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);
1767 To check whether the description of a set or relation depends
1768 on one or more given dimensions, it is not necessary to iterate over all
1769 constraints. Instead the following functions can be used.
1771 int isl_basic_set_involves_dims(
1772 __isl_keep isl_basic_set *bset,
1773 enum isl_dim_type type, unsigned first, unsigned n);
1774 int isl_set_involves_dims(__isl_keep isl_set *set,
1775 enum isl_dim_type type, unsigned first, unsigned n);
1776 int isl_basic_map_involves_dims(
1777 __isl_keep isl_basic_map *bmap,
1778 enum isl_dim_type type, unsigned first, unsigned n);
1779 int isl_map_involves_dims(__isl_keep isl_map *map,
1780 enum isl_dim_type type, unsigned first, unsigned n);
1782 Similarly, the following functions can be used to check whether
1783 a given dimension is involved in any lower or upper bound.
1785 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1786 enum isl_dim_type type, unsigned pos);
1787 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1788 enum isl_dim_type type, unsigned pos);
1790 Note that these functions return true even if there is a bound on
1791 the dimension on only some of the basic sets of C<set>.
1792 To check if they have a bound for all of the basic sets in C<set>,
1793 use the following functions instead.
1795 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1796 enum isl_dim_type type, unsigned pos);
1797 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1798 enum isl_dim_type type, unsigned pos);
1800 The identifiers or names of the domain and range spaces of a set
1801 or relation can be read off or set using the following functions.
1803 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1804 __isl_take isl_basic_set *bset,
1805 __isl_take isl_id *id);
1806 __isl_give isl_set *isl_set_set_tuple_id(
1807 __isl_take isl_set *set, __isl_take isl_id *id);
1808 __isl_give isl_set *isl_set_reset_tuple_id(
1809 __isl_take isl_set *set);
1810 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1811 __isl_give isl_id *isl_set_get_tuple_id(
1812 __isl_keep isl_set *set);
1813 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1814 __isl_take isl_basic_map *bmap,
1815 enum isl_dim_type type, __isl_take isl_id *id);
1816 __isl_give isl_map *isl_map_set_tuple_id(
1817 __isl_take isl_map *map, enum isl_dim_type type,
1818 __isl_take isl_id *id);
1819 __isl_give isl_map *isl_map_reset_tuple_id(
1820 __isl_take isl_map *map, enum isl_dim_type type);
1821 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1822 enum isl_dim_type type);
1823 __isl_give isl_id *isl_map_get_tuple_id(
1824 __isl_keep isl_map *map, enum isl_dim_type type);
1826 const char *isl_basic_set_get_tuple_name(
1827 __isl_keep isl_basic_set *bset);
1828 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1829 __isl_take isl_basic_set *set, const char *s);
1830 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1831 const char *isl_set_get_tuple_name(
1832 __isl_keep isl_set *set);
1833 const char *isl_basic_map_get_tuple_name(
1834 __isl_keep isl_basic_map *bmap,
1835 enum isl_dim_type type);
1836 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1837 __isl_take isl_basic_map *bmap,
1838 enum isl_dim_type type, const char *s);
1839 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1840 enum isl_dim_type type);
1841 const char *isl_map_get_tuple_name(
1842 __isl_keep isl_map *map,
1843 enum isl_dim_type type);
1845 As with C<isl_space_get_tuple_name>, the value returned points to
1846 an internal data structure.
1847 The identifiers, positions or names of individual dimensions can be
1848 read off using the following functions.
1850 __isl_give isl_id *isl_basic_set_get_dim_id(
1851 __isl_keep isl_basic_set *bset,
1852 enum isl_dim_type type, unsigned pos);
1853 __isl_give isl_set *isl_set_set_dim_id(
1854 __isl_take isl_set *set, enum isl_dim_type type,
1855 unsigned pos, __isl_take isl_id *id);
1856 int isl_set_has_dim_id(__isl_keep isl_set *set,
1857 enum isl_dim_type type, unsigned pos);
1858 __isl_give isl_id *isl_set_get_dim_id(
1859 __isl_keep isl_set *set, enum isl_dim_type type,
1861 int isl_basic_map_has_dim_id(
1862 __isl_keep isl_basic_map *bmap,
1863 enum isl_dim_type type, unsigned pos);
1864 __isl_give isl_map *isl_map_set_dim_id(
1865 __isl_take isl_map *map, enum isl_dim_type type,
1866 unsigned pos, __isl_take isl_id *id);
1867 int isl_map_has_dim_id(__isl_keep isl_map *map,
1868 enum isl_dim_type type, unsigned pos);
1869 __isl_give isl_id *isl_map_get_dim_id(
1870 __isl_keep isl_map *map, enum isl_dim_type type,
1873 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1874 enum isl_dim_type type, __isl_keep isl_id *id);
1875 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1876 enum isl_dim_type type, __isl_keep isl_id *id);
1877 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1878 enum isl_dim_type type, const char *name);
1879 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1880 enum isl_dim_type type, const char *name);
1882 const char *isl_constraint_get_dim_name(
1883 __isl_keep isl_constraint *constraint,
1884 enum isl_dim_type type, unsigned pos);
1885 const char *isl_basic_set_get_dim_name(
1886 __isl_keep isl_basic_set *bset,
1887 enum isl_dim_type type, unsigned pos);
1888 int isl_set_has_dim_name(__isl_keep isl_set *set,
1889 enum isl_dim_type type, unsigned pos);
1890 const char *isl_set_get_dim_name(
1891 __isl_keep isl_set *set,
1892 enum isl_dim_type type, unsigned pos);
1893 const char *isl_basic_map_get_dim_name(
1894 __isl_keep isl_basic_map *bmap,
1895 enum isl_dim_type type, unsigned pos);
1896 int isl_map_has_dim_name(__isl_keep isl_map *map,
1897 enum isl_dim_type type, unsigned pos);
1898 const char *isl_map_get_dim_name(
1899 __isl_keep isl_map *map,
1900 enum isl_dim_type type, unsigned pos);
1902 These functions are mostly useful to obtain the identifiers, positions
1903 or names of the parameters. Identifiers of individual dimensions are
1904 essentially only useful for printing. They are ignored by all other
1905 operations and may not be preserved across those operations.
1907 The user pointers on all parameters and tuples can be reset
1908 using the following functions.
1910 #include <isl/set.h>
1911 __isl_give isl_set *isl_set_reset_user(
1912 __isl_take isl_set *set);
1913 #include <isl/map.h>
1914 __isl_give isl_map *isl_map_reset_user(
1915 __isl_take isl_map *map);
1916 #include <isl/union_set.h>
1917 __isl_give isl_union_set *isl_union_set_reset_user(
1918 __isl_take isl_union_set *uset);
1919 #include <isl/union_map.h>
1920 __isl_give isl_union_map *isl_union_map_reset_user(
1921 __isl_take isl_union_map *umap);
1925 =head3 Unary Properties
1931 The following functions test whether the given set or relation
1932 contains any integer points. The ``plain'' variants do not perform
1933 any computations, but simply check if the given set or relation
1934 is already known to be empty.
1936 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1937 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1938 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1939 int isl_set_is_empty(__isl_keep isl_set *set);
1940 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1941 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1942 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1943 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1944 int isl_map_is_empty(__isl_keep isl_map *map);
1945 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1947 =item * Universality
1949 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1950 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1951 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1953 =item * Single-valuedness
1955 int isl_basic_map_is_single_valued(
1956 __isl_keep isl_basic_map *bmap);
1957 int isl_map_plain_is_single_valued(
1958 __isl_keep isl_map *map);
1959 int isl_map_is_single_valued(__isl_keep isl_map *map);
1960 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1964 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1965 int isl_map_is_injective(__isl_keep isl_map *map);
1966 int isl_union_map_plain_is_injective(
1967 __isl_keep isl_union_map *umap);
1968 int isl_union_map_is_injective(
1969 __isl_keep isl_union_map *umap);
1973 int isl_map_is_bijective(__isl_keep isl_map *map);
1974 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1978 __isl_give isl_val *
1979 isl_basic_map_plain_get_val_if_fixed(
1980 __isl_keep isl_basic_map *bmap,
1981 enum isl_dim_type type, unsigned pos);
1982 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
1983 __isl_keep isl_set *set,
1984 enum isl_dim_type type, unsigned pos);
1985 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
1986 __isl_keep isl_map *map,
1987 enum isl_dim_type type, unsigned pos);
1989 If the set or relation obviously lies on a hyperplane where the given dimension
1990 has a fixed value, then return that value.
1991 Otherwise return NaN.
1995 int isl_set_dim_residue_class_val(
1996 __isl_keep isl_set *set,
1997 int pos, __isl_give isl_val **modulo,
1998 __isl_give isl_val **residue);
2000 Check if the values of the given set dimension are equal to a fixed
2001 value modulo some integer value. If so, assign the modulo to C<*modulo>
2002 and the fixed value to C<*residue>. If the given dimension attains only
2003 a single value, then assign C<0> to C<*modulo> and the fixed value to
2005 If the dimension does not attain only a single value and if no modulo
2006 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
2010 To check whether a set is a parameter domain, use this function:
2012 int isl_set_is_params(__isl_keep isl_set *set);
2013 int isl_union_set_is_params(
2014 __isl_keep isl_union_set *uset);
2018 The following functions check whether the space of the given
2019 (basic) set or relation range is a wrapped relation.
2021 #include <isl/space.h>
2022 int isl_space_is_wrapping(
2023 __isl_keep isl_space *space);
2024 int isl_space_domain_is_wrapping(
2025 __isl_keep isl_space *space);
2026 int isl_space_range_is_wrapping(
2027 __isl_keep isl_space *space);
2029 #include <isl/set.h>
2030 int isl_basic_set_is_wrapping(
2031 __isl_keep isl_basic_set *bset);
2032 int isl_set_is_wrapping(__isl_keep isl_set *set);
2034 #include <isl/map.h>
2035 int isl_map_domain_is_wrapping(
2036 __isl_keep isl_map *map);
2037 int isl_map_range_is_wrapping(
2038 __isl_keep isl_map *map);
2040 The input to C<isl_space_is_wrapping> should
2041 be the space of a set, while that of
2042 C<isl_space_domain_is_wrapping> and
2043 C<isl_space_range_is_wrapping> should be the space of a relation.
2045 =item * Internal Product
2047 int isl_basic_map_can_zip(
2048 __isl_keep isl_basic_map *bmap);
2049 int isl_map_can_zip(__isl_keep isl_map *map);
2051 Check whether the product of domain and range of the given relation
2053 i.e., whether both domain and range are nested relations.
2057 int isl_basic_map_can_curry(
2058 __isl_keep isl_basic_map *bmap);
2059 int isl_map_can_curry(__isl_keep isl_map *map);
2061 Check whether the domain of the (basic) relation is a wrapped relation.
2063 int isl_basic_map_can_uncurry(
2064 __isl_keep isl_basic_map *bmap);
2065 int isl_map_can_uncurry(__isl_keep isl_map *map);
2067 Check whether the range of the (basic) relation is a wrapped relation.
2071 =head3 Binary Properties
2077 int isl_basic_set_plain_is_equal(
2078 __isl_keep isl_basic_set *bset1,
2079 __isl_keep isl_basic_set *bset2);
2080 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2081 __isl_keep isl_set *set2);
2082 int isl_set_is_equal(__isl_keep isl_set *set1,
2083 __isl_keep isl_set *set2);
2084 int isl_union_set_is_equal(
2085 __isl_keep isl_union_set *uset1,
2086 __isl_keep isl_union_set *uset2);
2087 int isl_basic_map_is_equal(
2088 __isl_keep isl_basic_map *bmap1,
2089 __isl_keep isl_basic_map *bmap2);
2090 int isl_map_is_equal(__isl_keep isl_map *map1,
2091 __isl_keep isl_map *map2);
2092 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2093 __isl_keep isl_map *map2);
2094 int isl_union_map_is_equal(
2095 __isl_keep isl_union_map *umap1,
2096 __isl_keep isl_union_map *umap2);
2098 =item * Disjointness
2100 int isl_basic_set_is_disjoint(
2101 __isl_keep isl_basic_set *bset1,
2102 __isl_keep isl_basic_set *bset2);
2103 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2104 __isl_keep isl_set *set2);
2105 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2106 __isl_keep isl_set *set2);
2107 int isl_basic_map_is_disjoint(
2108 __isl_keep isl_basic_map *bmap1,
2109 __isl_keep isl_basic_map *bmap2);
2110 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2111 __isl_keep isl_map *map2);
2115 int isl_basic_set_is_subset(
2116 __isl_keep isl_basic_set *bset1,
2117 __isl_keep isl_basic_set *bset2);
2118 int isl_set_is_subset(__isl_keep isl_set *set1,
2119 __isl_keep isl_set *set2);
2120 int isl_set_is_strict_subset(
2121 __isl_keep isl_set *set1,
2122 __isl_keep isl_set *set2);
2123 int isl_union_set_is_subset(
2124 __isl_keep isl_union_set *uset1,
2125 __isl_keep isl_union_set *uset2);
2126 int isl_union_set_is_strict_subset(
2127 __isl_keep isl_union_set *uset1,
2128 __isl_keep isl_union_set *uset2);
2129 int isl_basic_map_is_subset(
2130 __isl_keep isl_basic_map *bmap1,
2131 __isl_keep isl_basic_map *bmap2);
2132 int isl_basic_map_is_strict_subset(
2133 __isl_keep isl_basic_map *bmap1,
2134 __isl_keep isl_basic_map *bmap2);
2135 int isl_map_is_subset(
2136 __isl_keep isl_map *map1,
2137 __isl_keep isl_map *map2);
2138 int isl_map_is_strict_subset(
2139 __isl_keep isl_map *map1,
2140 __isl_keep isl_map *map2);
2141 int isl_union_map_is_subset(
2142 __isl_keep isl_union_map *umap1,
2143 __isl_keep isl_union_map *umap2);
2144 int isl_union_map_is_strict_subset(
2145 __isl_keep isl_union_map *umap1,
2146 __isl_keep isl_union_map *umap2);
2148 Check whether the first argument is a (strict) subset of the
2153 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2154 __isl_keep isl_set *set2);
2156 This function is useful for sorting C<isl_set>s.
2157 The order depends on the internal representation of the inputs.
2158 The order is fixed over different calls to the function (assuming
2159 the internal representation of the inputs has not changed), but may
2160 change over different versions of C<isl>.
2164 =head2 Unary Operations
2170 __isl_give isl_set *isl_set_complement(
2171 __isl_take isl_set *set);
2172 __isl_give isl_map *isl_map_complement(
2173 __isl_take isl_map *map);
2177 __isl_give isl_basic_map *isl_basic_map_reverse(
2178 __isl_take isl_basic_map *bmap);
2179 __isl_give isl_map *isl_map_reverse(
2180 __isl_take isl_map *map);
2181 __isl_give isl_union_map *isl_union_map_reverse(
2182 __isl_take isl_union_map *umap);
2186 #include <isl/local_space.h>
2187 __isl_give isl_local_space *isl_local_space_domain(
2188 __isl_take isl_local_space *ls);
2189 __isl_give isl_local_space *isl_local_space_range(
2190 __isl_take isl_local_space *ls);
2192 #include <isl/set.h>
2193 __isl_give isl_basic_set *isl_basic_set_project_out(
2194 __isl_take isl_basic_set *bset,
2195 enum isl_dim_type type, unsigned first, unsigned n);
2196 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2197 enum isl_dim_type type, unsigned first, unsigned n);
2198 __isl_give isl_basic_set *isl_basic_set_params(
2199 __isl_take isl_basic_set *bset);
2200 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2202 #include <isl/map.h>
2203 __isl_give isl_basic_map *isl_basic_map_project_out(
2204 __isl_take isl_basic_map *bmap,
2205 enum isl_dim_type type, unsigned first, unsigned n);
2206 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2207 enum isl_dim_type type, unsigned first, unsigned n);
2208 __isl_give isl_basic_set *isl_basic_map_domain(
2209 __isl_take isl_basic_map *bmap);
2210 __isl_give isl_basic_set *isl_basic_map_range(
2211 __isl_take isl_basic_map *bmap);
2212 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2213 __isl_give isl_set *isl_map_domain(
2214 __isl_take isl_map *bmap);
2215 __isl_give isl_set *isl_map_range(
2216 __isl_take isl_map *map);
2218 #include <isl/union_set.h>
2219 __isl_give isl_set *isl_union_set_params(
2220 __isl_take isl_union_set *uset);
2222 #include <isl/union_map.h>
2223 __isl_give isl_union_map *isl_union_map_project_out(
2224 __isl_take isl_union_map *umap,
2225 enum isl_dim_type type, unsigned first, unsigned n);
2226 __isl_give isl_set *isl_union_map_params(
2227 __isl_take isl_union_map *umap);
2228 __isl_give isl_union_set *isl_union_map_domain(
2229 __isl_take isl_union_map *umap);
2230 __isl_give isl_union_set *isl_union_map_range(
2231 __isl_take isl_union_map *umap);
2233 The function C<isl_union_map_project_out> can only project out
2236 #include <isl/map.h>
2237 __isl_give isl_basic_map *isl_basic_map_domain_map(
2238 __isl_take isl_basic_map *bmap);
2239 __isl_give isl_basic_map *isl_basic_map_range_map(
2240 __isl_take isl_basic_map *bmap);
2241 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2242 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2244 #include <isl/union_map.h>
2245 __isl_give isl_union_map *isl_union_map_domain_map(
2246 __isl_take isl_union_map *umap);
2247 __isl_give isl_union_map *isl_union_map_range_map(
2248 __isl_take isl_union_map *umap);
2250 The functions above construct a (basic, regular or union) relation
2251 that maps (a wrapped version of) the input relation to its domain or range.
2255 __isl_give isl_basic_set *isl_basic_set_eliminate(
2256 __isl_take isl_basic_set *bset,
2257 enum isl_dim_type type,
2258 unsigned first, unsigned n);
2259 __isl_give isl_set *isl_set_eliminate(
2260 __isl_take isl_set *set, enum isl_dim_type type,
2261 unsigned first, unsigned n);
2262 __isl_give isl_basic_map *isl_basic_map_eliminate(
2263 __isl_take isl_basic_map *bmap,
2264 enum isl_dim_type type,
2265 unsigned first, unsigned n);
2266 __isl_give isl_map *isl_map_eliminate(
2267 __isl_take isl_map *map, enum isl_dim_type type,
2268 unsigned first, unsigned n);
2270 Eliminate the coefficients for the given dimensions from the constraints,
2271 without removing the dimensions.
2273 =item * Constructing a relation from a set
2275 #include <isl/local_space.h>
2276 __isl_give isl_local_space *isl_local_space_from_domain(
2277 __isl_take isl_local_space *ls);
2279 #include <isl/map.h>
2280 __isl_give isl_map *isl_map_from_domain(
2281 __isl_take isl_set *set);
2282 __isl_give isl_map *isl_map_from_range(
2283 __isl_take isl_set *set);
2285 Create a relation with the given set as domain or range.
2286 The range or domain of the created relation is a zero-dimensional
2287 flat anonymous space.
2291 __isl_give isl_basic_set *isl_basic_set_fix_si(
2292 __isl_take isl_basic_set *bset,
2293 enum isl_dim_type type, unsigned pos, int value);
2294 __isl_give isl_basic_set *isl_basic_set_fix_val(
2295 __isl_take isl_basic_set *bset,
2296 enum isl_dim_type type, unsigned pos,
2297 __isl_take isl_val *v);
2298 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2299 enum isl_dim_type type, unsigned pos, int value);
2300 __isl_give isl_set *isl_set_fix_val(
2301 __isl_take isl_set *set,
2302 enum isl_dim_type type, unsigned pos,
2303 __isl_take isl_val *v);
2304 __isl_give isl_basic_map *isl_basic_map_fix_si(
2305 __isl_take isl_basic_map *bmap,
2306 enum isl_dim_type type, unsigned pos, int value);
2307 __isl_give isl_basic_map *isl_basic_map_fix_val(
2308 __isl_take isl_basic_map *bmap,
2309 enum isl_dim_type type, unsigned pos,
2310 __isl_take isl_val *v);
2311 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2312 enum isl_dim_type type, unsigned pos, int value);
2313 __isl_give isl_map *isl_map_fix_val(
2314 __isl_take isl_map *map,
2315 enum isl_dim_type type, unsigned pos,
2316 __isl_take isl_val *v);
2318 Intersect the set or relation with the hyperplane where the given
2319 dimension has the fixed given value.
2321 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2322 __isl_take isl_basic_map *bmap,
2323 enum isl_dim_type type, unsigned pos, int value);
2324 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2325 __isl_take isl_basic_map *bmap,
2326 enum isl_dim_type type, unsigned pos, int value);
2327 __isl_give isl_set *isl_set_lower_bound_si(
2328 __isl_take isl_set *set,
2329 enum isl_dim_type type, unsigned pos, int value);
2330 __isl_give isl_set *isl_set_lower_bound_val(
2331 __isl_take isl_set *set,
2332 enum isl_dim_type type, unsigned pos,
2333 __isl_take isl_val *value);
2334 __isl_give isl_map *isl_map_lower_bound_si(
2335 __isl_take isl_map *map,
2336 enum isl_dim_type type, unsigned pos, int value);
2337 __isl_give isl_set *isl_set_upper_bound_si(
2338 __isl_take isl_set *set,
2339 enum isl_dim_type type, unsigned pos, int value);
2340 __isl_give isl_set *isl_set_upper_bound_val(
2341 __isl_take isl_set *set,
2342 enum isl_dim_type type, unsigned pos,
2343 __isl_take isl_val *value);
2344 __isl_give isl_map *isl_map_upper_bound_si(
2345 __isl_take isl_map *map,
2346 enum isl_dim_type type, unsigned pos, int value);
2348 Intersect the set or relation with the half-space where the given
2349 dimension has a value bounded by the fixed given integer value.
2351 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2352 enum isl_dim_type type1, int pos1,
2353 enum isl_dim_type type2, int pos2);
2354 __isl_give isl_basic_map *isl_basic_map_equate(
2355 __isl_take isl_basic_map *bmap,
2356 enum isl_dim_type type1, int pos1,
2357 enum isl_dim_type type2, int pos2);
2358 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2359 enum isl_dim_type type1, int pos1,
2360 enum isl_dim_type type2, int pos2);
2362 Intersect the set or relation with the hyperplane where the given
2363 dimensions are equal to each other.
2365 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2366 enum isl_dim_type type1, int pos1,
2367 enum isl_dim_type type2, int pos2);
2369 Intersect the relation with the hyperplane where the given
2370 dimensions have opposite values.
2372 __isl_give isl_map *isl_map_order_le(
2373 __isl_take isl_map *map,
2374 enum isl_dim_type type1, int pos1,
2375 enum isl_dim_type type2, int pos2);
2376 __isl_give isl_basic_map *isl_basic_map_order_ge(
2377 __isl_take isl_basic_map *bmap,
2378 enum isl_dim_type type1, int pos1,
2379 enum isl_dim_type type2, int pos2);
2380 __isl_give isl_map *isl_map_order_ge(
2381 __isl_take isl_map *map,
2382 enum isl_dim_type type1, int pos1,
2383 enum isl_dim_type type2, int pos2);
2384 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2385 enum isl_dim_type type1, int pos1,
2386 enum isl_dim_type type2, int pos2);
2387 __isl_give isl_basic_map *isl_basic_map_order_gt(
2388 __isl_take isl_basic_map *bmap,
2389 enum isl_dim_type type1, int pos1,
2390 enum isl_dim_type type2, int pos2);
2391 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2392 enum isl_dim_type type1, int pos1,
2393 enum isl_dim_type type2, int pos2);
2395 Intersect the relation with the half-space where the given
2396 dimensions satisfy the given ordering.
2400 __isl_give isl_map *isl_set_identity(
2401 __isl_take isl_set *set);
2402 __isl_give isl_union_map *isl_union_set_identity(
2403 __isl_take isl_union_set *uset);
2405 Construct an identity relation on the given (union) set.
2409 __isl_give isl_basic_set *isl_basic_map_deltas(
2410 __isl_take isl_basic_map *bmap);
2411 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2412 __isl_give isl_union_set *isl_union_map_deltas(
2413 __isl_take isl_union_map *umap);
2415 These functions return a (basic) set containing the differences
2416 between image elements and corresponding domain elements in the input.
2418 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2419 __isl_take isl_basic_map *bmap);
2420 __isl_give isl_map *isl_map_deltas_map(
2421 __isl_take isl_map *map);
2422 __isl_give isl_union_map *isl_union_map_deltas_map(
2423 __isl_take isl_union_map *umap);
2425 The functions above construct a (basic, regular or union) relation
2426 that maps (a wrapped version of) the input relation to its delta set.
2430 Simplify the representation of a set or relation by trying
2431 to combine pairs of basic sets or relations into a single
2432 basic set or relation.
2434 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2435 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2436 __isl_give isl_union_set *isl_union_set_coalesce(
2437 __isl_take isl_union_set *uset);
2438 __isl_give isl_union_map *isl_union_map_coalesce(
2439 __isl_take isl_union_map *umap);
2441 One of the methods for combining pairs of basic sets or relations
2442 can result in coefficients that are much larger than those that appear
2443 in the constraints of the input. By default, the coefficients are
2444 not allowed to grow larger, but this can be changed by unsetting
2445 the following option.
2447 int isl_options_set_coalesce_bounded_wrapping(
2448 isl_ctx *ctx, int val);
2449 int isl_options_get_coalesce_bounded_wrapping(
2452 =item * Detecting equalities
2454 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2455 __isl_take isl_basic_set *bset);
2456 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2457 __isl_take isl_basic_map *bmap);
2458 __isl_give isl_set *isl_set_detect_equalities(
2459 __isl_take isl_set *set);
2460 __isl_give isl_map *isl_map_detect_equalities(
2461 __isl_take isl_map *map);
2462 __isl_give isl_union_set *isl_union_set_detect_equalities(
2463 __isl_take isl_union_set *uset);
2464 __isl_give isl_union_map *isl_union_map_detect_equalities(
2465 __isl_take isl_union_map *umap);
2467 Simplify the representation of a set or relation by detecting implicit
2470 =item * Removing redundant constraints
2472 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2473 __isl_take isl_basic_set *bset);
2474 __isl_give isl_set *isl_set_remove_redundancies(
2475 __isl_take isl_set *set);
2476 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2477 __isl_take isl_basic_map *bmap);
2478 __isl_give isl_map *isl_map_remove_redundancies(
2479 __isl_take isl_map *map);
2483 __isl_give isl_basic_set *isl_set_convex_hull(
2484 __isl_take isl_set *set);
2485 __isl_give isl_basic_map *isl_map_convex_hull(
2486 __isl_take isl_map *map);
2488 If the input set or relation has any existentially quantified
2489 variables, then the result of these operations is currently undefined.
2493 __isl_give isl_basic_set *
2494 isl_set_unshifted_simple_hull(
2495 __isl_take isl_set *set);
2496 __isl_give isl_basic_map *
2497 isl_map_unshifted_simple_hull(
2498 __isl_take isl_map *map);
2499 __isl_give isl_basic_set *isl_set_simple_hull(
2500 __isl_take isl_set *set);
2501 __isl_give isl_basic_map *isl_map_simple_hull(
2502 __isl_take isl_map *map);
2503 __isl_give isl_union_map *isl_union_map_simple_hull(
2504 __isl_take isl_union_map *umap);
2506 These functions compute a single basic set or relation
2507 that contains the whole input set or relation.
2508 In particular, the output is described by translates
2509 of the constraints describing the basic sets or relations in the input.
2510 In case of C<isl_set_unshifted_simple_hull>, only the original
2511 constraints are used, without any translation.
2515 (See \autoref{s:simple hull}.)
2521 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2522 __isl_take isl_basic_set *bset);
2523 __isl_give isl_basic_set *isl_set_affine_hull(
2524 __isl_take isl_set *set);
2525 __isl_give isl_union_set *isl_union_set_affine_hull(
2526 __isl_take isl_union_set *uset);
2527 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2528 __isl_take isl_basic_map *bmap);
2529 __isl_give isl_basic_map *isl_map_affine_hull(
2530 __isl_take isl_map *map);
2531 __isl_give isl_union_map *isl_union_map_affine_hull(
2532 __isl_take isl_union_map *umap);
2534 In case of union sets and relations, the affine hull is computed
2537 =item * Polyhedral hull
2539 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2540 __isl_take isl_set *set);
2541 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2542 __isl_take isl_map *map);
2543 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2544 __isl_take isl_union_set *uset);
2545 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2546 __isl_take isl_union_map *umap);
2548 These functions compute a single basic set or relation
2549 not involving any existentially quantified variables
2550 that contains the whole input set or relation.
2551 In case of union sets and relations, the polyhedral hull is computed
2554 =item * Other approximations
2556 __isl_give isl_basic_set *
2557 isl_basic_set_drop_constraints_involving_dims(
2558 __isl_take isl_basic_set *bset,
2559 enum isl_dim_type type,
2560 unsigned first, unsigned n);
2561 __isl_give isl_basic_map *
2562 isl_basic_map_drop_constraints_involving_dims(
2563 __isl_take isl_basic_map *bmap,
2564 enum isl_dim_type type,
2565 unsigned first, unsigned n);
2566 __isl_give isl_basic_set *
2567 isl_basic_set_drop_constraints_not_involving_dims(
2568 __isl_take isl_basic_set *bset,
2569 enum isl_dim_type type,
2570 unsigned first, unsigned n);
2571 __isl_give isl_set *
2572 isl_set_drop_constraints_involving_dims(
2573 __isl_take isl_set *set,
2574 enum isl_dim_type type,
2575 unsigned first, unsigned n);
2576 __isl_give isl_map *
2577 isl_map_drop_constraints_involving_dims(
2578 __isl_take isl_map *map,
2579 enum isl_dim_type type,
2580 unsigned first, unsigned n);
2582 These functions drop any constraints (not) involving the specified dimensions.
2583 Note that the result depends on the representation of the input.
2587 __isl_give isl_basic_set *isl_basic_set_sample(
2588 __isl_take isl_basic_set *bset);
2589 __isl_give isl_basic_set *isl_set_sample(
2590 __isl_take isl_set *set);
2591 __isl_give isl_basic_map *isl_basic_map_sample(
2592 __isl_take isl_basic_map *bmap);
2593 __isl_give isl_basic_map *isl_map_sample(
2594 __isl_take isl_map *map);
2596 If the input (basic) set or relation is non-empty, then return
2597 a singleton subset of the input. Otherwise, return an empty set.
2599 =item * Optimization
2601 #include <isl/ilp.h>
2602 __isl_give isl_val *isl_basic_set_max_val(
2603 __isl_keep isl_basic_set *bset,
2604 __isl_keep isl_aff *obj);
2605 __isl_give isl_val *isl_set_min_val(
2606 __isl_keep isl_set *set,
2607 __isl_keep isl_aff *obj);
2608 __isl_give isl_val *isl_set_max_val(
2609 __isl_keep isl_set *set,
2610 __isl_keep isl_aff *obj);
2612 Compute the minimum or maximum of the integer affine expression C<obj>
2613 over the points in C<set>, returning the result in C<opt>.
2614 The result is C<NULL> in case of an error, the optimal value in case
2615 there is one, negative infinity or infinity if the problem is unbounded and
2616 NaN if the problem is empty.
2618 =item * Parametric optimization
2620 __isl_give isl_pw_aff *isl_set_dim_min(
2621 __isl_take isl_set *set, int pos);
2622 __isl_give isl_pw_aff *isl_set_dim_max(
2623 __isl_take isl_set *set, int pos);
2624 __isl_give isl_pw_aff *isl_map_dim_max(
2625 __isl_take isl_map *map, int pos);
2627 Compute the minimum or maximum of the given set or output dimension
2628 as a function of the parameters (and input dimensions), but independently
2629 of the other set or output dimensions.
2630 For lexicographic optimization, see L<"Lexicographic Optimization">.
2634 The following functions compute either the set of (rational) coefficient
2635 values of valid constraints for the given set or the set of (rational)
2636 values satisfying the constraints with coefficients from the given set.
2637 Internally, these two sets of functions perform essentially the
2638 same operations, except that the set of coefficients is assumed to
2639 be a cone, while the set of values may be any polyhedron.
2640 The current implementation is based on the Farkas lemma and
2641 Fourier-Motzkin elimination, but this may change or be made optional
2642 in future. In particular, future implementations may use different
2643 dualization algorithms or skip the elimination step.
2645 __isl_give isl_basic_set *isl_basic_set_coefficients(
2646 __isl_take isl_basic_set *bset);
2647 __isl_give isl_basic_set *isl_set_coefficients(
2648 __isl_take isl_set *set);
2649 __isl_give isl_union_set *isl_union_set_coefficients(
2650 __isl_take isl_union_set *bset);
2651 __isl_give isl_basic_set *isl_basic_set_solutions(
2652 __isl_take isl_basic_set *bset);
2653 __isl_give isl_basic_set *isl_set_solutions(
2654 __isl_take isl_set *set);
2655 __isl_give isl_union_set *isl_union_set_solutions(
2656 __isl_take isl_union_set *bset);
2660 __isl_give isl_map *isl_map_fixed_power_val(
2661 __isl_take isl_map *map,
2662 __isl_take isl_val *exp);
2663 __isl_give isl_union_map *
2664 isl_union_map_fixed_power_val(
2665 __isl_take isl_union_map *umap,
2666 __isl_take isl_val *exp);
2668 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2669 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2670 of C<map> is computed.
2672 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2674 __isl_give isl_union_map *isl_union_map_power(
2675 __isl_take isl_union_map *umap, int *exact);
2677 Compute a parametric representation for all positive powers I<k> of C<map>.
2678 The result maps I<k> to a nested relation corresponding to the
2679 I<k>th power of C<map>.
2680 The result may be an overapproximation. If the result is known to be exact,
2681 then C<*exact> is set to C<1>.
2683 =item * Transitive closure
2685 __isl_give isl_map *isl_map_transitive_closure(
2686 __isl_take isl_map *map, int *exact);
2687 __isl_give isl_union_map *isl_union_map_transitive_closure(
2688 __isl_take isl_union_map *umap, int *exact);
2690 Compute the transitive closure of C<map>.
2691 The result may be an overapproximation. If the result is known to be exact,
2692 then C<*exact> is set to C<1>.
2694 =item * Reaching path lengths
2696 __isl_give isl_map *isl_map_reaching_path_lengths(
2697 __isl_take isl_map *map, int *exact);
2699 Compute a relation that maps each element in the range of C<map>
2700 to the lengths of all paths composed of edges in C<map> that
2701 end up in the given element.
2702 The result may be an overapproximation. If the result is known to be exact,
2703 then C<*exact> is set to C<1>.
2704 To compute the I<maximal> path length, the resulting relation
2705 should be postprocessed by C<isl_map_lexmax>.
2706 In particular, if the input relation is a dependence relation
2707 (mapping sources to sinks), then the maximal path length corresponds
2708 to the free schedule.
2709 Note, however, that C<isl_map_lexmax> expects the maximum to be
2710 finite, so if the path lengths are unbounded (possibly due to
2711 the overapproximation), then you will get an error message.
2715 #include <isl/space.h>
2716 __isl_give isl_space *isl_space_wrap(
2717 __isl_take isl_space *space);
2718 __isl_give isl_space *isl_space_unwrap(
2719 __isl_take isl_space *space);
2721 #include <isl/set.h>
2722 __isl_give isl_basic_map *isl_basic_set_unwrap(
2723 __isl_take isl_basic_set *bset);
2724 __isl_give isl_map *isl_set_unwrap(
2725 __isl_take isl_set *set);
2727 #include <isl/map.h>
2728 __isl_give isl_basic_set *isl_basic_map_wrap(
2729 __isl_take isl_basic_map *bmap);
2730 __isl_give isl_set *isl_map_wrap(
2731 __isl_take isl_map *map);
2733 #include <isl/union_set.h>
2734 __isl_give isl_union_map *isl_union_set_unwrap(
2735 __isl_take isl_union_set *uset);
2737 #include <isl/union_map.h>
2738 __isl_give isl_union_set *isl_union_map_wrap(
2739 __isl_take isl_union_map *umap);
2741 The input to C<isl_space_unwrap> should
2742 be the space of a set, while that of
2743 C<isl_space_wrap> should be the space of a relation.
2744 Conversely, the output of C<isl_space_unwrap> is the space
2745 of a relation, while that of C<isl_space_wrap> is the space of a set.
2749 Remove any internal structure of domain (and range) of the given
2750 set or relation. If there is any such internal structure in the input,
2751 then the name of the space is also removed.
2753 #include <isl/local_space.h>
2754 __isl_give isl_local_space *
2755 isl_local_space_flatten_domain(
2756 __isl_take isl_local_space *ls);
2757 __isl_give isl_local_space *
2758 isl_local_space_flatten_range(
2759 __isl_take isl_local_space *ls);
2761 #include <isl/set.h>
2762 __isl_give isl_basic_set *isl_basic_set_flatten(
2763 __isl_take isl_basic_set *bset);
2764 __isl_give isl_set *isl_set_flatten(
2765 __isl_take isl_set *set);
2767 #include <isl/map.h>
2768 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2769 __isl_take isl_basic_map *bmap);
2770 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2771 __isl_take isl_basic_map *bmap);
2772 __isl_give isl_map *isl_map_flatten_range(
2773 __isl_take isl_map *map);
2774 __isl_give isl_map *isl_map_flatten_domain(
2775 __isl_take isl_map *map);
2776 __isl_give isl_basic_map *isl_basic_map_flatten(
2777 __isl_take isl_basic_map *bmap);
2778 __isl_give isl_map *isl_map_flatten(
2779 __isl_take isl_map *map);
2781 #include <isl/map.h>
2782 __isl_give isl_map *isl_set_flatten_map(
2783 __isl_take isl_set *set);
2785 The function above constructs a relation
2786 that maps the input set to a flattened version of the set.
2790 Lift the input set to a space with extra dimensions corresponding
2791 to the existentially quantified variables in the input.
2792 In particular, the result lives in a wrapped map where the domain
2793 is the original space and the range corresponds to the original
2794 existentially quantified variables.
2796 __isl_give isl_basic_set *isl_basic_set_lift(
2797 __isl_take isl_basic_set *bset);
2798 __isl_give isl_set *isl_set_lift(
2799 __isl_take isl_set *set);
2800 __isl_give isl_union_set *isl_union_set_lift(
2801 __isl_take isl_union_set *uset);
2803 Given a local space that contains the existentially quantified
2804 variables of a set, a basic relation that, when applied to
2805 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2806 can be constructed using the following function.
2808 #include <isl/local_space.h>
2809 __isl_give isl_basic_map *isl_local_space_lifting(
2810 __isl_take isl_local_space *ls);
2812 =item * Internal Product
2814 __isl_give isl_basic_map *isl_basic_map_zip(
2815 __isl_take isl_basic_map *bmap);
2816 __isl_give isl_map *isl_map_zip(
2817 __isl_take isl_map *map);
2818 __isl_give isl_union_map *isl_union_map_zip(
2819 __isl_take isl_union_map *umap);
2821 Given a relation with nested relations for domain and range,
2822 interchange the range of the domain with the domain of the range.
2826 __isl_give isl_basic_map *isl_basic_map_curry(
2827 __isl_take isl_basic_map *bmap);
2828 __isl_give isl_basic_map *isl_basic_map_uncurry(
2829 __isl_take isl_basic_map *bmap);
2830 __isl_give isl_map *isl_map_curry(
2831 __isl_take isl_map *map);
2832 __isl_give isl_map *isl_map_uncurry(
2833 __isl_take isl_map *map);
2834 __isl_give isl_union_map *isl_union_map_curry(
2835 __isl_take isl_union_map *umap);
2836 __isl_give isl_union_map *isl_union_map_uncurry(
2837 __isl_take isl_union_map *umap);
2839 Given a relation with a nested relation for domain,
2840 the C<curry> functions
2841 move the range of the nested relation out of the domain
2842 and use it as the domain of a nested relation in the range,
2843 with the original range as range of this nested relation.
2844 The C<uncurry> functions perform the inverse operation.
2846 =item * Aligning parameters
2848 __isl_give isl_basic_set *isl_basic_set_align_params(
2849 __isl_take isl_basic_set *bset,
2850 __isl_take isl_space *model);
2851 __isl_give isl_set *isl_set_align_params(
2852 __isl_take isl_set *set,
2853 __isl_take isl_space *model);
2854 __isl_give isl_basic_map *isl_basic_map_align_params(
2855 __isl_take isl_basic_map *bmap,
2856 __isl_take isl_space *model);
2857 __isl_give isl_map *isl_map_align_params(
2858 __isl_take isl_map *map,
2859 __isl_take isl_space *model);
2861 Change the order of the parameters of the given set or relation
2862 such that the first parameters match those of C<model>.
2863 This may involve the introduction of extra parameters.
2864 All parameters need to be named.
2866 =item * Dimension manipulation
2868 #include <isl/local_space.h>
2869 __isl_give isl_local_space *isl_local_space_add_dims(
2870 __isl_take isl_local_space *ls,
2871 enum isl_dim_type type, unsigned n);
2872 __isl_give isl_local_space *isl_local_space_insert_dims(
2873 __isl_take isl_local_space *ls,
2874 enum isl_dim_type type, unsigned first, unsigned n);
2875 __isl_give isl_local_space *isl_local_space_drop_dims(
2876 __isl_take isl_local_space *ls,
2877 enum isl_dim_type type, unsigned first, unsigned n);
2879 #include <isl/set.h>
2880 __isl_give isl_basic_set *isl_basic_set_add_dims(
2881 __isl_take isl_basic_set *bset,
2882 enum isl_dim_type type, unsigned n);
2883 __isl_give isl_set *isl_set_add_dims(
2884 __isl_take isl_set *set,
2885 enum isl_dim_type type, unsigned n);
2886 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2887 __isl_take isl_basic_set *bset,
2888 enum isl_dim_type type, unsigned pos,
2890 __isl_give isl_set *isl_set_insert_dims(
2891 __isl_take isl_set *set,
2892 enum isl_dim_type type, unsigned pos, unsigned n);
2893 __isl_give isl_basic_set *isl_basic_set_move_dims(
2894 __isl_take isl_basic_set *bset,
2895 enum isl_dim_type dst_type, unsigned dst_pos,
2896 enum isl_dim_type src_type, unsigned src_pos,
2898 __isl_give isl_set *isl_set_move_dims(
2899 __isl_take isl_set *set,
2900 enum isl_dim_type dst_type, unsigned dst_pos,
2901 enum isl_dim_type src_type, unsigned src_pos,
2904 #include <isl/map.h>
2905 __isl_give isl_map *isl_map_add_dims(
2906 __isl_take isl_map *map,
2907 enum isl_dim_type type, unsigned n);
2908 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2909 __isl_take isl_basic_map *bmap,
2910 enum isl_dim_type type, unsigned pos,
2912 __isl_give isl_map *isl_map_insert_dims(
2913 __isl_take isl_map *map,
2914 enum isl_dim_type type, unsigned pos, unsigned n);
2915 __isl_give isl_basic_map *isl_basic_map_move_dims(
2916 __isl_take isl_basic_map *bmap,
2917 enum isl_dim_type dst_type, unsigned dst_pos,
2918 enum isl_dim_type src_type, unsigned src_pos,
2920 __isl_give isl_map *isl_map_move_dims(
2921 __isl_take isl_map *map,
2922 enum isl_dim_type dst_type, unsigned dst_pos,
2923 enum isl_dim_type src_type, unsigned src_pos,
2926 It is usually not advisable to directly change the (input or output)
2927 space of a set or a relation as this removes the name and the internal
2928 structure of the space. However, the above functions can be useful
2929 to add new parameters, assuming
2930 C<isl_set_align_params> and C<isl_map_align_params>
2935 =head2 Binary Operations
2937 The two arguments of a binary operation not only need to live
2938 in the same C<isl_ctx>, they currently also need to have
2939 the same (number of) parameters.
2941 =head3 Basic Operations
2945 =item * Intersection
2947 #include <isl/local_space.h>
2948 __isl_give isl_local_space *isl_local_space_intersect(
2949 __isl_take isl_local_space *ls1,
2950 __isl_take isl_local_space *ls2);
2952 #include <isl/set.h>
2953 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2954 __isl_take isl_basic_set *bset1,
2955 __isl_take isl_basic_set *bset2);
2956 __isl_give isl_basic_set *isl_basic_set_intersect(
2957 __isl_take isl_basic_set *bset1,
2958 __isl_take isl_basic_set *bset2);
2959 __isl_give isl_set *isl_set_intersect_params(
2960 __isl_take isl_set *set,
2961 __isl_take isl_set *params);
2962 __isl_give isl_set *isl_set_intersect(
2963 __isl_take isl_set *set1,
2964 __isl_take isl_set *set2);
2966 #include <isl/map.h>
2967 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2968 __isl_take isl_basic_map *bmap,
2969 __isl_take isl_basic_set *bset);
2970 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2971 __isl_take isl_basic_map *bmap,
2972 __isl_take isl_basic_set *bset);
2973 __isl_give isl_basic_map *isl_basic_map_intersect(
2974 __isl_take isl_basic_map *bmap1,
2975 __isl_take isl_basic_map *bmap2);
2976 __isl_give isl_map *isl_map_intersect_params(
2977 __isl_take isl_map *map,
2978 __isl_take isl_set *params);
2979 __isl_give isl_map *isl_map_intersect_domain(
2980 __isl_take isl_map *map,
2981 __isl_take isl_set *set);
2982 __isl_give isl_map *isl_map_intersect_range(
2983 __isl_take isl_map *map,
2984 __isl_take isl_set *set);
2985 __isl_give isl_map *isl_map_intersect(
2986 __isl_take isl_map *map1,
2987 __isl_take isl_map *map2);
2989 #include <isl/union_set.h>
2990 __isl_give isl_union_set *isl_union_set_intersect_params(
2991 __isl_take isl_union_set *uset,
2992 __isl_take isl_set *set);
2993 __isl_give isl_union_set *isl_union_set_intersect(
2994 __isl_take isl_union_set *uset1,
2995 __isl_take isl_union_set *uset2);
2997 #include <isl/union_map.h>
2998 __isl_give isl_union_map *isl_union_map_intersect_params(
2999 __isl_take isl_union_map *umap,
3000 __isl_take isl_set *set);
3001 __isl_give isl_union_map *isl_union_map_intersect_domain(
3002 __isl_take isl_union_map *umap,
3003 __isl_take isl_union_set *uset);
3004 __isl_give isl_union_map *isl_union_map_intersect_range(
3005 __isl_take isl_union_map *umap,
3006 __isl_take isl_union_set *uset);
3007 __isl_give isl_union_map *isl_union_map_intersect(
3008 __isl_take isl_union_map *umap1,
3009 __isl_take isl_union_map *umap2);
3011 The second argument to the C<_params> functions needs to be
3012 a parametric (basic) set. For the other functions, a parametric set
3013 for either argument is only allowed if the other argument is
3014 a parametric set as well.
3018 __isl_give isl_set *isl_basic_set_union(
3019 __isl_take isl_basic_set *bset1,
3020 __isl_take isl_basic_set *bset2);
3021 __isl_give isl_map *isl_basic_map_union(
3022 __isl_take isl_basic_map *bmap1,
3023 __isl_take isl_basic_map *bmap2);
3024 __isl_give isl_set *isl_set_union(
3025 __isl_take isl_set *set1,
3026 __isl_take isl_set *set2);
3027 __isl_give isl_map *isl_map_union(
3028 __isl_take isl_map *map1,
3029 __isl_take isl_map *map2);
3030 __isl_give isl_union_set *isl_union_set_union(
3031 __isl_take isl_union_set *uset1,
3032 __isl_take isl_union_set *uset2);
3033 __isl_give isl_union_map *isl_union_map_union(
3034 __isl_take isl_union_map *umap1,
3035 __isl_take isl_union_map *umap2);
3037 =item * Set difference
3039 __isl_give isl_set *isl_set_subtract(
3040 __isl_take isl_set *set1,
3041 __isl_take isl_set *set2);
3042 __isl_give isl_map *isl_map_subtract(
3043 __isl_take isl_map *map1,
3044 __isl_take isl_map *map2);
3045 __isl_give isl_map *isl_map_subtract_domain(
3046 __isl_take isl_map *map,
3047 __isl_take isl_set *dom);
3048 __isl_give isl_map *isl_map_subtract_range(
3049 __isl_take isl_map *map,
3050 __isl_take isl_set *dom);
3051 __isl_give isl_union_set *isl_union_set_subtract(
3052 __isl_take isl_union_set *uset1,
3053 __isl_take isl_union_set *uset2);
3054 __isl_give isl_union_map *isl_union_map_subtract(
3055 __isl_take isl_union_map *umap1,
3056 __isl_take isl_union_map *umap2);
3057 __isl_give isl_union_map *isl_union_map_subtract_domain(
3058 __isl_take isl_union_map *umap,
3059 __isl_take isl_union_set *dom);
3060 __isl_give isl_union_map *isl_union_map_subtract_range(
3061 __isl_take isl_union_map *umap,
3062 __isl_take isl_union_set *dom);
3066 __isl_give isl_basic_set *isl_basic_set_apply(
3067 __isl_take isl_basic_set *bset,
3068 __isl_take isl_basic_map *bmap);
3069 __isl_give isl_set *isl_set_apply(
3070 __isl_take isl_set *set,
3071 __isl_take isl_map *map);
3072 __isl_give isl_union_set *isl_union_set_apply(
3073 __isl_take isl_union_set *uset,
3074 __isl_take isl_union_map *umap);
3075 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3076 __isl_take isl_basic_map *bmap1,
3077 __isl_take isl_basic_map *bmap2);
3078 __isl_give isl_basic_map *isl_basic_map_apply_range(
3079 __isl_take isl_basic_map *bmap1,
3080 __isl_take isl_basic_map *bmap2);
3081 __isl_give isl_map *isl_map_apply_domain(
3082 __isl_take isl_map *map1,
3083 __isl_take isl_map *map2);
3084 __isl_give isl_union_map *isl_union_map_apply_domain(
3085 __isl_take isl_union_map *umap1,
3086 __isl_take isl_union_map *umap2);
3087 __isl_give isl_map *isl_map_apply_range(
3088 __isl_take isl_map *map1,
3089 __isl_take isl_map *map2);
3090 __isl_give isl_union_map *isl_union_map_apply_range(
3091 __isl_take isl_union_map *umap1,
3092 __isl_take isl_union_map *umap2);
3096 #include <isl/set.h>
3097 __isl_give isl_basic_set *
3098 isl_basic_set_preimage_multi_aff(
3099 __isl_take isl_basic_set *bset,
3100 __isl_take isl_multi_aff *ma);
3101 __isl_give isl_set *isl_set_preimage_multi_aff(
3102 __isl_take isl_set *set,
3103 __isl_take isl_multi_aff *ma);
3104 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3105 __isl_take isl_set *set,
3106 __isl_take isl_pw_multi_aff *pma);
3107 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
3108 __isl_take isl_set *set,
3109 __isl_take isl_multi_pw_aff *mpa);
3111 #include <isl/union_set.h>
3112 __isl_give isl_union_set *
3113 isl_union_set_preimage_multi_aff(
3114 __isl_take isl_union_set *uset,
3115 __isl_take isl_multi_aff *ma);
3116 __isl_give isl_union_set *
3117 isl_union_set_preimage_pw_multi_aff(
3118 __isl_take isl_union_set *uset,
3119 __isl_take isl_pw_multi_aff *pma);
3120 __isl_give isl_union_set *
3121 isl_union_set_preimage_union_pw_multi_aff(
3122 __isl_take isl_union_set *uset,
3123 __isl_take isl_union_pw_multi_aff *upma);
3125 #include <isl/map.h>
3126 __isl_give isl_basic_map *
3127 isl_basic_map_preimage_domain_multi_aff(
3128 __isl_take isl_basic_map *bmap,
3129 __isl_take isl_multi_aff *ma);
3130 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3131 __isl_take isl_map *map,
3132 __isl_take isl_multi_aff *ma);
3133 __isl_give isl_map *isl_map_preimage_range_multi_aff(
3134 __isl_take isl_map *map,
3135 __isl_take isl_multi_aff *ma);
3136 __isl_give isl_map *
3137 isl_map_preimage_domain_pw_multi_aff(
3138 __isl_take isl_map *map,
3139 __isl_take isl_pw_multi_aff *pma);
3140 __isl_give isl_map *
3141 isl_map_preimage_range_pw_multi_aff(
3142 __isl_take isl_map *map,
3143 __isl_take isl_pw_multi_aff *pma);
3144 __isl_give isl_map *
3145 isl_map_preimage_domain_multi_pw_aff(
3146 __isl_take isl_map *map,
3147 __isl_take isl_multi_pw_aff *mpa);
3148 __isl_give isl_basic_map *
3149 isl_basic_map_preimage_range_multi_aff(
3150 __isl_take isl_basic_map *bmap,
3151 __isl_take isl_multi_aff *ma);
3153 #include <isl/union_map.h>
3154 __isl_give isl_union_map *
3155 isl_union_map_preimage_domain_multi_aff(
3156 __isl_take isl_union_map *umap,
3157 __isl_take isl_multi_aff *ma);
3158 __isl_give isl_union_map *
3159 isl_union_map_preimage_range_multi_aff(
3160 __isl_take isl_union_map *umap,
3161 __isl_take isl_multi_aff *ma);
3162 __isl_give isl_union_map *
3163 isl_union_map_preimage_domain_pw_multi_aff(
3164 __isl_take isl_union_map *umap,
3165 __isl_take isl_pw_multi_aff *pma);
3166 __isl_give isl_union_map *
3167 isl_union_map_preimage_range_pw_multi_aff(
3168 __isl_take isl_union_map *umap,
3169 __isl_take isl_pw_multi_aff *pma);
3170 __isl_give isl_union_map *
3171 isl_union_map_preimage_domain_union_pw_multi_aff(
3172 __isl_take isl_union_map *umap,
3173 __isl_take isl_union_pw_multi_aff *upma);
3174 __isl_give isl_union_map *
3175 isl_union_map_preimage_range_union_pw_multi_aff(
3176 __isl_take isl_union_map *umap,
3177 __isl_take isl_union_pw_multi_aff *upma);
3179 These functions compute the preimage of the given set or map domain/range under
3180 the given function. In other words, the expression is plugged
3181 into the set description or into the domain/range of the map.
3182 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3183 L</"Piecewise Multiple Quasi Affine Expressions">.
3185 =item * Cartesian Product
3187 #include <isl/space.h>
3188 __isl_give isl_space *isl_space_product(
3189 __isl_take isl_space *space1,
3190 __isl_take isl_space *space2);
3191 __isl_give isl_space *isl_space_domain_product(
3192 __isl_take isl_space *space1,
3193 __isl_take isl_space *space2);
3194 __isl_give isl_space *isl_space_range_product(
3195 __isl_take isl_space *space1,
3196 __isl_take isl_space *space2);
3199 C<isl_space_product>, C<isl_space_domain_product>
3200 and C<isl_space_range_product> take pairs or relation spaces and
3201 produce a single relations space, where either the domain, the range
3202 or both domain and range are wrapped spaces of relations between
3203 the domains and/or ranges of the input spaces.
3204 If the product is only constructed over the domain or the range
3205 then the ranges or the domains of the inputs should be the same.
3206 The function C<isl_space_product> also accepts a pair of set spaces,
3207 in which case it returns a wrapped space of a relation between the
3210 #include <isl/set.h>
3211 __isl_give isl_set *isl_set_product(
3212 __isl_take isl_set *set1,
3213 __isl_take isl_set *set2);
3215 #include <isl/map.h>
3216 __isl_give isl_basic_map *isl_basic_map_domain_product(
3217 __isl_take isl_basic_map *bmap1,
3218 __isl_take isl_basic_map *bmap2);
3219 __isl_give isl_basic_map *isl_basic_map_range_product(
3220 __isl_take isl_basic_map *bmap1,
3221 __isl_take isl_basic_map *bmap2);
3222 __isl_give isl_basic_map *isl_basic_map_product(
3223 __isl_take isl_basic_map *bmap1,
3224 __isl_take isl_basic_map *bmap2);
3225 __isl_give isl_map *isl_map_domain_product(
3226 __isl_take isl_map *map1,
3227 __isl_take isl_map *map2);
3228 __isl_give isl_map *isl_map_range_product(
3229 __isl_take isl_map *map1,
3230 __isl_take isl_map *map2);
3231 __isl_give isl_map *isl_map_product(
3232 __isl_take isl_map *map1,
3233 __isl_take isl_map *map2);
3235 #include <isl/union_set.h>
3236 __isl_give isl_union_set *isl_union_set_product(
3237 __isl_take isl_union_set *uset1,
3238 __isl_take isl_union_set *uset2);
3240 #include <isl/union_map.h>
3241 __isl_give isl_union_map *isl_union_map_domain_product(
3242 __isl_take isl_union_map *umap1,
3243 __isl_take isl_union_map *umap2);
3244 __isl_give isl_union_map *isl_union_map_range_product(
3245 __isl_take isl_union_map *umap1,
3246 __isl_take isl_union_map *umap2);
3247 __isl_give isl_union_map *isl_union_map_product(
3248 __isl_take isl_union_map *umap1,
3249 __isl_take isl_union_map *umap2);
3251 The above functions compute the cross product of the given
3252 sets or relations. The domains and ranges of the results
3253 are wrapped maps between domains and ranges of the inputs.
3254 To obtain a ``flat'' product, use the following functions
3257 __isl_give isl_basic_set *isl_basic_set_flat_product(
3258 __isl_take isl_basic_set *bset1,
3259 __isl_take isl_basic_set *bset2);
3260 __isl_give isl_set *isl_set_flat_product(
3261 __isl_take isl_set *set1,
3262 __isl_take isl_set *set2);
3263 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3264 __isl_take isl_basic_map *bmap1,
3265 __isl_take isl_basic_map *bmap2);
3266 __isl_give isl_map *isl_map_flat_domain_product(
3267 __isl_take isl_map *map1,
3268 __isl_take isl_map *map2);
3269 __isl_give isl_map *isl_map_flat_range_product(
3270 __isl_take isl_map *map1,
3271 __isl_take isl_map *map2);
3272 __isl_give isl_union_map *isl_union_map_flat_range_product(
3273 __isl_take isl_union_map *umap1,
3274 __isl_take isl_union_map *umap2);
3275 __isl_give isl_basic_map *isl_basic_map_flat_product(
3276 __isl_take isl_basic_map *bmap1,
3277 __isl_take isl_basic_map *bmap2);
3278 __isl_give isl_map *isl_map_flat_product(
3279 __isl_take isl_map *map1,
3280 __isl_take isl_map *map2);
3282 #include <isl/space.h>
3283 __isl_give isl_space *isl_space_domain_factor_domain(
3284 __isl_take isl_space *space);
3285 __isl_give isl_space *isl_space_range_factor_domain(
3286 __isl_take isl_space *space);
3287 __isl_give isl_space *isl_space_range_factor_range(
3288 __isl_take isl_space *space);
3290 The functions C<isl_space_range_factor_domain> and
3291 C<isl_space_range_factor_range> extract the two arguments from
3292 the result of a call to C<isl_space_range_product>.
3294 The arguments of a call to C<isl_map_range_product> can be extracted
3295 from the result using the following two functions.
3297 #include <isl/map.h>
3298 __isl_give isl_map *isl_map_range_factor_domain(
3299 __isl_take isl_map *map);
3300 __isl_give isl_map *isl_map_range_factor_range(
3301 __isl_take isl_map *map);
3303 =item * Simplification
3305 __isl_give isl_basic_set *isl_basic_set_gist(
3306 __isl_take isl_basic_set *bset,
3307 __isl_take isl_basic_set *context);
3308 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3309 __isl_take isl_set *context);
3310 __isl_give isl_set *isl_set_gist_params(
3311 __isl_take isl_set *set,
3312 __isl_take isl_set *context);
3313 __isl_give isl_union_set *isl_union_set_gist(
3314 __isl_take isl_union_set *uset,
3315 __isl_take isl_union_set *context);
3316 __isl_give isl_union_set *isl_union_set_gist_params(
3317 __isl_take isl_union_set *uset,
3318 __isl_take isl_set *set);
3319 __isl_give isl_basic_map *isl_basic_map_gist(
3320 __isl_take isl_basic_map *bmap,
3321 __isl_take isl_basic_map *context);
3322 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3323 __isl_take isl_map *context);
3324 __isl_give isl_map *isl_map_gist_params(
3325 __isl_take isl_map *map,
3326 __isl_take isl_set *context);
3327 __isl_give isl_map *isl_map_gist_domain(
3328 __isl_take isl_map *map,
3329 __isl_take isl_set *context);
3330 __isl_give isl_map *isl_map_gist_range(
3331 __isl_take isl_map *map,
3332 __isl_take isl_set *context);
3333 __isl_give isl_union_map *isl_union_map_gist(
3334 __isl_take isl_union_map *umap,
3335 __isl_take isl_union_map *context);
3336 __isl_give isl_union_map *isl_union_map_gist_params(
3337 __isl_take isl_union_map *umap,
3338 __isl_take isl_set *set);
3339 __isl_give isl_union_map *isl_union_map_gist_domain(
3340 __isl_take isl_union_map *umap,
3341 __isl_take isl_union_set *uset);
3342 __isl_give isl_union_map *isl_union_map_gist_range(
3343 __isl_take isl_union_map *umap,
3344 __isl_take isl_union_set *uset);
3346 The gist operation returns a set or relation that has the
3347 same intersection with the context as the input set or relation.
3348 Any implicit equality in the intersection is made explicit in the result,
3349 while all inequalities that are redundant with respect to the intersection
3351 In case of union sets and relations, the gist operation is performed
3356 =head3 Lexicographic Optimization
3358 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3359 the following functions
3360 compute a set that contains the lexicographic minimum or maximum
3361 of the elements in C<set> (or C<bset>) for those values of the parameters
3362 that satisfy C<dom>.
3363 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3364 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3366 In other words, the union of the parameter values
3367 for which the result is non-empty and of C<*empty>
3370 __isl_give isl_set *isl_basic_set_partial_lexmin(
3371 __isl_take isl_basic_set *bset,
3372 __isl_take isl_basic_set *dom,
3373 __isl_give isl_set **empty);
3374 __isl_give isl_set *isl_basic_set_partial_lexmax(
3375 __isl_take isl_basic_set *bset,
3376 __isl_take isl_basic_set *dom,
3377 __isl_give isl_set **empty);
3378 __isl_give isl_set *isl_set_partial_lexmin(
3379 __isl_take isl_set *set, __isl_take isl_set *dom,
3380 __isl_give isl_set **empty);
3381 __isl_give isl_set *isl_set_partial_lexmax(
3382 __isl_take isl_set *set, __isl_take isl_set *dom,
3383 __isl_give isl_set **empty);
3385 Given a (basic) set C<set> (or C<bset>), the following functions simply
3386 return a set containing the lexicographic minimum or maximum
3387 of the elements in C<set> (or C<bset>).
3388 In case of union sets, the optimum is computed per space.
3390 __isl_give isl_set *isl_basic_set_lexmin(
3391 __isl_take isl_basic_set *bset);
3392 __isl_give isl_set *isl_basic_set_lexmax(
3393 __isl_take isl_basic_set *bset);
3394 __isl_give isl_set *isl_set_lexmin(
3395 __isl_take isl_set *set);
3396 __isl_give isl_set *isl_set_lexmax(
3397 __isl_take isl_set *set);
3398 __isl_give isl_union_set *isl_union_set_lexmin(
3399 __isl_take isl_union_set *uset);
3400 __isl_give isl_union_set *isl_union_set_lexmax(
3401 __isl_take isl_union_set *uset);
3403 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3404 the following functions
3405 compute a relation that maps each element of C<dom>
3406 to the single lexicographic minimum or maximum
3407 of the elements that are associated to that same
3408 element in C<map> (or C<bmap>).
3409 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3410 that contains the elements in C<dom> that do not map
3411 to any elements in C<map> (or C<bmap>).
3412 In other words, the union of the domain of the result and of C<*empty>
3415 __isl_give isl_map *isl_basic_map_partial_lexmax(
3416 __isl_take isl_basic_map *bmap,
3417 __isl_take isl_basic_set *dom,
3418 __isl_give isl_set **empty);
3419 __isl_give isl_map *isl_basic_map_partial_lexmin(
3420 __isl_take isl_basic_map *bmap,
3421 __isl_take isl_basic_set *dom,
3422 __isl_give isl_set **empty);
3423 __isl_give isl_map *isl_map_partial_lexmax(
3424 __isl_take isl_map *map, __isl_take isl_set *dom,
3425 __isl_give isl_set **empty);
3426 __isl_give isl_map *isl_map_partial_lexmin(
3427 __isl_take isl_map *map, __isl_take isl_set *dom,
3428 __isl_give isl_set **empty);
3430 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3431 return a map mapping each element in the domain of
3432 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3433 of all elements associated to that element.
3434 In case of union relations, the optimum is computed per space.
3436 __isl_give isl_map *isl_basic_map_lexmin(
3437 __isl_take isl_basic_map *bmap);
3438 __isl_give isl_map *isl_basic_map_lexmax(
3439 __isl_take isl_basic_map *bmap);
3440 __isl_give isl_map *isl_map_lexmin(
3441 __isl_take isl_map *map);
3442 __isl_give isl_map *isl_map_lexmax(
3443 __isl_take isl_map *map);
3444 __isl_give isl_union_map *isl_union_map_lexmin(
3445 __isl_take isl_union_map *umap);
3446 __isl_give isl_union_map *isl_union_map_lexmax(
3447 __isl_take isl_union_map *umap);
3449 The following functions return their result in the form of
3450 a piecewise multi-affine expression
3451 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3452 but are otherwise equivalent to the corresponding functions
3453 returning a basic set or relation.
3455 __isl_give isl_pw_multi_aff *
3456 isl_basic_map_lexmin_pw_multi_aff(
3457 __isl_take isl_basic_map *bmap);
3458 __isl_give isl_pw_multi_aff *
3459 isl_basic_set_partial_lexmin_pw_multi_aff(
3460 __isl_take isl_basic_set *bset,
3461 __isl_take isl_basic_set *dom,
3462 __isl_give isl_set **empty);
3463 __isl_give isl_pw_multi_aff *
3464 isl_basic_set_partial_lexmax_pw_multi_aff(
3465 __isl_take isl_basic_set *bset,
3466 __isl_take isl_basic_set *dom,
3467 __isl_give isl_set **empty);
3468 __isl_give isl_pw_multi_aff *
3469 isl_basic_map_partial_lexmin_pw_multi_aff(
3470 __isl_take isl_basic_map *bmap,
3471 __isl_take isl_basic_set *dom,
3472 __isl_give isl_set **empty);
3473 __isl_give isl_pw_multi_aff *
3474 isl_basic_map_partial_lexmax_pw_multi_aff(
3475 __isl_take isl_basic_map *bmap,
3476 __isl_take isl_basic_set *dom,
3477 __isl_give isl_set **empty);
3478 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3479 __isl_take isl_set *set);
3480 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3481 __isl_take isl_set *set);
3482 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3483 __isl_take isl_map *map);
3484 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3485 __isl_take isl_map *map);
3489 Lists are defined over several element types, including
3490 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3491 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3492 Here we take lists of C<isl_set>s as an example.
3493 Lists can be created, copied, modified and freed using the following functions.
3495 #include <isl/list.h>
3496 __isl_give isl_set_list *isl_set_list_from_set(
3497 __isl_take isl_set *el);
3498 __isl_give isl_set_list *isl_set_list_alloc(
3499 isl_ctx *ctx, int n);
3500 __isl_give isl_set_list *isl_set_list_copy(
3501 __isl_keep isl_set_list *list);
3502 __isl_give isl_set_list *isl_set_list_insert(
3503 __isl_take isl_set_list *list, unsigned pos,
3504 __isl_take isl_set *el);
3505 __isl_give isl_set_list *isl_set_list_add(
3506 __isl_take isl_set_list *list,
3507 __isl_take isl_set *el);
3508 __isl_give isl_set_list *isl_set_list_drop(
3509 __isl_take isl_set_list *list,
3510 unsigned first, unsigned n);
3511 __isl_give isl_set_list *isl_set_list_set_set(
3512 __isl_take isl_set_list *list, int index,
3513 __isl_take isl_set *set);
3514 __isl_give isl_set_list *isl_set_list_concat(
3515 __isl_take isl_set_list *list1,
3516 __isl_take isl_set_list *list2);
3517 __isl_give isl_set_list *isl_set_list_sort(
3518 __isl_take isl_set_list *list,
3519 int (*cmp)(__isl_keep isl_set *a,
3520 __isl_keep isl_set *b, void *user),
3522 __isl_null isl_set_list *isl_set_list_free(
3523 __isl_take isl_set_list *list);
3525 C<isl_set_list_alloc> creates an empty list with a capacity for
3526 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3529 Lists can be inspected using the following functions.
3531 #include <isl/list.h>
3532 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3533 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3534 __isl_give isl_set *isl_set_list_get_set(
3535 __isl_keep isl_set_list *list, int index);
3536 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3537 int (*fn)(__isl_take isl_set *el, void *user),
3539 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3540 int (*follows)(__isl_keep isl_set *a,
3541 __isl_keep isl_set *b, void *user),
3543 int (*fn)(__isl_take isl_set *el, void *user),
3546 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3547 strongly connected components of the graph with as vertices the elements
3548 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3549 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3550 should return C<-1> on error.
3552 Lists can be printed using
3554 #include <isl/list.h>
3555 __isl_give isl_printer *isl_printer_print_set_list(
3556 __isl_take isl_printer *p,
3557 __isl_keep isl_set_list *list);
3559 =head2 Associative arrays
3561 Associative arrays map isl objects of a specific type to isl objects
3562 of some (other) specific type. They are defined for several pairs
3563 of types, including (C<isl_map>, C<isl_basic_set>),
3564 (C<isl_id>, C<isl_ast_expr>) and.
3565 (C<isl_id>, C<isl_pw_aff>).
3566 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3569 Associative arrays can be created, copied and freed using
3570 the following functions.
3572 #include <isl/id_to_ast_expr.h>
3573 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3574 isl_ctx *ctx, int min_size);
3575 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3576 __isl_keep id_to_ast_expr *id2expr);
3577 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
3578 __isl_take id_to_ast_expr *id2expr);
3580 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3581 to specify the expected size of the associative array.
3582 The associative array will be grown automatically as needed.
3584 Associative arrays can be inspected using the following functions.
3586 #include <isl/id_to_ast_expr.h>
3587 isl_ctx *isl_id_to_ast_expr_get_ctx(
3588 __isl_keep id_to_ast_expr *id2expr);
3589 int isl_id_to_ast_expr_has(
3590 __isl_keep id_to_ast_expr *id2expr,
3591 __isl_keep isl_id *key);
3592 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3593 __isl_keep id_to_ast_expr *id2expr,
3594 __isl_take isl_id *key);
3595 int isl_id_to_ast_expr_foreach(
3596 __isl_keep id_to_ast_expr *id2expr,
3597 int (*fn)(__isl_take isl_id *key,
3598 __isl_take isl_ast_expr *val, void *user),
3601 They can be modified using the following function.
3603 #include <isl/id_to_ast_expr.h>
3604 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3605 __isl_take id_to_ast_expr *id2expr,
3606 __isl_take isl_id *key,
3607 __isl_take isl_ast_expr *val);
3608 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
3609 __isl_take id_to_ast_expr *id2expr,
3610 __isl_take isl_id *key);
3612 Associative arrays can be printed using the following function.
3614 #include <isl/id_to_ast_expr.h>
3615 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3616 __isl_take isl_printer *p,
3617 __isl_keep id_to_ast_expr *id2expr);
3619 =head2 Multiple Values
3621 An C<isl_multi_val> object represents a sequence of zero or more values,
3622 living in a set space.
3624 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3625 using the following function
3627 #include <isl/val.h>
3628 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3629 __isl_take isl_space *space,
3630 __isl_take isl_val_list *list);
3632 The zero multiple value (with value zero for each set dimension)
3633 can be created using the following function.
3635 #include <isl/val.h>
3636 __isl_give isl_multi_val *isl_multi_val_zero(
3637 __isl_take isl_space *space);
3639 Multiple values can be copied and freed using
3641 #include <isl/val.h>
3642 __isl_give isl_multi_val *isl_multi_val_copy(
3643 __isl_keep isl_multi_val *mv);
3644 __isl_null isl_multi_val *isl_multi_val_free(
3645 __isl_take isl_multi_val *mv);
3647 They can be inspected using
3649 #include <isl/val.h>
3650 isl_ctx *isl_multi_val_get_ctx(
3651 __isl_keep isl_multi_val *mv);
3652 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3653 enum isl_dim_type type);
3654 __isl_give isl_val *isl_multi_val_get_val(
3655 __isl_keep isl_multi_val *mv, int pos);
3656 int isl_multi_val_find_dim_by_id(
3657 __isl_keep isl_multi_val *mv,
3658 enum isl_dim_type type, __isl_keep isl_id *id);
3659 __isl_give isl_id *isl_multi_val_get_dim_id(
3660 __isl_keep isl_multi_val *mv,
3661 enum isl_dim_type type, unsigned pos);
3662 const char *isl_multi_val_get_tuple_name(
3663 __isl_keep isl_multi_val *mv,
3664 enum isl_dim_type type);
3665 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3666 enum isl_dim_type type);
3667 __isl_give isl_id *isl_multi_val_get_tuple_id(
3668 __isl_keep isl_multi_val *mv,
3669 enum isl_dim_type type);
3670 int isl_multi_val_range_is_wrapping(
3671 __isl_keep isl_multi_val *mv);
3673 They can be modified using
3675 #include <isl/val.h>
3676 __isl_give isl_multi_val *isl_multi_val_set_val(
3677 __isl_take isl_multi_val *mv, int pos,
3678 __isl_take isl_val *val);
3679 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3680 __isl_take isl_multi_val *mv,
3681 enum isl_dim_type type, unsigned pos, const char *s);
3682 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3683 __isl_take isl_multi_val *mv,
3684 enum isl_dim_type type, unsigned pos,
3685 __isl_take isl_id *id);
3686 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3687 __isl_take isl_multi_val *mv,
3688 enum isl_dim_type type, const char *s);
3689 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3690 __isl_take isl_multi_val *mv,
3691 enum isl_dim_type type, __isl_take isl_id *id);
3692 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3693 __isl_take isl_multi_val *mv,
3694 enum isl_dim_type type);
3695 __isl_give isl_multi_val *isl_multi_val_reset_user(
3696 __isl_take isl_multi_val *mv);
3698 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3699 __isl_take isl_multi_val *mv,
3700 enum isl_dim_type type, unsigned first, unsigned n);
3701 __isl_give isl_multi_val *isl_multi_val_add_dims(
3702 __isl_take isl_multi_val *mv,
3703 enum isl_dim_type type, unsigned n);
3704 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3705 __isl_take isl_multi_val *mv,
3706 enum isl_dim_type type, unsigned first, unsigned n);
3710 #include <isl/val.h>
3711 __isl_give isl_multi_val *isl_multi_val_align_params(
3712 __isl_take isl_multi_val *mv,
3713 __isl_take isl_space *model);
3714 __isl_give isl_multi_val *isl_multi_val_from_range(
3715 __isl_take isl_multi_val *mv);
3716 __isl_give isl_multi_val *isl_multi_val_range_splice(
3717 __isl_take isl_multi_val *mv1, unsigned pos,
3718 __isl_take isl_multi_val *mv2);
3719 __isl_give isl_multi_val *isl_multi_val_range_product(
3720 __isl_take isl_multi_val *mv1,
3721 __isl_take isl_multi_val *mv2);
3722 __isl_give isl_multi_val *
3723 isl_multi_val_range_factor_domain(
3724 __isl_take isl_multi_val *mv);
3725 __isl_give isl_multi_val *
3726 isl_multi_val_range_factor_range(
3727 __isl_take isl_multi_val *mv);
3728 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3729 __isl_take isl_multi_val *mv1,
3730 __isl_take isl_multi_aff *mv2);
3731 __isl_give isl_multi_val *isl_multi_val_product(
3732 __isl_take isl_multi_val *mv1,
3733 __isl_take isl_multi_val *mv2);
3734 __isl_give isl_multi_val *isl_multi_val_add_val(
3735 __isl_take isl_multi_val *mv,
3736 __isl_take isl_val *v);
3737 __isl_give isl_multi_val *isl_multi_val_mod_val(
3738 __isl_take isl_multi_val *mv,
3739 __isl_take isl_val *v);
3740 __isl_give isl_multi_val *isl_multi_val_scale_val(
3741 __isl_take isl_multi_val *mv,
3742 __isl_take isl_val *v);
3743 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3744 __isl_take isl_multi_val *mv1,
3745 __isl_take isl_multi_val *mv2);
3746 __isl_give isl_multi_val *
3747 isl_multi_val_scale_down_multi_val(
3748 __isl_take isl_multi_val *mv1,
3749 __isl_take isl_multi_val *mv2);
3751 A multiple value can be printed using
3753 __isl_give isl_printer *isl_printer_print_multi_val(
3754 __isl_take isl_printer *p,
3755 __isl_keep isl_multi_val *mv);
3759 Vectors can be created, copied and freed using the following functions.
3761 #include <isl/vec.h>
3762 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3764 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3765 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
3767 Note that the elements of a newly created vector may have arbitrary values.
3768 The elements can be changed and inspected using the following functions.
3770 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3771 int isl_vec_size(__isl_keep isl_vec *vec);
3772 __isl_give isl_val *isl_vec_get_element_val(
3773 __isl_keep isl_vec *vec, int pos);
3774 __isl_give isl_vec *isl_vec_set_element_si(
3775 __isl_take isl_vec *vec, int pos, int v);
3776 __isl_give isl_vec *isl_vec_set_element_val(
3777 __isl_take isl_vec *vec, int pos,
3778 __isl_take isl_val *v);
3779 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3781 __isl_give isl_vec *isl_vec_set_val(
3782 __isl_take isl_vec *vec, __isl_take isl_val *v);
3783 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3784 __isl_keep isl_vec *vec2, int pos);
3786 C<isl_vec_get_element> will return a negative value if anything went wrong.
3787 In that case, the value of C<*v> is undefined.
3789 The following function can be used to concatenate two vectors.
3791 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3792 __isl_take isl_vec *vec2);
3796 Matrices can be created, copied and freed using the following functions.
3798 #include <isl/mat.h>
3799 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3800 unsigned n_row, unsigned n_col);
3801 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3802 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
3804 Note that the elements of a newly created matrix may have arbitrary values.
3805 The elements can be changed and inspected using the following functions.
3807 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3808 int isl_mat_rows(__isl_keep isl_mat *mat);
3809 int isl_mat_cols(__isl_keep isl_mat *mat);
3810 __isl_give isl_val *isl_mat_get_element_val(
3811 __isl_keep isl_mat *mat, int row, int col);
3812 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3813 int row, int col, int v);
3814 __isl_give isl_mat *isl_mat_set_element_val(
3815 __isl_take isl_mat *mat, int row, int col,
3816 __isl_take isl_val *v);
3818 C<isl_mat_get_element> will return a negative value if anything went wrong.
3819 In that case, the value of C<*v> is undefined.
3821 The following function can be used to compute the (right) inverse
3822 of a matrix, i.e., a matrix such that the product of the original
3823 and the inverse (in that order) is a multiple of the identity matrix.
3824 The input matrix is assumed to be of full row-rank.
3826 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3828 The following function can be used to compute the (right) kernel
3829 (or null space) of a matrix, i.e., a matrix such that the product of
3830 the original and the kernel (in that order) is the zero matrix.
3832 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3834 =head2 Piecewise Quasi Affine Expressions
3836 The zero quasi affine expression or the quasi affine expression
3837 that is equal to a given value or
3838 a specified dimension on a given domain can be created using
3840 __isl_give isl_aff *isl_aff_zero_on_domain(
3841 __isl_take isl_local_space *ls);
3842 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3843 __isl_take isl_local_space *ls);
3844 __isl_give isl_aff *isl_aff_val_on_domain(
3845 __isl_take isl_local_space *ls,
3846 __isl_take isl_val *val);
3847 __isl_give isl_aff *isl_aff_var_on_domain(
3848 __isl_take isl_local_space *ls,
3849 enum isl_dim_type type, unsigned pos);
3850 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3851 __isl_take isl_local_space *ls,
3852 enum isl_dim_type type, unsigned pos);
3853 __isl_give isl_aff *isl_aff_nan_on_domain(
3854 __isl_take isl_local_space *ls);
3855 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3856 __isl_take isl_local_space *ls);
3858 Note that the space in which the resulting objects live is a map space
3859 with the given space as domain and a one-dimensional range.
3861 An empty piecewise quasi affine expression (one with no cells)
3862 or a piecewise quasi affine expression with a single cell can
3863 be created using the following functions.
3865 #include <isl/aff.h>
3866 __isl_give isl_pw_aff *isl_pw_aff_empty(
3867 __isl_take isl_space *space);
3868 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3869 __isl_take isl_set *set, __isl_take isl_aff *aff);
3870 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3871 __isl_take isl_aff *aff);
3873 A piecewise quasi affine expression that is equal to 1 on a set
3874 and 0 outside the set can be created using the following function.
3876 #include <isl/aff.h>
3877 __isl_give isl_pw_aff *isl_set_indicator_function(
3878 __isl_take isl_set *set);
3880 Quasi affine expressions can be copied and freed using
3882 #include <isl/aff.h>
3883 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3884 __isl_null isl_aff *isl_aff_free(__isl_take isl_aff *aff);
3886 __isl_give isl_pw_aff *isl_pw_aff_copy(
3887 __isl_keep isl_pw_aff *pwaff);
3888 __isl_null isl_pw_aff *isl_pw_aff_free(
3889 __isl_take isl_pw_aff *pwaff);
3891 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3892 using the following function. The constraint is required to have
3893 a non-zero coefficient for the specified dimension.
3895 #include <isl/constraint.h>
3896 __isl_give isl_aff *isl_constraint_get_bound(
3897 __isl_keep isl_constraint *constraint,
3898 enum isl_dim_type type, int pos);
3900 The entire affine expression of the constraint can also be extracted
3901 using the following function.
3903 #include <isl/constraint.h>
3904 __isl_give isl_aff *isl_constraint_get_aff(
3905 __isl_keep isl_constraint *constraint);
3907 Conversely, an equality constraint equating
3908 the affine expression to zero or an inequality constraint enforcing
3909 the affine expression to be non-negative, can be constructed using
3911 __isl_give isl_constraint *isl_equality_from_aff(
3912 __isl_take isl_aff *aff);
3913 __isl_give isl_constraint *isl_inequality_from_aff(
3914 __isl_take isl_aff *aff);
3916 The expression can be inspected using
3918 #include <isl/aff.h>
3919 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3920 int isl_aff_dim(__isl_keep isl_aff *aff,
3921 enum isl_dim_type type);
3922 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3923 __isl_keep isl_aff *aff);
3924 __isl_give isl_local_space *isl_aff_get_local_space(
3925 __isl_keep isl_aff *aff);
3926 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3927 enum isl_dim_type type, unsigned pos);
3928 const char *isl_pw_aff_get_dim_name(
3929 __isl_keep isl_pw_aff *pa,
3930 enum isl_dim_type type, unsigned pos);
3931 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3932 enum isl_dim_type type, unsigned pos);
3933 __isl_give isl_id *isl_pw_aff_get_dim_id(
3934 __isl_keep isl_pw_aff *pa,
3935 enum isl_dim_type type, unsigned pos);
3936 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
3937 enum isl_dim_type type);
3938 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3939 __isl_keep isl_pw_aff *pa,
3940 enum isl_dim_type type);
3941 __isl_give isl_val *isl_aff_get_constant_val(
3942 __isl_keep isl_aff *aff);
3943 __isl_give isl_val *isl_aff_get_coefficient_val(
3944 __isl_keep isl_aff *aff,
3945 enum isl_dim_type type, int pos);
3946 __isl_give isl_val *isl_aff_get_denominator_val(
3947 __isl_keep isl_aff *aff);
3948 __isl_give isl_aff *isl_aff_get_div(
3949 __isl_keep isl_aff *aff, int pos);
3951 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3952 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3953 int (*fn)(__isl_take isl_set *set,
3954 __isl_take isl_aff *aff,
3955 void *user), void *user);
3957 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3958 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3960 int isl_aff_is_nan(__isl_keep isl_aff *aff);
3961 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
3963 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3964 enum isl_dim_type type, unsigned first, unsigned n);
3965 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3966 enum isl_dim_type type, unsigned first, unsigned n);
3968 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3969 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3970 enum isl_dim_type type);
3971 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3973 It can be modified using
3975 #include <isl/aff.h>
3976 __isl_give isl_aff *isl_aff_set_tuple_id(
3977 __isl_take isl_aff *aff,
3978 enum isl_dim_type type, __isl_take isl_id *id);
3979 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3980 __isl_take isl_pw_aff *pwaff,
3981 enum isl_dim_type type, __isl_take isl_id *id);
3982 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
3983 __isl_take isl_pw_aff *pa,
3984 enum isl_dim_type type);
3985 __isl_give isl_aff *isl_aff_set_dim_name(
3986 __isl_take isl_aff *aff, enum isl_dim_type type,
3987 unsigned pos, const char *s);
3988 __isl_give isl_aff *isl_aff_set_dim_id(
3989 __isl_take isl_aff *aff, enum isl_dim_type type,
3990 unsigned pos, __isl_take isl_id *id);
3991 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3992 __isl_take isl_pw_aff *pma,
3993 enum isl_dim_type type, unsigned pos,
3994 __isl_take isl_id *id);
3995 __isl_give isl_aff *isl_aff_set_constant_si(
3996 __isl_take isl_aff *aff, int v);
3997 __isl_give isl_aff *isl_aff_set_constant_val(
3998 __isl_take isl_aff *aff, __isl_take isl_val *v);
3999 __isl_give isl_aff *isl_aff_set_coefficient_si(
4000 __isl_take isl_aff *aff,
4001 enum isl_dim_type type, int pos, int v);
4002 __isl_give isl_aff *isl_aff_set_coefficient_val(
4003 __isl_take isl_aff *aff,
4004 enum isl_dim_type type, int pos,
4005 __isl_take isl_val *v);
4007 __isl_give isl_aff *isl_aff_add_constant_si(
4008 __isl_take isl_aff *aff, int v);
4009 __isl_give isl_aff *isl_aff_add_constant_val(
4010 __isl_take isl_aff *aff, __isl_take isl_val *v);
4011 __isl_give isl_aff *isl_aff_add_constant_num_si(
4012 __isl_take isl_aff *aff, int v);
4013 __isl_give isl_aff *isl_aff_add_coefficient_si(
4014 __isl_take isl_aff *aff,
4015 enum isl_dim_type type, int pos, int v);
4016 __isl_give isl_aff *isl_aff_add_coefficient_val(
4017 __isl_take isl_aff *aff,
4018 enum isl_dim_type type, int pos,
4019 __isl_take isl_val *v);
4021 __isl_give isl_aff *isl_aff_insert_dims(
4022 __isl_take isl_aff *aff,
4023 enum isl_dim_type type, unsigned first, unsigned n);
4024 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
4025 __isl_take isl_pw_aff *pwaff,
4026 enum isl_dim_type type, unsigned first, unsigned n);
4027 __isl_give isl_aff *isl_aff_add_dims(
4028 __isl_take isl_aff *aff,
4029 enum isl_dim_type type, unsigned n);
4030 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
4031 __isl_take isl_pw_aff *pwaff,
4032 enum isl_dim_type type, unsigned n);
4033 __isl_give isl_aff *isl_aff_drop_dims(
4034 __isl_take isl_aff *aff,
4035 enum isl_dim_type type, unsigned first, unsigned n);
4036 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
4037 __isl_take isl_pw_aff *pwaff,
4038 enum isl_dim_type type, unsigned first, unsigned n);
4039 __isl_give isl_aff *isl_aff_move_dims(
4040 __isl_take isl_aff *aff,
4041 enum isl_dim_type dst_type, unsigned dst_pos,
4042 enum isl_dim_type src_type, unsigned src_pos,
4044 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
4045 __isl_take isl_pw_aff *pa,
4046 enum isl_dim_type dst_type, unsigned dst_pos,
4047 enum isl_dim_type src_type, unsigned src_pos,
4050 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
4051 set the I<numerator> of the constant or coefficient, while
4052 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
4053 the constant or coefficient as a whole.
4054 The C<add_constant> and C<add_coefficient> functions add an integer
4055 or rational value to
4056 the possibly rational constant or coefficient.
4057 The C<add_constant_num> functions add an integer value to
4060 To check whether an affine expressions is obviously zero
4061 or (obviously) equal to some other affine expression, use
4063 #include <isl/aff.h>
4064 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
4065 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
4066 __isl_keep isl_aff *aff2);
4067 int isl_pw_aff_plain_is_equal(
4068 __isl_keep isl_pw_aff *pwaff1,
4069 __isl_keep isl_pw_aff *pwaff2);
4070 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
4071 __isl_keep isl_pw_aff *pa2);
4072 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4073 __isl_keep isl_pw_aff *pa2);
4075 The function C<isl_pw_aff_plain_cmp> can be used to sort
4076 C<isl_pw_aff>s. The order is not strictly defined.
4077 The current order sorts expressions that only involve
4078 earlier dimensions before those that involve later dimensions.
4082 #include <isl/aff.h>
4083 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
4084 __isl_take isl_aff *aff2);
4085 __isl_give isl_pw_aff *isl_pw_aff_add(
4086 __isl_take isl_pw_aff *pwaff1,
4087 __isl_take isl_pw_aff *pwaff2);
4088 __isl_give isl_pw_aff *isl_pw_aff_min(
4089 __isl_take isl_pw_aff *pwaff1,
4090 __isl_take isl_pw_aff *pwaff2);
4091 __isl_give isl_pw_aff *isl_pw_aff_max(
4092 __isl_take isl_pw_aff *pwaff1,
4093 __isl_take isl_pw_aff *pwaff2);
4094 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
4095 __isl_take isl_aff *aff2);
4096 __isl_give isl_pw_aff *isl_pw_aff_sub(
4097 __isl_take isl_pw_aff *pwaff1,
4098 __isl_take isl_pw_aff *pwaff2);
4099 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
4100 __isl_give isl_pw_aff *isl_pw_aff_neg(
4101 __isl_take isl_pw_aff *pwaff);
4102 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
4103 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4104 __isl_take isl_pw_aff *pwaff);
4105 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
4106 __isl_give isl_pw_aff *isl_pw_aff_floor(
4107 __isl_take isl_pw_aff *pwaff);
4108 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
4109 __isl_take isl_val *mod);
4110 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
4111 __isl_take isl_pw_aff *pa,
4112 __isl_take isl_val *mod);
4113 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
4114 __isl_take isl_val *v);
4115 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
4116 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
4117 __isl_give isl_aff *isl_aff_scale_down_ui(
4118 __isl_take isl_aff *aff, unsigned f);
4119 __isl_give isl_aff *isl_aff_scale_down_val(
4120 __isl_take isl_aff *aff, __isl_take isl_val *v);
4121 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
4122 __isl_take isl_pw_aff *pa,
4123 __isl_take isl_val *f);
4125 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4126 __isl_take isl_pw_aff_list *list);
4127 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4128 __isl_take isl_pw_aff_list *list);
4130 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4131 __isl_take isl_pw_aff *pwqp);
4133 __isl_give isl_aff *isl_aff_align_params(
4134 __isl_take isl_aff *aff,
4135 __isl_take isl_space *model);
4136 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4137 __isl_take isl_pw_aff *pwaff,
4138 __isl_take isl_space *model);
4140 __isl_give isl_aff *isl_aff_project_domain_on_params(
4141 __isl_take isl_aff *aff);
4142 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4143 __isl_take isl_pw_aff *pwa);
4145 __isl_give isl_aff *isl_aff_gist_params(
4146 __isl_take isl_aff *aff,
4147 __isl_take isl_set *context);
4148 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
4149 __isl_take isl_set *context);
4150 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
4151 __isl_take isl_pw_aff *pwaff,
4152 __isl_take isl_set *context);
4153 __isl_give isl_pw_aff *isl_pw_aff_gist(
4154 __isl_take isl_pw_aff *pwaff,
4155 __isl_take isl_set *context);
4157 __isl_give isl_set *isl_pw_aff_domain(
4158 __isl_take isl_pw_aff *pwaff);
4159 __isl_give isl_set *isl_pw_aff_params(
4160 __isl_take isl_pw_aff *pwa);
4161 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4162 __isl_take isl_pw_aff *pa,
4163 __isl_take isl_set *set);
4164 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4165 __isl_take isl_pw_aff *pa,
4166 __isl_take isl_set *set);
4168 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
4169 __isl_take isl_aff *aff2);
4170 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
4171 __isl_take isl_aff *aff2);
4172 __isl_give isl_pw_aff *isl_pw_aff_mul(
4173 __isl_take isl_pw_aff *pwaff1,
4174 __isl_take isl_pw_aff *pwaff2);
4175 __isl_give isl_pw_aff *isl_pw_aff_div(
4176 __isl_take isl_pw_aff *pa1,
4177 __isl_take isl_pw_aff *pa2);
4178 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
4179 __isl_take isl_pw_aff *pa1,
4180 __isl_take isl_pw_aff *pa2);
4181 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
4182 __isl_take isl_pw_aff *pa1,
4183 __isl_take isl_pw_aff *pa2);
4185 When multiplying two affine expressions, at least one of the two needs
4186 to be a constant. Similarly, when dividing an affine expression by another,
4187 the second expression needs to be a constant.
4188 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
4189 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
4192 #include <isl/aff.h>
4193 __isl_give isl_aff *isl_aff_pullback_aff(
4194 __isl_take isl_aff *aff1,
4195 __isl_take isl_aff *aff2);
4196 __isl_give isl_aff *isl_aff_pullback_multi_aff(
4197 __isl_take isl_aff *aff,
4198 __isl_take isl_multi_aff *ma);
4199 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
4200 __isl_take isl_pw_aff *pa,
4201 __isl_take isl_multi_aff *ma);
4202 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
4203 __isl_take isl_pw_aff *pa,
4204 __isl_take isl_pw_multi_aff *pma);
4205 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
4206 __isl_take isl_pw_aff *pa,
4207 __isl_take isl_multi_pw_aff *mpa);
4209 These functions precompose the input expression by the given
4210 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
4211 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
4212 into the (piecewise) affine expression.
4213 Objects of type C<isl_multi_aff> are described in
4214 L</"Piecewise Multiple Quasi Affine Expressions">.
4216 #include <isl/aff.h>
4217 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4218 __isl_take isl_aff *aff);
4219 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4220 __isl_take isl_aff *aff);
4221 __isl_give isl_basic_set *isl_aff_le_basic_set(
4222 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4223 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4224 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4225 __isl_give isl_set *isl_pw_aff_eq_set(
4226 __isl_take isl_pw_aff *pwaff1,
4227 __isl_take isl_pw_aff *pwaff2);
4228 __isl_give isl_set *isl_pw_aff_ne_set(
4229 __isl_take isl_pw_aff *pwaff1,
4230 __isl_take isl_pw_aff *pwaff2);
4231 __isl_give isl_set *isl_pw_aff_le_set(
4232 __isl_take isl_pw_aff *pwaff1,
4233 __isl_take isl_pw_aff *pwaff2);
4234 __isl_give isl_set *isl_pw_aff_lt_set(
4235 __isl_take isl_pw_aff *pwaff1,
4236 __isl_take isl_pw_aff *pwaff2);
4237 __isl_give isl_set *isl_pw_aff_ge_set(
4238 __isl_take isl_pw_aff *pwaff1,
4239 __isl_take isl_pw_aff *pwaff2);
4240 __isl_give isl_set *isl_pw_aff_gt_set(
4241 __isl_take isl_pw_aff *pwaff1,
4242 __isl_take isl_pw_aff *pwaff2);
4244 __isl_give isl_set *isl_pw_aff_list_eq_set(
4245 __isl_take isl_pw_aff_list *list1,
4246 __isl_take isl_pw_aff_list *list2);
4247 __isl_give isl_set *isl_pw_aff_list_ne_set(
4248 __isl_take isl_pw_aff_list *list1,
4249 __isl_take isl_pw_aff_list *list2);
4250 __isl_give isl_set *isl_pw_aff_list_le_set(
4251 __isl_take isl_pw_aff_list *list1,
4252 __isl_take isl_pw_aff_list *list2);
4253 __isl_give isl_set *isl_pw_aff_list_lt_set(
4254 __isl_take isl_pw_aff_list *list1,
4255 __isl_take isl_pw_aff_list *list2);
4256 __isl_give isl_set *isl_pw_aff_list_ge_set(
4257 __isl_take isl_pw_aff_list *list1,
4258 __isl_take isl_pw_aff_list *list2);
4259 __isl_give isl_set *isl_pw_aff_list_gt_set(
4260 __isl_take isl_pw_aff_list *list1,
4261 __isl_take isl_pw_aff_list *list2);
4263 The function C<isl_aff_neg_basic_set> returns a basic set
4264 containing those elements in the domain space
4265 of C<aff> where C<aff> is negative.
4266 The function C<isl_aff_ge_basic_set> returns a basic set
4267 containing those elements in the shared space
4268 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4269 The function C<isl_pw_aff_ge_set> returns a set
4270 containing those elements in the shared domain
4271 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4272 The functions operating on C<isl_pw_aff_list> apply the corresponding
4273 C<isl_pw_aff> function to each pair of elements in the two lists.
4275 #include <isl/aff.h>
4276 __isl_give isl_set *isl_pw_aff_nonneg_set(
4277 __isl_take isl_pw_aff *pwaff);
4278 __isl_give isl_set *isl_pw_aff_zero_set(
4279 __isl_take isl_pw_aff *pwaff);
4280 __isl_give isl_set *isl_pw_aff_non_zero_set(
4281 __isl_take isl_pw_aff *pwaff);
4283 The function C<isl_pw_aff_nonneg_set> returns a set
4284 containing those elements in the domain
4285 of C<pwaff> where C<pwaff> is non-negative.
4287 #include <isl/aff.h>
4288 __isl_give isl_pw_aff *isl_pw_aff_cond(
4289 __isl_take isl_pw_aff *cond,
4290 __isl_take isl_pw_aff *pwaff_true,
4291 __isl_take isl_pw_aff *pwaff_false);
4293 The function C<isl_pw_aff_cond> performs a conditional operator
4294 and returns an expression that is equal to C<pwaff_true>
4295 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4296 where C<cond> is zero.
4298 #include <isl/aff.h>
4299 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4300 __isl_take isl_pw_aff *pwaff1,
4301 __isl_take isl_pw_aff *pwaff2);
4302 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4303 __isl_take isl_pw_aff *pwaff1,
4304 __isl_take isl_pw_aff *pwaff2);
4305 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4306 __isl_take isl_pw_aff *pwaff1,
4307 __isl_take isl_pw_aff *pwaff2);
4309 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4310 expression with a domain that is the union of those of C<pwaff1> and
4311 C<pwaff2> and such that on each cell, the quasi-affine expression is
4312 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4313 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4314 associated expression is the defined one.
4316 An expression can be read from input using
4318 #include <isl/aff.h>
4319 __isl_give isl_aff *isl_aff_read_from_str(
4320 isl_ctx *ctx, const char *str);
4321 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4322 isl_ctx *ctx, const char *str);
4324 An expression can be printed using
4326 #include <isl/aff.h>
4327 __isl_give isl_printer *isl_printer_print_aff(
4328 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4330 __isl_give isl_printer *isl_printer_print_pw_aff(
4331 __isl_take isl_printer *p,
4332 __isl_keep isl_pw_aff *pwaff);
4334 =head2 Piecewise Multiple Quasi Affine Expressions
4336 An C<isl_multi_aff> object represents a sequence of
4337 zero or more affine expressions, all defined on the same domain space.
4338 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4339 zero or more piecewise affine expressions.
4341 An C<isl_multi_aff> can be constructed from a single
4342 C<isl_aff> or an C<isl_aff_list> using the
4343 following functions. Similarly for C<isl_multi_pw_aff>
4344 and C<isl_pw_multi_aff>.
4346 #include <isl/aff.h>
4347 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4348 __isl_take isl_aff *aff);
4349 __isl_give isl_multi_pw_aff *
4350 isl_multi_pw_aff_from_multi_aff(
4351 __isl_take isl_multi_aff *ma);
4352 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4353 __isl_take isl_pw_aff *pa);
4354 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4355 __isl_take isl_pw_aff *pa);
4356 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4357 __isl_take isl_space *space,
4358 __isl_take isl_aff_list *list);
4360 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4361 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4362 Note however that the domain
4363 of the result is the intersection of the domains of the input.
4364 The reverse conversion is exact.
4366 #include <isl/aff.h>
4367 __isl_give isl_pw_multi_aff *
4368 isl_pw_multi_aff_from_multi_pw_aff(
4369 __isl_take isl_multi_pw_aff *mpa);
4370 __isl_give isl_multi_pw_aff *
4371 isl_multi_pw_aff_from_pw_multi_aff(
4372 __isl_take isl_pw_multi_aff *pma);
4374 An empty piecewise multiple quasi affine expression (one with no cells),
4375 the zero piecewise multiple quasi affine expression (with value zero
4376 for each output dimension),
4377 a piecewise multiple quasi affine expression with a single cell (with
4378 either a universe or a specified domain) or
4379 a zero-dimensional piecewise multiple quasi affine expression
4381 can be created using the following functions.
4383 #include <isl/aff.h>
4384 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4385 __isl_take isl_space *space);
4386 __isl_give isl_multi_aff *isl_multi_aff_zero(
4387 __isl_take isl_space *space);
4388 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4389 __isl_take isl_space *space);
4390 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4391 __isl_take isl_space *space);
4392 __isl_give isl_multi_aff *isl_multi_aff_identity(
4393 __isl_take isl_space *space);
4394 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4395 __isl_take isl_space *space);
4396 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4397 __isl_take isl_space *space);
4398 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4399 __isl_take isl_space *space);
4400 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4401 __isl_take isl_space *space);
4402 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4403 __isl_take isl_space *space,
4404 enum isl_dim_type type,
4405 unsigned first, unsigned n);
4406 __isl_give isl_pw_multi_aff *
4407 isl_pw_multi_aff_project_out_map(
4408 __isl_take isl_space *space,
4409 enum isl_dim_type type,
4410 unsigned first, unsigned n);
4411 __isl_give isl_pw_multi_aff *
4412 isl_pw_multi_aff_from_multi_aff(
4413 __isl_take isl_multi_aff *ma);
4414 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4415 __isl_take isl_set *set,
4416 __isl_take isl_multi_aff *maff);
4417 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4418 __isl_take isl_set *set);
4420 __isl_give isl_union_pw_multi_aff *
4421 isl_union_pw_multi_aff_empty(
4422 __isl_take isl_space *space);
4423 __isl_give isl_union_pw_multi_aff *
4424 isl_union_pw_multi_aff_add_pw_multi_aff(
4425 __isl_take isl_union_pw_multi_aff *upma,
4426 __isl_take isl_pw_multi_aff *pma);
4427 __isl_give isl_union_pw_multi_aff *
4428 isl_union_pw_multi_aff_from_domain(
4429 __isl_take isl_union_set *uset);
4431 A piecewise multiple quasi affine expression can also be initialized
4432 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4433 and the C<isl_map> is single-valued.
4434 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4435 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4437 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4438 __isl_take isl_set *set);
4439 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4440 __isl_take isl_map *map);
4442 __isl_give isl_union_pw_multi_aff *
4443 isl_union_pw_multi_aff_from_union_set(
4444 __isl_take isl_union_set *uset);
4445 __isl_give isl_union_pw_multi_aff *
4446 isl_union_pw_multi_aff_from_union_map(
4447 __isl_take isl_union_map *umap);
4449 Multiple quasi affine expressions can be copied and freed using
4451 #include <isl/aff.h>
4452 __isl_give isl_multi_aff *isl_multi_aff_copy(
4453 __isl_keep isl_multi_aff *maff);
4454 __isl_null isl_multi_aff *isl_multi_aff_free(
4455 __isl_take isl_multi_aff *maff);
4457 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4458 __isl_keep isl_pw_multi_aff *pma);
4459 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
4460 __isl_take isl_pw_multi_aff *pma);
4462 __isl_give isl_union_pw_multi_aff *
4463 isl_union_pw_multi_aff_copy(
4464 __isl_keep isl_union_pw_multi_aff *upma);
4465 __isl_null isl_union_pw_multi_aff *
4466 isl_union_pw_multi_aff_free(
4467 __isl_take isl_union_pw_multi_aff *upma);
4469 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4470 __isl_keep isl_multi_pw_aff *mpa);
4471 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
4472 __isl_take isl_multi_pw_aff *mpa);
4474 The expression can be inspected using
4476 #include <isl/aff.h>
4477 isl_ctx *isl_multi_aff_get_ctx(
4478 __isl_keep isl_multi_aff *maff);
4479 isl_ctx *isl_pw_multi_aff_get_ctx(
4480 __isl_keep isl_pw_multi_aff *pma);
4481 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4482 __isl_keep isl_union_pw_multi_aff *upma);
4483 isl_ctx *isl_multi_pw_aff_get_ctx(
4484 __isl_keep isl_multi_pw_aff *mpa);
4486 int isl_multi_aff_involves_dims(
4487 __isl_keep isl_multi_aff *ma,
4488 enum isl_dim_type type, unsigned first, unsigned n);
4489 int isl_multi_pw_aff_involves_dims(
4490 __isl_keep isl_multi_pw_aff *mpa,
4491 enum isl_dim_type type, unsigned first, unsigned n);
4493 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4494 enum isl_dim_type type);
4495 unsigned isl_pw_multi_aff_dim(
4496 __isl_keep isl_pw_multi_aff *pma,
4497 enum isl_dim_type type);
4498 unsigned isl_multi_pw_aff_dim(
4499 __isl_keep isl_multi_pw_aff *mpa,
4500 enum isl_dim_type type);
4501 __isl_give isl_aff *isl_multi_aff_get_aff(
4502 __isl_keep isl_multi_aff *multi, int pos);
4503 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4504 __isl_keep isl_pw_multi_aff *pma, int pos);
4505 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4506 __isl_keep isl_multi_pw_aff *mpa, int pos);
4507 int isl_multi_aff_find_dim_by_id(
4508 __isl_keep isl_multi_aff *ma,
4509 enum isl_dim_type type, __isl_keep isl_id *id);
4510 int isl_multi_pw_aff_find_dim_by_id(
4511 __isl_keep isl_multi_pw_aff *mpa,
4512 enum isl_dim_type type, __isl_keep isl_id *id);
4513 const char *isl_pw_multi_aff_get_dim_name(
4514 __isl_keep isl_pw_multi_aff *pma,
4515 enum isl_dim_type type, unsigned pos);
4516 __isl_give isl_id *isl_multi_aff_get_dim_id(
4517 __isl_keep isl_multi_aff *ma,
4518 enum isl_dim_type type, unsigned pos);
4519 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4520 __isl_keep isl_pw_multi_aff *pma,
4521 enum isl_dim_type type, unsigned pos);
4522 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4523 __isl_keep isl_multi_pw_aff *mpa,
4524 enum isl_dim_type type, unsigned pos);
4525 const char *isl_multi_aff_get_tuple_name(
4526 __isl_keep isl_multi_aff *multi,
4527 enum isl_dim_type type);
4528 int isl_pw_multi_aff_has_tuple_name(
4529 __isl_keep isl_pw_multi_aff *pma,
4530 enum isl_dim_type type);
4531 const char *isl_pw_multi_aff_get_tuple_name(
4532 __isl_keep isl_pw_multi_aff *pma,
4533 enum isl_dim_type type);
4534 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4535 enum isl_dim_type type);
4536 int isl_pw_multi_aff_has_tuple_id(
4537 __isl_keep isl_pw_multi_aff *pma,
4538 enum isl_dim_type type);
4539 int isl_multi_pw_aff_has_tuple_id(
4540 __isl_keep isl_multi_pw_aff *mpa,
4541 enum isl_dim_type type);
4542 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4543 __isl_keep isl_multi_aff *ma,
4544 enum isl_dim_type type);
4545 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4546 __isl_keep isl_pw_multi_aff *pma,
4547 enum isl_dim_type type);
4548 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4549 __isl_keep isl_multi_pw_aff *mpa,
4550 enum isl_dim_type type);
4551 int isl_multi_aff_range_is_wrapping(
4552 __isl_keep isl_multi_aff *ma);
4553 int isl_multi_pw_aff_range_is_wrapping(
4554 __isl_keep isl_multi_pw_aff *mpa);
4556 int isl_pw_multi_aff_foreach_piece(
4557 __isl_keep isl_pw_multi_aff *pma,
4558 int (*fn)(__isl_take isl_set *set,
4559 __isl_take isl_multi_aff *maff,
4560 void *user), void *user);
4562 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4563 __isl_keep isl_union_pw_multi_aff *upma,
4564 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4565 void *user), void *user);
4567 It can be modified using
4569 #include <isl/aff.h>
4570 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4571 __isl_take isl_multi_aff *multi, int pos,
4572 __isl_take isl_aff *aff);
4573 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4574 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4575 __isl_take isl_pw_aff *pa);
4576 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4577 __isl_take isl_multi_aff *maff,
4578 enum isl_dim_type type, unsigned pos, const char *s);
4579 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4580 __isl_take isl_multi_aff *maff,
4581 enum isl_dim_type type, unsigned pos,
4582 __isl_take isl_id *id);
4583 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4584 __isl_take isl_multi_aff *maff,
4585 enum isl_dim_type type, const char *s);
4586 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4587 __isl_take isl_multi_aff *maff,
4588 enum isl_dim_type type, __isl_take isl_id *id);
4589 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4590 __isl_take isl_pw_multi_aff *pma,
4591 enum isl_dim_type type, __isl_take isl_id *id);
4592 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4593 __isl_take isl_multi_aff *ma,
4594 enum isl_dim_type type);
4595 __isl_give isl_multi_pw_aff *
4596 isl_multi_pw_aff_reset_tuple_id(
4597 __isl_take isl_multi_pw_aff *mpa,
4598 enum isl_dim_type type);
4599 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4600 __isl_take isl_multi_aff *ma);
4601 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4602 __isl_take isl_multi_pw_aff *mpa);
4604 __isl_give isl_multi_pw_aff *
4605 isl_multi_pw_aff_set_dim_name(
4606 __isl_take isl_multi_pw_aff *mpa,
4607 enum isl_dim_type type, unsigned pos, const char *s);
4608 __isl_give isl_multi_pw_aff *
4609 isl_multi_pw_aff_set_dim_id(
4610 __isl_take isl_multi_pw_aff *mpa,
4611 enum isl_dim_type type, unsigned pos,
4612 __isl_take isl_id *id);
4613 __isl_give isl_multi_pw_aff *
4614 isl_multi_pw_aff_set_tuple_name(
4615 __isl_take isl_multi_pw_aff *mpa,
4616 enum isl_dim_type type, const char *s);
4618 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4619 __isl_take isl_multi_aff *ma);
4621 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4622 __isl_take isl_multi_aff *ma,
4623 enum isl_dim_type type, unsigned first, unsigned n);
4624 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4625 __isl_take isl_multi_aff *ma,
4626 enum isl_dim_type type, unsigned n);
4627 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4628 __isl_take isl_multi_aff *maff,
4629 enum isl_dim_type type, unsigned first, unsigned n);
4630 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4631 __isl_take isl_pw_multi_aff *pma,
4632 enum isl_dim_type type, unsigned first, unsigned n);
4634 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4635 __isl_take isl_multi_pw_aff *mpa,
4636 enum isl_dim_type type, unsigned first, unsigned n);
4637 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4638 __isl_take isl_multi_pw_aff *mpa,
4639 enum isl_dim_type type, unsigned n);
4640 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4641 __isl_take isl_multi_pw_aff *pma,
4642 enum isl_dim_type dst_type, unsigned dst_pos,
4643 enum isl_dim_type src_type, unsigned src_pos,
4646 To check whether two multiple affine expressions are
4647 (obviously) equal to each other, use
4649 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4650 __isl_keep isl_multi_aff *maff2);
4651 int isl_pw_multi_aff_plain_is_equal(
4652 __isl_keep isl_pw_multi_aff *pma1,
4653 __isl_keep isl_pw_multi_aff *pma2);
4654 int isl_multi_pw_aff_plain_is_equal(
4655 __isl_keep isl_multi_pw_aff *mpa1,
4656 __isl_keep isl_multi_pw_aff *mpa2);
4657 int isl_multi_pw_aff_is_equal(
4658 __isl_keep isl_multi_pw_aff *mpa1,
4659 __isl_keep isl_multi_pw_aff *mpa2);
4663 #include <isl/aff.h>
4664 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4665 __isl_take isl_pw_multi_aff *pma1,
4666 __isl_take isl_pw_multi_aff *pma2);
4667 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4668 __isl_take isl_pw_multi_aff *pma1,
4669 __isl_take isl_pw_multi_aff *pma2);
4670 __isl_give isl_multi_aff *isl_multi_aff_floor(
4671 __isl_take isl_multi_aff *ma);
4672 __isl_give isl_multi_aff *isl_multi_aff_add(
4673 __isl_take isl_multi_aff *maff1,
4674 __isl_take isl_multi_aff *maff2);
4675 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4676 __isl_take isl_pw_multi_aff *pma1,
4677 __isl_take isl_pw_multi_aff *pma2);
4678 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4679 __isl_take isl_union_pw_multi_aff *upma1,
4680 __isl_take isl_union_pw_multi_aff *upma2);
4681 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4682 __isl_take isl_pw_multi_aff *pma1,
4683 __isl_take isl_pw_multi_aff *pma2);
4684 __isl_give isl_multi_aff *isl_multi_aff_sub(
4685 __isl_take isl_multi_aff *ma1,
4686 __isl_take isl_multi_aff *ma2);
4687 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4688 __isl_take isl_pw_multi_aff *pma1,
4689 __isl_take isl_pw_multi_aff *pma2);
4690 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4691 __isl_take isl_union_pw_multi_aff *upma1,
4692 __isl_take isl_union_pw_multi_aff *upma2);
4694 C<isl_multi_aff_sub> subtracts the second argument from the first.
4696 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4697 __isl_take isl_multi_aff *ma,
4698 __isl_take isl_val *v);
4699 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4700 __isl_take isl_pw_multi_aff *pma,
4701 __isl_take isl_val *v);
4702 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4703 __isl_take isl_multi_pw_aff *mpa,
4704 __isl_take isl_val *v);
4705 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4706 __isl_take isl_multi_aff *ma,
4707 __isl_take isl_multi_val *mv);
4708 __isl_give isl_pw_multi_aff *
4709 isl_pw_multi_aff_scale_multi_val(
4710 __isl_take isl_pw_multi_aff *pma,
4711 __isl_take isl_multi_val *mv);
4712 __isl_give isl_multi_pw_aff *
4713 isl_multi_pw_aff_scale_multi_val(
4714 __isl_take isl_multi_pw_aff *mpa,
4715 __isl_take isl_multi_val *mv);
4716 __isl_give isl_union_pw_multi_aff *
4717 isl_union_pw_multi_aff_scale_multi_val(
4718 __isl_take isl_union_pw_multi_aff *upma,
4719 __isl_take isl_multi_val *mv);
4720 __isl_give isl_multi_aff *
4721 isl_multi_aff_scale_down_multi_val(
4722 __isl_take isl_multi_aff *ma,
4723 __isl_take isl_multi_val *mv);
4724 __isl_give isl_multi_pw_aff *
4725 isl_multi_pw_aff_scale_down_multi_val(
4726 __isl_take isl_multi_pw_aff *mpa,
4727 __isl_take isl_multi_val *mv);
4729 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4730 by the corresponding elements of C<mv>.
4732 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4733 __isl_take isl_pw_multi_aff *pma,
4734 enum isl_dim_type type, unsigned pos, int value);
4735 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4736 __isl_take isl_pw_multi_aff *pma,
4737 __isl_take isl_set *set);
4738 __isl_give isl_set *isl_multi_pw_aff_domain(
4739 __isl_take isl_multi_pw_aff *mpa);
4740 __isl_give isl_multi_pw_aff *
4741 isl_multi_pw_aff_intersect_params(
4742 __isl_take isl_multi_pw_aff *mpa,
4743 __isl_take isl_set *set);
4744 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4745 __isl_take isl_pw_multi_aff *pma,
4746 __isl_take isl_set *set);
4747 __isl_give isl_multi_pw_aff *
4748 isl_multi_pw_aff_intersect_domain(
4749 __isl_take isl_multi_pw_aff *mpa,
4750 __isl_take isl_set *domain);
4751 __isl_give isl_union_pw_multi_aff *
4752 isl_union_pw_multi_aff_intersect_domain(
4753 __isl_take isl_union_pw_multi_aff *upma,
4754 __isl_take isl_union_set *uset);
4755 __isl_give isl_multi_aff *isl_multi_aff_lift(
4756 __isl_take isl_multi_aff *maff,
4757 __isl_give isl_local_space **ls);
4758 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4759 __isl_take isl_pw_multi_aff *pma);
4760 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4761 __isl_take isl_multi_pw_aff *mpa);
4762 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4763 __isl_take isl_multi_aff *multi,
4764 __isl_take isl_space *model);
4765 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4766 __isl_take isl_pw_multi_aff *pma,
4767 __isl_take isl_space *model);
4768 __isl_give isl_union_pw_multi_aff *
4769 isl_union_pw_multi_aff_align_params(
4770 __isl_take isl_union_pw_multi_aff *upma,
4771 __isl_take isl_space *model);
4772 __isl_give isl_pw_multi_aff *
4773 isl_pw_multi_aff_project_domain_on_params(
4774 __isl_take isl_pw_multi_aff *pma);
4775 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4776 __isl_take isl_multi_aff *maff,
4777 __isl_take isl_set *context);
4778 __isl_give isl_multi_aff *isl_multi_aff_gist(
4779 __isl_take isl_multi_aff *maff,
4780 __isl_take isl_set *context);
4781 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4782 __isl_take isl_pw_multi_aff *pma,
4783 __isl_take isl_set *set);
4784 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4785 __isl_take isl_pw_multi_aff *pma,
4786 __isl_take isl_set *set);
4787 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4788 __isl_take isl_multi_pw_aff *mpa,
4789 __isl_take isl_set *set);
4790 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4791 __isl_take isl_multi_pw_aff *mpa,
4792 __isl_take isl_set *set);
4793 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4794 __isl_take isl_multi_aff *ma);
4795 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4796 __isl_take isl_multi_pw_aff *mpa);
4797 __isl_give isl_set *isl_pw_multi_aff_domain(
4798 __isl_take isl_pw_multi_aff *pma);
4799 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4800 __isl_take isl_union_pw_multi_aff *upma);
4801 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4802 __isl_take isl_multi_aff *ma1, unsigned pos,
4803 __isl_take isl_multi_aff *ma2);
4804 __isl_give isl_multi_aff *isl_multi_aff_splice(
4805 __isl_take isl_multi_aff *ma1,
4806 unsigned in_pos, unsigned out_pos,
4807 __isl_take isl_multi_aff *ma2);
4808 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4809 __isl_take isl_multi_aff *ma1,
4810 __isl_take isl_multi_aff *ma2);
4811 __isl_give isl_multi_aff *
4812 isl_multi_aff_range_factor_domain(
4813 __isl_take isl_multi_aff *ma);
4814 __isl_give isl_multi_aff *
4815 isl_multi_aff_range_factor_range(
4816 __isl_take isl_multi_aff *ma);
4817 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4818 __isl_take isl_multi_aff *ma1,
4819 __isl_take isl_multi_aff *ma2);
4820 __isl_give isl_multi_aff *isl_multi_aff_product(
4821 __isl_take isl_multi_aff *ma1,
4822 __isl_take isl_multi_aff *ma2);
4823 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4824 __isl_take isl_multi_pw_aff *mpa1,
4825 __isl_take isl_multi_pw_aff *mpa2);
4826 __isl_give isl_pw_multi_aff *
4827 isl_pw_multi_aff_range_product(
4828 __isl_take isl_pw_multi_aff *pma1,
4829 __isl_take isl_pw_multi_aff *pma2);
4830 __isl_give isl_multi_pw_aff *
4831 isl_multi_pw_aff_range_factor_domain(
4832 __isl_take isl_multi_pw_aff *mpa);
4833 __isl_give isl_multi_pw_aff *
4834 isl_multi_pw_aff_range_factor_range(
4835 __isl_take isl_multi_pw_aff *mpa);
4836 __isl_give isl_pw_multi_aff *
4837 isl_pw_multi_aff_flat_range_product(
4838 __isl_take isl_pw_multi_aff *pma1,
4839 __isl_take isl_pw_multi_aff *pma2);
4840 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4841 __isl_take isl_pw_multi_aff *pma1,
4842 __isl_take isl_pw_multi_aff *pma2);
4843 __isl_give isl_union_pw_multi_aff *
4844 isl_union_pw_multi_aff_flat_range_product(
4845 __isl_take isl_union_pw_multi_aff *upma1,
4846 __isl_take isl_union_pw_multi_aff *upma2);
4847 __isl_give isl_multi_pw_aff *
4848 isl_multi_pw_aff_range_splice(
4849 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4850 __isl_take isl_multi_pw_aff *mpa2);
4851 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4852 __isl_take isl_multi_pw_aff *mpa1,
4853 unsigned in_pos, unsigned out_pos,
4854 __isl_take isl_multi_pw_aff *mpa2);
4855 __isl_give isl_multi_pw_aff *
4856 isl_multi_pw_aff_range_product(
4857 __isl_take isl_multi_pw_aff *mpa1,
4858 __isl_take isl_multi_pw_aff *mpa2);
4859 __isl_give isl_multi_pw_aff *
4860 isl_multi_pw_aff_flat_range_product(
4861 __isl_take isl_multi_pw_aff *mpa1,
4862 __isl_take isl_multi_pw_aff *mpa2);
4864 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4865 then it is assigned the local space that lies at the basis of
4866 the lifting applied.
4868 #include <isl/aff.h>
4869 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4870 __isl_take isl_multi_aff *ma1,
4871 __isl_take isl_multi_aff *ma2);
4872 __isl_give isl_pw_multi_aff *
4873 isl_pw_multi_aff_pullback_multi_aff(
4874 __isl_take isl_pw_multi_aff *pma,
4875 __isl_take isl_multi_aff *ma);
4876 __isl_give isl_multi_pw_aff *
4877 isl_multi_pw_aff_pullback_multi_aff(
4878 __isl_take isl_multi_pw_aff *mpa,
4879 __isl_take isl_multi_aff *ma);
4880 __isl_give isl_pw_multi_aff *
4881 isl_pw_multi_aff_pullback_pw_multi_aff(
4882 __isl_take isl_pw_multi_aff *pma1,
4883 __isl_take isl_pw_multi_aff *pma2);
4884 __isl_give isl_multi_pw_aff *
4885 isl_multi_pw_aff_pullback_pw_multi_aff(
4886 __isl_take isl_multi_pw_aff *mpa,
4887 __isl_take isl_pw_multi_aff *pma);
4888 __isl_give isl_multi_pw_aff *
4889 isl_multi_pw_aff_pullback_multi_pw_aff(
4890 __isl_take isl_multi_pw_aff *mpa1,
4891 __isl_take isl_multi_pw_aff *mpa2);
4893 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4894 In other words, C<ma2> is plugged
4897 __isl_give isl_set *isl_multi_aff_lex_le_set(
4898 __isl_take isl_multi_aff *ma1,
4899 __isl_take isl_multi_aff *ma2);
4900 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4901 __isl_take isl_multi_aff *ma1,
4902 __isl_take isl_multi_aff *ma2);
4904 The function C<isl_multi_aff_lex_le_set> returns a set
4905 containing those elements in the shared domain space
4906 where C<ma1> is lexicographically smaller than or
4909 An expression can be read from input using
4911 #include <isl/aff.h>
4912 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4913 isl_ctx *ctx, const char *str);
4914 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4915 isl_ctx *ctx, const char *str);
4916 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4917 isl_ctx *ctx, const char *str);
4918 __isl_give isl_union_pw_multi_aff *
4919 isl_union_pw_multi_aff_read_from_str(
4920 isl_ctx *ctx, const char *str);
4922 An expression can be printed using
4924 #include <isl/aff.h>
4925 __isl_give isl_printer *isl_printer_print_multi_aff(
4926 __isl_take isl_printer *p,
4927 __isl_keep isl_multi_aff *maff);
4928 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4929 __isl_take isl_printer *p,
4930 __isl_keep isl_pw_multi_aff *pma);
4931 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4932 __isl_take isl_printer *p,
4933 __isl_keep isl_union_pw_multi_aff *upma);
4934 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4935 __isl_take isl_printer *p,
4936 __isl_keep isl_multi_pw_aff *mpa);
4940 Points are elements of a set. They can be used to construct
4941 simple sets (boxes) or they can be used to represent the
4942 individual elements of a set.
4943 The zero point (the origin) can be created using
4945 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4947 The coordinates of a point can be inspected, set and changed
4950 __isl_give isl_val *isl_point_get_coordinate_val(
4951 __isl_keep isl_point *pnt,
4952 enum isl_dim_type type, int pos);
4953 __isl_give isl_point *isl_point_set_coordinate_val(
4954 __isl_take isl_point *pnt,
4955 enum isl_dim_type type, int pos,
4956 __isl_take isl_val *v);
4958 __isl_give isl_point *isl_point_add_ui(
4959 __isl_take isl_point *pnt,
4960 enum isl_dim_type type, int pos, unsigned val);
4961 __isl_give isl_point *isl_point_sub_ui(
4962 __isl_take isl_point *pnt,
4963 enum isl_dim_type type, int pos, unsigned val);
4965 Other properties can be obtained using
4967 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4969 Points can be copied or freed using
4971 __isl_give isl_point *isl_point_copy(
4972 __isl_keep isl_point *pnt);
4973 void isl_point_free(__isl_take isl_point *pnt);
4975 A singleton set can be created from a point using
4977 __isl_give isl_basic_set *isl_basic_set_from_point(
4978 __isl_take isl_point *pnt);
4979 __isl_give isl_set *isl_set_from_point(
4980 __isl_take isl_point *pnt);
4982 and a box can be created from two opposite extremal points using
4984 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4985 __isl_take isl_point *pnt1,
4986 __isl_take isl_point *pnt2);
4987 __isl_give isl_set *isl_set_box_from_points(
4988 __isl_take isl_point *pnt1,
4989 __isl_take isl_point *pnt2);
4991 All elements of a B<bounded> (union) set can be enumerated using
4992 the following functions.
4994 int isl_set_foreach_point(__isl_keep isl_set *set,
4995 int (*fn)(__isl_take isl_point *pnt, void *user),
4997 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4998 int (*fn)(__isl_take isl_point *pnt, void *user),
5001 The function C<fn> is called for each integer point in
5002 C<set> with as second argument the last argument of
5003 the C<isl_set_foreach_point> call. The function C<fn>
5004 should return C<0> on success and C<-1> on failure.
5005 In the latter case, C<isl_set_foreach_point> will stop
5006 enumerating and return C<-1> as well.
5007 If the enumeration is performed successfully and to completion,
5008 then C<isl_set_foreach_point> returns C<0>.
5010 To obtain a single point of a (basic) set, use
5012 __isl_give isl_point *isl_basic_set_sample_point(
5013 __isl_take isl_basic_set *bset);
5014 __isl_give isl_point *isl_set_sample_point(
5015 __isl_take isl_set *set);
5017 If C<set> does not contain any (integer) points, then the
5018 resulting point will be ``void'', a property that can be
5021 int isl_point_is_void(__isl_keep isl_point *pnt);
5023 =head2 Piecewise Quasipolynomials
5025 A piecewise quasipolynomial is a particular kind of function that maps
5026 a parametric point to a rational value.
5027 More specifically, a quasipolynomial is a polynomial expression in greatest
5028 integer parts of affine expressions of parameters and variables.
5029 A piecewise quasipolynomial is a subdivision of a given parametric
5030 domain into disjoint cells with a quasipolynomial associated to
5031 each cell. The value of the piecewise quasipolynomial at a given
5032 point is the value of the quasipolynomial associated to the cell
5033 that contains the point. Outside of the union of cells,
5034 the value is assumed to be zero.
5035 For example, the piecewise quasipolynomial
5037 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
5039 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
5040 A given piecewise quasipolynomial has a fixed domain dimension.
5041 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
5042 defined over different domains.
5043 Piecewise quasipolynomials are mainly used by the C<barvinok>
5044 library for representing the number of elements in a parametric set or map.
5045 For example, the piecewise quasipolynomial above represents
5046 the number of points in the map
5048 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
5050 =head3 Input and Output
5052 Piecewise quasipolynomials can be read from input using
5054 __isl_give isl_union_pw_qpolynomial *
5055 isl_union_pw_qpolynomial_read_from_str(
5056 isl_ctx *ctx, const char *str);
5058 Quasipolynomials and piecewise quasipolynomials can be printed
5059 using the following functions.
5061 __isl_give isl_printer *isl_printer_print_qpolynomial(
5062 __isl_take isl_printer *p,
5063 __isl_keep isl_qpolynomial *qp);
5065 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
5066 __isl_take isl_printer *p,
5067 __isl_keep isl_pw_qpolynomial *pwqp);
5069 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
5070 __isl_take isl_printer *p,
5071 __isl_keep isl_union_pw_qpolynomial *upwqp);
5073 The output format of the printer
5074 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5075 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
5077 In case of printing in C<ISL_FORMAT_C>, the user may want
5078 to set the names of all dimensions
5080 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
5081 __isl_take isl_qpolynomial *qp,
5082 enum isl_dim_type type, unsigned pos,
5084 __isl_give isl_pw_qpolynomial *
5085 isl_pw_qpolynomial_set_dim_name(
5086 __isl_take isl_pw_qpolynomial *pwqp,
5087 enum isl_dim_type type, unsigned pos,
5090 =head3 Creating New (Piecewise) Quasipolynomials
5092 Some simple quasipolynomials can be created using the following functions.
5093 More complicated quasipolynomials can be created by applying
5094 operations such as addition and multiplication
5095 on the resulting quasipolynomials
5097 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
5098 __isl_take isl_space *domain);
5099 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
5100 __isl_take isl_space *domain);
5101 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
5102 __isl_take isl_space *domain);
5103 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
5104 __isl_take isl_space *domain);
5105 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
5106 __isl_take isl_space *domain);
5107 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
5108 __isl_take isl_space *domain,
5109 __isl_take isl_val *val);
5110 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
5111 __isl_take isl_space *domain,
5112 enum isl_dim_type type, unsigned pos);
5113 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
5114 __isl_take isl_aff *aff);
5116 Note that the space in which a quasipolynomial lives is a map space
5117 with a one-dimensional range. The C<domain> argument in some of
5118 the functions above corresponds to the domain of this map space.
5120 The zero piecewise quasipolynomial or a piecewise quasipolynomial
5121 with a single cell can be created using the following functions.
5122 Multiple of these single cell piecewise quasipolynomials can
5123 be combined to create more complicated piecewise quasipolynomials.
5125 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
5126 __isl_take isl_space *space);
5127 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
5128 __isl_take isl_set *set,
5129 __isl_take isl_qpolynomial *qp);
5130 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
5131 __isl_take isl_qpolynomial *qp);
5132 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
5133 __isl_take isl_pw_aff *pwaff);
5135 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
5136 __isl_take isl_space *space);
5137 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
5138 __isl_take isl_pw_qpolynomial *pwqp);
5139 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
5140 __isl_take isl_union_pw_qpolynomial *upwqp,
5141 __isl_take isl_pw_qpolynomial *pwqp);
5143 Quasipolynomials can be copied and freed again using the following
5146 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
5147 __isl_keep isl_qpolynomial *qp);
5148 __isl_null isl_qpolynomial *isl_qpolynomial_free(
5149 __isl_take isl_qpolynomial *qp);
5151 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
5152 __isl_keep isl_pw_qpolynomial *pwqp);
5153 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
5154 __isl_take isl_pw_qpolynomial *pwqp);
5156 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
5157 __isl_keep isl_union_pw_qpolynomial *upwqp);
5158 __isl_null isl_union_pw_qpolynomial *
5159 isl_union_pw_qpolynomial_free(
5160 __isl_take isl_union_pw_qpolynomial *upwqp);
5162 =head3 Inspecting (Piecewise) Quasipolynomials
5164 To iterate over all piecewise quasipolynomials in a union
5165 piecewise quasipolynomial, use the following function
5167 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
5168 __isl_keep isl_union_pw_qpolynomial *upwqp,
5169 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
5172 To extract the piecewise quasipolynomial in a given space from a union, use
5174 __isl_give isl_pw_qpolynomial *
5175 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
5176 __isl_keep isl_union_pw_qpolynomial *upwqp,
5177 __isl_take isl_space *space);
5179 To iterate over the cells in a piecewise quasipolynomial,
5180 use either of the following two functions
5182 int isl_pw_qpolynomial_foreach_piece(
5183 __isl_keep isl_pw_qpolynomial *pwqp,
5184 int (*fn)(__isl_take isl_set *set,
5185 __isl_take isl_qpolynomial *qp,
5186 void *user), void *user);
5187 int isl_pw_qpolynomial_foreach_lifted_piece(
5188 __isl_keep isl_pw_qpolynomial *pwqp,
5189 int (*fn)(__isl_take isl_set *set,
5190 __isl_take isl_qpolynomial *qp,
5191 void *user), void *user);
5193 As usual, the function C<fn> should return C<0> on success
5194 and C<-1> on failure. The difference between
5195 C<isl_pw_qpolynomial_foreach_piece> and
5196 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
5197 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
5198 compute unique representations for all existentially quantified
5199 variables and then turn these existentially quantified variables
5200 into extra set variables, adapting the associated quasipolynomial
5201 accordingly. This means that the C<set> passed to C<fn>
5202 will not have any existentially quantified variables, but that
5203 the dimensions of the sets may be different for different
5204 invocations of C<fn>.
5206 The constant term of a quasipolynomial can be extracted using
5208 __isl_give isl_val *isl_qpolynomial_get_constant_val(
5209 __isl_keep isl_qpolynomial *qp);
5211 To iterate over all terms in a quasipolynomial,
5214 int isl_qpolynomial_foreach_term(
5215 __isl_keep isl_qpolynomial *qp,
5216 int (*fn)(__isl_take isl_term *term,
5217 void *user), void *user);
5219 The terms themselves can be inspected and freed using
5222 unsigned isl_term_dim(__isl_keep isl_term *term,
5223 enum isl_dim_type type);
5224 __isl_give isl_val *isl_term_get_coefficient_val(
5225 __isl_keep isl_term *term);
5226 int isl_term_get_exp(__isl_keep isl_term *term,
5227 enum isl_dim_type type, unsigned pos);
5228 __isl_give isl_aff *isl_term_get_div(
5229 __isl_keep isl_term *term, unsigned pos);
5230 void isl_term_free(__isl_take isl_term *term);
5232 Each term is a product of parameters, set variables and
5233 integer divisions. The function C<isl_term_get_exp>
5234 returns the exponent of a given dimensions in the given term.
5236 =head3 Properties of (Piecewise) Quasipolynomials
5238 To check whether two union piecewise quasipolynomials are
5239 obviously equal, use
5241 int isl_union_pw_qpolynomial_plain_is_equal(
5242 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5243 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5245 =head3 Operations on (Piecewise) Quasipolynomials
5247 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5248 __isl_take isl_qpolynomial *qp,
5249 __isl_take isl_val *v);
5250 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5251 __isl_take isl_qpolynomial *qp);
5252 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5253 __isl_take isl_qpolynomial *qp1,
5254 __isl_take isl_qpolynomial *qp2);
5255 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5256 __isl_take isl_qpolynomial *qp1,
5257 __isl_take isl_qpolynomial *qp2);
5258 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5259 __isl_take isl_qpolynomial *qp1,
5260 __isl_take isl_qpolynomial *qp2);
5261 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5262 __isl_take isl_qpolynomial *qp, unsigned exponent);
5264 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5265 __isl_take isl_pw_qpolynomial *pwqp,
5266 enum isl_dim_type type, unsigned n,
5267 __isl_take isl_val *v);
5268 __isl_give isl_pw_qpolynomial *
5269 isl_pw_qpolynomial_scale_val(
5270 __isl_take isl_pw_qpolynomial *pwqp,
5271 __isl_take isl_val *v);
5272 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5273 __isl_take isl_pw_qpolynomial *pwqp1,
5274 __isl_take isl_pw_qpolynomial *pwqp2);
5275 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5276 __isl_take isl_pw_qpolynomial *pwqp1,
5277 __isl_take isl_pw_qpolynomial *pwqp2);
5278 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5279 __isl_take isl_pw_qpolynomial *pwqp1,
5280 __isl_take isl_pw_qpolynomial *pwqp2);
5281 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5282 __isl_take isl_pw_qpolynomial *pwqp);
5283 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5284 __isl_take isl_pw_qpolynomial *pwqp1,
5285 __isl_take isl_pw_qpolynomial *pwqp2);
5286 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5287 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5289 __isl_give isl_union_pw_qpolynomial *
5290 isl_union_pw_qpolynomial_scale_val(
5291 __isl_take isl_union_pw_qpolynomial *upwqp,
5292 __isl_take isl_val *v);
5293 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5294 __isl_take isl_union_pw_qpolynomial *upwqp1,
5295 __isl_take isl_union_pw_qpolynomial *upwqp2);
5296 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5297 __isl_take isl_union_pw_qpolynomial *upwqp1,
5298 __isl_take isl_union_pw_qpolynomial *upwqp2);
5299 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5300 __isl_take isl_union_pw_qpolynomial *upwqp1,
5301 __isl_take isl_union_pw_qpolynomial *upwqp2);
5303 __isl_give isl_val *isl_pw_qpolynomial_eval(
5304 __isl_take isl_pw_qpolynomial *pwqp,
5305 __isl_take isl_point *pnt);
5307 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5308 __isl_take isl_union_pw_qpolynomial *upwqp,
5309 __isl_take isl_point *pnt);
5311 __isl_give isl_set *isl_pw_qpolynomial_domain(
5312 __isl_take isl_pw_qpolynomial *pwqp);
5313 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5314 __isl_take isl_pw_qpolynomial *pwpq,
5315 __isl_take isl_set *set);
5316 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5317 __isl_take isl_pw_qpolynomial *pwpq,
5318 __isl_take isl_set *set);
5320 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5321 __isl_take isl_union_pw_qpolynomial *upwqp);
5322 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5323 __isl_take isl_union_pw_qpolynomial *upwpq,
5324 __isl_take isl_union_set *uset);
5325 __isl_give isl_union_pw_qpolynomial *
5326 isl_union_pw_qpolynomial_intersect_params(
5327 __isl_take isl_union_pw_qpolynomial *upwpq,
5328 __isl_take isl_set *set);
5330 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5331 __isl_take isl_qpolynomial *qp,
5332 __isl_take isl_space *model);
5334 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5335 __isl_take isl_qpolynomial *qp);
5336 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5337 __isl_take isl_pw_qpolynomial *pwqp);
5339 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5340 __isl_take isl_union_pw_qpolynomial *upwqp);
5342 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5343 __isl_take isl_qpolynomial *qp,
5344 __isl_take isl_set *context);
5345 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5346 __isl_take isl_qpolynomial *qp,
5347 __isl_take isl_set *context);
5349 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5350 __isl_take isl_pw_qpolynomial *pwqp,
5351 __isl_take isl_set *context);
5352 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5353 __isl_take isl_pw_qpolynomial *pwqp,
5354 __isl_take isl_set *context);
5356 __isl_give isl_union_pw_qpolynomial *
5357 isl_union_pw_qpolynomial_gist_params(
5358 __isl_take isl_union_pw_qpolynomial *upwqp,
5359 __isl_take isl_set *context);
5360 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5361 __isl_take isl_union_pw_qpolynomial *upwqp,
5362 __isl_take isl_union_set *context);
5364 The gist operation applies the gist operation to each of
5365 the cells in the domain of the input piecewise quasipolynomial.
5366 The context is also exploited
5367 to simplify the quasipolynomials associated to each cell.
5369 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5370 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5371 __isl_give isl_union_pw_qpolynomial *
5372 isl_union_pw_qpolynomial_to_polynomial(
5373 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5375 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5376 the polynomial will be an overapproximation. If C<sign> is negative,
5377 it will be an underapproximation. If C<sign> is zero, the approximation
5378 will lie somewhere in between.
5380 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5382 A piecewise quasipolynomial reduction is a piecewise
5383 reduction (or fold) of quasipolynomials.
5384 In particular, the reduction can be maximum or a minimum.
5385 The objects are mainly used to represent the result of
5386 an upper or lower bound on a quasipolynomial over its domain,
5387 i.e., as the result of the following function.
5389 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5390 __isl_take isl_pw_qpolynomial *pwqp,
5391 enum isl_fold type, int *tight);
5393 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5394 __isl_take isl_union_pw_qpolynomial *upwqp,
5395 enum isl_fold type, int *tight);
5397 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5398 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5399 is the returned bound is known be tight, i.e., for each value
5400 of the parameters there is at least
5401 one element in the domain that reaches the bound.
5402 If the domain of C<pwqp> is not wrapping, then the bound is computed
5403 over all elements in that domain and the result has a purely parametric
5404 domain. If the domain of C<pwqp> is wrapping, then the bound is
5405 computed over the range of the wrapped relation. The domain of the
5406 wrapped relation becomes the domain of the result.
5408 A (piecewise) quasipolynomial reduction can be copied or freed using the
5409 following functions.
5411 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5412 __isl_keep isl_qpolynomial_fold *fold);
5413 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5414 __isl_keep isl_pw_qpolynomial_fold *pwf);
5415 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5416 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5417 void isl_qpolynomial_fold_free(
5418 __isl_take isl_qpolynomial_fold *fold);
5419 __isl_null isl_pw_qpolynomial_fold *
5420 isl_pw_qpolynomial_fold_free(
5421 __isl_take isl_pw_qpolynomial_fold *pwf);
5422 __isl_null isl_union_pw_qpolynomial_fold *
5423 isl_union_pw_qpolynomial_fold_free(
5424 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5426 =head3 Printing Piecewise Quasipolynomial Reductions
5428 Piecewise quasipolynomial reductions can be printed
5429 using the following function.
5431 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5432 __isl_take isl_printer *p,
5433 __isl_keep isl_pw_qpolynomial_fold *pwf);
5434 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5435 __isl_take isl_printer *p,
5436 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5438 For C<isl_printer_print_pw_qpolynomial_fold>,
5439 output format of the printer
5440 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5441 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5442 output format of the printer
5443 needs to be set to C<ISL_FORMAT_ISL>.
5444 In case of printing in C<ISL_FORMAT_C>, the user may want
5445 to set the names of all dimensions
5447 __isl_give isl_pw_qpolynomial_fold *
5448 isl_pw_qpolynomial_fold_set_dim_name(
5449 __isl_take isl_pw_qpolynomial_fold *pwf,
5450 enum isl_dim_type type, unsigned pos,
5453 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5455 To iterate over all piecewise quasipolynomial reductions in a union
5456 piecewise quasipolynomial reduction, use the following function
5458 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5459 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5460 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5461 void *user), void *user);
5463 To iterate over the cells in a piecewise quasipolynomial reduction,
5464 use either of the following two functions
5466 int isl_pw_qpolynomial_fold_foreach_piece(
5467 __isl_keep isl_pw_qpolynomial_fold *pwf,
5468 int (*fn)(__isl_take isl_set *set,
5469 __isl_take isl_qpolynomial_fold *fold,
5470 void *user), void *user);
5471 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5472 __isl_keep isl_pw_qpolynomial_fold *pwf,
5473 int (*fn)(__isl_take isl_set *set,
5474 __isl_take isl_qpolynomial_fold *fold,
5475 void *user), void *user);
5477 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5478 of the difference between these two functions.
5480 To iterate over all quasipolynomials in a reduction, use
5482 int isl_qpolynomial_fold_foreach_qpolynomial(
5483 __isl_keep isl_qpolynomial_fold *fold,
5484 int (*fn)(__isl_take isl_qpolynomial *qp,
5485 void *user), void *user);
5487 =head3 Properties of Piecewise Quasipolynomial Reductions
5489 To check whether two union piecewise quasipolynomial reductions are
5490 obviously equal, use
5492 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5493 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5494 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5496 =head3 Operations on Piecewise Quasipolynomial Reductions
5498 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5499 __isl_take isl_qpolynomial_fold *fold,
5500 __isl_take isl_val *v);
5501 __isl_give isl_pw_qpolynomial_fold *
5502 isl_pw_qpolynomial_fold_scale_val(
5503 __isl_take isl_pw_qpolynomial_fold *pwf,
5504 __isl_take isl_val *v);
5505 __isl_give isl_union_pw_qpolynomial_fold *
5506 isl_union_pw_qpolynomial_fold_scale_val(
5507 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5508 __isl_take isl_val *v);
5510 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5511 __isl_take isl_pw_qpolynomial_fold *pwf1,
5512 __isl_take isl_pw_qpolynomial_fold *pwf2);
5514 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5515 __isl_take isl_pw_qpolynomial_fold *pwf1,
5516 __isl_take isl_pw_qpolynomial_fold *pwf2);
5518 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5519 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5520 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5522 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5523 __isl_take isl_pw_qpolynomial_fold *pwf,
5524 __isl_take isl_point *pnt);
5526 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5527 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5528 __isl_take isl_point *pnt);
5530 __isl_give isl_pw_qpolynomial_fold *
5531 isl_pw_qpolynomial_fold_intersect_params(
5532 __isl_take isl_pw_qpolynomial_fold *pwf,
5533 __isl_take isl_set *set);
5535 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5536 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5537 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5538 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5539 __isl_take isl_union_set *uset);
5540 __isl_give isl_union_pw_qpolynomial_fold *
5541 isl_union_pw_qpolynomial_fold_intersect_params(
5542 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5543 __isl_take isl_set *set);
5545 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5546 __isl_take isl_pw_qpolynomial_fold *pwf);
5548 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5549 __isl_take isl_pw_qpolynomial_fold *pwf);
5551 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5552 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5554 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5555 __isl_take isl_qpolynomial_fold *fold,
5556 __isl_take isl_set *context);
5557 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5558 __isl_take isl_qpolynomial_fold *fold,
5559 __isl_take isl_set *context);
5561 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5562 __isl_take isl_pw_qpolynomial_fold *pwf,
5563 __isl_take isl_set *context);
5564 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5565 __isl_take isl_pw_qpolynomial_fold *pwf,
5566 __isl_take isl_set *context);
5568 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5569 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5570 __isl_take isl_union_set *context);
5571 __isl_give isl_union_pw_qpolynomial_fold *
5572 isl_union_pw_qpolynomial_fold_gist_params(
5573 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5574 __isl_take isl_set *context);
5576 The gist operation applies the gist operation to each of
5577 the cells in the domain of the input piecewise quasipolynomial reduction.
5578 In future, the operation will also exploit the context
5579 to simplify the quasipolynomial reductions associated to each cell.
5581 __isl_give isl_pw_qpolynomial_fold *
5582 isl_set_apply_pw_qpolynomial_fold(
5583 __isl_take isl_set *set,
5584 __isl_take isl_pw_qpolynomial_fold *pwf,
5586 __isl_give isl_pw_qpolynomial_fold *
5587 isl_map_apply_pw_qpolynomial_fold(
5588 __isl_take isl_map *map,
5589 __isl_take isl_pw_qpolynomial_fold *pwf,
5591 __isl_give isl_union_pw_qpolynomial_fold *
5592 isl_union_set_apply_union_pw_qpolynomial_fold(
5593 __isl_take isl_union_set *uset,
5594 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5596 __isl_give isl_union_pw_qpolynomial_fold *
5597 isl_union_map_apply_union_pw_qpolynomial_fold(
5598 __isl_take isl_union_map *umap,
5599 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5602 The functions taking a map
5603 compose the given map with the given piecewise quasipolynomial reduction.
5604 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5605 over all elements in the intersection of the range of the map
5606 and the domain of the piecewise quasipolynomial reduction
5607 as a function of an element in the domain of the map.
5608 The functions taking a set compute a bound over all elements in the
5609 intersection of the set and the domain of the
5610 piecewise quasipolynomial reduction.
5612 =head2 Parametric Vertex Enumeration
5614 The parametric vertex enumeration described in this section
5615 is mainly intended to be used internally and by the C<barvinok>
5618 #include <isl/vertices.h>
5619 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5620 __isl_keep isl_basic_set *bset);
5622 The function C<isl_basic_set_compute_vertices> performs the
5623 actual computation of the parametric vertices and the chamber
5624 decomposition and store the result in an C<isl_vertices> object.
5625 This information can be queried by either iterating over all
5626 the vertices or iterating over all the chambers or cells
5627 and then iterating over all vertices that are active on the chamber.
5629 int isl_vertices_foreach_vertex(
5630 __isl_keep isl_vertices *vertices,
5631 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5634 int isl_vertices_foreach_cell(
5635 __isl_keep isl_vertices *vertices,
5636 int (*fn)(__isl_take isl_cell *cell, void *user),
5638 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5639 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5642 Other operations that can be performed on an C<isl_vertices> object are
5645 isl_ctx *isl_vertices_get_ctx(
5646 __isl_keep isl_vertices *vertices);
5647 int isl_vertices_get_n_vertices(
5648 __isl_keep isl_vertices *vertices);
5649 void isl_vertices_free(__isl_take isl_vertices *vertices);
5651 Vertices can be inspected and destroyed using the following functions.
5653 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5654 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5655 __isl_give isl_basic_set *isl_vertex_get_domain(
5656 __isl_keep isl_vertex *vertex);
5657 __isl_give isl_multi_aff *isl_vertex_get_expr(
5658 __isl_keep isl_vertex *vertex);
5659 void isl_vertex_free(__isl_take isl_vertex *vertex);
5661 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
5662 describing the vertex in terms of the parameters,
5663 while C<isl_vertex_get_domain> returns the activity domain
5666 Chambers can be inspected and destroyed using the following functions.
5668 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5669 __isl_give isl_basic_set *isl_cell_get_domain(
5670 __isl_keep isl_cell *cell);
5671 void isl_cell_free(__isl_take isl_cell *cell);
5673 =head1 Polyhedral Compilation Library
5675 This section collects functionality in C<isl> that has been specifically
5676 designed for use during polyhedral compilation.
5678 =head2 Dependence Analysis
5680 C<isl> contains specialized functionality for performing
5681 array dataflow analysis. That is, given a I<sink> access relation
5682 and a collection of possible I<source> access relations,
5683 C<isl> can compute relations that describe
5684 for each iteration of the sink access, which iteration
5685 of which of the source access relations was the last
5686 to access the same data element before the given iteration
5688 The resulting dependence relations map source iterations
5689 to the corresponding sink iterations.
5690 To compute standard flow dependences, the sink should be
5691 a read, while the sources should be writes.
5692 If any of the source accesses are marked as being I<may>
5693 accesses, then there will be a dependence from the last
5694 I<must> access B<and> from any I<may> access that follows
5695 this last I<must> access.
5696 In particular, if I<all> sources are I<may> accesses,
5697 then memory based dependence analysis is performed.
5698 If, on the other hand, all sources are I<must> accesses,
5699 then value based dependence analysis is performed.
5701 #include <isl/flow.h>
5703 typedef int (*isl_access_level_before)(void *first, void *second);
5705 __isl_give isl_access_info *isl_access_info_alloc(
5706 __isl_take isl_map *sink,
5707 void *sink_user, isl_access_level_before fn,
5709 __isl_give isl_access_info *isl_access_info_add_source(
5710 __isl_take isl_access_info *acc,
5711 __isl_take isl_map *source, int must,
5713 __isl_null isl_access_info *isl_access_info_free(
5714 __isl_take isl_access_info *acc);
5716 __isl_give isl_flow *isl_access_info_compute_flow(
5717 __isl_take isl_access_info *acc);
5719 int isl_flow_foreach(__isl_keep isl_flow *deps,
5720 int (*fn)(__isl_take isl_map *dep, int must,
5721 void *dep_user, void *user),
5723 __isl_give isl_map *isl_flow_get_no_source(
5724 __isl_keep isl_flow *deps, int must);
5725 void isl_flow_free(__isl_take isl_flow *deps);
5727 The function C<isl_access_info_compute_flow> performs the actual
5728 dependence analysis. The other functions are used to construct
5729 the input for this function or to read off the output.
5731 The input is collected in an C<isl_access_info>, which can
5732 be created through a call to C<isl_access_info_alloc>.
5733 The arguments to this functions are the sink access relation
5734 C<sink>, a token C<sink_user> used to identify the sink
5735 access to the user, a callback function for specifying the
5736 relative order of source and sink accesses, and the number
5737 of source access relations that will be added.
5738 The callback function has type C<int (*)(void *first, void *second)>.
5739 The function is called with two user supplied tokens identifying
5740 either a source or the sink and it should return the shared nesting
5741 level and the relative order of the two accesses.
5742 In particular, let I<n> be the number of loops shared by
5743 the two accesses. If C<first> precedes C<second> textually,
5744 then the function should return I<2 * n + 1>; otherwise,
5745 it should return I<2 * n>.
5746 The sources can be added to the C<isl_access_info> by performing
5747 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5748 C<must> indicates whether the source is a I<must> access
5749 or a I<may> access. Note that a multi-valued access relation
5750 should only be marked I<must> if every iteration in the domain
5751 of the relation accesses I<all> elements in its image.
5752 The C<source_user> token is again used to identify
5753 the source access. The range of the source access relation
5754 C<source> should have the same dimension as the range
5755 of the sink access relation.
5756 The C<isl_access_info_free> function should usually not be
5757 called explicitly, because it is called implicitly by
5758 C<isl_access_info_compute_flow>.
5760 The result of the dependence analysis is collected in an
5761 C<isl_flow>. There may be elements of
5762 the sink access for which no preceding source access could be
5763 found or for which all preceding sources are I<may> accesses.
5764 The relations containing these elements can be obtained through
5765 calls to C<isl_flow_get_no_source>, the first with C<must> set
5766 and the second with C<must> unset.
5767 In the case of standard flow dependence analysis,
5768 with the sink a read and the sources I<must> writes,
5769 the first relation corresponds to the reads from uninitialized
5770 array elements and the second relation is empty.
5771 The actual flow dependences can be extracted using
5772 C<isl_flow_foreach>. This function will call the user-specified
5773 callback function C<fn> for each B<non-empty> dependence between
5774 a source and the sink. The callback function is called
5775 with four arguments, the actual flow dependence relation
5776 mapping source iterations to sink iterations, a boolean that
5777 indicates whether it is a I<must> or I<may> dependence, a token
5778 identifying the source and an additional C<void *> with value
5779 equal to the third argument of the C<isl_flow_foreach> call.
5780 A dependence is marked I<must> if it originates from a I<must>
5781 source and if it is not followed by any I<may> sources.
5783 After finishing with an C<isl_flow>, the user should call
5784 C<isl_flow_free> to free all associated memory.
5786 A higher-level interface to dependence analysis is provided
5787 by the following function.
5789 #include <isl/flow.h>
5791 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5792 __isl_take isl_union_map *must_source,
5793 __isl_take isl_union_map *may_source,
5794 __isl_take isl_union_map *schedule,
5795 __isl_give isl_union_map **must_dep,
5796 __isl_give isl_union_map **may_dep,
5797 __isl_give isl_union_map **must_no_source,
5798 __isl_give isl_union_map **may_no_source);
5800 The arrays are identified by the tuple names of the ranges
5801 of the accesses. The iteration domains by the tuple names
5802 of the domains of the accesses and of the schedule.
5803 The relative order of the iteration domains is given by the
5804 schedule. The relations returned through C<must_no_source>
5805 and C<may_no_source> are subsets of C<sink>.
5806 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5807 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5808 any of the other arguments is treated as an error.
5810 =head3 Interaction with Dependence Analysis
5812 During the dependence analysis, we frequently need to perform
5813 the following operation. Given a relation between sink iterations
5814 and potential source iterations from a particular source domain,
5815 what is the last potential source iteration corresponding to each
5816 sink iteration. It can sometimes be convenient to adjust
5817 the set of potential source iterations before or after each such operation.
5818 The prototypical example is fuzzy array dataflow analysis,
5819 where we need to analyze if, based on data-dependent constraints,
5820 the sink iteration can ever be executed without one or more of
5821 the corresponding potential source iterations being executed.
5822 If so, we can introduce extra parameters and select an unknown
5823 but fixed source iteration from the potential source iterations.
5824 To be able to perform such manipulations, C<isl> provides the following
5827 #include <isl/flow.h>
5829 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5830 __isl_keep isl_map *source_map,
5831 __isl_keep isl_set *sink, void *source_user,
5833 __isl_give isl_access_info *isl_access_info_set_restrict(
5834 __isl_take isl_access_info *acc,
5835 isl_access_restrict fn, void *user);
5837 The function C<isl_access_info_set_restrict> should be called
5838 before calling C<isl_access_info_compute_flow> and registers a callback function
5839 that will be called any time C<isl> is about to compute the last
5840 potential source. The first argument is the (reverse) proto-dependence,
5841 mapping sink iterations to potential source iterations.
5842 The second argument represents the sink iterations for which
5843 we want to compute the last source iteration.
5844 The third argument is the token corresponding to the source
5845 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5846 The callback is expected to return a restriction on either the input or
5847 the output of the operation computing the last potential source.
5848 If the input needs to be restricted then restrictions are needed
5849 for both the source and the sink iterations. The sink iterations
5850 and the potential source iterations will be intersected with these sets.
5851 If the output needs to be restricted then only a restriction on the source
5852 iterations is required.
5853 If any error occurs, the callback should return C<NULL>.
5854 An C<isl_restriction> object can be created, freed and inspected
5855 using the following functions.
5857 #include <isl/flow.h>
5859 __isl_give isl_restriction *isl_restriction_input(
5860 __isl_take isl_set *source_restr,
5861 __isl_take isl_set *sink_restr);
5862 __isl_give isl_restriction *isl_restriction_output(
5863 __isl_take isl_set *source_restr);
5864 __isl_give isl_restriction *isl_restriction_none(
5865 __isl_take isl_map *source_map);
5866 __isl_give isl_restriction *isl_restriction_empty(
5867 __isl_take isl_map *source_map);
5868 __isl_null isl_restriction *isl_restriction_free(
5869 __isl_take isl_restriction *restr);
5870 isl_ctx *isl_restriction_get_ctx(
5871 __isl_keep isl_restriction *restr);
5873 C<isl_restriction_none> and C<isl_restriction_empty> are special
5874 cases of C<isl_restriction_input>. C<isl_restriction_none>
5875 is essentially equivalent to
5877 isl_restriction_input(isl_set_universe(
5878 isl_space_range(isl_map_get_space(source_map))),
5880 isl_space_domain(isl_map_get_space(source_map))));
5882 whereas C<isl_restriction_empty> is essentially equivalent to
5884 isl_restriction_input(isl_set_empty(
5885 isl_space_range(isl_map_get_space(source_map))),
5887 isl_space_domain(isl_map_get_space(source_map))));
5891 B<The functionality described in this section is fairly new
5892 and may be subject to change.>
5894 #include <isl/schedule.h>
5895 __isl_give isl_schedule *
5896 isl_schedule_constraints_compute_schedule(
5897 __isl_take isl_schedule_constraints *sc);
5898 __isl_null isl_schedule *isl_schedule_free(
5899 __isl_take isl_schedule *sched);
5901 The function C<isl_schedule_constraints_compute_schedule> can be
5902 used to compute a schedule that satisfy the given schedule constraints.
5903 These schedule constraints include the iteration domain for which
5904 a schedule should be computed and dependences between pairs of
5905 iterations. In particular, these dependences include
5906 I<validity> dependences and I<proximity> dependences.
5907 By default, the algorithm used to construct the schedule is similar
5908 to that of C<Pluto>.
5909 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5911 The generated schedule respects all validity dependences.
5912 That is, all dependence distances over these dependences in the
5913 scheduled space are lexicographically positive.
5914 The default algorithm tries to ensure that the dependence distances
5915 over coincidence constraints are zero and to minimize the
5916 dependence distances over proximity dependences.
5917 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5918 for groups of domains where the dependence distances over validity
5919 dependences have only non-negative values.
5920 When using Feautrier's algorithm, the coincidence and proximity constraints
5921 are only taken into account during the extension to a
5922 full-dimensional schedule.
5924 An C<isl_schedule_constraints> object can be constructed
5925 and manipulated using the following functions.
5927 #include <isl/schedule.h>
5928 __isl_give isl_schedule_constraints *
5929 isl_schedule_constraints_copy(
5930 __isl_keep isl_schedule_constraints *sc);
5931 __isl_give isl_schedule_constraints *
5932 isl_schedule_constraints_on_domain(
5933 __isl_take isl_union_set *domain);
5934 isl_ctx *isl_schedule_constraints_get_ctx(
5935 __isl_keep isl_schedule_constraints *sc);
5936 __isl_give isl_schedule_constraints *
5937 isl_schedule_constraints_set_validity(
5938 __isl_take isl_schedule_constraints *sc,
5939 __isl_take isl_union_map *validity);
5940 __isl_give isl_schedule_constraints *
5941 isl_schedule_constraints_set_coincidence(
5942 __isl_take isl_schedule_constraints *sc,
5943 __isl_take isl_union_map *coincidence);
5944 __isl_give isl_schedule_constraints *
5945 isl_schedule_constraints_set_proximity(
5946 __isl_take isl_schedule_constraints *sc,
5947 __isl_take isl_union_map *proximity);
5948 __isl_give isl_schedule_constraints *
5949 isl_schedule_constraints_set_conditional_validity(
5950 __isl_take isl_schedule_constraints *sc,
5951 __isl_take isl_union_map *condition,
5952 __isl_take isl_union_map *validity);
5953 __isl_null isl_schedule_constraints *
5954 isl_schedule_constraints_free(
5955 __isl_take isl_schedule_constraints *sc);
5957 The initial C<isl_schedule_constraints> object created by
5958 C<isl_schedule_constraints_on_domain> does not impose any constraints.
5959 That is, it has an empty set of dependences.
5960 The function C<isl_schedule_constraints_set_validity> replaces the
5961 validity dependences, mapping domain elements I<i> to domain
5962 elements that should be scheduled after I<i>.
5963 The function C<isl_schedule_constraints_set_coincidence> replaces the
5964 coincidence dependences, mapping domain elements I<i> to domain
5965 elements that should be scheduled together with I<I>, if possible.
5966 The function C<isl_schedule_constraints_set_proximity> replaces the
5967 proximity dependences, mapping domain elements I<i> to domain
5968 elements that should be scheduled either before I<I>
5969 or as early as possible after I<i>.
5971 The function C<isl_schedule_constraints_set_conditional_validity>
5972 replaces the conditional validity constraints.
5973 A conditional validity constraint is only imposed when any of the corresponding
5974 conditions is satisfied, i.e., when any of them is non-zero.
5975 That is, the scheduler ensures that within each band if the dependence
5976 distances over the condition constraints are not all zero
5977 then all corresponding conditional validity constraints are respected.
5978 A conditional validity constraint corresponds to a condition
5979 if the two are adjacent, i.e., if the domain of one relation intersect
5980 the range of the other relation.
5981 The typical use case of conditional validity constraints is
5982 to allow order constraints between live ranges to be violated
5983 as long as the live ranges themselves are local to the band.
5984 To allow more fine-grained control over which conditions correspond
5985 to which conditional validity constraints, the domains and ranges
5986 of these relations may include I<tags>. That is, the domains and
5987 ranges of those relation may themselves be wrapped relations
5988 where the iteration domain appears in the domain of those wrapped relations
5989 and the range of the wrapped relations can be arbitrarily chosen
5990 by the user. Conditions and conditional validity constraints are only
5991 considere adjacent to each other if the entire wrapped relation matches.
5992 In particular, a relation with a tag will never be considered adjacent
5993 to a relation without a tag.
5995 The following function computes a schedule directly from
5996 an iteration domain and validity and proximity dependences
5997 and is implemented in terms of the functions described above.
5998 The use of C<isl_union_set_compute_schedule> is discouraged.
6000 #include <isl/schedule.h>
6001 __isl_give isl_schedule *isl_union_set_compute_schedule(
6002 __isl_take isl_union_set *domain,
6003 __isl_take isl_union_map *validity,
6004 __isl_take isl_union_map *proximity);
6006 A mapping from the domains to the scheduled space can be obtained
6007 from an C<isl_schedule> using the following function.
6009 __isl_give isl_union_map *isl_schedule_get_map(
6010 __isl_keep isl_schedule *sched);
6012 A representation of the schedule can be printed using
6014 __isl_give isl_printer *isl_printer_print_schedule(
6015 __isl_take isl_printer *p,
6016 __isl_keep isl_schedule *schedule);
6018 A representation of the schedule as a forest of bands can be obtained
6019 using the following function.
6021 __isl_give isl_band_list *isl_schedule_get_band_forest(
6022 __isl_keep isl_schedule *schedule);
6024 The individual bands can be visited in depth-first post-order
6025 using the following function.
6027 #include <isl/schedule.h>
6028 int isl_schedule_foreach_band(
6029 __isl_keep isl_schedule *sched,
6030 int (*fn)(__isl_keep isl_band *band, void *user),
6033 The list can be manipulated as explained in L<"Lists">.
6034 The bands inside the list can be copied and freed using the following
6037 #include <isl/band.h>
6038 __isl_give isl_band *isl_band_copy(
6039 __isl_keep isl_band *band);
6040 __isl_null isl_band *isl_band_free(
6041 __isl_take isl_band *band);
6043 Each band contains zero or more scheduling dimensions.
6044 These are referred to as the members of the band.
6045 The section of the schedule that corresponds to the band is
6046 referred to as the partial schedule of the band.
6047 For those nodes that participate in a band, the outer scheduling
6048 dimensions form the prefix schedule, while the inner scheduling
6049 dimensions form the suffix schedule.
6050 That is, if we take a cut of the band forest, then the union of
6051 the concatenations of the prefix, partial and suffix schedules of
6052 each band in the cut is equal to the entire schedule (modulo
6053 some possible padding at the end with zero scheduling dimensions).
6054 The properties of a band can be inspected using the following functions.
6056 #include <isl/band.h>
6057 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
6059 int isl_band_has_children(__isl_keep isl_band *band);
6060 __isl_give isl_band_list *isl_band_get_children(
6061 __isl_keep isl_band *band);
6063 __isl_give isl_union_map *isl_band_get_prefix_schedule(
6064 __isl_keep isl_band *band);
6065 __isl_give isl_union_map *isl_band_get_partial_schedule(
6066 __isl_keep isl_band *band);
6067 __isl_give isl_union_map *isl_band_get_suffix_schedule(
6068 __isl_keep isl_band *band);
6070 int isl_band_n_member(__isl_keep isl_band *band);
6071 int isl_band_member_is_coincident(
6072 __isl_keep isl_band *band, int pos);
6074 int isl_band_list_foreach_band(
6075 __isl_keep isl_band_list *list,
6076 int (*fn)(__isl_keep isl_band *band, void *user),
6079 Note that a scheduling dimension is considered to be ``coincident''
6080 if it satisfies the coincidence constraints within its band.
6081 That is, if the dependence distances of the coincidence
6082 constraints are all zero in that direction (for fixed
6083 iterations of outer bands).
6084 Like C<isl_schedule_foreach_band>,
6085 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
6086 in depth-first post-order.
6088 A band can be tiled using the following function.
6090 #include <isl/band.h>
6091 int isl_band_tile(__isl_keep isl_band *band,
6092 __isl_take isl_vec *sizes);
6094 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
6096 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
6097 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
6099 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
6101 The C<isl_band_tile> function tiles the band using the given tile sizes
6102 inside its schedule.
6103 A new child band is created to represent the point loops and it is
6104 inserted between the modified band and its children.
6105 The C<tile_scale_tile_loops> option specifies whether the tile
6106 loops iterators should be scaled by the tile sizes.
6107 If the C<tile_shift_point_loops> option is set, then the point loops
6108 are shifted to start at zero.
6110 A band can be split into two nested bands using the following function.
6112 int isl_band_split(__isl_keep isl_band *band, int pos);
6114 The resulting outer band contains the first C<pos> dimensions of C<band>
6115 while the inner band contains the remaining dimensions.
6117 A representation of the band can be printed using
6119 #include <isl/band.h>
6120 __isl_give isl_printer *isl_printer_print_band(
6121 __isl_take isl_printer *p,
6122 __isl_keep isl_band *band);
6126 #include <isl/schedule.h>
6127 int isl_options_set_schedule_max_coefficient(
6128 isl_ctx *ctx, int val);
6129 int isl_options_get_schedule_max_coefficient(
6131 int isl_options_set_schedule_max_constant_term(
6132 isl_ctx *ctx, int val);
6133 int isl_options_get_schedule_max_constant_term(
6135 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
6136 int isl_options_get_schedule_fuse(isl_ctx *ctx);
6137 int isl_options_set_schedule_maximize_band_depth(
6138 isl_ctx *ctx, int val);
6139 int isl_options_get_schedule_maximize_band_depth(
6141 int isl_options_set_schedule_outer_coincidence(
6142 isl_ctx *ctx, int val);
6143 int isl_options_get_schedule_outer_coincidence(
6145 int isl_options_set_schedule_split_scaled(
6146 isl_ctx *ctx, int val);
6147 int isl_options_get_schedule_split_scaled(
6149 int isl_options_set_schedule_algorithm(
6150 isl_ctx *ctx, int val);
6151 int isl_options_get_schedule_algorithm(
6153 int isl_options_set_schedule_separate_components(
6154 isl_ctx *ctx, int val);
6155 int isl_options_get_schedule_separate_components(
6160 =item * schedule_max_coefficient
6162 This option enforces that the coefficients for variable and parameter
6163 dimensions in the calculated schedule are not larger than the specified value.
6164 This option can significantly increase the speed of the scheduling calculation
6165 and may also prevent fusing of unrelated dimensions. A value of -1 means that
6166 this option does not introduce bounds on the variable or parameter
6169 =item * schedule_max_constant_term
6171 This option enforces that the constant coefficients in the calculated schedule
6172 are not larger than the maximal constant term. This option can significantly
6173 increase the speed of the scheduling calculation and may also prevent fusing of
6174 unrelated dimensions. A value of -1 means that this option does not introduce
6175 bounds on the constant coefficients.
6177 =item * schedule_fuse
6179 This option controls the level of fusion.
6180 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6181 resulting schedule will be distributed as much as possible.
6182 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6183 try to fuse loops in the resulting schedule.
6185 =item * schedule_maximize_band_depth
6187 If this option is set, we do not split bands at the point
6188 where we detect splitting is necessary. Instead, we
6189 backtrack and split bands as early as possible. This
6190 reduces the number of splits and maximizes the width of
6191 the bands. Wider bands give more possibilities for tiling.
6192 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6193 then bands will be split as early as possible, even if there is no need.
6194 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6196 =item * schedule_outer_coincidence
6198 If this option is set, then we try to construct schedules
6199 where the outermost scheduling dimension in each band
6200 satisfies the coincidence constraints.
6202 =item * schedule_split_scaled
6204 If this option is set, then we try to construct schedules in which the
6205 constant term is split off from the linear part if the linear parts of
6206 the scheduling rows for all nodes in the graphs have a common non-trivial
6208 The constant term is then placed in a separate band and the linear
6211 =item * schedule_algorithm
6213 Selects the scheduling algorithm to be used.
6214 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6215 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6217 =item * schedule_separate_components
6219 If at any point the dependence graph contains any (weakly connected) components,
6220 then these components are scheduled separately.
6221 If this option is not set, then some iterations of the domains
6222 in these components may be scheduled together.
6223 If this option is set, then the components are given consecutive
6228 =head2 AST Generation
6230 This section describes the C<isl> functionality for generating
6231 ASTs that visit all the elements
6232 in a domain in an order specified by a schedule.
6233 In particular, given a C<isl_union_map>, an AST is generated
6234 that visits all the elements in the domain of the C<isl_union_map>
6235 according to the lexicographic order of the corresponding image
6236 element(s). If the range of the C<isl_union_map> consists of
6237 elements in more than one space, then each of these spaces is handled
6238 separately in an arbitrary order.
6239 It should be noted that the image elements only specify the I<order>
6240 in which the corresponding domain elements should be visited.
6241 No direct relation between the image elements and the loop iterators
6242 in the generated AST should be assumed.
6244 Each AST is generated within a build. The initial build
6245 simply specifies the constraints on the parameters (if any)
6246 and can be created, inspected, copied and freed using the following functions.
6248 #include <isl/ast_build.h>
6249 __isl_give isl_ast_build *isl_ast_build_from_context(
6250 __isl_take isl_set *set);
6251 isl_ctx *isl_ast_build_get_ctx(
6252 __isl_keep isl_ast_build *build);
6253 __isl_give isl_ast_build *isl_ast_build_copy(
6254 __isl_keep isl_ast_build *build);
6255 __isl_null isl_ast_build *isl_ast_build_free(
6256 __isl_take isl_ast_build *build);
6258 The C<set> argument is usually a parameter set with zero or more parameters.
6259 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6260 and L</"Fine-grained Control over AST Generation">.
6261 Finally, the AST itself can be constructed using the following
6264 #include <isl/ast_build.h>
6265 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6266 __isl_keep isl_ast_build *build,
6267 __isl_take isl_union_map *schedule);
6269 =head3 Inspecting the AST
6271 The basic properties of an AST node can be obtained as follows.
6273 #include <isl/ast.h>
6274 isl_ctx *isl_ast_node_get_ctx(
6275 __isl_keep isl_ast_node *node);
6276 enum isl_ast_node_type isl_ast_node_get_type(
6277 __isl_keep isl_ast_node *node);
6279 The type of an AST node is one of
6280 C<isl_ast_node_for>,
6282 C<isl_ast_node_block> or
6283 C<isl_ast_node_user>.
6284 An C<isl_ast_node_for> represents a for node.
6285 An C<isl_ast_node_if> represents an if node.
6286 An C<isl_ast_node_block> represents a compound node.
6287 An C<isl_ast_node_user> represents an expression statement.
6288 An expression statement typically corresponds to a domain element, i.e.,
6289 one of the elements that is visited by the AST.
6291 Each type of node has its own additional properties.
6293 #include <isl/ast.h>
6294 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6295 __isl_keep isl_ast_node *node);
6296 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6297 __isl_keep isl_ast_node *node);
6298 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6299 __isl_keep isl_ast_node *node);
6300 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6301 __isl_keep isl_ast_node *node);
6302 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6303 __isl_keep isl_ast_node *node);
6304 int isl_ast_node_for_is_degenerate(
6305 __isl_keep isl_ast_node *node);
6307 An C<isl_ast_for> is considered degenerate if it is known to execute
6310 #include <isl/ast.h>
6311 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6312 __isl_keep isl_ast_node *node);
6313 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6314 __isl_keep isl_ast_node *node);
6315 int isl_ast_node_if_has_else(
6316 __isl_keep isl_ast_node *node);
6317 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6318 __isl_keep isl_ast_node *node);
6320 __isl_give isl_ast_node_list *
6321 isl_ast_node_block_get_children(
6322 __isl_keep isl_ast_node *node);
6324 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6325 __isl_keep isl_ast_node *node);
6327 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6328 the following functions.
6330 #include <isl/ast.h>
6331 isl_ctx *isl_ast_expr_get_ctx(
6332 __isl_keep isl_ast_expr *expr);
6333 enum isl_ast_expr_type isl_ast_expr_get_type(
6334 __isl_keep isl_ast_expr *expr);
6336 The type of an AST expression is one of
6338 C<isl_ast_expr_id> or
6339 C<isl_ast_expr_int>.
6340 An C<isl_ast_expr_op> represents the result of an operation.
6341 An C<isl_ast_expr_id> represents an identifier.
6342 An C<isl_ast_expr_int> represents an integer value.
6344 Each type of expression has its own additional properties.
6346 #include <isl/ast.h>
6347 enum isl_ast_op_type isl_ast_expr_get_op_type(
6348 __isl_keep isl_ast_expr *expr);
6349 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6350 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6351 __isl_keep isl_ast_expr *expr, int pos);
6352 int isl_ast_node_foreach_ast_op_type(
6353 __isl_keep isl_ast_node *node,
6354 int (*fn)(enum isl_ast_op_type type, void *user),
6357 C<isl_ast_expr_get_op_type> returns the type of the operation
6358 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6359 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6361 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6362 C<isl_ast_op_type> that appears in C<node>.
6363 The operation type is one of the following.
6367 =item C<isl_ast_op_and>
6369 Logical I<and> of two arguments.
6370 Both arguments can be evaluated.
6372 =item C<isl_ast_op_and_then>
6374 Logical I<and> of two arguments.
6375 The second argument can only be evaluated if the first evaluates to true.
6377 =item C<isl_ast_op_or>
6379 Logical I<or> of two arguments.
6380 Both arguments can be evaluated.
6382 =item C<isl_ast_op_or_else>
6384 Logical I<or> of two arguments.
6385 The second argument can only be evaluated if the first evaluates to false.
6387 =item C<isl_ast_op_max>
6389 Maximum of two or more arguments.
6391 =item C<isl_ast_op_min>
6393 Minimum of two or more arguments.
6395 =item C<isl_ast_op_minus>
6399 =item C<isl_ast_op_add>
6401 Sum of two arguments.
6403 =item C<isl_ast_op_sub>
6405 Difference of two arguments.
6407 =item C<isl_ast_op_mul>
6409 Product of two arguments.
6411 =item C<isl_ast_op_div>
6413 Exact division. That is, the result is known to be an integer.
6415 =item C<isl_ast_op_fdiv_q>
6417 Result of integer division, rounded towards negative
6420 =item C<isl_ast_op_pdiv_q>
6422 Result of integer division, where dividend is known to be non-negative.
6424 =item C<isl_ast_op_pdiv_r>
6426 Remainder of integer division, where dividend is known to be non-negative.
6428 =item C<isl_ast_op_cond>
6430 Conditional operator defined on three arguments.
6431 If the first argument evaluates to true, then the result
6432 is equal to the second argument. Otherwise, the result
6433 is equal to the third argument.
6434 The second and third argument may only be evaluated if
6435 the first argument evaluates to true and false, respectively.
6436 Corresponds to C<a ? b : c> in C.
6438 =item C<isl_ast_op_select>
6440 Conditional operator defined on three arguments.
6441 If the first argument evaluates to true, then the result
6442 is equal to the second argument. Otherwise, the result
6443 is equal to the third argument.
6444 The second and third argument may be evaluated independently
6445 of the value of the first argument.
6446 Corresponds to C<a * b + (1 - a) * c> in C.
6448 =item C<isl_ast_op_eq>
6452 =item C<isl_ast_op_le>
6454 Less than or equal relation.
6456 =item C<isl_ast_op_lt>
6460 =item C<isl_ast_op_ge>
6462 Greater than or equal relation.
6464 =item C<isl_ast_op_gt>
6466 Greater than relation.
6468 =item C<isl_ast_op_call>
6471 The number of arguments of the C<isl_ast_expr> is one more than
6472 the number of arguments in the function call, the first argument
6473 representing the function being called.
6475 =item C<isl_ast_op_access>
6478 The number of arguments of the C<isl_ast_expr> is one more than
6479 the number of index expressions in the array access, the first argument
6480 representing the array being accessed.
6482 =item C<isl_ast_op_member>
6485 This operation has two arguments, a structure and the name of
6486 the member of the structure being accessed.
6490 #include <isl/ast.h>
6491 __isl_give isl_id *isl_ast_expr_get_id(
6492 __isl_keep isl_ast_expr *expr);
6494 Return the identifier represented by the AST expression.
6496 #include <isl/ast.h>
6497 __isl_give isl_val *isl_ast_expr_get_val(
6498 __isl_keep isl_ast_expr *expr);
6500 Return the integer represented by the AST expression.
6502 =head3 Properties of ASTs
6504 #include <isl/ast.h>
6505 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6506 __isl_keep isl_ast_expr *expr2);
6508 Check if two C<isl_ast_expr>s are equal to each other.
6510 =head3 Manipulating and printing the AST
6512 AST nodes can be copied and freed using the following functions.
6514 #include <isl/ast.h>
6515 __isl_give isl_ast_node *isl_ast_node_copy(
6516 __isl_keep isl_ast_node *node);
6517 __isl_null isl_ast_node *isl_ast_node_free(
6518 __isl_take isl_ast_node *node);
6520 AST expressions can be copied and freed using the following functions.
6522 #include <isl/ast.h>
6523 __isl_give isl_ast_expr *isl_ast_expr_copy(
6524 __isl_keep isl_ast_expr *expr);
6525 __isl_null isl_ast_expr *isl_ast_expr_free(
6526 __isl_take isl_ast_expr *expr);
6528 New AST expressions can be created either directly or within
6529 the context of an C<isl_ast_build>.
6531 #include <isl/ast.h>
6532 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6533 __isl_take isl_val *v);
6534 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6535 __isl_take isl_id *id);
6536 __isl_give isl_ast_expr *isl_ast_expr_neg(
6537 __isl_take isl_ast_expr *expr);
6538 __isl_give isl_ast_expr *isl_ast_expr_add(
6539 __isl_take isl_ast_expr *expr1,
6540 __isl_take isl_ast_expr *expr2);
6541 __isl_give isl_ast_expr *isl_ast_expr_sub(
6542 __isl_take isl_ast_expr *expr1,
6543 __isl_take isl_ast_expr *expr2);
6544 __isl_give isl_ast_expr *isl_ast_expr_mul(
6545 __isl_take isl_ast_expr *expr1,
6546 __isl_take isl_ast_expr *expr2);
6547 __isl_give isl_ast_expr *isl_ast_expr_div(
6548 __isl_take isl_ast_expr *expr1,
6549 __isl_take isl_ast_expr *expr2);
6550 __isl_give isl_ast_expr *isl_ast_expr_and(
6551 __isl_take isl_ast_expr *expr1,
6552 __isl_take isl_ast_expr *expr2)
6553 __isl_give isl_ast_expr *isl_ast_expr_or(
6554 __isl_take isl_ast_expr *expr1,
6555 __isl_take isl_ast_expr *expr2)
6556 __isl_give isl_ast_expr *isl_ast_expr_access(
6557 __isl_take isl_ast_expr *array,
6558 __isl_take isl_ast_expr_list *indices);
6560 #include <isl/ast_build.h>
6561 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6562 __isl_keep isl_ast_build *build,
6563 __isl_take isl_pw_aff *pa);
6564 __isl_give isl_ast_expr *
6565 isl_ast_build_access_from_pw_multi_aff(
6566 __isl_keep isl_ast_build *build,
6567 __isl_take isl_pw_multi_aff *pma);
6568 __isl_give isl_ast_expr *
6569 isl_ast_build_access_from_multi_pw_aff(
6570 __isl_keep isl_ast_build *build,
6571 __isl_take isl_multi_pw_aff *mpa);
6572 __isl_give isl_ast_expr *
6573 isl_ast_build_call_from_pw_multi_aff(
6574 __isl_keep isl_ast_build *build,
6575 __isl_take isl_pw_multi_aff *pma);
6576 __isl_give isl_ast_expr *
6577 isl_ast_build_call_from_multi_pw_aff(
6578 __isl_keep isl_ast_build *build,
6579 __isl_take isl_multi_pw_aff *mpa);
6581 The domains of C<pa>, C<mpa> and C<pma> should correspond
6582 to the schedule space of C<build>.
6583 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6584 the function being called.
6585 If the accessed space is a nested relation, then it is taken
6586 to represent an access of the member specified by the range
6587 of this nested relation of the structure specified by the domain
6588 of the nested relation.
6590 The following functions can be used to modify an C<isl_ast_expr>.
6592 #include <isl/ast.h>
6593 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6594 __isl_take isl_ast_expr *expr, int pos,
6595 __isl_take isl_ast_expr *arg);
6597 Replace the argument of C<expr> at position C<pos> by C<arg>.
6599 #include <isl/ast.h>
6600 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6601 __isl_take isl_ast_expr *expr,
6602 __isl_take isl_id_to_ast_expr *id2expr);
6604 The function C<isl_ast_expr_substitute_ids> replaces the
6605 subexpressions of C<expr> of type C<isl_ast_expr_id>
6606 by the corresponding expression in C<id2expr>, if there is any.
6609 User specified data can be attached to an C<isl_ast_node> and obtained
6610 from the same C<isl_ast_node> using the following functions.
6612 #include <isl/ast.h>
6613 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6614 __isl_take isl_ast_node *node,
6615 __isl_take isl_id *annotation);
6616 __isl_give isl_id *isl_ast_node_get_annotation(
6617 __isl_keep isl_ast_node *node);
6619 Basic printing can be performed using the following functions.
6621 #include <isl/ast.h>
6622 __isl_give isl_printer *isl_printer_print_ast_expr(
6623 __isl_take isl_printer *p,
6624 __isl_keep isl_ast_expr *expr);
6625 __isl_give isl_printer *isl_printer_print_ast_node(
6626 __isl_take isl_printer *p,
6627 __isl_keep isl_ast_node *node);
6629 More advanced printing can be performed using the following functions.
6631 #include <isl/ast.h>
6632 __isl_give isl_printer *isl_ast_op_type_print_macro(
6633 enum isl_ast_op_type type,
6634 __isl_take isl_printer *p);
6635 __isl_give isl_printer *isl_ast_node_print_macros(
6636 __isl_keep isl_ast_node *node,
6637 __isl_take isl_printer *p);
6638 __isl_give isl_printer *isl_ast_node_print(
6639 __isl_keep isl_ast_node *node,
6640 __isl_take isl_printer *p,
6641 __isl_take isl_ast_print_options *options);
6642 __isl_give isl_printer *isl_ast_node_for_print(
6643 __isl_keep isl_ast_node *node,
6644 __isl_take isl_printer *p,
6645 __isl_take isl_ast_print_options *options);
6646 __isl_give isl_printer *isl_ast_node_if_print(
6647 __isl_keep isl_ast_node *node,
6648 __isl_take isl_printer *p,
6649 __isl_take isl_ast_print_options *options);
6651 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6652 C<isl> may print out an AST that makes use of macros such
6653 as C<floord>, C<min> and C<max>.
6654 C<isl_ast_op_type_print_macro> prints out the macro
6655 corresponding to a specific C<isl_ast_op_type>.
6656 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6657 for expressions where these macros would be used and prints
6658 out the required macro definitions.
6659 Essentially, C<isl_ast_node_print_macros> calls
6660 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6661 as function argument.
6662 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6663 C<isl_ast_node_if_print> print an C<isl_ast_node>
6664 in C<ISL_FORMAT_C>, but allow for some extra control
6665 through an C<isl_ast_print_options> object.
6666 This object can be created using the following functions.
6668 #include <isl/ast.h>
6669 __isl_give isl_ast_print_options *
6670 isl_ast_print_options_alloc(isl_ctx *ctx);
6671 __isl_give isl_ast_print_options *
6672 isl_ast_print_options_copy(
6673 __isl_keep isl_ast_print_options *options);
6674 __isl_null isl_ast_print_options *
6675 isl_ast_print_options_free(
6676 __isl_take isl_ast_print_options *options);
6678 __isl_give isl_ast_print_options *
6679 isl_ast_print_options_set_print_user(
6680 __isl_take isl_ast_print_options *options,
6681 __isl_give isl_printer *(*print_user)(
6682 __isl_take isl_printer *p,
6683 __isl_take isl_ast_print_options *options,
6684 __isl_keep isl_ast_node *node, void *user),
6686 __isl_give isl_ast_print_options *
6687 isl_ast_print_options_set_print_for(
6688 __isl_take isl_ast_print_options *options,
6689 __isl_give isl_printer *(*print_for)(
6690 __isl_take isl_printer *p,
6691 __isl_take isl_ast_print_options *options,
6692 __isl_keep isl_ast_node *node, void *user),
6695 The callback set by C<isl_ast_print_options_set_print_user>
6696 is called whenever a node of type C<isl_ast_node_user> needs to
6698 The callback set by C<isl_ast_print_options_set_print_for>
6699 is called whenever a node of type C<isl_ast_node_for> needs to
6701 Note that C<isl_ast_node_for_print> will I<not> call the
6702 callback set by C<isl_ast_print_options_set_print_for> on the node
6703 on which C<isl_ast_node_for_print> is called, but only on nested
6704 nodes of type C<isl_ast_node_for>. It is therefore safe to
6705 call C<isl_ast_node_for_print> from within the callback set by
6706 C<isl_ast_print_options_set_print_for>.
6708 The following option determines the type to be used for iterators
6709 while printing the AST.
6711 int isl_options_set_ast_iterator_type(
6712 isl_ctx *ctx, const char *val);
6713 const char *isl_options_get_ast_iterator_type(
6718 #include <isl/ast_build.h>
6719 int isl_options_set_ast_build_atomic_upper_bound(
6720 isl_ctx *ctx, int val);
6721 int isl_options_get_ast_build_atomic_upper_bound(
6723 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6725 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6726 int isl_options_set_ast_build_exploit_nested_bounds(
6727 isl_ctx *ctx, int val);
6728 int isl_options_get_ast_build_exploit_nested_bounds(
6730 int isl_options_set_ast_build_group_coscheduled(
6731 isl_ctx *ctx, int val);
6732 int isl_options_get_ast_build_group_coscheduled(
6734 int isl_options_set_ast_build_scale_strides(
6735 isl_ctx *ctx, int val);
6736 int isl_options_get_ast_build_scale_strides(
6738 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6740 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6741 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6743 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6747 =item * ast_build_atomic_upper_bound
6749 Generate loop upper bounds that consist of the current loop iterator,
6750 an operator and an expression not involving the iterator.
6751 If this option is not set, then the current loop iterator may appear
6752 several times in the upper bound.
6753 For example, when this option is turned off, AST generation
6756 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6760 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6763 When the option is turned on, the following AST is generated
6765 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6768 =item * ast_build_prefer_pdiv
6770 If this option is turned off, then the AST generation will
6771 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6772 operators, but no C<isl_ast_op_pdiv_q> or
6773 C<isl_ast_op_pdiv_r> operators.
6774 If this options is turned on, then C<isl> will try to convert
6775 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6776 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6778 =item * ast_build_exploit_nested_bounds
6780 Simplify conditions based on bounds of nested for loops.
6781 In particular, remove conditions that are implied by the fact
6782 that one or more nested loops have at least one iteration,
6783 meaning that the upper bound is at least as large as the lower bound.
6784 For example, when this option is turned off, AST generation
6787 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6793 for (int c0 = 0; c0 <= N; c0 += 1)
6794 for (int c1 = 0; c1 <= M; c1 += 1)
6797 When the option is turned on, the following AST is generated
6799 for (int c0 = 0; c0 <= N; c0 += 1)
6800 for (int c1 = 0; c1 <= M; c1 += 1)
6803 =item * ast_build_group_coscheduled
6805 If two domain elements are assigned the same schedule point, then
6806 they may be executed in any order and they may even appear in different
6807 loops. If this options is set, then the AST generator will make
6808 sure that coscheduled domain elements do not appear in separate parts
6809 of the AST. This is useful in case of nested AST generation
6810 if the outer AST generation is given only part of a schedule
6811 and the inner AST generation should handle the domains that are
6812 coscheduled by this initial part of the schedule together.
6813 For example if an AST is generated for a schedule
6815 { A[i] -> [0]; B[i] -> [0] }
6817 then the C<isl_ast_build_set_create_leaf> callback described
6818 below may get called twice, once for each domain.
6819 Setting this option ensures that the callback is only called once
6820 on both domains together.
6822 =item * ast_build_separation_bounds
6824 This option specifies which bounds to use during separation.
6825 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6826 then all (possibly implicit) bounds on the current dimension will
6827 be used during separation.
6828 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6829 then only those bounds that are explicitly available will
6830 be used during separation.
6832 =item * ast_build_scale_strides
6834 This option specifies whether the AST generator is allowed
6835 to scale down iterators of strided loops.
6837 =item * ast_build_allow_else
6839 This option specifies whether the AST generator is allowed
6840 to construct if statements with else branches.
6842 =item * ast_build_allow_or
6844 This option specifies whether the AST generator is allowed
6845 to construct if conditions with disjunctions.
6849 =head3 Fine-grained Control over AST Generation
6851 Besides specifying the constraints on the parameters,
6852 an C<isl_ast_build> object can be used to control
6853 various aspects of the AST generation process.
6854 The most prominent way of control is through ``options'',
6855 which can be set using the following function.
6857 #include <isl/ast_build.h>
6858 __isl_give isl_ast_build *
6859 isl_ast_build_set_options(
6860 __isl_take isl_ast_build *control,
6861 __isl_take isl_union_map *options);
6863 The options are encoded in an <isl_union_map>.
6864 The domain of this union relation refers to the schedule domain,
6865 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6866 In the case of nested AST generation (see L</"Nested AST Generation">),
6867 the domain of C<options> should refer to the extra piece of the schedule.
6868 That is, it should be equal to the range of the wrapped relation in the
6869 range of the schedule.
6870 The range of the options can consist of elements in one or more spaces,
6871 the names of which determine the effect of the option.
6872 The values of the range typically also refer to the schedule dimension
6873 to which the option applies. In case of nested AST generation
6874 (see L</"Nested AST Generation">), these values refer to the position
6875 of the schedule dimension within the innermost AST generation.
6876 The constraints on the domain elements of
6877 the option should only refer to this dimension and earlier dimensions.
6878 We consider the following spaces.
6882 =item C<separation_class>
6884 This space is a wrapped relation between two one dimensional spaces.
6885 The input space represents the schedule dimension to which the option
6886 applies and the output space represents the separation class.
6887 While constructing a loop corresponding to the specified schedule
6888 dimension(s), the AST generator will try to generate separate loops
6889 for domain elements that are assigned different classes.
6890 If only some of the elements are assigned a class, then those elements
6891 that are not assigned any class will be treated as belonging to a class
6892 that is separate from the explicitly assigned classes.
6893 The typical use case for this option is to separate full tiles from
6895 The other options, described below, are applied after the separation
6898 As an example, consider the separation into full and partial tiles
6899 of a tiling of a triangular domain.
6900 Take, for example, the domain
6902 { A[i,j] : 0 <= i,j and i + j <= 100 }
6904 and a tiling into tiles of 10 by 10. The input to the AST generator
6905 is then the schedule
6907 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6910 Without any options, the following AST is generated
6912 for (int c0 = 0; c0 <= 10; c0 += 1)
6913 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6914 for (int c2 = 10 * c0;
6915 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6917 for (int c3 = 10 * c1;
6918 c3 <= min(10 * c1 + 9, -c2 + 100);
6922 Separation into full and partial tiles can be obtained by assigning
6923 a class, say C<0>, to the full tiles. The full tiles are represented by those
6924 values of the first and second schedule dimensions for which there are
6925 values of the third and fourth dimensions to cover an entire tile.
6926 That is, we need to specify the following option
6928 { [a,b,c,d] -> separation_class[[0]->[0]] :
6929 exists b': 0 <= 10a,10b' and
6930 10a+9+10b'+9 <= 100;
6931 [a,b,c,d] -> separation_class[[1]->[0]] :
6932 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6936 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6937 a >= 0 and b >= 0 and b <= 8 - a;
6938 [a, b, c, d] -> separation_class[[0] -> [0]] :
6941 With this option, the generated AST is as follows
6944 for (int c0 = 0; c0 <= 8; c0 += 1) {
6945 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6946 for (int c2 = 10 * c0;
6947 c2 <= 10 * c0 + 9; c2 += 1)
6948 for (int c3 = 10 * c1;
6949 c3 <= 10 * c1 + 9; c3 += 1)
6951 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6952 for (int c2 = 10 * c0;
6953 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6955 for (int c3 = 10 * c1;
6956 c3 <= min(-c2 + 100, 10 * c1 + 9);
6960 for (int c0 = 9; c0 <= 10; c0 += 1)
6961 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6962 for (int c2 = 10 * c0;
6963 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6965 for (int c3 = 10 * c1;
6966 c3 <= min(10 * c1 + 9, -c2 + 100);
6973 This is a single-dimensional space representing the schedule dimension(s)
6974 to which ``separation'' should be applied. Separation tries to split
6975 a loop into several pieces if this can avoid the generation of guards
6977 See also the C<atomic> option.
6981 This is a single-dimensional space representing the schedule dimension(s)
6982 for which the domains should be considered ``atomic''. That is, the
6983 AST generator will make sure that any given domain space will only appear
6984 in a single loop at the specified level.
6986 Consider the following schedule
6988 { a[i] -> [i] : 0 <= i < 10;
6989 b[i] -> [i+1] : 0 <= i < 10 }
6991 If the following option is specified
6993 { [i] -> separate[x] }
6995 then the following AST will be generated
6999 for (int c0 = 1; c0 <= 9; c0 += 1) {
7006 If, on the other hand, the following option is specified
7008 { [i] -> atomic[x] }
7010 then the following AST will be generated
7012 for (int c0 = 0; c0 <= 10; c0 += 1) {
7019 If neither C<atomic> nor C<separate> is specified, then the AST generator
7020 may produce either of these two results or some intermediate form.
7024 This is a single-dimensional space representing the schedule dimension(s)
7025 that should be I<completely> unrolled.
7026 To obtain a partial unrolling, the user should apply an additional
7027 strip-mining to the schedule and fully unroll the inner loop.
7031 Additional control is available through the following functions.
7033 #include <isl/ast_build.h>
7034 __isl_give isl_ast_build *
7035 isl_ast_build_set_iterators(
7036 __isl_take isl_ast_build *control,
7037 __isl_take isl_id_list *iterators);
7039 The function C<isl_ast_build_set_iterators> allows the user to
7040 specify a list of iterator C<isl_id>s to be used as iterators.
7041 If the input schedule is injective, then
7042 the number of elements in this list should be as large as the dimension
7043 of the schedule space, but no direct correspondence should be assumed
7044 between dimensions and elements.
7045 If the input schedule is not injective, then an additional number
7046 of C<isl_id>s equal to the largest dimension of the input domains
7048 If the number of provided C<isl_id>s is insufficient, then additional
7049 names are automatically generated.
7051 #include <isl/ast_build.h>
7052 __isl_give isl_ast_build *
7053 isl_ast_build_set_create_leaf(
7054 __isl_take isl_ast_build *control,
7055 __isl_give isl_ast_node *(*fn)(
7056 __isl_take isl_ast_build *build,
7057 void *user), void *user);
7060 C<isl_ast_build_set_create_leaf> function allows for the
7061 specification of a callback that should be called whenever the AST
7062 generator arrives at an element of the schedule domain.
7063 The callback should return an AST node that should be inserted
7064 at the corresponding position of the AST. The default action (when
7065 the callback is not set) is to continue generating parts of the AST to scan
7066 all the domain elements associated to the schedule domain element
7067 and to insert user nodes, ``calling'' the domain element, for each of them.
7068 The C<build> argument contains the current state of the C<isl_ast_build>.
7069 To ease nested AST generation (see L</"Nested AST Generation">),
7070 all control information that is
7071 specific to the current AST generation such as the options and
7072 the callbacks has been removed from this C<isl_ast_build>.
7073 The callback would typically return the result of a nested
7075 user defined node created using the following function.
7077 #include <isl/ast.h>
7078 __isl_give isl_ast_node *isl_ast_node_alloc_user(
7079 __isl_take isl_ast_expr *expr);
7081 #include <isl/ast_build.h>
7082 __isl_give isl_ast_build *
7083 isl_ast_build_set_at_each_domain(
7084 __isl_take isl_ast_build *build,
7085 __isl_give isl_ast_node *(*fn)(
7086 __isl_take isl_ast_node *node,
7087 __isl_keep isl_ast_build *build,
7088 void *user), void *user);
7089 __isl_give isl_ast_build *
7090 isl_ast_build_set_before_each_for(
7091 __isl_take isl_ast_build *build,
7092 __isl_give isl_id *(*fn)(
7093 __isl_keep isl_ast_build *build,
7094 void *user), void *user);
7095 __isl_give isl_ast_build *
7096 isl_ast_build_set_after_each_for(
7097 __isl_take isl_ast_build *build,
7098 __isl_give isl_ast_node *(*fn)(
7099 __isl_take isl_ast_node *node,
7100 __isl_keep isl_ast_build *build,
7101 void *user), void *user);
7103 The callback set by C<isl_ast_build_set_at_each_domain> will
7104 be called for each domain AST node.
7105 The callbacks set by C<isl_ast_build_set_before_each_for>
7106 and C<isl_ast_build_set_after_each_for> will be called
7107 for each for AST node. The first will be called in depth-first
7108 pre-order, while the second will be called in depth-first post-order.
7109 Since C<isl_ast_build_set_before_each_for> is called before the for
7110 node is actually constructed, it is only passed an C<isl_ast_build>.
7111 The returned C<isl_id> will be added as an annotation (using
7112 C<isl_ast_node_set_annotation>) to the constructed for node.
7113 In particular, if the user has also specified an C<after_each_for>
7114 callback, then the annotation can be retrieved from the node passed to
7115 that callback using C<isl_ast_node_get_annotation>.
7116 All callbacks should C<NULL> on failure.
7117 The given C<isl_ast_build> can be used to create new
7118 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
7119 or C<isl_ast_build_call_from_pw_multi_aff>.
7121 =head3 Nested AST Generation
7123 C<isl> allows the user to create an AST within the context
7124 of another AST. These nested ASTs are created using the
7125 same C<isl_ast_build_ast_from_schedule> function that is used to create the
7126 outer AST. The C<build> argument should be an C<isl_ast_build>
7127 passed to a callback set by
7128 C<isl_ast_build_set_create_leaf>.
7129 The space of the range of the C<schedule> argument should refer
7130 to this build. In particular, the space should be a wrapped
7131 relation and the domain of this wrapped relation should be the
7132 same as that of the range of the schedule returned by
7133 C<isl_ast_build_get_schedule> below.
7134 In practice, the new schedule is typically
7135 created by calling C<isl_union_map_range_product> on the old schedule
7136 and some extra piece of the schedule.
7137 The space of the schedule domain is also available from
7138 the C<isl_ast_build>.
7140 #include <isl/ast_build.h>
7141 __isl_give isl_union_map *isl_ast_build_get_schedule(
7142 __isl_keep isl_ast_build *build);
7143 __isl_give isl_space *isl_ast_build_get_schedule_space(
7144 __isl_keep isl_ast_build *build);
7145 __isl_give isl_ast_build *isl_ast_build_restrict(
7146 __isl_take isl_ast_build *build,
7147 __isl_take isl_set *set);
7149 The C<isl_ast_build_get_schedule> function returns a (partial)
7150 schedule for the domains elements for which part of the AST still needs to
7151 be generated in the current build.
7152 In particular, the domain elements are mapped to those iterations of the loops
7153 enclosing the current point of the AST generation inside which
7154 the domain elements are executed.
7155 No direct correspondence between
7156 the input schedule and this schedule should be assumed.
7157 The space obtained from C<isl_ast_build_get_schedule_space> can be used
7158 to create a set for C<isl_ast_build_restrict> to intersect
7159 with the current build. In particular, the set passed to
7160 C<isl_ast_build_restrict> can have additional parameters.
7161 The ids of the set dimensions in the space returned by
7162 C<isl_ast_build_get_schedule_space> correspond to the
7163 iterators of the already generated loops.
7164 The user should not rely on the ids of the output dimensions
7165 of the relations in the union relation returned by
7166 C<isl_ast_build_get_schedule> having any particular value.
7170 Although C<isl> is mainly meant to be used as a library,
7171 it also contains some basic applications that use some
7172 of the functionality of C<isl>.
7173 The input may be specified in either the L<isl format>
7174 or the L<PolyLib format>.
7176 =head2 C<isl_polyhedron_sample>
7178 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7179 an integer element of the polyhedron, if there is any.
7180 The first column in the output is the denominator and is always
7181 equal to 1. If the polyhedron contains no integer points,
7182 then a vector of length zero is printed.
7186 C<isl_pip> takes the same input as the C<example> program
7187 from the C<piplib> distribution, i.e., a set of constraints
7188 on the parameters, a line containing only -1 and finally a set
7189 of constraints on a parametric polyhedron.
7190 The coefficients of the parameters appear in the last columns
7191 (but before the final constant column).
7192 The output is the lexicographic minimum of the parametric polyhedron.
7193 As C<isl> currently does not have its own output format, the output
7194 is just a dump of the internal state.
7196 =head2 C<isl_polyhedron_minimize>
7198 C<isl_polyhedron_minimize> computes the minimum of some linear
7199 or affine objective function over the integer points in a polyhedron.
7200 If an affine objective function
7201 is given, then the constant should appear in the last column.
7203 =head2 C<isl_polytope_scan>
7205 Given a polytope, C<isl_polytope_scan> prints
7206 all integer points in the polytope.
7208 =head2 C<isl_codegen>
7210 Given a schedule, a context set and an options relation,
7211 C<isl_codegen> prints out an AST that scans the domain elements
7212 of the schedule in the order of their image(s) taking into account
7213 the constraints in the context set.