PolyLib> format
1161 or the C<isl> format.
1165 Before anything can be printed, an C<isl_printer> needs to
1168 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1170 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1171 __isl_null isl_printer *isl_printer_free(
1172 __isl_take isl_printer *printer);
1173 __isl_give char *isl_printer_get_str(
1174 __isl_keep isl_printer *printer);
1176 The printer can be inspected using the following functions.
1178 FILE *isl_printer_get_file(
1179 __isl_keep isl_printer *printer);
1180 int isl_printer_get_output_format(
1181 __isl_keep isl_printer *p);
1183 The behavior of the printer can be modified in various ways
1185 __isl_give isl_printer *isl_printer_set_output_format(
1186 __isl_take isl_printer *p, int output_format);
1187 __isl_give isl_printer *isl_printer_set_indent(
1188 __isl_take isl_printer *p, int indent);
1189 __isl_give isl_printer *isl_printer_set_indent_prefix(
1190 __isl_take isl_printer *p, const char *prefix);
1191 __isl_give isl_printer *isl_printer_indent(
1192 __isl_take isl_printer *p, int indent);
1193 __isl_give isl_printer *isl_printer_set_prefix(
1194 __isl_take isl_printer *p, const char *prefix);
1195 __isl_give isl_printer *isl_printer_set_suffix(
1196 __isl_take isl_printer *p, const char *suffix);
1198 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1199 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1200 and defaults to C<ISL_FORMAT_ISL>.
1201 Each line in the output is prefixed by C<indent_prefix>,
1202 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
1203 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1204 In the C<PolyLib> format output,
1205 the coefficients of the existentially quantified variables
1206 appear between those of the set variables and those
1208 The function C<isl_printer_indent> increases the indentation
1209 by the specified amount (which may be negative).
1211 To actually print something, use
1213 #include <isl/printer.h>
1214 __isl_give isl_printer *isl_printer_print_double(
1215 __isl_take isl_printer *p, double d);
1217 #include <isl/set.h>
1218 __isl_give isl_printer *isl_printer_print_basic_set(
1219 __isl_take isl_printer *printer,
1220 __isl_keep isl_basic_set *bset);
1221 __isl_give isl_printer *isl_printer_print_set(
1222 __isl_take isl_printer *printer,
1223 __isl_keep isl_set *set);
1225 #include <isl/map.h>
1226 __isl_give isl_printer *isl_printer_print_basic_map(
1227 __isl_take isl_printer *printer,
1228 __isl_keep isl_basic_map *bmap);
1229 __isl_give isl_printer *isl_printer_print_map(
1230 __isl_take isl_printer *printer,
1231 __isl_keep isl_map *map);
1233 #include <isl/union_set.h>
1234 __isl_give isl_printer *isl_printer_print_union_set(
1235 __isl_take isl_printer *p,
1236 __isl_keep isl_union_set *uset);
1238 #include <isl/union_map.h>
1239 __isl_give isl_printer *isl_printer_print_union_map(
1240 __isl_take isl_printer *p,
1241 __isl_keep isl_union_map *umap);
1243 When called on a file printer, the following function flushes
1244 the file. When called on a string printer, the buffer is cleared.
1246 __isl_give isl_printer *isl_printer_flush(
1247 __isl_take isl_printer *p);
1249 =head2 Creating New Sets and Relations
1251 C<isl> has functions for creating some standard sets and relations.
1255 =item * Empty sets and relations
1257 __isl_give isl_basic_set *isl_basic_set_empty(
1258 __isl_take isl_space *space);
1259 __isl_give isl_basic_map *isl_basic_map_empty(
1260 __isl_take isl_space *space);
1261 __isl_give isl_set *isl_set_empty(
1262 __isl_take isl_space *space);
1263 __isl_give isl_map *isl_map_empty(
1264 __isl_take isl_space *space);
1265 __isl_give isl_union_set *isl_union_set_empty(
1266 __isl_take isl_space *space);
1267 __isl_give isl_union_map *isl_union_map_empty(
1268 __isl_take isl_space *space);
1270 For C<isl_union_set>s and C<isl_union_map>s, the space
1271 is only used to specify the parameters.
1273 =item * Universe sets and relations
1275 __isl_give isl_basic_set *isl_basic_set_universe(
1276 __isl_take isl_space *space);
1277 __isl_give isl_basic_map *isl_basic_map_universe(
1278 __isl_take isl_space *space);
1279 __isl_give isl_set *isl_set_universe(
1280 __isl_take isl_space *space);
1281 __isl_give isl_map *isl_map_universe(
1282 __isl_take isl_space *space);
1283 __isl_give isl_union_set *isl_union_set_universe(
1284 __isl_take isl_union_set *uset);
1285 __isl_give isl_union_map *isl_union_map_universe(
1286 __isl_take isl_union_map *umap);
1288 The sets and relations constructed by the functions above
1289 contain all integer values, while those constructed by the
1290 functions below only contain non-negative values.
1292 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1293 __isl_take isl_space *space);
1294 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1295 __isl_take isl_space *space);
1296 __isl_give isl_set *isl_set_nat_universe(
1297 __isl_take isl_space *space);
1298 __isl_give isl_map *isl_map_nat_universe(
1299 __isl_take isl_space *space);
1301 =item * Identity relations
1303 __isl_give isl_basic_map *isl_basic_map_identity(
1304 __isl_take isl_space *space);
1305 __isl_give isl_map *isl_map_identity(
1306 __isl_take isl_space *space);
1308 The number of input and output dimensions in C<space> needs
1311 =item * Lexicographic order
1313 __isl_give isl_map *isl_map_lex_lt(
1314 __isl_take isl_space *set_space);
1315 __isl_give isl_map *isl_map_lex_le(
1316 __isl_take isl_space *set_space);
1317 __isl_give isl_map *isl_map_lex_gt(
1318 __isl_take isl_space *set_space);
1319 __isl_give isl_map *isl_map_lex_ge(
1320 __isl_take isl_space *set_space);
1321 __isl_give isl_map *isl_map_lex_lt_first(
1322 __isl_take isl_space *space, unsigned n);
1323 __isl_give isl_map *isl_map_lex_le_first(
1324 __isl_take isl_space *space, unsigned n);
1325 __isl_give isl_map *isl_map_lex_gt_first(
1326 __isl_take isl_space *space, unsigned n);
1327 __isl_give isl_map *isl_map_lex_ge_first(
1328 __isl_take isl_space *space, unsigned n);
1330 The first four functions take a space for a B<set>
1331 and return relations that express that the elements in the domain
1332 are lexicographically less
1333 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1334 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1335 than the elements in the range.
1336 The last four functions take a space for a map
1337 and return relations that express that the first C<n> dimensions
1338 in the domain are lexicographically less
1339 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1340 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1341 than the first C<n> dimensions in the range.
1345 A basic set or relation can be converted to a set or relation
1346 using the following functions.
1348 __isl_give isl_set *isl_set_from_basic_set(
1349 __isl_take isl_basic_set *bset);
1350 __isl_give isl_map *isl_map_from_basic_map(
1351 __isl_take isl_basic_map *bmap);
1353 Sets and relations can be converted to union sets and relations
1354 using the following functions.
1356 __isl_give isl_union_set *isl_union_set_from_basic_set(
1357 __isl_take isl_basic_set *bset);
1358 __isl_give isl_union_map *isl_union_map_from_basic_map(
1359 __isl_take isl_basic_map *bmap);
1360 __isl_give isl_union_set *isl_union_set_from_set(
1361 __isl_take isl_set *set);
1362 __isl_give isl_union_map *isl_union_map_from_map(
1363 __isl_take isl_map *map);
1365 The inverse conversions below can only be used if the input
1366 union set or relation is known to contain elements in exactly one
1369 __isl_give isl_set *isl_set_from_union_set(
1370 __isl_take isl_union_set *uset);
1371 __isl_give isl_map *isl_map_from_union_map(
1372 __isl_take isl_union_map *umap);
1374 A zero-dimensional (basic) set can be constructed on a given parameter domain
1375 using the following function.
1377 __isl_give isl_basic_set *isl_basic_set_from_params(
1378 __isl_take isl_basic_set *bset);
1379 __isl_give isl_set *isl_set_from_params(
1380 __isl_take isl_set *set);
1382 Sets and relations can be copied and freed again using the following
1385 __isl_give isl_basic_set *isl_basic_set_copy(
1386 __isl_keep isl_basic_set *bset);
1387 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1388 __isl_give isl_union_set *isl_union_set_copy(
1389 __isl_keep isl_union_set *uset);
1390 __isl_give isl_basic_map *isl_basic_map_copy(
1391 __isl_keep isl_basic_map *bmap);
1392 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1393 __isl_give isl_union_map *isl_union_map_copy(
1394 __isl_keep isl_union_map *umap);
1395 __isl_null isl_basic_set *isl_basic_set_free(
1396 __isl_take isl_basic_set *bset);
1397 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1398 __isl_null isl_union_set *isl_union_set_free(
1399 __isl_take isl_union_set *uset);
1400 __isl_null isl_basic_map *isl_basic_map_free(
1401 __isl_take isl_basic_map *bmap);
1402 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1403 __isl_null isl_union_map *isl_union_map_free(
1404 __isl_take isl_union_map *umap);
1406 Other sets and relations can be constructed by starting
1407 from a universe set or relation, adding equality and/or
1408 inequality constraints and then projecting out the
1409 existentially quantified variables, if any.
1410 Constraints can be constructed, manipulated and
1411 added to (or removed from) (basic) sets and relations
1412 using the following functions.
1414 #include <isl/constraint.h>
1415 __isl_give isl_constraint *isl_equality_alloc(
1416 __isl_take isl_local_space *ls);
1417 __isl_give isl_constraint *isl_inequality_alloc(
1418 __isl_take isl_local_space *ls);
1419 __isl_give isl_constraint *isl_constraint_set_constant_si(
1420 __isl_take isl_constraint *constraint, int v);
1421 __isl_give isl_constraint *isl_constraint_set_constant_val(
1422 __isl_take isl_constraint *constraint,
1423 __isl_take isl_val *v);
1424 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1425 __isl_take isl_constraint *constraint,
1426 enum isl_dim_type type, int pos, int v);
1427 __isl_give isl_constraint *
1428 isl_constraint_set_coefficient_val(
1429 __isl_take isl_constraint *constraint,
1430 enum isl_dim_type type, int pos,
1431 __isl_take isl_val *v);
1432 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1433 __isl_take isl_basic_map *bmap,
1434 __isl_take isl_constraint *constraint);
1435 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1436 __isl_take isl_basic_set *bset,
1437 __isl_take isl_constraint *constraint);
1438 __isl_give isl_map *isl_map_add_constraint(
1439 __isl_take isl_map *map,
1440 __isl_take isl_constraint *constraint);
1441 __isl_give isl_set *isl_set_add_constraint(
1442 __isl_take isl_set *set,
1443 __isl_take isl_constraint *constraint);
1444 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1445 __isl_take isl_basic_set *bset,
1446 __isl_take isl_constraint *constraint);
1448 For example, to create a set containing the even integers
1449 between 10 and 42, you would use the following code.
1452 isl_local_space *ls;
1454 isl_basic_set *bset;
1456 space = isl_space_set_alloc(ctx, 0, 2);
1457 bset = isl_basic_set_universe(isl_space_copy(space));
1458 ls = isl_local_space_from_space(space);
1460 c = isl_equality_alloc(isl_local_space_copy(ls));
1461 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1462 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1463 bset = isl_basic_set_add_constraint(bset, c);
1465 c = isl_inequality_alloc(isl_local_space_copy(ls));
1466 c = isl_constraint_set_constant_si(c, -10);
1467 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1468 bset = isl_basic_set_add_constraint(bset, c);
1470 c = isl_inequality_alloc(ls);
1471 c = isl_constraint_set_constant_si(c, 42);
1472 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1473 bset = isl_basic_set_add_constraint(bset, c);
1475 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1479 isl_basic_set *bset;
1480 bset = isl_basic_set_read_from_str(ctx,
1481 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1483 A basic set or relation can also be constructed from two matrices
1484 describing the equalities and the inequalities.
1486 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1487 __isl_take isl_space *space,
1488 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1489 enum isl_dim_type c1,
1490 enum isl_dim_type c2, enum isl_dim_type c3,
1491 enum isl_dim_type c4);
1492 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1493 __isl_take isl_space *space,
1494 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1495 enum isl_dim_type c1,
1496 enum isl_dim_type c2, enum isl_dim_type c3,
1497 enum isl_dim_type c4, enum isl_dim_type c5);
1499 The C<isl_dim_type> arguments indicate the order in which
1500 different kinds of variables appear in the input matrices
1501 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1502 C<isl_dim_set> and C<isl_dim_div> for sets and
1503 of C<isl_dim_cst>, C<isl_dim_param>,
1504 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1506 A (basic or union) set or relation can also be constructed from a
1507 (union) (piecewise) (multiple) affine expression
1508 or a list of affine expressions
1509 (See L<"Piecewise Quasi Affine Expressions"> and
1510 L<"Piecewise Multiple Quasi Affine Expressions">).
1512 __isl_give isl_basic_map *isl_basic_map_from_aff(
1513 __isl_take isl_aff *aff);
1514 __isl_give isl_map *isl_map_from_aff(
1515 __isl_take isl_aff *aff);
1516 __isl_give isl_set *isl_set_from_pw_aff(
1517 __isl_take isl_pw_aff *pwaff);
1518 __isl_give isl_map *isl_map_from_pw_aff(
1519 __isl_take isl_pw_aff *pwaff);
1520 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1521 __isl_take isl_space *domain_space,
1522 __isl_take isl_aff_list *list);
1523 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1524 __isl_take isl_multi_aff *maff)
1525 __isl_give isl_map *isl_map_from_multi_aff(
1526 __isl_take isl_multi_aff *maff)
1527 __isl_give isl_set *isl_set_from_pw_multi_aff(
1528 __isl_take isl_pw_multi_aff *pma);
1529 __isl_give isl_map *isl_map_from_pw_multi_aff(
1530 __isl_take isl_pw_multi_aff *pma);
1531 __isl_give isl_set *isl_set_from_multi_pw_aff(
1532 __isl_take isl_multi_pw_aff *mpa);
1533 __isl_give isl_map *isl_map_from_multi_pw_aff(
1534 __isl_take isl_multi_pw_aff *mpa);
1535 __isl_give isl_union_map *
1536 isl_union_map_from_union_pw_multi_aff(
1537 __isl_take isl_union_pw_multi_aff *upma);
1539 The C<domain_space> argument describes the domain of the resulting
1540 basic relation. It is required because the C<list> may consist
1541 of zero affine expressions.
1543 =head2 Inspecting Sets and Relations
1545 Usually, the user should not have to care about the actual constraints
1546 of the sets and maps, but should instead apply the abstract operations
1547 explained in the following sections.
1548 Occasionally, however, it may be required to inspect the individual
1549 coefficients of the constraints. This section explains how to do so.
1550 In these cases, it may also be useful to have C<isl> compute
1551 an explicit representation of the existentially quantified variables.
1553 __isl_give isl_set *isl_set_compute_divs(
1554 __isl_take isl_set *set);
1555 __isl_give isl_map *isl_map_compute_divs(
1556 __isl_take isl_map *map);
1557 __isl_give isl_union_set *isl_union_set_compute_divs(
1558 __isl_take isl_union_set *uset);
1559 __isl_give isl_union_map *isl_union_map_compute_divs(
1560 __isl_take isl_union_map *umap);
1562 This explicit representation defines the existentially quantified
1563 variables as integer divisions of the other variables, possibly
1564 including earlier existentially quantified variables.
1565 An explicitly represented existentially quantified variable therefore
1566 has a unique value when the values of the other variables are known.
1567 If, furthermore, the same existentials, i.e., existentials
1568 with the same explicit representations, should appear in the
1569 same order in each of the disjuncts of a set or map, then the user should call
1570 either of the following functions.
1572 __isl_give isl_set *isl_set_align_divs(
1573 __isl_take isl_set *set);
1574 __isl_give isl_map *isl_map_align_divs(
1575 __isl_take isl_map *map);
1577 Alternatively, the existentially quantified variables can be removed
1578 using the following functions, which compute an overapproximation.
1580 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1581 __isl_take isl_basic_set *bset);
1582 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1583 __isl_take isl_basic_map *bmap);
1584 __isl_give isl_set *isl_set_remove_divs(
1585 __isl_take isl_set *set);
1586 __isl_give isl_map *isl_map_remove_divs(
1587 __isl_take isl_map *map);
1589 It is also possible to only remove those divs that are defined
1590 in terms of a given range of dimensions or only those for which
1591 no explicit representation is known.
1593 __isl_give isl_basic_set *
1594 isl_basic_set_remove_divs_involving_dims(
1595 __isl_take isl_basic_set *bset,
1596 enum isl_dim_type type,
1597 unsigned first, unsigned n);
1598 __isl_give isl_basic_map *
1599 isl_basic_map_remove_divs_involving_dims(
1600 __isl_take isl_basic_map *bmap,
1601 enum isl_dim_type type,
1602 unsigned first, unsigned n);
1603 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1604 __isl_take isl_set *set, enum isl_dim_type type,
1605 unsigned first, unsigned n);
1606 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1607 __isl_take isl_map *map, enum isl_dim_type type,
1608 unsigned first, unsigned n);
1610 __isl_give isl_basic_set *
1611 isl_basic_set_remove_unknown_divs(
1612 __isl_take isl_basic_set *bset);
1613 __isl_give isl_set *isl_set_remove_unknown_divs(
1614 __isl_take isl_set *set);
1615 __isl_give isl_map *isl_map_remove_unknown_divs(
1616 __isl_take isl_map *map);
1618 To iterate over all the sets or maps in a union set or map, use
1620 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1621 int (*fn)(__isl_take isl_set *set, void *user),
1623 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1624 int (*fn)(__isl_take isl_map *map, void *user),
1627 The number of sets or maps in a union set or map can be obtained
1630 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1631 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1633 To extract the set or map in a given space from a union, use
1635 __isl_give isl_set *isl_union_set_extract_set(
1636 __isl_keep isl_union_set *uset,
1637 __isl_take isl_space *space);
1638 __isl_give isl_map *isl_union_map_extract_map(
1639 __isl_keep isl_union_map *umap,
1640 __isl_take isl_space *space);
1642 To iterate over all the basic sets or maps in a set or map, use
1644 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1645 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1647 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1648 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1651 The callback function C<fn> should return 0 if successful and
1652 -1 if an error occurs. In the latter case, or if any other error
1653 occurs, the above functions will return -1.
1655 It should be noted that C<isl> does not guarantee that
1656 the basic sets or maps passed to C<fn> are disjoint.
1657 If this is required, then the user should call one of
1658 the following functions first.
1660 __isl_give isl_set *isl_set_make_disjoint(
1661 __isl_take isl_set *set);
1662 __isl_give isl_map *isl_map_make_disjoint(
1663 __isl_take isl_map *map);
1665 The number of basic sets in a set can be obtained
1668 int isl_set_n_basic_set(__isl_keep isl_set *set);
1670 To iterate over the constraints of a basic set or map, use
1672 #include <isl/constraint.h>
1674 int isl_basic_set_n_constraint(
1675 __isl_keep isl_basic_set *bset);
1676 int isl_basic_set_foreach_constraint(
1677 __isl_keep isl_basic_set *bset,
1678 int (*fn)(__isl_take isl_constraint *c, void *user),
1680 int isl_basic_map_foreach_constraint(
1681 __isl_keep isl_basic_map *bmap,
1682 int (*fn)(__isl_take isl_constraint *c, void *user),
1684 __isl_null isl_constraint *isl_constraint_free(
1685 __isl_take isl_constraint *c);
1687 Again, the callback function C<fn> should return 0 if successful and
1688 -1 if an error occurs. In the latter case, or if any other error
1689 occurs, the above functions will return -1.
1690 The constraint C<c> represents either an equality or an inequality.
1691 Use the following function to find out whether a constraint
1692 represents an equality. If not, it represents an inequality.
1694 int isl_constraint_is_equality(
1695 __isl_keep isl_constraint *constraint);
1697 The coefficients of the constraints can be inspected using
1698 the following functions.
1700 int isl_constraint_is_lower_bound(
1701 __isl_keep isl_constraint *constraint,
1702 enum isl_dim_type type, unsigned pos);
1703 int isl_constraint_is_upper_bound(
1704 __isl_keep isl_constraint *constraint,
1705 enum isl_dim_type type, unsigned pos);
1706 __isl_give isl_val *isl_constraint_get_constant_val(
1707 __isl_keep isl_constraint *constraint);
1708 __isl_give isl_val *isl_constraint_get_coefficient_val(
1709 __isl_keep isl_constraint *constraint,
1710 enum isl_dim_type type, int pos);
1711 int isl_constraint_involves_dims(
1712 __isl_keep isl_constraint *constraint,
1713 enum isl_dim_type type, unsigned first, unsigned n);
1715 The explicit representations of the existentially quantified
1716 variables can be inspected using the following function.
1717 Note that the user is only allowed to use this function
1718 if the inspected set or map is the result of a call
1719 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1720 The existentially quantified variable is equal to the floor
1721 of the returned affine expression. The affine expression
1722 itself can be inspected using the functions in
1723 L<"Piecewise Quasi Affine Expressions">.
1725 __isl_give isl_aff *isl_constraint_get_div(
1726 __isl_keep isl_constraint *constraint, int pos);
1728 To obtain the constraints of a basic set or map in matrix
1729 form, use the following functions.
1731 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1732 __isl_keep isl_basic_set *bset,
1733 enum isl_dim_type c1, enum isl_dim_type c2,
1734 enum isl_dim_type c3, enum isl_dim_type c4);
1735 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1736 __isl_keep isl_basic_set *bset,
1737 enum isl_dim_type c1, enum isl_dim_type c2,
1738 enum isl_dim_type c3, enum isl_dim_type c4);
1739 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1740 __isl_keep isl_basic_map *bmap,
1741 enum isl_dim_type c1,
1742 enum isl_dim_type c2, enum isl_dim_type c3,
1743 enum isl_dim_type c4, enum isl_dim_type c5);
1744 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1745 __isl_keep isl_basic_map *bmap,
1746 enum isl_dim_type c1,
1747 enum isl_dim_type c2, enum isl_dim_type c3,
1748 enum isl_dim_type c4, enum isl_dim_type c5);
1750 The C<isl_dim_type> arguments dictate the order in which
1751 different kinds of variables appear in the resulting matrix
1752 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1753 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1755 The number of parameters, input, output or set dimensions can
1756 be obtained using the following functions.
1758 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1759 enum isl_dim_type type);
1760 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1761 enum isl_dim_type type);
1762 unsigned isl_set_dim(__isl_keep isl_set *set,
1763 enum isl_dim_type type);
1764 unsigned isl_map_dim(__isl_keep isl_map *map,
1765 enum isl_dim_type type);
1766 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1767 enum isl_dim_type type);
1769 Note that a C<isl_union_map> only has parameters.
1771 To check whether the description of a set or relation depends
1772 on one or more given dimensions, it is not necessary to iterate over all
1773 constraints. Instead the following functions can be used.
1775 int isl_basic_set_involves_dims(
1776 __isl_keep isl_basic_set *bset,
1777 enum isl_dim_type type, unsigned first, unsigned n);
1778 int isl_set_involves_dims(__isl_keep isl_set *set,
1779 enum isl_dim_type type, unsigned first, unsigned n);
1780 int isl_basic_map_involves_dims(
1781 __isl_keep isl_basic_map *bmap,
1782 enum isl_dim_type type, unsigned first, unsigned n);
1783 int isl_map_involves_dims(__isl_keep isl_map *map,
1784 enum isl_dim_type type, unsigned first, unsigned n);
1786 Similarly, the following functions can be used to check whether
1787 a given dimension is involved in any lower or upper bound.
1789 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1790 enum isl_dim_type type, unsigned pos);
1791 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1792 enum isl_dim_type type, unsigned pos);
1794 Note that these functions return true even if there is a bound on
1795 the dimension on only some of the basic sets of C<set>.
1796 To check if they have a bound for all of the basic sets in C<set>,
1797 use the following functions instead.
1799 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1800 enum isl_dim_type type, unsigned pos);
1801 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1802 enum isl_dim_type type, unsigned pos);
1804 The identifiers or names of the domain and range spaces of a set
1805 or relation can be read off or set using the following functions.
1807 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1808 __isl_take isl_basic_set *bset,
1809 __isl_take isl_id *id);
1810 __isl_give isl_set *isl_set_set_tuple_id(
1811 __isl_take isl_set *set, __isl_take isl_id *id);
1812 __isl_give isl_set *isl_set_reset_tuple_id(
1813 __isl_take isl_set *set);
1814 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1815 __isl_give isl_id *isl_set_get_tuple_id(
1816 __isl_keep isl_set *set);
1817 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1818 __isl_take isl_basic_map *bmap,
1819 enum isl_dim_type type, __isl_take isl_id *id);
1820 __isl_give isl_map *isl_map_set_tuple_id(
1821 __isl_take isl_map *map, enum isl_dim_type type,
1822 __isl_take isl_id *id);
1823 __isl_give isl_map *isl_map_reset_tuple_id(
1824 __isl_take isl_map *map, enum isl_dim_type type);
1825 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1826 enum isl_dim_type type);
1827 __isl_give isl_id *isl_map_get_tuple_id(
1828 __isl_keep isl_map *map, enum isl_dim_type type);
1830 const char *isl_basic_set_get_tuple_name(
1831 __isl_keep isl_basic_set *bset);
1832 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1833 __isl_take isl_basic_set *set, const char *s);
1834 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1835 const char *isl_set_get_tuple_name(
1836 __isl_keep isl_set *set);
1837 const char *isl_basic_map_get_tuple_name(
1838 __isl_keep isl_basic_map *bmap,
1839 enum isl_dim_type type);
1840 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1841 __isl_take isl_basic_map *bmap,
1842 enum isl_dim_type type, const char *s);
1843 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1844 enum isl_dim_type type);
1845 const char *isl_map_get_tuple_name(
1846 __isl_keep isl_map *map,
1847 enum isl_dim_type type);
1849 As with C<isl_space_get_tuple_name>, the value returned points to
1850 an internal data structure.
1851 The identifiers, positions or names of individual dimensions can be
1852 read off using the following functions.
1854 __isl_give isl_id *isl_basic_set_get_dim_id(
1855 __isl_keep isl_basic_set *bset,
1856 enum isl_dim_type type, unsigned pos);
1857 __isl_give isl_set *isl_set_set_dim_id(
1858 __isl_take isl_set *set, enum isl_dim_type type,
1859 unsigned pos, __isl_take isl_id *id);
1860 int isl_set_has_dim_id(__isl_keep isl_set *set,
1861 enum isl_dim_type type, unsigned pos);
1862 __isl_give isl_id *isl_set_get_dim_id(
1863 __isl_keep isl_set *set, enum isl_dim_type type,
1865 int isl_basic_map_has_dim_id(
1866 __isl_keep isl_basic_map *bmap,
1867 enum isl_dim_type type, unsigned pos);
1868 __isl_give isl_map *isl_map_set_dim_id(
1869 __isl_take isl_map *map, enum isl_dim_type type,
1870 unsigned pos, __isl_take isl_id *id);
1871 int isl_map_has_dim_id(__isl_keep isl_map *map,
1872 enum isl_dim_type type, unsigned pos);
1873 __isl_give isl_id *isl_map_get_dim_id(
1874 __isl_keep isl_map *map, enum isl_dim_type type,
1876 __isl_give isl_id *isl_union_map_get_dim_id(
1877 __isl_keep isl_union_map *umap,
1878 enum isl_dim_type type, unsigned pos);
1880 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1881 enum isl_dim_type type, __isl_keep isl_id *id);
1882 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1883 enum isl_dim_type type, __isl_keep isl_id *id);
1884 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1885 enum isl_dim_type type, const char *name);
1886 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1887 enum isl_dim_type type, const char *name);
1889 const char *isl_constraint_get_dim_name(
1890 __isl_keep isl_constraint *constraint,
1891 enum isl_dim_type type, unsigned pos);
1892 const char *isl_basic_set_get_dim_name(
1893 __isl_keep isl_basic_set *bset,
1894 enum isl_dim_type type, unsigned pos);
1895 int isl_set_has_dim_name(__isl_keep isl_set *set,
1896 enum isl_dim_type type, unsigned pos);
1897 const char *isl_set_get_dim_name(
1898 __isl_keep isl_set *set,
1899 enum isl_dim_type type, unsigned pos);
1900 const char *isl_basic_map_get_dim_name(
1901 __isl_keep isl_basic_map *bmap,
1902 enum isl_dim_type type, unsigned pos);
1903 int isl_map_has_dim_name(__isl_keep isl_map *map,
1904 enum isl_dim_type type, unsigned pos);
1905 const char *isl_map_get_dim_name(
1906 __isl_keep isl_map *map,
1907 enum isl_dim_type type, unsigned pos);
1909 These functions are mostly useful to obtain the identifiers, positions
1910 or names of the parameters. Identifiers of individual dimensions are
1911 essentially only useful for printing. They are ignored by all other
1912 operations and may not be preserved across those operations.
1914 The user pointers on all parameters and tuples can be reset
1915 using the following functions.
1917 #include <isl/set.h>
1918 __isl_give isl_set *isl_set_reset_user(
1919 __isl_take isl_set *set);
1920 #include <isl/map.h>
1921 __isl_give isl_map *isl_map_reset_user(
1922 __isl_take isl_map *map);
1923 #include <isl/union_set.h>
1924 __isl_give isl_union_set *isl_union_set_reset_user(
1925 __isl_take isl_union_set *uset);
1926 #include <isl/union_map.h>
1927 __isl_give isl_union_map *isl_union_map_reset_user(
1928 __isl_take isl_union_map *umap);
1932 =head3 Unary Properties
1938 The following functions test whether the given set or relation
1939 contains any integer points. The ``plain'' variants do not perform
1940 any computations, but simply check if the given set or relation
1941 is already known to be empty.
1943 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1944 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1945 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1946 int isl_set_is_empty(__isl_keep isl_set *set);
1947 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1948 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1949 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1950 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1951 int isl_map_is_empty(__isl_keep isl_map *map);
1952 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1954 =item * Universality
1956 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1957 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1958 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1960 =item * Single-valuedness
1962 int isl_basic_map_is_single_valued(
1963 __isl_keep isl_basic_map *bmap);
1964 int isl_map_plain_is_single_valued(
1965 __isl_keep isl_map *map);
1966 int isl_map_is_single_valued(__isl_keep isl_map *map);
1967 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1971 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1972 int isl_map_is_injective(__isl_keep isl_map *map);
1973 int isl_union_map_plain_is_injective(
1974 __isl_keep isl_union_map *umap);
1975 int isl_union_map_is_injective(
1976 __isl_keep isl_union_map *umap);
1980 int isl_map_is_bijective(__isl_keep isl_map *map);
1981 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1985 __isl_give isl_val *
1986 isl_basic_map_plain_get_val_if_fixed(
1987 __isl_keep isl_basic_map *bmap,
1988 enum isl_dim_type type, unsigned pos);
1989 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
1990 __isl_keep isl_set *set,
1991 enum isl_dim_type type, unsigned pos);
1992 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
1993 __isl_keep isl_map *map,
1994 enum isl_dim_type type, unsigned pos);
1996 If the set or relation obviously lies on a hyperplane where the given dimension
1997 has a fixed value, then return that value.
1998 Otherwise return NaN.
2002 int isl_set_dim_residue_class_val(
2003 __isl_keep isl_set *set,
2004 int pos, __isl_give isl_val **modulo,
2005 __isl_give isl_val **residue);
2007 Check if the values of the given set dimension are equal to a fixed
2008 value modulo some integer value. If so, assign the modulo to C<*modulo>
2009 and the fixed value to C<*residue>. If the given dimension attains only
2010 a single value, then assign C<0> to C<*modulo> and the fixed value to
2012 If the dimension does not attain only a single value and if no modulo
2013 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
2017 To check whether a set is a parameter domain, use this function:
2019 int isl_set_is_params(__isl_keep isl_set *set);
2020 int isl_union_set_is_params(
2021 __isl_keep isl_union_set *uset);
2025 The following functions check whether the space of the given
2026 (basic) set or relation range is a wrapped relation.
2028 #include <isl/space.h>
2029 int isl_space_is_wrapping(
2030 __isl_keep isl_space *space);
2031 int isl_space_domain_is_wrapping(
2032 __isl_keep isl_space *space);
2033 int isl_space_range_is_wrapping(
2034 __isl_keep isl_space *space);
2036 #include <isl/set.h>
2037 int isl_basic_set_is_wrapping(
2038 __isl_keep isl_basic_set *bset);
2039 int isl_set_is_wrapping(__isl_keep isl_set *set);
2041 #include <isl/map.h>
2042 int isl_map_domain_is_wrapping(
2043 __isl_keep isl_map *map);
2044 int isl_map_range_is_wrapping(
2045 __isl_keep isl_map *map);
2047 The input to C<isl_space_is_wrapping> should
2048 be the space of a set, while that of
2049 C<isl_space_domain_is_wrapping> and
2050 C<isl_space_range_is_wrapping> should be the space of a relation.
2052 =item * Internal Product
2054 int isl_basic_map_can_zip(
2055 __isl_keep isl_basic_map *bmap);
2056 int isl_map_can_zip(__isl_keep isl_map *map);
2058 Check whether the product of domain and range of the given relation
2060 i.e., whether both domain and range are nested relations.
2064 int isl_basic_map_can_curry(
2065 __isl_keep isl_basic_map *bmap);
2066 int isl_map_can_curry(__isl_keep isl_map *map);
2068 Check whether the domain of the (basic) relation is a wrapped relation.
2070 int isl_basic_map_can_uncurry(
2071 __isl_keep isl_basic_map *bmap);
2072 int isl_map_can_uncurry(__isl_keep isl_map *map);
2074 Check whether the range of the (basic) relation is a wrapped relation.
2078 =head3 Binary Properties
2084 int isl_basic_set_plain_is_equal(
2085 __isl_keep isl_basic_set *bset1,
2086 __isl_keep isl_basic_set *bset2);
2087 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2088 __isl_keep isl_set *set2);
2089 int isl_set_is_equal(__isl_keep isl_set *set1,
2090 __isl_keep isl_set *set2);
2091 int isl_union_set_is_equal(
2092 __isl_keep isl_union_set *uset1,
2093 __isl_keep isl_union_set *uset2);
2094 int isl_basic_map_is_equal(
2095 __isl_keep isl_basic_map *bmap1,
2096 __isl_keep isl_basic_map *bmap2);
2097 int isl_map_is_equal(__isl_keep isl_map *map1,
2098 __isl_keep isl_map *map2);
2099 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2100 __isl_keep isl_map *map2);
2101 int isl_union_map_is_equal(
2102 __isl_keep isl_union_map *umap1,
2103 __isl_keep isl_union_map *umap2);
2105 =item * Disjointness
2107 int isl_basic_set_is_disjoint(
2108 __isl_keep isl_basic_set *bset1,
2109 __isl_keep isl_basic_set *bset2);
2110 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2111 __isl_keep isl_set *set2);
2112 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2113 __isl_keep isl_set *set2);
2114 int isl_basic_map_is_disjoint(
2115 __isl_keep isl_basic_map *bmap1,
2116 __isl_keep isl_basic_map *bmap2);
2117 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2118 __isl_keep isl_map *map2);
2122 int isl_basic_set_is_subset(
2123 __isl_keep isl_basic_set *bset1,
2124 __isl_keep isl_basic_set *bset2);
2125 int isl_set_is_subset(__isl_keep isl_set *set1,
2126 __isl_keep isl_set *set2);
2127 int isl_set_is_strict_subset(
2128 __isl_keep isl_set *set1,
2129 __isl_keep isl_set *set2);
2130 int isl_union_set_is_subset(
2131 __isl_keep isl_union_set *uset1,
2132 __isl_keep isl_union_set *uset2);
2133 int isl_union_set_is_strict_subset(
2134 __isl_keep isl_union_set *uset1,
2135 __isl_keep isl_union_set *uset2);
2136 int isl_basic_map_is_subset(
2137 __isl_keep isl_basic_map *bmap1,
2138 __isl_keep isl_basic_map *bmap2);
2139 int isl_basic_map_is_strict_subset(
2140 __isl_keep isl_basic_map *bmap1,
2141 __isl_keep isl_basic_map *bmap2);
2142 int isl_map_is_subset(
2143 __isl_keep isl_map *map1,
2144 __isl_keep isl_map *map2);
2145 int isl_map_is_strict_subset(
2146 __isl_keep isl_map *map1,
2147 __isl_keep isl_map *map2);
2148 int isl_union_map_is_subset(
2149 __isl_keep isl_union_map *umap1,
2150 __isl_keep isl_union_map *umap2);
2151 int isl_union_map_is_strict_subset(
2152 __isl_keep isl_union_map *umap1,
2153 __isl_keep isl_union_map *umap2);
2155 Check whether the first argument is a (strict) subset of the
2160 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2161 __isl_keep isl_set *set2);
2163 This function is useful for sorting C<isl_set>s.
2164 The order depends on the internal representation of the inputs.
2165 The order is fixed over different calls to the function (assuming
2166 the internal representation of the inputs has not changed), but may
2167 change over different versions of C<isl>.
2171 =head2 Unary Operations
2177 __isl_give isl_set *isl_set_complement(
2178 __isl_take isl_set *set);
2179 __isl_give isl_map *isl_map_complement(
2180 __isl_take isl_map *map);
2184 __isl_give isl_basic_map *isl_basic_map_reverse(
2185 __isl_take isl_basic_map *bmap);
2186 __isl_give isl_map *isl_map_reverse(
2187 __isl_take isl_map *map);
2188 __isl_give isl_union_map *isl_union_map_reverse(
2189 __isl_take isl_union_map *umap);
2193 #include <isl/local_space.h>
2194 __isl_give isl_local_space *isl_local_space_domain(
2195 __isl_take isl_local_space *ls);
2196 __isl_give isl_local_space *isl_local_space_range(
2197 __isl_take isl_local_space *ls);
2199 #include <isl/set.h>
2200 __isl_give isl_basic_set *isl_basic_set_project_out(
2201 __isl_take isl_basic_set *bset,
2202 enum isl_dim_type type, unsigned first, unsigned n);
2203 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2204 enum isl_dim_type type, unsigned first, unsigned n);
2205 __isl_give isl_basic_set *isl_basic_set_params(
2206 __isl_take isl_basic_set *bset);
2207 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2209 #include <isl/map.h>
2210 __isl_give isl_basic_map *isl_basic_map_project_out(
2211 __isl_take isl_basic_map *bmap,
2212 enum isl_dim_type type, unsigned first, unsigned n);
2213 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2214 enum isl_dim_type type, unsigned first, unsigned n);
2215 __isl_give isl_basic_set *isl_basic_map_domain(
2216 __isl_take isl_basic_map *bmap);
2217 __isl_give isl_basic_set *isl_basic_map_range(
2218 __isl_take isl_basic_map *bmap);
2219 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2220 __isl_give isl_set *isl_map_domain(
2221 __isl_take isl_map *bmap);
2222 __isl_give isl_set *isl_map_range(
2223 __isl_take isl_map *map);
2225 #include <isl/union_set.h>
2226 __isl_give isl_set *isl_union_set_params(
2227 __isl_take isl_union_set *uset);
2229 #include <isl/union_map.h>
2230 __isl_give isl_union_map *isl_union_map_project_out(
2231 __isl_take isl_union_map *umap,
2232 enum isl_dim_type type, unsigned first, unsigned n);
2233 __isl_give isl_set *isl_union_map_params(
2234 __isl_take isl_union_map *umap);
2235 __isl_give isl_union_set *isl_union_map_domain(
2236 __isl_take isl_union_map *umap);
2237 __isl_give isl_union_set *isl_union_map_range(
2238 __isl_take isl_union_map *umap);
2240 The function C<isl_union_map_project_out> can only project out
2243 #include <isl/map.h>
2244 __isl_give isl_basic_map *isl_basic_map_domain_map(
2245 __isl_take isl_basic_map *bmap);
2246 __isl_give isl_basic_map *isl_basic_map_range_map(
2247 __isl_take isl_basic_map *bmap);
2248 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2249 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2251 #include <isl/union_map.h>
2252 __isl_give isl_union_map *isl_union_map_domain_map(
2253 __isl_take isl_union_map *umap);
2254 __isl_give isl_union_map *isl_union_map_range_map(
2255 __isl_take isl_union_map *umap);
2257 The functions above construct a (basic, regular or union) relation
2258 that maps (a wrapped version of) the input relation to its domain or range.
2262 __isl_give isl_basic_set *isl_basic_set_eliminate(
2263 __isl_take isl_basic_set *bset,
2264 enum isl_dim_type type,
2265 unsigned first, unsigned n);
2266 __isl_give isl_set *isl_set_eliminate(
2267 __isl_take isl_set *set, enum isl_dim_type type,
2268 unsigned first, unsigned n);
2269 __isl_give isl_basic_map *isl_basic_map_eliminate(
2270 __isl_take isl_basic_map *bmap,
2271 enum isl_dim_type type,
2272 unsigned first, unsigned n);
2273 __isl_give isl_map *isl_map_eliminate(
2274 __isl_take isl_map *map, enum isl_dim_type type,
2275 unsigned first, unsigned n);
2277 Eliminate the coefficients for the given dimensions from the constraints,
2278 without removing the dimensions.
2280 =item * Constructing a relation from a set
2282 #include <isl/local_space.h>
2283 __isl_give isl_local_space *isl_local_space_from_domain(
2284 __isl_take isl_local_space *ls);
2286 #include <isl/map.h>
2287 __isl_give isl_map *isl_map_from_domain(
2288 __isl_take isl_set *set);
2289 __isl_give isl_map *isl_map_from_range(
2290 __isl_take isl_set *set);
2292 Create a relation with the given set as domain or range.
2293 The range or domain of the created relation is a zero-dimensional
2294 flat anonymous space.
2298 __isl_give isl_basic_set *isl_basic_set_fix_si(
2299 __isl_take isl_basic_set *bset,
2300 enum isl_dim_type type, unsigned pos, int value);
2301 __isl_give isl_basic_set *isl_basic_set_fix_val(
2302 __isl_take isl_basic_set *bset,
2303 enum isl_dim_type type, unsigned pos,
2304 __isl_take isl_val *v);
2305 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2306 enum isl_dim_type type, unsigned pos, int value);
2307 __isl_give isl_set *isl_set_fix_val(
2308 __isl_take isl_set *set,
2309 enum isl_dim_type type, unsigned pos,
2310 __isl_take isl_val *v);
2311 __isl_give isl_basic_map *isl_basic_map_fix_si(
2312 __isl_take isl_basic_map *bmap,
2313 enum isl_dim_type type, unsigned pos, int value);
2314 __isl_give isl_basic_map *isl_basic_map_fix_val(
2315 __isl_take isl_basic_map *bmap,
2316 enum isl_dim_type type, unsigned pos,
2317 __isl_take isl_val *v);
2318 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2319 enum isl_dim_type type, unsigned pos, int value);
2320 __isl_give isl_map *isl_map_fix_val(
2321 __isl_take isl_map *map,
2322 enum isl_dim_type type, unsigned pos,
2323 __isl_take isl_val *v);
2325 Intersect the set or relation with the hyperplane where the given
2326 dimension has the fixed given value.
2328 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2329 __isl_take isl_basic_map *bmap,
2330 enum isl_dim_type type, unsigned pos, int value);
2331 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2332 __isl_take isl_basic_map *bmap,
2333 enum isl_dim_type type, unsigned pos, int value);
2334 __isl_give isl_set *isl_set_lower_bound_si(
2335 __isl_take isl_set *set,
2336 enum isl_dim_type type, unsigned pos, int value);
2337 __isl_give isl_set *isl_set_lower_bound_val(
2338 __isl_take isl_set *set,
2339 enum isl_dim_type type, unsigned pos,
2340 __isl_take isl_val *value);
2341 __isl_give isl_map *isl_map_lower_bound_si(
2342 __isl_take isl_map *map,
2343 enum isl_dim_type type, unsigned pos, int value);
2344 __isl_give isl_set *isl_set_upper_bound_si(
2345 __isl_take isl_set *set,
2346 enum isl_dim_type type, unsigned pos, int value);
2347 __isl_give isl_set *isl_set_upper_bound_val(
2348 __isl_take isl_set *set,
2349 enum isl_dim_type type, unsigned pos,
2350 __isl_take isl_val *value);
2351 __isl_give isl_map *isl_map_upper_bound_si(
2352 __isl_take isl_map *map,
2353 enum isl_dim_type type, unsigned pos, int value);
2355 Intersect the set or relation with the half-space where the given
2356 dimension has a value bounded by the fixed given integer value.
2358 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2359 enum isl_dim_type type1, int pos1,
2360 enum isl_dim_type type2, int pos2);
2361 __isl_give isl_basic_map *isl_basic_map_equate(
2362 __isl_take isl_basic_map *bmap,
2363 enum isl_dim_type type1, int pos1,
2364 enum isl_dim_type type2, int pos2);
2365 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2366 enum isl_dim_type type1, int pos1,
2367 enum isl_dim_type type2, int pos2);
2369 Intersect the set or relation with the hyperplane where the given
2370 dimensions are equal to each other.
2372 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2373 enum isl_dim_type type1, int pos1,
2374 enum isl_dim_type type2, int pos2);
2376 Intersect the relation with the hyperplane where the given
2377 dimensions have opposite values.
2379 __isl_give isl_map *isl_map_order_le(
2380 __isl_take isl_map *map,
2381 enum isl_dim_type type1, int pos1,
2382 enum isl_dim_type type2, int pos2);
2383 __isl_give isl_basic_map *isl_basic_map_order_ge(
2384 __isl_take isl_basic_map *bmap,
2385 enum isl_dim_type type1, int pos1,
2386 enum isl_dim_type type2, int pos2);
2387 __isl_give isl_map *isl_map_order_ge(
2388 __isl_take isl_map *map,
2389 enum isl_dim_type type1, int pos1,
2390 enum isl_dim_type type2, int pos2);
2391 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2392 enum isl_dim_type type1, int pos1,
2393 enum isl_dim_type type2, int pos2);
2394 __isl_give isl_basic_map *isl_basic_map_order_gt(
2395 __isl_take isl_basic_map *bmap,
2396 enum isl_dim_type type1, int pos1,
2397 enum isl_dim_type type2, int pos2);
2398 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2399 enum isl_dim_type type1, int pos1,
2400 enum isl_dim_type type2, int pos2);
2402 Intersect the relation with the half-space where the given
2403 dimensions satisfy the given ordering.
2407 __isl_give isl_map *isl_set_identity(
2408 __isl_take isl_set *set);
2409 __isl_give isl_union_map *isl_union_set_identity(
2410 __isl_take isl_union_set *uset);
2412 Construct an identity relation on the given (union) set.
2416 __isl_give isl_basic_set *isl_basic_map_deltas(
2417 __isl_take isl_basic_map *bmap);
2418 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2419 __isl_give isl_union_set *isl_union_map_deltas(
2420 __isl_take isl_union_map *umap);
2422 These functions return a (basic) set containing the differences
2423 between image elements and corresponding domain elements in the input.
2425 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2426 __isl_take isl_basic_map *bmap);
2427 __isl_give isl_map *isl_map_deltas_map(
2428 __isl_take isl_map *map);
2429 __isl_give isl_union_map *isl_union_map_deltas_map(
2430 __isl_take isl_union_map *umap);
2432 The functions above construct a (basic, regular or union) relation
2433 that maps (a wrapped version of) the input relation to its delta set.
2437 Simplify the representation of a set or relation by trying
2438 to combine pairs of basic sets or relations into a single
2439 basic set or relation.
2441 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2442 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2443 __isl_give isl_union_set *isl_union_set_coalesce(
2444 __isl_take isl_union_set *uset);
2445 __isl_give isl_union_map *isl_union_map_coalesce(
2446 __isl_take isl_union_map *umap);
2448 One of the methods for combining pairs of basic sets or relations
2449 can result in coefficients that are much larger than those that appear
2450 in the constraints of the input. By default, the coefficients are
2451 not allowed to grow larger, but this can be changed by unsetting
2452 the following option.
2454 int isl_options_set_coalesce_bounded_wrapping(
2455 isl_ctx *ctx, int val);
2456 int isl_options_get_coalesce_bounded_wrapping(
2459 =item * Detecting equalities
2461 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2462 __isl_take isl_basic_set *bset);
2463 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2464 __isl_take isl_basic_map *bmap);
2465 __isl_give isl_set *isl_set_detect_equalities(
2466 __isl_take isl_set *set);
2467 __isl_give isl_map *isl_map_detect_equalities(
2468 __isl_take isl_map *map);
2469 __isl_give isl_union_set *isl_union_set_detect_equalities(
2470 __isl_take isl_union_set *uset);
2471 __isl_give isl_union_map *isl_union_map_detect_equalities(
2472 __isl_take isl_union_map *umap);
2474 Simplify the representation of a set or relation by detecting implicit
2477 =item * Removing redundant constraints
2479 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2480 __isl_take isl_basic_set *bset);
2481 __isl_give isl_set *isl_set_remove_redundancies(
2482 __isl_take isl_set *set);
2483 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2484 __isl_take isl_basic_map *bmap);
2485 __isl_give isl_map *isl_map_remove_redundancies(
2486 __isl_take isl_map *map);
2490 __isl_give isl_basic_set *isl_set_convex_hull(
2491 __isl_take isl_set *set);
2492 __isl_give isl_basic_map *isl_map_convex_hull(
2493 __isl_take isl_map *map);
2495 If the input set or relation has any existentially quantified
2496 variables, then the result of these operations is currently undefined.
2500 __isl_give isl_basic_set *
2501 isl_set_unshifted_simple_hull(
2502 __isl_take isl_set *set);
2503 __isl_give isl_basic_map *
2504 isl_map_unshifted_simple_hull(
2505 __isl_take isl_map *map);
2506 __isl_give isl_basic_set *isl_set_simple_hull(
2507 __isl_take isl_set *set);
2508 __isl_give isl_basic_map *isl_map_simple_hull(
2509 __isl_take isl_map *map);
2510 __isl_give isl_union_map *isl_union_map_simple_hull(
2511 __isl_take isl_union_map *umap);
2513 These functions compute a single basic set or relation
2514 that contains the whole input set or relation.
2515 In particular, the output is described by translates
2516 of the constraints describing the basic sets or relations in the input.
2517 In case of C<isl_set_unshifted_simple_hull>, only the original
2518 constraints are used, without any translation.
2522 (See \autoref{s:simple hull}.)
2528 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2529 __isl_take isl_basic_set *bset);
2530 __isl_give isl_basic_set *isl_set_affine_hull(
2531 __isl_take isl_set *set);
2532 __isl_give isl_union_set *isl_union_set_affine_hull(
2533 __isl_take isl_union_set *uset);
2534 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2535 __isl_take isl_basic_map *bmap);
2536 __isl_give isl_basic_map *isl_map_affine_hull(
2537 __isl_take isl_map *map);
2538 __isl_give isl_union_map *isl_union_map_affine_hull(
2539 __isl_take isl_union_map *umap);
2541 In case of union sets and relations, the affine hull is computed
2544 =item * Polyhedral hull
2546 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2547 __isl_take isl_set *set);
2548 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2549 __isl_take isl_map *map);
2550 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2551 __isl_take isl_union_set *uset);
2552 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2553 __isl_take isl_union_map *umap);
2555 These functions compute a single basic set or relation
2556 not involving any existentially quantified variables
2557 that contains the whole input set or relation.
2558 In case of union sets and relations, the polyhedral hull is computed
2561 =item * Other approximations
2563 __isl_give isl_basic_set *
2564 isl_basic_set_drop_constraints_involving_dims(
2565 __isl_take isl_basic_set *bset,
2566 enum isl_dim_type type,
2567 unsigned first, unsigned n);
2568 __isl_give isl_basic_map *
2569 isl_basic_map_drop_constraints_involving_dims(
2570 __isl_take isl_basic_map *bmap,
2571 enum isl_dim_type type,
2572 unsigned first, unsigned n);
2573 __isl_give isl_basic_set *
2574 isl_basic_set_drop_constraints_not_involving_dims(
2575 __isl_take isl_basic_set *bset,
2576 enum isl_dim_type type,
2577 unsigned first, unsigned n);
2578 __isl_give isl_set *
2579 isl_set_drop_constraints_involving_dims(
2580 __isl_take isl_set *set,
2581 enum isl_dim_type type,
2582 unsigned first, unsigned n);
2583 __isl_give isl_map *
2584 isl_map_drop_constraints_involving_dims(
2585 __isl_take isl_map *map,
2586 enum isl_dim_type type,
2587 unsigned first, unsigned n);
2589 These functions drop any constraints (not) involving the specified dimensions.
2590 Note that the result depends on the representation of the input.
2594 __isl_give isl_basic_set *isl_basic_set_sample(
2595 __isl_take isl_basic_set *bset);
2596 __isl_give isl_basic_set *isl_set_sample(
2597 __isl_take isl_set *set);
2598 __isl_give isl_basic_map *isl_basic_map_sample(
2599 __isl_take isl_basic_map *bmap);
2600 __isl_give isl_basic_map *isl_map_sample(
2601 __isl_take isl_map *map);
2603 If the input (basic) set or relation is non-empty, then return
2604 a singleton subset of the input. Otherwise, return an empty set.
2606 =item * Optimization
2608 #include <isl/ilp.h>
2609 __isl_give isl_val *isl_basic_set_max_val(
2610 __isl_keep isl_basic_set *bset,
2611 __isl_keep isl_aff *obj);
2612 __isl_give isl_val *isl_set_min_val(
2613 __isl_keep isl_set *set,
2614 __isl_keep isl_aff *obj);
2615 __isl_give isl_val *isl_set_max_val(
2616 __isl_keep isl_set *set,
2617 __isl_keep isl_aff *obj);
2619 Compute the minimum or maximum of the integer affine expression C<obj>
2620 over the points in C<set>, returning the result in C<opt>.
2621 The result is C<NULL> in case of an error, the optimal value in case
2622 there is one, negative infinity or infinity if the problem is unbounded and
2623 NaN if the problem is empty.
2625 =item * Parametric optimization
2627 __isl_give isl_pw_aff *isl_set_dim_min(
2628 __isl_take isl_set *set, int pos);
2629 __isl_give isl_pw_aff *isl_set_dim_max(
2630 __isl_take isl_set *set, int pos);
2631 __isl_give isl_pw_aff *isl_map_dim_max(
2632 __isl_take isl_map *map, int pos);
2634 Compute the minimum or maximum of the given set or output dimension
2635 as a function of the parameters (and input dimensions), but independently
2636 of the other set or output dimensions.
2637 For lexicographic optimization, see L<"Lexicographic Optimization">.
2641 The following functions compute either the set of (rational) coefficient
2642 values of valid constraints for the given set or the set of (rational)
2643 values satisfying the constraints with coefficients from the given set.
2644 Internally, these two sets of functions perform essentially the
2645 same operations, except that the set of coefficients is assumed to
2646 be a cone, while the set of values may be any polyhedron.
2647 The current implementation is based on the Farkas lemma and
2648 Fourier-Motzkin elimination, but this may change or be made optional
2649 in future. In particular, future implementations may use different
2650 dualization algorithms or skip the elimination step.
2652 __isl_give isl_basic_set *isl_basic_set_coefficients(
2653 __isl_take isl_basic_set *bset);
2654 __isl_give isl_basic_set *isl_set_coefficients(
2655 __isl_take isl_set *set);
2656 __isl_give isl_union_set *isl_union_set_coefficients(
2657 __isl_take isl_union_set *bset);
2658 __isl_give isl_basic_set *isl_basic_set_solutions(
2659 __isl_take isl_basic_set *bset);
2660 __isl_give isl_basic_set *isl_set_solutions(
2661 __isl_take isl_set *set);
2662 __isl_give isl_union_set *isl_union_set_solutions(
2663 __isl_take isl_union_set *bset);
2667 __isl_give isl_map *isl_map_fixed_power_val(
2668 __isl_take isl_map *map,
2669 __isl_take isl_val *exp);
2670 __isl_give isl_union_map *
2671 isl_union_map_fixed_power_val(
2672 __isl_take isl_union_map *umap,
2673 __isl_take isl_val *exp);
2675 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2676 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2677 of C<map> is computed.
2679 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2681 __isl_give isl_union_map *isl_union_map_power(
2682 __isl_take isl_union_map *umap, int *exact);
2684 Compute a parametric representation for all positive powers I<k> of C<map>.
2685 The result maps I<k> to a nested relation corresponding to the
2686 I<k>th power of C<map>.
2687 The result may be an overapproximation. If the result is known to be exact,
2688 then C<*exact> is set to C<1>.
2690 =item * Transitive closure
2692 __isl_give isl_map *isl_map_transitive_closure(
2693 __isl_take isl_map *map, int *exact);
2694 __isl_give isl_union_map *isl_union_map_transitive_closure(
2695 __isl_take isl_union_map *umap, int *exact);
2697 Compute the transitive closure of C<map>.
2698 The result may be an overapproximation. If the result is known to be exact,
2699 then C<*exact> is set to C<1>.
2701 =item * Reaching path lengths
2703 __isl_give isl_map *isl_map_reaching_path_lengths(
2704 __isl_take isl_map *map, int *exact);
2706 Compute a relation that maps each element in the range of C<map>
2707 to the lengths of all paths composed of edges in C<map> that
2708 end up in the given element.
2709 The result may be an overapproximation. If the result is known to be exact,
2710 then C<*exact> is set to C<1>.
2711 To compute the I<maximal> path length, the resulting relation
2712 should be postprocessed by C<isl_map_lexmax>.
2713 In particular, if the input relation is a dependence relation
2714 (mapping sources to sinks), then the maximal path length corresponds
2715 to the free schedule.
2716 Note, however, that C<isl_map_lexmax> expects the maximum to be
2717 finite, so if the path lengths are unbounded (possibly due to
2718 the overapproximation), then you will get an error message.
2722 #include <isl/space.h>
2723 __isl_give isl_space *isl_space_wrap(
2724 __isl_take isl_space *space);
2725 __isl_give isl_space *isl_space_unwrap(
2726 __isl_take isl_space *space);
2728 #include <isl/set.h>
2729 __isl_give isl_basic_map *isl_basic_set_unwrap(
2730 __isl_take isl_basic_set *bset);
2731 __isl_give isl_map *isl_set_unwrap(
2732 __isl_take isl_set *set);
2734 #include <isl/map.h>
2735 __isl_give isl_basic_set *isl_basic_map_wrap(
2736 __isl_take isl_basic_map *bmap);
2737 __isl_give isl_set *isl_map_wrap(
2738 __isl_take isl_map *map);
2740 #include <isl/union_set.h>
2741 __isl_give isl_union_map *isl_union_set_unwrap(
2742 __isl_take isl_union_set *uset);
2744 #include <isl/union_map.h>
2745 __isl_give isl_union_set *isl_union_map_wrap(
2746 __isl_take isl_union_map *umap);
2748 The input to C<isl_space_unwrap> should
2749 be the space of a set, while that of
2750 C<isl_space_wrap> should be the space of a relation.
2751 Conversely, the output of C<isl_space_unwrap> is the space
2752 of a relation, while that of C<isl_space_wrap> is the space of a set.
2756 Remove any internal structure of domain (and range) of the given
2757 set or relation. If there is any such internal structure in the input,
2758 then the name of the space is also removed.
2760 #include <isl/local_space.h>
2761 __isl_give isl_local_space *
2762 isl_local_space_flatten_domain(
2763 __isl_take isl_local_space *ls);
2764 __isl_give isl_local_space *
2765 isl_local_space_flatten_range(
2766 __isl_take isl_local_space *ls);
2768 #include <isl/set.h>
2769 __isl_give isl_basic_set *isl_basic_set_flatten(
2770 __isl_take isl_basic_set *bset);
2771 __isl_give isl_set *isl_set_flatten(
2772 __isl_take isl_set *set);
2774 #include <isl/map.h>
2775 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2776 __isl_take isl_basic_map *bmap);
2777 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2778 __isl_take isl_basic_map *bmap);
2779 __isl_give isl_map *isl_map_flatten_range(
2780 __isl_take isl_map *map);
2781 __isl_give isl_map *isl_map_flatten_domain(
2782 __isl_take isl_map *map);
2783 __isl_give isl_basic_map *isl_basic_map_flatten(
2784 __isl_take isl_basic_map *bmap);
2785 __isl_give isl_map *isl_map_flatten(
2786 __isl_take isl_map *map);
2788 #include <isl/map.h>
2789 __isl_give isl_map *isl_set_flatten_map(
2790 __isl_take isl_set *set);
2792 The function above constructs a relation
2793 that maps the input set to a flattened version of the set.
2797 Lift the input set to a space with extra dimensions corresponding
2798 to the existentially quantified variables in the input.
2799 In particular, the result lives in a wrapped map where the domain
2800 is the original space and the range corresponds to the original
2801 existentially quantified variables.
2803 __isl_give isl_basic_set *isl_basic_set_lift(
2804 __isl_take isl_basic_set *bset);
2805 __isl_give isl_set *isl_set_lift(
2806 __isl_take isl_set *set);
2807 __isl_give isl_union_set *isl_union_set_lift(
2808 __isl_take isl_union_set *uset);
2810 Given a local space that contains the existentially quantified
2811 variables of a set, a basic relation that, when applied to
2812 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2813 can be constructed using the following function.
2815 #include <isl/local_space.h>
2816 __isl_give isl_basic_map *isl_local_space_lifting(
2817 __isl_take isl_local_space *ls);
2819 =item * Internal Product
2821 __isl_give isl_basic_map *isl_basic_map_zip(
2822 __isl_take isl_basic_map *bmap);
2823 __isl_give isl_map *isl_map_zip(
2824 __isl_take isl_map *map);
2825 __isl_give isl_union_map *isl_union_map_zip(
2826 __isl_take isl_union_map *umap);
2828 Given a relation with nested relations for domain and range,
2829 interchange the range of the domain with the domain of the range.
2833 __isl_give isl_basic_map *isl_basic_map_curry(
2834 __isl_take isl_basic_map *bmap);
2835 __isl_give isl_basic_map *isl_basic_map_uncurry(
2836 __isl_take isl_basic_map *bmap);
2837 __isl_give isl_map *isl_map_curry(
2838 __isl_take isl_map *map);
2839 __isl_give isl_map *isl_map_uncurry(
2840 __isl_take isl_map *map);
2841 __isl_give isl_union_map *isl_union_map_curry(
2842 __isl_take isl_union_map *umap);
2843 __isl_give isl_union_map *isl_union_map_uncurry(
2844 __isl_take isl_union_map *umap);
2846 Given a relation with a nested relation for domain,
2847 the C<curry> functions
2848 move the range of the nested relation out of the domain
2849 and use it as the domain of a nested relation in the range,
2850 with the original range as range of this nested relation.
2851 The C<uncurry> functions perform the inverse operation.
2853 =item * Aligning parameters
2855 __isl_give isl_basic_set *isl_basic_set_align_params(
2856 __isl_take isl_basic_set *bset,
2857 __isl_take isl_space *model);
2858 __isl_give isl_set *isl_set_align_params(
2859 __isl_take isl_set *set,
2860 __isl_take isl_space *model);
2861 __isl_give isl_basic_map *isl_basic_map_align_params(
2862 __isl_take isl_basic_map *bmap,
2863 __isl_take isl_space *model);
2864 __isl_give isl_map *isl_map_align_params(
2865 __isl_take isl_map *map,
2866 __isl_take isl_space *model);
2868 Change the order of the parameters of the given set or relation
2869 such that the first parameters match those of C<model>.
2870 This may involve the introduction of extra parameters.
2871 All parameters need to be named.
2873 =item * Dimension manipulation
2875 #include <isl/local_space.h>
2876 __isl_give isl_local_space *isl_local_space_add_dims(
2877 __isl_take isl_local_space *ls,
2878 enum isl_dim_type type, unsigned n);
2879 __isl_give isl_local_space *isl_local_space_insert_dims(
2880 __isl_take isl_local_space *ls,
2881 enum isl_dim_type type, unsigned first, unsigned n);
2882 __isl_give isl_local_space *isl_local_space_drop_dims(
2883 __isl_take isl_local_space *ls,
2884 enum isl_dim_type type, unsigned first, unsigned n);
2886 #include <isl/set.h>
2887 __isl_give isl_basic_set *isl_basic_set_add_dims(
2888 __isl_take isl_basic_set *bset,
2889 enum isl_dim_type type, unsigned n);
2890 __isl_give isl_set *isl_set_add_dims(
2891 __isl_take isl_set *set,
2892 enum isl_dim_type type, unsigned n);
2893 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2894 __isl_take isl_basic_set *bset,
2895 enum isl_dim_type type, unsigned pos,
2897 __isl_give isl_set *isl_set_insert_dims(
2898 __isl_take isl_set *set,
2899 enum isl_dim_type type, unsigned pos, unsigned n);
2900 __isl_give isl_basic_set *isl_basic_set_move_dims(
2901 __isl_take isl_basic_set *bset,
2902 enum isl_dim_type dst_type, unsigned dst_pos,
2903 enum isl_dim_type src_type, unsigned src_pos,
2905 __isl_give isl_set *isl_set_move_dims(
2906 __isl_take isl_set *set,
2907 enum isl_dim_type dst_type, unsigned dst_pos,
2908 enum isl_dim_type src_type, unsigned src_pos,
2911 #include <isl/map.h>
2912 __isl_give isl_map *isl_map_add_dims(
2913 __isl_take isl_map *map,
2914 enum isl_dim_type type, unsigned n);
2915 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2916 __isl_take isl_basic_map *bmap,
2917 enum isl_dim_type type, unsigned pos,
2919 __isl_give isl_map *isl_map_insert_dims(
2920 __isl_take isl_map *map,
2921 enum isl_dim_type type, unsigned pos, unsigned n);
2922 __isl_give isl_basic_map *isl_basic_map_move_dims(
2923 __isl_take isl_basic_map *bmap,
2924 enum isl_dim_type dst_type, unsigned dst_pos,
2925 enum isl_dim_type src_type, unsigned src_pos,
2927 __isl_give isl_map *isl_map_move_dims(
2928 __isl_take isl_map *map,
2929 enum isl_dim_type dst_type, unsigned dst_pos,
2930 enum isl_dim_type src_type, unsigned src_pos,
2933 It is usually not advisable to directly change the (input or output)
2934 space of a set or a relation as this removes the name and the internal
2935 structure of the space. However, the above functions can be useful
2936 to add new parameters, assuming
2937 C<isl_set_align_params> and C<isl_map_align_params>
2942 =head2 Binary Operations
2944 The two arguments of a binary operation not only need to live
2945 in the same C<isl_ctx>, they currently also need to have
2946 the same (number of) parameters.
2948 =head3 Basic Operations
2952 =item * Intersection
2954 #include <isl/local_space.h>
2955 __isl_give isl_local_space *isl_local_space_intersect(
2956 __isl_take isl_local_space *ls1,
2957 __isl_take isl_local_space *ls2);
2959 #include <isl/set.h>
2960 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2961 __isl_take isl_basic_set *bset1,
2962 __isl_take isl_basic_set *bset2);
2963 __isl_give isl_basic_set *isl_basic_set_intersect(
2964 __isl_take isl_basic_set *bset1,
2965 __isl_take isl_basic_set *bset2);
2966 __isl_give isl_set *isl_set_intersect_params(
2967 __isl_take isl_set *set,
2968 __isl_take isl_set *params);
2969 __isl_give isl_set *isl_set_intersect(
2970 __isl_take isl_set *set1,
2971 __isl_take isl_set *set2);
2973 #include <isl/map.h>
2974 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2975 __isl_take isl_basic_map *bmap,
2976 __isl_take isl_basic_set *bset);
2977 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2978 __isl_take isl_basic_map *bmap,
2979 __isl_take isl_basic_set *bset);
2980 __isl_give isl_basic_map *isl_basic_map_intersect(
2981 __isl_take isl_basic_map *bmap1,
2982 __isl_take isl_basic_map *bmap2);
2983 __isl_give isl_map *isl_map_intersect_params(
2984 __isl_take isl_map *map,
2985 __isl_take isl_set *params);
2986 __isl_give isl_map *isl_map_intersect_domain(
2987 __isl_take isl_map *map,
2988 __isl_take isl_set *set);
2989 __isl_give isl_map *isl_map_intersect_range(
2990 __isl_take isl_map *map,
2991 __isl_take isl_set *set);
2992 __isl_give isl_map *isl_map_intersect(
2993 __isl_take isl_map *map1,
2994 __isl_take isl_map *map2);
2996 #include <isl/union_set.h>
2997 __isl_give isl_union_set *isl_union_set_intersect_params(
2998 __isl_take isl_union_set *uset,
2999 __isl_take isl_set *set);
3000 __isl_give isl_union_set *isl_union_set_intersect(
3001 __isl_take isl_union_set *uset1,
3002 __isl_take isl_union_set *uset2);
3004 #include <isl/union_map.h>
3005 __isl_give isl_union_map *isl_union_map_intersect_params(
3006 __isl_take isl_union_map *umap,
3007 __isl_take isl_set *set);
3008 __isl_give isl_union_map *isl_union_map_intersect_domain(
3009 __isl_take isl_union_map *umap,
3010 __isl_take isl_union_set *uset);
3011 __isl_give isl_union_map *isl_union_map_intersect_range(
3012 __isl_take isl_union_map *umap,
3013 __isl_take isl_union_set *uset);
3014 __isl_give isl_union_map *isl_union_map_intersect(
3015 __isl_take isl_union_map *umap1,
3016 __isl_take isl_union_map *umap2);
3018 The second argument to the C<_params> functions needs to be
3019 a parametric (basic) set. For the other functions, a parametric set
3020 for either argument is only allowed if the other argument is
3021 a parametric set as well.
3025 __isl_give isl_set *isl_basic_set_union(
3026 __isl_take isl_basic_set *bset1,
3027 __isl_take isl_basic_set *bset2);
3028 __isl_give isl_map *isl_basic_map_union(
3029 __isl_take isl_basic_map *bmap1,
3030 __isl_take isl_basic_map *bmap2);
3031 __isl_give isl_set *isl_set_union(
3032 __isl_take isl_set *set1,
3033 __isl_take isl_set *set2);
3034 __isl_give isl_map *isl_map_union(
3035 __isl_take isl_map *map1,
3036 __isl_take isl_map *map2);
3037 __isl_give isl_union_set *isl_union_set_union(
3038 __isl_take isl_union_set *uset1,
3039 __isl_take isl_union_set *uset2);
3040 __isl_give isl_union_map *isl_union_map_union(
3041 __isl_take isl_union_map *umap1,
3042 __isl_take isl_union_map *umap2);
3044 =item * Set difference
3046 __isl_give isl_set *isl_set_subtract(
3047 __isl_take isl_set *set1,
3048 __isl_take isl_set *set2);
3049 __isl_give isl_map *isl_map_subtract(
3050 __isl_take isl_map *map1,
3051 __isl_take isl_map *map2);
3052 __isl_give isl_map *isl_map_subtract_domain(
3053 __isl_take isl_map *map,
3054 __isl_take isl_set *dom);
3055 __isl_give isl_map *isl_map_subtract_range(
3056 __isl_take isl_map *map,
3057 __isl_take isl_set *dom);
3058 __isl_give isl_union_set *isl_union_set_subtract(
3059 __isl_take isl_union_set *uset1,
3060 __isl_take isl_union_set *uset2);
3061 __isl_give isl_union_map *isl_union_map_subtract(
3062 __isl_take isl_union_map *umap1,
3063 __isl_take isl_union_map *umap2);
3064 __isl_give isl_union_map *isl_union_map_subtract_domain(
3065 __isl_take isl_union_map *umap,
3066 __isl_take isl_union_set *dom);
3067 __isl_give isl_union_map *isl_union_map_subtract_range(
3068 __isl_take isl_union_map *umap,
3069 __isl_take isl_union_set *dom);
3073 __isl_give isl_basic_set *isl_basic_set_apply(
3074 __isl_take isl_basic_set *bset,
3075 __isl_take isl_basic_map *bmap);
3076 __isl_give isl_set *isl_set_apply(
3077 __isl_take isl_set *set,
3078 __isl_take isl_map *map);
3079 __isl_give isl_union_set *isl_union_set_apply(
3080 __isl_take isl_union_set *uset,
3081 __isl_take isl_union_map *umap);
3082 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3083 __isl_take isl_basic_map *bmap1,
3084 __isl_take isl_basic_map *bmap2);
3085 __isl_give isl_basic_map *isl_basic_map_apply_range(
3086 __isl_take isl_basic_map *bmap1,
3087 __isl_take isl_basic_map *bmap2);
3088 __isl_give isl_map *isl_map_apply_domain(
3089 __isl_take isl_map *map1,
3090 __isl_take isl_map *map2);
3091 __isl_give isl_union_map *isl_union_map_apply_domain(
3092 __isl_take isl_union_map *umap1,
3093 __isl_take isl_union_map *umap2);
3094 __isl_give isl_map *isl_map_apply_range(
3095 __isl_take isl_map *map1,
3096 __isl_take isl_map *map2);
3097 __isl_give isl_union_map *isl_union_map_apply_range(
3098 __isl_take isl_union_map *umap1,
3099 __isl_take isl_union_map *umap2);
3103 #include <isl/set.h>
3104 __isl_give isl_basic_set *
3105 isl_basic_set_preimage_multi_aff(
3106 __isl_take isl_basic_set *bset,
3107 __isl_take isl_multi_aff *ma);
3108 __isl_give isl_set *isl_set_preimage_multi_aff(
3109 __isl_take isl_set *set,
3110 __isl_take isl_multi_aff *ma);
3111 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3112 __isl_take isl_set *set,
3113 __isl_take isl_pw_multi_aff *pma);
3114 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
3115 __isl_take isl_set *set,
3116 __isl_take isl_multi_pw_aff *mpa);
3118 #include <isl/union_set.h>
3119 __isl_give isl_union_set *
3120 isl_union_set_preimage_multi_aff(
3121 __isl_take isl_union_set *uset,
3122 __isl_take isl_multi_aff *ma);
3123 __isl_give isl_union_set *
3124 isl_union_set_preimage_pw_multi_aff(
3125 __isl_take isl_union_set *uset,
3126 __isl_take isl_pw_multi_aff *pma);
3127 __isl_give isl_union_set *
3128 isl_union_set_preimage_union_pw_multi_aff(
3129 __isl_take isl_union_set *uset,
3130 __isl_take isl_union_pw_multi_aff *upma);
3132 #include <isl/map.h>
3133 __isl_give isl_basic_map *
3134 isl_basic_map_preimage_domain_multi_aff(
3135 __isl_take isl_basic_map *bmap,
3136 __isl_take isl_multi_aff *ma);
3137 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3138 __isl_take isl_map *map,
3139 __isl_take isl_multi_aff *ma);
3140 __isl_give isl_map *isl_map_preimage_range_multi_aff(
3141 __isl_take isl_map *map,
3142 __isl_take isl_multi_aff *ma);
3143 __isl_give isl_map *
3144 isl_map_preimage_domain_pw_multi_aff(
3145 __isl_take isl_map *map,
3146 __isl_take isl_pw_multi_aff *pma);
3147 __isl_give isl_map *
3148 isl_map_preimage_range_pw_multi_aff(
3149 __isl_take isl_map *map,
3150 __isl_take isl_pw_multi_aff *pma);
3151 __isl_give isl_map *
3152 isl_map_preimage_domain_multi_pw_aff(
3153 __isl_take isl_map *map,
3154 __isl_take isl_multi_pw_aff *mpa);
3155 __isl_give isl_basic_map *
3156 isl_basic_map_preimage_range_multi_aff(
3157 __isl_take isl_basic_map *bmap,
3158 __isl_take isl_multi_aff *ma);
3160 #include <isl/union_map.h>
3161 __isl_give isl_union_map *
3162 isl_union_map_preimage_domain_multi_aff(
3163 __isl_take isl_union_map *umap,
3164 __isl_take isl_multi_aff *ma);
3165 __isl_give isl_union_map *
3166 isl_union_map_preimage_range_multi_aff(
3167 __isl_take isl_union_map *umap,
3168 __isl_take isl_multi_aff *ma);
3169 __isl_give isl_union_map *
3170 isl_union_map_preimage_domain_pw_multi_aff(
3171 __isl_take isl_union_map *umap,
3172 __isl_take isl_pw_multi_aff *pma);
3173 __isl_give isl_union_map *
3174 isl_union_map_preimage_range_pw_multi_aff(
3175 __isl_take isl_union_map *umap,
3176 __isl_take isl_pw_multi_aff *pma);
3177 __isl_give isl_union_map *
3178 isl_union_map_preimage_domain_union_pw_multi_aff(
3179 __isl_take isl_union_map *umap,
3180 __isl_take isl_union_pw_multi_aff *upma);
3181 __isl_give isl_union_map *
3182 isl_union_map_preimage_range_union_pw_multi_aff(
3183 __isl_take isl_union_map *umap,
3184 __isl_take isl_union_pw_multi_aff *upma);
3186 These functions compute the preimage of the given set or map domain/range under
3187 the given function. In other words, the expression is plugged
3188 into the set description or into the domain/range of the map.
3189 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3190 L</"Piecewise Multiple Quasi Affine Expressions">.
3192 =item * Cartesian Product
3194 #include <isl/space.h>
3195 __isl_give isl_space *isl_space_product(
3196 __isl_take isl_space *space1,
3197 __isl_take isl_space *space2);
3198 __isl_give isl_space *isl_space_domain_product(
3199 __isl_take isl_space *space1,
3200 __isl_take isl_space *space2);
3201 __isl_give isl_space *isl_space_range_product(
3202 __isl_take isl_space *space1,
3203 __isl_take isl_space *space2);
3206 C<isl_space_product>, C<isl_space_domain_product>
3207 and C<isl_space_range_product> take pairs or relation spaces and
3208 produce a single relations space, where either the domain, the range
3209 or both domain and range are wrapped spaces of relations between
3210 the domains and/or ranges of the input spaces.
3211 If the product is only constructed over the domain or the range
3212 then the ranges or the domains of the inputs should be the same.
3213 The function C<isl_space_product> also accepts a pair of set spaces,
3214 in which case it returns a wrapped space of a relation between the
3217 #include <isl/set.h>
3218 __isl_give isl_set *isl_set_product(
3219 __isl_take isl_set *set1,
3220 __isl_take isl_set *set2);
3222 #include <isl/map.h>
3223 __isl_give isl_basic_map *isl_basic_map_domain_product(
3224 __isl_take isl_basic_map *bmap1,
3225 __isl_take isl_basic_map *bmap2);
3226 __isl_give isl_basic_map *isl_basic_map_range_product(
3227 __isl_take isl_basic_map *bmap1,
3228 __isl_take isl_basic_map *bmap2);
3229 __isl_give isl_basic_map *isl_basic_map_product(
3230 __isl_take isl_basic_map *bmap1,
3231 __isl_take isl_basic_map *bmap2);
3232 __isl_give isl_map *isl_map_domain_product(
3233 __isl_take isl_map *map1,
3234 __isl_take isl_map *map2);
3235 __isl_give isl_map *isl_map_range_product(
3236 __isl_take isl_map *map1,
3237 __isl_take isl_map *map2);
3238 __isl_give isl_map *isl_map_product(
3239 __isl_take isl_map *map1,
3240 __isl_take isl_map *map2);
3242 #include <isl/union_set.h>
3243 __isl_give isl_union_set *isl_union_set_product(
3244 __isl_take isl_union_set *uset1,
3245 __isl_take isl_union_set *uset2);
3247 #include <isl/union_map.h>
3248 __isl_give isl_union_map *isl_union_map_domain_product(
3249 __isl_take isl_union_map *umap1,
3250 __isl_take isl_union_map *umap2);
3251 __isl_give isl_union_map *isl_union_map_range_product(
3252 __isl_take isl_union_map *umap1,
3253 __isl_take isl_union_map *umap2);
3254 __isl_give isl_union_map *isl_union_map_product(
3255 __isl_take isl_union_map *umap1,
3256 __isl_take isl_union_map *umap2);
3258 The above functions compute the cross product of the given
3259 sets or relations. The domains and ranges of the results
3260 are wrapped maps between domains and ranges of the inputs.
3261 To obtain a ``flat'' product, use the following functions
3264 __isl_give isl_basic_set *isl_basic_set_flat_product(
3265 __isl_take isl_basic_set *bset1,
3266 __isl_take isl_basic_set *bset2);
3267 __isl_give isl_set *isl_set_flat_product(
3268 __isl_take isl_set *set1,
3269 __isl_take isl_set *set2);
3270 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3271 __isl_take isl_basic_map *bmap1,
3272 __isl_take isl_basic_map *bmap2);
3273 __isl_give isl_map *isl_map_flat_domain_product(
3274 __isl_take isl_map *map1,
3275 __isl_take isl_map *map2);
3276 __isl_give isl_map *isl_map_flat_range_product(
3277 __isl_take isl_map *map1,
3278 __isl_take isl_map *map2);
3279 __isl_give isl_union_map *isl_union_map_flat_range_product(
3280 __isl_take isl_union_map *umap1,
3281 __isl_take isl_union_map *umap2);
3282 __isl_give isl_basic_map *isl_basic_map_flat_product(
3283 __isl_take isl_basic_map *bmap1,
3284 __isl_take isl_basic_map *bmap2);
3285 __isl_give isl_map *isl_map_flat_product(
3286 __isl_take isl_map *map1,
3287 __isl_take isl_map *map2);
3289 #include <isl/space.h>
3290 __isl_give isl_space *isl_space_domain_factor_domain(
3291 __isl_take isl_space *space);
3292 __isl_give isl_space *isl_space_range_factor_domain(
3293 __isl_take isl_space *space);
3294 __isl_give isl_space *isl_space_range_factor_range(
3295 __isl_take isl_space *space);
3297 The functions C<isl_space_range_factor_domain> and
3298 C<isl_space_range_factor_range> extract the two arguments from
3299 the result of a call to C<isl_space_range_product>.
3301 The arguments of a call to C<isl_map_range_product> can be extracted
3302 from the result using the following two functions.
3304 #include <isl/map.h>
3305 __isl_give isl_map *isl_map_range_factor_domain(
3306 __isl_take isl_map *map);
3307 __isl_give isl_map *isl_map_range_factor_range(
3308 __isl_take isl_map *map);
3310 =item * Simplification
3312 __isl_give isl_basic_set *isl_basic_set_gist(
3313 __isl_take isl_basic_set *bset,
3314 __isl_take isl_basic_set *context);
3315 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3316 __isl_take isl_set *context);
3317 __isl_give isl_set *isl_set_gist_params(
3318 __isl_take isl_set *set,
3319 __isl_take isl_set *context);
3320 __isl_give isl_union_set *isl_union_set_gist(
3321 __isl_take isl_union_set *uset,
3322 __isl_take isl_union_set *context);
3323 __isl_give isl_union_set *isl_union_set_gist_params(
3324 __isl_take isl_union_set *uset,
3325 __isl_take isl_set *set);
3326 __isl_give isl_basic_map *isl_basic_map_gist(
3327 __isl_take isl_basic_map *bmap,
3328 __isl_take isl_basic_map *context);
3329 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3330 __isl_take isl_map *context);
3331 __isl_give isl_map *isl_map_gist_params(
3332 __isl_take isl_map *map,
3333 __isl_take isl_set *context);
3334 __isl_give isl_map *isl_map_gist_domain(
3335 __isl_take isl_map *map,
3336 __isl_take isl_set *context);
3337 __isl_give isl_map *isl_map_gist_range(
3338 __isl_take isl_map *map,
3339 __isl_take isl_set *context);
3340 __isl_give isl_union_map *isl_union_map_gist(
3341 __isl_take isl_union_map *umap,
3342 __isl_take isl_union_map *context);
3343 __isl_give isl_union_map *isl_union_map_gist_params(
3344 __isl_take isl_union_map *umap,
3345 __isl_take isl_set *set);
3346 __isl_give isl_union_map *isl_union_map_gist_domain(
3347 __isl_take isl_union_map *umap,
3348 __isl_take isl_union_set *uset);
3349 __isl_give isl_union_map *isl_union_map_gist_range(
3350 __isl_take isl_union_map *umap,
3351 __isl_take isl_union_set *uset);
3353 The gist operation returns a set or relation that has the
3354 same intersection with the context as the input set or relation.
3355 Any implicit equality in the intersection is made explicit in the result,
3356 while all inequalities that are redundant with respect to the intersection
3358 In case of union sets and relations, the gist operation is performed
3363 =head3 Lexicographic Optimization
3365 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3366 the following functions
3367 compute a set that contains the lexicographic minimum or maximum
3368 of the elements in C<set> (or C<bset>) for those values of the parameters
3369 that satisfy C<dom>.
3370 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3371 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3373 In other words, the union of the parameter values
3374 for which the result is non-empty and of C<*empty>
3377 __isl_give isl_set *isl_basic_set_partial_lexmin(
3378 __isl_take isl_basic_set *bset,
3379 __isl_take isl_basic_set *dom,
3380 __isl_give isl_set **empty);
3381 __isl_give isl_set *isl_basic_set_partial_lexmax(
3382 __isl_take isl_basic_set *bset,
3383 __isl_take isl_basic_set *dom,
3384 __isl_give isl_set **empty);
3385 __isl_give isl_set *isl_set_partial_lexmin(
3386 __isl_take isl_set *set, __isl_take isl_set *dom,
3387 __isl_give isl_set **empty);
3388 __isl_give isl_set *isl_set_partial_lexmax(
3389 __isl_take isl_set *set, __isl_take isl_set *dom,
3390 __isl_give isl_set **empty);
3392 Given a (basic) set C<set> (or C<bset>), the following functions simply
3393 return a set containing the lexicographic minimum or maximum
3394 of the elements in C<set> (or C<bset>).
3395 In case of union sets, the optimum is computed per space.
3397 __isl_give isl_set *isl_basic_set_lexmin(
3398 __isl_take isl_basic_set *bset);
3399 __isl_give isl_set *isl_basic_set_lexmax(
3400 __isl_take isl_basic_set *bset);
3401 __isl_give isl_set *isl_set_lexmin(
3402 __isl_take isl_set *set);
3403 __isl_give isl_set *isl_set_lexmax(
3404 __isl_take isl_set *set);
3405 __isl_give isl_union_set *isl_union_set_lexmin(
3406 __isl_take isl_union_set *uset);
3407 __isl_give isl_union_set *isl_union_set_lexmax(
3408 __isl_take isl_union_set *uset);
3410 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3411 the following functions
3412 compute a relation that maps each element of C<dom>
3413 to the single lexicographic minimum or maximum
3414 of the elements that are associated to that same
3415 element in C<map> (or C<bmap>).
3416 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3417 that contains the elements in C<dom> that do not map
3418 to any elements in C<map> (or C<bmap>).
3419 In other words, the union of the domain of the result and of C<*empty>
3422 __isl_give isl_map *isl_basic_map_partial_lexmax(
3423 __isl_take isl_basic_map *bmap,
3424 __isl_take isl_basic_set *dom,
3425 __isl_give isl_set **empty);
3426 __isl_give isl_map *isl_basic_map_partial_lexmin(
3427 __isl_take isl_basic_map *bmap,
3428 __isl_take isl_basic_set *dom,
3429 __isl_give isl_set **empty);
3430 __isl_give isl_map *isl_map_partial_lexmax(
3431 __isl_take isl_map *map, __isl_take isl_set *dom,
3432 __isl_give isl_set **empty);
3433 __isl_give isl_map *isl_map_partial_lexmin(
3434 __isl_take isl_map *map, __isl_take isl_set *dom,
3435 __isl_give isl_set **empty);
3437 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3438 return a map mapping each element in the domain of
3439 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3440 of all elements associated to that element.
3441 In case of union relations, the optimum is computed per space.
3443 __isl_give isl_map *isl_basic_map_lexmin(
3444 __isl_take isl_basic_map *bmap);
3445 __isl_give isl_map *isl_basic_map_lexmax(
3446 __isl_take isl_basic_map *bmap);
3447 __isl_give isl_map *isl_map_lexmin(
3448 __isl_take isl_map *map);
3449 __isl_give isl_map *isl_map_lexmax(
3450 __isl_take isl_map *map);
3451 __isl_give isl_union_map *isl_union_map_lexmin(
3452 __isl_take isl_union_map *umap);
3453 __isl_give isl_union_map *isl_union_map_lexmax(
3454 __isl_take isl_union_map *umap);
3456 The following functions return their result in the form of
3457 a piecewise multi-affine expression
3458 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3459 but are otherwise equivalent to the corresponding functions
3460 returning a basic set or relation.
3462 __isl_give isl_pw_multi_aff *
3463 isl_basic_map_lexmin_pw_multi_aff(
3464 __isl_take isl_basic_map *bmap);
3465 __isl_give isl_pw_multi_aff *
3466 isl_basic_set_partial_lexmin_pw_multi_aff(
3467 __isl_take isl_basic_set *bset,
3468 __isl_take isl_basic_set *dom,
3469 __isl_give isl_set **empty);
3470 __isl_give isl_pw_multi_aff *
3471 isl_basic_set_partial_lexmax_pw_multi_aff(
3472 __isl_take isl_basic_set *bset,
3473 __isl_take isl_basic_set *dom,
3474 __isl_give isl_set **empty);
3475 __isl_give isl_pw_multi_aff *
3476 isl_basic_map_partial_lexmin_pw_multi_aff(
3477 __isl_take isl_basic_map *bmap,
3478 __isl_take isl_basic_set *dom,
3479 __isl_give isl_set **empty);
3480 __isl_give isl_pw_multi_aff *
3481 isl_basic_map_partial_lexmax_pw_multi_aff(
3482 __isl_take isl_basic_map *bmap,
3483 __isl_take isl_basic_set *dom,
3484 __isl_give isl_set **empty);
3485 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3486 __isl_take isl_set *set);
3487 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3488 __isl_take isl_set *set);
3489 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3490 __isl_take isl_map *map);
3491 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3492 __isl_take isl_map *map);
3496 Lists are defined over several element types, including
3497 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3498 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3499 Here we take lists of C<isl_set>s as an example.
3500 Lists can be created, copied, modified and freed using the following functions.
3502 #include <isl/list.h>
3503 __isl_give isl_set_list *isl_set_list_from_set(
3504 __isl_take isl_set *el);
3505 __isl_give isl_set_list *isl_set_list_alloc(
3506 isl_ctx *ctx, int n);
3507 __isl_give isl_set_list *isl_set_list_copy(
3508 __isl_keep isl_set_list *list);
3509 __isl_give isl_set_list *isl_set_list_insert(
3510 __isl_take isl_set_list *list, unsigned pos,
3511 __isl_take isl_set *el);
3512 __isl_give isl_set_list *isl_set_list_add(
3513 __isl_take isl_set_list *list,
3514 __isl_take isl_set *el);
3515 __isl_give isl_set_list *isl_set_list_drop(
3516 __isl_take isl_set_list *list,
3517 unsigned first, unsigned n);
3518 __isl_give isl_set_list *isl_set_list_set_set(
3519 __isl_take isl_set_list *list, int index,
3520 __isl_take isl_set *set);
3521 __isl_give isl_set_list *isl_set_list_concat(
3522 __isl_take isl_set_list *list1,
3523 __isl_take isl_set_list *list2);
3524 __isl_give isl_set_list *isl_set_list_sort(
3525 __isl_take isl_set_list *list,
3526 int (*cmp)(__isl_keep isl_set *a,
3527 __isl_keep isl_set *b, void *user),
3529 __isl_null isl_set_list *isl_set_list_free(
3530 __isl_take isl_set_list *list);
3532 C<isl_set_list_alloc> creates an empty list with a capacity for
3533 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3536 Lists can be inspected using the following functions.
3538 #include <isl/list.h>
3539 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3540 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3541 __isl_give isl_set *isl_set_list_get_set(
3542 __isl_keep isl_set_list *list, int index);
3543 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3544 int (*fn)(__isl_take isl_set *el, void *user),
3546 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3547 int (*follows)(__isl_keep isl_set *a,
3548 __isl_keep isl_set *b, void *user),
3550 int (*fn)(__isl_take isl_set *el, void *user),
3553 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3554 strongly connected components of the graph with as vertices the elements
3555 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3556 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3557 should return C<-1> on error.
3559 Lists can be printed using
3561 #include <isl/list.h>
3562 __isl_give isl_printer *isl_printer_print_set_list(
3563 __isl_take isl_printer *p,
3564 __isl_keep isl_set_list *list);
3566 =head2 Associative arrays
3568 Associative arrays map isl objects of a specific type to isl objects
3569 of some (other) specific type. They are defined for several pairs
3570 of types, including (C<isl_map>, C<isl_basic_set>),
3571 (C<isl_id>, C<isl_ast_expr>) and.
3572 (C<isl_id>, C<isl_pw_aff>).
3573 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3576 Associative arrays can be created, copied and freed using
3577 the following functions.
3579 #include <isl/id_to_ast_expr.h>
3580 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3581 isl_ctx *ctx, int min_size);
3582 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3583 __isl_keep id_to_ast_expr *id2expr);
3584 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
3585 __isl_take id_to_ast_expr *id2expr);
3587 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3588 to specify the expected size of the associative array.
3589 The associative array will be grown automatically as needed.
3591 Associative arrays can be inspected using the following functions.
3593 #include <isl/id_to_ast_expr.h>
3594 isl_ctx *isl_id_to_ast_expr_get_ctx(
3595 __isl_keep id_to_ast_expr *id2expr);
3596 int isl_id_to_ast_expr_has(
3597 __isl_keep id_to_ast_expr *id2expr,
3598 __isl_keep isl_id *key);
3599 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3600 __isl_keep id_to_ast_expr *id2expr,
3601 __isl_take isl_id *key);
3602 int isl_id_to_ast_expr_foreach(
3603 __isl_keep id_to_ast_expr *id2expr,
3604 int (*fn)(__isl_take isl_id *key,
3605 __isl_take isl_ast_expr *val, void *user),
3608 They can be modified using the following function.
3610 #include <isl/id_to_ast_expr.h>
3611 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3612 __isl_take id_to_ast_expr *id2expr,
3613 __isl_take isl_id *key,
3614 __isl_take isl_ast_expr *val);
3615 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
3616 __isl_take id_to_ast_expr *id2expr,
3617 __isl_take isl_id *key);
3619 Associative arrays can be printed using the following function.
3621 #include <isl/id_to_ast_expr.h>
3622 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3623 __isl_take isl_printer *p,
3624 __isl_keep id_to_ast_expr *id2expr);
3626 =head2 Multiple Values
3628 An C<isl_multi_val> object represents a sequence of zero or more values,
3629 living in a set space.
3631 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3632 using the following function
3634 #include <isl/val.h>
3635 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3636 __isl_take isl_space *space,
3637 __isl_take isl_val_list *list);
3639 The zero multiple value (with value zero for each set dimension)
3640 can be created using the following function.
3642 #include <isl/val.h>
3643 __isl_give isl_multi_val *isl_multi_val_zero(
3644 __isl_take isl_space *space);
3646 Multiple values can be copied and freed using
3648 #include <isl/val.h>
3649 __isl_give isl_multi_val *isl_multi_val_copy(
3650 __isl_keep isl_multi_val *mv);
3651 __isl_null isl_multi_val *isl_multi_val_free(
3652 __isl_take isl_multi_val *mv);
3654 They can be inspected using
3656 #include <isl/val.h>
3657 isl_ctx *isl_multi_val_get_ctx(
3658 __isl_keep isl_multi_val *mv);
3659 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3660 enum isl_dim_type type);
3661 __isl_give isl_val *isl_multi_val_get_val(
3662 __isl_keep isl_multi_val *mv, int pos);
3663 int isl_multi_val_find_dim_by_id(
3664 __isl_keep isl_multi_val *mv,
3665 enum isl_dim_type type, __isl_keep isl_id *id);
3666 __isl_give isl_id *isl_multi_val_get_dim_id(
3667 __isl_keep isl_multi_val *mv,
3668 enum isl_dim_type type, unsigned pos);
3669 const char *isl_multi_val_get_tuple_name(
3670 __isl_keep isl_multi_val *mv,
3671 enum isl_dim_type type);
3672 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3673 enum isl_dim_type type);
3674 __isl_give isl_id *isl_multi_val_get_tuple_id(
3675 __isl_keep isl_multi_val *mv,
3676 enum isl_dim_type type);
3677 int isl_multi_val_range_is_wrapping(
3678 __isl_keep isl_multi_val *mv);
3680 They can be modified using
3682 #include <isl/val.h>
3683 __isl_give isl_multi_val *isl_multi_val_set_val(
3684 __isl_take isl_multi_val *mv, int pos,
3685 __isl_take isl_val *val);
3686 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3687 __isl_take isl_multi_val *mv,
3688 enum isl_dim_type type, unsigned pos, const char *s);
3689 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3690 __isl_take isl_multi_val *mv,
3691 enum isl_dim_type type, unsigned pos,
3692 __isl_take isl_id *id);
3693 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3694 __isl_take isl_multi_val *mv,
3695 enum isl_dim_type type, const char *s);
3696 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3697 __isl_take isl_multi_val *mv,
3698 enum isl_dim_type type, __isl_take isl_id *id);
3699 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3700 __isl_take isl_multi_val *mv,
3701 enum isl_dim_type type);
3702 __isl_give isl_multi_val *isl_multi_val_reset_user(
3703 __isl_take isl_multi_val *mv);
3705 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3706 __isl_take isl_multi_val *mv,
3707 enum isl_dim_type type, unsigned first, unsigned n);
3708 __isl_give isl_multi_val *isl_multi_val_add_dims(
3709 __isl_take isl_multi_val *mv,
3710 enum isl_dim_type type, unsigned n);
3711 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3712 __isl_take isl_multi_val *mv,
3713 enum isl_dim_type type, unsigned first, unsigned n);
3717 #include <isl/val.h>
3718 __isl_give isl_multi_val *isl_multi_val_align_params(
3719 __isl_take isl_multi_val *mv,
3720 __isl_take isl_space *model);
3721 __isl_give isl_multi_val *isl_multi_val_from_range(
3722 __isl_take isl_multi_val *mv);
3723 __isl_give isl_multi_val *isl_multi_val_range_splice(
3724 __isl_take isl_multi_val *mv1, unsigned pos,
3725 __isl_take isl_multi_val *mv2);
3726 __isl_give isl_multi_val *isl_multi_val_range_product(
3727 __isl_take isl_multi_val *mv1,
3728 __isl_take isl_multi_val *mv2);
3729 __isl_give isl_multi_val *
3730 isl_multi_val_range_factor_domain(
3731 __isl_take isl_multi_val *mv);
3732 __isl_give isl_multi_val *
3733 isl_multi_val_range_factor_range(
3734 __isl_take isl_multi_val *mv);
3735 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3736 __isl_take isl_multi_val *mv1,
3737 __isl_take isl_multi_aff *mv2);
3738 __isl_give isl_multi_val *isl_multi_val_product(
3739 __isl_take isl_multi_val *mv1,
3740 __isl_take isl_multi_val *mv2);
3741 __isl_give isl_multi_val *isl_multi_val_add_val(
3742 __isl_take isl_multi_val *mv,
3743 __isl_take isl_val *v);
3744 __isl_give isl_multi_val *isl_multi_val_mod_val(
3745 __isl_take isl_multi_val *mv,
3746 __isl_take isl_val *v);
3747 __isl_give isl_multi_val *isl_multi_val_scale_val(
3748 __isl_take isl_multi_val *mv,
3749 __isl_take isl_val *v);
3750 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3751 __isl_take isl_multi_val *mv1,
3752 __isl_take isl_multi_val *mv2);
3753 __isl_give isl_multi_val *
3754 isl_multi_val_scale_down_multi_val(
3755 __isl_take isl_multi_val *mv1,
3756 __isl_take isl_multi_val *mv2);
3758 A multiple value can be printed using
3760 __isl_give isl_printer *isl_printer_print_multi_val(
3761 __isl_take isl_printer *p,
3762 __isl_keep isl_multi_val *mv);
3766 Vectors can be created, copied and freed using the following functions.
3768 #include <isl/vec.h>
3769 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3771 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3772 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
3774 Note that the elements of a newly created vector may have arbitrary values.
3775 The elements can be changed and inspected using the following functions.
3777 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3778 int isl_vec_size(__isl_keep isl_vec *vec);
3779 __isl_give isl_val *isl_vec_get_element_val(
3780 __isl_keep isl_vec *vec, int pos);
3781 __isl_give isl_vec *isl_vec_set_element_si(
3782 __isl_take isl_vec *vec, int pos, int v);
3783 __isl_give isl_vec *isl_vec_set_element_val(
3784 __isl_take isl_vec *vec, int pos,
3785 __isl_take isl_val *v);
3786 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3788 __isl_give isl_vec *isl_vec_set_val(
3789 __isl_take isl_vec *vec, __isl_take isl_val *v);
3790 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3791 __isl_keep isl_vec *vec2, int pos);
3793 C<isl_vec_get_element> will return a negative value if anything went wrong.
3794 In that case, the value of C<*v> is undefined.
3796 The following function can be used to concatenate two vectors.
3798 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3799 __isl_take isl_vec *vec2);
3803 Matrices can be created, copied and freed using the following functions.
3805 #include <isl/mat.h>
3806 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3807 unsigned n_row, unsigned n_col);
3808 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3809 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
3811 Note that the elements of a newly created matrix may have arbitrary values.
3812 The elements can be changed and inspected using the following functions.
3814 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3815 int isl_mat_rows(__isl_keep isl_mat *mat);
3816 int isl_mat_cols(__isl_keep isl_mat *mat);
3817 __isl_give isl_val *isl_mat_get_element_val(
3818 __isl_keep isl_mat *mat, int row, int col);
3819 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3820 int row, int col, int v);
3821 __isl_give isl_mat *isl_mat_set_element_val(
3822 __isl_take isl_mat *mat, int row, int col,
3823 __isl_take isl_val *v);
3825 C<isl_mat_get_element> will return a negative value if anything went wrong.
3826 In that case, the value of C<*v> is undefined.
3828 The following function can be used to compute the (right) inverse
3829 of a matrix, i.e., a matrix such that the product of the original
3830 and the inverse (in that order) is a multiple of the identity matrix.
3831 The input matrix is assumed to be of full row-rank.
3833 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3835 The following function can be used to compute the (right) kernel
3836 (or null space) of a matrix, i.e., a matrix such that the product of
3837 the original and the kernel (in that order) is the zero matrix.
3839 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3841 =head2 Piecewise Quasi Affine Expressions
3843 The zero quasi affine expression or the quasi affine expression
3844 that is equal to a given value or
3845 a specified dimension on a given domain can be created using
3847 __isl_give isl_aff *isl_aff_zero_on_domain(
3848 __isl_take isl_local_space *ls);
3849 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3850 __isl_take isl_local_space *ls);
3851 __isl_give isl_aff *isl_aff_val_on_domain(
3852 __isl_take isl_local_space *ls,
3853 __isl_take isl_val *val);
3854 __isl_give isl_aff *isl_aff_var_on_domain(
3855 __isl_take isl_local_space *ls,
3856 enum isl_dim_type type, unsigned pos);
3857 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3858 __isl_take isl_local_space *ls,
3859 enum isl_dim_type type, unsigned pos);
3860 __isl_give isl_aff *isl_aff_nan_on_domain(
3861 __isl_take isl_local_space *ls);
3862 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3863 __isl_take isl_local_space *ls);
3865 Note that the space in which the resulting objects live is a map space
3866 with the given space as domain and a one-dimensional range.
3868 An empty piecewise quasi affine expression (one with no cells)
3869 or a piecewise quasi affine expression with a single cell can
3870 be created using the following functions.
3872 #include <isl/aff.h>
3873 __isl_give isl_pw_aff *isl_pw_aff_empty(
3874 __isl_take isl_space *space);
3875 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3876 __isl_take isl_set *set, __isl_take isl_aff *aff);
3877 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3878 __isl_take isl_aff *aff);
3880 A piecewise quasi affine expression that is equal to 1 on a set
3881 and 0 outside the set can be created using the following function.
3883 #include <isl/aff.h>
3884 __isl_give isl_pw_aff *isl_set_indicator_function(
3885 __isl_take isl_set *set);
3887 Quasi affine expressions can be copied and freed using
3889 #include <isl/aff.h>
3890 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3891 __isl_null isl_aff *isl_aff_free(__isl_take isl_aff *aff);
3893 __isl_give isl_pw_aff *isl_pw_aff_copy(
3894 __isl_keep isl_pw_aff *pwaff);
3895 __isl_null isl_pw_aff *isl_pw_aff_free(
3896 __isl_take isl_pw_aff *pwaff);
3898 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3899 using the following function. The constraint is required to have
3900 a non-zero coefficient for the specified dimension.
3902 #include <isl/constraint.h>
3903 __isl_give isl_aff *isl_constraint_get_bound(
3904 __isl_keep isl_constraint *constraint,
3905 enum isl_dim_type type, int pos);
3907 The entire affine expression of the constraint can also be extracted
3908 using the following function.
3910 #include <isl/constraint.h>
3911 __isl_give isl_aff *isl_constraint_get_aff(
3912 __isl_keep isl_constraint *constraint);
3914 Conversely, an equality constraint equating
3915 the affine expression to zero or an inequality constraint enforcing
3916 the affine expression to be non-negative, can be constructed using
3918 __isl_give isl_constraint *isl_equality_from_aff(
3919 __isl_take isl_aff *aff);
3920 __isl_give isl_constraint *isl_inequality_from_aff(
3921 __isl_take isl_aff *aff);
3923 The expression can be inspected using
3925 #include <isl/aff.h>
3926 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3927 int isl_aff_dim(__isl_keep isl_aff *aff,
3928 enum isl_dim_type type);
3929 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3930 __isl_keep isl_aff *aff);
3931 __isl_give isl_local_space *isl_aff_get_local_space(
3932 __isl_keep isl_aff *aff);
3933 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3934 enum isl_dim_type type, unsigned pos);
3935 const char *isl_pw_aff_get_dim_name(
3936 __isl_keep isl_pw_aff *pa,
3937 enum isl_dim_type type, unsigned pos);
3938 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3939 enum isl_dim_type type, unsigned pos);
3940 __isl_give isl_id *isl_pw_aff_get_dim_id(
3941 __isl_keep isl_pw_aff *pa,
3942 enum isl_dim_type type, unsigned pos);
3943 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
3944 enum isl_dim_type type);
3945 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3946 __isl_keep isl_pw_aff *pa,
3947 enum isl_dim_type type);
3948 __isl_give isl_val *isl_aff_get_constant_val(
3949 __isl_keep isl_aff *aff);
3950 __isl_give isl_val *isl_aff_get_coefficient_val(
3951 __isl_keep isl_aff *aff,
3952 enum isl_dim_type type, int pos);
3953 __isl_give isl_val *isl_aff_get_denominator_val(
3954 __isl_keep isl_aff *aff);
3955 __isl_give isl_aff *isl_aff_get_div(
3956 __isl_keep isl_aff *aff, int pos);
3958 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3959 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3960 int (*fn)(__isl_take isl_set *set,
3961 __isl_take isl_aff *aff,
3962 void *user), void *user);
3964 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3965 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3967 int isl_aff_is_nan(__isl_keep isl_aff *aff);
3968 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
3970 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3971 enum isl_dim_type type, unsigned first, unsigned n);
3972 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3973 enum isl_dim_type type, unsigned first, unsigned n);
3975 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3976 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3977 enum isl_dim_type type);
3978 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3980 It can be modified using
3982 #include <isl/aff.h>
3983 __isl_give isl_aff *isl_aff_set_tuple_id(
3984 __isl_take isl_aff *aff,
3985 enum isl_dim_type type, __isl_take isl_id *id);
3986 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3987 __isl_take isl_pw_aff *pwaff,
3988 enum isl_dim_type type, __isl_take isl_id *id);
3989 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
3990 __isl_take isl_pw_aff *pa,
3991 enum isl_dim_type type);
3992 __isl_give isl_aff *isl_aff_set_dim_name(
3993 __isl_take isl_aff *aff, enum isl_dim_type type,
3994 unsigned pos, const char *s);
3995 __isl_give isl_aff *isl_aff_set_dim_id(
3996 __isl_take isl_aff *aff, enum isl_dim_type type,
3997 unsigned pos, __isl_take isl_id *id);
3998 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3999 __isl_take isl_pw_aff *pma,
4000 enum isl_dim_type type, unsigned pos,
4001 __isl_take isl_id *id);
4002 __isl_give isl_aff *isl_aff_set_constant_si(
4003 __isl_take isl_aff *aff, int v);
4004 __isl_give isl_aff *isl_aff_set_constant_val(
4005 __isl_take isl_aff *aff, __isl_take isl_val *v);
4006 __isl_give isl_aff *isl_aff_set_coefficient_si(
4007 __isl_take isl_aff *aff,
4008 enum isl_dim_type type, int pos, int v);
4009 __isl_give isl_aff *isl_aff_set_coefficient_val(
4010 __isl_take isl_aff *aff,
4011 enum isl_dim_type type, int pos,
4012 __isl_take isl_val *v);
4014 __isl_give isl_aff *isl_aff_add_constant_si(
4015 __isl_take isl_aff *aff, int v);
4016 __isl_give isl_aff *isl_aff_add_constant_val(
4017 __isl_take isl_aff *aff, __isl_take isl_val *v);
4018 __isl_give isl_aff *isl_aff_add_constant_num_si(
4019 __isl_take isl_aff *aff, int v);
4020 __isl_give isl_aff *isl_aff_add_coefficient_si(
4021 __isl_take isl_aff *aff,
4022 enum isl_dim_type type, int pos, int v);
4023 __isl_give isl_aff *isl_aff_add_coefficient_val(
4024 __isl_take isl_aff *aff,
4025 enum isl_dim_type type, int pos,
4026 __isl_take isl_val *v);
4028 __isl_give isl_aff *isl_aff_insert_dims(
4029 __isl_take isl_aff *aff,
4030 enum isl_dim_type type, unsigned first, unsigned n);
4031 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
4032 __isl_take isl_pw_aff *pwaff,
4033 enum isl_dim_type type, unsigned first, unsigned n);
4034 __isl_give isl_aff *isl_aff_add_dims(
4035 __isl_take isl_aff *aff,
4036 enum isl_dim_type type, unsigned n);
4037 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
4038 __isl_take isl_pw_aff *pwaff,
4039 enum isl_dim_type type, unsigned n);
4040 __isl_give isl_aff *isl_aff_drop_dims(
4041 __isl_take isl_aff *aff,
4042 enum isl_dim_type type, unsigned first, unsigned n);
4043 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
4044 __isl_take isl_pw_aff *pwaff,
4045 enum isl_dim_type type, unsigned first, unsigned n);
4046 __isl_give isl_aff *isl_aff_move_dims(
4047 __isl_take isl_aff *aff,
4048 enum isl_dim_type dst_type, unsigned dst_pos,
4049 enum isl_dim_type src_type, unsigned src_pos,
4051 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
4052 __isl_take isl_pw_aff *pa,
4053 enum isl_dim_type dst_type, unsigned dst_pos,
4054 enum isl_dim_type src_type, unsigned src_pos,
4057 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
4058 set the I<numerator> of the constant or coefficient, while
4059 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
4060 the constant or coefficient as a whole.
4061 The C<add_constant> and C<add_coefficient> functions add an integer
4062 or rational value to
4063 the possibly rational constant or coefficient.
4064 The C<add_constant_num> functions add an integer value to
4067 To check whether an affine expressions is obviously zero
4068 or (obviously) equal to some other affine expression, use
4070 #include <isl/aff.h>
4071 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
4072 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
4073 __isl_keep isl_aff *aff2);
4074 int isl_pw_aff_plain_is_equal(
4075 __isl_keep isl_pw_aff *pwaff1,
4076 __isl_keep isl_pw_aff *pwaff2);
4077 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
4078 __isl_keep isl_pw_aff *pa2);
4079 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4080 __isl_keep isl_pw_aff *pa2);
4082 The function C<isl_pw_aff_plain_cmp> can be used to sort
4083 C<isl_pw_aff>s. The order is not strictly defined.
4084 The current order sorts expressions that only involve
4085 earlier dimensions before those that involve later dimensions.
4089 #include <isl/aff.h>
4090 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
4091 __isl_take isl_aff *aff2);
4092 __isl_give isl_pw_aff *isl_pw_aff_add(
4093 __isl_take isl_pw_aff *pwaff1,
4094 __isl_take isl_pw_aff *pwaff2);
4095 __isl_give isl_pw_aff *isl_pw_aff_min(
4096 __isl_take isl_pw_aff *pwaff1,
4097 __isl_take isl_pw_aff *pwaff2);
4098 __isl_give isl_pw_aff *isl_pw_aff_max(
4099 __isl_take isl_pw_aff *pwaff1,
4100 __isl_take isl_pw_aff *pwaff2);
4101 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
4102 __isl_take isl_aff *aff2);
4103 __isl_give isl_pw_aff *isl_pw_aff_sub(
4104 __isl_take isl_pw_aff *pwaff1,
4105 __isl_take isl_pw_aff *pwaff2);
4106 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
4107 __isl_give isl_pw_aff *isl_pw_aff_neg(
4108 __isl_take isl_pw_aff *pwaff);
4109 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
4110 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4111 __isl_take isl_pw_aff *pwaff);
4112 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
4113 __isl_give isl_pw_aff *isl_pw_aff_floor(
4114 __isl_take isl_pw_aff *pwaff);
4115 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
4116 __isl_take isl_val *mod);
4117 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
4118 __isl_take isl_pw_aff *pa,
4119 __isl_take isl_val *mod);
4120 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
4121 __isl_take isl_val *v);
4122 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
4123 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
4124 __isl_give isl_aff *isl_aff_scale_down_ui(
4125 __isl_take isl_aff *aff, unsigned f);
4126 __isl_give isl_aff *isl_aff_scale_down_val(
4127 __isl_take isl_aff *aff, __isl_take isl_val *v);
4128 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
4129 __isl_take isl_pw_aff *pa,
4130 __isl_take isl_val *f);
4132 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4133 __isl_take isl_pw_aff_list *list);
4134 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4135 __isl_take isl_pw_aff_list *list);
4137 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4138 __isl_take isl_pw_aff *pwqp);
4140 __isl_give isl_aff *isl_aff_align_params(
4141 __isl_take isl_aff *aff,
4142 __isl_take isl_space *model);
4143 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4144 __isl_take isl_pw_aff *pwaff,
4145 __isl_take isl_space *model);
4147 __isl_give isl_aff *isl_aff_project_domain_on_params(
4148 __isl_take isl_aff *aff);
4149 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4150 __isl_take isl_pw_aff *pwa);
4152 __isl_give isl_aff *isl_aff_gist_params(
4153 __isl_take isl_aff *aff,
4154 __isl_take isl_set *context);
4155 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
4156 __isl_take isl_set *context);
4157 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
4158 __isl_take isl_pw_aff *pwaff,
4159 __isl_take isl_set *context);
4160 __isl_give isl_pw_aff *isl_pw_aff_gist(
4161 __isl_take isl_pw_aff *pwaff,
4162 __isl_take isl_set *context);
4164 __isl_give isl_set *isl_pw_aff_domain(
4165 __isl_take isl_pw_aff *pwaff);
4166 __isl_give isl_set *isl_pw_aff_params(
4167 __isl_take isl_pw_aff *pwa);
4168 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4169 __isl_take isl_pw_aff *pa,
4170 __isl_take isl_set *set);
4171 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4172 __isl_take isl_pw_aff *pa,
4173 __isl_take isl_set *set);
4175 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
4176 __isl_take isl_aff *aff2);
4177 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
4178 __isl_take isl_aff *aff2);
4179 __isl_give isl_pw_aff *isl_pw_aff_mul(
4180 __isl_take isl_pw_aff *pwaff1,
4181 __isl_take isl_pw_aff *pwaff2);
4182 __isl_give isl_pw_aff *isl_pw_aff_div(
4183 __isl_take isl_pw_aff *pa1,
4184 __isl_take isl_pw_aff *pa2);
4185 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
4186 __isl_take isl_pw_aff *pa1,
4187 __isl_take isl_pw_aff *pa2);
4188 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
4189 __isl_take isl_pw_aff *pa1,
4190 __isl_take isl_pw_aff *pa2);
4192 When multiplying two affine expressions, at least one of the two needs
4193 to be a constant. Similarly, when dividing an affine expression by another,
4194 the second expression needs to be a constant.
4195 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
4196 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
4199 #include <isl/aff.h>
4200 __isl_give isl_aff *isl_aff_pullback_aff(
4201 __isl_take isl_aff *aff1,
4202 __isl_take isl_aff *aff2);
4203 __isl_give isl_aff *isl_aff_pullback_multi_aff(
4204 __isl_take isl_aff *aff,
4205 __isl_take isl_multi_aff *ma);
4206 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
4207 __isl_take isl_pw_aff *pa,
4208 __isl_take isl_multi_aff *ma);
4209 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
4210 __isl_take isl_pw_aff *pa,
4211 __isl_take isl_pw_multi_aff *pma);
4212 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
4213 __isl_take isl_pw_aff *pa,
4214 __isl_take isl_multi_pw_aff *mpa);
4216 These functions precompose the input expression by the given
4217 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
4218 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
4219 into the (piecewise) affine expression.
4220 Objects of type C<isl_multi_aff> are described in
4221 L</"Piecewise Multiple Quasi Affine Expressions">.
4223 #include <isl/aff.h>
4224 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4225 __isl_take isl_aff *aff);
4226 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4227 __isl_take isl_aff *aff);
4228 __isl_give isl_basic_set *isl_aff_le_basic_set(
4229 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4230 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4231 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4232 __isl_give isl_set *isl_pw_aff_eq_set(
4233 __isl_take isl_pw_aff *pwaff1,
4234 __isl_take isl_pw_aff *pwaff2);
4235 __isl_give isl_set *isl_pw_aff_ne_set(
4236 __isl_take isl_pw_aff *pwaff1,
4237 __isl_take isl_pw_aff *pwaff2);
4238 __isl_give isl_set *isl_pw_aff_le_set(
4239 __isl_take isl_pw_aff *pwaff1,
4240 __isl_take isl_pw_aff *pwaff2);
4241 __isl_give isl_set *isl_pw_aff_lt_set(
4242 __isl_take isl_pw_aff *pwaff1,
4243 __isl_take isl_pw_aff *pwaff2);
4244 __isl_give isl_set *isl_pw_aff_ge_set(
4245 __isl_take isl_pw_aff *pwaff1,
4246 __isl_take isl_pw_aff *pwaff2);
4247 __isl_give isl_set *isl_pw_aff_gt_set(
4248 __isl_take isl_pw_aff *pwaff1,
4249 __isl_take isl_pw_aff *pwaff2);
4251 __isl_give isl_set *isl_pw_aff_list_eq_set(
4252 __isl_take isl_pw_aff_list *list1,
4253 __isl_take isl_pw_aff_list *list2);
4254 __isl_give isl_set *isl_pw_aff_list_ne_set(
4255 __isl_take isl_pw_aff_list *list1,
4256 __isl_take isl_pw_aff_list *list2);
4257 __isl_give isl_set *isl_pw_aff_list_le_set(
4258 __isl_take isl_pw_aff_list *list1,
4259 __isl_take isl_pw_aff_list *list2);
4260 __isl_give isl_set *isl_pw_aff_list_lt_set(
4261 __isl_take isl_pw_aff_list *list1,
4262 __isl_take isl_pw_aff_list *list2);
4263 __isl_give isl_set *isl_pw_aff_list_ge_set(
4264 __isl_take isl_pw_aff_list *list1,
4265 __isl_take isl_pw_aff_list *list2);
4266 __isl_give isl_set *isl_pw_aff_list_gt_set(
4267 __isl_take isl_pw_aff_list *list1,
4268 __isl_take isl_pw_aff_list *list2);
4270 The function C<isl_aff_neg_basic_set> returns a basic set
4271 containing those elements in the domain space
4272 of C<aff> where C<aff> is negative.
4273 The function C<isl_aff_ge_basic_set> returns a basic set
4274 containing those elements in the shared space
4275 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4276 The function C<isl_pw_aff_ge_set> returns a set
4277 containing those elements in the shared domain
4278 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4279 The functions operating on C<isl_pw_aff_list> apply the corresponding
4280 C<isl_pw_aff> function to each pair of elements in the two lists.
4282 #include <isl/aff.h>
4283 __isl_give isl_set *isl_pw_aff_nonneg_set(
4284 __isl_take isl_pw_aff *pwaff);
4285 __isl_give isl_set *isl_pw_aff_zero_set(
4286 __isl_take isl_pw_aff *pwaff);
4287 __isl_give isl_set *isl_pw_aff_non_zero_set(
4288 __isl_take isl_pw_aff *pwaff);
4290 The function C<isl_pw_aff_nonneg_set> returns a set
4291 containing those elements in the domain
4292 of C<pwaff> where C<pwaff> is non-negative.
4294 #include <isl/aff.h>
4295 __isl_give isl_pw_aff *isl_pw_aff_cond(
4296 __isl_take isl_pw_aff *cond,
4297 __isl_take isl_pw_aff *pwaff_true,
4298 __isl_take isl_pw_aff *pwaff_false);
4300 The function C<isl_pw_aff_cond> performs a conditional operator
4301 and returns an expression that is equal to C<pwaff_true>
4302 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4303 where C<cond> is zero.
4305 #include <isl/aff.h>
4306 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4307 __isl_take isl_pw_aff *pwaff1,
4308 __isl_take isl_pw_aff *pwaff2);
4309 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4310 __isl_take isl_pw_aff *pwaff1,
4311 __isl_take isl_pw_aff *pwaff2);
4312 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4313 __isl_take isl_pw_aff *pwaff1,
4314 __isl_take isl_pw_aff *pwaff2);
4316 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4317 expression with a domain that is the union of those of C<pwaff1> and
4318 C<pwaff2> and such that on each cell, the quasi-affine expression is
4319 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4320 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4321 associated expression is the defined one.
4323 An expression can be read from input using
4325 #include <isl/aff.h>
4326 __isl_give isl_aff *isl_aff_read_from_str(
4327 isl_ctx *ctx, const char *str);
4328 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4329 isl_ctx *ctx, const char *str);
4331 An expression can be printed using
4333 #include <isl/aff.h>
4334 __isl_give isl_printer *isl_printer_print_aff(
4335 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4337 __isl_give isl_printer *isl_printer_print_pw_aff(
4338 __isl_take isl_printer *p,
4339 __isl_keep isl_pw_aff *pwaff);
4341 =head2 Piecewise Multiple Quasi Affine Expressions
4343 An C<isl_multi_aff> object represents a sequence of
4344 zero or more affine expressions, all defined on the same domain space.
4345 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4346 zero or more piecewise affine expressions.
4348 An C<isl_multi_aff> can be constructed from a single
4349 C<isl_aff> or an C<isl_aff_list> using the
4350 following functions. Similarly for C<isl_multi_pw_aff>
4351 and C<isl_pw_multi_aff>.
4353 #include <isl/aff.h>
4354 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4355 __isl_take isl_aff *aff);
4356 __isl_give isl_multi_pw_aff *
4357 isl_multi_pw_aff_from_multi_aff(
4358 __isl_take isl_multi_aff *ma);
4359 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4360 __isl_take isl_pw_aff *pa);
4361 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4362 __isl_take isl_pw_aff *pa);
4363 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4364 __isl_take isl_space *space,
4365 __isl_take isl_aff_list *list);
4367 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4368 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4369 Note however that the domain
4370 of the result is the intersection of the domains of the input.
4371 The reverse conversion is exact.
4373 #include <isl/aff.h>
4374 __isl_give isl_pw_multi_aff *
4375 isl_pw_multi_aff_from_multi_pw_aff(
4376 __isl_take isl_multi_pw_aff *mpa);
4377 __isl_give isl_multi_pw_aff *
4378 isl_multi_pw_aff_from_pw_multi_aff(
4379 __isl_take isl_pw_multi_aff *pma);
4381 An empty piecewise multiple quasi affine expression (one with no cells),
4382 the zero piecewise multiple quasi affine expression (with value zero
4383 for each output dimension),
4384 a piecewise multiple quasi affine expression with a single cell (with
4385 either a universe or a specified domain) or
4386 a zero-dimensional piecewise multiple quasi affine expression
4388 can be created using the following functions.
4390 #include <isl/aff.h>
4391 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4392 __isl_take isl_space *space);
4393 __isl_give isl_multi_aff *isl_multi_aff_zero(
4394 __isl_take isl_space *space);
4395 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4396 __isl_take isl_space *space);
4397 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4398 __isl_take isl_space *space);
4399 __isl_give isl_multi_aff *isl_multi_aff_identity(
4400 __isl_take isl_space *space);
4401 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4402 __isl_take isl_space *space);
4403 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4404 __isl_take isl_space *space);
4405 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4406 __isl_take isl_space *space);
4407 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4408 __isl_take isl_space *space);
4409 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4410 __isl_take isl_space *space,
4411 enum isl_dim_type type,
4412 unsigned first, unsigned n);
4413 __isl_give isl_pw_multi_aff *
4414 isl_pw_multi_aff_project_out_map(
4415 __isl_take isl_space *space,
4416 enum isl_dim_type type,
4417 unsigned first, unsigned n);
4418 __isl_give isl_pw_multi_aff *
4419 isl_pw_multi_aff_from_multi_aff(
4420 __isl_take isl_multi_aff *ma);
4421 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4422 __isl_take isl_set *set,
4423 __isl_take isl_multi_aff *maff);
4424 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4425 __isl_take isl_set *set);
4427 __isl_give isl_union_pw_multi_aff *
4428 isl_union_pw_multi_aff_empty(
4429 __isl_take isl_space *space);
4430 __isl_give isl_union_pw_multi_aff *
4431 isl_union_pw_multi_aff_add_pw_multi_aff(
4432 __isl_take isl_union_pw_multi_aff *upma,
4433 __isl_take isl_pw_multi_aff *pma);
4434 __isl_give isl_union_pw_multi_aff *
4435 isl_union_pw_multi_aff_from_domain(
4436 __isl_take isl_union_set *uset);
4438 A piecewise multiple quasi affine expression can also be initialized
4439 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4440 and the C<isl_map> is single-valued.
4441 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4442 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4444 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4445 __isl_take isl_set *set);
4446 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4447 __isl_take isl_map *map);
4449 __isl_give isl_union_pw_multi_aff *
4450 isl_union_pw_multi_aff_from_union_set(
4451 __isl_take isl_union_set *uset);
4452 __isl_give isl_union_pw_multi_aff *
4453 isl_union_pw_multi_aff_from_union_map(
4454 __isl_take isl_union_map *umap);
4456 Multiple quasi affine expressions can be copied and freed using
4458 #include <isl/aff.h>
4459 __isl_give isl_multi_aff *isl_multi_aff_copy(
4460 __isl_keep isl_multi_aff *maff);
4461 __isl_null isl_multi_aff *isl_multi_aff_free(
4462 __isl_take isl_multi_aff *maff);
4464 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4465 __isl_keep isl_pw_multi_aff *pma);
4466 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
4467 __isl_take isl_pw_multi_aff *pma);
4469 __isl_give isl_union_pw_multi_aff *
4470 isl_union_pw_multi_aff_copy(
4471 __isl_keep isl_union_pw_multi_aff *upma);
4472 __isl_null isl_union_pw_multi_aff *
4473 isl_union_pw_multi_aff_free(
4474 __isl_take isl_union_pw_multi_aff *upma);
4476 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4477 __isl_keep isl_multi_pw_aff *mpa);
4478 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
4479 __isl_take isl_multi_pw_aff *mpa);
4481 The expression can be inspected using
4483 #include <isl/aff.h>
4484 isl_ctx *isl_multi_aff_get_ctx(
4485 __isl_keep isl_multi_aff *maff);
4486 isl_ctx *isl_pw_multi_aff_get_ctx(
4487 __isl_keep isl_pw_multi_aff *pma);
4488 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4489 __isl_keep isl_union_pw_multi_aff *upma);
4490 isl_ctx *isl_multi_pw_aff_get_ctx(
4491 __isl_keep isl_multi_pw_aff *mpa);
4493 int isl_multi_aff_involves_dims(
4494 __isl_keep isl_multi_aff *ma,
4495 enum isl_dim_type type, unsigned first, unsigned n);
4496 int isl_multi_pw_aff_involves_dims(
4497 __isl_keep isl_multi_pw_aff *mpa,
4498 enum isl_dim_type type, unsigned first, unsigned n);
4500 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4501 enum isl_dim_type type);
4502 unsigned isl_pw_multi_aff_dim(
4503 __isl_keep isl_pw_multi_aff *pma,
4504 enum isl_dim_type type);
4505 unsigned isl_multi_pw_aff_dim(
4506 __isl_keep isl_multi_pw_aff *mpa,
4507 enum isl_dim_type type);
4508 __isl_give isl_aff *isl_multi_aff_get_aff(
4509 __isl_keep isl_multi_aff *multi, int pos);
4510 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4511 __isl_keep isl_pw_multi_aff *pma, int pos);
4512 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4513 __isl_keep isl_multi_pw_aff *mpa, int pos);
4514 int isl_multi_aff_find_dim_by_id(
4515 __isl_keep isl_multi_aff *ma,
4516 enum isl_dim_type type, __isl_keep isl_id *id);
4517 int isl_multi_pw_aff_find_dim_by_id(
4518 __isl_keep isl_multi_pw_aff *mpa,
4519 enum isl_dim_type type, __isl_keep isl_id *id);
4520 const char *isl_pw_multi_aff_get_dim_name(
4521 __isl_keep isl_pw_multi_aff *pma,
4522 enum isl_dim_type type, unsigned pos);
4523 __isl_give isl_id *isl_multi_aff_get_dim_id(
4524 __isl_keep isl_multi_aff *ma,
4525 enum isl_dim_type type, unsigned pos);
4526 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4527 __isl_keep isl_pw_multi_aff *pma,
4528 enum isl_dim_type type, unsigned pos);
4529 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4530 __isl_keep isl_multi_pw_aff *mpa,
4531 enum isl_dim_type type, unsigned pos);
4532 const char *isl_multi_aff_get_tuple_name(
4533 __isl_keep isl_multi_aff *multi,
4534 enum isl_dim_type type);
4535 int isl_pw_multi_aff_has_tuple_name(
4536 __isl_keep isl_pw_multi_aff *pma,
4537 enum isl_dim_type type);
4538 const char *isl_pw_multi_aff_get_tuple_name(
4539 __isl_keep isl_pw_multi_aff *pma,
4540 enum isl_dim_type type);
4541 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4542 enum isl_dim_type type);
4543 int isl_pw_multi_aff_has_tuple_id(
4544 __isl_keep isl_pw_multi_aff *pma,
4545 enum isl_dim_type type);
4546 int isl_multi_pw_aff_has_tuple_id(
4547 __isl_keep isl_multi_pw_aff *mpa,
4548 enum isl_dim_type type);
4549 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4550 __isl_keep isl_multi_aff *ma,
4551 enum isl_dim_type type);
4552 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4553 __isl_keep isl_pw_multi_aff *pma,
4554 enum isl_dim_type type);
4555 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4556 __isl_keep isl_multi_pw_aff *mpa,
4557 enum isl_dim_type type);
4558 int isl_multi_aff_range_is_wrapping(
4559 __isl_keep isl_multi_aff *ma);
4560 int isl_multi_pw_aff_range_is_wrapping(
4561 __isl_keep isl_multi_pw_aff *mpa);
4563 int isl_pw_multi_aff_foreach_piece(
4564 __isl_keep isl_pw_multi_aff *pma,
4565 int (*fn)(__isl_take isl_set *set,
4566 __isl_take isl_multi_aff *maff,
4567 void *user), void *user);
4569 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4570 __isl_keep isl_union_pw_multi_aff *upma,
4571 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4572 void *user), void *user);
4574 It can be modified using
4576 #include <isl/aff.h>
4577 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4578 __isl_take isl_multi_aff *multi, int pos,
4579 __isl_take isl_aff *aff);
4580 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4581 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4582 __isl_take isl_pw_aff *pa);
4583 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4584 __isl_take isl_multi_aff *maff,
4585 enum isl_dim_type type, unsigned pos, const char *s);
4586 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4587 __isl_take isl_multi_aff *maff,
4588 enum isl_dim_type type, unsigned pos,
4589 __isl_take isl_id *id);
4590 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4591 __isl_take isl_multi_aff *maff,
4592 enum isl_dim_type type, const char *s);
4593 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4594 __isl_take isl_multi_aff *maff,
4595 enum isl_dim_type type, __isl_take isl_id *id);
4596 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4597 __isl_take isl_pw_multi_aff *pma,
4598 enum isl_dim_type type, __isl_take isl_id *id);
4599 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4600 __isl_take isl_multi_aff *ma,
4601 enum isl_dim_type type);
4602 __isl_give isl_multi_pw_aff *
4603 isl_multi_pw_aff_reset_tuple_id(
4604 __isl_take isl_multi_pw_aff *mpa,
4605 enum isl_dim_type type);
4606 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4607 __isl_take isl_multi_aff *ma);
4608 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4609 __isl_take isl_multi_pw_aff *mpa);
4611 __isl_give isl_multi_pw_aff *
4612 isl_multi_pw_aff_set_dim_name(
4613 __isl_take isl_multi_pw_aff *mpa,
4614 enum isl_dim_type type, unsigned pos, const char *s);
4615 __isl_give isl_multi_pw_aff *
4616 isl_multi_pw_aff_set_dim_id(
4617 __isl_take isl_multi_pw_aff *mpa,
4618 enum isl_dim_type type, unsigned pos,
4619 __isl_take isl_id *id);
4620 __isl_give isl_multi_pw_aff *
4621 isl_multi_pw_aff_set_tuple_name(
4622 __isl_take isl_multi_pw_aff *mpa,
4623 enum isl_dim_type type, const char *s);
4625 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4626 __isl_take isl_multi_aff *ma);
4628 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4629 __isl_take isl_multi_aff *ma,
4630 enum isl_dim_type type, unsigned first, unsigned n);
4631 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4632 __isl_take isl_multi_aff *ma,
4633 enum isl_dim_type type, unsigned n);
4634 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4635 __isl_take isl_multi_aff *maff,
4636 enum isl_dim_type type, unsigned first, unsigned n);
4637 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4638 __isl_take isl_pw_multi_aff *pma,
4639 enum isl_dim_type type, unsigned first, unsigned n);
4641 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4642 __isl_take isl_multi_pw_aff *mpa,
4643 enum isl_dim_type type, unsigned first, unsigned n);
4644 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4645 __isl_take isl_multi_pw_aff *mpa,
4646 enum isl_dim_type type, unsigned n);
4647 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4648 __isl_take isl_multi_pw_aff *pma,
4649 enum isl_dim_type dst_type, unsigned dst_pos,
4650 enum isl_dim_type src_type, unsigned src_pos,
4653 To check whether two multiple affine expressions are
4654 (obviously) equal to each other, use
4656 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4657 __isl_keep isl_multi_aff *maff2);
4658 int isl_pw_multi_aff_plain_is_equal(
4659 __isl_keep isl_pw_multi_aff *pma1,
4660 __isl_keep isl_pw_multi_aff *pma2);
4661 int isl_multi_pw_aff_plain_is_equal(
4662 __isl_keep isl_multi_pw_aff *mpa1,
4663 __isl_keep isl_multi_pw_aff *mpa2);
4664 int isl_multi_pw_aff_is_equal(
4665 __isl_keep isl_multi_pw_aff *mpa1,
4666 __isl_keep isl_multi_pw_aff *mpa2);
4670 #include <isl/aff.h>
4671 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4672 __isl_take isl_pw_multi_aff *pma1,
4673 __isl_take isl_pw_multi_aff *pma2);
4674 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4675 __isl_take isl_pw_multi_aff *pma1,
4676 __isl_take isl_pw_multi_aff *pma2);
4677 __isl_give isl_multi_aff *isl_multi_aff_floor(
4678 __isl_take isl_multi_aff *ma);
4679 __isl_give isl_multi_aff *isl_multi_aff_add(
4680 __isl_take isl_multi_aff *maff1,
4681 __isl_take isl_multi_aff *maff2);
4682 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4683 __isl_take isl_pw_multi_aff *pma1,
4684 __isl_take isl_pw_multi_aff *pma2);
4685 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4686 __isl_take isl_union_pw_multi_aff *upma1,
4687 __isl_take isl_union_pw_multi_aff *upma2);
4688 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4689 __isl_take isl_pw_multi_aff *pma1,
4690 __isl_take isl_pw_multi_aff *pma2);
4691 __isl_give isl_multi_aff *isl_multi_aff_sub(
4692 __isl_take isl_multi_aff *ma1,
4693 __isl_take isl_multi_aff *ma2);
4694 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4695 __isl_take isl_pw_multi_aff *pma1,
4696 __isl_take isl_pw_multi_aff *pma2);
4697 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4698 __isl_take isl_union_pw_multi_aff *upma1,
4699 __isl_take isl_union_pw_multi_aff *upma2);
4701 C<isl_multi_aff_sub> subtracts the second argument from the first.
4703 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4704 __isl_take isl_multi_aff *ma,
4705 __isl_take isl_val *v);
4706 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4707 __isl_take isl_pw_multi_aff *pma,
4708 __isl_take isl_val *v);
4709 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4710 __isl_take isl_multi_pw_aff *mpa,
4711 __isl_take isl_val *v);
4712 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4713 __isl_take isl_multi_aff *ma,
4714 __isl_take isl_multi_val *mv);
4715 __isl_give isl_pw_multi_aff *
4716 isl_pw_multi_aff_scale_multi_val(
4717 __isl_take isl_pw_multi_aff *pma,
4718 __isl_take isl_multi_val *mv);
4719 __isl_give isl_multi_pw_aff *
4720 isl_multi_pw_aff_scale_multi_val(
4721 __isl_take isl_multi_pw_aff *mpa,
4722 __isl_take isl_multi_val *mv);
4723 __isl_give isl_union_pw_multi_aff *
4724 isl_union_pw_multi_aff_scale_multi_val(
4725 __isl_take isl_union_pw_multi_aff *upma,
4726 __isl_take isl_multi_val *mv);
4727 __isl_give isl_multi_aff *
4728 isl_multi_aff_scale_down_multi_val(
4729 __isl_take isl_multi_aff *ma,
4730 __isl_take isl_multi_val *mv);
4731 __isl_give isl_multi_pw_aff *
4732 isl_multi_pw_aff_scale_down_multi_val(
4733 __isl_take isl_multi_pw_aff *mpa,
4734 __isl_take isl_multi_val *mv);
4736 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4737 by the corresponding elements of C<mv>.
4739 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4740 __isl_take isl_pw_multi_aff *pma,
4741 enum isl_dim_type type, unsigned pos, int value);
4742 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4743 __isl_take isl_pw_multi_aff *pma,
4744 __isl_take isl_set *set);
4745 __isl_give isl_set *isl_multi_pw_aff_domain(
4746 __isl_take isl_multi_pw_aff *mpa);
4747 __isl_give isl_multi_pw_aff *
4748 isl_multi_pw_aff_intersect_params(
4749 __isl_take isl_multi_pw_aff *mpa,
4750 __isl_take isl_set *set);
4751 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4752 __isl_take isl_pw_multi_aff *pma,
4753 __isl_take isl_set *set);
4754 __isl_give isl_multi_pw_aff *
4755 isl_multi_pw_aff_intersect_domain(
4756 __isl_take isl_multi_pw_aff *mpa,
4757 __isl_take isl_set *domain);
4758 __isl_give isl_union_pw_multi_aff *
4759 isl_union_pw_multi_aff_intersect_domain(
4760 __isl_take isl_union_pw_multi_aff *upma,
4761 __isl_take isl_union_set *uset);
4762 __isl_give isl_multi_aff *isl_multi_aff_lift(
4763 __isl_take isl_multi_aff *maff,
4764 __isl_give isl_local_space **ls);
4765 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4766 __isl_take isl_pw_multi_aff *pma);
4767 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4768 __isl_take isl_multi_pw_aff *mpa);
4769 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4770 __isl_take isl_multi_aff *multi,
4771 __isl_take isl_space *model);
4772 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4773 __isl_take isl_pw_multi_aff *pma,
4774 __isl_take isl_space *model);
4775 __isl_give isl_union_pw_multi_aff *
4776 isl_union_pw_multi_aff_align_params(
4777 __isl_take isl_union_pw_multi_aff *upma,
4778 __isl_take isl_space *model);
4779 __isl_give isl_pw_multi_aff *
4780 isl_pw_multi_aff_project_domain_on_params(
4781 __isl_take isl_pw_multi_aff *pma);
4782 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4783 __isl_take isl_multi_aff *maff,
4784 __isl_take isl_set *context);
4785 __isl_give isl_multi_aff *isl_multi_aff_gist(
4786 __isl_take isl_multi_aff *maff,
4787 __isl_take isl_set *context);
4788 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4789 __isl_take isl_pw_multi_aff *pma,
4790 __isl_take isl_set *set);
4791 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4792 __isl_take isl_pw_multi_aff *pma,
4793 __isl_take isl_set *set);
4794 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4795 __isl_take isl_multi_pw_aff *mpa,
4796 __isl_take isl_set *set);
4797 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4798 __isl_take isl_multi_pw_aff *mpa,
4799 __isl_take isl_set *set);
4800 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4801 __isl_take isl_multi_aff *ma);
4802 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4803 __isl_take isl_multi_pw_aff *mpa);
4804 __isl_give isl_set *isl_pw_multi_aff_domain(
4805 __isl_take isl_pw_multi_aff *pma);
4806 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4807 __isl_take isl_union_pw_multi_aff *upma);
4808 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4809 __isl_take isl_multi_aff *ma1, unsigned pos,
4810 __isl_take isl_multi_aff *ma2);
4811 __isl_give isl_multi_aff *isl_multi_aff_splice(
4812 __isl_take isl_multi_aff *ma1,
4813 unsigned in_pos, unsigned out_pos,
4814 __isl_take isl_multi_aff *ma2);
4815 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4816 __isl_take isl_multi_aff *ma1,
4817 __isl_take isl_multi_aff *ma2);
4818 __isl_give isl_multi_aff *
4819 isl_multi_aff_range_factor_domain(
4820 __isl_take isl_multi_aff *ma);
4821 __isl_give isl_multi_aff *
4822 isl_multi_aff_range_factor_range(
4823 __isl_take isl_multi_aff *ma);
4824 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4825 __isl_take isl_multi_aff *ma1,
4826 __isl_take isl_multi_aff *ma2);
4827 __isl_give isl_multi_aff *isl_multi_aff_product(
4828 __isl_take isl_multi_aff *ma1,
4829 __isl_take isl_multi_aff *ma2);
4830 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4831 __isl_take isl_multi_pw_aff *mpa1,
4832 __isl_take isl_multi_pw_aff *mpa2);
4833 __isl_give isl_pw_multi_aff *
4834 isl_pw_multi_aff_range_product(
4835 __isl_take isl_pw_multi_aff *pma1,
4836 __isl_take isl_pw_multi_aff *pma2);
4837 __isl_give isl_multi_pw_aff *
4838 isl_multi_pw_aff_range_factor_domain(
4839 __isl_take isl_multi_pw_aff *mpa);
4840 __isl_give isl_multi_pw_aff *
4841 isl_multi_pw_aff_range_factor_range(
4842 __isl_take isl_multi_pw_aff *mpa);
4843 __isl_give isl_pw_multi_aff *
4844 isl_pw_multi_aff_flat_range_product(
4845 __isl_take isl_pw_multi_aff *pma1,
4846 __isl_take isl_pw_multi_aff *pma2);
4847 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4848 __isl_take isl_pw_multi_aff *pma1,
4849 __isl_take isl_pw_multi_aff *pma2);
4850 __isl_give isl_union_pw_multi_aff *
4851 isl_union_pw_multi_aff_flat_range_product(
4852 __isl_take isl_union_pw_multi_aff *upma1,
4853 __isl_take isl_union_pw_multi_aff *upma2);
4854 __isl_give isl_multi_pw_aff *
4855 isl_multi_pw_aff_range_splice(
4856 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4857 __isl_take isl_multi_pw_aff *mpa2);
4858 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4859 __isl_take isl_multi_pw_aff *mpa1,
4860 unsigned in_pos, unsigned out_pos,
4861 __isl_take isl_multi_pw_aff *mpa2);
4862 __isl_give isl_multi_pw_aff *
4863 isl_multi_pw_aff_range_product(
4864 __isl_take isl_multi_pw_aff *mpa1,
4865 __isl_take isl_multi_pw_aff *mpa2);
4866 __isl_give isl_multi_pw_aff *
4867 isl_multi_pw_aff_flat_range_product(
4868 __isl_take isl_multi_pw_aff *mpa1,
4869 __isl_take isl_multi_pw_aff *mpa2);
4871 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4872 then it is assigned the local space that lies at the basis of
4873 the lifting applied.
4875 #include <isl/aff.h>
4876 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4877 __isl_take isl_multi_aff *ma1,
4878 __isl_take isl_multi_aff *ma2);
4879 __isl_give isl_pw_multi_aff *
4880 isl_pw_multi_aff_pullback_multi_aff(
4881 __isl_take isl_pw_multi_aff *pma,
4882 __isl_take isl_multi_aff *ma);
4883 __isl_give isl_multi_pw_aff *
4884 isl_multi_pw_aff_pullback_multi_aff(
4885 __isl_take isl_multi_pw_aff *mpa,
4886 __isl_take isl_multi_aff *ma);
4887 __isl_give isl_pw_multi_aff *
4888 isl_pw_multi_aff_pullback_pw_multi_aff(
4889 __isl_take isl_pw_multi_aff *pma1,
4890 __isl_take isl_pw_multi_aff *pma2);
4891 __isl_give isl_multi_pw_aff *
4892 isl_multi_pw_aff_pullback_pw_multi_aff(
4893 __isl_take isl_multi_pw_aff *mpa,
4894 __isl_take isl_pw_multi_aff *pma);
4895 __isl_give isl_multi_pw_aff *
4896 isl_multi_pw_aff_pullback_multi_pw_aff(
4897 __isl_take isl_multi_pw_aff *mpa1,
4898 __isl_take isl_multi_pw_aff *mpa2);
4900 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4901 In other words, C<ma2> is plugged
4904 __isl_give isl_set *isl_multi_aff_lex_le_set(
4905 __isl_take isl_multi_aff *ma1,
4906 __isl_take isl_multi_aff *ma2);
4907 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4908 __isl_take isl_multi_aff *ma1,
4909 __isl_take isl_multi_aff *ma2);
4911 The function C<isl_multi_aff_lex_le_set> returns a set
4912 containing those elements in the shared domain space
4913 where C<ma1> is lexicographically smaller than or
4916 An expression can be read from input using
4918 #include <isl/aff.h>
4919 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4920 isl_ctx *ctx, const char *str);
4921 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4922 isl_ctx *ctx, const char *str);
4923 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4924 isl_ctx *ctx, const char *str);
4925 __isl_give isl_union_pw_multi_aff *
4926 isl_union_pw_multi_aff_read_from_str(
4927 isl_ctx *ctx, const char *str);
4929 An expression can be printed using
4931 #include <isl/aff.h>
4932 __isl_give isl_printer *isl_printer_print_multi_aff(
4933 __isl_take isl_printer *p,
4934 __isl_keep isl_multi_aff *maff);
4935 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4936 __isl_take isl_printer *p,
4937 __isl_keep isl_pw_multi_aff *pma);
4938 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4939 __isl_take isl_printer *p,
4940 __isl_keep isl_union_pw_multi_aff *upma);
4941 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4942 __isl_take isl_printer *p,
4943 __isl_keep isl_multi_pw_aff *mpa);
4947 Points are elements of a set. They can be used to construct
4948 simple sets (boxes) or they can be used to represent the
4949 individual elements of a set.
4950 The zero point (the origin) can be created using
4952 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4954 The coordinates of a point can be inspected, set and changed
4957 __isl_give isl_val *isl_point_get_coordinate_val(
4958 __isl_keep isl_point *pnt,
4959 enum isl_dim_type type, int pos);
4960 __isl_give isl_point *isl_point_set_coordinate_val(
4961 __isl_take isl_point *pnt,
4962 enum isl_dim_type type, int pos,
4963 __isl_take isl_val *v);
4965 __isl_give isl_point *isl_point_add_ui(
4966 __isl_take isl_point *pnt,
4967 enum isl_dim_type type, int pos, unsigned val);
4968 __isl_give isl_point *isl_point_sub_ui(
4969 __isl_take isl_point *pnt,
4970 enum isl_dim_type type, int pos, unsigned val);
4972 Other properties can be obtained using
4974 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4976 Points can be copied or freed using
4978 __isl_give isl_point *isl_point_copy(
4979 __isl_keep isl_point *pnt);
4980 void isl_point_free(__isl_take isl_point *pnt);
4982 A singleton set can be created from a point using
4984 __isl_give isl_basic_set *isl_basic_set_from_point(
4985 __isl_take isl_point *pnt);
4986 __isl_give isl_set *isl_set_from_point(
4987 __isl_take isl_point *pnt);
4989 and a box can be created from two opposite extremal points using
4991 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4992 __isl_take isl_point *pnt1,
4993 __isl_take isl_point *pnt2);
4994 __isl_give isl_set *isl_set_box_from_points(
4995 __isl_take isl_point *pnt1,
4996 __isl_take isl_point *pnt2);
4998 All elements of a B<bounded> (union) set can be enumerated using
4999 the following functions.
5001 int isl_set_foreach_point(__isl_keep isl_set *set,
5002 int (*fn)(__isl_take isl_point *pnt, void *user),
5004 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
5005 int (*fn)(__isl_take isl_point *pnt, void *user),
5008 The function C<fn> is called for each integer point in
5009 C<set> with as second argument the last argument of
5010 the C<isl_set_foreach_point> call. The function C<fn>
5011 should return C<0> on success and C<-1> on failure.
5012 In the latter case, C<isl_set_foreach_point> will stop
5013 enumerating and return C<-1> as well.
5014 If the enumeration is performed successfully and to completion,
5015 then C<isl_set_foreach_point> returns C<0>.
5017 To obtain a single point of a (basic) set, use
5019 __isl_give isl_point *isl_basic_set_sample_point(
5020 __isl_take isl_basic_set *bset);
5021 __isl_give isl_point *isl_set_sample_point(
5022 __isl_take isl_set *set);
5024 If C<set> does not contain any (integer) points, then the
5025 resulting point will be ``void'', a property that can be
5028 int isl_point_is_void(__isl_keep isl_point *pnt);
5030 =head2 Piecewise Quasipolynomials
5032 A piecewise quasipolynomial is a particular kind of function that maps
5033 a parametric point to a rational value.
5034 More specifically, a quasipolynomial is a polynomial expression in greatest
5035 integer parts of affine expressions of parameters and variables.
5036 A piecewise quasipolynomial is a subdivision of a given parametric
5037 domain into disjoint cells with a quasipolynomial associated to
5038 each cell. The value of the piecewise quasipolynomial at a given
5039 point is the value of the quasipolynomial associated to the cell
5040 that contains the point. Outside of the union of cells,
5041 the value is assumed to be zero.
5042 For example, the piecewise quasipolynomial
5044 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
5046 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
5047 A given piecewise quasipolynomial has a fixed domain dimension.
5048 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
5049 defined over different domains.
5050 Piecewise quasipolynomials are mainly used by the C<barvinok>
5051 library for representing the number of elements in a parametric set or map.
5052 For example, the piecewise quasipolynomial above represents
5053 the number of points in the map
5055 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
5057 =head3 Input and Output
5059 Piecewise quasipolynomials can be read from input using
5061 __isl_give isl_union_pw_qpolynomial *
5062 isl_union_pw_qpolynomial_read_from_str(
5063 isl_ctx *ctx, const char *str);
5065 Quasipolynomials and piecewise quasipolynomials can be printed
5066 using the following functions.
5068 __isl_give isl_printer *isl_printer_print_qpolynomial(
5069 __isl_take isl_printer *p,
5070 __isl_keep isl_qpolynomial *qp);
5072 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
5073 __isl_take isl_printer *p,
5074 __isl_keep isl_pw_qpolynomial *pwqp);
5076 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
5077 __isl_take isl_printer *p,
5078 __isl_keep isl_union_pw_qpolynomial *upwqp);
5080 The output format of the printer
5081 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5082 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
5084 In case of printing in C<ISL_FORMAT_C>, the user may want
5085 to set the names of all dimensions
5087 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
5088 __isl_take isl_qpolynomial *qp,
5089 enum isl_dim_type type, unsigned pos,
5091 __isl_give isl_pw_qpolynomial *
5092 isl_pw_qpolynomial_set_dim_name(
5093 __isl_take isl_pw_qpolynomial *pwqp,
5094 enum isl_dim_type type, unsigned pos,
5097 =head3 Creating New (Piecewise) Quasipolynomials
5099 Some simple quasipolynomials can be created using the following functions.
5100 More complicated quasipolynomials can be created by applying
5101 operations such as addition and multiplication
5102 on the resulting quasipolynomials
5104 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
5105 __isl_take isl_space *domain);
5106 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
5107 __isl_take isl_space *domain);
5108 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
5109 __isl_take isl_space *domain);
5110 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
5111 __isl_take isl_space *domain);
5112 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
5113 __isl_take isl_space *domain);
5114 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
5115 __isl_take isl_space *domain,
5116 __isl_take isl_val *val);
5117 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
5118 __isl_take isl_space *domain,
5119 enum isl_dim_type type, unsigned pos);
5120 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
5121 __isl_take isl_aff *aff);
5123 Note that the space in which a quasipolynomial lives is a map space
5124 with a one-dimensional range. The C<domain> argument in some of
5125 the functions above corresponds to the domain of this map space.
5127 The zero piecewise quasipolynomial or a piecewise quasipolynomial
5128 with a single cell can be created using the following functions.
5129 Multiple of these single cell piecewise quasipolynomials can
5130 be combined to create more complicated piecewise quasipolynomials.
5132 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
5133 __isl_take isl_space *space);
5134 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
5135 __isl_take isl_set *set,
5136 __isl_take isl_qpolynomial *qp);
5137 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
5138 __isl_take isl_qpolynomial *qp);
5139 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
5140 __isl_take isl_pw_aff *pwaff);
5142 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
5143 __isl_take isl_space *space);
5144 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
5145 __isl_take isl_pw_qpolynomial *pwqp);
5146 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
5147 __isl_take isl_union_pw_qpolynomial *upwqp,
5148 __isl_take isl_pw_qpolynomial *pwqp);
5150 Quasipolynomials can be copied and freed again using the following
5153 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
5154 __isl_keep isl_qpolynomial *qp);
5155 __isl_null isl_qpolynomial *isl_qpolynomial_free(
5156 __isl_take isl_qpolynomial *qp);
5158 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
5159 __isl_keep isl_pw_qpolynomial *pwqp);
5160 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
5161 __isl_take isl_pw_qpolynomial *pwqp);
5163 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
5164 __isl_keep isl_union_pw_qpolynomial *upwqp);
5165 __isl_null isl_union_pw_qpolynomial *
5166 isl_union_pw_qpolynomial_free(
5167 __isl_take isl_union_pw_qpolynomial *upwqp);
5169 =head3 Inspecting (Piecewise) Quasipolynomials
5171 To iterate over all piecewise quasipolynomials in a union
5172 piecewise quasipolynomial, use the following function
5174 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
5175 __isl_keep isl_union_pw_qpolynomial *upwqp,
5176 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
5179 To extract the piecewise quasipolynomial in a given space from a union, use
5181 __isl_give isl_pw_qpolynomial *
5182 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
5183 __isl_keep isl_union_pw_qpolynomial *upwqp,
5184 __isl_take isl_space *space);
5186 To iterate over the cells in a piecewise quasipolynomial,
5187 use either of the following two functions
5189 int isl_pw_qpolynomial_foreach_piece(
5190 __isl_keep isl_pw_qpolynomial *pwqp,
5191 int (*fn)(__isl_take isl_set *set,
5192 __isl_take isl_qpolynomial *qp,
5193 void *user), void *user);
5194 int isl_pw_qpolynomial_foreach_lifted_piece(
5195 __isl_keep isl_pw_qpolynomial *pwqp,
5196 int (*fn)(__isl_take isl_set *set,
5197 __isl_take isl_qpolynomial *qp,
5198 void *user), void *user);
5200 As usual, the function C<fn> should return C<0> on success
5201 and C<-1> on failure. The difference between
5202 C<isl_pw_qpolynomial_foreach_piece> and
5203 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
5204 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
5205 compute unique representations for all existentially quantified
5206 variables and then turn these existentially quantified variables
5207 into extra set variables, adapting the associated quasipolynomial
5208 accordingly. This means that the C<set> passed to C<fn>
5209 will not have any existentially quantified variables, but that
5210 the dimensions of the sets may be different for different
5211 invocations of C<fn>.
5213 The constant term of a quasipolynomial can be extracted using
5215 __isl_give isl_val *isl_qpolynomial_get_constant_val(
5216 __isl_keep isl_qpolynomial *qp);
5218 To iterate over all terms in a quasipolynomial,
5221 int isl_qpolynomial_foreach_term(
5222 __isl_keep isl_qpolynomial *qp,
5223 int (*fn)(__isl_take isl_term *term,
5224 void *user), void *user);
5226 The terms themselves can be inspected and freed using
5229 unsigned isl_term_dim(__isl_keep isl_term *term,
5230 enum isl_dim_type type);
5231 __isl_give isl_val *isl_term_get_coefficient_val(
5232 __isl_keep isl_term *term);
5233 int isl_term_get_exp(__isl_keep isl_term *term,
5234 enum isl_dim_type type, unsigned pos);
5235 __isl_give isl_aff *isl_term_get_div(
5236 __isl_keep isl_term *term, unsigned pos);
5237 void isl_term_free(__isl_take isl_term *term);
5239 Each term is a product of parameters, set variables and
5240 integer divisions. The function C<isl_term_get_exp>
5241 returns the exponent of a given dimensions in the given term.
5243 =head3 Properties of (Piecewise) Quasipolynomials
5245 To check whether two union piecewise quasipolynomials are
5246 obviously equal, use
5248 int isl_union_pw_qpolynomial_plain_is_equal(
5249 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5250 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5252 =head3 Operations on (Piecewise) Quasipolynomials
5254 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5255 __isl_take isl_qpolynomial *qp,
5256 __isl_take isl_val *v);
5257 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5258 __isl_take isl_qpolynomial *qp);
5259 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5260 __isl_take isl_qpolynomial *qp1,
5261 __isl_take isl_qpolynomial *qp2);
5262 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5263 __isl_take isl_qpolynomial *qp1,
5264 __isl_take isl_qpolynomial *qp2);
5265 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5266 __isl_take isl_qpolynomial *qp1,
5267 __isl_take isl_qpolynomial *qp2);
5268 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5269 __isl_take isl_qpolynomial *qp, unsigned exponent);
5271 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5272 __isl_take isl_pw_qpolynomial *pwqp,
5273 enum isl_dim_type type, unsigned n,
5274 __isl_take isl_val *v);
5275 __isl_give isl_pw_qpolynomial *
5276 isl_pw_qpolynomial_scale_val(
5277 __isl_take isl_pw_qpolynomial *pwqp,
5278 __isl_take isl_val *v);
5279 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5280 __isl_take isl_pw_qpolynomial *pwqp1,
5281 __isl_take isl_pw_qpolynomial *pwqp2);
5282 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5283 __isl_take isl_pw_qpolynomial *pwqp1,
5284 __isl_take isl_pw_qpolynomial *pwqp2);
5285 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5286 __isl_take isl_pw_qpolynomial *pwqp1,
5287 __isl_take isl_pw_qpolynomial *pwqp2);
5288 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5289 __isl_take isl_pw_qpolynomial *pwqp);
5290 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5291 __isl_take isl_pw_qpolynomial *pwqp1,
5292 __isl_take isl_pw_qpolynomial *pwqp2);
5293 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5294 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5296 __isl_give isl_union_pw_qpolynomial *
5297 isl_union_pw_qpolynomial_scale_val(
5298 __isl_take isl_union_pw_qpolynomial *upwqp,
5299 __isl_take isl_val *v);
5300 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5301 __isl_take isl_union_pw_qpolynomial *upwqp1,
5302 __isl_take isl_union_pw_qpolynomial *upwqp2);
5303 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5304 __isl_take isl_union_pw_qpolynomial *upwqp1,
5305 __isl_take isl_union_pw_qpolynomial *upwqp2);
5306 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5307 __isl_take isl_union_pw_qpolynomial *upwqp1,
5308 __isl_take isl_union_pw_qpolynomial *upwqp2);
5310 __isl_give isl_val *isl_pw_qpolynomial_eval(
5311 __isl_take isl_pw_qpolynomial *pwqp,
5312 __isl_take isl_point *pnt);
5314 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5315 __isl_take isl_union_pw_qpolynomial *upwqp,
5316 __isl_take isl_point *pnt);
5318 __isl_give isl_set *isl_pw_qpolynomial_domain(
5319 __isl_take isl_pw_qpolynomial *pwqp);
5320 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5321 __isl_take isl_pw_qpolynomial *pwpq,
5322 __isl_take isl_set *set);
5323 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5324 __isl_take isl_pw_qpolynomial *pwpq,
5325 __isl_take isl_set *set);
5327 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5328 __isl_take isl_union_pw_qpolynomial *upwqp);
5329 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5330 __isl_take isl_union_pw_qpolynomial *upwpq,
5331 __isl_take isl_union_set *uset);
5332 __isl_give isl_union_pw_qpolynomial *
5333 isl_union_pw_qpolynomial_intersect_params(
5334 __isl_take isl_union_pw_qpolynomial *upwpq,
5335 __isl_take isl_set *set);
5337 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5338 __isl_take isl_qpolynomial *qp,
5339 __isl_take isl_space *model);
5341 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5342 __isl_take isl_qpolynomial *qp);
5343 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5344 __isl_take isl_pw_qpolynomial *pwqp);
5346 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5347 __isl_take isl_union_pw_qpolynomial *upwqp);
5349 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5350 __isl_take isl_qpolynomial *qp,
5351 __isl_take isl_set *context);
5352 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5353 __isl_take isl_qpolynomial *qp,
5354 __isl_take isl_set *context);
5356 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5357 __isl_take isl_pw_qpolynomial *pwqp,
5358 __isl_take isl_set *context);
5359 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5360 __isl_take isl_pw_qpolynomial *pwqp,
5361 __isl_take isl_set *context);
5363 __isl_give isl_union_pw_qpolynomial *
5364 isl_union_pw_qpolynomial_gist_params(
5365 __isl_take isl_union_pw_qpolynomial *upwqp,
5366 __isl_take isl_set *context);
5367 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5368 __isl_take isl_union_pw_qpolynomial *upwqp,
5369 __isl_take isl_union_set *context);
5371 The gist operation applies the gist operation to each of
5372 the cells in the domain of the input piecewise quasipolynomial.
5373 The context is also exploited
5374 to simplify the quasipolynomials associated to each cell.
5376 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5377 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5378 __isl_give isl_union_pw_qpolynomial *
5379 isl_union_pw_qpolynomial_to_polynomial(
5380 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5382 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5383 the polynomial will be an overapproximation. If C<sign> is negative,
5384 it will be an underapproximation. If C<sign> is zero, the approximation
5385 will lie somewhere in between.
5387 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5389 A piecewise quasipolynomial reduction is a piecewise
5390 reduction (or fold) of quasipolynomials.
5391 In particular, the reduction can be maximum or a minimum.
5392 The objects are mainly used to represent the result of
5393 an upper or lower bound on a quasipolynomial over its domain,
5394 i.e., as the result of the following function.
5396 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5397 __isl_take isl_pw_qpolynomial *pwqp,
5398 enum isl_fold type, int *tight);
5400 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5401 __isl_take isl_union_pw_qpolynomial *upwqp,
5402 enum isl_fold type, int *tight);
5404 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5405 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5406 is the returned bound is known be tight, i.e., for each value
5407 of the parameters there is at least
5408 one element in the domain that reaches the bound.
5409 If the domain of C<pwqp> is not wrapping, then the bound is computed
5410 over all elements in that domain and the result has a purely parametric
5411 domain. If the domain of C<pwqp> is wrapping, then the bound is
5412 computed over the range of the wrapped relation. The domain of the
5413 wrapped relation becomes the domain of the result.
5415 A (piecewise) quasipolynomial reduction can be copied or freed using the
5416 following functions.
5418 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5419 __isl_keep isl_qpolynomial_fold *fold);
5420 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5421 __isl_keep isl_pw_qpolynomial_fold *pwf);
5422 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5423 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5424 void isl_qpolynomial_fold_free(
5425 __isl_take isl_qpolynomial_fold *fold);
5426 __isl_null isl_pw_qpolynomial_fold *
5427 isl_pw_qpolynomial_fold_free(
5428 __isl_take isl_pw_qpolynomial_fold *pwf);
5429 __isl_null isl_union_pw_qpolynomial_fold *
5430 isl_union_pw_qpolynomial_fold_free(
5431 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5433 =head3 Printing Piecewise Quasipolynomial Reductions
5435 Piecewise quasipolynomial reductions can be printed
5436 using the following function.
5438 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5439 __isl_take isl_printer *p,
5440 __isl_keep isl_pw_qpolynomial_fold *pwf);
5441 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5442 __isl_take isl_printer *p,
5443 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5445 For C<isl_printer_print_pw_qpolynomial_fold>,
5446 output format of the printer
5447 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5448 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5449 output format of the printer
5450 needs to be set to C<ISL_FORMAT_ISL>.
5451 In case of printing in C<ISL_FORMAT_C>, the user may want
5452 to set the names of all dimensions
5454 __isl_give isl_pw_qpolynomial_fold *
5455 isl_pw_qpolynomial_fold_set_dim_name(
5456 __isl_take isl_pw_qpolynomial_fold *pwf,
5457 enum isl_dim_type type, unsigned pos,
5460 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5462 To iterate over all piecewise quasipolynomial reductions in a union
5463 piecewise quasipolynomial reduction, use the following function
5465 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5466 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5467 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5468 void *user), void *user);
5470 To iterate over the cells in a piecewise quasipolynomial reduction,
5471 use either of the following two functions
5473 int isl_pw_qpolynomial_fold_foreach_piece(
5474 __isl_keep isl_pw_qpolynomial_fold *pwf,
5475 int (*fn)(__isl_take isl_set *set,
5476 __isl_take isl_qpolynomial_fold *fold,
5477 void *user), void *user);
5478 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5479 __isl_keep isl_pw_qpolynomial_fold *pwf,
5480 int (*fn)(__isl_take isl_set *set,
5481 __isl_take isl_qpolynomial_fold *fold,
5482 void *user), void *user);
5484 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5485 of the difference between these two functions.
5487 To iterate over all quasipolynomials in a reduction, use
5489 int isl_qpolynomial_fold_foreach_qpolynomial(
5490 __isl_keep isl_qpolynomial_fold *fold,
5491 int (*fn)(__isl_take isl_qpolynomial *qp,
5492 void *user), void *user);
5494 =head3 Properties of Piecewise Quasipolynomial Reductions
5496 To check whether two union piecewise quasipolynomial reductions are
5497 obviously equal, use
5499 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5500 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5501 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5503 =head3 Operations on Piecewise Quasipolynomial Reductions
5505 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5506 __isl_take isl_qpolynomial_fold *fold,
5507 __isl_take isl_val *v);
5508 __isl_give isl_pw_qpolynomial_fold *
5509 isl_pw_qpolynomial_fold_scale_val(
5510 __isl_take isl_pw_qpolynomial_fold *pwf,
5511 __isl_take isl_val *v);
5512 __isl_give isl_union_pw_qpolynomial_fold *
5513 isl_union_pw_qpolynomial_fold_scale_val(
5514 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5515 __isl_take isl_val *v);
5517 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5518 __isl_take isl_pw_qpolynomial_fold *pwf1,
5519 __isl_take isl_pw_qpolynomial_fold *pwf2);
5521 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5522 __isl_take isl_pw_qpolynomial_fold *pwf1,
5523 __isl_take isl_pw_qpolynomial_fold *pwf2);
5525 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5526 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5527 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5529 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5530 __isl_take isl_pw_qpolynomial_fold *pwf,
5531 __isl_take isl_point *pnt);
5533 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5534 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5535 __isl_take isl_point *pnt);
5537 __isl_give isl_pw_qpolynomial_fold *
5538 isl_pw_qpolynomial_fold_intersect_params(
5539 __isl_take isl_pw_qpolynomial_fold *pwf,
5540 __isl_take isl_set *set);
5542 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5543 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5544 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5545 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5546 __isl_take isl_union_set *uset);
5547 __isl_give isl_union_pw_qpolynomial_fold *
5548 isl_union_pw_qpolynomial_fold_intersect_params(
5549 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5550 __isl_take isl_set *set);
5552 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5553 __isl_take isl_pw_qpolynomial_fold *pwf);
5555 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5556 __isl_take isl_pw_qpolynomial_fold *pwf);
5558 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5559 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5561 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5562 __isl_take isl_qpolynomial_fold *fold,
5563 __isl_take isl_set *context);
5564 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5565 __isl_take isl_qpolynomial_fold *fold,
5566 __isl_take isl_set *context);
5568 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5569 __isl_take isl_pw_qpolynomial_fold *pwf,
5570 __isl_take isl_set *context);
5571 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5572 __isl_take isl_pw_qpolynomial_fold *pwf,
5573 __isl_take isl_set *context);
5575 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5576 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5577 __isl_take isl_union_set *context);
5578 __isl_give isl_union_pw_qpolynomial_fold *
5579 isl_union_pw_qpolynomial_fold_gist_params(
5580 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5581 __isl_take isl_set *context);
5583 The gist operation applies the gist operation to each of
5584 the cells in the domain of the input piecewise quasipolynomial reduction.
5585 In future, the operation will also exploit the context
5586 to simplify the quasipolynomial reductions associated to each cell.
5588 __isl_give isl_pw_qpolynomial_fold *
5589 isl_set_apply_pw_qpolynomial_fold(
5590 __isl_take isl_set *set,
5591 __isl_take isl_pw_qpolynomial_fold *pwf,
5593 __isl_give isl_pw_qpolynomial_fold *
5594 isl_map_apply_pw_qpolynomial_fold(
5595 __isl_take isl_map *map,
5596 __isl_take isl_pw_qpolynomial_fold *pwf,
5598 __isl_give isl_union_pw_qpolynomial_fold *
5599 isl_union_set_apply_union_pw_qpolynomial_fold(
5600 __isl_take isl_union_set *uset,
5601 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5603 __isl_give isl_union_pw_qpolynomial_fold *
5604 isl_union_map_apply_union_pw_qpolynomial_fold(
5605 __isl_take isl_union_map *umap,
5606 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5609 The functions taking a map
5610 compose the given map with the given piecewise quasipolynomial reduction.
5611 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5612 over all elements in the intersection of the range of the map
5613 and the domain of the piecewise quasipolynomial reduction
5614 as a function of an element in the domain of the map.
5615 The functions taking a set compute a bound over all elements in the
5616 intersection of the set and the domain of the
5617 piecewise quasipolynomial reduction.
5619 =head2 Parametric Vertex Enumeration
5621 The parametric vertex enumeration described in this section
5622 is mainly intended to be used internally and by the C<barvinok>
5625 #include <isl/vertices.h>
5626 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5627 __isl_keep isl_basic_set *bset);
5629 The function C<isl_basic_set_compute_vertices> performs the
5630 actual computation of the parametric vertices and the chamber
5631 decomposition and store the result in an C<isl_vertices> object.
5632 This information can be queried by either iterating over all
5633 the vertices or iterating over all the chambers or cells
5634 and then iterating over all vertices that are active on the chamber.
5636 int isl_vertices_foreach_vertex(
5637 __isl_keep isl_vertices *vertices,
5638 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5641 int isl_vertices_foreach_cell(
5642 __isl_keep isl_vertices *vertices,
5643 int (*fn)(__isl_take isl_cell *cell, void *user),
5645 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5646 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5649 Other operations that can be performed on an C<isl_vertices> object are
5652 isl_ctx *isl_vertices_get_ctx(
5653 __isl_keep isl_vertices *vertices);
5654 int isl_vertices_get_n_vertices(
5655 __isl_keep isl_vertices *vertices);
5656 void isl_vertices_free(__isl_take isl_vertices *vertices);
5658 Vertices can be inspected and destroyed using the following functions.
5660 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5661 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5662 __isl_give isl_basic_set *isl_vertex_get_domain(
5663 __isl_keep isl_vertex *vertex);
5664 __isl_give isl_multi_aff *isl_vertex_get_expr(
5665 __isl_keep isl_vertex *vertex);
5666 void isl_vertex_free(__isl_take isl_vertex *vertex);
5668 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
5669 describing the vertex in terms of the parameters,
5670 while C<isl_vertex_get_domain> returns the activity domain
5673 Chambers can be inspected and destroyed using the following functions.
5675 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5676 __isl_give isl_basic_set *isl_cell_get_domain(
5677 __isl_keep isl_cell *cell);
5678 void isl_cell_free(__isl_take isl_cell *cell);
5680 =head1 Polyhedral Compilation Library
5682 This section collects functionality in C<isl> that has been specifically
5683 designed for use during polyhedral compilation.
5685 =head2 Dependence Analysis
5687 C<isl> contains specialized functionality for performing
5688 array dataflow analysis. That is, given a I<sink> access relation
5689 and a collection of possible I<source> access relations,
5690 C<isl> can compute relations that describe
5691 for each iteration of the sink access, which iteration
5692 of which of the source access relations was the last
5693 to access the same data element before the given iteration
5695 The resulting dependence relations map source iterations
5696 to the corresponding sink iterations.
5697 To compute standard flow dependences, the sink should be
5698 a read, while the sources should be writes.
5699 If any of the source accesses are marked as being I<may>
5700 accesses, then there will be a dependence from the last
5701 I<must> access B<and> from any I<may> access that follows
5702 this last I<must> access.
5703 In particular, if I<all> sources are I<may> accesses,
5704 then memory based dependence analysis is performed.
5705 If, on the other hand, all sources are I<must> accesses,
5706 then value based dependence analysis is performed.
5708 #include <isl/flow.h>
5710 typedef int (*isl_access_level_before)(void *first, void *second);
5712 __isl_give isl_access_info *isl_access_info_alloc(
5713 __isl_take isl_map *sink,
5714 void *sink_user, isl_access_level_before fn,
5716 __isl_give isl_access_info *isl_access_info_add_source(
5717 __isl_take isl_access_info *acc,
5718 __isl_take isl_map *source, int must,
5720 __isl_null isl_access_info *isl_access_info_free(
5721 __isl_take isl_access_info *acc);
5723 __isl_give isl_flow *isl_access_info_compute_flow(
5724 __isl_take isl_access_info *acc);
5726 int isl_flow_foreach(__isl_keep isl_flow *deps,
5727 int (*fn)(__isl_take isl_map *dep, int must,
5728 void *dep_user, void *user),
5730 __isl_give isl_map *isl_flow_get_no_source(
5731 __isl_keep isl_flow *deps, int must);
5732 void isl_flow_free(__isl_take isl_flow *deps);
5734 The function C<isl_access_info_compute_flow> performs the actual
5735 dependence analysis. The other functions are used to construct
5736 the input for this function or to read off the output.
5738 The input is collected in an C<isl_access_info>, which can
5739 be created through a call to C<isl_access_info_alloc>.
5740 The arguments to this functions are the sink access relation
5741 C<sink>, a token C<sink_user> used to identify the sink
5742 access to the user, a callback function for specifying the
5743 relative order of source and sink accesses, and the number
5744 of source access relations that will be added.
5745 The callback function has type C<int (*)(void *first, void *second)>.
5746 The function is called with two user supplied tokens identifying
5747 either a source or the sink and it should return the shared nesting
5748 level and the relative order of the two accesses.
5749 In particular, let I<n> be the number of loops shared by
5750 the two accesses. If C<first> precedes C<second> textually,
5751 then the function should return I<2 * n + 1>; otherwise,
5752 it should return I<2 * n>.
5753 The sources can be added to the C<isl_access_info> by performing
5754 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5755 C<must> indicates whether the source is a I<must> access
5756 or a I<may> access. Note that a multi-valued access relation
5757 should only be marked I<must> if every iteration in the domain
5758 of the relation accesses I<all> elements in its image.
5759 The C<source_user> token is again used to identify
5760 the source access. The range of the source access relation
5761 C<source> should have the same dimension as the range
5762 of the sink access relation.
5763 The C<isl_access_info_free> function should usually not be
5764 called explicitly, because it is called implicitly by
5765 C<isl_access_info_compute_flow>.
5767 The result of the dependence analysis is collected in an
5768 C<isl_flow>. There may be elements of
5769 the sink access for which no preceding source access could be
5770 found or for which all preceding sources are I<may> accesses.
5771 The relations containing these elements can be obtained through
5772 calls to C<isl_flow_get_no_source>, the first with C<must> set
5773 and the second with C<must> unset.
5774 In the case of standard flow dependence analysis,
5775 with the sink a read and the sources I<must> writes,
5776 the first relation corresponds to the reads from uninitialized
5777 array elements and the second relation is empty.
5778 The actual flow dependences can be extracted using
5779 C<isl_flow_foreach>. This function will call the user-specified
5780 callback function C<fn> for each B<non-empty> dependence between
5781 a source and the sink. The callback function is called
5782 with four arguments, the actual flow dependence relation
5783 mapping source iterations to sink iterations, a boolean that
5784 indicates whether it is a I<must> or I<may> dependence, a token
5785 identifying the source and an additional C<void *> with value
5786 equal to the third argument of the C<isl_flow_foreach> call.
5787 A dependence is marked I<must> if it originates from a I<must>
5788 source and if it is not followed by any I<may> sources.
5790 After finishing with an C<isl_flow>, the user should call
5791 C<isl_flow_free> to free all associated memory.
5793 A higher-level interface to dependence analysis is provided
5794 by the following function.
5796 #include <isl/flow.h>
5798 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5799 __isl_take isl_union_map *must_source,
5800 __isl_take isl_union_map *may_source,
5801 __isl_take isl_union_map *schedule,
5802 __isl_give isl_union_map **must_dep,
5803 __isl_give isl_union_map **may_dep,
5804 __isl_give isl_union_map **must_no_source,
5805 __isl_give isl_union_map **may_no_source);
5807 The arrays are identified by the tuple names of the ranges
5808 of the accesses. The iteration domains by the tuple names
5809 of the domains of the accesses and of the schedule.
5810 The relative order of the iteration domains is given by the
5811 schedule. The relations returned through C<must_no_source>
5812 and C<may_no_source> are subsets of C<sink>.
5813 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5814 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5815 any of the other arguments is treated as an error.
5817 =head3 Interaction with Dependence Analysis
5819 During the dependence analysis, we frequently need to perform
5820 the following operation. Given a relation between sink iterations
5821 and potential source iterations from a particular source domain,
5822 what is the last potential source iteration corresponding to each
5823 sink iteration. It can sometimes be convenient to adjust
5824 the set of potential source iterations before or after each such operation.
5825 The prototypical example is fuzzy array dataflow analysis,
5826 where we need to analyze if, based on data-dependent constraints,
5827 the sink iteration can ever be executed without one or more of
5828 the corresponding potential source iterations being executed.
5829 If so, we can introduce extra parameters and select an unknown
5830 but fixed source iteration from the potential source iterations.
5831 To be able to perform such manipulations, C<isl> provides the following
5834 #include <isl/flow.h>
5836 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5837 __isl_keep isl_map *source_map,
5838 __isl_keep isl_set *sink, void *source_user,
5840 __isl_give isl_access_info *isl_access_info_set_restrict(
5841 __isl_take isl_access_info *acc,
5842 isl_access_restrict fn, void *user);
5844 The function C<isl_access_info_set_restrict> should be called
5845 before calling C<isl_access_info_compute_flow> and registers a callback function
5846 that will be called any time C<isl> is about to compute the last
5847 potential source. The first argument is the (reverse) proto-dependence,
5848 mapping sink iterations to potential source iterations.
5849 The second argument represents the sink iterations for which
5850 we want to compute the last source iteration.
5851 The third argument is the token corresponding to the source
5852 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5853 The callback is expected to return a restriction on either the input or
5854 the output of the operation computing the last potential source.
5855 If the input needs to be restricted then restrictions are needed
5856 for both the source and the sink iterations. The sink iterations
5857 and the potential source iterations will be intersected with these sets.
5858 If the output needs to be restricted then only a restriction on the source
5859 iterations is required.
5860 If any error occurs, the callback should return C<NULL>.
5861 An C<isl_restriction> object can be created, freed and inspected
5862 using the following functions.
5864 #include <isl/flow.h>
5866 __isl_give isl_restriction *isl_restriction_input(
5867 __isl_take isl_set *source_restr,
5868 __isl_take isl_set *sink_restr);
5869 __isl_give isl_restriction *isl_restriction_output(
5870 __isl_take isl_set *source_restr);
5871 __isl_give isl_restriction *isl_restriction_none(
5872 __isl_take isl_map *source_map);
5873 __isl_give isl_restriction *isl_restriction_empty(
5874 __isl_take isl_map *source_map);
5875 __isl_null isl_restriction *isl_restriction_free(
5876 __isl_take isl_restriction *restr);
5877 isl_ctx *isl_restriction_get_ctx(
5878 __isl_keep isl_restriction *restr);
5880 C<isl_restriction_none> and C<isl_restriction_empty> are special
5881 cases of C<isl_restriction_input>. C<isl_restriction_none>
5882 is essentially equivalent to
5884 isl_restriction_input(isl_set_universe(
5885 isl_space_range(isl_map_get_space(source_map))),
5887 isl_space_domain(isl_map_get_space(source_map))));
5889 whereas C<isl_restriction_empty> is essentially equivalent to
5891 isl_restriction_input(isl_set_empty(
5892 isl_space_range(isl_map_get_space(source_map))),
5894 isl_space_domain(isl_map_get_space(source_map))));
5898 B<The functionality described in this section is fairly new
5899 and may be subject to change.>
5901 #include <isl/schedule.h>
5902 __isl_give isl_schedule *
5903 isl_schedule_constraints_compute_schedule(
5904 __isl_take isl_schedule_constraints *sc);
5905 __isl_null isl_schedule *isl_schedule_free(
5906 __isl_take isl_schedule *sched);
5908 The function C<isl_schedule_constraints_compute_schedule> can be
5909 used to compute a schedule that satisfy the given schedule constraints.
5910 These schedule constraints include the iteration domain for which
5911 a schedule should be computed and dependences between pairs of
5912 iterations. In particular, these dependences include
5913 I<validity> dependences and I<proximity> dependences.
5914 By default, the algorithm used to construct the schedule is similar
5915 to that of C<Pluto>.
5916 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5918 The generated schedule respects all validity dependences.
5919 That is, all dependence distances over these dependences in the
5920 scheduled space are lexicographically positive.
5921 The default algorithm tries to ensure that the dependence distances
5922 over coincidence constraints are zero and to minimize the
5923 dependence distances over proximity dependences.
5924 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5925 for groups of domains where the dependence distances over validity
5926 dependences have only non-negative values.
5927 When using Feautrier's algorithm, the coincidence and proximity constraints
5928 are only taken into account during the extension to a
5929 full-dimensional schedule.
5931 An C<isl_schedule_constraints> object can be constructed
5932 and manipulated using the following functions.
5934 #include <isl/schedule.h>
5935 __isl_give isl_schedule_constraints *
5936 isl_schedule_constraints_copy(
5937 __isl_keep isl_schedule_constraints *sc);
5938 __isl_give isl_schedule_constraints *
5939 isl_schedule_constraints_on_domain(
5940 __isl_take isl_union_set *domain);
5941 isl_ctx *isl_schedule_constraints_get_ctx(
5942 __isl_keep isl_schedule_constraints *sc);
5943 __isl_give isl_schedule_constraints *
5944 isl_schedule_constraints_set_validity(
5945 __isl_take isl_schedule_constraints *sc,
5946 __isl_take isl_union_map *validity);
5947 __isl_give isl_schedule_constraints *
5948 isl_schedule_constraints_set_coincidence(
5949 __isl_take isl_schedule_constraints *sc,
5950 __isl_take isl_union_map *coincidence);
5951 __isl_give isl_schedule_constraints *
5952 isl_schedule_constraints_set_proximity(
5953 __isl_take isl_schedule_constraints *sc,
5954 __isl_take isl_union_map *proximity);
5955 __isl_give isl_schedule_constraints *
5956 isl_schedule_constraints_set_conditional_validity(
5957 __isl_take isl_schedule_constraints *sc,
5958 __isl_take isl_union_map *condition,
5959 __isl_take isl_union_map *validity);
5960 __isl_null isl_schedule_constraints *
5961 isl_schedule_constraints_free(
5962 __isl_take isl_schedule_constraints *sc);
5964 The initial C<isl_schedule_constraints> object created by
5965 C<isl_schedule_constraints_on_domain> does not impose any constraints.
5966 That is, it has an empty set of dependences.
5967 The function C<isl_schedule_constraints_set_validity> replaces the
5968 validity dependences, mapping domain elements I<i> to domain
5969 elements that should be scheduled after I<i>.
5970 The function C<isl_schedule_constraints_set_coincidence> replaces the
5971 coincidence dependences, mapping domain elements I<i> to domain
5972 elements that should be scheduled together with I<I>, if possible.
5973 The function C<isl_schedule_constraints_set_proximity> replaces the
5974 proximity dependences, mapping domain elements I<i> to domain
5975 elements that should be scheduled either before I<I>
5976 or as early as possible after I<i>.
5978 The function C<isl_schedule_constraints_set_conditional_validity>
5979 replaces the conditional validity constraints.
5980 A conditional validity constraint is only imposed when any of the corresponding
5981 conditions is satisfied, i.e., when any of them is non-zero.
5982 That is, the scheduler ensures that within each band if the dependence
5983 distances over the condition constraints are not all zero
5984 then all corresponding conditional validity constraints are respected.
5985 A conditional validity constraint corresponds to a condition
5986 if the two are adjacent, i.e., if the domain of one relation intersect
5987 the range of the other relation.
5988 The typical use case of conditional validity constraints is
5989 to allow order constraints between live ranges to be violated
5990 as long as the live ranges themselves are local to the band.
5991 To allow more fine-grained control over which conditions correspond
5992 to which conditional validity constraints, the domains and ranges
5993 of these relations may include I<tags>. That is, the domains and
5994 ranges of those relation may themselves be wrapped relations
5995 where the iteration domain appears in the domain of those wrapped relations
5996 and the range of the wrapped relations can be arbitrarily chosen
5997 by the user. Conditions and conditional validity constraints are only
5998 considere adjacent to each other if the entire wrapped relation matches.
5999 In particular, a relation with a tag will never be considered adjacent
6000 to a relation without a tag.
6002 The following function computes a schedule directly from
6003 an iteration domain and validity and proximity dependences
6004 and is implemented in terms of the functions described above.
6005 The use of C<isl_union_set_compute_schedule> is discouraged.
6007 #include <isl/schedule.h>
6008 __isl_give isl_schedule *isl_union_set_compute_schedule(
6009 __isl_take isl_union_set *domain,
6010 __isl_take isl_union_map *validity,
6011 __isl_take isl_union_map *proximity);
6013 A mapping from the domains to the scheduled space can be obtained
6014 from an C<isl_schedule> using the following function.
6016 __isl_give isl_union_map *isl_schedule_get_map(
6017 __isl_keep isl_schedule *sched);
6019 A representation of the schedule can be printed using
6021 __isl_give isl_printer *isl_printer_print_schedule(
6022 __isl_take isl_printer *p,
6023 __isl_keep isl_schedule *schedule);
6025 A representation of the schedule as a forest of bands can be obtained
6026 using the following function.
6028 __isl_give isl_band_list *isl_schedule_get_band_forest(
6029 __isl_keep isl_schedule *schedule);
6031 The individual bands can be visited in depth-first post-order
6032 using the following function.
6034 #include <isl/schedule.h>
6035 int isl_schedule_foreach_band(
6036 __isl_keep isl_schedule *sched,
6037 int (*fn)(__isl_keep isl_band *band, void *user),
6040 The list can be manipulated as explained in L<"Lists">.
6041 The bands inside the list can be copied and freed using the following
6044 #include <isl/band.h>
6045 __isl_give isl_band *isl_band_copy(
6046 __isl_keep isl_band *band);
6047 __isl_null isl_band *isl_band_free(
6048 __isl_take isl_band *band);
6050 Each band contains zero or more scheduling dimensions.
6051 These are referred to as the members of the band.
6052 The section of the schedule that corresponds to the band is
6053 referred to as the partial schedule of the band.
6054 For those nodes that participate in a band, the outer scheduling
6055 dimensions form the prefix schedule, while the inner scheduling
6056 dimensions form the suffix schedule.
6057 That is, if we take a cut of the band forest, then the union of
6058 the concatenations of the prefix, partial and suffix schedules of
6059 each band in the cut is equal to the entire schedule (modulo
6060 some possible padding at the end with zero scheduling dimensions).
6061 The properties of a band can be inspected using the following functions.
6063 #include <isl/band.h>
6064 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
6066 int isl_band_has_children(__isl_keep isl_band *band);
6067 __isl_give isl_band_list *isl_band_get_children(
6068 __isl_keep isl_band *band);
6070 __isl_give isl_union_map *isl_band_get_prefix_schedule(
6071 __isl_keep isl_band *band);
6072 __isl_give isl_union_map *isl_band_get_partial_schedule(
6073 __isl_keep isl_band *band);
6074 __isl_give isl_union_map *isl_band_get_suffix_schedule(
6075 __isl_keep isl_band *band);
6077 int isl_band_n_member(__isl_keep isl_band *band);
6078 int isl_band_member_is_coincident(
6079 __isl_keep isl_band *band, int pos);
6081 int isl_band_list_foreach_band(
6082 __isl_keep isl_band_list *list,
6083 int (*fn)(__isl_keep isl_band *band, void *user),
6086 Note that a scheduling dimension is considered to be ``coincident''
6087 if it satisfies the coincidence constraints within its band.
6088 That is, if the dependence distances of the coincidence
6089 constraints are all zero in that direction (for fixed
6090 iterations of outer bands).
6091 Like C<isl_schedule_foreach_band>,
6092 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
6093 in depth-first post-order.
6095 A band can be tiled using the following function.
6097 #include <isl/band.h>
6098 int isl_band_tile(__isl_keep isl_band *band,
6099 __isl_take isl_vec *sizes);
6101 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
6103 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
6104 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
6106 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
6108 The C<isl_band_tile> function tiles the band using the given tile sizes
6109 inside its schedule.
6110 A new child band is created to represent the point loops and it is
6111 inserted between the modified band and its children.
6112 The C<tile_scale_tile_loops> option specifies whether the tile
6113 loops iterators should be scaled by the tile sizes.
6114 If the C<tile_shift_point_loops> option is set, then the point loops
6115 are shifted to start at zero.
6117 A band can be split into two nested bands using the following function.
6119 int isl_band_split(__isl_keep isl_band *band, int pos);
6121 The resulting outer band contains the first C<pos> dimensions of C<band>
6122 while the inner band contains the remaining dimensions.
6124 A representation of the band can be printed using
6126 #include <isl/band.h>
6127 __isl_give isl_printer *isl_printer_print_band(
6128 __isl_take isl_printer *p,
6129 __isl_keep isl_band *band);
6133 #include <isl/schedule.h>
6134 int isl_options_set_schedule_max_coefficient(
6135 isl_ctx *ctx, int val);
6136 int isl_options_get_schedule_max_coefficient(
6138 int isl_options_set_schedule_max_constant_term(
6139 isl_ctx *ctx, int val);
6140 int isl_options_get_schedule_max_constant_term(
6142 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
6143 int isl_options_get_schedule_fuse(isl_ctx *ctx);
6144 int isl_options_set_schedule_maximize_band_depth(
6145 isl_ctx *ctx, int val);
6146 int isl_options_get_schedule_maximize_band_depth(
6148 int isl_options_set_schedule_outer_coincidence(
6149 isl_ctx *ctx, int val);
6150 int isl_options_get_schedule_outer_coincidence(
6152 int isl_options_set_schedule_split_scaled(
6153 isl_ctx *ctx, int val);
6154 int isl_options_get_schedule_split_scaled(
6156 int isl_options_set_schedule_algorithm(
6157 isl_ctx *ctx, int val);
6158 int isl_options_get_schedule_algorithm(
6160 int isl_options_set_schedule_separate_components(
6161 isl_ctx *ctx, int val);
6162 int isl_options_get_schedule_separate_components(
6167 =item * schedule_max_coefficient
6169 This option enforces that the coefficients for variable and parameter
6170 dimensions in the calculated schedule are not larger than the specified value.
6171 This option can significantly increase the speed of the scheduling calculation
6172 and may also prevent fusing of unrelated dimensions. A value of -1 means that
6173 this option does not introduce bounds on the variable or parameter
6176 =item * schedule_max_constant_term
6178 This option enforces that the constant coefficients in the calculated schedule
6179 are not larger than the maximal constant term. This option can significantly
6180 increase the speed of the scheduling calculation and may also prevent fusing of
6181 unrelated dimensions. A value of -1 means that this option does not introduce
6182 bounds on the constant coefficients.
6184 =item * schedule_fuse
6186 This option controls the level of fusion.
6187 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6188 resulting schedule will be distributed as much as possible.
6189 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6190 try to fuse loops in the resulting schedule.
6192 =item * schedule_maximize_band_depth
6194 If this option is set, we do not split bands at the point
6195 where we detect splitting is necessary. Instead, we
6196 backtrack and split bands as early as possible. This
6197 reduces the number of splits and maximizes the width of
6198 the bands. Wider bands give more possibilities for tiling.
6199 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6200 then bands will be split as early as possible, even if there is no need.
6201 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6203 =item * schedule_outer_coincidence
6205 If this option is set, then we try to construct schedules
6206 where the outermost scheduling dimension in each band
6207 satisfies the coincidence constraints.
6209 =item * schedule_split_scaled
6211 If this option is set, then we try to construct schedules in which the
6212 constant term is split off from the linear part if the linear parts of
6213 the scheduling rows for all nodes in the graphs have a common non-trivial
6215 The constant term is then placed in a separate band and the linear
6218 =item * schedule_algorithm
6220 Selects the scheduling algorithm to be used.
6221 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6222 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6224 =item * schedule_separate_components
6226 If at any point the dependence graph contains any (weakly connected) components,
6227 then these components are scheduled separately.
6228 If this option is not set, then some iterations of the domains
6229 in these components may be scheduled together.
6230 If this option is set, then the components are given consecutive
6235 =head2 AST Generation
6237 This section describes the C<isl> functionality for generating
6238 ASTs that visit all the elements
6239 in a domain in an order specified by a schedule.
6240 In particular, given a C<isl_union_map>, an AST is generated
6241 that visits all the elements in the domain of the C<isl_union_map>
6242 according to the lexicographic order of the corresponding image
6243 element(s). If the range of the C<isl_union_map> consists of
6244 elements in more than one space, then each of these spaces is handled
6245 separately in an arbitrary order.
6246 It should be noted that the image elements only specify the I<order>
6247 in which the corresponding domain elements should be visited.
6248 No direct relation between the image elements and the loop iterators
6249 in the generated AST should be assumed.
6251 Each AST is generated within a build. The initial build
6252 simply specifies the constraints on the parameters (if any)
6253 and can be created, inspected, copied and freed using the following functions.
6255 #include <isl/ast_build.h>
6256 __isl_give isl_ast_build *isl_ast_build_from_context(
6257 __isl_take isl_set *set);
6258 isl_ctx *isl_ast_build_get_ctx(
6259 __isl_keep isl_ast_build *build);
6260 __isl_give isl_ast_build *isl_ast_build_copy(
6261 __isl_keep isl_ast_build *build);
6262 __isl_null isl_ast_build *isl_ast_build_free(
6263 __isl_take isl_ast_build *build);
6265 The C<set> argument is usually a parameter set with zero or more parameters.
6266 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6267 and L</"Fine-grained Control over AST Generation">.
6268 Finally, the AST itself can be constructed using the following
6271 #include <isl/ast_build.h>
6272 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6273 __isl_keep isl_ast_build *build,
6274 __isl_take isl_union_map *schedule);
6276 =head3 Inspecting the AST
6278 The basic properties of an AST node can be obtained as follows.
6280 #include <isl/ast.h>
6281 isl_ctx *isl_ast_node_get_ctx(
6282 __isl_keep isl_ast_node *node);
6283 enum isl_ast_node_type isl_ast_node_get_type(
6284 __isl_keep isl_ast_node *node);
6286 The type of an AST node is one of
6287 C<isl_ast_node_for>,
6289 C<isl_ast_node_block> or
6290 C<isl_ast_node_user>.
6291 An C<isl_ast_node_for> represents a for node.
6292 An C<isl_ast_node_if> represents an if node.
6293 An C<isl_ast_node_block> represents a compound node.
6294 An C<isl_ast_node_user> represents an expression statement.
6295 An expression statement typically corresponds to a domain element, i.e.,
6296 one of the elements that is visited by the AST.
6298 Each type of node has its own additional properties.
6300 #include <isl/ast.h>
6301 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6302 __isl_keep isl_ast_node *node);
6303 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6304 __isl_keep isl_ast_node *node);
6305 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6306 __isl_keep isl_ast_node *node);
6307 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6308 __isl_keep isl_ast_node *node);
6309 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6310 __isl_keep isl_ast_node *node);
6311 int isl_ast_node_for_is_degenerate(
6312 __isl_keep isl_ast_node *node);
6314 An C<isl_ast_for> is considered degenerate if it is known to execute
6317 #include <isl/ast.h>
6318 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6319 __isl_keep isl_ast_node *node);
6320 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6321 __isl_keep isl_ast_node *node);
6322 int isl_ast_node_if_has_else(
6323 __isl_keep isl_ast_node *node);
6324 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6325 __isl_keep isl_ast_node *node);
6327 __isl_give isl_ast_node_list *
6328 isl_ast_node_block_get_children(
6329 __isl_keep isl_ast_node *node);
6331 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6332 __isl_keep isl_ast_node *node);
6334 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6335 the following functions.
6337 #include <isl/ast.h>
6338 isl_ctx *isl_ast_expr_get_ctx(
6339 __isl_keep isl_ast_expr *expr);
6340 enum isl_ast_expr_type isl_ast_expr_get_type(
6341 __isl_keep isl_ast_expr *expr);
6343 The type of an AST expression is one of
6345 C<isl_ast_expr_id> or
6346 C<isl_ast_expr_int>.
6347 An C<isl_ast_expr_op> represents the result of an operation.
6348 An C<isl_ast_expr_id> represents an identifier.
6349 An C<isl_ast_expr_int> represents an integer value.
6351 Each type of expression has its own additional properties.
6353 #include <isl/ast.h>
6354 enum isl_ast_op_type isl_ast_expr_get_op_type(
6355 __isl_keep isl_ast_expr *expr);
6356 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6357 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6358 __isl_keep isl_ast_expr *expr, int pos);
6359 int isl_ast_node_foreach_ast_op_type(
6360 __isl_keep isl_ast_node *node,
6361 int (*fn)(enum isl_ast_op_type type, void *user),
6364 C<isl_ast_expr_get_op_type> returns the type of the operation
6365 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6366 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6368 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6369 C<isl_ast_op_type> that appears in C<node>.
6370 The operation type is one of the following.
6374 =item C<isl_ast_op_and>
6376 Logical I<and> of two arguments.
6377 Both arguments can be evaluated.
6379 =item C<isl_ast_op_and_then>
6381 Logical I<and> of two arguments.
6382 The second argument can only be evaluated if the first evaluates to true.
6384 =item C<isl_ast_op_or>
6386 Logical I<or> of two arguments.
6387 Both arguments can be evaluated.
6389 =item C<isl_ast_op_or_else>
6391 Logical I<or> of two arguments.
6392 The second argument can only be evaluated if the first evaluates to false.
6394 =item C<isl_ast_op_max>
6396 Maximum of two or more arguments.
6398 =item C<isl_ast_op_min>
6400 Minimum of two or more arguments.
6402 =item C<isl_ast_op_minus>
6406 =item C<isl_ast_op_add>
6408 Sum of two arguments.
6410 =item C<isl_ast_op_sub>
6412 Difference of two arguments.
6414 =item C<isl_ast_op_mul>
6416 Product of two arguments.
6418 =item C<isl_ast_op_div>
6420 Exact division. That is, the result is known to be an integer.
6422 =item C<isl_ast_op_fdiv_q>
6424 Result of integer division, rounded towards negative
6427 =item C<isl_ast_op_pdiv_q>
6429 Result of integer division, where dividend is known to be non-negative.
6431 =item C<isl_ast_op_pdiv_r>
6433 Remainder of integer division, where dividend is known to be non-negative.
6435 =item C<isl_ast_op_cond>
6437 Conditional operator defined on three arguments.
6438 If the first argument evaluates to true, then the result
6439 is equal to the second argument. Otherwise, the result
6440 is equal to the third argument.
6441 The second and third argument may only be evaluated if
6442 the first argument evaluates to true and false, respectively.
6443 Corresponds to C<a ? b : c> in C.
6445 =item C<isl_ast_op_select>
6447 Conditional operator defined on three arguments.
6448 If the first argument evaluates to true, then the result
6449 is equal to the second argument. Otherwise, the result
6450 is equal to the third argument.
6451 The second and third argument may be evaluated independently
6452 of the value of the first argument.
6453 Corresponds to C<a * b + (1 - a) * c> in C.
6455 =item C<isl_ast_op_eq>
6459 =item C<isl_ast_op_le>
6461 Less than or equal relation.
6463 =item C<isl_ast_op_lt>
6467 =item C<isl_ast_op_ge>
6469 Greater than or equal relation.
6471 =item C<isl_ast_op_gt>
6473 Greater than relation.
6475 =item C<isl_ast_op_call>
6478 The number of arguments of the C<isl_ast_expr> is one more than
6479 the number of arguments in the function call, the first argument
6480 representing the function being called.
6482 =item C<isl_ast_op_access>
6485 The number of arguments of the C<isl_ast_expr> is one more than
6486 the number of index expressions in the array access, the first argument
6487 representing the array being accessed.
6489 =item C<isl_ast_op_member>
6492 This operation has two arguments, a structure and the name of
6493 the member of the structure being accessed.
6497 #include <isl/ast.h>
6498 __isl_give isl_id *isl_ast_expr_get_id(
6499 __isl_keep isl_ast_expr *expr);
6501 Return the identifier represented by the AST expression.
6503 #include <isl/ast.h>
6504 __isl_give isl_val *isl_ast_expr_get_val(
6505 __isl_keep isl_ast_expr *expr);
6507 Return the integer represented by the AST expression.
6509 =head3 Properties of ASTs
6511 #include <isl/ast.h>
6512 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6513 __isl_keep isl_ast_expr *expr2);
6515 Check if two C<isl_ast_expr>s are equal to each other.
6517 =head3 Manipulating and printing the AST
6519 AST nodes can be copied and freed using the following functions.
6521 #include <isl/ast.h>
6522 __isl_give isl_ast_node *isl_ast_node_copy(
6523 __isl_keep isl_ast_node *node);
6524 __isl_null isl_ast_node *isl_ast_node_free(
6525 __isl_take isl_ast_node *node);
6527 AST expressions can be copied and freed using the following functions.
6529 #include <isl/ast.h>
6530 __isl_give isl_ast_expr *isl_ast_expr_copy(
6531 __isl_keep isl_ast_expr *expr);
6532 __isl_null isl_ast_expr *isl_ast_expr_free(
6533 __isl_take isl_ast_expr *expr);
6535 New AST expressions can be created either directly or within
6536 the context of an C<isl_ast_build>.
6538 #include <isl/ast.h>
6539 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6540 __isl_take isl_val *v);
6541 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6542 __isl_take isl_id *id);
6543 __isl_give isl_ast_expr *isl_ast_expr_neg(
6544 __isl_take isl_ast_expr *expr);
6545 __isl_give isl_ast_expr *isl_ast_expr_add(
6546 __isl_take isl_ast_expr *expr1,
6547 __isl_take isl_ast_expr *expr2);
6548 __isl_give isl_ast_expr *isl_ast_expr_sub(
6549 __isl_take isl_ast_expr *expr1,
6550 __isl_take isl_ast_expr *expr2);
6551 __isl_give isl_ast_expr *isl_ast_expr_mul(
6552 __isl_take isl_ast_expr *expr1,
6553 __isl_take isl_ast_expr *expr2);
6554 __isl_give isl_ast_expr *isl_ast_expr_div(
6555 __isl_take isl_ast_expr *expr1,
6556 __isl_take isl_ast_expr *expr2);
6557 __isl_give isl_ast_expr *isl_ast_expr_and(
6558 __isl_take isl_ast_expr *expr1,
6559 __isl_take isl_ast_expr *expr2)
6560 __isl_give isl_ast_expr *isl_ast_expr_or(
6561 __isl_take isl_ast_expr *expr1,
6562 __isl_take isl_ast_expr *expr2)
6563 __isl_give isl_ast_expr *isl_ast_expr_access(
6564 __isl_take isl_ast_expr *array,
6565 __isl_take isl_ast_expr_list *indices);
6567 #include <isl/ast_build.h>
6568 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6569 __isl_keep isl_ast_build *build,
6570 __isl_take isl_pw_aff *pa);
6571 __isl_give isl_ast_expr *
6572 isl_ast_build_access_from_pw_multi_aff(
6573 __isl_keep isl_ast_build *build,
6574 __isl_take isl_pw_multi_aff *pma);
6575 __isl_give isl_ast_expr *
6576 isl_ast_build_access_from_multi_pw_aff(
6577 __isl_keep isl_ast_build *build,
6578 __isl_take isl_multi_pw_aff *mpa);
6579 __isl_give isl_ast_expr *
6580 isl_ast_build_call_from_pw_multi_aff(
6581 __isl_keep isl_ast_build *build,
6582 __isl_take isl_pw_multi_aff *pma);
6583 __isl_give isl_ast_expr *
6584 isl_ast_build_call_from_multi_pw_aff(
6585 __isl_keep isl_ast_build *build,
6586 __isl_take isl_multi_pw_aff *mpa);
6588 The domains of C<pa>, C<mpa> and C<pma> should correspond
6589 to the schedule space of C<build>.
6590 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6591 the function being called.
6592 If the accessed space is a nested relation, then it is taken
6593 to represent an access of the member specified by the range
6594 of this nested relation of the structure specified by the domain
6595 of the nested relation.
6597 The following functions can be used to modify an C<isl_ast_expr>.
6599 #include <isl/ast.h>
6600 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6601 __isl_take isl_ast_expr *expr, int pos,
6602 __isl_take isl_ast_expr *arg);
6604 Replace the argument of C<expr> at position C<pos> by C<arg>.
6606 #include <isl/ast.h>
6607 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6608 __isl_take isl_ast_expr *expr,
6609 __isl_take isl_id_to_ast_expr *id2expr);
6611 The function C<isl_ast_expr_substitute_ids> replaces the
6612 subexpressions of C<expr> of type C<isl_ast_expr_id>
6613 by the corresponding expression in C<id2expr>, if there is any.
6616 User specified data can be attached to an C<isl_ast_node> and obtained
6617 from the same C<isl_ast_node> using the following functions.
6619 #include <isl/ast.h>
6620 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6621 __isl_take isl_ast_node *node,
6622 __isl_take isl_id *annotation);
6623 __isl_give isl_id *isl_ast_node_get_annotation(
6624 __isl_keep isl_ast_node *node);
6626 Basic printing can be performed using the following functions.
6628 #include <isl/ast.h>
6629 __isl_give isl_printer *isl_printer_print_ast_expr(
6630 __isl_take isl_printer *p,
6631 __isl_keep isl_ast_expr *expr);
6632 __isl_give isl_printer *isl_printer_print_ast_node(
6633 __isl_take isl_printer *p,
6634 __isl_keep isl_ast_node *node);
6636 More advanced printing can be performed using the following functions.
6638 #include <isl/ast.h>
6639 __isl_give isl_printer *isl_ast_op_type_print_macro(
6640 enum isl_ast_op_type type,
6641 __isl_take isl_printer *p);
6642 __isl_give isl_printer *isl_ast_node_print_macros(
6643 __isl_keep isl_ast_node *node,
6644 __isl_take isl_printer *p);
6645 __isl_give isl_printer *isl_ast_node_print(
6646 __isl_keep isl_ast_node *node,
6647 __isl_take isl_printer *p,
6648 __isl_take isl_ast_print_options *options);
6649 __isl_give isl_printer *isl_ast_node_for_print(
6650 __isl_keep isl_ast_node *node,
6651 __isl_take isl_printer *p,
6652 __isl_take isl_ast_print_options *options);
6653 __isl_give isl_printer *isl_ast_node_if_print(
6654 __isl_keep isl_ast_node *node,
6655 __isl_take isl_printer *p,
6656 __isl_take isl_ast_print_options *options);
6658 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6659 C<isl> may print out an AST that makes use of macros such
6660 as C<floord>, C<min> and C<max>.
6661 C<isl_ast_op_type_print_macro> prints out the macro
6662 corresponding to a specific C<isl_ast_op_type>.
6663 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6664 for expressions where these macros would be used and prints
6665 out the required macro definitions.
6666 Essentially, C<isl_ast_node_print_macros> calls
6667 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6668 as function argument.
6669 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6670 C<isl_ast_node_if_print> print an C<isl_ast_node>
6671 in C<ISL_FORMAT_C>, but allow for some extra control
6672 through an C<isl_ast_print_options> object.
6673 This object can be created using the following functions.
6675 #include <isl/ast.h>
6676 __isl_give isl_ast_print_options *
6677 isl_ast_print_options_alloc(isl_ctx *ctx);
6678 __isl_give isl_ast_print_options *
6679 isl_ast_print_options_copy(
6680 __isl_keep isl_ast_print_options *options);
6681 __isl_null isl_ast_print_options *
6682 isl_ast_print_options_free(
6683 __isl_take isl_ast_print_options *options);
6685 __isl_give isl_ast_print_options *
6686 isl_ast_print_options_set_print_user(
6687 __isl_take isl_ast_print_options *options,
6688 __isl_give isl_printer *(*print_user)(
6689 __isl_take isl_printer *p,
6690 __isl_take isl_ast_print_options *options,
6691 __isl_keep isl_ast_node *node, void *user),
6693 __isl_give isl_ast_print_options *
6694 isl_ast_print_options_set_print_for(
6695 __isl_take isl_ast_print_options *options,
6696 __isl_give isl_printer *(*print_for)(
6697 __isl_take isl_printer *p,
6698 __isl_take isl_ast_print_options *options,
6699 __isl_keep isl_ast_node *node, void *user),
6702 The callback set by C<isl_ast_print_options_set_print_user>
6703 is called whenever a node of type C<isl_ast_node_user> needs to
6705 The callback set by C<isl_ast_print_options_set_print_for>
6706 is called whenever a node of type C<isl_ast_node_for> needs to
6708 Note that C<isl_ast_node_for_print> will I<not> call the
6709 callback set by C<isl_ast_print_options_set_print_for> on the node
6710 on which C<isl_ast_node_for_print> is called, but only on nested
6711 nodes of type C<isl_ast_node_for>. It is therefore safe to
6712 call C<isl_ast_node_for_print> from within the callback set by
6713 C<isl_ast_print_options_set_print_for>.
6715 The following option determines the type to be used for iterators
6716 while printing the AST.
6718 int isl_options_set_ast_iterator_type(
6719 isl_ctx *ctx, const char *val);
6720 const char *isl_options_get_ast_iterator_type(
6725 #include <isl/ast_build.h>
6726 int isl_options_set_ast_build_atomic_upper_bound(
6727 isl_ctx *ctx, int val);
6728 int isl_options_get_ast_build_atomic_upper_bound(
6730 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6732 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6733 int isl_options_set_ast_build_exploit_nested_bounds(
6734 isl_ctx *ctx, int val);
6735 int isl_options_get_ast_build_exploit_nested_bounds(
6737 int isl_options_set_ast_build_group_coscheduled(
6738 isl_ctx *ctx, int val);
6739 int isl_options_get_ast_build_group_coscheduled(
6741 int isl_options_set_ast_build_scale_strides(
6742 isl_ctx *ctx, int val);
6743 int isl_options_get_ast_build_scale_strides(
6745 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6747 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6748 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6750 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6754 =item * ast_build_atomic_upper_bound
6756 Generate loop upper bounds that consist of the current loop iterator,
6757 an operator and an expression not involving the iterator.
6758 If this option is not set, then the current loop iterator may appear
6759 several times in the upper bound.
6760 For example, when this option is turned off, AST generation
6763 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6767 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6770 When the option is turned on, the following AST is generated
6772 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6775 =item * ast_build_prefer_pdiv
6777 If this option is turned off, then the AST generation will
6778 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6779 operators, but no C<isl_ast_op_pdiv_q> or
6780 C<isl_ast_op_pdiv_r> operators.
6781 If this options is turned on, then C<isl> will try to convert
6782 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6783 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6785 =item * ast_build_exploit_nested_bounds
6787 Simplify conditions based on bounds of nested for loops.
6788 In particular, remove conditions that are implied by the fact
6789 that one or more nested loops have at least one iteration,
6790 meaning that the upper bound is at least as large as the lower bound.
6791 For example, when this option is turned off, AST generation
6794 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6800 for (int c0 = 0; c0 <= N; c0 += 1)
6801 for (int c1 = 0; c1 <= M; c1 += 1)
6804 When the option is turned on, the following AST is generated
6806 for (int c0 = 0; c0 <= N; c0 += 1)
6807 for (int c1 = 0; c1 <= M; c1 += 1)
6810 =item * ast_build_group_coscheduled
6812 If two domain elements are assigned the same schedule point, then
6813 they may be executed in any order and they may even appear in different
6814 loops. If this options is set, then the AST generator will make
6815 sure that coscheduled domain elements do not appear in separate parts
6816 of the AST. This is useful in case of nested AST generation
6817 if the outer AST generation is given only part of a schedule
6818 and the inner AST generation should handle the domains that are
6819 coscheduled by this initial part of the schedule together.
6820 For example if an AST is generated for a schedule
6822 { A[i] -> [0]; B[i] -> [0] }
6824 then the C<isl_ast_build_set_create_leaf> callback described
6825 below may get called twice, once for each domain.
6826 Setting this option ensures that the callback is only called once
6827 on both domains together.
6829 =item * ast_build_separation_bounds
6831 This option specifies which bounds to use during separation.
6832 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6833 then all (possibly implicit) bounds on the current dimension will
6834 be used during separation.
6835 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6836 then only those bounds that are explicitly available will
6837 be used during separation.
6839 =item * ast_build_scale_strides
6841 This option specifies whether the AST generator is allowed
6842 to scale down iterators of strided loops.
6844 =item * ast_build_allow_else
6846 This option specifies whether the AST generator is allowed
6847 to construct if statements with else branches.
6849 =item * ast_build_allow_or
6851 This option specifies whether the AST generator is allowed
6852 to construct if conditions with disjunctions.
6856 =head3 Fine-grained Control over AST Generation
6858 Besides specifying the constraints on the parameters,
6859 an C<isl_ast_build> object can be used to control
6860 various aspects of the AST generation process.
6861 The most prominent way of control is through ``options'',
6862 which can be set using the following function.
6864 #include <isl/ast_build.h>
6865 __isl_give isl_ast_build *
6866 isl_ast_build_set_options(
6867 __isl_take isl_ast_build *control,
6868 __isl_take isl_union_map *options);
6870 The options are encoded in an <isl_union_map>.
6871 The domain of this union relation refers to the schedule domain,
6872 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6873 In the case of nested AST generation (see L</"Nested AST Generation">),
6874 the domain of C<options> should refer to the extra piece of the schedule.
6875 That is, it should be equal to the range of the wrapped relation in the
6876 range of the schedule.
6877 The range of the options can consist of elements in one or more spaces,
6878 the names of which determine the effect of the option.
6879 The values of the range typically also refer to the schedule dimension
6880 to which the option applies. In case of nested AST generation
6881 (see L</"Nested AST Generation">), these values refer to the position
6882 of the schedule dimension within the innermost AST generation.
6883 The constraints on the domain elements of
6884 the option should only refer to this dimension and earlier dimensions.
6885 We consider the following spaces.
6889 =item C<separation_class>
6891 This space is a wrapped relation between two one dimensional spaces.
6892 The input space represents the schedule dimension to which the option
6893 applies and the output space represents the separation class.
6894 While constructing a loop corresponding to the specified schedule
6895 dimension(s), the AST generator will try to generate separate loops
6896 for domain elements that are assigned different classes.
6897 If only some of the elements are assigned a class, then those elements
6898 that are not assigned any class will be treated as belonging to a class
6899 that is separate from the explicitly assigned classes.
6900 The typical use case for this option is to separate full tiles from
6902 The other options, described below, are applied after the separation
6905 As an example, consider the separation into full and partial tiles
6906 of a tiling of a triangular domain.
6907 Take, for example, the domain
6909 { A[i,j] : 0 <= i,j and i + j <= 100 }
6911 and a tiling into tiles of 10 by 10. The input to the AST generator
6912 is then the schedule
6914 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6917 Without any options, the following AST is generated
6919 for (int c0 = 0; c0 <= 10; c0 += 1)
6920 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6921 for (int c2 = 10 * c0;
6922 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6924 for (int c3 = 10 * c1;
6925 c3 <= min(10 * c1 + 9, -c2 + 100);
6929 Separation into full and partial tiles can be obtained by assigning
6930 a class, say C<0>, to the full tiles. The full tiles are represented by those
6931 values of the first and second schedule dimensions for which there are
6932 values of the third and fourth dimensions to cover an entire tile.
6933 That is, we need to specify the following option
6935 { [a,b,c,d] -> separation_class[[0]->[0]] :
6936 exists b': 0 <= 10a,10b' and
6937 10a+9+10b'+9 <= 100;
6938 [a,b,c,d] -> separation_class[[1]->[0]] :
6939 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6943 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6944 a >= 0 and b >= 0 and b <= 8 - a;
6945 [a, b, c, d] -> separation_class[[0] -> [0]] :
6948 With this option, the generated AST is as follows
6951 for (int c0 = 0; c0 <= 8; c0 += 1) {
6952 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6953 for (int c2 = 10 * c0;
6954 c2 <= 10 * c0 + 9; c2 += 1)
6955 for (int c3 = 10 * c1;
6956 c3 <= 10 * c1 + 9; c3 += 1)
6958 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6959 for (int c2 = 10 * c0;
6960 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6962 for (int c3 = 10 * c1;
6963 c3 <= min(-c2 + 100, 10 * c1 + 9);
6967 for (int c0 = 9; c0 <= 10; c0 += 1)
6968 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6969 for (int c2 = 10 * c0;
6970 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6972 for (int c3 = 10 * c1;
6973 c3 <= min(10 * c1 + 9, -c2 + 100);
6980 This is a single-dimensional space representing the schedule dimension(s)
6981 to which ``separation'' should be applied. Separation tries to split
6982 a loop into several pieces if this can avoid the generation of guards
6984 See also the C<atomic> option.
6988 This is a single-dimensional space representing the schedule dimension(s)
6989 for which the domains should be considered ``atomic''. That is, the
6990 AST generator will make sure that any given domain space will only appear
6991 in a single loop at the specified level.
6993 Consider the following schedule
6995 { a[i] -> [i] : 0 <= i < 10;
6996 b[i] -> [i+1] : 0 <= i < 10 }
6998 If the following option is specified
7000 { [i] -> separate[x] }
7002 then the following AST will be generated
7006 for (int c0 = 1; c0 <= 9; c0 += 1) {
7013 If, on the other hand, the following option is specified
7015 { [i] -> atomic[x] }
7017 then the following AST will be generated
7019 for (int c0 = 0; c0 <= 10; c0 += 1) {
7026 If neither C<atomic> nor C<separate> is specified, then the AST generator
7027 may produce either of these two results or some intermediate form.
7031 This is a single-dimensional space representing the schedule dimension(s)
7032 that should be I<completely> unrolled.
7033 To obtain a partial unrolling, the user should apply an additional
7034 strip-mining to the schedule and fully unroll the inner loop.
7038 Additional control is available through the following functions.
7040 #include <isl/ast_build.h>
7041 __isl_give isl_ast_build *
7042 isl_ast_build_set_iterators(
7043 __isl_take isl_ast_build *control,
7044 __isl_take isl_id_list *iterators);
7046 The function C<isl_ast_build_set_iterators> allows the user to
7047 specify a list of iterator C<isl_id>s to be used as iterators.
7048 If the input schedule is injective, then
7049 the number of elements in this list should be as large as the dimension
7050 of the schedule space, but no direct correspondence should be assumed
7051 between dimensions and elements.
7052 If the input schedule is not injective, then an additional number
7053 of C<isl_id>s equal to the largest dimension of the input domains
7055 If the number of provided C<isl_id>s is insufficient, then additional
7056 names are automatically generated.
7058 #include <isl/ast_build.h>
7059 __isl_give isl_ast_build *
7060 isl_ast_build_set_create_leaf(
7061 __isl_take isl_ast_build *control,
7062 __isl_give isl_ast_node *(*fn)(
7063 __isl_take isl_ast_build *build,
7064 void *user), void *user);
7067 C<isl_ast_build_set_create_leaf> function allows for the
7068 specification of a callback that should be called whenever the AST
7069 generator arrives at an element of the schedule domain.
7070 The callback should return an AST node that should be inserted
7071 at the corresponding position of the AST. The default action (when
7072 the callback is not set) is to continue generating parts of the AST to scan
7073 all the domain elements associated to the schedule domain element
7074 and to insert user nodes, ``calling'' the domain element, for each of them.
7075 The C<build> argument contains the current state of the C<isl_ast_build>.
7076 To ease nested AST generation (see L</"Nested AST Generation">),
7077 all control information that is
7078 specific to the current AST generation such as the options and
7079 the callbacks has been removed from this C<isl_ast_build>.
7080 The callback would typically return the result of a nested
7082 user defined node created using the following function.
7084 #include <isl/ast.h>
7085 __isl_give isl_ast_node *isl_ast_node_alloc_user(
7086 __isl_take isl_ast_expr *expr);
7088 #include <isl/ast_build.h>
7089 __isl_give isl_ast_build *
7090 isl_ast_build_set_at_each_domain(
7091 __isl_take isl_ast_build *build,
7092 __isl_give isl_ast_node *(*fn)(
7093 __isl_take isl_ast_node *node,
7094 __isl_keep isl_ast_build *build,
7095 void *user), void *user);
7096 __isl_give isl_ast_build *
7097 isl_ast_build_set_before_each_for(
7098 __isl_take isl_ast_build *build,
7099 __isl_give isl_id *(*fn)(
7100 __isl_keep isl_ast_build *build,
7101 void *user), void *user);
7102 __isl_give isl_ast_build *
7103 isl_ast_build_set_after_each_for(
7104 __isl_take isl_ast_build *build,
7105 __isl_give isl_ast_node *(*fn)(
7106 __isl_take isl_ast_node *node,
7107 __isl_keep isl_ast_build *build,
7108 void *user), void *user);
7110 The callback set by C<isl_ast_build_set_at_each_domain> will
7111 be called for each domain AST node.
7112 The callbacks set by C<isl_ast_build_set_before_each_for>
7113 and C<isl_ast_build_set_after_each_for> will be called
7114 for each for AST node. The first will be called in depth-first
7115 pre-order, while the second will be called in depth-first post-order.
7116 Since C<isl_ast_build_set_before_each_for> is called before the for
7117 node is actually constructed, it is only passed an C<isl_ast_build>.
7118 The returned C<isl_id> will be added as an annotation (using
7119 C<isl_ast_node_set_annotation>) to the constructed for node.
7120 In particular, if the user has also specified an C<after_each_for>
7121 callback, then the annotation can be retrieved from the node passed to
7122 that callback using C<isl_ast_node_get_annotation>.
7123 All callbacks should C<NULL> on failure.
7124 The given C<isl_ast_build> can be used to create new
7125 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
7126 or C<isl_ast_build_call_from_pw_multi_aff>.
7128 =head3 Nested AST Generation
7130 C<isl> allows the user to create an AST within the context
7131 of another AST. These nested ASTs are created using the
7132 same C<isl_ast_build_ast_from_schedule> function that is used to create the
7133 outer AST. The C<build> argument should be an C<isl_ast_build>
7134 passed to a callback set by
7135 C<isl_ast_build_set_create_leaf>.
7136 The space of the range of the C<schedule> argument should refer
7137 to this build. In particular, the space should be a wrapped
7138 relation and the domain of this wrapped relation should be the
7139 same as that of the range of the schedule returned by
7140 C<isl_ast_build_get_schedule> below.
7141 In practice, the new schedule is typically
7142 created by calling C<isl_union_map_range_product> on the old schedule
7143 and some extra piece of the schedule.
7144 The space of the schedule domain is also available from
7145 the C<isl_ast_build>.
7147 #include <isl/ast_build.h>
7148 __isl_give isl_union_map *isl_ast_build_get_schedule(
7149 __isl_keep isl_ast_build *build);
7150 __isl_give isl_space *isl_ast_build_get_schedule_space(
7151 __isl_keep isl_ast_build *build);
7152 __isl_give isl_ast_build *isl_ast_build_restrict(
7153 __isl_take isl_ast_build *build,
7154 __isl_take isl_set *set);
7156 The C<isl_ast_build_get_schedule> function returns a (partial)
7157 schedule for the domains elements for which part of the AST still needs to
7158 be generated in the current build.
7159 In particular, the domain elements are mapped to those iterations of the loops
7160 enclosing the current point of the AST generation inside which
7161 the domain elements are executed.
7162 No direct correspondence between
7163 the input schedule and this schedule should be assumed.
7164 The space obtained from C<isl_ast_build_get_schedule_space> can be used
7165 to create a set for C<isl_ast_build_restrict> to intersect
7166 with the current build. In particular, the set passed to
7167 C<isl_ast_build_restrict> can have additional parameters.
7168 The ids of the set dimensions in the space returned by
7169 C<isl_ast_build_get_schedule_space> correspond to the
7170 iterators of the already generated loops.
7171 The user should not rely on the ids of the output dimensions
7172 of the relations in the union relation returned by
7173 C<isl_ast_build_get_schedule> having any particular value.
7177 Although C<isl> is mainly meant to be used as a library,
7178 it also contains some basic applications that use some
7179 of the functionality of C<isl>.
7180 The input may be specified in either the L<isl format>
7181 or the L<PolyLib format>.
7183 =head2 C<isl_polyhedron_sample>
7185 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7186 an integer element of the polyhedron, if there is any.
7187 The first column in the output is the denominator and is always
7188 equal to 1. If the polyhedron contains no integer points,
7189 then a vector of length zero is printed.
7193 C<isl_pip> takes the same input as the C<example> program
7194 from the C<piplib> distribution, i.e., a set of constraints
7195 on the parameters, a line containing only -1 and finally a set
7196 of constraints on a parametric polyhedron.
7197 The coefficients of the parameters appear in the last columns
7198 (but before the final constant column).
7199 The output is the lexicographic minimum of the parametric polyhedron.
7200 As C<isl> currently does not have its own output format, the output
7201 is just a dump of the internal state.
7203 =head2 C<isl_polyhedron_minimize>
7205 C<isl_polyhedron_minimize> computes the minimum of some linear
7206 or affine objective function over the integer points in a polyhedron.
7207 If an affine objective function
7208 is given, then the constant should appear in the last column.
7210 =head2 C<isl_polytope_scan>
7212 Given a polytope, C<isl_polytope_scan> prints
7213 all integer points in the polytope.
7215 =head2 C<isl_codegen>
7217 Given a schedule, a context set and an options relation,
7218 C<isl_codegen> prints out an AST that scans the domain elements
7219 of the schedule in the order of their image(s) taking into account
7220 the constraints in the context set.