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_set *isl_union_map_params(
2224 __isl_take isl_union_map *umap);
2225 __isl_give isl_union_set *isl_union_map_domain(
2226 __isl_take isl_union_map *umap);
2227 __isl_give isl_union_set *isl_union_map_range(
2228 __isl_take isl_union_map *umap);
2230 #include <isl/map.h>
2231 __isl_give isl_basic_map *isl_basic_map_domain_map(
2232 __isl_take isl_basic_map *bmap);
2233 __isl_give isl_basic_map *isl_basic_map_range_map(
2234 __isl_take isl_basic_map *bmap);
2235 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2236 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2238 #include <isl/union_map.h>
2239 __isl_give isl_union_map *isl_union_map_domain_map(
2240 __isl_take isl_union_map *umap);
2241 __isl_give isl_union_map *isl_union_map_range_map(
2242 __isl_take isl_union_map *umap);
2244 The functions above construct a (basic, regular or union) relation
2245 that maps (a wrapped version of) the input relation to its domain or range.
2249 __isl_give isl_basic_set *isl_basic_set_eliminate(
2250 __isl_take isl_basic_set *bset,
2251 enum isl_dim_type type,
2252 unsigned first, unsigned n);
2253 __isl_give isl_set *isl_set_eliminate(
2254 __isl_take isl_set *set, enum isl_dim_type type,
2255 unsigned first, unsigned n);
2256 __isl_give isl_basic_map *isl_basic_map_eliminate(
2257 __isl_take isl_basic_map *bmap,
2258 enum isl_dim_type type,
2259 unsigned first, unsigned n);
2260 __isl_give isl_map *isl_map_eliminate(
2261 __isl_take isl_map *map, enum isl_dim_type type,
2262 unsigned first, unsigned n);
2264 Eliminate the coefficients for the given dimensions from the constraints,
2265 without removing the dimensions.
2267 =item * Constructing a relation from a set
2269 #include <isl/local_space.h>
2270 __isl_give isl_local_space *isl_local_space_from_domain(
2271 __isl_take isl_local_space *ls);
2273 #include <isl/map.h>
2274 __isl_give isl_map *isl_map_from_domain(
2275 __isl_take isl_set *set);
2276 __isl_give isl_map *isl_map_from_range(
2277 __isl_take isl_set *set);
2279 Create a relation with the given set as domain or range.
2280 The range or domain of the created relation is a zero-dimensional
2281 flat anonymous space.
2285 __isl_give isl_basic_set *isl_basic_set_fix_si(
2286 __isl_take isl_basic_set *bset,
2287 enum isl_dim_type type, unsigned pos, int value);
2288 __isl_give isl_basic_set *isl_basic_set_fix_val(
2289 __isl_take isl_basic_set *bset,
2290 enum isl_dim_type type, unsigned pos,
2291 __isl_take isl_val *v);
2292 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2293 enum isl_dim_type type, unsigned pos, int value);
2294 __isl_give isl_set *isl_set_fix_val(
2295 __isl_take isl_set *set,
2296 enum isl_dim_type type, unsigned pos,
2297 __isl_take isl_val *v);
2298 __isl_give isl_basic_map *isl_basic_map_fix_si(
2299 __isl_take isl_basic_map *bmap,
2300 enum isl_dim_type type, unsigned pos, int value);
2301 __isl_give isl_basic_map *isl_basic_map_fix_val(
2302 __isl_take isl_basic_map *bmap,
2303 enum isl_dim_type type, unsigned pos,
2304 __isl_take isl_val *v);
2305 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2306 enum isl_dim_type type, unsigned pos, int value);
2307 __isl_give isl_map *isl_map_fix_val(
2308 __isl_take isl_map *map,
2309 enum isl_dim_type type, unsigned pos,
2310 __isl_take isl_val *v);
2312 Intersect the set or relation with the hyperplane where the given
2313 dimension has the fixed given value.
2315 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2316 __isl_take isl_basic_map *bmap,
2317 enum isl_dim_type type, unsigned pos, int value);
2318 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2319 __isl_take isl_basic_map *bmap,
2320 enum isl_dim_type type, unsigned pos, int value);
2321 __isl_give isl_set *isl_set_lower_bound_si(
2322 __isl_take isl_set *set,
2323 enum isl_dim_type type, unsigned pos, int value);
2324 __isl_give isl_set *isl_set_lower_bound_val(
2325 __isl_take isl_set *set,
2326 enum isl_dim_type type, unsigned pos,
2327 __isl_take isl_val *value);
2328 __isl_give isl_map *isl_map_lower_bound_si(
2329 __isl_take isl_map *map,
2330 enum isl_dim_type type, unsigned pos, int value);
2331 __isl_give isl_set *isl_set_upper_bound_si(
2332 __isl_take isl_set *set,
2333 enum isl_dim_type type, unsigned pos, int value);
2334 __isl_give isl_set *isl_set_upper_bound_val(
2335 __isl_take isl_set *set,
2336 enum isl_dim_type type, unsigned pos,
2337 __isl_take isl_val *value);
2338 __isl_give isl_map *isl_map_upper_bound_si(
2339 __isl_take isl_map *map,
2340 enum isl_dim_type type, unsigned pos, int value);
2342 Intersect the set or relation with the half-space where the given
2343 dimension has a value bounded by the fixed given integer value.
2345 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2346 enum isl_dim_type type1, int pos1,
2347 enum isl_dim_type type2, int pos2);
2348 __isl_give isl_basic_map *isl_basic_map_equate(
2349 __isl_take isl_basic_map *bmap,
2350 enum isl_dim_type type1, int pos1,
2351 enum isl_dim_type type2, int pos2);
2352 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2353 enum isl_dim_type type1, int pos1,
2354 enum isl_dim_type type2, int pos2);
2356 Intersect the set or relation with the hyperplane where the given
2357 dimensions are equal to each other.
2359 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2360 enum isl_dim_type type1, int pos1,
2361 enum isl_dim_type type2, int pos2);
2363 Intersect the relation with the hyperplane where the given
2364 dimensions have opposite values.
2366 __isl_give isl_map *isl_map_order_le(
2367 __isl_take isl_map *map,
2368 enum isl_dim_type type1, int pos1,
2369 enum isl_dim_type type2, int pos2);
2370 __isl_give isl_basic_map *isl_basic_map_order_ge(
2371 __isl_take isl_basic_map *bmap,
2372 enum isl_dim_type type1, int pos1,
2373 enum isl_dim_type type2, int pos2);
2374 __isl_give isl_map *isl_map_order_ge(
2375 __isl_take isl_map *map,
2376 enum isl_dim_type type1, int pos1,
2377 enum isl_dim_type type2, int pos2);
2378 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2379 enum isl_dim_type type1, int pos1,
2380 enum isl_dim_type type2, int pos2);
2381 __isl_give isl_basic_map *isl_basic_map_order_gt(
2382 __isl_take isl_basic_map *bmap,
2383 enum isl_dim_type type1, int pos1,
2384 enum isl_dim_type type2, int pos2);
2385 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2386 enum isl_dim_type type1, int pos1,
2387 enum isl_dim_type type2, int pos2);
2389 Intersect the relation with the half-space where the given
2390 dimensions satisfy the given ordering.
2394 __isl_give isl_map *isl_set_identity(
2395 __isl_take isl_set *set);
2396 __isl_give isl_union_map *isl_union_set_identity(
2397 __isl_take isl_union_set *uset);
2399 Construct an identity relation on the given (union) set.
2403 __isl_give isl_basic_set *isl_basic_map_deltas(
2404 __isl_take isl_basic_map *bmap);
2405 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2406 __isl_give isl_union_set *isl_union_map_deltas(
2407 __isl_take isl_union_map *umap);
2409 These functions return a (basic) set containing the differences
2410 between image elements and corresponding domain elements in the input.
2412 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2413 __isl_take isl_basic_map *bmap);
2414 __isl_give isl_map *isl_map_deltas_map(
2415 __isl_take isl_map *map);
2416 __isl_give isl_union_map *isl_union_map_deltas_map(
2417 __isl_take isl_union_map *umap);
2419 The functions above construct a (basic, regular or union) relation
2420 that maps (a wrapped version of) the input relation to its delta set.
2424 Simplify the representation of a set or relation by trying
2425 to combine pairs of basic sets or relations into a single
2426 basic set or relation.
2428 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2429 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2430 __isl_give isl_union_set *isl_union_set_coalesce(
2431 __isl_take isl_union_set *uset);
2432 __isl_give isl_union_map *isl_union_map_coalesce(
2433 __isl_take isl_union_map *umap);
2435 One of the methods for combining pairs of basic sets or relations
2436 can result in coefficients that are much larger than those that appear
2437 in the constraints of the input. By default, the coefficients are
2438 not allowed to grow larger, but this can be changed by unsetting
2439 the following option.
2441 int isl_options_set_coalesce_bounded_wrapping(
2442 isl_ctx *ctx, int val);
2443 int isl_options_get_coalesce_bounded_wrapping(
2446 =item * Detecting equalities
2448 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2449 __isl_take isl_basic_set *bset);
2450 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2451 __isl_take isl_basic_map *bmap);
2452 __isl_give isl_set *isl_set_detect_equalities(
2453 __isl_take isl_set *set);
2454 __isl_give isl_map *isl_map_detect_equalities(
2455 __isl_take isl_map *map);
2456 __isl_give isl_union_set *isl_union_set_detect_equalities(
2457 __isl_take isl_union_set *uset);
2458 __isl_give isl_union_map *isl_union_map_detect_equalities(
2459 __isl_take isl_union_map *umap);
2461 Simplify the representation of a set or relation by detecting implicit
2464 =item * Removing redundant constraints
2466 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2467 __isl_take isl_basic_set *bset);
2468 __isl_give isl_set *isl_set_remove_redundancies(
2469 __isl_take isl_set *set);
2470 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2471 __isl_take isl_basic_map *bmap);
2472 __isl_give isl_map *isl_map_remove_redundancies(
2473 __isl_take isl_map *map);
2477 __isl_give isl_basic_set *isl_set_convex_hull(
2478 __isl_take isl_set *set);
2479 __isl_give isl_basic_map *isl_map_convex_hull(
2480 __isl_take isl_map *map);
2482 If the input set or relation has any existentially quantified
2483 variables, then the result of these operations is currently undefined.
2487 __isl_give isl_basic_set *
2488 isl_set_unshifted_simple_hull(
2489 __isl_take isl_set *set);
2490 __isl_give isl_basic_map *
2491 isl_map_unshifted_simple_hull(
2492 __isl_take isl_map *map);
2493 __isl_give isl_basic_set *isl_set_simple_hull(
2494 __isl_take isl_set *set);
2495 __isl_give isl_basic_map *isl_map_simple_hull(
2496 __isl_take isl_map *map);
2497 __isl_give isl_union_map *isl_union_map_simple_hull(
2498 __isl_take isl_union_map *umap);
2500 These functions compute a single basic set or relation
2501 that contains the whole input set or relation.
2502 In particular, the output is described by translates
2503 of the constraints describing the basic sets or relations in the input.
2504 In case of C<isl_set_unshifted_simple_hull>, only the original
2505 constraints are used, without any translation.
2509 (See \autoref{s:simple hull}.)
2515 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2516 __isl_take isl_basic_set *bset);
2517 __isl_give isl_basic_set *isl_set_affine_hull(
2518 __isl_take isl_set *set);
2519 __isl_give isl_union_set *isl_union_set_affine_hull(
2520 __isl_take isl_union_set *uset);
2521 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2522 __isl_take isl_basic_map *bmap);
2523 __isl_give isl_basic_map *isl_map_affine_hull(
2524 __isl_take isl_map *map);
2525 __isl_give isl_union_map *isl_union_map_affine_hull(
2526 __isl_take isl_union_map *umap);
2528 In case of union sets and relations, the affine hull is computed
2531 =item * Polyhedral hull
2533 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2534 __isl_take isl_set *set);
2535 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2536 __isl_take isl_map *map);
2537 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2538 __isl_take isl_union_set *uset);
2539 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2540 __isl_take isl_union_map *umap);
2542 These functions compute a single basic set or relation
2543 not involving any existentially quantified variables
2544 that contains the whole input set or relation.
2545 In case of union sets and relations, the polyhedral hull is computed
2548 =item * Other approximations
2550 __isl_give isl_basic_set *
2551 isl_basic_set_drop_constraints_involving_dims(
2552 __isl_take isl_basic_set *bset,
2553 enum isl_dim_type type,
2554 unsigned first, unsigned n);
2555 __isl_give isl_basic_map *
2556 isl_basic_map_drop_constraints_involving_dims(
2557 __isl_take isl_basic_map *bmap,
2558 enum isl_dim_type type,
2559 unsigned first, unsigned n);
2560 __isl_give isl_basic_set *
2561 isl_basic_set_drop_constraints_not_involving_dims(
2562 __isl_take isl_basic_set *bset,
2563 enum isl_dim_type type,
2564 unsigned first, unsigned n);
2565 __isl_give isl_set *
2566 isl_set_drop_constraints_involving_dims(
2567 __isl_take isl_set *set,
2568 enum isl_dim_type type,
2569 unsigned first, unsigned n);
2570 __isl_give isl_map *
2571 isl_map_drop_constraints_involving_dims(
2572 __isl_take isl_map *map,
2573 enum isl_dim_type type,
2574 unsigned first, unsigned n);
2576 These functions drop any constraints (not) involving the specified dimensions.
2577 Note that the result depends on the representation of the input.
2581 __isl_give isl_basic_set *isl_basic_set_sample(
2582 __isl_take isl_basic_set *bset);
2583 __isl_give isl_basic_set *isl_set_sample(
2584 __isl_take isl_set *set);
2585 __isl_give isl_basic_map *isl_basic_map_sample(
2586 __isl_take isl_basic_map *bmap);
2587 __isl_give isl_basic_map *isl_map_sample(
2588 __isl_take isl_map *map);
2590 If the input (basic) set or relation is non-empty, then return
2591 a singleton subset of the input. Otherwise, return an empty set.
2593 =item * Optimization
2595 #include <isl/ilp.h>
2596 __isl_give isl_val *isl_basic_set_max_val(
2597 __isl_keep isl_basic_set *bset,
2598 __isl_keep isl_aff *obj);
2599 __isl_give isl_val *isl_set_min_val(
2600 __isl_keep isl_set *set,
2601 __isl_keep isl_aff *obj);
2602 __isl_give isl_val *isl_set_max_val(
2603 __isl_keep isl_set *set,
2604 __isl_keep isl_aff *obj);
2606 Compute the minimum or maximum of the integer affine expression C<obj>
2607 over the points in C<set>, returning the result in C<opt>.
2608 The result is C<NULL> in case of an error, the optimal value in case
2609 there is one, negative infinity or infinity if the problem is unbounded and
2610 NaN if the problem is empty.
2612 =item * Parametric optimization
2614 __isl_give isl_pw_aff *isl_set_dim_min(
2615 __isl_take isl_set *set, int pos);
2616 __isl_give isl_pw_aff *isl_set_dim_max(
2617 __isl_take isl_set *set, int pos);
2618 __isl_give isl_pw_aff *isl_map_dim_max(
2619 __isl_take isl_map *map, int pos);
2621 Compute the minimum or maximum of the given set or output dimension
2622 as a function of the parameters (and input dimensions), but independently
2623 of the other set or output dimensions.
2624 For lexicographic optimization, see L<"Lexicographic Optimization">.
2628 The following functions compute either the set of (rational) coefficient
2629 values of valid constraints for the given set or the set of (rational)
2630 values satisfying the constraints with coefficients from the given set.
2631 Internally, these two sets of functions perform essentially the
2632 same operations, except that the set of coefficients is assumed to
2633 be a cone, while the set of values may be any polyhedron.
2634 The current implementation is based on the Farkas lemma and
2635 Fourier-Motzkin elimination, but this may change or be made optional
2636 in future. In particular, future implementations may use different
2637 dualization algorithms or skip the elimination step.
2639 __isl_give isl_basic_set *isl_basic_set_coefficients(
2640 __isl_take isl_basic_set *bset);
2641 __isl_give isl_basic_set *isl_set_coefficients(
2642 __isl_take isl_set *set);
2643 __isl_give isl_union_set *isl_union_set_coefficients(
2644 __isl_take isl_union_set *bset);
2645 __isl_give isl_basic_set *isl_basic_set_solutions(
2646 __isl_take isl_basic_set *bset);
2647 __isl_give isl_basic_set *isl_set_solutions(
2648 __isl_take isl_set *set);
2649 __isl_give isl_union_set *isl_union_set_solutions(
2650 __isl_take isl_union_set *bset);
2654 __isl_give isl_map *isl_map_fixed_power_val(
2655 __isl_take isl_map *map,
2656 __isl_take isl_val *exp);
2657 __isl_give isl_union_map *
2658 isl_union_map_fixed_power_val(
2659 __isl_take isl_union_map *umap,
2660 __isl_take isl_val *exp);
2662 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2663 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2664 of C<map> is computed.
2666 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2668 __isl_give isl_union_map *isl_union_map_power(
2669 __isl_take isl_union_map *umap, int *exact);
2671 Compute a parametric representation for all positive powers I<k> of C<map>.
2672 The result maps I<k> to a nested relation corresponding to the
2673 I<k>th power of C<map>.
2674 The result may be an overapproximation. If the result is known to be exact,
2675 then C<*exact> is set to C<1>.
2677 =item * Transitive closure
2679 __isl_give isl_map *isl_map_transitive_closure(
2680 __isl_take isl_map *map, int *exact);
2681 __isl_give isl_union_map *isl_union_map_transitive_closure(
2682 __isl_take isl_union_map *umap, int *exact);
2684 Compute the transitive closure of C<map>.
2685 The result may be an overapproximation. If the result is known to be exact,
2686 then C<*exact> is set to C<1>.
2688 =item * Reaching path lengths
2690 __isl_give isl_map *isl_map_reaching_path_lengths(
2691 __isl_take isl_map *map, int *exact);
2693 Compute a relation that maps each element in the range of C<map>
2694 to the lengths of all paths composed of edges in C<map> that
2695 end up in the given element.
2696 The result may be an overapproximation. If the result is known to be exact,
2697 then C<*exact> is set to C<1>.
2698 To compute the I<maximal> path length, the resulting relation
2699 should be postprocessed by C<isl_map_lexmax>.
2700 In particular, if the input relation is a dependence relation
2701 (mapping sources to sinks), then the maximal path length corresponds
2702 to the free schedule.
2703 Note, however, that C<isl_map_lexmax> expects the maximum to be
2704 finite, so if the path lengths are unbounded (possibly due to
2705 the overapproximation), then you will get an error message.
2709 #include <isl/space.h>
2710 __isl_give isl_space *isl_space_wrap(
2711 __isl_take isl_space *space);
2712 __isl_give isl_space *isl_space_unwrap(
2713 __isl_take isl_space *space);
2715 #include <isl/set.h>
2716 __isl_give isl_basic_map *isl_basic_set_unwrap(
2717 __isl_take isl_basic_set *bset);
2718 __isl_give isl_map *isl_set_unwrap(
2719 __isl_take isl_set *set);
2721 #include <isl/map.h>
2722 __isl_give isl_basic_set *isl_basic_map_wrap(
2723 __isl_take isl_basic_map *bmap);
2724 __isl_give isl_set *isl_map_wrap(
2725 __isl_take isl_map *map);
2727 #include <isl/union_set.h>
2728 __isl_give isl_union_map *isl_union_set_unwrap(
2729 __isl_take isl_union_set *uset);
2731 #include <isl/union_map.h>
2732 __isl_give isl_union_set *isl_union_map_wrap(
2733 __isl_take isl_union_map *umap);
2735 The input to C<isl_space_unwrap> should
2736 be the space of a set, while that of
2737 C<isl_space_wrap> should be the space of a relation.
2738 Conversely, the output of C<isl_space_unwrap> is the space
2739 of a relation, while that of C<isl_space_wrap> is the space of a set.
2743 Remove any internal structure of domain (and range) of the given
2744 set or relation. If there is any such internal structure in the input,
2745 then the name of the space is also removed.
2747 #include <isl/local_space.h>
2748 __isl_give isl_local_space *
2749 isl_local_space_flatten_domain(
2750 __isl_take isl_local_space *ls);
2751 __isl_give isl_local_space *
2752 isl_local_space_flatten_range(
2753 __isl_take isl_local_space *ls);
2755 #include <isl/set.h>
2756 __isl_give isl_basic_set *isl_basic_set_flatten(
2757 __isl_take isl_basic_set *bset);
2758 __isl_give isl_set *isl_set_flatten(
2759 __isl_take isl_set *set);
2761 #include <isl/map.h>
2762 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2763 __isl_take isl_basic_map *bmap);
2764 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2765 __isl_take isl_basic_map *bmap);
2766 __isl_give isl_map *isl_map_flatten_range(
2767 __isl_take isl_map *map);
2768 __isl_give isl_map *isl_map_flatten_domain(
2769 __isl_take isl_map *map);
2770 __isl_give isl_basic_map *isl_basic_map_flatten(
2771 __isl_take isl_basic_map *bmap);
2772 __isl_give isl_map *isl_map_flatten(
2773 __isl_take isl_map *map);
2775 #include <isl/map.h>
2776 __isl_give isl_map *isl_set_flatten_map(
2777 __isl_take isl_set *set);
2779 The function above constructs a relation
2780 that maps the input set to a flattened version of the set.
2784 Lift the input set to a space with extra dimensions corresponding
2785 to the existentially quantified variables in the input.
2786 In particular, the result lives in a wrapped map where the domain
2787 is the original space and the range corresponds to the original
2788 existentially quantified variables.
2790 __isl_give isl_basic_set *isl_basic_set_lift(
2791 __isl_take isl_basic_set *bset);
2792 __isl_give isl_set *isl_set_lift(
2793 __isl_take isl_set *set);
2794 __isl_give isl_union_set *isl_union_set_lift(
2795 __isl_take isl_union_set *uset);
2797 Given a local space that contains the existentially quantified
2798 variables of a set, a basic relation that, when applied to
2799 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2800 can be constructed using the following function.
2802 #include <isl/local_space.h>
2803 __isl_give isl_basic_map *isl_local_space_lifting(
2804 __isl_take isl_local_space *ls);
2806 =item * Internal Product
2808 __isl_give isl_basic_map *isl_basic_map_zip(
2809 __isl_take isl_basic_map *bmap);
2810 __isl_give isl_map *isl_map_zip(
2811 __isl_take isl_map *map);
2812 __isl_give isl_union_map *isl_union_map_zip(
2813 __isl_take isl_union_map *umap);
2815 Given a relation with nested relations for domain and range,
2816 interchange the range of the domain with the domain of the range.
2820 __isl_give isl_basic_map *isl_basic_map_curry(
2821 __isl_take isl_basic_map *bmap);
2822 __isl_give isl_basic_map *isl_basic_map_uncurry(
2823 __isl_take isl_basic_map *bmap);
2824 __isl_give isl_map *isl_map_curry(
2825 __isl_take isl_map *map);
2826 __isl_give isl_map *isl_map_uncurry(
2827 __isl_take isl_map *map);
2828 __isl_give isl_union_map *isl_union_map_curry(
2829 __isl_take isl_union_map *umap);
2830 __isl_give isl_union_map *isl_union_map_uncurry(
2831 __isl_take isl_union_map *umap);
2833 Given a relation with a nested relation for domain,
2834 the C<curry> functions
2835 move the range of the nested relation out of the domain
2836 and use it as the domain of a nested relation in the range,
2837 with the original range as range of this nested relation.
2838 The C<uncurry> functions perform the inverse operation.
2840 =item * Aligning parameters
2842 __isl_give isl_basic_set *isl_basic_set_align_params(
2843 __isl_take isl_basic_set *bset,
2844 __isl_take isl_space *model);
2845 __isl_give isl_set *isl_set_align_params(
2846 __isl_take isl_set *set,
2847 __isl_take isl_space *model);
2848 __isl_give isl_basic_map *isl_basic_map_align_params(
2849 __isl_take isl_basic_map *bmap,
2850 __isl_take isl_space *model);
2851 __isl_give isl_map *isl_map_align_params(
2852 __isl_take isl_map *map,
2853 __isl_take isl_space *model);
2855 Change the order of the parameters of the given set or relation
2856 such that the first parameters match those of C<model>.
2857 This may involve the introduction of extra parameters.
2858 All parameters need to be named.
2860 =item * Dimension manipulation
2862 #include <isl/local_space.h>
2863 __isl_give isl_local_space *isl_local_space_add_dims(
2864 __isl_take isl_local_space *ls,
2865 enum isl_dim_type type, unsigned n);
2866 __isl_give isl_local_space *isl_local_space_insert_dims(
2867 __isl_take isl_local_space *ls,
2868 enum isl_dim_type type, unsigned first, unsigned n);
2869 __isl_give isl_local_space *isl_local_space_drop_dims(
2870 __isl_take isl_local_space *ls,
2871 enum isl_dim_type type, unsigned first, unsigned n);
2873 #include <isl/set.h>
2874 __isl_give isl_basic_set *isl_basic_set_add_dims(
2875 __isl_take isl_basic_set *bset,
2876 enum isl_dim_type type, unsigned n);
2877 __isl_give isl_set *isl_set_add_dims(
2878 __isl_take isl_set *set,
2879 enum isl_dim_type type, unsigned n);
2880 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2881 __isl_take isl_basic_set *bset,
2882 enum isl_dim_type type, unsigned pos,
2884 __isl_give isl_set *isl_set_insert_dims(
2885 __isl_take isl_set *set,
2886 enum isl_dim_type type, unsigned pos, unsigned n);
2887 __isl_give isl_basic_set *isl_basic_set_move_dims(
2888 __isl_take isl_basic_set *bset,
2889 enum isl_dim_type dst_type, unsigned dst_pos,
2890 enum isl_dim_type src_type, unsigned src_pos,
2892 __isl_give isl_set *isl_set_move_dims(
2893 __isl_take isl_set *set,
2894 enum isl_dim_type dst_type, unsigned dst_pos,
2895 enum isl_dim_type src_type, unsigned src_pos,
2898 #include <isl/map.h>
2899 __isl_give isl_map *isl_map_add_dims(
2900 __isl_take isl_map *map,
2901 enum isl_dim_type type, unsigned n);
2902 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2903 __isl_take isl_basic_map *bmap,
2904 enum isl_dim_type type, unsigned pos,
2906 __isl_give isl_map *isl_map_insert_dims(
2907 __isl_take isl_map *map,
2908 enum isl_dim_type type, unsigned pos, unsigned n);
2909 __isl_give isl_basic_map *isl_basic_map_move_dims(
2910 __isl_take isl_basic_map *bmap,
2911 enum isl_dim_type dst_type, unsigned dst_pos,
2912 enum isl_dim_type src_type, unsigned src_pos,
2914 __isl_give isl_map *isl_map_move_dims(
2915 __isl_take isl_map *map,
2916 enum isl_dim_type dst_type, unsigned dst_pos,
2917 enum isl_dim_type src_type, unsigned src_pos,
2920 It is usually not advisable to directly change the (input or output)
2921 space of a set or a relation as this removes the name and the internal
2922 structure of the space. However, the above functions can be useful
2923 to add new parameters, assuming
2924 C<isl_set_align_params> and C<isl_map_align_params>
2929 =head2 Binary Operations
2931 The two arguments of a binary operation not only need to live
2932 in the same C<isl_ctx>, they currently also need to have
2933 the same (number of) parameters.
2935 =head3 Basic Operations
2939 =item * Intersection
2941 #include <isl/local_space.h>
2942 __isl_give isl_local_space *isl_local_space_intersect(
2943 __isl_take isl_local_space *ls1,
2944 __isl_take isl_local_space *ls2);
2946 #include <isl/set.h>
2947 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2948 __isl_take isl_basic_set *bset1,
2949 __isl_take isl_basic_set *bset2);
2950 __isl_give isl_basic_set *isl_basic_set_intersect(
2951 __isl_take isl_basic_set *bset1,
2952 __isl_take isl_basic_set *bset2);
2953 __isl_give isl_set *isl_set_intersect_params(
2954 __isl_take isl_set *set,
2955 __isl_take isl_set *params);
2956 __isl_give isl_set *isl_set_intersect(
2957 __isl_take isl_set *set1,
2958 __isl_take isl_set *set2);
2960 #include <isl/map.h>
2961 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2962 __isl_take isl_basic_map *bmap,
2963 __isl_take isl_basic_set *bset);
2964 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2965 __isl_take isl_basic_map *bmap,
2966 __isl_take isl_basic_set *bset);
2967 __isl_give isl_basic_map *isl_basic_map_intersect(
2968 __isl_take isl_basic_map *bmap1,
2969 __isl_take isl_basic_map *bmap2);
2970 __isl_give isl_map *isl_map_intersect_params(
2971 __isl_take isl_map *map,
2972 __isl_take isl_set *params);
2973 __isl_give isl_map *isl_map_intersect_domain(
2974 __isl_take isl_map *map,
2975 __isl_take isl_set *set);
2976 __isl_give isl_map *isl_map_intersect_range(
2977 __isl_take isl_map *map,
2978 __isl_take isl_set *set);
2979 __isl_give isl_map *isl_map_intersect(
2980 __isl_take isl_map *map1,
2981 __isl_take isl_map *map2);
2983 #include <isl/union_set.h>
2984 __isl_give isl_union_set *isl_union_set_intersect_params(
2985 __isl_take isl_union_set *uset,
2986 __isl_take isl_set *set);
2987 __isl_give isl_union_set *isl_union_set_intersect(
2988 __isl_take isl_union_set *uset1,
2989 __isl_take isl_union_set *uset2);
2991 #include <isl/union_map.h>
2992 __isl_give isl_union_map *isl_union_map_intersect_params(
2993 __isl_take isl_union_map *umap,
2994 __isl_take isl_set *set);
2995 __isl_give isl_union_map *isl_union_map_intersect_domain(
2996 __isl_take isl_union_map *umap,
2997 __isl_take isl_union_set *uset);
2998 __isl_give isl_union_map *isl_union_map_intersect_range(
2999 __isl_take isl_union_map *umap,
3000 __isl_take isl_union_set *uset);
3001 __isl_give isl_union_map *isl_union_map_intersect(
3002 __isl_take isl_union_map *umap1,
3003 __isl_take isl_union_map *umap2);
3005 The second argument to the C<_params> functions needs to be
3006 a parametric (basic) set. For the other functions, a parametric set
3007 for either argument is only allowed if the other argument is
3008 a parametric set as well.
3012 __isl_give isl_set *isl_basic_set_union(
3013 __isl_take isl_basic_set *bset1,
3014 __isl_take isl_basic_set *bset2);
3015 __isl_give isl_map *isl_basic_map_union(
3016 __isl_take isl_basic_map *bmap1,
3017 __isl_take isl_basic_map *bmap2);
3018 __isl_give isl_set *isl_set_union(
3019 __isl_take isl_set *set1,
3020 __isl_take isl_set *set2);
3021 __isl_give isl_map *isl_map_union(
3022 __isl_take isl_map *map1,
3023 __isl_take isl_map *map2);
3024 __isl_give isl_union_set *isl_union_set_union(
3025 __isl_take isl_union_set *uset1,
3026 __isl_take isl_union_set *uset2);
3027 __isl_give isl_union_map *isl_union_map_union(
3028 __isl_take isl_union_map *umap1,
3029 __isl_take isl_union_map *umap2);
3031 =item * Set difference
3033 __isl_give isl_set *isl_set_subtract(
3034 __isl_take isl_set *set1,
3035 __isl_take isl_set *set2);
3036 __isl_give isl_map *isl_map_subtract(
3037 __isl_take isl_map *map1,
3038 __isl_take isl_map *map2);
3039 __isl_give isl_map *isl_map_subtract_domain(
3040 __isl_take isl_map *map,
3041 __isl_take isl_set *dom);
3042 __isl_give isl_map *isl_map_subtract_range(
3043 __isl_take isl_map *map,
3044 __isl_take isl_set *dom);
3045 __isl_give isl_union_set *isl_union_set_subtract(
3046 __isl_take isl_union_set *uset1,
3047 __isl_take isl_union_set *uset2);
3048 __isl_give isl_union_map *isl_union_map_subtract(
3049 __isl_take isl_union_map *umap1,
3050 __isl_take isl_union_map *umap2);
3051 __isl_give isl_union_map *isl_union_map_subtract_domain(
3052 __isl_take isl_union_map *umap,
3053 __isl_take isl_union_set *dom);
3054 __isl_give isl_union_map *isl_union_map_subtract_range(
3055 __isl_take isl_union_map *umap,
3056 __isl_take isl_union_set *dom);
3060 __isl_give isl_basic_set *isl_basic_set_apply(
3061 __isl_take isl_basic_set *bset,
3062 __isl_take isl_basic_map *bmap);
3063 __isl_give isl_set *isl_set_apply(
3064 __isl_take isl_set *set,
3065 __isl_take isl_map *map);
3066 __isl_give isl_union_set *isl_union_set_apply(
3067 __isl_take isl_union_set *uset,
3068 __isl_take isl_union_map *umap);
3069 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3070 __isl_take isl_basic_map *bmap1,
3071 __isl_take isl_basic_map *bmap2);
3072 __isl_give isl_basic_map *isl_basic_map_apply_range(
3073 __isl_take isl_basic_map *bmap1,
3074 __isl_take isl_basic_map *bmap2);
3075 __isl_give isl_map *isl_map_apply_domain(
3076 __isl_take isl_map *map1,
3077 __isl_take isl_map *map2);
3078 __isl_give isl_union_map *isl_union_map_apply_domain(
3079 __isl_take isl_union_map *umap1,
3080 __isl_take isl_union_map *umap2);
3081 __isl_give isl_map *isl_map_apply_range(
3082 __isl_take isl_map *map1,
3083 __isl_take isl_map *map2);
3084 __isl_give isl_union_map *isl_union_map_apply_range(
3085 __isl_take isl_union_map *umap1,
3086 __isl_take isl_union_map *umap2);
3090 #include <isl/set.h>
3091 __isl_give isl_basic_set *
3092 isl_basic_set_preimage_multi_aff(
3093 __isl_take isl_basic_set *bset,
3094 __isl_take isl_multi_aff *ma);
3095 __isl_give isl_set *isl_set_preimage_multi_aff(
3096 __isl_take isl_set *set,
3097 __isl_take isl_multi_aff *ma);
3098 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3099 __isl_take isl_set *set,
3100 __isl_take isl_pw_multi_aff *pma);
3101 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
3102 __isl_take isl_set *set,
3103 __isl_take isl_multi_pw_aff *mpa);
3105 #include <isl/union_set.h>
3106 __isl_give isl_union_set *
3107 isl_union_set_preimage_multi_aff(
3108 __isl_take isl_union_set *uset,
3109 __isl_take isl_multi_aff *ma);
3110 __isl_give isl_union_set *
3111 isl_union_set_preimage_pw_multi_aff(
3112 __isl_take isl_union_set *uset,
3113 __isl_take isl_pw_multi_aff *pma);
3114 __isl_give isl_union_set *
3115 isl_union_set_preimage_union_pw_multi_aff(
3116 __isl_take isl_union_set *uset,
3117 __isl_take isl_union_pw_multi_aff *upma);
3119 #include <isl/map.h>
3120 __isl_give isl_basic_map *
3121 isl_basic_map_preimage_domain_multi_aff(
3122 __isl_take isl_basic_map *bmap,
3123 __isl_take isl_multi_aff *ma);
3124 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3125 __isl_take isl_map *map,
3126 __isl_take isl_multi_aff *ma);
3127 __isl_give isl_map *isl_map_preimage_range_multi_aff(
3128 __isl_take isl_map *map,
3129 __isl_take isl_multi_aff *ma);
3130 __isl_give isl_map *
3131 isl_map_preimage_domain_pw_multi_aff(
3132 __isl_take isl_map *map,
3133 __isl_take isl_pw_multi_aff *pma);
3134 __isl_give isl_map *
3135 isl_map_preimage_range_pw_multi_aff(
3136 __isl_take isl_map *map,
3137 __isl_take isl_pw_multi_aff *pma);
3138 __isl_give isl_map *
3139 isl_map_preimage_domain_multi_pw_aff(
3140 __isl_take isl_map *map,
3141 __isl_take isl_multi_pw_aff *mpa);
3142 __isl_give isl_basic_map *
3143 isl_basic_map_preimage_range_multi_aff(
3144 __isl_take isl_basic_map *bmap,
3145 __isl_take isl_multi_aff *ma);
3147 #include <isl/union_map.h>
3148 __isl_give isl_union_map *
3149 isl_union_map_preimage_domain_multi_aff(
3150 __isl_take isl_union_map *umap,
3151 __isl_take isl_multi_aff *ma);
3152 __isl_give isl_union_map *
3153 isl_union_map_preimage_range_multi_aff(
3154 __isl_take isl_union_map *umap,
3155 __isl_take isl_multi_aff *ma);
3156 __isl_give isl_union_map *
3157 isl_union_map_preimage_domain_pw_multi_aff(
3158 __isl_take isl_union_map *umap,
3159 __isl_take isl_pw_multi_aff *pma);
3160 __isl_give isl_union_map *
3161 isl_union_map_preimage_range_pw_multi_aff(
3162 __isl_take isl_union_map *umap,
3163 __isl_take isl_pw_multi_aff *pma);
3164 __isl_give isl_union_map *
3165 isl_union_map_preimage_domain_union_pw_multi_aff(
3166 __isl_take isl_union_map *umap,
3167 __isl_take isl_union_pw_multi_aff *upma);
3168 __isl_give isl_union_map *
3169 isl_union_map_preimage_range_union_pw_multi_aff(
3170 __isl_take isl_union_map *umap,
3171 __isl_take isl_union_pw_multi_aff *upma);
3173 These functions compute the preimage of the given set or map domain/range under
3174 the given function. In other words, the expression is plugged
3175 into the set description or into the domain/range of the map.
3176 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3177 L</"Piecewise Multiple Quasi Affine Expressions">.
3179 =item * Cartesian Product
3181 #include <isl/space.h>
3182 __isl_give isl_space *isl_space_product(
3183 __isl_take isl_space *space1,
3184 __isl_take isl_space *space2);
3185 __isl_give isl_space *isl_space_domain_product(
3186 __isl_take isl_space *space1,
3187 __isl_take isl_space *space2);
3188 __isl_give isl_space *isl_space_range_product(
3189 __isl_take isl_space *space1,
3190 __isl_take isl_space *space2);
3193 C<isl_space_product>, C<isl_space_domain_product>
3194 and C<isl_space_range_product> take pairs or relation spaces and
3195 produce a single relations space, where either the domain, the range
3196 or both domain and range are wrapped spaces of relations between
3197 the domains and/or ranges of the input spaces.
3198 If the product is only constructed over the domain or the range
3199 then the ranges or the domains of the inputs should be the same.
3200 The function C<isl_space_product> also accepts a pair of set spaces,
3201 in which case it returns a wrapped space of a relation between the
3204 #include <isl/set.h>
3205 __isl_give isl_set *isl_set_product(
3206 __isl_take isl_set *set1,
3207 __isl_take isl_set *set2);
3209 #include <isl/map.h>
3210 __isl_give isl_basic_map *isl_basic_map_domain_product(
3211 __isl_take isl_basic_map *bmap1,
3212 __isl_take isl_basic_map *bmap2);
3213 __isl_give isl_basic_map *isl_basic_map_range_product(
3214 __isl_take isl_basic_map *bmap1,
3215 __isl_take isl_basic_map *bmap2);
3216 __isl_give isl_basic_map *isl_basic_map_product(
3217 __isl_take isl_basic_map *bmap1,
3218 __isl_take isl_basic_map *bmap2);
3219 __isl_give isl_map *isl_map_domain_product(
3220 __isl_take isl_map *map1,
3221 __isl_take isl_map *map2);
3222 __isl_give isl_map *isl_map_range_product(
3223 __isl_take isl_map *map1,
3224 __isl_take isl_map *map2);
3225 __isl_give isl_map *isl_map_product(
3226 __isl_take isl_map *map1,
3227 __isl_take isl_map *map2);
3229 #include <isl/union_set.h>
3230 __isl_give isl_union_set *isl_union_set_product(
3231 __isl_take isl_union_set *uset1,
3232 __isl_take isl_union_set *uset2);
3234 #include <isl/union_map.h>
3235 __isl_give isl_union_map *isl_union_map_domain_product(
3236 __isl_take isl_union_map *umap1,
3237 __isl_take isl_union_map *umap2);
3238 __isl_give isl_union_map *isl_union_map_range_product(
3239 __isl_take isl_union_map *umap1,
3240 __isl_take isl_union_map *umap2);
3241 __isl_give isl_union_map *isl_union_map_product(
3242 __isl_take isl_union_map *umap1,
3243 __isl_take isl_union_map *umap2);
3245 The above functions compute the cross product of the given
3246 sets or relations. The domains and ranges of the results
3247 are wrapped maps between domains and ranges of the inputs.
3248 To obtain a ``flat'' product, use the following functions
3251 __isl_give isl_basic_set *isl_basic_set_flat_product(
3252 __isl_take isl_basic_set *bset1,
3253 __isl_take isl_basic_set *bset2);
3254 __isl_give isl_set *isl_set_flat_product(
3255 __isl_take isl_set *set1,
3256 __isl_take isl_set *set2);
3257 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3258 __isl_take isl_basic_map *bmap1,
3259 __isl_take isl_basic_map *bmap2);
3260 __isl_give isl_map *isl_map_flat_domain_product(
3261 __isl_take isl_map *map1,
3262 __isl_take isl_map *map2);
3263 __isl_give isl_map *isl_map_flat_range_product(
3264 __isl_take isl_map *map1,
3265 __isl_take isl_map *map2);
3266 __isl_give isl_union_map *isl_union_map_flat_range_product(
3267 __isl_take isl_union_map *umap1,
3268 __isl_take isl_union_map *umap2);
3269 __isl_give isl_basic_map *isl_basic_map_flat_product(
3270 __isl_take isl_basic_map *bmap1,
3271 __isl_take isl_basic_map *bmap2);
3272 __isl_give isl_map *isl_map_flat_product(
3273 __isl_take isl_map *map1,
3274 __isl_take isl_map *map2);
3276 #include <isl/space.h>
3277 __isl_give isl_space *isl_space_domain_factor_domain(
3278 __isl_take isl_space *space);
3279 __isl_give isl_space *isl_space_range_factor_domain(
3280 __isl_take isl_space *space);
3281 __isl_give isl_space *isl_space_range_factor_range(
3282 __isl_take isl_space *space);
3284 The functions C<isl_space_range_factor_domain> and
3285 C<isl_space_range_factor_range> extract the two arguments from
3286 the result of a call to C<isl_space_range_product>.
3288 The arguments of a call to C<isl_map_range_product> can be extracted
3289 from the result using the following two functions.
3291 #include <isl/map.h>
3292 __isl_give isl_map *isl_map_range_factor_domain(
3293 __isl_take isl_map *map);
3294 __isl_give isl_map *isl_map_range_factor_range(
3295 __isl_take isl_map *map);
3297 =item * Simplification
3299 __isl_give isl_basic_set *isl_basic_set_gist(
3300 __isl_take isl_basic_set *bset,
3301 __isl_take isl_basic_set *context);
3302 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3303 __isl_take isl_set *context);
3304 __isl_give isl_set *isl_set_gist_params(
3305 __isl_take isl_set *set,
3306 __isl_take isl_set *context);
3307 __isl_give isl_union_set *isl_union_set_gist(
3308 __isl_take isl_union_set *uset,
3309 __isl_take isl_union_set *context);
3310 __isl_give isl_union_set *isl_union_set_gist_params(
3311 __isl_take isl_union_set *uset,
3312 __isl_take isl_set *set);
3313 __isl_give isl_basic_map *isl_basic_map_gist(
3314 __isl_take isl_basic_map *bmap,
3315 __isl_take isl_basic_map *context);
3316 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3317 __isl_take isl_map *context);
3318 __isl_give isl_map *isl_map_gist_params(
3319 __isl_take isl_map *map,
3320 __isl_take isl_set *context);
3321 __isl_give isl_map *isl_map_gist_domain(
3322 __isl_take isl_map *map,
3323 __isl_take isl_set *context);
3324 __isl_give isl_map *isl_map_gist_range(
3325 __isl_take isl_map *map,
3326 __isl_take isl_set *context);
3327 __isl_give isl_union_map *isl_union_map_gist(
3328 __isl_take isl_union_map *umap,
3329 __isl_take isl_union_map *context);
3330 __isl_give isl_union_map *isl_union_map_gist_params(
3331 __isl_take isl_union_map *umap,
3332 __isl_take isl_set *set);
3333 __isl_give isl_union_map *isl_union_map_gist_domain(
3334 __isl_take isl_union_map *umap,
3335 __isl_take isl_union_set *uset);
3336 __isl_give isl_union_map *isl_union_map_gist_range(
3337 __isl_take isl_union_map *umap,
3338 __isl_take isl_union_set *uset);
3340 The gist operation returns a set or relation that has the
3341 same intersection with the context as the input set or relation.
3342 Any implicit equality in the intersection is made explicit in the result,
3343 while all inequalities that are redundant with respect to the intersection
3345 In case of union sets and relations, the gist operation is performed
3350 =head3 Lexicographic Optimization
3352 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3353 the following functions
3354 compute a set that contains the lexicographic minimum or maximum
3355 of the elements in C<set> (or C<bset>) for those values of the parameters
3356 that satisfy C<dom>.
3357 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3358 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3360 In other words, the union of the parameter values
3361 for which the result is non-empty and of C<*empty>
3364 __isl_give isl_set *isl_basic_set_partial_lexmin(
3365 __isl_take isl_basic_set *bset,
3366 __isl_take isl_basic_set *dom,
3367 __isl_give isl_set **empty);
3368 __isl_give isl_set *isl_basic_set_partial_lexmax(
3369 __isl_take isl_basic_set *bset,
3370 __isl_take isl_basic_set *dom,
3371 __isl_give isl_set **empty);
3372 __isl_give isl_set *isl_set_partial_lexmin(
3373 __isl_take isl_set *set, __isl_take isl_set *dom,
3374 __isl_give isl_set **empty);
3375 __isl_give isl_set *isl_set_partial_lexmax(
3376 __isl_take isl_set *set, __isl_take isl_set *dom,
3377 __isl_give isl_set **empty);
3379 Given a (basic) set C<set> (or C<bset>), the following functions simply
3380 return a set containing the lexicographic minimum or maximum
3381 of the elements in C<set> (or C<bset>).
3382 In case of union sets, the optimum is computed per space.
3384 __isl_give isl_set *isl_basic_set_lexmin(
3385 __isl_take isl_basic_set *bset);
3386 __isl_give isl_set *isl_basic_set_lexmax(
3387 __isl_take isl_basic_set *bset);
3388 __isl_give isl_set *isl_set_lexmin(
3389 __isl_take isl_set *set);
3390 __isl_give isl_set *isl_set_lexmax(
3391 __isl_take isl_set *set);
3392 __isl_give isl_union_set *isl_union_set_lexmin(
3393 __isl_take isl_union_set *uset);
3394 __isl_give isl_union_set *isl_union_set_lexmax(
3395 __isl_take isl_union_set *uset);
3397 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3398 the following functions
3399 compute a relation that maps each element of C<dom>
3400 to the single lexicographic minimum or maximum
3401 of the elements that are associated to that same
3402 element in C<map> (or C<bmap>).
3403 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3404 that contains the elements in C<dom> that do not map
3405 to any elements in C<map> (or C<bmap>).
3406 In other words, the union of the domain of the result and of C<*empty>
3409 __isl_give isl_map *isl_basic_map_partial_lexmax(
3410 __isl_take isl_basic_map *bmap,
3411 __isl_take isl_basic_set *dom,
3412 __isl_give isl_set **empty);
3413 __isl_give isl_map *isl_basic_map_partial_lexmin(
3414 __isl_take isl_basic_map *bmap,
3415 __isl_take isl_basic_set *dom,
3416 __isl_give isl_set **empty);
3417 __isl_give isl_map *isl_map_partial_lexmax(
3418 __isl_take isl_map *map, __isl_take isl_set *dom,
3419 __isl_give isl_set **empty);
3420 __isl_give isl_map *isl_map_partial_lexmin(
3421 __isl_take isl_map *map, __isl_take isl_set *dom,
3422 __isl_give isl_set **empty);
3424 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3425 return a map mapping each element in the domain of
3426 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3427 of all elements associated to that element.
3428 In case of union relations, the optimum is computed per space.
3430 __isl_give isl_map *isl_basic_map_lexmin(
3431 __isl_take isl_basic_map *bmap);
3432 __isl_give isl_map *isl_basic_map_lexmax(
3433 __isl_take isl_basic_map *bmap);
3434 __isl_give isl_map *isl_map_lexmin(
3435 __isl_take isl_map *map);
3436 __isl_give isl_map *isl_map_lexmax(
3437 __isl_take isl_map *map);
3438 __isl_give isl_union_map *isl_union_map_lexmin(
3439 __isl_take isl_union_map *umap);
3440 __isl_give isl_union_map *isl_union_map_lexmax(
3441 __isl_take isl_union_map *umap);
3443 The following functions return their result in the form of
3444 a piecewise multi-affine expression
3445 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3446 but are otherwise equivalent to the corresponding functions
3447 returning a basic set or relation.
3449 __isl_give isl_pw_multi_aff *
3450 isl_basic_map_lexmin_pw_multi_aff(
3451 __isl_take isl_basic_map *bmap);
3452 __isl_give isl_pw_multi_aff *
3453 isl_basic_set_partial_lexmin_pw_multi_aff(
3454 __isl_take isl_basic_set *bset,
3455 __isl_take isl_basic_set *dom,
3456 __isl_give isl_set **empty);
3457 __isl_give isl_pw_multi_aff *
3458 isl_basic_set_partial_lexmax_pw_multi_aff(
3459 __isl_take isl_basic_set *bset,
3460 __isl_take isl_basic_set *dom,
3461 __isl_give isl_set **empty);
3462 __isl_give isl_pw_multi_aff *
3463 isl_basic_map_partial_lexmin_pw_multi_aff(
3464 __isl_take isl_basic_map *bmap,
3465 __isl_take isl_basic_set *dom,
3466 __isl_give isl_set **empty);
3467 __isl_give isl_pw_multi_aff *
3468 isl_basic_map_partial_lexmax_pw_multi_aff(
3469 __isl_take isl_basic_map *bmap,
3470 __isl_take isl_basic_set *dom,
3471 __isl_give isl_set **empty);
3472 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3473 __isl_take isl_set *set);
3474 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3475 __isl_take isl_set *set);
3476 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3477 __isl_take isl_map *map);
3478 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3479 __isl_take isl_map *map);
3483 Lists are defined over several element types, including
3484 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3485 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3486 Here we take lists of C<isl_set>s as an example.
3487 Lists can be created, copied, modified and freed using the following functions.
3489 #include <isl/list.h>
3490 __isl_give isl_set_list *isl_set_list_from_set(
3491 __isl_take isl_set *el);
3492 __isl_give isl_set_list *isl_set_list_alloc(
3493 isl_ctx *ctx, int n);
3494 __isl_give isl_set_list *isl_set_list_copy(
3495 __isl_keep isl_set_list *list);
3496 __isl_give isl_set_list *isl_set_list_insert(
3497 __isl_take isl_set_list *list, unsigned pos,
3498 __isl_take isl_set *el);
3499 __isl_give isl_set_list *isl_set_list_add(
3500 __isl_take isl_set_list *list,
3501 __isl_take isl_set *el);
3502 __isl_give isl_set_list *isl_set_list_drop(
3503 __isl_take isl_set_list *list,
3504 unsigned first, unsigned n);
3505 __isl_give isl_set_list *isl_set_list_set_set(
3506 __isl_take isl_set_list *list, int index,
3507 __isl_take isl_set *set);
3508 __isl_give isl_set_list *isl_set_list_concat(
3509 __isl_take isl_set_list *list1,
3510 __isl_take isl_set_list *list2);
3511 __isl_give isl_set_list *isl_set_list_sort(
3512 __isl_take isl_set_list *list,
3513 int (*cmp)(__isl_keep isl_set *a,
3514 __isl_keep isl_set *b, void *user),
3516 __isl_null isl_set_list *isl_set_list_free(
3517 __isl_take isl_set_list *list);
3519 C<isl_set_list_alloc> creates an empty list with a capacity for
3520 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3523 Lists can be inspected using the following functions.
3525 #include <isl/list.h>
3526 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3527 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3528 __isl_give isl_set *isl_set_list_get_set(
3529 __isl_keep isl_set_list *list, int index);
3530 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3531 int (*fn)(__isl_take isl_set *el, void *user),
3533 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3534 int (*follows)(__isl_keep isl_set *a,
3535 __isl_keep isl_set *b, void *user),
3537 int (*fn)(__isl_take isl_set *el, void *user),
3540 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3541 strongly connected components of the graph with as vertices the elements
3542 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3543 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3544 should return C<-1> on error.
3546 Lists can be printed using
3548 #include <isl/list.h>
3549 __isl_give isl_printer *isl_printer_print_set_list(
3550 __isl_take isl_printer *p,
3551 __isl_keep isl_set_list *list);
3553 =head2 Associative arrays
3555 Associative arrays map isl objects of a specific type to isl objects
3556 of some (other) specific type. They are defined for several pairs
3557 of types, including (C<isl_map>, C<isl_basic_set>),
3558 (C<isl_id>, C<isl_ast_expr>) and.
3559 (C<isl_id>, C<isl_pw_aff>).
3560 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3563 Associative arrays can be created, copied and freed using
3564 the following functions.
3566 #include <isl/id_to_ast_expr.h>
3567 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3568 isl_ctx *ctx, int min_size);
3569 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3570 __isl_keep id_to_ast_expr *id2expr);
3571 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
3572 __isl_take id_to_ast_expr *id2expr);
3574 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3575 to specify the expected size of the associative array.
3576 The associative array will be grown automatically as needed.
3578 Associative arrays can be inspected using the following functions.
3580 #include <isl/id_to_ast_expr.h>
3581 isl_ctx *isl_id_to_ast_expr_get_ctx(
3582 __isl_keep id_to_ast_expr *id2expr);
3583 int isl_id_to_ast_expr_has(
3584 __isl_keep id_to_ast_expr *id2expr,
3585 __isl_keep isl_id *key);
3586 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3587 __isl_keep id_to_ast_expr *id2expr,
3588 __isl_take isl_id *key);
3589 int isl_id_to_ast_expr_foreach(
3590 __isl_keep id_to_ast_expr *id2expr,
3591 int (*fn)(__isl_take isl_id *key,
3592 __isl_take isl_ast_expr *val, void *user),
3595 They can be modified using the following function.
3597 #include <isl/id_to_ast_expr.h>
3598 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3599 __isl_take id_to_ast_expr *id2expr,
3600 __isl_take isl_id *key,
3601 __isl_take isl_ast_expr *val);
3602 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
3603 __isl_take id_to_ast_expr *id2expr,
3604 __isl_take isl_id *key);
3606 Associative arrays can be printed using the following function.
3608 #include <isl/id_to_ast_expr.h>
3609 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3610 __isl_take isl_printer *p,
3611 __isl_keep id_to_ast_expr *id2expr);
3613 =head2 Multiple Values
3615 An C<isl_multi_val> object represents a sequence of zero or more values,
3616 living in a set space.
3618 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3619 using the following function
3621 #include <isl/val.h>
3622 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3623 __isl_take isl_space *space,
3624 __isl_take isl_val_list *list);
3626 The zero multiple value (with value zero for each set dimension)
3627 can be created using the following function.
3629 #include <isl/val.h>
3630 __isl_give isl_multi_val *isl_multi_val_zero(
3631 __isl_take isl_space *space);
3633 Multiple values can be copied and freed using
3635 #include <isl/val.h>
3636 __isl_give isl_multi_val *isl_multi_val_copy(
3637 __isl_keep isl_multi_val *mv);
3638 __isl_null isl_multi_val *isl_multi_val_free(
3639 __isl_take isl_multi_val *mv);
3641 They can be inspected using
3643 #include <isl/val.h>
3644 isl_ctx *isl_multi_val_get_ctx(
3645 __isl_keep isl_multi_val *mv);
3646 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3647 enum isl_dim_type type);
3648 __isl_give isl_val *isl_multi_val_get_val(
3649 __isl_keep isl_multi_val *mv, int pos);
3650 int isl_multi_val_find_dim_by_id(
3651 __isl_keep isl_multi_val *mv,
3652 enum isl_dim_type type, __isl_keep isl_id *id);
3653 __isl_give isl_id *isl_multi_val_get_dim_id(
3654 __isl_keep isl_multi_val *mv,
3655 enum isl_dim_type type, unsigned pos);
3656 const char *isl_multi_val_get_tuple_name(
3657 __isl_keep isl_multi_val *mv,
3658 enum isl_dim_type type);
3659 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3660 enum isl_dim_type type);
3661 __isl_give isl_id *isl_multi_val_get_tuple_id(
3662 __isl_keep isl_multi_val *mv,
3663 enum isl_dim_type type);
3664 int isl_multi_val_range_is_wrapping(
3665 __isl_keep isl_multi_val *mv);
3667 They can be modified using
3669 #include <isl/val.h>
3670 __isl_give isl_multi_val *isl_multi_val_set_val(
3671 __isl_take isl_multi_val *mv, int pos,
3672 __isl_take isl_val *val);
3673 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3674 __isl_take isl_multi_val *mv,
3675 enum isl_dim_type type, unsigned pos, const char *s);
3676 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3677 __isl_take isl_multi_val *mv,
3678 enum isl_dim_type type, unsigned pos,
3679 __isl_take isl_id *id);
3680 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3681 __isl_take isl_multi_val *mv,
3682 enum isl_dim_type type, const char *s);
3683 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3684 __isl_take isl_multi_val *mv,
3685 enum isl_dim_type type, __isl_take isl_id *id);
3686 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3687 __isl_take isl_multi_val *mv,
3688 enum isl_dim_type type);
3689 __isl_give isl_multi_val *isl_multi_val_reset_user(
3690 __isl_take isl_multi_val *mv);
3692 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3693 __isl_take isl_multi_val *mv,
3694 enum isl_dim_type type, unsigned first, unsigned n);
3695 __isl_give isl_multi_val *isl_multi_val_add_dims(
3696 __isl_take isl_multi_val *mv,
3697 enum isl_dim_type type, unsigned n);
3698 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3699 __isl_take isl_multi_val *mv,
3700 enum isl_dim_type type, unsigned first, unsigned n);
3704 #include <isl/val.h>
3705 __isl_give isl_multi_val *isl_multi_val_align_params(
3706 __isl_take isl_multi_val *mv,
3707 __isl_take isl_space *model);
3708 __isl_give isl_multi_val *isl_multi_val_from_range(
3709 __isl_take isl_multi_val *mv);
3710 __isl_give isl_multi_val *isl_multi_val_range_splice(
3711 __isl_take isl_multi_val *mv1, unsigned pos,
3712 __isl_take isl_multi_val *mv2);
3713 __isl_give isl_multi_val *isl_multi_val_range_product(
3714 __isl_take isl_multi_val *mv1,
3715 __isl_take isl_multi_val *mv2);
3716 __isl_give isl_multi_val *
3717 isl_multi_val_range_factor_domain(
3718 __isl_take isl_multi_val *mv);
3719 __isl_give isl_multi_val *
3720 isl_multi_val_range_factor_range(
3721 __isl_take isl_multi_val *mv);
3722 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3723 __isl_take isl_multi_val *mv1,
3724 __isl_take isl_multi_aff *mv2);
3725 __isl_give isl_multi_val *isl_multi_val_product(
3726 __isl_take isl_multi_val *mv1,
3727 __isl_take isl_multi_val *mv2);
3728 __isl_give isl_multi_val *isl_multi_val_add_val(
3729 __isl_take isl_multi_val *mv,
3730 __isl_take isl_val *v);
3731 __isl_give isl_multi_val *isl_multi_val_mod_val(
3732 __isl_take isl_multi_val *mv,
3733 __isl_take isl_val *v);
3734 __isl_give isl_multi_val *isl_multi_val_scale_val(
3735 __isl_take isl_multi_val *mv,
3736 __isl_take isl_val *v);
3737 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3738 __isl_take isl_multi_val *mv1,
3739 __isl_take isl_multi_val *mv2);
3740 __isl_give isl_multi_val *
3741 isl_multi_val_scale_down_multi_val(
3742 __isl_take isl_multi_val *mv1,
3743 __isl_take isl_multi_val *mv2);
3745 A multiple value can be printed using
3747 __isl_give isl_printer *isl_printer_print_multi_val(
3748 __isl_take isl_printer *p,
3749 __isl_keep isl_multi_val *mv);
3753 Vectors can be created, copied and freed using the following functions.
3755 #include <isl/vec.h>
3756 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3758 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3759 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
3761 Note that the elements of a newly created vector may have arbitrary values.
3762 The elements can be changed and inspected using the following functions.
3764 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3765 int isl_vec_size(__isl_keep isl_vec *vec);
3766 __isl_give isl_val *isl_vec_get_element_val(
3767 __isl_keep isl_vec *vec, int pos);
3768 __isl_give isl_vec *isl_vec_set_element_si(
3769 __isl_take isl_vec *vec, int pos, int v);
3770 __isl_give isl_vec *isl_vec_set_element_val(
3771 __isl_take isl_vec *vec, int pos,
3772 __isl_take isl_val *v);
3773 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3775 __isl_give isl_vec *isl_vec_set_val(
3776 __isl_take isl_vec *vec, __isl_take isl_val *v);
3777 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3778 __isl_keep isl_vec *vec2, int pos);
3780 C<isl_vec_get_element> will return a negative value if anything went wrong.
3781 In that case, the value of C<*v> is undefined.
3783 The following function can be used to concatenate two vectors.
3785 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3786 __isl_take isl_vec *vec2);
3790 Matrices can be created, copied and freed using the following functions.
3792 #include <isl/mat.h>
3793 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3794 unsigned n_row, unsigned n_col);
3795 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3796 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
3798 Note that the elements of a newly created matrix may have arbitrary values.
3799 The elements can be changed and inspected using the following functions.
3801 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3802 int isl_mat_rows(__isl_keep isl_mat *mat);
3803 int isl_mat_cols(__isl_keep isl_mat *mat);
3804 __isl_give isl_val *isl_mat_get_element_val(
3805 __isl_keep isl_mat *mat, int row, int col);
3806 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3807 int row, int col, int v);
3808 __isl_give isl_mat *isl_mat_set_element_val(
3809 __isl_take isl_mat *mat, int row, int col,
3810 __isl_take isl_val *v);
3812 C<isl_mat_get_element> will return a negative value if anything went wrong.
3813 In that case, the value of C<*v> is undefined.
3815 The following function can be used to compute the (right) inverse
3816 of a matrix, i.e., a matrix such that the product of the original
3817 and the inverse (in that order) is a multiple of the identity matrix.
3818 The input matrix is assumed to be of full row-rank.
3820 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3822 The following function can be used to compute the (right) kernel
3823 (or null space) of a matrix, i.e., a matrix such that the product of
3824 the original and the kernel (in that order) is the zero matrix.
3826 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3828 =head2 Piecewise Quasi Affine Expressions
3830 The zero quasi affine expression or the quasi affine expression
3831 that is equal to a given value or
3832 a specified dimension on a given domain can be created using
3834 __isl_give isl_aff *isl_aff_zero_on_domain(
3835 __isl_take isl_local_space *ls);
3836 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3837 __isl_take isl_local_space *ls);
3838 __isl_give isl_aff *isl_aff_val_on_domain(
3839 __isl_take isl_local_space *ls,
3840 __isl_take isl_val *val);
3841 __isl_give isl_aff *isl_aff_var_on_domain(
3842 __isl_take isl_local_space *ls,
3843 enum isl_dim_type type, unsigned pos);
3844 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3845 __isl_take isl_local_space *ls,
3846 enum isl_dim_type type, unsigned pos);
3847 __isl_give isl_aff *isl_aff_nan_on_domain(
3848 __isl_take isl_local_space *ls);
3849 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3850 __isl_take isl_local_space *ls);
3852 Note that the space in which the resulting objects live is a map space
3853 with the given space as domain and a one-dimensional range.
3855 An empty piecewise quasi affine expression (one with no cells)
3856 or a piecewise quasi affine expression with a single cell can
3857 be created using the following functions.
3859 #include <isl/aff.h>
3860 __isl_give isl_pw_aff *isl_pw_aff_empty(
3861 __isl_take isl_space *space);
3862 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3863 __isl_take isl_set *set, __isl_take isl_aff *aff);
3864 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3865 __isl_take isl_aff *aff);
3867 A piecewise quasi affine expression that is equal to 1 on a set
3868 and 0 outside the set can be created using the following function.
3870 #include <isl/aff.h>
3871 __isl_give isl_pw_aff *isl_set_indicator_function(
3872 __isl_take isl_set *set);
3874 Quasi affine expressions can be copied and freed using
3876 #include <isl/aff.h>
3877 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3878 __isl_null isl_aff *isl_aff_free(__isl_take isl_aff *aff);
3880 __isl_give isl_pw_aff *isl_pw_aff_copy(
3881 __isl_keep isl_pw_aff *pwaff);
3882 __isl_null isl_pw_aff *isl_pw_aff_free(
3883 __isl_take isl_pw_aff *pwaff);
3885 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3886 using the following function. The constraint is required to have
3887 a non-zero coefficient for the specified dimension.
3889 #include <isl/constraint.h>
3890 __isl_give isl_aff *isl_constraint_get_bound(
3891 __isl_keep isl_constraint *constraint,
3892 enum isl_dim_type type, int pos);
3894 The entire affine expression of the constraint can also be extracted
3895 using the following function.
3897 #include <isl/constraint.h>
3898 __isl_give isl_aff *isl_constraint_get_aff(
3899 __isl_keep isl_constraint *constraint);
3901 Conversely, an equality constraint equating
3902 the affine expression to zero or an inequality constraint enforcing
3903 the affine expression to be non-negative, can be constructed using
3905 __isl_give isl_constraint *isl_equality_from_aff(
3906 __isl_take isl_aff *aff);
3907 __isl_give isl_constraint *isl_inequality_from_aff(
3908 __isl_take isl_aff *aff);
3910 The expression can be inspected using
3912 #include <isl/aff.h>
3913 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3914 int isl_aff_dim(__isl_keep isl_aff *aff,
3915 enum isl_dim_type type);
3916 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3917 __isl_keep isl_aff *aff);
3918 __isl_give isl_local_space *isl_aff_get_local_space(
3919 __isl_keep isl_aff *aff);
3920 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3921 enum isl_dim_type type, unsigned pos);
3922 const char *isl_pw_aff_get_dim_name(
3923 __isl_keep isl_pw_aff *pa,
3924 enum isl_dim_type type, unsigned pos);
3925 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3926 enum isl_dim_type type, unsigned pos);
3927 __isl_give isl_id *isl_pw_aff_get_dim_id(
3928 __isl_keep isl_pw_aff *pa,
3929 enum isl_dim_type type, unsigned pos);
3930 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
3931 enum isl_dim_type type);
3932 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3933 __isl_keep isl_pw_aff *pa,
3934 enum isl_dim_type type);
3935 __isl_give isl_val *isl_aff_get_constant_val(
3936 __isl_keep isl_aff *aff);
3937 __isl_give isl_val *isl_aff_get_coefficient_val(
3938 __isl_keep isl_aff *aff,
3939 enum isl_dim_type type, int pos);
3940 __isl_give isl_val *isl_aff_get_denominator_val(
3941 __isl_keep isl_aff *aff);
3942 __isl_give isl_aff *isl_aff_get_div(
3943 __isl_keep isl_aff *aff, int pos);
3945 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3946 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3947 int (*fn)(__isl_take isl_set *set,
3948 __isl_take isl_aff *aff,
3949 void *user), void *user);
3951 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3952 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3954 int isl_aff_is_nan(__isl_keep isl_aff *aff);
3955 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
3957 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3958 enum isl_dim_type type, unsigned first, unsigned n);
3959 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3960 enum isl_dim_type type, unsigned first, unsigned n);
3962 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3963 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3964 enum isl_dim_type type);
3965 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3967 It can be modified using
3969 #include <isl/aff.h>
3970 __isl_give isl_aff *isl_aff_set_tuple_id(
3971 __isl_take isl_aff *aff,
3972 enum isl_dim_type type, __isl_take isl_id *id);
3973 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3974 __isl_take isl_pw_aff *pwaff,
3975 enum isl_dim_type type, __isl_take isl_id *id);
3976 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
3977 __isl_take isl_pw_aff *pa,
3978 enum isl_dim_type type);
3979 __isl_give isl_aff *isl_aff_set_dim_name(
3980 __isl_take isl_aff *aff, enum isl_dim_type type,
3981 unsigned pos, const char *s);
3982 __isl_give isl_aff *isl_aff_set_dim_id(
3983 __isl_take isl_aff *aff, enum isl_dim_type type,
3984 unsigned pos, __isl_take isl_id *id);
3985 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3986 __isl_take isl_pw_aff *pma,
3987 enum isl_dim_type type, unsigned pos,
3988 __isl_take isl_id *id);
3989 __isl_give isl_aff *isl_aff_set_constant_si(
3990 __isl_take isl_aff *aff, int v);
3991 __isl_give isl_aff *isl_aff_set_constant_val(
3992 __isl_take isl_aff *aff, __isl_take isl_val *v);
3993 __isl_give isl_aff *isl_aff_set_coefficient_si(
3994 __isl_take isl_aff *aff,
3995 enum isl_dim_type type, int pos, int v);
3996 __isl_give isl_aff *isl_aff_set_coefficient_val(
3997 __isl_take isl_aff *aff,
3998 enum isl_dim_type type, int pos,
3999 __isl_take isl_val *v);
4001 __isl_give isl_aff *isl_aff_add_constant_si(
4002 __isl_take isl_aff *aff, int v);
4003 __isl_give isl_aff *isl_aff_add_constant_val(
4004 __isl_take isl_aff *aff, __isl_take isl_val *v);
4005 __isl_give isl_aff *isl_aff_add_constant_num_si(
4006 __isl_take isl_aff *aff, int v);
4007 __isl_give isl_aff *isl_aff_add_coefficient_si(
4008 __isl_take isl_aff *aff,
4009 enum isl_dim_type type, int pos, int v);
4010 __isl_give isl_aff *isl_aff_add_coefficient_val(
4011 __isl_take isl_aff *aff,
4012 enum isl_dim_type type, int pos,
4013 __isl_take isl_val *v);
4015 __isl_give isl_aff *isl_aff_insert_dims(
4016 __isl_take isl_aff *aff,
4017 enum isl_dim_type type, unsigned first, unsigned n);
4018 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
4019 __isl_take isl_pw_aff *pwaff,
4020 enum isl_dim_type type, unsigned first, unsigned n);
4021 __isl_give isl_aff *isl_aff_add_dims(
4022 __isl_take isl_aff *aff,
4023 enum isl_dim_type type, unsigned n);
4024 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
4025 __isl_take isl_pw_aff *pwaff,
4026 enum isl_dim_type type, unsigned n);
4027 __isl_give isl_aff *isl_aff_drop_dims(
4028 __isl_take isl_aff *aff,
4029 enum isl_dim_type type, unsigned first, unsigned n);
4030 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
4031 __isl_take isl_pw_aff *pwaff,
4032 enum isl_dim_type type, unsigned first, unsigned n);
4033 __isl_give isl_aff *isl_aff_move_dims(
4034 __isl_take isl_aff *aff,
4035 enum isl_dim_type dst_type, unsigned dst_pos,
4036 enum isl_dim_type src_type, unsigned src_pos,
4038 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
4039 __isl_take isl_pw_aff *pa,
4040 enum isl_dim_type dst_type, unsigned dst_pos,
4041 enum isl_dim_type src_type, unsigned src_pos,
4044 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
4045 set the I<numerator> of the constant or coefficient, while
4046 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
4047 the constant or coefficient as a whole.
4048 The C<add_constant> and C<add_coefficient> functions add an integer
4049 or rational value to
4050 the possibly rational constant or coefficient.
4051 The C<add_constant_num> functions add an integer value to
4054 To check whether an affine expressions is obviously zero
4055 or (obviously) equal to some other affine expression, use
4057 #include <isl/aff.h>
4058 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
4059 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
4060 __isl_keep isl_aff *aff2);
4061 int isl_pw_aff_plain_is_equal(
4062 __isl_keep isl_pw_aff *pwaff1,
4063 __isl_keep isl_pw_aff *pwaff2);
4064 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
4065 __isl_keep isl_pw_aff *pa2);
4066 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4067 __isl_keep isl_pw_aff *pa2);
4069 The function C<isl_pw_aff_plain_cmp> can be used to sort
4070 C<isl_pw_aff>s. The order is not strictly defined.
4071 The current order sorts expressions that only involve
4072 earlier dimensions before those that involve later dimensions.
4076 #include <isl/aff.h>
4077 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
4078 __isl_take isl_aff *aff2);
4079 __isl_give isl_pw_aff *isl_pw_aff_add(
4080 __isl_take isl_pw_aff *pwaff1,
4081 __isl_take isl_pw_aff *pwaff2);
4082 __isl_give isl_pw_aff *isl_pw_aff_min(
4083 __isl_take isl_pw_aff *pwaff1,
4084 __isl_take isl_pw_aff *pwaff2);
4085 __isl_give isl_pw_aff *isl_pw_aff_max(
4086 __isl_take isl_pw_aff *pwaff1,
4087 __isl_take isl_pw_aff *pwaff2);
4088 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
4089 __isl_take isl_aff *aff2);
4090 __isl_give isl_pw_aff *isl_pw_aff_sub(
4091 __isl_take isl_pw_aff *pwaff1,
4092 __isl_take isl_pw_aff *pwaff2);
4093 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
4094 __isl_give isl_pw_aff *isl_pw_aff_neg(
4095 __isl_take isl_pw_aff *pwaff);
4096 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
4097 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4098 __isl_take isl_pw_aff *pwaff);
4099 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
4100 __isl_give isl_pw_aff *isl_pw_aff_floor(
4101 __isl_take isl_pw_aff *pwaff);
4102 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
4103 __isl_take isl_val *mod);
4104 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
4105 __isl_take isl_pw_aff *pa,
4106 __isl_take isl_val *mod);
4107 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
4108 __isl_take isl_val *v);
4109 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
4110 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
4111 __isl_give isl_aff *isl_aff_scale_down_ui(
4112 __isl_take isl_aff *aff, unsigned f);
4113 __isl_give isl_aff *isl_aff_scale_down_val(
4114 __isl_take isl_aff *aff, __isl_take isl_val *v);
4115 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
4116 __isl_take isl_pw_aff *pa,
4117 __isl_take isl_val *f);
4119 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4120 __isl_take isl_pw_aff_list *list);
4121 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4122 __isl_take isl_pw_aff_list *list);
4124 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4125 __isl_take isl_pw_aff *pwqp);
4127 __isl_give isl_aff *isl_aff_align_params(
4128 __isl_take isl_aff *aff,
4129 __isl_take isl_space *model);
4130 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4131 __isl_take isl_pw_aff *pwaff,
4132 __isl_take isl_space *model);
4134 __isl_give isl_aff *isl_aff_project_domain_on_params(
4135 __isl_take isl_aff *aff);
4136 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4137 __isl_take isl_pw_aff *pwa);
4139 __isl_give isl_aff *isl_aff_gist_params(
4140 __isl_take isl_aff *aff,
4141 __isl_take isl_set *context);
4142 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
4143 __isl_take isl_set *context);
4144 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
4145 __isl_take isl_pw_aff *pwaff,
4146 __isl_take isl_set *context);
4147 __isl_give isl_pw_aff *isl_pw_aff_gist(
4148 __isl_take isl_pw_aff *pwaff,
4149 __isl_take isl_set *context);
4151 __isl_give isl_set *isl_pw_aff_domain(
4152 __isl_take isl_pw_aff *pwaff);
4153 __isl_give isl_set *isl_pw_aff_params(
4154 __isl_take isl_pw_aff *pwa);
4155 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4156 __isl_take isl_pw_aff *pa,
4157 __isl_take isl_set *set);
4158 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4159 __isl_take isl_pw_aff *pa,
4160 __isl_take isl_set *set);
4162 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
4163 __isl_take isl_aff *aff2);
4164 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
4165 __isl_take isl_aff *aff2);
4166 __isl_give isl_pw_aff *isl_pw_aff_mul(
4167 __isl_take isl_pw_aff *pwaff1,
4168 __isl_take isl_pw_aff *pwaff2);
4169 __isl_give isl_pw_aff *isl_pw_aff_div(
4170 __isl_take isl_pw_aff *pa1,
4171 __isl_take isl_pw_aff *pa2);
4172 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
4173 __isl_take isl_pw_aff *pa1,
4174 __isl_take isl_pw_aff *pa2);
4175 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
4176 __isl_take isl_pw_aff *pa1,
4177 __isl_take isl_pw_aff *pa2);
4179 When multiplying two affine expressions, at least one of the two needs
4180 to be a constant. Similarly, when dividing an affine expression by another,
4181 the second expression needs to be a constant.
4182 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
4183 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
4186 #include <isl/aff.h>
4187 __isl_give isl_aff *isl_aff_pullback_aff(
4188 __isl_take isl_aff *aff1,
4189 __isl_take isl_aff *aff2);
4190 __isl_give isl_aff *isl_aff_pullback_multi_aff(
4191 __isl_take isl_aff *aff,
4192 __isl_take isl_multi_aff *ma);
4193 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
4194 __isl_take isl_pw_aff *pa,
4195 __isl_take isl_multi_aff *ma);
4196 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
4197 __isl_take isl_pw_aff *pa,
4198 __isl_take isl_pw_multi_aff *pma);
4199 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
4200 __isl_take isl_pw_aff *pa,
4201 __isl_take isl_multi_pw_aff *mpa);
4203 These functions precompose the input expression by the given
4204 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
4205 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
4206 into the (piecewise) affine expression.
4207 Objects of type C<isl_multi_aff> are described in
4208 L</"Piecewise Multiple Quasi Affine Expressions">.
4210 #include <isl/aff.h>
4211 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4212 __isl_take isl_aff *aff);
4213 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4214 __isl_take isl_aff *aff);
4215 __isl_give isl_basic_set *isl_aff_le_basic_set(
4216 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4217 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4218 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4219 __isl_give isl_set *isl_pw_aff_eq_set(
4220 __isl_take isl_pw_aff *pwaff1,
4221 __isl_take isl_pw_aff *pwaff2);
4222 __isl_give isl_set *isl_pw_aff_ne_set(
4223 __isl_take isl_pw_aff *pwaff1,
4224 __isl_take isl_pw_aff *pwaff2);
4225 __isl_give isl_set *isl_pw_aff_le_set(
4226 __isl_take isl_pw_aff *pwaff1,
4227 __isl_take isl_pw_aff *pwaff2);
4228 __isl_give isl_set *isl_pw_aff_lt_set(
4229 __isl_take isl_pw_aff *pwaff1,
4230 __isl_take isl_pw_aff *pwaff2);
4231 __isl_give isl_set *isl_pw_aff_ge_set(
4232 __isl_take isl_pw_aff *pwaff1,
4233 __isl_take isl_pw_aff *pwaff2);
4234 __isl_give isl_set *isl_pw_aff_gt_set(
4235 __isl_take isl_pw_aff *pwaff1,
4236 __isl_take isl_pw_aff *pwaff2);
4238 __isl_give isl_set *isl_pw_aff_list_eq_set(
4239 __isl_take isl_pw_aff_list *list1,
4240 __isl_take isl_pw_aff_list *list2);
4241 __isl_give isl_set *isl_pw_aff_list_ne_set(
4242 __isl_take isl_pw_aff_list *list1,
4243 __isl_take isl_pw_aff_list *list2);
4244 __isl_give isl_set *isl_pw_aff_list_le_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_lt_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_ge_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_gt_set(
4254 __isl_take isl_pw_aff_list *list1,
4255 __isl_take isl_pw_aff_list *list2);
4257 The function C<isl_aff_neg_basic_set> returns a basic set
4258 containing those elements in the domain space
4259 of C<aff> where C<aff> is negative.
4260 The function C<isl_aff_ge_basic_set> returns a basic set
4261 containing those elements in the shared space
4262 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4263 The function C<isl_pw_aff_ge_set> returns a set
4264 containing those elements in the shared domain
4265 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4266 The functions operating on C<isl_pw_aff_list> apply the corresponding
4267 C<isl_pw_aff> function to each pair of elements in the two lists.
4269 #include <isl/aff.h>
4270 __isl_give isl_set *isl_pw_aff_nonneg_set(
4271 __isl_take isl_pw_aff *pwaff);
4272 __isl_give isl_set *isl_pw_aff_zero_set(
4273 __isl_take isl_pw_aff *pwaff);
4274 __isl_give isl_set *isl_pw_aff_non_zero_set(
4275 __isl_take isl_pw_aff *pwaff);
4277 The function C<isl_pw_aff_nonneg_set> returns a set
4278 containing those elements in the domain
4279 of C<pwaff> where C<pwaff> is non-negative.
4281 #include <isl/aff.h>
4282 __isl_give isl_pw_aff *isl_pw_aff_cond(
4283 __isl_take isl_pw_aff *cond,
4284 __isl_take isl_pw_aff *pwaff_true,
4285 __isl_take isl_pw_aff *pwaff_false);
4287 The function C<isl_pw_aff_cond> performs a conditional operator
4288 and returns an expression that is equal to C<pwaff_true>
4289 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4290 where C<cond> is zero.
4292 #include <isl/aff.h>
4293 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4294 __isl_take isl_pw_aff *pwaff1,
4295 __isl_take isl_pw_aff *pwaff2);
4296 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4297 __isl_take isl_pw_aff *pwaff1,
4298 __isl_take isl_pw_aff *pwaff2);
4299 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4300 __isl_take isl_pw_aff *pwaff1,
4301 __isl_take isl_pw_aff *pwaff2);
4303 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4304 expression with a domain that is the union of those of C<pwaff1> and
4305 C<pwaff2> and such that on each cell, the quasi-affine expression is
4306 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4307 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4308 associated expression is the defined one.
4310 An expression can be read from input using
4312 #include <isl/aff.h>
4313 __isl_give isl_aff *isl_aff_read_from_str(
4314 isl_ctx *ctx, const char *str);
4315 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4316 isl_ctx *ctx, const char *str);
4318 An expression can be printed using
4320 #include <isl/aff.h>
4321 __isl_give isl_printer *isl_printer_print_aff(
4322 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4324 __isl_give isl_printer *isl_printer_print_pw_aff(
4325 __isl_take isl_printer *p,
4326 __isl_keep isl_pw_aff *pwaff);
4328 =head2 Piecewise Multiple Quasi Affine Expressions
4330 An C<isl_multi_aff> object represents a sequence of
4331 zero or more affine expressions, all defined on the same domain space.
4332 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4333 zero or more piecewise affine expressions.
4335 An C<isl_multi_aff> can be constructed from a single
4336 C<isl_aff> or an C<isl_aff_list> using the
4337 following functions. Similarly for C<isl_multi_pw_aff>
4338 and C<isl_pw_multi_aff>.
4340 #include <isl/aff.h>
4341 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4342 __isl_take isl_aff *aff);
4343 __isl_give isl_multi_pw_aff *
4344 isl_multi_pw_aff_from_multi_aff(
4345 __isl_take isl_multi_aff *ma);
4346 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4347 __isl_take isl_pw_aff *pa);
4348 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4349 __isl_take isl_pw_aff *pa);
4350 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4351 __isl_take isl_space *space,
4352 __isl_take isl_aff_list *list);
4354 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4355 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4356 Note however that the domain
4357 of the result is the intersection of the domains of the input.
4358 The reverse conversion is exact.
4360 #include <isl/aff.h>
4361 __isl_give isl_pw_multi_aff *
4362 isl_pw_multi_aff_from_multi_pw_aff(
4363 __isl_take isl_multi_pw_aff *mpa);
4364 __isl_give isl_multi_pw_aff *
4365 isl_multi_pw_aff_from_pw_multi_aff(
4366 __isl_take isl_pw_multi_aff *pma);
4368 An empty piecewise multiple quasi affine expression (one with no cells),
4369 the zero piecewise multiple quasi affine expression (with value zero
4370 for each output dimension),
4371 a piecewise multiple quasi affine expression with a single cell (with
4372 either a universe or a specified domain) or
4373 a zero-dimensional piecewise multiple quasi affine expression
4375 can be created using the following functions.
4377 #include <isl/aff.h>
4378 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4379 __isl_take isl_space *space);
4380 __isl_give isl_multi_aff *isl_multi_aff_zero(
4381 __isl_take isl_space *space);
4382 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4383 __isl_take isl_space *space);
4384 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4385 __isl_take isl_space *space);
4386 __isl_give isl_multi_aff *isl_multi_aff_identity(
4387 __isl_take isl_space *space);
4388 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4389 __isl_take isl_space *space);
4390 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4391 __isl_take isl_space *space);
4392 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4393 __isl_take isl_space *space);
4394 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4395 __isl_take isl_space *space);
4396 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4397 __isl_take isl_space *space,
4398 enum isl_dim_type type,
4399 unsigned first, unsigned n);
4400 __isl_give isl_pw_multi_aff *
4401 isl_pw_multi_aff_project_out_map(
4402 __isl_take isl_space *space,
4403 enum isl_dim_type type,
4404 unsigned first, unsigned n);
4405 __isl_give isl_pw_multi_aff *
4406 isl_pw_multi_aff_from_multi_aff(
4407 __isl_take isl_multi_aff *ma);
4408 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4409 __isl_take isl_set *set,
4410 __isl_take isl_multi_aff *maff);
4411 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4412 __isl_take isl_set *set);
4414 __isl_give isl_union_pw_multi_aff *
4415 isl_union_pw_multi_aff_empty(
4416 __isl_take isl_space *space);
4417 __isl_give isl_union_pw_multi_aff *
4418 isl_union_pw_multi_aff_add_pw_multi_aff(
4419 __isl_take isl_union_pw_multi_aff *upma,
4420 __isl_take isl_pw_multi_aff *pma);
4421 __isl_give isl_union_pw_multi_aff *
4422 isl_union_pw_multi_aff_from_domain(
4423 __isl_take isl_union_set *uset);
4425 A piecewise multiple quasi affine expression can also be initialized
4426 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4427 and the C<isl_map> is single-valued.
4428 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4429 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4431 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4432 __isl_take isl_set *set);
4433 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4434 __isl_take isl_map *map);
4436 __isl_give isl_union_pw_multi_aff *
4437 isl_union_pw_multi_aff_from_union_set(
4438 __isl_take isl_union_set *uset);
4439 __isl_give isl_union_pw_multi_aff *
4440 isl_union_pw_multi_aff_from_union_map(
4441 __isl_take isl_union_map *umap);
4443 Multiple quasi affine expressions can be copied and freed using
4445 #include <isl/aff.h>
4446 __isl_give isl_multi_aff *isl_multi_aff_copy(
4447 __isl_keep isl_multi_aff *maff);
4448 __isl_null isl_multi_aff *isl_multi_aff_free(
4449 __isl_take isl_multi_aff *maff);
4451 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4452 __isl_keep isl_pw_multi_aff *pma);
4453 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
4454 __isl_take isl_pw_multi_aff *pma);
4456 __isl_give isl_union_pw_multi_aff *
4457 isl_union_pw_multi_aff_copy(
4458 __isl_keep isl_union_pw_multi_aff *upma);
4459 __isl_null isl_union_pw_multi_aff *
4460 isl_union_pw_multi_aff_free(
4461 __isl_take isl_union_pw_multi_aff *upma);
4463 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4464 __isl_keep isl_multi_pw_aff *mpa);
4465 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
4466 __isl_take isl_multi_pw_aff *mpa);
4468 The expression can be inspected using
4470 #include <isl/aff.h>
4471 isl_ctx *isl_multi_aff_get_ctx(
4472 __isl_keep isl_multi_aff *maff);
4473 isl_ctx *isl_pw_multi_aff_get_ctx(
4474 __isl_keep isl_pw_multi_aff *pma);
4475 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4476 __isl_keep isl_union_pw_multi_aff *upma);
4477 isl_ctx *isl_multi_pw_aff_get_ctx(
4478 __isl_keep isl_multi_pw_aff *mpa);
4480 int isl_multi_aff_involves_dims(
4481 __isl_keep isl_multi_aff *ma,
4482 enum isl_dim_type type, unsigned first, unsigned n);
4483 int isl_multi_pw_aff_involves_dims(
4484 __isl_keep isl_multi_pw_aff *mpa,
4485 enum isl_dim_type type, unsigned first, unsigned n);
4487 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4488 enum isl_dim_type type);
4489 unsigned isl_pw_multi_aff_dim(
4490 __isl_keep isl_pw_multi_aff *pma,
4491 enum isl_dim_type type);
4492 unsigned isl_multi_pw_aff_dim(
4493 __isl_keep isl_multi_pw_aff *mpa,
4494 enum isl_dim_type type);
4495 __isl_give isl_aff *isl_multi_aff_get_aff(
4496 __isl_keep isl_multi_aff *multi, int pos);
4497 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4498 __isl_keep isl_pw_multi_aff *pma, int pos);
4499 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4500 __isl_keep isl_multi_pw_aff *mpa, int pos);
4501 int isl_multi_aff_find_dim_by_id(
4502 __isl_keep isl_multi_aff *ma,
4503 enum isl_dim_type type, __isl_keep isl_id *id);
4504 int isl_multi_pw_aff_find_dim_by_id(
4505 __isl_keep isl_multi_pw_aff *mpa,
4506 enum isl_dim_type type, __isl_keep isl_id *id);
4507 const char *isl_pw_multi_aff_get_dim_name(
4508 __isl_keep isl_pw_multi_aff *pma,
4509 enum isl_dim_type type, unsigned pos);
4510 __isl_give isl_id *isl_multi_aff_get_dim_id(
4511 __isl_keep isl_multi_aff *ma,
4512 enum isl_dim_type type, unsigned pos);
4513 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4514 __isl_keep isl_pw_multi_aff *pma,
4515 enum isl_dim_type type, unsigned pos);
4516 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4517 __isl_keep isl_multi_pw_aff *mpa,
4518 enum isl_dim_type type, unsigned pos);
4519 const char *isl_multi_aff_get_tuple_name(
4520 __isl_keep isl_multi_aff *multi,
4521 enum isl_dim_type type);
4522 int isl_pw_multi_aff_has_tuple_name(
4523 __isl_keep isl_pw_multi_aff *pma,
4524 enum isl_dim_type type);
4525 const char *isl_pw_multi_aff_get_tuple_name(
4526 __isl_keep isl_pw_multi_aff *pma,
4527 enum isl_dim_type type);
4528 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4529 enum isl_dim_type type);
4530 int isl_pw_multi_aff_has_tuple_id(
4531 __isl_keep isl_pw_multi_aff *pma,
4532 enum isl_dim_type type);
4533 int isl_multi_pw_aff_has_tuple_id(
4534 __isl_keep isl_multi_pw_aff *mpa,
4535 enum isl_dim_type type);
4536 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4537 __isl_keep isl_multi_aff *ma,
4538 enum isl_dim_type type);
4539 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4540 __isl_keep isl_pw_multi_aff *pma,
4541 enum isl_dim_type type);
4542 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4543 __isl_keep isl_multi_pw_aff *mpa,
4544 enum isl_dim_type type);
4545 int isl_multi_aff_range_is_wrapping(
4546 __isl_keep isl_multi_aff *ma);
4547 int isl_multi_pw_aff_range_is_wrapping(
4548 __isl_keep isl_multi_pw_aff *mpa);
4550 int isl_pw_multi_aff_foreach_piece(
4551 __isl_keep isl_pw_multi_aff *pma,
4552 int (*fn)(__isl_take isl_set *set,
4553 __isl_take isl_multi_aff *maff,
4554 void *user), void *user);
4556 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4557 __isl_keep isl_union_pw_multi_aff *upma,
4558 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4559 void *user), void *user);
4561 It can be modified using
4563 #include <isl/aff.h>
4564 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4565 __isl_take isl_multi_aff *multi, int pos,
4566 __isl_take isl_aff *aff);
4567 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4568 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4569 __isl_take isl_pw_aff *pa);
4570 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4571 __isl_take isl_multi_aff *maff,
4572 enum isl_dim_type type, unsigned pos, const char *s);
4573 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4574 __isl_take isl_multi_aff *maff,
4575 enum isl_dim_type type, unsigned pos,
4576 __isl_take isl_id *id);
4577 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4578 __isl_take isl_multi_aff *maff,
4579 enum isl_dim_type type, const char *s);
4580 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4581 __isl_take isl_multi_aff *maff,
4582 enum isl_dim_type type, __isl_take isl_id *id);
4583 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4584 __isl_take isl_pw_multi_aff *pma,
4585 enum isl_dim_type type, __isl_take isl_id *id);
4586 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4587 __isl_take isl_multi_aff *ma,
4588 enum isl_dim_type type);
4589 __isl_give isl_multi_pw_aff *
4590 isl_multi_pw_aff_reset_tuple_id(
4591 __isl_take isl_multi_pw_aff *mpa,
4592 enum isl_dim_type type);
4593 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4594 __isl_take isl_multi_aff *ma);
4595 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4596 __isl_take isl_multi_pw_aff *mpa);
4598 __isl_give isl_multi_pw_aff *
4599 isl_multi_pw_aff_set_dim_name(
4600 __isl_take isl_multi_pw_aff *mpa,
4601 enum isl_dim_type type, unsigned pos, const char *s);
4602 __isl_give isl_multi_pw_aff *
4603 isl_multi_pw_aff_set_dim_id(
4604 __isl_take isl_multi_pw_aff *mpa,
4605 enum isl_dim_type type, unsigned pos,
4606 __isl_take isl_id *id);
4607 __isl_give isl_multi_pw_aff *
4608 isl_multi_pw_aff_set_tuple_name(
4609 __isl_take isl_multi_pw_aff *mpa,
4610 enum isl_dim_type type, const char *s);
4612 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4613 __isl_take isl_multi_aff *ma);
4615 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4616 __isl_take isl_multi_aff *ma,
4617 enum isl_dim_type type, unsigned first, unsigned n);
4618 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4619 __isl_take isl_multi_aff *ma,
4620 enum isl_dim_type type, unsigned n);
4621 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4622 __isl_take isl_multi_aff *maff,
4623 enum isl_dim_type type, unsigned first, unsigned n);
4624 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4625 __isl_take isl_pw_multi_aff *pma,
4626 enum isl_dim_type type, unsigned first, unsigned n);
4628 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4629 __isl_take isl_multi_pw_aff *mpa,
4630 enum isl_dim_type type, unsigned first, unsigned n);
4631 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4632 __isl_take isl_multi_pw_aff *mpa,
4633 enum isl_dim_type type, unsigned n);
4634 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4635 __isl_take isl_multi_pw_aff *pma,
4636 enum isl_dim_type dst_type, unsigned dst_pos,
4637 enum isl_dim_type src_type, unsigned src_pos,
4640 To check whether two multiple affine expressions are
4641 (obviously) equal to each other, use
4643 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4644 __isl_keep isl_multi_aff *maff2);
4645 int isl_pw_multi_aff_plain_is_equal(
4646 __isl_keep isl_pw_multi_aff *pma1,
4647 __isl_keep isl_pw_multi_aff *pma2);
4648 int isl_multi_pw_aff_plain_is_equal(
4649 __isl_keep isl_multi_pw_aff *mpa1,
4650 __isl_keep isl_multi_pw_aff *mpa2);
4651 int isl_multi_pw_aff_is_equal(
4652 __isl_keep isl_multi_pw_aff *mpa1,
4653 __isl_keep isl_multi_pw_aff *mpa2);
4657 #include <isl/aff.h>
4658 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4659 __isl_take isl_pw_multi_aff *pma1,
4660 __isl_take isl_pw_multi_aff *pma2);
4661 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4662 __isl_take isl_pw_multi_aff *pma1,
4663 __isl_take isl_pw_multi_aff *pma2);
4664 __isl_give isl_multi_aff *isl_multi_aff_floor(
4665 __isl_take isl_multi_aff *ma);
4666 __isl_give isl_multi_aff *isl_multi_aff_add(
4667 __isl_take isl_multi_aff *maff1,
4668 __isl_take isl_multi_aff *maff2);
4669 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4670 __isl_take isl_pw_multi_aff *pma1,
4671 __isl_take isl_pw_multi_aff *pma2);
4672 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4673 __isl_take isl_union_pw_multi_aff *upma1,
4674 __isl_take isl_union_pw_multi_aff *upma2);
4675 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4676 __isl_take isl_pw_multi_aff *pma1,
4677 __isl_take isl_pw_multi_aff *pma2);
4678 __isl_give isl_multi_aff *isl_multi_aff_sub(
4679 __isl_take isl_multi_aff *ma1,
4680 __isl_take isl_multi_aff *ma2);
4681 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4682 __isl_take isl_pw_multi_aff *pma1,
4683 __isl_take isl_pw_multi_aff *pma2);
4684 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4685 __isl_take isl_union_pw_multi_aff *upma1,
4686 __isl_take isl_union_pw_multi_aff *upma2);
4688 C<isl_multi_aff_sub> subtracts the second argument from the first.
4690 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4691 __isl_take isl_multi_aff *ma,
4692 __isl_take isl_val *v);
4693 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4694 __isl_take isl_pw_multi_aff *pma,
4695 __isl_take isl_val *v);
4696 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4697 __isl_take isl_multi_pw_aff *mpa,
4698 __isl_take isl_val *v);
4699 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4700 __isl_take isl_multi_aff *ma,
4701 __isl_take isl_multi_val *mv);
4702 __isl_give isl_pw_multi_aff *
4703 isl_pw_multi_aff_scale_multi_val(
4704 __isl_take isl_pw_multi_aff *pma,
4705 __isl_take isl_multi_val *mv);
4706 __isl_give isl_multi_pw_aff *
4707 isl_multi_pw_aff_scale_multi_val(
4708 __isl_take isl_multi_pw_aff *mpa,
4709 __isl_take isl_multi_val *mv);
4710 __isl_give isl_union_pw_multi_aff *
4711 isl_union_pw_multi_aff_scale_multi_val(
4712 __isl_take isl_union_pw_multi_aff *upma,
4713 __isl_take isl_multi_val *mv);
4714 __isl_give isl_multi_aff *
4715 isl_multi_aff_scale_down_multi_val(
4716 __isl_take isl_multi_aff *ma,
4717 __isl_take isl_multi_val *mv);
4718 __isl_give isl_multi_pw_aff *
4719 isl_multi_pw_aff_scale_down_multi_val(
4720 __isl_take isl_multi_pw_aff *mpa,
4721 __isl_take isl_multi_val *mv);
4723 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4724 by the corresponding elements of C<mv>.
4726 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4727 __isl_take isl_pw_multi_aff *pma,
4728 enum isl_dim_type type, unsigned pos, int value);
4729 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4730 __isl_take isl_pw_multi_aff *pma,
4731 __isl_take isl_set *set);
4732 __isl_give isl_set *isl_multi_pw_aff_domain(
4733 __isl_take isl_multi_pw_aff *mpa);
4734 __isl_give isl_multi_pw_aff *
4735 isl_multi_pw_aff_intersect_params(
4736 __isl_take isl_multi_pw_aff *mpa,
4737 __isl_take isl_set *set);
4738 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4739 __isl_take isl_pw_multi_aff *pma,
4740 __isl_take isl_set *set);
4741 __isl_give isl_multi_pw_aff *
4742 isl_multi_pw_aff_intersect_domain(
4743 __isl_take isl_multi_pw_aff *mpa,
4744 __isl_take isl_set *domain);
4745 __isl_give isl_union_pw_multi_aff *
4746 isl_union_pw_multi_aff_intersect_domain(
4747 __isl_take isl_union_pw_multi_aff *upma,
4748 __isl_take isl_union_set *uset);
4749 __isl_give isl_multi_aff *isl_multi_aff_lift(
4750 __isl_take isl_multi_aff *maff,
4751 __isl_give isl_local_space **ls);
4752 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4753 __isl_take isl_pw_multi_aff *pma);
4754 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4755 __isl_take isl_multi_pw_aff *mpa);
4756 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4757 __isl_take isl_multi_aff *multi,
4758 __isl_take isl_space *model);
4759 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4760 __isl_take isl_pw_multi_aff *pma,
4761 __isl_take isl_space *model);
4762 __isl_give isl_union_pw_multi_aff *
4763 isl_union_pw_multi_aff_align_params(
4764 __isl_take isl_union_pw_multi_aff *upma,
4765 __isl_take isl_space *model);
4766 __isl_give isl_pw_multi_aff *
4767 isl_pw_multi_aff_project_domain_on_params(
4768 __isl_take isl_pw_multi_aff *pma);
4769 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4770 __isl_take isl_multi_aff *maff,
4771 __isl_take isl_set *context);
4772 __isl_give isl_multi_aff *isl_multi_aff_gist(
4773 __isl_take isl_multi_aff *maff,
4774 __isl_take isl_set *context);
4775 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4776 __isl_take isl_pw_multi_aff *pma,
4777 __isl_take isl_set *set);
4778 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4779 __isl_take isl_pw_multi_aff *pma,
4780 __isl_take isl_set *set);
4781 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4782 __isl_take isl_multi_pw_aff *mpa,
4783 __isl_take isl_set *set);
4784 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4785 __isl_take isl_multi_pw_aff *mpa,
4786 __isl_take isl_set *set);
4787 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4788 __isl_take isl_multi_aff *ma);
4789 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4790 __isl_take isl_multi_pw_aff *mpa);
4791 __isl_give isl_set *isl_pw_multi_aff_domain(
4792 __isl_take isl_pw_multi_aff *pma);
4793 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4794 __isl_take isl_union_pw_multi_aff *upma);
4795 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4796 __isl_take isl_multi_aff *ma1, unsigned pos,
4797 __isl_take isl_multi_aff *ma2);
4798 __isl_give isl_multi_aff *isl_multi_aff_splice(
4799 __isl_take isl_multi_aff *ma1,
4800 unsigned in_pos, unsigned out_pos,
4801 __isl_take isl_multi_aff *ma2);
4802 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4803 __isl_take isl_multi_aff *ma1,
4804 __isl_take isl_multi_aff *ma2);
4805 __isl_give isl_multi_aff *
4806 isl_multi_aff_range_factor_domain(
4807 __isl_take isl_multi_aff *ma);
4808 __isl_give isl_multi_aff *
4809 isl_multi_aff_range_factor_range(
4810 __isl_take isl_multi_aff *ma);
4811 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4812 __isl_take isl_multi_aff *ma1,
4813 __isl_take isl_multi_aff *ma2);
4814 __isl_give isl_multi_aff *isl_multi_aff_product(
4815 __isl_take isl_multi_aff *ma1,
4816 __isl_take isl_multi_aff *ma2);
4817 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4818 __isl_take isl_multi_pw_aff *mpa1,
4819 __isl_take isl_multi_pw_aff *mpa2);
4820 __isl_give isl_pw_multi_aff *
4821 isl_pw_multi_aff_range_product(
4822 __isl_take isl_pw_multi_aff *pma1,
4823 __isl_take isl_pw_multi_aff *pma2);
4824 __isl_give isl_multi_pw_aff *
4825 isl_multi_pw_aff_range_factor_domain(
4826 __isl_take isl_multi_pw_aff *mpa);
4827 __isl_give isl_multi_pw_aff *
4828 isl_multi_pw_aff_range_factor_range(
4829 __isl_take isl_multi_pw_aff *mpa);
4830 __isl_give isl_pw_multi_aff *
4831 isl_pw_multi_aff_flat_range_product(
4832 __isl_take isl_pw_multi_aff *pma1,
4833 __isl_take isl_pw_multi_aff *pma2);
4834 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4835 __isl_take isl_pw_multi_aff *pma1,
4836 __isl_take isl_pw_multi_aff *pma2);
4837 __isl_give isl_union_pw_multi_aff *
4838 isl_union_pw_multi_aff_flat_range_product(
4839 __isl_take isl_union_pw_multi_aff *upma1,
4840 __isl_take isl_union_pw_multi_aff *upma2);
4841 __isl_give isl_multi_pw_aff *
4842 isl_multi_pw_aff_range_splice(
4843 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4844 __isl_take isl_multi_pw_aff *mpa2);
4845 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4846 __isl_take isl_multi_pw_aff *mpa1,
4847 unsigned in_pos, unsigned out_pos,
4848 __isl_take isl_multi_pw_aff *mpa2);
4849 __isl_give isl_multi_pw_aff *
4850 isl_multi_pw_aff_range_product(
4851 __isl_take isl_multi_pw_aff *mpa1,
4852 __isl_take isl_multi_pw_aff *mpa2);
4853 __isl_give isl_multi_pw_aff *
4854 isl_multi_pw_aff_flat_range_product(
4855 __isl_take isl_multi_pw_aff *mpa1,
4856 __isl_take isl_multi_pw_aff *mpa2);
4858 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4859 then it is assigned the local space that lies at the basis of
4860 the lifting applied.
4862 #include <isl/aff.h>
4863 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4864 __isl_take isl_multi_aff *ma1,
4865 __isl_take isl_multi_aff *ma2);
4866 __isl_give isl_pw_multi_aff *
4867 isl_pw_multi_aff_pullback_multi_aff(
4868 __isl_take isl_pw_multi_aff *pma,
4869 __isl_take isl_multi_aff *ma);
4870 __isl_give isl_multi_pw_aff *
4871 isl_multi_pw_aff_pullback_multi_aff(
4872 __isl_take isl_multi_pw_aff *mpa,
4873 __isl_take isl_multi_aff *ma);
4874 __isl_give isl_pw_multi_aff *
4875 isl_pw_multi_aff_pullback_pw_multi_aff(
4876 __isl_take isl_pw_multi_aff *pma1,
4877 __isl_take isl_pw_multi_aff *pma2);
4878 __isl_give isl_multi_pw_aff *
4879 isl_multi_pw_aff_pullback_pw_multi_aff(
4880 __isl_take isl_multi_pw_aff *mpa,
4881 __isl_take isl_pw_multi_aff *pma);
4882 __isl_give isl_multi_pw_aff *
4883 isl_multi_pw_aff_pullback_multi_pw_aff(
4884 __isl_take isl_multi_pw_aff *mpa1,
4885 __isl_take isl_multi_pw_aff *mpa2);
4887 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4888 In other words, C<ma2> is plugged
4891 __isl_give isl_set *isl_multi_aff_lex_le_set(
4892 __isl_take isl_multi_aff *ma1,
4893 __isl_take isl_multi_aff *ma2);
4894 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4895 __isl_take isl_multi_aff *ma1,
4896 __isl_take isl_multi_aff *ma2);
4898 The function C<isl_multi_aff_lex_le_set> returns a set
4899 containing those elements in the shared domain space
4900 where C<ma1> is lexicographically smaller than or
4903 An expression can be read from input using
4905 #include <isl/aff.h>
4906 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4907 isl_ctx *ctx, const char *str);
4908 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4909 isl_ctx *ctx, const char *str);
4910 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4911 isl_ctx *ctx, const char *str);
4912 __isl_give isl_union_pw_multi_aff *
4913 isl_union_pw_multi_aff_read_from_str(
4914 isl_ctx *ctx, const char *str);
4916 An expression can be printed using
4918 #include <isl/aff.h>
4919 __isl_give isl_printer *isl_printer_print_multi_aff(
4920 __isl_take isl_printer *p,
4921 __isl_keep isl_multi_aff *maff);
4922 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4923 __isl_take isl_printer *p,
4924 __isl_keep isl_pw_multi_aff *pma);
4925 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4926 __isl_take isl_printer *p,
4927 __isl_keep isl_union_pw_multi_aff *upma);
4928 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4929 __isl_take isl_printer *p,
4930 __isl_keep isl_multi_pw_aff *mpa);
4934 Points are elements of a set. They can be used to construct
4935 simple sets (boxes) or they can be used to represent the
4936 individual elements of a set.
4937 The zero point (the origin) can be created using
4939 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4941 The coordinates of a point can be inspected, set and changed
4944 __isl_give isl_val *isl_point_get_coordinate_val(
4945 __isl_keep isl_point *pnt,
4946 enum isl_dim_type type, int pos);
4947 __isl_give isl_point *isl_point_set_coordinate_val(
4948 __isl_take isl_point *pnt,
4949 enum isl_dim_type type, int pos,
4950 __isl_take isl_val *v);
4952 __isl_give isl_point *isl_point_add_ui(
4953 __isl_take isl_point *pnt,
4954 enum isl_dim_type type, int pos, unsigned val);
4955 __isl_give isl_point *isl_point_sub_ui(
4956 __isl_take isl_point *pnt,
4957 enum isl_dim_type type, int pos, unsigned val);
4959 Other properties can be obtained using
4961 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4963 Points can be copied or freed using
4965 __isl_give isl_point *isl_point_copy(
4966 __isl_keep isl_point *pnt);
4967 void isl_point_free(__isl_take isl_point *pnt);
4969 A singleton set can be created from a point using
4971 __isl_give isl_basic_set *isl_basic_set_from_point(
4972 __isl_take isl_point *pnt);
4973 __isl_give isl_set *isl_set_from_point(
4974 __isl_take isl_point *pnt);
4976 and a box can be created from two opposite extremal points using
4978 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4979 __isl_take isl_point *pnt1,
4980 __isl_take isl_point *pnt2);
4981 __isl_give isl_set *isl_set_box_from_points(
4982 __isl_take isl_point *pnt1,
4983 __isl_take isl_point *pnt2);
4985 All elements of a B<bounded> (union) set can be enumerated using
4986 the following functions.
4988 int isl_set_foreach_point(__isl_keep isl_set *set,
4989 int (*fn)(__isl_take isl_point *pnt, void *user),
4991 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4992 int (*fn)(__isl_take isl_point *pnt, void *user),
4995 The function C<fn> is called for each integer point in
4996 C<set> with as second argument the last argument of
4997 the C<isl_set_foreach_point> call. The function C<fn>
4998 should return C<0> on success and C<-1> on failure.
4999 In the latter case, C<isl_set_foreach_point> will stop
5000 enumerating and return C<-1> as well.
5001 If the enumeration is performed successfully and to completion,
5002 then C<isl_set_foreach_point> returns C<0>.
5004 To obtain a single point of a (basic) set, use
5006 __isl_give isl_point *isl_basic_set_sample_point(
5007 __isl_take isl_basic_set *bset);
5008 __isl_give isl_point *isl_set_sample_point(
5009 __isl_take isl_set *set);
5011 If C<set> does not contain any (integer) points, then the
5012 resulting point will be ``void'', a property that can be
5015 int isl_point_is_void(__isl_keep isl_point *pnt);
5017 =head2 Piecewise Quasipolynomials
5019 A piecewise quasipolynomial is a particular kind of function that maps
5020 a parametric point to a rational value.
5021 More specifically, a quasipolynomial is a polynomial expression in greatest
5022 integer parts of affine expressions of parameters and variables.
5023 A piecewise quasipolynomial is a subdivision of a given parametric
5024 domain into disjoint cells with a quasipolynomial associated to
5025 each cell. The value of the piecewise quasipolynomial at a given
5026 point is the value of the quasipolynomial associated to the cell
5027 that contains the point. Outside of the union of cells,
5028 the value is assumed to be zero.
5029 For example, the piecewise quasipolynomial
5031 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
5033 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
5034 A given piecewise quasipolynomial has a fixed domain dimension.
5035 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
5036 defined over different domains.
5037 Piecewise quasipolynomials are mainly used by the C<barvinok>
5038 library for representing the number of elements in a parametric set or map.
5039 For example, the piecewise quasipolynomial above represents
5040 the number of points in the map
5042 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
5044 =head3 Input and Output
5046 Piecewise quasipolynomials can be read from input using
5048 __isl_give isl_union_pw_qpolynomial *
5049 isl_union_pw_qpolynomial_read_from_str(
5050 isl_ctx *ctx, const char *str);
5052 Quasipolynomials and piecewise quasipolynomials can be printed
5053 using the following functions.
5055 __isl_give isl_printer *isl_printer_print_qpolynomial(
5056 __isl_take isl_printer *p,
5057 __isl_keep isl_qpolynomial *qp);
5059 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
5060 __isl_take isl_printer *p,
5061 __isl_keep isl_pw_qpolynomial *pwqp);
5063 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
5064 __isl_take isl_printer *p,
5065 __isl_keep isl_union_pw_qpolynomial *upwqp);
5067 The output format of the printer
5068 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5069 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
5071 In case of printing in C<ISL_FORMAT_C>, the user may want
5072 to set the names of all dimensions
5074 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
5075 __isl_take isl_qpolynomial *qp,
5076 enum isl_dim_type type, unsigned pos,
5078 __isl_give isl_pw_qpolynomial *
5079 isl_pw_qpolynomial_set_dim_name(
5080 __isl_take isl_pw_qpolynomial *pwqp,
5081 enum isl_dim_type type, unsigned pos,
5084 =head3 Creating New (Piecewise) Quasipolynomials
5086 Some simple quasipolynomials can be created using the following functions.
5087 More complicated quasipolynomials can be created by applying
5088 operations such as addition and multiplication
5089 on the resulting quasipolynomials
5091 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
5092 __isl_take isl_space *domain);
5093 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
5094 __isl_take isl_space *domain);
5095 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
5096 __isl_take isl_space *domain);
5097 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
5098 __isl_take isl_space *domain);
5099 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
5100 __isl_take isl_space *domain);
5101 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
5102 __isl_take isl_space *domain,
5103 __isl_take isl_val *val);
5104 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
5105 __isl_take isl_space *domain,
5106 enum isl_dim_type type, unsigned pos);
5107 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
5108 __isl_take isl_aff *aff);
5110 Note that the space in which a quasipolynomial lives is a map space
5111 with a one-dimensional range. The C<domain> argument in some of
5112 the functions above corresponds to the domain of this map space.
5114 The zero piecewise quasipolynomial or a piecewise quasipolynomial
5115 with a single cell can be created using the following functions.
5116 Multiple of these single cell piecewise quasipolynomials can
5117 be combined to create more complicated piecewise quasipolynomials.
5119 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
5120 __isl_take isl_space *space);
5121 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
5122 __isl_take isl_set *set,
5123 __isl_take isl_qpolynomial *qp);
5124 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
5125 __isl_take isl_qpolynomial *qp);
5126 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
5127 __isl_take isl_pw_aff *pwaff);
5129 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
5130 __isl_take isl_space *space);
5131 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
5132 __isl_take isl_pw_qpolynomial *pwqp);
5133 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
5134 __isl_take isl_union_pw_qpolynomial *upwqp,
5135 __isl_take isl_pw_qpolynomial *pwqp);
5137 Quasipolynomials can be copied and freed again using the following
5140 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
5141 __isl_keep isl_qpolynomial *qp);
5142 __isl_null isl_qpolynomial *isl_qpolynomial_free(
5143 __isl_take isl_qpolynomial *qp);
5145 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
5146 __isl_keep isl_pw_qpolynomial *pwqp);
5147 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
5148 __isl_take isl_pw_qpolynomial *pwqp);
5150 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
5151 __isl_keep isl_union_pw_qpolynomial *upwqp);
5152 __isl_null isl_union_pw_qpolynomial *
5153 isl_union_pw_qpolynomial_free(
5154 __isl_take isl_union_pw_qpolynomial *upwqp);
5156 =head3 Inspecting (Piecewise) Quasipolynomials
5158 To iterate over all piecewise quasipolynomials in a union
5159 piecewise quasipolynomial, use the following function
5161 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
5162 __isl_keep isl_union_pw_qpolynomial *upwqp,
5163 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
5166 To extract the piecewise quasipolynomial in a given space from a union, use
5168 __isl_give isl_pw_qpolynomial *
5169 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
5170 __isl_keep isl_union_pw_qpolynomial *upwqp,
5171 __isl_take isl_space *space);
5173 To iterate over the cells in a piecewise quasipolynomial,
5174 use either of the following two functions
5176 int isl_pw_qpolynomial_foreach_piece(
5177 __isl_keep isl_pw_qpolynomial *pwqp,
5178 int (*fn)(__isl_take isl_set *set,
5179 __isl_take isl_qpolynomial *qp,
5180 void *user), void *user);
5181 int isl_pw_qpolynomial_foreach_lifted_piece(
5182 __isl_keep isl_pw_qpolynomial *pwqp,
5183 int (*fn)(__isl_take isl_set *set,
5184 __isl_take isl_qpolynomial *qp,
5185 void *user), void *user);
5187 As usual, the function C<fn> should return C<0> on success
5188 and C<-1> on failure. The difference between
5189 C<isl_pw_qpolynomial_foreach_piece> and
5190 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
5191 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
5192 compute unique representations for all existentially quantified
5193 variables and then turn these existentially quantified variables
5194 into extra set variables, adapting the associated quasipolynomial
5195 accordingly. This means that the C<set> passed to C<fn>
5196 will not have any existentially quantified variables, but that
5197 the dimensions of the sets may be different for different
5198 invocations of C<fn>.
5200 The constant term of a quasipolynomial can be extracted using
5202 __isl_give isl_val *isl_qpolynomial_get_constant_val(
5203 __isl_keep isl_qpolynomial *qp);
5205 To iterate over all terms in a quasipolynomial,
5208 int isl_qpolynomial_foreach_term(
5209 __isl_keep isl_qpolynomial *qp,
5210 int (*fn)(__isl_take isl_term *term,
5211 void *user), void *user);
5213 The terms themselves can be inspected and freed using
5216 unsigned isl_term_dim(__isl_keep isl_term *term,
5217 enum isl_dim_type type);
5218 __isl_give isl_val *isl_term_get_coefficient_val(
5219 __isl_keep isl_term *term);
5220 int isl_term_get_exp(__isl_keep isl_term *term,
5221 enum isl_dim_type type, unsigned pos);
5222 __isl_give isl_aff *isl_term_get_div(
5223 __isl_keep isl_term *term, unsigned pos);
5224 void isl_term_free(__isl_take isl_term *term);
5226 Each term is a product of parameters, set variables and
5227 integer divisions. The function C<isl_term_get_exp>
5228 returns the exponent of a given dimensions in the given term.
5230 =head3 Properties of (Piecewise) Quasipolynomials
5232 To check whether two union piecewise quasipolynomials are
5233 obviously equal, use
5235 int isl_union_pw_qpolynomial_plain_is_equal(
5236 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5237 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5239 =head3 Operations on (Piecewise) Quasipolynomials
5241 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5242 __isl_take isl_qpolynomial *qp,
5243 __isl_take isl_val *v);
5244 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5245 __isl_take isl_qpolynomial *qp);
5246 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5247 __isl_take isl_qpolynomial *qp1,
5248 __isl_take isl_qpolynomial *qp2);
5249 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5250 __isl_take isl_qpolynomial *qp1,
5251 __isl_take isl_qpolynomial *qp2);
5252 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5253 __isl_take isl_qpolynomial *qp1,
5254 __isl_take isl_qpolynomial *qp2);
5255 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5256 __isl_take isl_qpolynomial *qp, unsigned exponent);
5258 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5259 __isl_take isl_pw_qpolynomial *pwqp,
5260 enum isl_dim_type type, unsigned n,
5261 __isl_take isl_val *v);
5262 __isl_give isl_pw_qpolynomial *
5263 isl_pw_qpolynomial_scale_val(
5264 __isl_take isl_pw_qpolynomial *pwqp,
5265 __isl_take isl_val *v);
5266 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5267 __isl_take isl_pw_qpolynomial *pwqp1,
5268 __isl_take isl_pw_qpolynomial *pwqp2);
5269 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5270 __isl_take isl_pw_qpolynomial *pwqp1,
5271 __isl_take isl_pw_qpolynomial *pwqp2);
5272 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5273 __isl_take isl_pw_qpolynomial *pwqp1,
5274 __isl_take isl_pw_qpolynomial *pwqp2);
5275 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5276 __isl_take isl_pw_qpolynomial *pwqp);
5277 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5278 __isl_take isl_pw_qpolynomial *pwqp1,
5279 __isl_take isl_pw_qpolynomial *pwqp2);
5280 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5281 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5283 __isl_give isl_union_pw_qpolynomial *
5284 isl_union_pw_qpolynomial_scale_val(
5285 __isl_take isl_union_pw_qpolynomial *upwqp,
5286 __isl_take isl_val *v);
5287 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5288 __isl_take isl_union_pw_qpolynomial *upwqp1,
5289 __isl_take isl_union_pw_qpolynomial *upwqp2);
5290 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5291 __isl_take isl_union_pw_qpolynomial *upwqp1,
5292 __isl_take isl_union_pw_qpolynomial *upwqp2);
5293 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5294 __isl_take isl_union_pw_qpolynomial *upwqp1,
5295 __isl_take isl_union_pw_qpolynomial *upwqp2);
5297 __isl_give isl_val *isl_pw_qpolynomial_eval(
5298 __isl_take isl_pw_qpolynomial *pwqp,
5299 __isl_take isl_point *pnt);
5301 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5302 __isl_take isl_union_pw_qpolynomial *upwqp,
5303 __isl_take isl_point *pnt);
5305 __isl_give isl_set *isl_pw_qpolynomial_domain(
5306 __isl_take isl_pw_qpolynomial *pwqp);
5307 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5308 __isl_take isl_pw_qpolynomial *pwpq,
5309 __isl_take isl_set *set);
5310 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5311 __isl_take isl_pw_qpolynomial *pwpq,
5312 __isl_take isl_set *set);
5314 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5315 __isl_take isl_union_pw_qpolynomial *upwqp);
5316 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5317 __isl_take isl_union_pw_qpolynomial *upwpq,
5318 __isl_take isl_union_set *uset);
5319 __isl_give isl_union_pw_qpolynomial *
5320 isl_union_pw_qpolynomial_intersect_params(
5321 __isl_take isl_union_pw_qpolynomial *upwpq,
5322 __isl_take isl_set *set);
5324 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5325 __isl_take isl_qpolynomial *qp,
5326 __isl_take isl_space *model);
5328 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5329 __isl_take isl_qpolynomial *qp);
5330 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5331 __isl_take isl_pw_qpolynomial *pwqp);
5333 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5334 __isl_take isl_union_pw_qpolynomial *upwqp);
5336 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5337 __isl_take isl_qpolynomial *qp,
5338 __isl_take isl_set *context);
5339 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5340 __isl_take isl_qpolynomial *qp,
5341 __isl_take isl_set *context);
5343 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5344 __isl_take isl_pw_qpolynomial *pwqp,
5345 __isl_take isl_set *context);
5346 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5347 __isl_take isl_pw_qpolynomial *pwqp,
5348 __isl_take isl_set *context);
5350 __isl_give isl_union_pw_qpolynomial *
5351 isl_union_pw_qpolynomial_gist_params(
5352 __isl_take isl_union_pw_qpolynomial *upwqp,
5353 __isl_take isl_set *context);
5354 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5355 __isl_take isl_union_pw_qpolynomial *upwqp,
5356 __isl_take isl_union_set *context);
5358 The gist operation applies the gist operation to each of
5359 the cells in the domain of the input piecewise quasipolynomial.
5360 The context is also exploited
5361 to simplify the quasipolynomials associated to each cell.
5363 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5364 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5365 __isl_give isl_union_pw_qpolynomial *
5366 isl_union_pw_qpolynomial_to_polynomial(
5367 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5369 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5370 the polynomial will be an overapproximation. If C<sign> is negative,
5371 it will be an underapproximation. If C<sign> is zero, the approximation
5372 will lie somewhere in between.
5374 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5376 A piecewise quasipolynomial reduction is a piecewise
5377 reduction (or fold) of quasipolynomials.
5378 In particular, the reduction can be maximum or a minimum.
5379 The objects are mainly used to represent the result of
5380 an upper or lower bound on a quasipolynomial over its domain,
5381 i.e., as the result of the following function.
5383 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5384 __isl_take isl_pw_qpolynomial *pwqp,
5385 enum isl_fold type, int *tight);
5387 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5388 __isl_take isl_union_pw_qpolynomial *upwqp,
5389 enum isl_fold type, int *tight);
5391 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5392 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5393 is the returned bound is known be tight, i.e., for each value
5394 of the parameters there is at least
5395 one element in the domain that reaches the bound.
5396 If the domain of C<pwqp> is not wrapping, then the bound is computed
5397 over all elements in that domain and the result has a purely parametric
5398 domain. If the domain of C<pwqp> is wrapping, then the bound is
5399 computed over the range of the wrapped relation. The domain of the
5400 wrapped relation becomes the domain of the result.
5402 A (piecewise) quasipolynomial reduction can be copied or freed using the
5403 following functions.
5405 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5406 __isl_keep isl_qpolynomial_fold *fold);
5407 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5408 __isl_keep isl_pw_qpolynomial_fold *pwf);
5409 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5410 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5411 void isl_qpolynomial_fold_free(
5412 __isl_take isl_qpolynomial_fold *fold);
5413 __isl_null isl_pw_qpolynomial_fold *
5414 isl_pw_qpolynomial_fold_free(
5415 __isl_take isl_pw_qpolynomial_fold *pwf);
5416 __isl_null isl_union_pw_qpolynomial_fold *
5417 isl_union_pw_qpolynomial_fold_free(
5418 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5420 =head3 Printing Piecewise Quasipolynomial Reductions
5422 Piecewise quasipolynomial reductions can be printed
5423 using the following function.
5425 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5426 __isl_take isl_printer *p,
5427 __isl_keep isl_pw_qpolynomial_fold *pwf);
5428 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5429 __isl_take isl_printer *p,
5430 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5432 For C<isl_printer_print_pw_qpolynomial_fold>,
5433 output format of the printer
5434 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5435 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5436 output format of the printer
5437 needs to be set to C<ISL_FORMAT_ISL>.
5438 In case of printing in C<ISL_FORMAT_C>, the user may want
5439 to set the names of all dimensions
5441 __isl_give isl_pw_qpolynomial_fold *
5442 isl_pw_qpolynomial_fold_set_dim_name(
5443 __isl_take isl_pw_qpolynomial_fold *pwf,
5444 enum isl_dim_type type, unsigned pos,
5447 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5449 To iterate over all piecewise quasipolynomial reductions in a union
5450 piecewise quasipolynomial reduction, use the following function
5452 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5453 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5454 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5455 void *user), void *user);
5457 To iterate over the cells in a piecewise quasipolynomial reduction,
5458 use either of the following two functions
5460 int isl_pw_qpolynomial_fold_foreach_piece(
5461 __isl_keep isl_pw_qpolynomial_fold *pwf,
5462 int (*fn)(__isl_take isl_set *set,
5463 __isl_take isl_qpolynomial_fold *fold,
5464 void *user), void *user);
5465 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5466 __isl_keep isl_pw_qpolynomial_fold *pwf,
5467 int (*fn)(__isl_take isl_set *set,
5468 __isl_take isl_qpolynomial_fold *fold,
5469 void *user), void *user);
5471 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5472 of the difference between these two functions.
5474 To iterate over all quasipolynomials in a reduction, use
5476 int isl_qpolynomial_fold_foreach_qpolynomial(
5477 __isl_keep isl_qpolynomial_fold *fold,
5478 int (*fn)(__isl_take isl_qpolynomial *qp,
5479 void *user), void *user);
5481 =head3 Properties of Piecewise Quasipolynomial Reductions
5483 To check whether two union piecewise quasipolynomial reductions are
5484 obviously equal, use
5486 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5487 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5488 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5490 =head3 Operations on Piecewise Quasipolynomial Reductions
5492 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5493 __isl_take isl_qpolynomial_fold *fold,
5494 __isl_take isl_val *v);
5495 __isl_give isl_pw_qpolynomial_fold *
5496 isl_pw_qpolynomial_fold_scale_val(
5497 __isl_take isl_pw_qpolynomial_fold *pwf,
5498 __isl_take isl_val *v);
5499 __isl_give isl_union_pw_qpolynomial_fold *
5500 isl_union_pw_qpolynomial_fold_scale_val(
5501 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5502 __isl_take isl_val *v);
5504 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5505 __isl_take isl_pw_qpolynomial_fold *pwf1,
5506 __isl_take isl_pw_qpolynomial_fold *pwf2);
5508 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5509 __isl_take isl_pw_qpolynomial_fold *pwf1,
5510 __isl_take isl_pw_qpolynomial_fold *pwf2);
5512 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5513 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5514 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5516 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5517 __isl_take isl_pw_qpolynomial_fold *pwf,
5518 __isl_take isl_point *pnt);
5520 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5521 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5522 __isl_take isl_point *pnt);
5524 __isl_give isl_pw_qpolynomial_fold *
5525 isl_pw_qpolynomial_fold_intersect_params(
5526 __isl_take isl_pw_qpolynomial_fold *pwf,
5527 __isl_take isl_set *set);
5529 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5530 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5531 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5532 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5533 __isl_take isl_union_set *uset);
5534 __isl_give isl_union_pw_qpolynomial_fold *
5535 isl_union_pw_qpolynomial_fold_intersect_params(
5536 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5537 __isl_take isl_set *set);
5539 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5540 __isl_take isl_pw_qpolynomial_fold *pwf);
5542 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5543 __isl_take isl_pw_qpolynomial_fold *pwf);
5545 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5546 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5548 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5549 __isl_take isl_qpolynomial_fold *fold,
5550 __isl_take isl_set *context);
5551 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5552 __isl_take isl_qpolynomial_fold *fold,
5553 __isl_take isl_set *context);
5555 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5556 __isl_take isl_pw_qpolynomial_fold *pwf,
5557 __isl_take isl_set *context);
5558 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5559 __isl_take isl_pw_qpolynomial_fold *pwf,
5560 __isl_take isl_set *context);
5562 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5563 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5564 __isl_take isl_union_set *context);
5565 __isl_give isl_union_pw_qpolynomial_fold *
5566 isl_union_pw_qpolynomial_fold_gist_params(
5567 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5568 __isl_take isl_set *context);
5570 The gist operation applies the gist operation to each of
5571 the cells in the domain of the input piecewise quasipolynomial reduction.
5572 In future, the operation will also exploit the context
5573 to simplify the quasipolynomial reductions associated to each cell.
5575 __isl_give isl_pw_qpolynomial_fold *
5576 isl_set_apply_pw_qpolynomial_fold(
5577 __isl_take isl_set *set,
5578 __isl_take isl_pw_qpolynomial_fold *pwf,
5580 __isl_give isl_pw_qpolynomial_fold *
5581 isl_map_apply_pw_qpolynomial_fold(
5582 __isl_take isl_map *map,
5583 __isl_take isl_pw_qpolynomial_fold *pwf,
5585 __isl_give isl_union_pw_qpolynomial_fold *
5586 isl_union_set_apply_union_pw_qpolynomial_fold(
5587 __isl_take isl_union_set *uset,
5588 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5590 __isl_give isl_union_pw_qpolynomial_fold *
5591 isl_union_map_apply_union_pw_qpolynomial_fold(
5592 __isl_take isl_union_map *umap,
5593 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5596 The functions taking a map
5597 compose the given map with the given piecewise quasipolynomial reduction.
5598 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5599 over all elements in the intersection of the range of the map
5600 and the domain of the piecewise quasipolynomial reduction
5601 as a function of an element in the domain of the map.
5602 The functions taking a set compute a bound over all elements in the
5603 intersection of the set and the domain of the
5604 piecewise quasipolynomial reduction.
5606 =head2 Parametric Vertex Enumeration
5608 The parametric vertex enumeration described in this section
5609 is mainly intended to be used internally and by the C<barvinok>
5612 #include <isl/vertices.h>
5613 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5614 __isl_keep isl_basic_set *bset);
5616 The function C<isl_basic_set_compute_vertices> performs the
5617 actual computation of the parametric vertices and the chamber
5618 decomposition and store the result in an C<isl_vertices> object.
5619 This information can be queried by either iterating over all
5620 the vertices or iterating over all the chambers or cells
5621 and then iterating over all vertices that are active on the chamber.
5623 int isl_vertices_foreach_vertex(
5624 __isl_keep isl_vertices *vertices,
5625 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5628 int isl_vertices_foreach_cell(
5629 __isl_keep isl_vertices *vertices,
5630 int (*fn)(__isl_take isl_cell *cell, void *user),
5632 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5633 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5636 Other operations that can be performed on an C<isl_vertices> object are
5639 isl_ctx *isl_vertices_get_ctx(
5640 __isl_keep isl_vertices *vertices);
5641 int isl_vertices_get_n_vertices(
5642 __isl_keep isl_vertices *vertices);
5643 void isl_vertices_free(__isl_take isl_vertices *vertices);
5645 Vertices can be inspected and destroyed using the following functions.
5647 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5648 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5649 __isl_give isl_basic_set *isl_vertex_get_domain(
5650 __isl_keep isl_vertex *vertex);
5651 __isl_give isl_multi_aff *isl_vertex_get_expr(
5652 __isl_keep isl_vertex *vertex);
5653 void isl_vertex_free(__isl_take isl_vertex *vertex);
5655 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
5656 describing the vertex in terms of the parameters,
5657 while C<isl_vertex_get_domain> returns the activity domain
5660 Chambers can be inspected and destroyed using the following functions.
5662 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5663 __isl_give isl_basic_set *isl_cell_get_domain(
5664 __isl_keep isl_cell *cell);
5665 void isl_cell_free(__isl_take isl_cell *cell);
5667 =head1 Polyhedral Compilation Library
5669 This section collects functionality in C<isl> that has been specifically
5670 designed for use during polyhedral compilation.
5672 =head2 Dependence Analysis
5674 C<isl> contains specialized functionality for performing
5675 array dataflow analysis. That is, given a I<sink> access relation
5676 and a collection of possible I<source> access relations,
5677 C<isl> can compute relations that describe
5678 for each iteration of the sink access, which iteration
5679 of which of the source access relations was the last
5680 to access the same data element before the given iteration
5682 The resulting dependence relations map source iterations
5683 to the corresponding sink iterations.
5684 To compute standard flow dependences, the sink should be
5685 a read, while the sources should be writes.
5686 If any of the source accesses are marked as being I<may>
5687 accesses, then there will be a dependence from the last
5688 I<must> access B<and> from any I<may> access that follows
5689 this last I<must> access.
5690 In particular, if I<all> sources are I<may> accesses,
5691 then memory based dependence analysis is performed.
5692 If, on the other hand, all sources are I<must> accesses,
5693 then value based dependence analysis is performed.
5695 #include <isl/flow.h>
5697 typedef int (*isl_access_level_before)(void *first, void *second);
5699 __isl_give isl_access_info *isl_access_info_alloc(
5700 __isl_take isl_map *sink,
5701 void *sink_user, isl_access_level_before fn,
5703 __isl_give isl_access_info *isl_access_info_add_source(
5704 __isl_take isl_access_info *acc,
5705 __isl_take isl_map *source, int must,
5707 __isl_null isl_access_info *isl_access_info_free(
5708 __isl_take isl_access_info *acc);
5710 __isl_give isl_flow *isl_access_info_compute_flow(
5711 __isl_take isl_access_info *acc);
5713 int isl_flow_foreach(__isl_keep isl_flow *deps,
5714 int (*fn)(__isl_take isl_map *dep, int must,
5715 void *dep_user, void *user),
5717 __isl_give isl_map *isl_flow_get_no_source(
5718 __isl_keep isl_flow *deps, int must);
5719 void isl_flow_free(__isl_take isl_flow *deps);
5721 The function C<isl_access_info_compute_flow> performs the actual
5722 dependence analysis. The other functions are used to construct
5723 the input for this function or to read off the output.
5725 The input is collected in an C<isl_access_info>, which can
5726 be created through a call to C<isl_access_info_alloc>.
5727 The arguments to this functions are the sink access relation
5728 C<sink>, a token C<sink_user> used to identify the sink
5729 access to the user, a callback function for specifying the
5730 relative order of source and sink accesses, and the number
5731 of source access relations that will be added.
5732 The callback function has type C<int (*)(void *first, void *second)>.
5733 The function is called with two user supplied tokens identifying
5734 either a source or the sink and it should return the shared nesting
5735 level and the relative order of the two accesses.
5736 In particular, let I<n> be the number of loops shared by
5737 the two accesses. If C<first> precedes C<second> textually,
5738 then the function should return I<2 * n + 1>; otherwise,
5739 it should return I<2 * n>.
5740 The sources can be added to the C<isl_access_info> by performing
5741 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5742 C<must> indicates whether the source is a I<must> access
5743 or a I<may> access. Note that a multi-valued access relation
5744 should only be marked I<must> if every iteration in the domain
5745 of the relation accesses I<all> elements in its image.
5746 The C<source_user> token is again used to identify
5747 the source access. The range of the source access relation
5748 C<source> should have the same dimension as the range
5749 of the sink access relation.
5750 The C<isl_access_info_free> function should usually not be
5751 called explicitly, because it is called implicitly by
5752 C<isl_access_info_compute_flow>.
5754 The result of the dependence analysis is collected in an
5755 C<isl_flow>. There may be elements of
5756 the sink access for which no preceding source access could be
5757 found or for which all preceding sources are I<may> accesses.
5758 The relations containing these elements can be obtained through
5759 calls to C<isl_flow_get_no_source>, the first with C<must> set
5760 and the second with C<must> unset.
5761 In the case of standard flow dependence analysis,
5762 with the sink a read and the sources I<must> writes,
5763 the first relation corresponds to the reads from uninitialized
5764 array elements and the second relation is empty.
5765 The actual flow dependences can be extracted using
5766 C<isl_flow_foreach>. This function will call the user-specified
5767 callback function C<fn> for each B<non-empty> dependence between
5768 a source and the sink. The callback function is called
5769 with four arguments, the actual flow dependence relation
5770 mapping source iterations to sink iterations, a boolean that
5771 indicates whether it is a I<must> or I<may> dependence, a token
5772 identifying the source and an additional C<void *> with value
5773 equal to the third argument of the C<isl_flow_foreach> call.
5774 A dependence is marked I<must> if it originates from a I<must>
5775 source and if it is not followed by any I<may> sources.
5777 After finishing with an C<isl_flow>, the user should call
5778 C<isl_flow_free> to free all associated memory.
5780 A higher-level interface to dependence analysis is provided
5781 by the following function.
5783 #include <isl/flow.h>
5785 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5786 __isl_take isl_union_map *must_source,
5787 __isl_take isl_union_map *may_source,
5788 __isl_take isl_union_map *schedule,
5789 __isl_give isl_union_map **must_dep,
5790 __isl_give isl_union_map **may_dep,
5791 __isl_give isl_union_map **must_no_source,
5792 __isl_give isl_union_map **may_no_source);
5794 The arrays are identified by the tuple names of the ranges
5795 of the accesses. The iteration domains by the tuple names
5796 of the domains of the accesses and of the schedule.
5797 The relative order of the iteration domains is given by the
5798 schedule. The relations returned through C<must_no_source>
5799 and C<may_no_source> are subsets of C<sink>.
5800 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5801 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5802 any of the other arguments is treated as an error.
5804 =head3 Interaction with Dependence Analysis
5806 During the dependence analysis, we frequently need to perform
5807 the following operation. Given a relation between sink iterations
5808 and potential source iterations from a particular source domain,
5809 what is the last potential source iteration corresponding to each
5810 sink iteration. It can sometimes be convenient to adjust
5811 the set of potential source iterations before or after each such operation.
5812 The prototypical example is fuzzy array dataflow analysis,
5813 where we need to analyze if, based on data-dependent constraints,
5814 the sink iteration can ever be executed without one or more of
5815 the corresponding potential source iterations being executed.
5816 If so, we can introduce extra parameters and select an unknown
5817 but fixed source iteration from the potential source iterations.
5818 To be able to perform such manipulations, C<isl> provides the following
5821 #include <isl/flow.h>
5823 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5824 __isl_keep isl_map *source_map,
5825 __isl_keep isl_set *sink, void *source_user,
5827 __isl_give isl_access_info *isl_access_info_set_restrict(
5828 __isl_take isl_access_info *acc,
5829 isl_access_restrict fn, void *user);
5831 The function C<isl_access_info_set_restrict> should be called
5832 before calling C<isl_access_info_compute_flow> and registers a callback function
5833 that will be called any time C<isl> is about to compute the last
5834 potential source. The first argument is the (reverse) proto-dependence,
5835 mapping sink iterations to potential source iterations.
5836 The second argument represents the sink iterations for which
5837 we want to compute the last source iteration.
5838 The third argument is the token corresponding to the source
5839 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5840 The callback is expected to return a restriction on either the input or
5841 the output of the operation computing the last potential source.
5842 If the input needs to be restricted then restrictions are needed
5843 for both the source and the sink iterations. The sink iterations
5844 and the potential source iterations will be intersected with these sets.
5845 If the output needs to be restricted then only a restriction on the source
5846 iterations is required.
5847 If any error occurs, the callback should return C<NULL>.
5848 An C<isl_restriction> object can be created, freed and inspected
5849 using the following functions.
5851 #include <isl/flow.h>
5853 __isl_give isl_restriction *isl_restriction_input(
5854 __isl_take isl_set *source_restr,
5855 __isl_take isl_set *sink_restr);
5856 __isl_give isl_restriction *isl_restriction_output(
5857 __isl_take isl_set *source_restr);
5858 __isl_give isl_restriction *isl_restriction_none(
5859 __isl_take isl_map *source_map);
5860 __isl_give isl_restriction *isl_restriction_empty(
5861 __isl_take isl_map *source_map);
5862 __isl_null isl_restriction *isl_restriction_free(
5863 __isl_take isl_restriction *restr);
5864 isl_ctx *isl_restriction_get_ctx(
5865 __isl_keep isl_restriction *restr);
5867 C<isl_restriction_none> and C<isl_restriction_empty> are special
5868 cases of C<isl_restriction_input>. C<isl_restriction_none>
5869 is essentially equivalent to
5871 isl_restriction_input(isl_set_universe(
5872 isl_space_range(isl_map_get_space(source_map))),
5874 isl_space_domain(isl_map_get_space(source_map))));
5876 whereas C<isl_restriction_empty> is essentially equivalent to
5878 isl_restriction_input(isl_set_empty(
5879 isl_space_range(isl_map_get_space(source_map))),
5881 isl_space_domain(isl_map_get_space(source_map))));
5885 B<The functionality described in this section is fairly new
5886 and may be subject to change.>
5888 #include <isl/schedule.h>
5889 __isl_give isl_schedule *
5890 isl_schedule_constraints_compute_schedule(
5891 __isl_take isl_schedule_constraints *sc);
5892 __isl_null isl_schedule *isl_schedule_free(
5893 __isl_take isl_schedule *sched);
5895 The function C<isl_schedule_constraints_compute_schedule> can be
5896 used to compute a schedule that satisfy the given schedule constraints.
5897 These schedule constraints include the iteration domain for which
5898 a schedule should be computed and dependences between pairs of
5899 iterations. In particular, these dependences include
5900 I<validity> dependences and I<proximity> dependences.
5901 By default, the algorithm used to construct the schedule is similar
5902 to that of C<Pluto>.
5903 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5905 The generated schedule respects all validity dependences.
5906 That is, all dependence distances over these dependences in the
5907 scheduled space are lexicographically positive.
5908 The default algorithm tries to ensure that the dependence distances
5909 over coincidence constraints are zero and to minimize the
5910 dependence distances over proximity dependences.
5911 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5912 for groups of domains where the dependence distances over validity
5913 dependences have only non-negative values.
5914 When using Feautrier's algorithm, the coincidence and proximity constraints
5915 are only taken into account during the extension to a
5916 full-dimensional schedule.
5918 An C<isl_schedule_constraints> object can be constructed
5919 and manipulated using the following functions.
5921 #include <isl/schedule.h>
5922 __isl_give isl_schedule_constraints *
5923 isl_schedule_constraints_copy(
5924 __isl_keep isl_schedule_constraints *sc);
5925 __isl_give isl_schedule_constraints *
5926 isl_schedule_constraints_on_domain(
5927 __isl_take isl_union_set *domain);
5928 isl_ctx *isl_schedule_constraints_get_ctx(
5929 __isl_keep isl_schedule_constraints *sc);
5930 __isl_give isl_schedule_constraints *
5931 isl_schedule_constraints_set_validity(
5932 __isl_take isl_schedule_constraints *sc,
5933 __isl_take isl_union_map *validity);
5934 __isl_give isl_schedule_constraints *
5935 isl_schedule_constraints_set_coincidence(
5936 __isl_take isl_schedule_constraints *sc,
5937 __isl_take isl_union_map *coincidence);
5938 __isl_give isl_schedule_constraints *
5939 isl_schedule_constraints_set_proximity(
5940 __isl_take isl_schedule_constraints *sc,
5941 __isl_take isl_union_map *proximity);
5942 __isl_give isl_schedule_constraints *
5943 isl_schedule_constraints_set_conditional_validity(
5944 __isl_take isl_schedule_constraints *sc,
5945 __isl_take isl_union_map *condition,
5946 __isl_take isl_union_map *validity);
5947 __isl_null isl_schedule_constraints *
5948 isl_schedule_constraints_free(
5949 __isl_take isl_schedule_constraints *sc);
5951 The initial C<isl_schedule_constraints> object created by
5952 C<isl_schedule_constraints_on_domain> does not impose any constraints.
5953 That is, it has an empty set of dependences.
5954 The function C<isl_schedule_constraints_set_validity> replaces the
5955 validity dependences, mapping domain elements I<i> to domain
5956 elements that should be scheduled after I<i>.
5957 The function C<isl_schedule_constraints_set_coincidence> replaces the
5958 coincidence dependences, mapping domain elements I<i> to domain
5959 elements that should be scheduled together with I<I>, if possible.
5960 The function C<isl_schedule_constraints_set_proximity> replaces the
5961 proximity dependences, mapping domain elements I<i> to domain
5962 elements that should be scheduled either before I<I>
5963 or as early as possible after I<i>.
5965 The function C<isl_schedule_constraints_set_conditional_validity>
5966 replaces the conditional validity constraints.
5967 A conditional validity constraint is only imposed when any of the corresponding
5968 conditions is satisfied, i.e., when any of them is non-zero.
5969 That is, the scheduler ensures that within each band if the dependence
5970 distances over the condition constraints are not all zero
5971 then all corresponding conditional validity constraints are respected.
5972 A conditional validity constraint corresponds to a condition
5973 if the two are adjacent, i.e., if the domain of one relation intersect
5974 the range of the other relation.
5975 The typical use case of conditional validity constraints is
5976 to allow order constraints between live ranges to be violated
5977 as long as the live ranges themselves are local to the band.
5978 To allow more fine-grained control over which conditions correspond
5979 to which conditional validity constraints, the domains and ranges
5980 of these relations may include I<tags>. That is, the domains and
5981 ranges of those relation may themselves be wrapped relations
5982 where the iteration domain appears in the domain of those wrapped relations
5983 and the range of the wrapped relations can be arbitrarily chosen
5984 by the user. Conditions and conditional validity constraints are only
5985 considere adjacent to each other if the entire wrapped relation matches.
5986 In particular, a relation with a tag will never be considered adjacent
5987 to a relation without a tag.
5989 The following function computes a schedule directly from
5990 an iteration domain and validity and proximity dependences
5991 and is implemented in terms of the functions described above.
5992 The use of C<isl_union_set_compute_schedule> is discouraged.
5994 #include <isl/schedule.h>
5995 __isl_give isl_schedule *isl_union_set_compute_schedule(
5996 __isl_take isl_union_set *domain,
5997 __isl_take isl_union_map *validity,
5998 __isl_take isl_union_map *proximity);
6000 A mapping from the domains to the scheduled space can be obtained
6001 from an C<isl_schedule> using the following function.
6003 __isl_give isl_union_map *isl_schedule_get_map(
6004 __isl_keep isl_schedule *sched);
6006 A representation of the schedule can be printed using
6008 __isl_give isl_printer *isl_printer_print_schedule(
6009 __isl_take isl_printer *p,
6010 __isl_keep isl_schedule *schedule);
6012 A representation of the schedule as a forest of bands can be obtained
6013 using the following function.
6015 __isl_give isl_band_list *isl_schedule_get_band_forest(
6016 __isl_keep isl_schedule *schedule);
6018 The individual bands can be visited in depth-first post-order
6019 using the following function.
6021 #include <isl/schedule.h>
6022 int isl_schedule_foreach_band(
6023 __isl_keep isl_schedule *sched,
6024 int (*fn)(__isl_keep isl_band *band, void *user),
6027 The list can be manipulated as explained in L<"Lists">.
6028 The bands inside the list can be copied and freed using the following
6031 #include <isl/band.h>
6032 __isl_give isl_band *isl_band_copy(
6033 __isl_keep isl_band *band);
6034 __isl_null isl_band *isl_band_free(
6035 __isl_take isl_band *band);
6037 Each band contains zero or more scheduling dimensions.
6038 These are referred to as the members of the band.
6039 The section of the schedule that corresponds to the band is
6040 referred to as the partial schedule of the band.
6041 For those nodes that participate in a band, the outer scheduling
6042 dimensions form the prefix schedule, while the inner scheduling
6043 dimensions form the suffix schedule.
6044 That is, if we take a cut of the band forest, then the union of
6045 the concatenations of the prefix, partial and suffix schedules of
6046 each band in the cut is equal to the entire schedule (modulo
6047 some possible padding at the end with zero scheduling dimensions).
6048 The properties of a band can be inspected using the following functions.
6050 #include <isl/band.h>
6051 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
6053 int isl_band_has_children(__isl_keep isl_band *band);
6054 __isl_give isl_band_list *isl_band_get_children(
6055 __isl_keep isl_band *band);
6057 __isl_give isl_union_map *isl_band_get_prefix_schedule(
6058 __isl_keep isl_band *band);
6059 __isl_give isl_union_map *isl_band_get_partial_schedule(
6060 __isl_keep isl_band *band);
6061 __isl_give isl_union_map *isl_band_get_suffix_schedule(
6062 __isl_keep isl_band *band);
6064 int isl_band_n_member(__isl_keep isl_band *band);
6065 int isl_band_member_is_coincident(
6066 __isl_keep isl_band *band, int pos);
6068 int isl_band_list_foreach_band(
6069 __isl_keep isl_band_list *list,
6070 int (*fn)(__isl_keep isl_band *band, void *user),
6073 Note that a scheduling dimension is considered to be ``coincident''
6074 if it satisfies the coincidence constraints within its band.
6075 That is, if the dependence distances of the coincidence
6076 constraints are all zero in that direction (for fixed
6077 iterations of outer bands).
6078 Like C<isl_schedule_foreach_band>,
6079 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
6080 in depth-first post-order.
6082 A band can be tiled using the following function.
6084 #include <isl/band.h>
6085 int isl_band_tile(__isl_keep isl_band *band,
6086 __isl_take isl_vec *sizes);
6088 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
6090 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
6091 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
6093 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
6095 The C<isl_band_tile> function tiles the band using the given tile sizes
6096 inside its schedule.
6097 A new child band is created to represent the point loops and it is
6098 inserted between the modified band and its children.
6099 The C<tile_scale_tile_loops> option specifies whether the tile
6100 loops iterators should be scaled by the tile sizes.
6101 If the C<tile_shift_point_loops> option is set, then the point loops
6102 are shifted to start at zero.
6104 A band can be split into two nested bands using the following function.
6106 int isl_band_split(__isl_keep isl_band *band, int pos);
6108 The resulting outer band contains the first C<pos> dimensions of C<band>
6109 while the inner band contains the remaining dimensions.
6111 A representation of the band can be printed using
6113 #include <isl/band.h>
6114 __isl_give isl_printer *isl_printer_print_band(
6115 __isl_take isl_printer *p,
6116 __isl_keep isl_band *band);
6120 #include <isl/schedule.h>
6121 int isl_options_set_schedule_max_coefficient(
6122 isl_ctx *ctx, int val);
6123 int isl_options_get_schedule_max_coefficient(
6125 int isl_options_set_schedule_max_constant_term(
6126 isl_ctx *ctx, int val);
6127 int isl_options_get_schedule_max_constant_term(
6129 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
6130 int isl_options_get_schedule_fuse(isl_ctx *ctx);
6131 int isl_options_set_schedule_maximize_band_depth(
6132 isl_ctx *ctx, int val);
6133 int isl_options_get_schedule_maximize_band_depth(
6135 int isl_options_set_schedule_outer_coincidence(
6136 isl_ctx *ctx, int val);
6137 int isl_options_get_schedule_outer_coincidence(
6139 int isl_options_set_schedule_split_scaled(
6140 isl_ctx *ctx, int val);
6141 int isl_options_get_schedule_split_scaled(
6143 int isl_options_set_schedule_algorithm(
6144 isl_ctx *ctx, int val);
6145 int isl_options_get_schedule_algorithm(
6147 int isl_options_set_schedule_separate_components(
6148 isl_ctx *ctx, int val);
6149 int isl_options_get_schedule_separate_components(
6154 =item * schedule_max_coefficient
6156 This option enforces that the coefficients for variable and parameter
6157 dimensions in the calculated schedule are not larger than the specified value.
6158 This option can significantly increase the speed of the scheduling calculation
6159 and may also prevent fusing of unrelated dimensions. A value of -1 means that
6160 this option does not introduce bounds on the variable or parameter
6163 =item * schedule_max_constant_term
6165 This option enforces that the constant coefficients in the calculated schedule
6166 are not larger than the maximal constant term. This option can significantly
6167 increase the speed of the scheduling calculation and may also prevent fusing of
6168 unrelated dimensions. A value of -1 means that this option does not introduce
6169 bounds on the constant coefficients.
6171 =item * schedule_fuse
6173 This option controls the level of fusion.
6174 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6175 resulting schedule will be distributed as much as possible.
6176 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6177 try to fuse loops in the resulting schedule.
6179 =item * schedule_maximize_band_depth
6181 If this option is set, we do not split bands at the point
6182 where we detect splitting is necessary. Instead, we
6183 backtrack and split bands as early as possible. This
6184 reduces the number of splits and maximizes the width of
6185 the bands. Wider bands give more possibilities for tiling.
6186 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6187 then bands will be split as early as possible, even if there is no need.
6188 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6190 =item * schedule_outer_coincidence
6192 If this option is set, then we try to construct schedules
6193 where the outermost scheduling dimension in each band
6194 satisfies the coincidence constraints.
6196 =item * schedule_split_scaled
6198 If this option is set, then we try to construct schedules in which the
6199 constant term is split off from the linear part if the linear parts of
6200 the scheduling rows for all nodes in the graphs have a common non-trivial
6202 The constant term is then placed in a separate band and the linear
6205 =item * schedule_algorithm
6207 Selects the scheduling algorithm to be used.
6208 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6209 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6211 =item * schedule_separate_components
6213 If at any point the dependence graph contains any (weakly connected) components,
6214 then these components are scheduled separately.
6215 If this option is not set, then some iterations of the domains
6216 in these components may be scheduled together.
6217 If this option is set, then the components are given consecutive
6222 =head2 AST Generation
6224 This section describes the C<isl> functionality for generating
6225 ASTs that visit all the elements
6226 in a domain in an order specified by a schedule.
6227 In particular, given a C<isl_union_map>, an AST is generated
6228 that visits all the elements in the domain of the C<isl_union_map>
6229 according to the lexicographic order of the corresponding image
6230 element(s). If the range of the C<isl_union_map> consists of
6231 elements in more than one space, then each of these spaces is handled
6232 separately in an arbitrary order.
6233 It should be noted that the image elements only specify the I<order>
6234 in which the corresponding domain elements should be visited.
6235 No direct relation between the image elements and the loop iterators
6236 in the generated AST should be assumed.
6238 Each AST is generated within a build. The initial build
6239 simply specifies the constraints on the parameters (if any)
6240 and can be created, inspected, copied and freed using the following functions.
6242 #include <isl/ast_build.h>
6243 __isl_give isl_ast_build *isl_ast_build_from_context(
6244 __isl_take isl_set *set);
6245 isl_ctx *isl_ast_build_get_ctx(
6246 __isl_keep isl_ast_build *build);
6247 __isl_give isl_ast_build *isl_ast_build_copy(
6248 __isl_keep isl_ast_build *build);
6249 __isl_null isl_ast_build *isl_ast_build_free(
6250 __isl_take isl_ast_build *build);
6252 The C<set> argument is usually a parameter set with zero or more parameters.
6253 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6254 and L</"Fine-grained Control over AST Generation">.
6255 Finally, the AST itself can be constructed using the following
6258 #include <isl/ast_build.h>
6259 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6260 __isl_keep isl_ast_build *build,
6261 __isl_take isl_union_map *schedule);
6263 =head3 Inspecting the AST
6265 The basic properties of an AST node can be obtained as follows.
6267 #include <isl/ast.h>
6268 isl_ctx *isl_ast_node_get_ctx(
6269 __isl_keep isl_ast_node *node);
6270 enum isl_ast_node_type isl_ast_node_get_type(
6271 __isl_keep isl_ast_node *node);
6273 The type of an AST node is one of
6274 C<isl_ast_node_for>,
6276 C<isl_ast_node_block> or
6277 C<isl_ast_node_user>.
6278 An C<isl_ast_node_for> represents a for node.
6279 An C<isl_ast_node_if> represents an if node.
6280 An C<isl_ast_node_block> represents a compound node.
6281 An C<isl_ast_node_user> represents an expression statement.
6282 An expression statement typically corresponds to a domain element, i.e.,
6283 one of the elements that is visited by the AST.
6285 Each type of node has its own additional properties.
6287 #include <isl/ast.h>
6288 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6289 __isl_keep isl_ast_node *node);
6290 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6291 __isl_keep isl_ast_node *node);
6292 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6293 __isl_keep isl_ast_node *node);
6294 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6295 __isl_keep isl_ast_node *node);
6296 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6297 __isl_keep isl_ast_node *node);
6298 int isl_ast_node_for_is_degenerate(
6299 __isl_keep isl_ast_node *node);
6301 An C<isl_ast_for> is considered degenerate if it is known to execute
6304 #include <isl/ast.h>
6305 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6306 __isl_keep isl_ast_node *node);
6307 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6308 __isl_keep isl_ast_node *node);
6309 int isl_ast_node_if_has_else(
6310 __isl_keep isl_ast_node *node);
6311 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6312 __isl_keep isl_ast_node *node);
6314 __isl_give isl_ast_node_list *
6315 isl_ast_node_block_get_children(
6316 __isl_keep isl_ast_node *node);
6318 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6319 __isl_keep isl_ast_node *node);
6321 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6322 the following functions.
6324 #include <isl/ast.h>
6325 isl_ctx *isl_ast_expr_get_ctx(
6326 __isl_keep isl_ast_expr *expr);
6327 enum isl_ast_expr_type isl_ast_expr_get_type(
6328 __isl_keep isl_ast_expr *expr);
6330 The type of an AST expression is one of
6332 C<isl_ast_expr_id> or
6333 C<isl_ast_expr_int>.
6334 An C<isl_ast_expr_op> represents the result of an operation.
6335 An C<isl_ast_expr_id> represents an identifier.
6336 An C<isl_ast_expr_int> represents an integer value.
6338 Each type of expression has its own additional properties.
6340 #include <isl/ast.h>
6341 enum isl_ast_op_type isl_ast_expr_get_op_type(
6342 __isl_keep isl_ast_expr *expr);
6343 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6344 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6345 __isl_keep isl_ast_expr *expr, int pos);
6346 int isl_ast_node_foreach_ast_op_type(
6347 __isl_keep isl_ast_node *node,
6348 int (*fn)(enum isl_ast_op_type type, void *user),
6351 C<isl_ast_expr_get_op_type> returns the type of the operation
6352 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6353 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6355 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6356 C<isl_ast_op_type> that appears in C<node>.
6357 The operation type is one of the following.
6361 =item C<isl_ast_op_and>
6363 Logical I<and> of two arguments.
6364 Both arguments can be evaluated.
6366 =item C<isl_ast_op_and_then>
6368 Logical I<and> of two arguments.
6369 The second argument can only be evaluated if the first evaluates to true.
6371 =item C<isl_ast_op_or>
6373 Logical I<or> of two arguments.
6374 Both arguments can be evaluated.
6376 =item C<isl_ast_op_or_else>
6378 Logical I<or> of two arguments.
6379 The second argument can only be evaluated if the first evaluates to false.
6381 =item C<isl_ast_op_max>
6383 Maximum of two or more arguments.
6385 =item C<isl_ast_op_min>
6387 Minimum of two or more arguments.
6389 =item C<isl_ast_op_minus>
6393 =item C<isl_ast_op_add>
6395 Sum of two arguments.
6397 =item C<isl_ast_op_sub>
6399 Difference of two arguments.
6401 =item C<isl_ast_op_mul>
6403 Product of two arguments.
6405 =item C<isl_ast_op_div>
6407 Exact division. That is, the result is known to be an integer.
6409 =item C<isl_ast_op_fdiv_q>
6411 Result of integer division, rounded towards negative
6414 =item C<isl_ast_op_pdiv_q>
6416 Result of integer division, where dividend is known to be non-negative.
6418 =item C<isl_ast_op_pdiv_r>
6420 Remainder of integer division, where dividend is known to be non-negative.
6422 =item C<isl_ast_op_cond>
6424 Conditional operator defined on three arguments.
6425 If the first argument evaluates to true, then the result
6426 is equal to the second argument. Otherwise, the result
6427 is equal to the third argument.
6428 The second and third argument may only be evaluated if
6429 the first argument evaluates to true and false, respectively.
6430 Corresponds to C<a ? b : c> in C.
6432 =item C<isl_ast_op_select>
6434 Conditional operator defined on three arguments.
6435 If the first argument evaluates to true, then the result
6436 is equal to the second argument. Otherwise, the result
6437 is equal to the third argument.
6438 The second and third argument may be evaluated independently
6439 of the value of the first argument.
6440 Corresponds to C<a * b + (1 - a) * c> in C.
6442 =item C<isl_ast_op_eq>
6446 =item C<isl_ast_op_le>
6448 Less than or equal relation.
6450 =item C<isl_ast_op_lt>
6454 =item C<isl_ast_op_ge>
6456 Greater than or equal relation.
6458 =item C<isl_ast_op_gt>
6460 Greater than relation.
6462 =item C<isl_ast_op_call>
6465 The number of arguments of the C<isl_ast_expr> is one more than
6466 the number of arguments in the function call, the first argument
6467 representing the function being called.
6469 =item C<isl_ast_op_access>
6472 The number of arguments of the C<isl_ast_expr> is one more than
6473 the number of index expressions in the array access, the first argument
6474 representing the array being accessed.
6476 =item C<isl_ast_op_member>
6479 This operation has two arguments, a structure and the name of
6480 the member of the structure being accessed.
6484 #include <isl/ast.h>
6485 __isl_give isl_id *isl_ast_expr_get_id(
6486 __isl_keep isl_ast_expr *expr);
6488 Return the identifier represented by the AST expression.
6490 #include <isl/ast.h>
6491 __isl_give isl_val *isl_ast_expr_get_val(
6492 __isl_keep isl_ast_expr *expr);
6494 Return the integer represented by the AST expression.
6496 =head3 Properties of ASTs
6498 #include <isl/ast.h>
6499 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6500 __isl_keep isl_ast_expr *expr2);
6502 Check if two C<isl_ast_expr>s are equal to each other.
6504 =head3 Manipulating and printing the AST
6506 AST nodes can be copied and freed using the following functions.
6508 #include <isl/ast.h>
6509 __isl_give isl_ast_node *isl_ast_node_copy(
6510 __isl_keep isl_ast_node *node);
6511 __isl_null isl_ast_node *isl_ast_node_free(
6512 __isl_take isl_ast_node *node);
6514 AST expressions can be copied and freed using the following functions.
6516 #include <isl/ast.h>
6517 __isl_give isl_ast_expr *isl_ast_expr_copy(
6518 __isl_keep isl_ast_expr *expr);
6519 __isl_null isl_ast_expr *isl_ast_expr_free(
6520 __isl_take isl_ast_expr *expr);
6522 New AST expressions can be created either directly or within
6523 the context of an C<isl_ast_build>.
6525 #include <isl/ast.h>
6526 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6527 __isl_take isl_val *v);
6528 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6529 __isl_take isl_id *id);
6530 __isl_give isl_ast_expr *isl_ast_expr_neg(
6531 __isl_take isl_ast_expr *expr);
6532 __isl_give isl_ast_expr *isl_ast_expr_add(
6533 __isl_take isl_ast_expr *expr1,
6534 __isl_take isl_ast_expr *expr2);
6535 __isl_give isl_ast_expr *isl_ast_expr_sub(
6536 __isl_take isl_ast_expr *expr1,
6537 __isl_take isl_ast_expr *expr2);
6538 __isl_give isl_ast_expr *isl_ast_expr_mul(
6539 __isl_take isl_ast_expr *expr1,
6540 __isl_take isl_ast_expr *expr2);
6541 __isl_give isl_ast_expr *isl_ast_expr_div(
6542 __isl_take isl_ast_expr *expr1,
6543 __isl_take isl_ast_expr *expr2);
6544 __isl_give isl_ast_expr *isl_ast_expr_and(
6545 __isl_take isl_ast_expr *expr1,
6546 __isl_take isl_ast_expr *expr2)
6547 __isl_give isl_ast_expr *isl_ast_expr_or(
6548 __isl_take isl_ast_expr *expr1,
6549 __isl_take isl_ast_expr *expr2)
6550 __isl_give isl_ast_expr *isl_ast_expr_access(
6551 __isl_take isl_ast_expr *array,
6552 __isl_take isl_ast_expr_list *indices);
6554 #include <isl/ast_build.h>
6555 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6556 __isl_keep isl_ast_build *build,
6557 __isl_take isl_pw_aff *pa);
6558 __isl_give isl_ast_expr *
6559 isl_ast_build_access_from_pw_multi_aff(
6560 __isl_keep isl_ast_build *build,
6561 __isl_take isl_pw_multi_aff *pma);
6562 __isl_give isl_ast_expr *
6563 isl_ast_build_access_from_multi_pw_aff(
6564 __isl_keep isl_ast_build *build,
6565 __isl_take isl_multi_pw_aff *mpa);
6566 __isl_give isl_ast_expr *
6567 isl_ast_build_call_from_pw_multi_aff(
6568 __isl_keep isl_ast_build *build,
6569 __isl_take isl_pw_multi_aff *pma);
6570 __isl_give isl_ast_expr *
6571 isl_ast_build_call_from_multi_pw_aff(
6572 __isl_keep isl_ast_build *build,
6573 __isl_take isl_multi_pw_aff *mpa);
6575 The domains of C<pa>, C<mpa> and C<pma> should correspond
6576 to the schedule space of C<build>.
6577 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6578 the function being called.
6579 If the accessed space is a nested relation, then it is taken
6580 to represent an access of the member specified by the range
6581 of this nested relation of the structure specified by the domain
6582 of the nested relation.
6584 The following functions can be used to modify an C<isl_ast_expr>.
6586 #include <isl/ast.h>
6587 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6588 __isl_take isl_ast_expr *expr, int pos,
6589 __isl_take isl_ast_expr *arg);
6591 Replace the argument of C<expr> at position C<pos> by C<arg>.
6593 #include <isl/ast.h>
6594 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6595 __isl_take isl_ast_expr *expr,
6596 __isl_take isl_id_to_ast_expr *id2expr);
6598 The function C<isl_ast_expr_substitute_ids> replaces the
6599 subexpressions of C<expr> of type C<isl_ast_expr_id>
6600 by the corresponding expression in C<id2expr>, if there is any.
6603 User specified data can be attached to an C<isl_ast_node> and obtained
6604 from the same C<isl_ast_node> using the following functions.
6606 #include <isl/ast.h>
6607 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6608 __isl_take isl_ast_node *node,
6609 __isl_take isl_id *annotation);
6610 __isl_give isl_id *isl_ast_node_get_annotation(
6611 __isl_keep isl_ast_node *node);
6613 Basic printing can be performed using the following functions.
6615 #include <isl/ast.h>
6616 __isl_give isl_printer *isl_printer_print_ast_expr(
6617 __isl_take isl_printer *p,
6618 __isl_keep isl_ast_expr *expr);
6619 __isl_give isl_printer *isl_printer_print_ast_node(
6620 __isl_take isl_printer *p,
6621 __isl_keep isl_ast_node *node);
6623 More advanced printing can be performed using the following functions.
6625 #include <isl/ast.h>
6626 __isl_give isl_printer *isl_ast_op_type_print_macro(
6627 enum isl_ast_op_type type,
6628 __isl_take isl_printer *p);
6629 __isl_give isl_printer *isl_ast_node_print_macros(
6630 __isl_keep isl_ast_node *node,
6631 __isl_take isl_printer *p);
6632 __isl_give isl_printer *isl_ast_node_print(
6633 __isl_keep isl_ast_node *node,
6634 __isl_take isl_printer *p,
6635 __isl_take isl_ast_print_options *options);
6636 __isl_give isl_printer *isl_ast_node_for_print(
6637 __isl_keep isl_ast_node *node,
6638 __isl_take isl_printer *p,
6639 __isl_take isl_ast_print_options *options);
6640 __isl_give isl_printer *isl_ast_node_if_print(
6641 __isl_keep isl_ast_node *node,
6642 __isl_take isl_printer *p,
6643 __isl_take isl_ast_print_options *options);
6645 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6646 C<isl> may print out an AST that makes use of macros such
6647 as C<floord>, C<min> and C<max>.
6648 C<isl_ast_op_type_print_macro> prints out the macro
6649 corresponding to a specific C<isl_ast_op_type>.
6650 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6651 for expressions where these macros would be used and prints
6652 out the required macro definitions.
6653 Essentially, C<isl_ast_node_print_macros> calls
6654 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6655 as function argument.
6656 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6657 C<isl_ast_node_if_print> print an C<isl_ast_node>
6658 in C<ISL_FORMAT_C>, but allow for some extra control
6659 through an C<isl_ast_print_options> object.
6660 This object can be created using the following functions.
6662 #include <isl/ast.h>
6663 __isl_give isl_ast_print_options *
6664 isl_ast_print_options_alloc(isl_ctx *ctx);
6665 __isl_give isl_ast_print_options *
6666 isl_ast_print_options_copy(
6667 __isl_keep isl_ast_print_options *options);
6668 __isl_null isl_ast_print_options *
6669 isl_ast_print_options_free(
6670 __isl_take isl_ast_print_options *options);
6672 __isl_give isl_ast_print_options *
6673 isl_ast_print_options_set_print_user(
6674 __isl_take isl_ast_print_options *options,
6675 __isl_give isl_printer *(*print_user)(
6676 __isl_take isl_printer *p,
6677 __isl_take isl_ast_print_options *options,
6678 __isl_keep isl_ast_node *node, void *user),
6680 __isl_give isl_ast_print_options *
6681 isl_ast_print_options_set_print_for(
6682 __isl_take isl_ast_print_options *options,
6683 __isl_give isl_printer *(*print_for)(
6684 __isl_take isl_printer *p,
6685 __isl_take isl_ast_print_options *options,
6686 __isl_keep isl_ast_node *node, void *user),
6689 The callback set by C<isl_ast_print_options_set_print_user>
6690 is called whenever a node of type C<isl_ast_node_user> needs to
6692 The callback set by C<isl_ast_print_options_set_print_for>
6693 is called whenever a node of type C<isl_ast_node_for> needs to
6695 Note that C<isl_ast_node_for_print> will I<not> call the
6696 callback set by C<isl_ast_print_options_set_print_for> on the node
6697 on which C<isl_ast_node_for_print> is called, but only on nested
6698 nodes of type C<isl_ast_node_for>. It is therefore safe to
6699 call C<isl_ast_node_for_print> from within the callback set by
6700 C<isl_ast_print_options_set_print_for>.
6702 The following option determines the type to be used for iterators
6703 while printing the AST.
6705 int isl_options_set_ast_iterator_type(
6706 isl_ctx *ctx, const char *val);
6707 const char *isl_options_get_ast_iterator_type(
6712 #include <isl/ast_build.h>
6713 int isl_options_set_ast_build_atomic_upper_bound(
6714 isl_ctx *ctx, int val);
6715 int isl_options_get_ast_build_atomic_upper_bound(
6717 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6719 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6720 int isl_options_set_ast_build_exploit_nested_bounds(
6721 isl_ctx *ctx, int val);
6722 int isl_options_get_ast_build_exploit_nested_bounds(
6724 int isl_options_set_ast_build_group_coscheduled(
6725 isl_ctx *ctx, int val);
6726 int isl_options_get_ast_build_group_coscheduled(
6728 int isl_options_set_ast_build_scale_strides(
6729 isl_ctx *ctx, int val);
6730 int isl_options_get_ast_build_scale_strides(
6732 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6734 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6735 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6737 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6741 =item * ast_build_atomic_upper_bound
6743 Generate loop upper bounds that consist of the current loop iterator,
6744 an operator and an expression not involving the iterator.
6745 If this option is not set, then the current loop iterator may appear
6746 several times in the upper bound.
6747 For example, when this option is turned off, AST generation
6750 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6754 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6757 When the option is turned on, the following AST is generated
6759 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6762 =item * ast_build_prefer_pdiv
6764 If this option is turned off, then the AST generation will
6765 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6766 operators, but no C<isl_ast_op_pdiv_q> or
6767 C<isl_ast_op_pdiv_r> operators.
6768 If this options is turned on, then C<isl> will try to convert
6769 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6770 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6772 =item * ast_build_exploit_nested_bounds
6774 Simplify conditions based on bounds of nested for loops.
6775 In particular, remove conditions that are implied by the fact
6776 that one or more nested loops have at least one iteration,
6777 meaning that the upper bound is at least as large as the lower bound.
6778 For example, when this option is turned off, AST generation
6781 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6787 for (int c0 = 0; c0 <= N; c0 += 1)
6788 for (int c1 = 0; c1 <= M; c1 += 1)
6791 When the option is turned on, the following AST is generated
6793 for (int c0 = 0; c0 <= N; c0 += 1)
6794 for (int c1 = 0; c1 <= M; c1 += 1)
6797 =item * ast_build_group_coscheduled
6799 If two domain elements are assigned the same schedule point, then
6800 they may be executed in any order and they may even appear in different
6801 loops. If this options is set, then the AST generator will make
6802 sure that coscheduled domain elements do not appear in separate parts
6803 of the AST. This is useful in case of nested AST generation
6804 if the outer AST generation is given only part of a schedule
6805 and the inner AST generation should handle the domains that are
6806 coscheduled by this initial part of the schedule together.
6807 For example if an AST is generated for a schedule
6809 { A[i] -> [0]; B[i] -> [0] }
6811 then the C<isl_ast_build_set_create_leaf> callback described
6812 below may get called twice, once for each domain.
6813 Setting this option ensures that the callback is only called once
6814 on both domains together.
6816 =item * ast_build_separation_bounds
6818 This option specifies which bounds to use during separation.
6819 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6820 then all (possibly implicit) bounds on the current dimension will
6821 be used during separation.
6822 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6823 then only those bounds that are explicitly available will
6824 be used during separation.
6826 =item * ast_build_scale_strides
6828 This option specifies whether the AST generator is allowed
6829 to scale down iterators of strided loops.
6831 =item * ast_build_allow_else
6833 This option specifies whether the AST generator is allowed
6834 to construct if statements with else branches.
6836 =item * ast_build_allow_or
6838 This option specifies whether the AST generator is allowed
6839 to construct if conditions with disjunctions.
6843 =head3 Fine-grained Control over AST Generation
6845 Besides specifying the constraints on the parameters,
6846 an C<isl_ast_build> object can be used to control
6847 various aspects of the AST generation process.
6848 The most prominent way of control is through ``options'',
6849 which can be set using the following function.
6851 #include <isl/ast_build.h>
6852 __isl_give isl_ast_build *
6853 isl_ast_build_set_options(
6854 __isl_take isl_ast_build *control,
6855 __isl_take isl_union_map *options);
6857 The options are encoded in an <isl_union_map>.
6858 The domain of this union relation refers to the schedule domain,
6859 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6860 In the case of nested AST generation (see L</"Nested AST Generation">),
6861 the domain of C<options> should refer to the extra piece of the schedule.
6862 That is, it should be equal to the range of the wrapped relation in the
6863 range of the schedule.
6864 The range of the options can consist of elements in one or more spaces,
6865 the names of which determine the effect of the option.
6866 The values of the range typically also refer to the schedule dimension
6867 to which the option applies. In case of nested AST generation
6868 (see L</"Nested AST Generation">), these values refer to the position
6869 of the schedule dimension within the innermost AST generation.
6870 The constraints on the domain elements of
6871 the option should only refer to this dimension and earlier dimensions.
6872 We consider the following spaces.
6876 =item C<separation_class>
6878 This space is a wrapped relation between two one dimensional spaces.
6879 The input space represents the schedule dimension to which the option
6880 applies and the output space represents the separation class.
6881 While constructing a loop corresponding to the specified schedule
6882 dimension(s), the AST generator will try to generate separate loops
6883 for domain elements that are assigned different classes.
6884 If only some of the elements are assigned a class, then those elements
6885 that are not assigned any class will be treated as belonging to a class
6886 that is separate from the explicitly assigned classes.
6887 The typical use case for this option is to separate full tiles from
6889 The other options, described below, are applied after the separation
6892 As an example, consider the separation into full and partial tiles
6893 of a tiling of a triangular domain.
6894 Take, for example, the domain
6896 { A[i,j] : 0 <= i,j and i + j <= 100 }
6898 and a tiling into tiles of 10 by 10. The input to the AST generator
6899 is then the schedule
6901 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6904 Without any options, the following AST is generated
6906 for (int c0 = 0; c0 <= 10; c0 += 1)
6907 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6908 for (int c2 = 10 * c0;
6909 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6911 for (int c3 = 10 * c1;
6912 c3 <= min(10 * c1 + 9, -c2 + 100);
6916 Separation into full and partial tiles can be obtained by assigning
6917 a class, say C<0>, to the full tiles. The full tiles are represented by those
6918 values of the first and second schedule dimensions for which there are
6919 values of the third and fourth dimensions to cover an entire tile.
6920 That is, we need to specify the following option
6922 { [a,b,c,d] -> separation_class[[0]->[0]] :
6923 exists b': 0 <= 10a,10b' and
6924 10a+9+10b'+9 <= 100;
6925 [a,b,c,d] -> separation_class[[1]->[0]] :
6926 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6930 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6931 a >= 0 and b >= 0 and b <= 8 - a;
6932 [a, b, c, d] -> separation_class[[0] -> [0]] :
6935 With this option, the generated AST is as follows
6938 for (int c0 = 0; c0 <= 8; c0 += 1) {
6939 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6940 for (int c2 = 10 * c0;
6941 c2 <= 10 * c0 + 9; c2 += 1)
6942 for (int c3 = 10 * c1;
6943 c3 <= 10 * c1 + 9; c3 += 1)
6945 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6946 for (int c2 = 10 * c0;
6947 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6949 for (int c3 = 10 * c1;
6950 c3 <= min(-c2 + 100, 10 * c1 + 9);
6954 for (int c0 = 9; c0 <= 10; c0 += 1)
6955 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6956 for (int c2 = 10 * c0;
6957 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6959 for (int c3 = 10 * c1;
6960 c3 <= min(10 * c1 + 9, -c2 + 100);
6967 This is a single-dimensional space representing the schedule dimension(s)
6968 to which ``separation'' should be applied. Separation tries to split
6969 a loop into several pieces if this can avoid the generation of guards
6971 See also the C<atomic> option.
6975 This is a single-dimensional space representing the schedule dimension(s)
6976 for which the domains should be considered ``atomic''. That is, the
6977 AST generator will make sure that any given domain space will only appear
6978 in a single loop at the specified level.
6980 Consider the following schedule
6982 { a[i] -> [i] : 0 <= i < 10;
6983 b[i] -> [i+1] : 0 <= i < 10 }
6985 If the following option is specified
6987 { [i] -> separate[x] }
6989 then the following AST will be generated
6993 for (int c0 = 1; c0 <= 9; c0 += 1) {
7000 If, on the other hand, the following option is specified
7002 { [i] -> atomic[x] }
7004 then the following AST will be generated
7006 for (int c0 = 0; c0 <= 10; c0 += 1) {
7013 If neither C<atomic> nor C<separate> is specified, then the AST generator
7014 may produce either of these two results or some intermediate form.
7018 This is a single-dimensional space representing the schedule dimension(s)
7019 that should be I<completely> unrolled.
7020 To obtain a partial unrolling, the user should apply an additional
7021 strip-mining to the schedule and fully unroll the inner loop.
7025 Additional control is available through the following functions.
7027 #include <isl/ast_build.h>
7028 __isl_give isl_ast_build *
7029 isl_ast_build_set_iterators(
7030 __isl_take isl_ast_build *control,
7031 __isl_take isl_id_list *iterators);
7033 The function C<isl_ast_build_set_iterators> allows the user to
7034 specify a list of iterator C<isl_id>s to be used as iterators.
7035 If the input schedule is injective, then
7036 the number of elements in this list should be as large as the dimension
7037 of the schedule space, but no direct correspondence should be assumed
7038 between dimensions and elements.
7039 If the input schedule is not injective, then an additional number
7040 of C<isl_id>s equal to the largest dimension of the input domains
7042 If the number of provided C<isl_id>s is insufficient, then additional
7043 names are automatically generated.
7045 #include <isl/ast_build.h>
7046 __isl_give isl_ast_build *
7047 isl_ast_build_set_create_leaf(
7048 __isl_take isl_ast_build *control,
7049 __isl_give isl_ast_node *(*fn)(
7050 __isl_take isl_ast_build *build,
7051 void *user), void *user);
7054 C<isl_ast_build_set_create_leaf> function allows for the
7055 specification of a callback that should be called whenever the AST
7056 generator arrives at an element of the schedule domain.
7057 The callback should return an AST node that should be inserted
7058 at the corresponding position of the AST. The default action (when
7059 the callback is not set) is to continue generating parts of the AST to scan
7060 all the domain elements associated to the schedule domain element
7061 and to insert user nodes, ``calling'' the domain element, for each of them.
7062 The C<build> argument contains the current state of the C<isl_ast_build>.
7063 To ease nested AST generation (see L</"Nested AST Generation">),
7064 all control information that is
7065 specific to the current AST generation such as the options and
7066 the callbacks has been removed from this C<isl_ast_build>.
7067 The callback would typically return the result of a nested
7069 user defined node created using the following function.
7071 #include <isl/ast.h>
7072 __isl_give isl_ast_node *isl_ast_node_alloc_user(
7073 __isl_take isl_ast_expr *expr);
7075 #include <isl/ast_build.h>
7076 __isl_give isl_ast_build *
7077 isl_ast_build_set_at_each_domain(
7078 __isl_take isl_ast_build *build,
7079 __isl_give isl_ast_node *(*fn)(
7080 __isl_take isl_ast_node *node,
7081 __isl_keep isl_ast_build *build,
7082 void *user), void *user);
7083 __isl_give isl_ast_build *
7084 isl_ast_build_set_before_each_for(
7085 __isl_take isl_ast_build *build,
7086 __isl_give isl_id *(*fn)(
7087 __isl_keep isl_ast_build *build,
7088 void *user), void *user);
7089 __isl_give isl_ast_build *
7090 isl_ast_build_set_after_each_for(
7091 __isl_take isl_ast_build *build,
7092 __isl_give isl_ast_node *(*fn)(
7093 __isl_take isl_ast_node *node,
7094 __isl_keep isl_ast_build *build,
7095 void *user), void *user);
7097 The callback set by C<isl_ast_build_set_at_each_domain> will
7098 be called for each domain AST node.
7099 The callbacks set by C<isl_ast_build_set_before_each_for>
7100 and C<isl_ast_build_set_after_each_for> will be called
7101 for each for AST node. The first will be called in depth-first
7102 pre-order, while the second will be called in depth-first post-order.
7103 Since C<isl_ast_build_set_before_each_for> is called before the for
7104 node is actually constructed, it is only passed an C<isl_ast_build>.
7105 The returned C<isl_id> will be added as an annotation (using
7106 C<isl_ast_node_set_annotation>) to the constructed for node.
7107 In particular, if the user has also specified an C<after_each_for>
7108 callback, then the annotation can be retrieved from the node passed to
7109 that callback using C<isl_ast_node_get_annotation>.
7110 All callbacks should C<NULL> on failure.
7111 The given C<isl_ast_build> can be used to create new
7112 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
7113 or C<isl_ast_build_call_from_pw_multi_aff>.
7115 =head3 Nested AST Generation
7117 C<isl> allows the user to create an AST within the context
7118 of another AST. These nested ASTs are created using the
7119 same C<isl_ast_build_ast_from_schedule> function that is used to create the
7120 outer AST. The C<build> argument should be an C<isl_ast_build>
7121 passed to a callback set by
7122 C<isl_ast_build_set_create_leaf>.
7123 The space of the range of the C<schedule> argument should refer
7124 to this build. In particular, the space should be a wrapped
7125 relation and the domain of this wrapped relation should be the
7126 same as that of the range of the schedule returned by
7127 C<isl_ast_build_get_schedule> below.
7128 In practice, the new schedule is typically
7129 created by calling C<isl_union_map_range_product> on the old schedule
7130 and some extra piece of the schedule.
7131 The space of the schedule domain is also available from
7132 the C<isl_ast_build>.
7134 #include <isl/ast_build.h>
7135 __isl_give isl_union_map *isl_ast_build_get_schedule(
7136 __isl_keep isl_ast_build *build);
7137 __isl_give isl_space *isl_ast_build_get_schedule_space(
7138 __isl_keep isl_ast_build *build);
7139 __isl_give isl_ast_build *isl_ast_build_restrict(
7140 __isl_take isl_ast_build *build,
7141 __isl_take isl_set *set);
7143 The C<isl_ast_build_get_schedule> function returns a (partial)
7144 schedule for the domains elements for which part of the AST still needs to
7145 be generated in the current build.
7146 In particular, the domain elements are mapped to those iterations of the loops
7147 enclosing the current point of the AST generation inside which
7148 the domain elements are executed.
7149 No direct correspondence between
7150 the input schedule and this schedule should be assumed.
7151 The space obtained from C<isl_ast_build_get_schedule_space> can be used
7152 to create a set for C<isl_ast_build_restrict> to intersect
7153 with the current build. In particular, the set passed to
7154 C<isl_ast_build_restrict> can have additional parameters.
7155 The ids of the set dimensions in the space returned by
7156 C<isl_ast_build_get_schedule_space> correspond to the
7157 iterators of the already generated loops.
7158 The user should not rely on the ids of the output dimensions
7159 of the relations in the union relation returned by
7160 C<isl_ast_build_get_schedule> having any particular value.
7164 Although C<isl> is mainly meant to be used as a library,
7165 it also contains some basic applications that use some
7166 of the functionality of C<isl>.
7167 The input may be specified in either the L<isl format>
7168 or the L<PolyLib format>.
7170 =head2 C<isl_polyhedron_sample>
7172 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7173 an integer element of the polyhedron, if there is any.
7174 The first column in the output is the denominator and is always
7175 equal to 1. If the polyhedron contains no integer points,
7176 then a vector of length zero is printed.
7180 C<isl_pip> takes the same input as the C<example> program
7181 from the C<piplib> distribution, i.e., a set of constraints
7182 on the parameters, a line containing only -1 and finally a set
7183 of constraints on a parametric polyhedron.
7184 The coefficients of the parameters appear in the last columns
7185 (but before the final constant column).
7186 The output is the lexicographic minimum of the parametric polyhedron.
7187 As C<isl> currently does not have its own output format, the output
7188 is just a dump of the internal state.
7190 =head2 C<isl_polyhedron_minimize>
7192 C<isl_polyhedron_minimize> computes the minimum of some linear
7193 or affine objective function over the integer points in a polyhedron.
7194 If an affine objective function
7195 is given, then the constant should appear in the last column.
7197 =head2 C<isl_polytope_scan>
7199 Given a polytope, C<isl_polytope_scan> prints
7200 all integer points in the polytope.
7202 =head2 C<isl_codegen>
7204 Given a schedule, a context set and an options relation,
7205 C<isl_codegen> prints out an AST that scans the domain elements
7206 of the schedule in the order of their image(s) taking into account
7207 the constraints in the context set.