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.
3201 #include <isl/set.h>
3202 __isl_give isl_set *isl_set_product(
3203 __isl_take isl_set *set1,
3204 __isl_take isl_set *set2);
3206 #include <isl/map.h>
3207 __isl_give isl_basic_map *isl_basic_map_domain_product(
3208 __isl_take isl_basic_map *bmap1,
3209 __isl_take isl_basic_map *bmap2);
3210 __isl_give isl_basic_map *isl_basic_map_range_product(
3211 __isl_take isl_basic_map *bmap1,
3212 __isl_take isl_basic_map *bmap2);
3213 __isl_give isl_basic_map *isl_basic_map_product(
3214 __isl_take isl_basic_map *bmap1,
3215 __isl_take isl_basic_map *bmap2);
3216 __isl_give isl_map *isl_map_domain_product(
3217 __isl_take isl_map *map1,
3218 __isl_take isl_map *map2);
3219 __isl_give isl_map *isl_map_range_product(
3220 __isl_take isl_map *map1,
3221 __isl_take isl_map *map2);
3222 __isl_give isl_map *isl_map_product(
3223 __isl_take isl_map *map1,
3224 __isl_take isl_map *map2);
3226 #include <isl/union_set.h>
3227 __isl_give isl_union_set *isl_union_set_product(
3228 __isl_take isl_union_set *uset1,
3229 __isl_take isl_union_set *uset2);
3231 #include <isl/union_map.h>
3232 __isl_give isl_union_map *isl_union_map_domain_product(
3233 __isl_take isl_union_map *umap1,
3234 __isl_take isl_union_map *umap2);
3235 __isl_give isl_union_map *isl_union_map_range_product(
3236 __isl_take isl_union_map *umap1,
3237 __isl_take isl_union_map *umap2);
3238 __isl_give isl_union_map *isl_union_map_product(
3239 __isl_take isl_union_map *umap1,
3240 __isl_take isl_union_map *umap2);
3242 The above functions compute the cross product of the given
3243 sets or relations. The domains and ranges of the results
3244 are wrapped maps between domains and ranges of the inputs.
3245 To obtain a ``flat'' product, use the following functions
3248 __isl_give isl_basic_set *isl_basic_set_flat_product(
3249 __isl_take isl_basic_set *bset1,
3250 __isl_take isl_basic_set *bset2);
3251 __isl_give isl_set *isl_set_flat_product(
3252 __isl_take isl_set *set1,
3253 __isl_take isl_set *set2);
3254 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3255 __isl_take isl_basic_map *bmap1,
3256 __isl_take isl_basic_map *bmap2);
3257 __isl_give isl_map *isl_map_flat_domain_product(
3258 __isl_take isl_map *map1,
3259 __isl_take isl_map *map2);
3260 __isl_give isl_map *isl_map_flat_range_product(
3261 __isl_take isl_map *map1,
3262 __isl_take isl_map *map2);
3263 __isl_give isl_union_map *isl_union_map_flat_range_product(
3264 __isl_take isl_union_map *umap1,
3265 __isl_take isl_union_map *umap2);
3266 __isl_give isl_basic_map *isl_basic_map_flat_product(
3267 __isl_take isl_basic_map *bmap1,
3268 __isl_take isl_basic_map *bmap2);
3269 __isl_give isl_map *isl_map_flat_product(
3270 __isl_take isl_map *map1,
3271 __isl_take isl_map *map2);
3273 #include <isl/space.h>
3274 __isl_give isl_space *isl_space_domain_factor_domain(
3275 __isl_take isl_space *space);
3276 __isl_give isl_space *isl_space_range_factor_domain(
3277 __isl_take isl_space *space);
3278 __isl_give isl_space *isl_space_range_factor_range(
3279 __isl_take isl_space *space);
3281 The functions C<isl_space_range_factor_domain> and
3282 C<isl_space_range_factor_range> extract the two arguments from
3283 the result of a call to C<isl_space_range_product>.
3285 The arguments of a call to C<isl_map_range_product> can be extracted
3286 from the result using the following two functions.
3288 #include <isl/map.h>
3289 __isl_give isl_map *isl_map_range_factor_domain(
3290 __isl_take isl_map *map);
3291 __isl_give isl_map *isl_map_range_factor_range(
3292 __isl_take isl_map *map);
3294 =item * Simplification
3296 __isl_give isl_basic_set *isl_basic_set_gist(
3297 __isl_take isl_basic_set *bset,
3298 __isl_take isl_basic_set *context);
3299 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3300 __isl_take isl_set *context);
3301 __isl_give isl_set *isl_set_gist_params(
3302 __isl_take isl_set *set,
3303 __isl_take isl_set *context);
3304 __isl_give isl_union_set *isl_union_set_gist(
3305 __isl_take isl_union_set *uset,
3306 __isl_take isl_union_set *context);
3307 __isl_give isl_union_set *isl_union_set_gist_params(
3308 __isl_take isl_union_set *uset,
3309 __isl_take isl_set *set);
3310 __isl_give isl_basic_map *isl_basic_map_gist(
3311 __isl_take isl_basic_map *bmap,
3312 __isl_take isl_basic_map *context);
3313 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3314 __isl_take isl_map *context);
3315 __isl_give isl_map *isl_map_gist_params(
3316 __isl_take isl_map *map,
3317 __isl_take isl_set *context);
3318 __isl_give isl_map *isl_map_gist_domain(
3319 __isl_take isl_map *map,
3320 __isl_take isl_set *context);
3321 __isl_give isl_map *isl_map_gist_range(
3322 __isl_take isl_map *map,
3323 __isl_take isl_set *context);
3324 __isl_give isl_union_map *isl_union_map_gist(
3325 __isl_take isl_union_map *umap,
3326 __isl_take isl_union_map *context);
3327 __isl_give isl_union_map *isl_union_map_gist_params(
3328 __isl_take isl_union_map *umap,
3329 __isl_take isl_set *set);
3330 __isl_give isl_union_map *isl_union_map_gist_domain(
3331 __isl_take isl_union_map *umap,
3332 __isl_take isl_union_set *uset);
3333 __isl_give isl_union_map *isl_union_map_gist_range(
3334 __isl_take isl_union_map *umap,
3335 __isl_take isl_union_set *uset);
3337 The gist operation returns a set or relation that has the
3338 same intersection with the context as the input set or relation.
3339 Any implicit equality in the intersection is made explicit in the result,
3340 while all inequalities that are redundant with respect to the intersection
3342 In case of union sets and relations, the gist operation is performed
3347 =head3 Lexicographic Optimization
3349 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3350 the following functions
3351 compute a set that contains the lexicographic minimum or maximum
3352 of the elements in C<set> (or C<bset>) for those values of the parameters
3353 that satisfy C<dom>.
3354 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3355 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3357 In other words, the union of the parameter values
3358 for which the result is non-empty and of C<*empty>
3361 __isl_give isl_set *isl_basic_set_partial_lexmin(
3362 __isl_take isl_basic_set *bset,
3363 __isl_take isl_basic_set *dom,
3364 __isl_give isl_set **empty);
3365 __isl_give isl_set *isl_basic_set_partial_lexmax(
3366 __isl_take isl_basic_set *bset,
3367 __isl_take isl_basic_set *dom,
3368 __isl_give isl_set **empty);
3369 __isl_give isl_set *isl_set_partial_lexmin(
3370 __isl_take isl_set *set, __isl_take isl_set *dom,
3371 __isl_give isl_set **empty);
3372 __isl_give isl_set *isl_set_partial_lexmax(
3373 __isl_take isl_set *set, __isl_take isl_set *dom,
3374 __isl_give isl_set **empty);
3376 Given a (basic) set C<set> (or C<bset>), the following functions simply
3377 return a set containing the lexicographic minimum or maximum
3378 of the elements in C<set> (or C<bset>).
3379 In case of union sets, the optimum is computed per space.
3381 __isl_give isl_set *isl_basic_set_lexmin(
3382 __isl_take isl_basic_set *bset);
3383 __isl_give isl_set *isl_basic_set_lexmax(
3384 __isl_take isl_basic_set *bset);
3385 __isl_give isl_set *isl_set_lexmin(
3386 __isl_take isl_set *set);
3387 __isl_give isl_set *isl_set_lexmax(
3388 __isl_take isl_set *set);
3389 __isl_give isl_union_set *isl_union_set_lexmin(
3390 __isl_take isl_union_set *uset);
3391 __isl_give isl_union_set *isl_union_set_lexmax(
3392 __isl_take isl_union_set *uset);
3394 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3395 the following functions
3396 compute a relation that maps each element of C<dom>
3397 to the single lexicographic minimum or maximum
3398 of the elements that are associated to that same
3399 element in C<map> (or C<bmap>).
3400 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3401 that contains the elements in C<dom> that do not map
3402 to any elements in C<map> (or C<bmap>).
3403 In other words, the union of the domain of the result and of C<*empty>
3406 __isl_give isl_map *isl_basic_map_partial_lexmax(
3407 __isl_take isl_basic_map *bmap,
3408 __isl_take isl_basic_set *dom,
3409 __isl_give isl_set **empty);
3410 __isl_give isl_map *isl_basic_map_partial_lexmin(
3411 __isl_take isl_basic_map *bmap,
3412 __isl_take isl_basic_set *dom,
3413 __isl_give isl_set **empty);
3414 __isl_give isl_map *isl_map_partial_lexmax(
3415 __isl_take isl_map *map, __isl_take isl_set *dom,
3416 __isl_give isl_set **empty);
3417 __isl_give isl_map *isl_map_partial_lexmin(
3418 __isl_take isl_map *map, __isl_take isl_set *dom,
3419 __isl_give isl_set **empty);
3421 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3422 return a map mapping each element in the domain of
3423 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3424 of all elements associated to that element.
3425 In case of union relations, the optimum is computed per space.
3427 __isl_give isl_map *isl_basic_map_lexmin(
3428 __isl_take isl_basic_map *bmap);
3429 __isl_give isl_map *isl_basic_map_lexmax(
3430 __isl_take isl_basic_map *bmap);
3431 __isl_give isl_map *isl_map_lexmin(
3432 __isl_take isl_map *map);
3433 __isl_give isl_map *isl_map_lexmax(
3434 __isl_take isl_map *map);
3435 __isl_give isl_union_map *isl_union_map_lexmin(
3436 __isl_take isl_union_map *umap);
3437 __isl_give isl_union_map *isl_union_map_lexmax(
3438 __isl_take isl_union_map *umap);
3440 The following functions return their result in the form of
3441 a piecewise multi-affine expression
3442 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3443 but are otherwise equivalent to the corresponding functions
3444 returning a basic set or relation.
3446 __isl_give isl_pw_multi_aff *
3447 isl_basic_map_lexmin_pw_multi_aff(
3448 __isl_take isl_basic_map *bmap);
3449 __isl_give isl_pw_multi_aff *
3450 isl_basic_set_partial_lexmin_pw_multi_aff(
3451 __isl_take isl_basic_set *bset,
3452 __isl_take isl_basic_set *dom,
3453 __isl_give isl_set **empty);
3454 __isl_give isl_pw_multi_aff *
3455 isl_basic_set_partial_lexmax_pw_multi_aff(
3456 __isl_take isl_basic_set *bset,
3457 __isl_take isl_basic_set *dom,
3458 __isl_give isl_set **empty);
3459 __isl_give isl_pw_multi_aff *
3460 isl_basic_map_partial_lexmin_pw_multi_aff(
3461 __isl_take isl_basic_map *bmap,
3462 __isl_take isl_basic_set *dom,
3463 __isl_give isl_set **empty);
3464 __isl_give isl_pw_multi_aff *
3465 isl_basic_map_partial_lexmax_pw_multi_aff(
3466 __isl_take isl_basic_map *bmap,
3467 __isl_take isl_basic_set *dom,
3468 __isl_give isl_set **empty);
3469 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3470 __isl_take isl_set *set);
3471 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3472 __isl_take isl_set *set);
3473 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3474 __isl_take isl_map *map);
3475 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3476 __isl_take isl_map *map);
3480 Lists are defined over several element types, including
3481 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3482 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3483 Here we take lists of C<isl_set>s as an example.
3484 Lists can be created, copied, modified and freed using the following functions.
3486 #include <isl/list.h>
3487 __isl_give isl_set_list *isl_set_list_from_set(
3488 __isl_take isl_set *el);
3489 __isl_give isl_set_list *isl_set_list_alloc(
3490 isl_ctx *ctx, int n);
3491 __isl_give isl_set_list *isl_set_list_copy(
3492 __isl_keep isl_set_list *list);
3493 __isl_give isl_set_list *isl_set_list_insert(
3494 __isl_take isl_set_list *list, unsigned pos,
3495 __isl_take isl_set *el);
3496 __isl_give isl_set_list *isl_set_list_add(
3497 __isl_take isl_set_list *list,
3498 __isl_take isl_set *el);
3499 __isl_give isl_set_list *isl_set_list_drop(
3500 __isl_take isl_set_list *list,
3501 unsigned first, unsigned n);
3502 __isl_give isl_set_list *isl_set_list_set_set(
3503 __isl_take isl_set_list *list, int index,
3504 __isl_take isl_set *set);
3505 __isl_give isl_set_list *isl_set_list_concat(
3506 __isl_take isl_set_list *list1,
3507 __isl_take isl_set_list *list2);
3508 __isl_give isl_set_list *isl_set_list_sort(
3509 __isl_take isl_set_list *list,
3510 int (*cmp)(__isl_keep isl_set *a,
3511 __isl_keep isl_set *b, void *user),
3513 __isl_null isl_set_list *isl_set_list_free(
3514 __isl_take isl_set_list *list);
3516 C<isl_set_list_alloc> creates an empty list with a capacity for
3517 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3520 Lists can be inspected using the following functions.
3522 #include <isl/list.h>
3523 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3524 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3525 __isl_give isl_set *isl_set_list_get_set(
3526 __isl_keep isl_set_list *list, int index);
3527 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3528 int (*fn)(__isl_take isl_set *el, void *user),
3530 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3531 int (*follows)(__isl_keep isl_set *a,
3532 __isl_keep isl_set *b, void *user),
3534 int (*fn)(__isl_take isl_set *el, void *user),
3537 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3538 strongly connected components of the graph with as vertices the elements
3539 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3540 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3541 should return C<-1> on error.
3543 Lists can be printed using
3545 #include <isl/list.h>
3546 __isl_give isl_printer *isl_printer_print_set_list(
3547 __isl_take isl_printer *p,
3548 __isl_keep isl_set_list *list);
3550 =head2 Associative arrays
3552 Associative arrays map isl objects of a specific type to isl objects
3553 of some (other) specific type. They are defined for several pairs
3554 of types, including (C<isl_map>, C<isl_basic_set>),
3555 (C<isl_id>, C<isl_ast_expr>) and.
3556 (C<isl_id>, C<isl_pw_aff>).
3557 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3560 Associative arrays can be created, copied and freed using
3561 the following functions.
3563 #include <isl/id_to_ast_expr.h>
3564 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3565 isl_ctx *ctx, int min_size);
3566 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3567 __isl_keep id_to_ast_expr *id2expr);
3568 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
3569 __isl_take id_to_ast_expr *id2expr);
3571 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3572 to specify the expected size of the associative array.
3573 The associative array will be grown automatically as needed.
3575 Associative arrays can be inspected using the following functions.
3577 #include <isl/id_to_ast_expr.h>
3578 isl_ctx *isl_id_to_ast_expr_get_ctx(
3579 __isl_keep id_to_ast_expr *id2expr);
3580 int isl_id_to_ast_expr_has(
3581 __isl_keep id_to_ast_expr *id2expr,
3582 __isl_keep isl_id *key);
3583 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3584 __isl_keep id_to_ast_expr *id2expr,
3585 __isl_take isl_id *key);
3586 int isl_id_to_ast_expr_foreach(
3587 __isl_keep id_to_ast_expr *id2expr,
3588 int (*fn)(__isl_take isl_id *key,
3589 __isl_take isl_ast_expr *val, void *user),
3592 They can be modified using the following function.
3594 #include <isl/id_to_ast_expr.h>
3595 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3596 __isl_take id_to_ast_expr *id2expr,
3597 __isl_take isl_id *key,
3598 __isl_take isl_ast_expr *val);
3599 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
3600 __isl_take id_to_ast_expr *id2expr,
3601 __isl_take isl_id *key);
3603 Associative arrays can be printed using the following function.
3605 #include <isl/id_to_ast_expr.h>
3606 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3607 __isl_take isl_printer *p,
3608 __isl_keep id_to_ast_expr *id2expr);
3610 =head2 Multiple Values
3612 An C<isl_multi_val> object represents a sequence of zero or more values,
3613 living in a set space.
3615 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3616 using the following function
3618 #include <isl/val.h>
3619 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3620 __isl_take isl_space *space,
3621 __isl_take isl_val_list *list);
3623 The zero multiple value (with value zero for each set dimension)
3624 can be created using the following function.
3626 #include <isl/val.h>
3627 __isl_give isl_multi_val *isl_multi_val_zero(
3628 __isl_take isl_space *space);
3630 Multiple values can be copied and freed using
3632 #include <isl/val.h>
3633 __isl_give isl_multi_val *isl_multi_val_copy(
3634 __isl_keep isl_multi_val *mv);
3635 __isl_null isl_multi_val *isl_multi_val_free(
3636 __isl_take isl_multi_val *mv);
3638 They can be inspected using
3640 #include <isl/val.h>
3641 isl_ctx *isl_multi_val_get_ctx(
3642 __isl_keep isl_multi_val *mv);
3643 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3644 enum isl_dim_type type);
3645 __isl_give isl_val *isl_multi_val_get_val(
3646 __isl_keep isl_multi_val *mv, int pos);
3647 int isl_multi_val_find_dim_by_id(
3648 __isl_keep isl_multi_val *mv,
3649 enum isl_dim_type type, __isl_keep isl_id *id);
3650 __isl_give isl_id *isl_multi_val_get_dim_id(
3651 __isl_keep isl_multi_val *mv,
3652 enum isl_dim_type type, unsigned pos);
3653 const char *isl_multi_val_get_tuple_name(
3654 __isl_keep isl_multi_val *mv,
3655 enum isl_dim_type type);
3656 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3657 enum isl_dim_type type);
3658 __isl_give isl_id *isl_multi_val_get_tuple_id(
3659 __isl_keep isl_multi_val *mv,
3660 enum isl_dim_type type);
3661 int isl_multi_val_range_is_wrapping(
3662 __isl_keep isl_multi_val *mv);
3664 They can be modified using
3666 #include <isl/val.h>
3667 __isl_give isl_multi_val *isl_multi_val_set_val(
3668 __isl_take isl_multi_val *mv, int pos,
3669 __isl_take isl_val *val);
3670 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3671 __isl_take isl_multi_val *mv,
3672 enum isl_dim_type type, unsigned pos, const char *s);
3673 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3674 __isl_take isl_multi_val *mv,
3675 enum isl_dim_type type, unsigned pos,
3676 __isl_take isl_id *id);
3677 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3678 __isl_take isl_multi_val *mv,
3679 enum isl_dim_type type, const char *s);
3680 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3681 __isl_take isl_multi_val *mv,
3682 enum isl_dim_type type, __isl_take isl_id *id);
3683 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3684 __isl_take isl_multi_val *mv,
3685 enum isl_dim_type type);
3686 __isl_give isl_multi_val *isl_multi_val_reset_user(
3687 __isl_take isl_multi_val *mv);
3689 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3690 __isl_take isl_multi_val *mv,
3691 enum isl_dim_type type, unsigned first, unsigned n);
3692 __isl_give isl_multi_val *isl_multi_val_add_dims(
3693 __isl_take isl_multi_val *mv,
3694 enum isl_dim_type type, unsigned n);
3695 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3696 __isl_take isl_multi_val *mv,
3697 enum isl_dim_type type, unsigned first, unsigned n);
3701 #include <isl/val.h>
3702 __isl_give isl_multi_val *isl_multi_val_align_params(
3703 __isl_take isl_multi_val *mv,
3704 __isl_take isl_space *model);
3705 __isl_give isl_multi_val *isl_multi_val_from_range(
3706 __isl_take isl_multi_val *mv);
3707 __isl_give isl_multi_val *isl_multi_val_range_splice(
3708 __isl_take isl_multi_val *mv1, unsigned pos,
3709 __isl_take isl_multi_val *mv2);
3710 __isl_give isl_multi_val *isl_multi_val_range_product(
3711 __isl_take isl_multi_val *mv1,
3712 __isl_take isl_multi_val *mv2);
3713 __isl_give isl_multi_val *
3714 isl_multi_val_range_factor_domain(
3715 __isl_take isl_multi_val *mv);
3716 __isl_give isl_multi_val *
3717 isl_multi_val_range_factor_range(
3718 __isl_take isl_multi_val *mv);
3719 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3720 __isl_take isl_multi_val *mv1,
3721 __isl_take isl_multi_aff *mv2);
3722 __isl_give isl_multi_val *isl_multi_val_product(
3723 __isl_take isl_multi_val *mv1,
3724 __isl_take isl_multi_val *mv2);
3725 __isl_give isl_multi_val *isl_multi_val_add_val(
3726 __isl_take isl_multi_val *mv,
3727 __isl_take isl_val *v);
3728 __isl_give isl_multi_val *isl_multi_val_mod_val(
3729 __isl_take isl_multi_val *mv,
3730 __isl_take isl_val *v);
3731 __isl_give isl_multi_val *isl_multi_val_scale_val(
3732 __isl_take isl_multi_val *mv,
3733 __isl_take isl_val *v);
3734 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3735 __isl_take isl_multi_val *mv1,
3736 __isl_take isl_multi_val *mv2);
3737 __isl_give isl_multi_val *
3738 isl_multi_val_scale_down_multi_val(
3739 __isl_take isl_multi_val *mv1,
3740 __isl_take isl_multi_val *mv2);
3742 A multiple value can be printed using
3744 __isl_give isl_printer *isl_printer_print_multi_val(
3745 __isl_take isl_printer *p,
3746 __isl_keep isl_multi_val *mv);
3750 Vectors can be created, copied and freed using the following functions.
3752 #include <isl/vec.h>
3753 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3755 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3756 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
3758 Note that the elements of a newly created vector may have arbitrary values.
3759 The elements can be changed and inspected using the following functions.
3761 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3762 int isl_vec_size(__isl_keep isl_vec *vec);
3763 __isl_give isl_val *isl_vec_get_element_val(
3764 __isl_keep isl_vec *vec, int pos);
3765 __isl_give isl_vec *isl_vec_set_element_si(
3766 __isl_take isl_vec *vec, int pos, int v);
3767 __isl_give isl_vec *isl_vec_set_element_val(
3768 __isl_take isl_vec *vec, int pos,
3769 __isl_take isl_val *v);
3770 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3772 __isl_give isl_vec *isl_vec_set_val(
3773 __isl_take isl_vec *vec, __isl_take isl_val *v);
3774 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3775 __isl_keep isl_vec *vec2, int pos);
3777 C<isl_vec_get_element> will return a negative value if anything went wrong.
3778 In that case, the value of C<*v> is undefined.
3780 The following function can be used to concatenate two vectors.
3782 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3783 __isl_take isl_vec *vec2);
3787 Matrices can be created, copied and freed using the following functions.
3789 #include <isl/mat.h>
3790 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3791 unsigned n_row, unsigned n_col);
3792 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3793 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
3795 Note that the elements of a newly created matrix may have arbitrary values.
3796 The elements can be changed and inspected using the following functions.
3798 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3799 int isl_mat_rows(__isl_keep isl_mat *mat);
3800 int isl_mat_cols(__isl_keep isl_mat *mat);
3801 __isl_give isl_val *isl_mat_get_element_val(
3802 __isl_keep isl_mat *mat, int row, int col);
3803 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3804 int row, int col, int v);
3805 __isl_give isl_mat *isl_mat_set_element_val(
3806 __isl_take isl_mat *mat, int row, int col,
3807 __isl_take isl_val *v);
3809 C<isl_mat_get_element> will return a negative value if anything went wrong.
3810 In that case, the value of C<*v> is undefined.
3812 The following function can be used to compute the (right) inverse
3813 of a matrix, i.e., a matrix such that the product of the original
3814 and the inverse (in that order) is a multiple of the identity matrix.
3815 The input matrix is assumed to be of full row-rank.
3817 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3819 The following function can be used to compute the (right) kernel
3820 (or null space) of a matrix, i.e., a matrix such that the product of
3821 the original and the kernel (in that order) is the zero matrix.
3823 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3825 =head2 Piecewise Quasi Affine Expressions
3827 The zero quasi affine expression or the quasi affine expression
3828 that is equal to a given value or
3829 a specified dimension on a given domain can be created using
3831 __isl_give isl_aff *isl_aff_zero_on_domain(
3832 __isl_take isl_local_space *ls);
3833 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3834 __isl_take isl_local_space *ls);
3835 __isl_give isl_aff *isl_aff_val_on_domain(
3836 __isl_take isl_local_space *ls,
3837 __isl_take isl_val *val);
3838 __isl_give isl_aff *isl_aff_var_on_domain(
3839 __isl_take isl_local_space *ls,
3840 enum isl_dim_type type, unsigned pos);
3841 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3842 __isl_take isl_local_space *ls,
3843 enum isl_dim_type type, unsigned pos);
3844 __isl_give isl_aff *isl_aff_nan_on_domain(
3845 __isl_take isl_local_space *ls);
3846 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3847 __isl_take isl_local_space *ls);
3849 Note that the space in which the resulting objects live is a map space
3850 with the given space as domain and a one-dimensional range.
3852 An empty piecewise quasi affine expression (one with no cells)
3853 or a piecewise quasi affine expression with a single cell can
3854 be created using the following functions.
3856 #include <isl/aff.h>
3857 __isl_give isl_pw_aff *isl_pw_aff_empty(
3858 __isl_take isl_space *space);
3859 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3860 __isl_take isl_set *set, __isl_take isl_aff *aff);
3861 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3862 __isl_take isl_aff *aff);
3864 A piecewise quasi affine expression that is equal to 1 on a set
3865 and 0 outside the set can be created using the following function.
3867 #include <isl/aff.h>
3868 __isl_give isl_pw_aff *isl_set_indicator_function(
3869 __isl_take isl_set *set);
3871 Quasi affine expressions can be copied and freed using
3873 #include <isl/aff.h>
3874 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3875 __isl_null isl_aff *isl_aff_free(__isl_take isl_aff *aff);
3877 __isl_give isl_pw_aff *isl_pw_aff_copy(
3878 __isl_keep isl_pw_aff *pwaff);
3879 __isl_null isl_pw_aff *isl_pw_aff_free(
3880 __isl_take isl_pw_aff *pwaff);
3882 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3883 using the following function. The constraint is required to have
3884 a non-zero coefficient for the specified dimension.
3886 #include <isl/constraint.h>
3887 __isl_give isl_aff *isl_constraint_get_bound(
3888 __isl_keep isl_constraint *constraint,
3889 enum isl_dim_type type, int pos);
3891 The entire affine expression of the constraint can also be extracted
3892 using the following function.
3894 #include <isl/constraint.h>
3895 __isl_give isl_aff *isl_constraint_get_aff(
3896 __isl_keep isl_constraint *constraint);
3898 Conversely, an equality constraint equating
3899 the affine expression to zero or an inequality constraint enforcing
3900 the affine expression to be non-negative, can be constructed using
3902 __isl_give isl_constraint *isl_equality_from_aff(
3903 __isl_take isl_aff *aff);
3904 __isl_give isl_constraint *isl_inequality_from_aff(
3905 __isl_take isl_aff *aff);
3907 The expression can be inspected using
3909 #include <isl/aff.h>
3910 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3911 int isl_aff_dim(__isl_keep isl_aff *aff,
3912 enum isl_dim_type type);
3913 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3914 __isl_keep isl_aff *aff);
3915 __isl_give isl_local_space *isl_aff_get_local_space(
3916 __isl_keep isl_aff *aff);
3917 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3918 enum isl_dim_type type, unsigned pos);
3919 const char *isl_pw_aff_get_dim_name(
3920 __isl_keep isl_pw_aff *pa,
3921 enum isl_dim_type type, unsigned pos);
3922 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3923 enum isl_dim_type type, unsigned pos);
3924 __isl_give isl_id *isl_pw_aff_get_dim_id(
3925 __isl_keep isl_pw_aff *pa,
3926 enum isl_dim_type type, unsigned pos);
3927 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
3928 enum isl_dim_type type);
3929 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3930 __isl_keep isl_pw_aff *pa,
3931 enum isl_dim_type type);
3932 __isl_give isl_val *isl_aff_get_constant_val(
3933 __isl_keep isl_aff *aff);
3934 __isl_give isl_val *isl_aff_get_coefficient_val(
3935 __isl_keep isl_aff *aff,
3936 enum isl_dim_type type, int pos);
3937 __isl_give isl_val *isl_aff_get_denominator_val(
3938 __isl_keep isl_aff *aff);
3939 __isl_give isl_aff *isl_aff_get_div(
3940 __isl_keep isl_aff *aff, int pos);
3942 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3943 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3944 int (*fn)(__isl_take isl_set *set,
3945 __isl_take isl_aff *aff,
3946 void *user), void *user);
3948 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3949 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3951 int isl_aff_is_nan(__isl_keep isl_aff *aff);
3952 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
3954 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3955 enum isl_dim_type type, unsigned first, unsigned n);
3956 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3957 enum isl_dim_type type, unsigned first, unsigned n);
3959 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3960 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3961 enum isl_dim_type type);
3962 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3964 It can be modified using
3966 #include <isl/aff.h>
3967 __isl_give isl_aff *isl_aff_set_tuple_id(
3968 __isl_take isl_aff *aff,
3969 enum isl_dim_type type, __isl_take isl_id *id);
3970 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3971 __isl_take isl_pw_aff *pwaff,
3972 enum isl_dim_type type, __isl_take isl_id *id);
3973 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
3974 __isl_take isl_pw_aff *pa,
3975 enum isl_dim_type type);
3976 __isl_give isl_aff *isl_aff_set_dim_name(
3977 __isl_take isl_aff *aff, enum isl_dim_type type,
3978 unsigned pos, const char *s);
3979 __isl_give isl_aff *isl_aff_set_dim_id(
3980 __isl_take isl_aff *aff, enum isl_dim_type type,
3981 unsigned pos, __isl_take isl_id *id);
3982 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3983 __isl_take isl_pw_aff *pma,
3984 enum isl_dim_type type, unsigned pos,
3985 __isl_take isl_id *id);
3986 __isl_give isl_aff *isl_aff_set_constant_si(
3987 __isl_take isl_aff *aff, int v);
3988 __isl_give isl_aff *isl_aff_set_constant_val(
3989 __isl_take isl_aff *aff, __isl_take isl_val *v);
3990 __isl_give isl_aff *isl_aff_set_coefficient_si(
3991 __isl_take isl_aff *aff,
3992 enum isl_dim_type type, int pos, int v);
3993 __isl_give isl_aff *isl_aff_set_coefficient_val(
3994 __isl_take isl_aff *aff,
3995 enum isl_dim_type type, int pos,
3996 __isl_take isl_val *v);
3998 __isl_give isl_aff *isl_aff_add_constant_si(
3999 __isl_take isl_aff *aff, int v);
4000 __isl_give isl_aff *isl_aff_add_constant_val(
4001 __isl_take isl_aff *aff, __isl_take isl_val *v);
4002 __isl_give isl_aff *isl_aff_add_constant_num_si(
4003 __isl_take isl_aff *aff, int v);
4004 __isl_give isl_aff *isl_aff_add_coefficient_si(
4005 __isl_take isl_aff *aff,
4006 enum isl_dim_type type, int pos, int v);
4007 __isl_give isl_aff *isl_aff_add_coefficient_val(
4008 __isl_take isl_aff *aff,
4009 enum isl_dim_type type, int pos,
4010 __isl_take isl_val *v);
4012 __isl_give isl_aff *isl_aff_insert_dims(
4013 __isl_take isl_aff *aff,
4014 enum isl_dim_type type, unsigned first, unsigned n);
4015 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
4016 __isl_take isl_pw_aff *pwaff,
4017 enum isl_dim_type type, unsigned first, unsigned n);
4018 __isl_give isl_aff *isl_aff_add_dims(
4019 __isl_take isl_aff *aff,
4020 enum isl_dim_type type, unsigned n);
4021 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
4022 __isl_take isl_pw_aff *pwaff,
4023 enum isl_dim_type type, unsigned n);
4024 __isl_give isl_aff *isl_aff_drop_dims(
4025 __isl_take isl_aff *aff,
4026 enum isl_dim_type type, unsigned first, unsigned n);
4027 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
4028 __isl_take isl_pw_aff *pwaff,
4029 enum isl_dim_type type, unsigned first, unsigned n);
4030 __isl_give isl_aff *isl_aff_move_dims(
4031 __isl_take isl_aff *aff,
4032 enum isl_dim_type dst_type, unsigned dst_pos,
4033 enum isl_dim_type src_type, unsigned src_pos,
4035 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
4036 __isl_take isl_pw_aff *pa,
4037 enum isl_dim_type dst_type, unsigned dst_pos,
4038 enum isl_dim_type src_type, unsigned src_pos,
4041 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
4042 set the I<numerator> of the constant or coefficient, while
4043 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
4044 the constant or coefficient as a whole.
4045 The C<add_constant> and C<add_coefficient> functions add an integer
4046 or rational value to
4047 the possibly rational constant or coefficient.
4048 The C<add_constant_num> functions add an integer value to
4051 To check whether an affine expressions is obviously zero
4052 or (obviously) equal to some other affine expression, use
4054 #include <isl/aff.h>
4055 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
4056 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
4057 __isl_keep isl_aff *aff2);
4058 int isl_pw_aff_plain_is_equal(
4059 __isl_keep isl_pw_aff *pwaff1,
4060 __isl_keep isl_pw_aff *pwaff2);
4061 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
4062 __isl_keep isl_pw_aff *pa2);
4063 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4064 __isl_keep isl_pw_aff *pa2);
4066 The function C<isl_pw_aff_plain_cmp> can be used to sort
4067 C<isl_pw_aff>s. The order is not strictly defined.
4068 The current order sorts expressions that only involve
4069 earlier dimensions before those that involve later dimensions.
4073 #include <isl/aff.h>
4074 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
4075 __isl_take isl_aff *aff2);
4076 __isl_give isl_pw_aff *isl_pw_aff_add(
4077 __isl_take isl_pw_aff *pwaff1,
4078 __isl_take isl_pw_aff *pwaff2);
4079 __isl_give isl_pw_aff *isl_pw_aff_min(
4080 __isl_take isl_pw_aff *pwaff1,
4081 __isl_take isl_pw_aff *pwaff2);
4082 __isl_give isl_pw_aff *isl_pw_aff_max(
4083 __isl_take isl_pw_aff *pwaff1,
4084 __isl_take isl_pw_aff *pwaff2);
4085 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
4086 __isl_take isl_aff *aff2);
4087 __isl_give isl_pw_aff *isl_pw_aff_sub(
4088 __isl_take isl_pw_aff *pwaff1,
4089 __isl_take isl_pw_aff *pwaff2);
4090 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
4091 __isl_give isl_pw_aff *isl_pw_aff_neg(
4092 __isl_take isl_pw_aff *pwaff);
4093 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
4094 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4095 __isl_take isl_pw_aff *pwaff);
4096 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
4097 __isl_give isl_pw_aff *isl_pw_aff_floor(
4098 __isl_take isl_pw_aff *pwaff);
4099 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
4100 __isl_take isl_val *mod);
4101 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
4102 __isl_take isl_pw_aff *pa,
4103 __isl_take isl_val *mod);
4104 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
4105 __isl_take isl_val *v);
4106 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
4107 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
4108 __isl_give isl_aff *isl_aff_scale_down_ui(
4109 __isl_take isl_aff *aff, unsigned f);
4110 __isl_give isl_aff *isl_aff_scale_down_val(
4111 __isl_take isl_aff *aff, __isl_take isl_val *v);
4112 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
4113 __isl_take isl_pw_aff *pa,
4114 __isl_take isl_val *f);
4116 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4117 __isl_take isl_pw_aff_list *list);
4118 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4119 __isl_take isl_pw_aff_list *list);
4121 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4122 __isl_take isl_pw_aff *pwqp);
4124 __isl_give isl_aff *isl_aff_align_params(
4125 __isl_take isl_aff *aff,
4126 __isl_take isl_space *model);
4127 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4128 __isl_take isl_pw_aff *pwaff,
4129 __isl_take isl_space *model);
4131 __isl_give isl_aff *isl_aff_project_domain_on_params(
4132 __isl_take isl_aff *aff);
4133 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4134 __isl_take isl_pw_aff *pwa);
4136 __isl_give isl_aff *isl_aff_gist_params(
4137 __isl_take isl_aff *aff,
4138 __isl_take isl_set *context);
4139 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
4140 __isl_take isl_set *context);
4141 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
4142 __isl_take isl_pw_aff *pwaff,
4143 __isl_take isl_set *context);
4144 __isl_give isl_pw_aff *isl_pw_aff_gist(
4145 __isl_take isl_pw_aff *pwaff,
4146 __isl_take isl_set *context);
4148 __isl_give isl_set *isl_pw_aff_domain(
4149 __isl_take isl_pw_aff *pwaff);
4150 __isl_give isl_set *isl_pw_aff_params(
4151 __isl_take isl_pw_aff *pwa);
4152 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4153 __isl_take isl_pw_aff *pa,
4154 __isl_take isl_set *set);
4155 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4156 __isl_take isl_pw_aff *pa,
4157 __isl_take isl_set *set);
4159 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
4160 __isl_take isl_aff *aff2);
4161 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
4162 __isl_take isl_aff *aff2);
4163 __isl_give isl_pw_aff *isl_pw_aff_mul(
4164 __isl_take isl_pw_aff *pwaff1,
4165 __isl_take isl_pw_aff *pwaff2);
4166 __isl_give isl_pw_aff *isl_pw_aff_div(
4167 __isl_take isl_pw_aff *pa1,
4168 __isl_take isl_pw_aff *pa2);
4169 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
4170 __isl_take isl_pw_aff *pa1,
4171 __isl_take isl_pw_aff *pa2);
4172 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
4173 __isl_take isl_pw_aff *pa1,
4174 __isl_take isl_pw_aff *pa2);
4176 When multiplying two affine expressions, at least one of the two needs
4177 to be a constant. Similarly, when dividing an affine expression by another,
4178 the second expression needs to be a constant.
4179 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
4180 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
4183 #include <isl/aff.h>
4184 __isl_give isl_aff *isl_aff_pullback_aff(
4185 __isl_take isl_aff *aff1,
4186 __isl_take isl_aff *aff2);
4187 __isl_give isl_aff *isl_aff_pullback_multi_aff(
4188 __isl_take isl_aff *aff,
4189 __isl_take isl_multi_aff *ma);
4190 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
4191 __isl_take isl_pw_aff *pa,
4192 __isl_take isl_multi_aff *ma);
4193 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
4194 __isl_take isl_pw_aff *pa,
4195 __isl_take isl_pw_multi_aff *pma);
4196 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
4197 __isl_take isl_pw_aff *pa,
4198 __isl_take isl_multi_pw_aff *mpa);
4200 These functions precompose the input expression by the given
4201 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
4202 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
4203 into the (piecewise) affine expression.
4204 Objects of type C<isl_multi_aff> are described in
4205 L</"Piecewise Multiple Quasi Affine Expressions">.
4207 #include <isl/aff.h>
4208 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4209 __isl_take isl_aff *aff);
4210 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4211 __isl_take isl_aff *aff);
4212 __isl_give isl_basic_set *isl_aff_le_basic_set(
4213 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4214 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4215 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4216 __isl_give isl_set *isl_pw_aff_eq_set(
4217 __isl_take isl_pw_aff *pwaff1,
4218 __isl_take isl_pw_aff *pwaff2);
4219 __isl_give isl_set *isl_pw_aff_ne_set(
4220 __isl_take isl_pw_aff *pwaff1,
4221 __isl_take isl_pw_aff *pwaff2);
4222 __isl_give isl_set *isl_pw_aff_le_set(
4223 __isl_take isl_pw_aff *pwaff1,
4224 __isl_take isl_pw_aff *pwaff2);
4225 __isl_give isl_set *isl_pw_aff_lt_set(
4226 __isl_take isl_pw_aff *pwaff1,
4227 __isl_take isl_pw_aff *pwaff2);
4228 __isl_give isl_set *isl_pw_aff_ge_set(
4229 __isl_take isl_pw_aff *pwaff1,
4230 __isl_take isl_pw_aff *pwaff2);
4231 __isl_give isl_set *isl_pw_aff_gt_set(
4232 __isl_take isl_pw_aff *pwaff1,
4233 __isl_take isl_pw_aff *pwaff2);
4235 __isl_give isl_set *isl_pw_aff_list_eq_set(
4236 __isl_take isl_pw_aff_list *list1,
4237 __isl_take isl_pw_aff_list *list2);
4238 __isl_give isl_set *isl_pw_aff_list_ne_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_le_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_lt_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_ge_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_gt_set(
4251 __isl_take isl_pw_aff_list *list1,
4252 __isl_take isl_pw_aff_list *list2);
4254 The function C<isl_aff_neg_basic_set> returns a basic set
4255 containing those elements in the domain space
4256 of C<aff> where C<aff> is negative.
4257 The function C<isl_aff_ge_basic_set> returns a basic set
4258 containing those elements in the shared space
4259 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4260 The function C<isl_pw_aff_ge_set> returns a set
4261 containing those elements in the shared domain
4262 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4263 The functions operating on C<isl_pw_aff_list> apply the corresponding
4264 C<isl_pw_aff> function to each pair of elements in the two lists.
4266 #include <isl/aff.h>
4267 __isl_give isl_set *isl_pw_aff_nonneg_set(
4268 __isl_take isl_pw_aff *pwaff);
4269 __isl_give isl_set *isl_pw_aff_zero_set(
4270 __isl_take isl_pw_aff *pwaff);
4271 __isl_give isl_set *isl_pw_aff_non_zero_set(
4272 __isl_take isl_pw_aff *pwaff);
4274 The function C<isl_pw_aff_nonneg_set> returns a set
4275 containing those elements in the domain
4276 of C<pwaff> where C<pwaff> is non-negative.
4278 #include <isl/aff.h>
4279 __isl_give isl_pw_aff *isl_pw_aff_cond(
4280 __isl_take isl_pw_aff *cond,
4281 __isl_take isl_pw_aff *pwaff_true,
4282 __isl_take isl_pw_aff *pwaff_false);
4284 The function C<isl_pw_aff_cond> performs a conditional operator
4285 and returns an expression that is equal to C<pwaff_true>
4286 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4287 where C<cond> is zero.
4289 #include <isl/aff.h>
4290 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4291 __isl_take isl_pw_aff *pwaff1,
4292 __isl_take isl_pw_aff *pwaff2);
4293 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4294 __isl_take isl_pw_aff *pwaff1,
4295 __isl_take isl_pw_aff *pwaff2);
4296 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4297 __isl_take isl_pw_aff *pwaff1,
4298 __isl_take isl_pw_aff *pwaff2);
4300 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4301 expression with a domain that is the union of those of C<pwaff1> and
4302 C<pwaff2> and such that on each cell, the quasi-affine expression is
4303 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4304 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4305 associated expression is the defined one.
4307 An expression can be read from input using
4309 #include <isl/aff.h>
4310 __isl_give isl_aff *isl_aff_read_from_str(
4311 isl_ctx *ctx, const char *str);
4312 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4313 isl_ctx *ctx, const char *str);
4315 An expression can be printed using
4317 #include <isl/aff.h>
4318 __isl_give isl_printer *isl_printer_print_aff(
4319 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4321 __isl_give isl_printer *isl_printer_print_pw_aff(
4322 __isl_take isl_printer *p,
4323 __isl_keep isl_pw_aff *pwaff);
4325 =head2 Piecewise Multiple Quasi Affine Expressions
4327 An C<isl_multi_aff> object represents a sequence of
4328 zero or more affine expressions, all defined on the same domain space.
4329 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4330 zero or more piecewise affine expressions.
4332 An C<isl_multi_aff> can be constructed from a single
4333 C<isl_aff> or an C<isl_aff_list> using the
4334 following functions. Similarly for C<isl_multi_pw_aff>
4335 and C<isl_pw_multi_aff>.
4337 #include <isl/aff.h>
4338 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4339 __isl_take isl_aff *aff);
4340 __isl_give isl_multi_pw_aff *
4341 isl_multi_pw_aff_from_multi_aff(
4342 __isl_take isl_multi_aff *ma);
4343 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4344 __isl_take isl_pw_aff *pa);
4345 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4346 __isl_take isl_pw_aff *pa);
4347 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4348 __isl_take isl_space *space,
4349 __isl_take isl_aff_list *list);
4351 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4352 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4353 Note however that the domain
4354 of the result is the intersection of the domains of the input.
4355 The reverse conversion is exact.
4357 #include <isl/aff.h>
4358 __isl_give isl_pw_multi_aff *
4359 isl_pw_multi_aff_from_multi_pw_aff(
4360 __isl_take isl_multi_pw_aff *mpa);
4361 __isl_give isl_multi_pw_aff *
4362 isl_multi_pw_aff_from_pw_multi_aff(
4363 __isl_take isl_pw_multi_aff *pma);
4365 An empty piecewise multiple quasi affine expression (one with no cells),
4366 the zero piecewise multiple quasi affine expression (with value zero
4367 for each output dimension),
4368 a piecewise multiple quasi affine expression with a single cell (with
4369 either a universe or a specified domain) or
4370 a zero-dimensional piecewise multiple quasi affine expression
4372 can be created using the following functions.
4374 #include <isl/aff.h>
4375 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4376 __isl_take isl_space *space);
4377 __isl_give isl_multi_aff *isl_multi_aff_zero(
4378 __isl_take isl_space *space);
4379 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4380 __isl_take isl_space *space);
4381 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4382 __isl_take isl_space *space);
4383 __isl_give isl_multi_aff *isl_multi_aff_identity(
4384 __isl_take isl_space *space);
4385 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4386 __isl_take isl_space *space);
4387 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4388 __isl_take isl_space *space);
4389 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4390 __isl_take isl_space *space);
4391 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4392 __isl_take isl_space *space);
4393 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4394 __isl_take isl_space *space,
4395 enum isl_dim_type type,
4396 unsigned first, unsigned n);
4397 __isl_give isl_pw_multi_aff *
4398 isl_pw_multi_aff_project_out_map(
4399 __isl_take isl_space *space,
4400 enum isl_dim_type type,
4401 unsigned first, unsigned n);
4402 __isl_give isl_pw_multi_aff *
4403 isl_pw_multi_aff_from_multi_aff(
4404 __isl_take isl_multi_aff *ma);
4405 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4406 __isl_take isl_set *set,
4407 __isl_take isl_multi_aff *maff);
4408 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4409 __isl_take isl_set *set);
4411 __isl_give isl_union_pw_multi_aff *
4412 isl_union_pw_multi_aff_empty(
4413 __isl_take isl_space *space);
4414 __isl_give isl_union_pw_multi_aff *
4415 isl_union_pw_multi_aff_add_pw_multi_aff(
4416 __isl_take isl_union_pw_multi_aff *upma,
4417 __isl_take isl_pw_multi_aff *pma);
4418 __isl_give isl_union_pw_multi_aff *
4419 isl_union_pw_multi_aff_from_domain(
4420 __isl_take isl_union_set *uset);
4422 A piecewise multiple quasi affine expression can also be initialized
4423 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4424 and the C<isl_map> is single-valued.
4425 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4426 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4428 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4429 __isl_take isl_set *set);
4430 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4431 __isl_take isl_map *map);
4433 __isl_give isl_union_pw_multi_aff *
4434 isl_union_pw_multi_aff_from_union_set(
4435 __isl_take isl_union_set *uset);
4436 __isl_give isl_union_pw_multi_aff *
4437 isl_union_pw_multi_aff_from_union_map(
4438 __isl_take isl_union_map *umap);
4440 Multiple quasi affine expressions can be copied and freed using
4442 #include <isl/aff.h>
4443 __isl_give isl_multi_aff *isl_multi_aff_copy(
4444 __isl_keep isl_multi_aff *maff);
4445 __isl_null isl_multi_aff *isl_multi_aff_free(
4446 __isl_take isl_multi_aff *maff);
4448 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4449 __isl_keep isl_pw_multi_aff *pma);
4450 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
4451 __isl_take isl_pw_multi_aff *pma);
4453 __isl_give isl_union_pw_multi_aff *
4454 isl_union_pw_multi_aff_copy(
4455 __isl_keep isl_union_pw_multi_aff *upma);
4456 __isl_null isl_union_pw_multi_aff *
4457 isl_union_pw_multi_aff_free(
4458 __isl_take isl_union_pw_multi_aff *upma);
4460 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4461 __isl_keep isl_multi_pw_aff *mpa);
4462 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
4463 __isl_take isl_multi_pw_aff *mpa);
4465 The expression can be inspected using
4467 #include <isl/aff.h>
4468 isl_ctx *isl_multi_aff_get_ctx(
4469 __isl_keep isl_multi_aff *maff);
4470 isl_ctx *isl_pw_multi_aff_get_ctx(
4471 __isl_keep isl_pw_multi_aff *pma);
4472 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4473 __isl_keep isl_union_pw_multi_aff *upma);
4474 isl_ctx *isl_multi_pw_aff_get_ctx(
4475 __isl_keep isl_multi_pw_aff *mpa);
4477 int isl_multi_aff_involves_dims(
4478 __isl_keep isl_multi_aff *ma,
4479 enum isl_dim_type type, unsigned first, unsigned n);
4480 int isl_multi_pw_aff_involves_dims(
4481 __isl_keep isl_multi_pw_aff *mpa,
4482 enum isl_dim_type type, unsigned first, unsigned n);
4484 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4485 enum isl_dim_type type);
4486 unsigned isl_pw_multi_aff_dim(
4487 __isl_keep isl_pw_multi_aff *pma,
4488 enum isl_dim_type type);
4489 unsigned isl_multi_pw_aff_dim(
4490 __isl_keep isl_multi_pw_aff *mpa,
4491 enum isl_dim_type type);
4492 __isl_give isl_aff *isl_multi_aff_get_aff(
4493 __isl_keep isl_multi_aff *multi, int pos);
4494 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4495 __isl_keep isl_pw_multi_aff *pma, int pos);
4496 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4497 __isl_keep isl_multi_pw_aff *mpa, int pos);
4498 int isl_multi_aff_find_dim_by_id(
4499 __isl_keep isl_multi_aff *ma,
4500 enum isl_dim_type type, __isl_keep isl_id *id);
4501 int isl_multi_pw_aff_find_dim_by_id(
4502 __isl_keep isl_multi_pw_aff *mpa,
4503 enum isl_dim_type type, __isl_keep isl_id *id);
4504 const char *isl_pw_multi_aff_get_dim_name(
4505 __isl_keep isl_pw_multi_aff *pma,
4506 enum isl_dim_type type, unsigned pos);
4507 __isl_give isl_id *isl_multi_aff_get_dim_id(
4508 __isl_keep isl_multi_aff *ma,
4509 enum isl_dim_type type, unsigned pos);
4510 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4511 __isl_keep isl_pw_multi_aff *pma,
4512 enum isl_dim_type type, unsigned pos);
4513 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4514 __isl_keep isl_multi_pw_aff *mpa,
4515 enum isl_dim_type type, unsigned pos);
4516 const char *isl_multi_aff_get_tuple_name(
4517 __isl_keep isl_multi_aff *multi,
4518 enum isl_dim_type type);
4519 int isl_pw_multi_aff_has_tuple_name(
4520 __isl_keep isl_pw_multi_aff *pma,
4521 enum isl_dim_type type);
4522 const char *isl_pw_multi_aff_get_tuple_name(
4523 __isl_keep isl_pw_multi_aff *pma,
4524 enum isl_dim_type type);
4525 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4526 enum isl_dim_type type);
4527 int isl_pw_multi_aff_has_tuple_id(
4528 __isl_keep isl_pw_multi_aff *pma,
4529 enum isl_dim_type type);
4530 int isl_multi_pw_aff_has_tuple_id(
4531 __isl_keep isl_multi_pw_aff *mpa,
4532 enum isl_dim_type type);
4533 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4534 __isl_keep isl_multi_aff *ma,
4535 enum isl_dim_type type);
4536 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4537 __isl_keep isl_pw_multi_aff *pma,
4538 enum isl_dim_type type);
4539 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4540 __isl_keep isl_multi_pw_aff *mpa,
4541 enum isl_dim_type type);
4542 int isl_multi_aff_range_is_wrapping(
4543 __isl_keep isl_multi_aff *ma);
4544 int isl_multi_pw_aff_range_is_wrapping(
4545 __isl_keep isl_multi_pw_aff *mpa);
4547 int isl_pw_multi_aff_foreach_piece(
4548 __isl_keep isl_pw_multi_aff *pma,
4549 int (*fn)(__isl_take isl_set *set,
4550 __isl_take isl_multi_aff *maff,
4551 void *user), void *user);
4553 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4554 __isl_keep isl_union_pw_multi_aff *upma,
4555 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4556 void *user), void *user);
4558 It can be modified using
4560 #include <isl/aff.h>
4561 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4562 __isl_take isl_multi_aff *multi, int pos,
4563 __isl_take isl_aff *aff);
4564 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4565 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4566 __isl_take isl_pw_aff *pa);
4567 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4568 __isl_take isl_multi_aff *maff,
4569 enum isl_dim_type type, unsigned pos, const char *s);
4570 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4571 __isl_take isl_multi_aff *maff,
4572 enum isl_dim_type type, unsigned pos,
4573 __isl_take isl_id *id);
4574 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4575 __isl_take isl_multi_aff *maff,
4576 enum isl_dim_type type, const char *s);
4577 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4578 __isl_take isl_multi_aff *maff,
4579 enum isl_dim_type type, __isl_take isl_id *id);
4580 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4581 __isl_take isl_pw_multi_aff *pma,
4582 enum isl_dim_type type, __isl_take isl_id *id);
4583 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4584 __isl_take isl_multi_aff *ma,
4585 enum isl_dim_type type);
4586 __isl_give isl_multi_pw_aff *
4587 isl_multi_pw_aff_reset_tuple_id(
4588 __isl_take isl_multi_pw_aff *mpa,
4589 enum isl_dim_type type);
4590 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4591 __isl_take isl_multi_aff *ma);
4592 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4593 __isl_take isl_multi_pw_aff *mpa);
4595 __isl_give isl_multi_pw_aff *
4596 isl_multi_pw_aff_set_dim_name(
4597 __isl_take isl_multi_pw_aff *mpa,
4598 enum isl_dim_type type, unsigned pos, const char *s);
4599 __isl_give isl_multi_pw_aff *
4600 isl_multi_pw_aff_set_dim_id(
4601 __isl_take isl_multi_pw_aff *mpa,
4602 enum isl_dim_type type, unsigned pos,
4603 __isl_take isl_id *id);
4604 __isl_give isl_multi_pw_aff *
4605 isl_multi_pw_aff_set_tuple_name(
4606 __isl_take isl_multi_pw_aff *mpa,
4607 enum isl_dim_type type, const char *s);
4609 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4610 __isl_take isl_multi_aff *ma);
4612 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4613 __isl_take isl_multi_aff *ma,
4614 enum isl_dim_type type, unsigned first, unsigned n);
4615 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4616 __isl_take isl_multi_aff *ma,
4617 enum isl_dim_type type, unsigned n);
4618 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4619 __isl_take isl_multi_aff *maff,
4620 enum isl_dim_type type, unsigned first, unsigned n);
4621 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4622 __isl_take isl_pw_multi_aff *pma,
4623 enum isl_dim_type type, unsigned first, unsigned n);
4625 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4626 __isl_take isl_multi_pw_aff *mpa,
4627 enum isl_dim_type type, unsigned first, unsigned n);
4628 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4629 __isl_take isl_multi_pw_aff *mpa,
4630 enum isl_dim_type type, unsigned n);
4631 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4632 __isl_take isl_multi_pw_aff *pma,
4633 enum isl_dim_type dst_type, unsigned dst_pos,
4634 enum isl_dim_type src_type, unsigned src_pos,
4637 To check whether two multiple affine expressions are
4638 (obviously) equal to each other, use
4640 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4641 __isl_keep isl_multi_aff *maff2);
4642 int isl_pw_multi_aff_plain_is_equal(
4643 __isl_keep isl_pw_multi_aff *pma1,
4644 __isl_keep isl_pw_multi_aff *pma2);
4645 int isl_multi_pw_aff_plain_is_equal(
4646 __isl_keep isl_multi_pw_aff *mpa1,
4647 __isl_keep isl_multi_pw_aff *mpa2);
4648 int isl_multi_pw_aff_is_equal(
4649 __isl_keep isl_multi_pw_aff *mpa1,
4650 __isl_keep isl_multi_pw_aff *mpa2);
4654 #include <isl/aff.h>
4655 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4656 __isl_take isl_pw_multi_aff *pma1,
4657 __isl_take isl_pw_multi_aff *pma2);
4658 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4659 __isl_take isl_pw_multi_aff *pma1,
4660 __isl_take isl_pw_multi_aff *pma2);
4661 __isl_give isl_multi_aff *isl_multi_aff_floor(
4662 __isl_take isl_multi_aff *ma);
4663 __isl_give isl_multi_aff *isl_multi_aff_add(
4664 __isl_take isl_multi_aff *maff1,
4665 __isl_take isl_multi_aff *maff2);
4666 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4667 __isl_take isl_pw_multi_aff *pma1,
4668 __isl_take isl_pw_multi_aff *pma2);
4669 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4670 __isl_take isl_union_pw_multi_aff *upma1,
4671 __isl_take isl_union_pw_multi_aff *upma2);
4672 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4673 __isl_take isl_pw_multi_aff *pma1,
4674 __isl_take isl_pw_multi_aff *pma2);
4675 __isl_give isl_multi_aff *isl_multi_aff_sub(
4676 __isl_take isl_multi_aff *ma1,
4677 __isl_take isl_multi_aff *ma2);
4678 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4679 __isl_take isl_pw_multi_aff *pma1,
4680 __isl_take isl_pw_multi_aff *pma2);
4681 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4682 __isl_take isl_union_pw_multi_aff *upma1,
4683 __isl_take isl_union_pw_multi_aff *upma2);
4685 C<isl_multi_aff_sub> subtracts the second argument from the first.
4687 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4688 __isl_take isl_multi_aff *ma,
4689 __isl_take isl_val *v);
4690 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4691 __isl_take isl_pw_multi_aff *pma,
4692 __isl_take isl_val *v);
4693 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4694 __isl_take isl_multi_pw_aff *mpa,
4695 __isl_take isl_val *v);
4696 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4697 __isl_take isl_multi_aff *ma,
4698 __isl_take isl_multi_val *mv);
4699 __isl_give isl_pw_multi_aff *
4700 isl_pw_multi_aff_scale_multi_val(
4701 __isl_take isl_pw_multi_aff *pma,
4702 __isl_take isl_multi_val *mv);
4703 __isl_give isl_multi_pw_aff *
4704 isl_multi_pw_aff_scale_multi_val(
4705 __isl_take isl_multi_pw_aff *mpa,
4706 __isl_take isl_multi_val *mv);
4707 __isl_give isl_union_pw_multi_aff *
4708 isl_union_pw_multi_aff_scale_multi_val(
4709 __isl_take isl_union_pw_multi_aff *upma,
4710 __isl_take isl_multi_val *mv);
4711 __isl_give isl_multi_aff *
4712 isl_multi_aff_scale_down_multi_val(
4713 __isl_take isl_multi_aff *ma,
4714 __isl_take isl_multi_val *mv);
4715 __isl_give isl_multi_pw_aff *
4716 isl_multi_pw_aff_scale_down_multi_val(
4717 __isl_take isl_multi_pw_aff *mpa,
4718 __isl_take isl_multi_val *mv);
4720 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4721 by the corresponding elements of C<mv>.
4723 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4724 __isl_take isl_pw_multi_aff *pma,
4725 enum isl_dim_type type, unsigned pos, int value);
4726 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4727 __isl_take isl_pw_multi_aff *pma,
4728 __isl_take isl_set *set);
4729 __isl_give isl_set *isl_multi_pw_aff_domain(
4730 __isl_take isl_multi_pw_aff *mpa);
4731 __isl_give isl_multi_pw_aff *
4732 isl_multi_pw_aff_intersect_params(
4733 __isl_take isl_multi_pw_aff *mpa,
4734 __isl_take isl_set *set);
4735 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4736 __isl_take isl_pw_multi_aff *pma,
4737 __isl_take isl_set *set);
4738 __isl_give isl_multi_pw_aff *
4739 isl_multi_pw_aff_intersect_domain(
4740 __isl_take isl_multi_pw_aff *mpa,
4741 __isl_take isl_set *domain);
4742 __isl_give isl_union_pw_multi_aff *
4743 isl_union_pw_multi_aff_intersect_domain(
4744 __isl_take isl_union_pw_multi_aff *upma,
4745 __isl_take isl_union_set *uset);
4746 __isl_give isl_multi_aff *isl_multi_aff_lift(
4747 __isl_take isl_multi_aff *maff,
4748 __isl_give isl_local_space **ls);
4749 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4750 __isl_take isl_pw_multi_aff *pma);
4751 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4752 __isl_take isl_multi_pw_aff *mpa);
4753 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4754 __isl_take isl_multi_aff *multi,
4755 __isl_take isl_space *model);
4756 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4757 __isl_take isl_pw_multi_aff *pma,
4758 __isl_take isl_space *model);
4759 __isl_give isl_union_pw_multi_aff *
4760 isl_union_pw_multi_aff_align_params(
4761 __isl_take isl_union_pw_multi_aff *upma,
4762 __isl_take isl_space *model);
4763 __isl_give isl_pw_multi_aff *
4764 isl_pw_multi_aff_project_domain_on_params(
4765 __isl_take isl_pw_multi_aff *pma);
4766 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4767 __isl_take isl_multi_aff *maff,
4768 __isl_take isl_set *context);
4769 __isl_give isl_multi_aff *isl_multi_aff_gist(
4770 __isl_take isl_multi_aff *maff,
4771 __isl_take isl_set *context);
4772 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4773 __isl_take isl_pw_multi_aff *pma,
4774 __isl_take isl_set *set);
4775 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4776 __isl_take isl_pw_multi_aff *pma,
4777 __isl_take isl_set *set);
4778 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4779 __isl_take isl_multi_pw_aff *mpa,
4780 __isl_take isl_set *set);
4781 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4782 __isl_take isl_multi_pw_aff *mpa,
4783 __isl_take isl_set *set);
4784 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4785 __isl_take isl_multi_aff *ma);
4786 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4787 __isl_take isl_multi_pw_aff *mpa);
4788 __isl_give isl_set *isl_pw_multi_aff_domain(
4789 __isl_take isl_pw_multi_aff *pma);
4790 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4791 __isl_take isl_union_pw_multi_aff *upma);
4792 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4793 __isl_take isl_multi_aff *ma1, unsigned pos,
4794 __isl_take isl_multi_aff *ma2);
4795 __isl_give isl_multi_aff *isl_multi_aff_splice(
4796 __isl_take isl_multi_aff *ma1,
4797 unsigned in_pos, unsigned out_pos,
4798 __isl_take isl_multi_aff *ma2);
4799 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4800 __isl_take isl_multi_aff *ma1,
4801 __isl_take isl_multi_aff *ma2);
4802 __isl_give isl_multi_aff *
4803 isl_multi_aff_range_factor_domain(
4804 __isl_take isl_multi_aff *ma);
4805 __isl_give isl_multi_aff *
4806 isl_multi_aff_range_factor_range(
4807 __isl_take isl_multi_aff *ma);
4808 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4809 __isl_take isl_multi_aff *ma1,
4810 __isl_take isl_multi_aff *ma2);
4811 __isl_give isl_multi_aff *isl_multi_aff_product(
4812 __isl_take isl_multi_aff *ma1,
4813 __isl_take isl_multi_aff *ma2);
4814 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4815 __isl_take isl_multi_pw_aff *mpa1,
4816 __isl_take isl_multi_pw_aff *mpa2);
4817 __isl_give isl_pw_multi_aff *
4818 isl_pw_multi_aff_range_product(
4819 __isl_take isl_pw_multi_aff *pma1,
4820 __isl_take isl_pw_multi_aff *pma2);
4821 __isl_give isl_multi_pw_aff *
4822 isl_multi_pw_aff_range_factor_domain(
4823 __isl_take isl_multi_pw_aff *mpa);
4824 __isl_give isl_multi_pw_aff *
4825 isl_multi_pw_aff_range_factor_range(
4826 __isl_take isl_multi_pw_aff *mpa);
4827 __isl_give isl_pw_multi_aff *
4828 isl_pw_multi_aff_flat_range_product(
4829 __isl_take isl_pw_multi_aff *pma1,
4830 __isl_take isl_pw_multi_aff *pma2);
4831 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4832 __isl_take isl_pw_multi_aff *pma1,
4833 __isl_take isl_pw_multi_aff *pma2);
4834 __isl_give isl_union_pw_multi_aff *
4835 isl_union_pw_multi_aff_flat_range_product(
4836 __isl_take isl_union_pw_multi_aff *upma1,
4837 __isl_take isl_union_pw_multi_aff *upma2);
4838 __isl_give isl_multi_pw_aff *
4839 isl_multi_pw_aff_range_splice(
4840 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4841 __isl_take isl_multi_pw_aff *mpa2);
4842 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4843 __isl_take isl_multi_pw_aff *mpa1,
4844 unsigned in_pos, unsigned out_pos,
4845 __isl_take isl_multi_pw_aff *mpa2);
4846 __isl_give isl_multi_pw_aff *
4847 isl_multi_pw_aff_range_product(
4848 __isl_take isl_multi_pw_aff *mpa1,
4849 __isl_take isl_multi_pw_aff *mpa2);
4850 __isl_give isl_multi_pw_aff *
4851 isl_multi_pw_aff_flat_range_product(
4852 __isl_take isl_multi_pw_aff *mpa1,
4853 __isl_take isl_multi_pw_aff *mpa2);
4855 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4856 then it is assigned the local space that lies at the basis of
4857 the lifting applied.
4859 #include <isl/aff.h>
4860 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4861 __isl_take isl_multi_aff *ma1,
4862 __isl_take isl_multi_aff *ma2);
4863 __isl_give isl_pw_multi_aff *
4864 isl_pw_multi_aff_pullback_multi_aff(
4865 __isl_take isl_pw_multi_aff *pma,
4866 __isl_take isl_multi_aff *ma);
4867 __isl_give isl_multi_pw_aff *
4868 isl_multi_pw_aff_pullback_multi_aff(
4869 __isl_take isl_multi_pw_aff *mpa,
4870 __isl_take isl_multi_aff *ma);
4871 __isl_give isl_pw_multi_aff *
4872 isl_pw_multi_aff_pullback_pw_multi_aff(
4873 __isl_take isl_pw_multi_aff *pma1,
4874 __isl_take isl_pw_multi_aff *pma2);
4875 __isl_give isl_multi_pw_aff *
4876 isl_multi_pw_aff_pullback_pw_multi_aff(
4877 __isl_take isl_multi_pw_aff *mpa,
4878 __isl_take isl_pw_multi_aff *pma);
4879 __isl_give isl_multi_pw_aff *
4880 isl_multi_pw_aff_pullback_multi_pw_aff(
4881 __isl_take isl_multi_pw_aff *mpa1,
4882 __isl_take isl_multi_pw_aff *mpa2);
4884 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4885 In other words, C<ma2> is plugged
4888 __isl_give isl_set *isl_multi_aff_lex_le_set(
4889 __isl_take isl_multi_aff *ma1,
4890 __isl_take isl_multi_aff *ma2);
4891 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4892 __isl_take isl_multi_aff *ma1,
4893 __isl_take isl_multi_aff *ma2);
4895 The function C<isl_multi_aff_lex_le_set> returns a set
4896 containing those elements in the shared domain space
4897 where C<ma1> is lexicographically smaller than or
4900 An expression can be read from input using
4902 #include <isl/aff.h>
4903 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4904 isl_ctx *ctx, const char *str);
4905 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4906 isl_ctx *ctx, const char *str);
4907 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4908 isl_ctx *ctx, const char *str);
4909 __isl_give isl_union_pw_multi_aff *
4910 isl_union_pw_multi_aff_read_from_str(
4911 isl_ctx *ctx, const char *str);
4913 An expression can be printed using
4915 #include <isl/aff.h>
4916 __isl_give isl_printer *isl_printer_print_multi_aff(
4917 __isl_take isl_printer *p,
4918 __isl_keep isl_multi_aff *maff);
4919 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4920 __isl_take isl_printer *p,
4921 __isl_keep isl_pw_multi_aff *pma);
4922 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4923 __isl_take isl_printer *p,
4924 __isl_keep isl_union_pw_multi_aff *upma);
4925 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4926 __isl_take isl_printer *p,
4927 __isl_keep isl_multi_pw_aff *mpa);
4931 Points are elements of a set. They can be used to construct
4932 simple sets (boxes) or they can be used to represent the
4933 individual elements of a set.
4934 The zero point (the origin) can be created using
4936 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4938 The coordinates of a point can be inspected, set and changed
4941 __isl_give isl_val *isl_point_get_coordinate_val(
4942 __isl_keep isl_point *pnt,
4943 enum isl_dim_type type, int pos);
4944 __isl_give isl_point *isl_point_set_coordinate_val(
4945 __isl_take isl_point *pnt,
4946 enum isl_dim_type type, int pos,
4947 __isl_take isl_val *v);
4949 __isl_give isl_point *isl_point_add_ui(
4950 __isl_take isl_point *pnt,
4951 enum isl_dim_type type, int pos, unsigned val);
4952 __isl_give isl_point *isl_point_sub_ui(
4953 __isl_take isl_point *pnt,
4954 enum isl_dim_type type, int pos, unsigned val);
4956 Other properties can be obtained using
4958 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4960 Points can be copied or freed using
4962 __isl_give isl_point *isl_point_copy(
4963 __isl_keep isl_point *pnt);
4964 void isl_point_free(__isl_take isl_point *pnt);
4966 A singleton set can be created from a point using
4968 __isl_give isl_basic_set *isl_basic_set_from_point(
4969 __isl_take isl_point *pnt);
4970 __isl_give isl_set *isl_set_from_point(
4971 __isl_take isl_point *pnt);
4973 and a box can be created from two opposite extremal points using
4975 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4976 __isl_take isl_point *pnt1,
4977 __isl_take isl_point *pnt2);
4978 __isl_give isl_set *isl_set_box_from_points(
4979 __isl_take isl_point *pnt1,
4980 __isl_take isl_point *pnt2);
4982 All elements of a B<bounded> (union) set can be enumerated using
4983 the following functions.
4985 int isl_set_foreach_point(__isl_keep isl_set *set,
4986 int (*fn)(__isl_take isl_point *pnt, void *user),
4988 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4989 int (*fn)(__isl_take isl_point *pnt, void *user),
4992 The function C<fn> is called for each integer point in
4993 C<set> with as second argument the last argument of
4994 the C<isl_set_foreach_point> call. The function C<fn>
4995 should return C<0> on success and C<-1> on failure.
4996 In the latter case, C<isl_set_foreach_point> will stop
4997 enumerating and return C<-1> as well.
4998 If the enumeration is performed successfully and to completion,
4999 then C<isl_set_foreach_point> returns C<0>.
5001 To obtain a single point of a (basic) set, use
5003 __isl_give isl_point *isl_basic_set_sample_point(
5004 __isl_take isl_basic_set *bset);
5005 __isl_give isl_point *isl_set_sample_point(
5006 __isl_take isl_set *set);
5008 If C<set> does not contain any (integer) points, then the
5009 resulting point will be ``void'', a property that can be
5012 int isl_point_is_void(__isl_keep isl_point *pnt);
5014 =head2 Piecewise Quasipolynomials
5016 A piecewise quasipolynomial is a particular kind of function that maps
5017 a parametric point to a rational value.
5018 More specifically, a quasipolynomial is a polynomial expression in greatest
5019 integer parts of affine expressions of parameters and variables.
5020 A piecewise quasipolynomial is a subdivision of a given parametric
5021 domain into disjoint cells with a quasipolynomial associated to
5022 each cell. The value of the piecewise quasipolynomial at a given
5023 point is the value of the quasipolynomial associated to the cell
5024 that contains the point. Outside of the union of cells,
5025 the value is assumed to be zero.
5026 For example, the piecewise quasipolynomial
5028 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
5030 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
5031 A given piecewise quasipolynomial has a fixed domain dimension.
5032 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
5033 defined over different domains.
5034 Piecewise quasipolynomials are mainly used by the C<barvinok>
5035 library for representing the number of elements in a parametric set or map.
5036 For example, the piecewise quasipolynomial above represents
5037 the number of points in the map
5039 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
5041 =head3 Input and Output
5043 Piecewise quasipolynomials can be read from input using
5045 __isl_give isl_union_pw_qpolynomial *
5046 isl_union_pw_qpolynomial_read_from_str(
5047 isl_ctx *ctx, const char *str);
5049 Quasipolynomials and piecewise quasipolynomials can be printed
5050 using the following functions.
5052 __isl_give isl_printer *isl_printer_print_qpolynomial(
5053 __isl_take isl_printer *p,
5054 __isl_keep isl_qpolynomial *qp);
5056 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
5057 __isl_take isl_printer *p,
5058 __isl_keep isl_pw_qpolynomial *pwqp);
5060 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
5061 __isl_take isl_printer *p,
5062 __isl_keep isl_union_pw_qpolynomial *upwqp);
5064 The output format of the printer
5065 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5066 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
5068 In case of printing in C<ISL_FORMAT_C>, the user may want
5069 to set the names of all dimensions
5071 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
5072 __isl_take isl_qpolynomial *qp,
5073 enum isl_dim_type type, unsigned pos,
5075 __isl_give isl_pw_qpolynomial *
5076 isl_pw_qpolynomial_set_dim_name(
5077 __isl_take isl_pw_qpolynomial *pwqp,
5078 enum isl_dim_type type, unsigned pos,
5081 =head3 Creating New (Piecewise) Quasipolynomials
5083 Some simple quasipolynomials can be created using the following functions.
5084 More complicated quasipolynomials can be created by applying
5085 operations such as addition and multiplication
5086 on the resulting quasipolynomials
5088 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
5089 __isl_take isl_space *domain);
5090 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
5091 __isl_take isl_space *domain);
5092 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
5093 __isl_take isl_space *domain);
5094 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
5095 __isl_take isl_space *domain);
5096 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
5097 __isl_take isl_space *domain);
5098 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
5099 __isl_take isl_space *domain,
5100 __isl_take isl_val *val);
5101 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
5102 __isl_take isl_space *domain,
5103 enum isl_dim_type type, unsigned pos);
5104 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
5105 __isl_take isl_aff *aff);
5107 Note that the space in which a quasipolynomial lives is a map space
5108 with a one-dimensional range. The C<domain> argument in some of
5109 the functions above corresponds to the domain of this map space.
5111 The zero piecewise quasipolynomial or a piecewise quasipolynomial
5112 with a single cell can be created using the following functions.
5113 Multiple of these single cell piecewise quasipolynomials can
5114 be combined to create more complicated piecewise quasipolynomials.
5116 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
5117 __isl_take isl_space *space);
5118 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
5119 __isl_take isl_set *set,
5120 __isl_take isl_qpolynomial *qp);
5121 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
5122 __isl_take isl_qpolynomial *qp);
5123 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
5124 __isl_take isl_pw_aff *pwaff);
5126 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
5127 __isl_take isl_space *space);
5128 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
5129 __isl_take isl_pw_qpolynomial *pwqp);
5130 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
5131 __isl_take isl_union_pw_qpolynomial *upwqp,
5132 __isl_take isl_pw_qpolynomial *pwqp);
5134 Quasipolynomials can be copied and freed again using the following
5137 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
5138 __isl_keep isl_qpolynomial *qp);
5139 __isl_null isl_qpolynomial *isl_qpolynomial_free(
5140 __isl_take isl_qpolynomial *qp);
5142 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
5143 __isl_keep isl_pw_qpolynomial *pwqp);
5144 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
5145 __isl_take isl_pw_qpolynomial *pwqp);
5147 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
5148 __isl_keep isl_union_pw_qpolynomial *upwqp);
5149 __isl_null isl_union_pw_qpolynomial *
5150 isl_union_pw_qpolynomial_free(
5151 __isl_take isl_union_pw_qpolynomial *upwqp);
5153 =head3 Inspecting (Piecewise) Quasipolynomials
5155 To iterate over all piecewise quasipolynomials in a union
5156 piecewise quasipolynomial, use the following function
5158 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
5159 __isl_keep isl_union_pw_qpolynomial *upwqp,
5160 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
5163 To extract the piecewise quasipolynomial in a given space from a union, use
5165 __isl_give isl_pw_qpolynomial *
5166 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
5167 __isl_keep isl_union_pw_qpolynomial *upwqp,
5168 __isl_take isl_space *space);
5170 To iterate over the cells in a piecewise quasipolynomial,
5171 use either of the following two functions
5173 int isl_pw_qpolynomial_foreach_piece(
5174 __isl_keep isl_pw_qpolynomial *pwqp,
5175 int (*fn)(__isl_take isl_set *set,
5176 __isl_take isl_qpolynomial *qp,
5177 void *user), void *user);
5178 int isl_pw_qpolynomial_foreach_lifted_piece(
5179 __isl_keep isl_pw_qpolynomial *pwqp,
5180 int (*fn)(__isl_take isl_set *set,
5181 __isl_take isl_qpolynomial *qp,
5182 void *user), void *user);
5184 As usual, the function C<fn> should return C<0> on success
5185 and C<-1> on failure. The difference between
5186 C<isl_pw_qpolynomial_foreach_piece> and
5187 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
5188 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
5189 compute unique representations for all existentially quantified
5190 variables and then turn these existentially quantified variables
5191 into extra set variables, adapting the associated quasipolynomial
5192 accordingly. This means that the C<set> passed to C<fn>
5193 will not have any existentially quantified variables, but that
5194 the dimensions of the sets may be different for different
5195 invocations of C<fn>.
5197 The constant term of a quasipolynomial can be extracted using
5199 __isl_give isl_val *isl_qpolynomial_get_constant_val(
5200 __isl_keep isl_qpolynomial *qp);
5202 To iterate over all terms in a quasipolynomial,
5205 int isl_qpolynomial_foreach_term(
5206 __isl_keep isl_qpolynomial *qp,
5207 int (*fn)(__isl_take isl_term *term,
5208 void *user), void *user);
5210 The terms themselves can be inspected and freed using
5213 unsigned isl_term_dim(__isl_keep isl_term *term,
5214 enum isl_dim_type type);
5215 __isl_give isl_val *isl_term_get_coefficient_val(
5216 __isl_keep isl_term *term);
5217 int isl_term_get_exp(__isl_keep isl_term *term,
5218 enum isl_dim_type type, unsigned pos);
5219 __isl_give isl_aff *isl_term_get_div(
5220 __isl_keep isl_term *term, unsigned pos);
5221 void isl_term_free(__isl_take isl_term *term);
5223 Each term is a product of parameters, set variables and
5224 integer divisions. The function C<isl_term_get_exp>
5225 returns the exponent of a given dimensions in the given term.
5227 =head3 Properties of (Piecewise) Quasipolynomials
5229 To check whether two union piecewise quasipolynomials are
5230 obviously equal, use
5232 int isl_union_pw_qpolynomial_plain_is_equal(
5233 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5234 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5236 =head3 Operations on (Piecewise) Quasipolynomials
5238 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5239 __isl_take isl_qpolynomial *qp,
5240 __isl_take isl_val *v);
5241 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5242 __isl_take isl_qpolynomial *qp);
5243 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5244 __isl_take isl_qpolynomial *qp1,
5245 __isl_take isl_qpolynomial *qp2);
5246 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5247 __isl_take isl_qpolynomial *qp1,
5248 __isl_take isl_qpolynomial *qp2);
5249 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5250 __isl_take isl_qpolynomial *qp1,
5251 __isl_take isl_qpolynomial *qp2);
5252 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5253 __isl_take isl_qpolynomial *qp, unsigned exponent);
5255 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5256 __isl_take isl_pw_qpolynomial *pwqp,
5257 enum isl_dim_type type, unsigned n,
5258 __isl_take isl_val *v);
5259 __isl_give isl_pw_qpolynomial *
5260 isl_pw_qpolynomial_scale_val(
5261 __isl_take isl_pw_qpolynomial *pwqp,
5262 __isl_take isl_val *v);
5263 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5264 __isl_take isl_pw_qpolynomial *pwqp1,
5265 __isl_take isl_pw_qpolynomial *pwqp2);
5266 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5267 __isl_take isl_pw_qpolynomial *pwqp1,
5268 __isl_take isl_pw_qpolynomial *pwqp2);
5269 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5270 __isl_take isl_pw_qpolynomial *pwqp1,
5271 __isl_take isl_pw_qpolynomial *pwqp2);
5272 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5273 __isl_take isl_pw_qpolynomial *pwqp);
5274 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5275 __isl_take isl_pw_qpolynomial *pwqp1,
5276 __isl_take isl_pw_qpolynomial *pwqp2);
5277 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5278 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5280 __isl_give isl_union_pw_qpolynomial *
5281 isl_union_pw_qpolynomial_scale_val(
5282 __isl_take isl_union_pw_qpolynomial *upwqp,
5283 __isl_take isl_val *v);
5284 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5285 __isl_take isl_union_pw_qpolynomial *upwqp1,
5286 __isl_take isl_union_pw_qpolynomial *upwqp2);
5287 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
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_mul(
5291 __isl_take isl_union_pw_qpolynomial *upwqp1,
5292 __isl_take isl_union_pw_qpolynomial *upwqp2);
5294 __isl_give isl_val *isl_pw_qpolynomial_eval(
5295 __isl_take isl_pw_qpolynomial *pwqp,
5296 __isl_take isl_point *pnt);
5298 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5299 __isl_take isl_union_pw_qpolynomial *upwqp,
5300 __isl_take isl_point *pnt);
5302 __isl_give isl_set *isl_pw_qpolynomial_domain(
5303 __isl_take isl_pw_qpolynomial *pwqp);
5304 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5305 __isl_take isl_pw_qpolynomial *pwpq,
5306 __isl_take isl_set *set);
5307 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5308 __isl_take isl_pw_qpolynomial *pwpq,
5309 __isl_take isl_set *set);
5311 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5312 __isl_take isl_union_pw_qpolynomial *upwqp);
5313 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5314 __isl_take isl_union_pw_qpolynomial *upwpq,
5315 __isl_take isl_union_set *uset);
5316 __isl_give isl_union_pw_qpolynomial *
5317 isl_union_pw_qpolynomial_intersect_params(
5318 __isl_take isl_union_pw_qpolynomial *upwpq,
5319 __isl_take isl_set *set);
5321 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5322 __isl_take isl_qpolynomial *qp,
5323 __isl_take isl_space *model);
5325 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5326 __isl_take isl_qpolynomial *qp);
5327 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5328 __isl_take isl_pw_qpolynomial *pwqp);
5330 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5331 __isl_take isl_union_pw_qpolynomial *upwqp);
5333 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5334 __isl_take isl_qpolynomial *qp,
5335 __isl_take isl_set *context);
5336 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5337 __isl_take isl_qpolynomial *qp,
5338 __isl_take isl_set *context);
5340 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5341 __isl_take isl_pw_qpolynomial *pwqp,
5342 __isl_take isl_set *context);
5343 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5344 __isl_take isl_pw_qpolynomial *pwqp,
5345 __isl_take isl_set *context);
5347 __isl_give isl_union_pw_qpolynomial *
5348 isl_union_pw_qpolynomial_gist_params(
5349 __isl_take isl_union_pw_qpolynomial *upwqp,
5350 __isl_take isl_set *context);
5351 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5352 __isl_take isl_union_pw_qpolynomial *upwqp,
5353 __isl_take isl_union_set *context);
5355 The gist operation applies the gist operation to each of
5356 the cells in the domain of the input piecewise quasipolynomial.
5357 The context is also exploited
5358 to simplify the quasipolynomials associated to each cell.
5360 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5361 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5362 __isl_give isl_union_pw_qpolynomial *
5363 isl_union_pw_qpolynomial_to_polynomial(
5364 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5366 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5367 the polynomial will be an overapproximation. If C<sign> is negative,
5368 it will be an underapproximation. If C<sign> is zero, the approximation
5369 will lie somewhere in between.
5371 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5373 A piecewise quasipolynomial reduction is a piecewise
5374 reduction (or fold) of quasipolynomials.
5375 In particular, the reduction can be maximum or a minimum.
5376 The objects are mainly used to represent the result of
5377 an upper or lower bound on a quasipolynomial over its domain,
5378 i.e., as the result of the following function.
5380 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5381 __isl_take isl_pw_qpolynomial *pwqp,
5382 enum isl_fold type, int *tight);
5384 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5385 __isl_take isl_union_pw_qpolynomial *upwqp,
5386 enum isl_fold type, int *tight);
5388 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5389 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5390 is the returned bound is known be tight, i.e., for each value
5391 of the parameters there is at least
5392 one element in the domain that reaches the bound.
5393 If the domain of C<pwqp> is not wrapping, then the bound is computed
5394 over all elements in that domain and the result has a purely parametric
5395 domain. If the domain of C<pwqp> is wrapping, then the bound is
5396 computed over the range of the wrapped relation. The domain of the
5397 wrapped relation becomes the domain of the result.
5399 A (piecewise) quasipolynomial reduction can be copied or freed using the
5400 following functions.
5402 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5403 __isl_keep isl_qpolynomial_fold *fold);
5404 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5405 __isl_keep isl_pw_qpolynomial_fold *pwf);
5406 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5407 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5408 void isl_qpolynomial_fold_free(
5409 __isl_take isl_qpolynomial_fold *fold);
5410 __isl_null isl_pw_qpolynomial_fold *
5411 isl_pw_qpolynomial_fold_free(
5412 __isl_take isl_pw_qpolynomial_fold *pwf);
5413 __isl_null isl_union_pw_qpolynomial_fold *
5414 isl_union_pw_qpolynomial_fold_free(
5415 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5417 =head3 Printing Piecewise Quasipolynomial Reductions
5419 Piecewise quasipolynomial reductions can be printed
5420 using the following function.
5422 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5423 __isl_take isl_printer *p,
5424 __isl_keep isl_pw_qpolynomial_fold *pwf);
5425 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5426 __isl_take isl_printer *p,
5427 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5429 For C<isl_printer_print_pw_qpolynomial_fold>,
5430 output format of the printer
5431 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5432 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5433 output format of the printer
5434 needs to be set to C<ISL_FORMAT_ISL>.
5435 In case of printing in C<ISL_FORMAT_C>, the user may want
5436 to set the names of all dimensions
5438 __isl_give isl_pw_qpolynomial_fold *
5439 isl_pw_qpolynomial_fold_set_dim_name(
5440 __isl_take isl_pw_qpolynomial_fold *pwf,
5441 enum isl_dim_type type, unsigned pos,
5444 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5446 To iterate over all piecewise quasipolynomial reductions in a union
5447 piecewise quasipolynomial reduction, use the following function
5449 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5450 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5451 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5452 void *user), void *user);
5454 To iterate over the cells in a piecewise quasipolynomial reduction,
5455 use either of the following two functions
5457 int isl_pw_qpolynomial_fold_foreach_piece(
5458 __isl_keep isl_pw_qpolynomial_fold *pwf,
5459 int (*fn)(__isl_take isl_set *set,
5460 __isl_take isl_qpolynomial_fold *fold,
5461 void *user), void *user);
5462 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5463 __isl_keep isl_pw_qpolynomial_fold *pwf,
5464 int (*fn)(__isl_take isl_set *set,
5465 __isl_take isl_qpolynomial_fold *fold,
5466 void *user), void *user);
5468 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5469 of the difference between these two functions.
5471 To iterate over all quasipolynomials in a reduction, use
5473 int isl_qpolynomial_fold_foreach_qpolynomial(
5474 __isl_keep isl_qpolynomial_fold *fold,
5475 int (*fn)(__isl_take isl_qpolynomial *qp,
5476 void *user), void *user);
5478 =head3 Properties of Piecewise Quasipolynomial Reductions
5480 To check whether two union piecewise quasipolynomial reductions are
5481 obviously equal, use
5483 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5484 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5485 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5487 =head3 Operations on Piecewise Quasipolynomial Reductions
5489 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5490 __isl_take isl_qpolynomial_fold *fold,
5491 __isl_take isl_val *v);
5492 __isl_give isl_pw_qpolynomial_fold *
5493 isl_pw_qpolynomial_fold_scale_val(
5494 __isl_take isl_pw_qpolynomial_fold *pwf,
5495 __isl_take isl_val *v);
5496 __isl_give isl_union_pw_qpolynomial_fold *
5497 isl_union_pw_qpolynomial_fold_scale_val(
5498 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5499 __isl_take isl_val *v);
5501 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5502 __isl_take isl_pw_qpolynomial_fold *pwf1,
5503 __isl_take isl_pw_qpolynomial_fold *pwf2);
5505 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5506 __isl_take isl_pw_qpolynomial_fold *pwf1,
5507 __isl_take isl_pw_qpolynomial_fold *pwf2);
5509 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5510 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5511 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5513 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5514 __isl_take isl_pw_qpolynomial_fold *pwf,
5515 __isl_take isl_point *pnt);
5517 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5518 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5519 __isl_take isl_point *pnt);
5521 __isl_give isl_pw_qpolynomial_fold *
5522 isl_pw_qpolynomial_fold_intersect_params(
5523 __isl_take isl_pw_qpolynomial_fold *pwf,
5524 __isl_take isl_set *set);
5526 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5527 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5528 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5529 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5530 __isl_take isl_union_set *uset);
5531 __isl_give isl_union_pw_qpolynomial_fold *
5532 isl_union_pw_qpolynomial_fold_intersect_params(
5533 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5534 __isl_take isl_set *set);
5536 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5537 __isl_take isl_pw_qpolynomial_fold *pwf);
5539 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5540 __isl_take isl_pw_qpolynomial_fold *pwf);
5542 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5543 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5545 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5546 __isl_take isl_qpolynomial_fold *fold,
5547 __isl_take isl_set *context);
5548 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5549 __isl_take isl_qpolynomial_fold *fold,
5550 __isl_take isl_set *context);
5552 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5553 __isl_take isl_pw_qpolynomial_fold *pwf,
5554 __isl_take isl_set *context);
5555 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5556 __isl_take isl_pw_qpolynomial_fold *pwf,
5557 __isl_take isl_set *context);
5559 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5560 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5561 __isl_take isl_union_set *context);
5562 __isl_give isl_union_pw_qpolynomial_fold *
5563 isl_union_pw_qpolynomial_fold_gist_params(
5564 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5565 __isl_take isl_set *context);
5567 The gist operation applies the gist operation to each of
5568 the cells in the domain of the input piecewise quasipolynomial reduction.
5569 In future, the operation will also exploit the context
5570 to simplify the quasipolynomial reductions associated to each cell.
5572 __isl_give isl_pw_qpolynomial_fold *
5573 isl_set_apply_pw_qpolynomial_fold(
5574 __isl_take isl_set *set,
5575 __isl_take isl_pw_qpolynomial_fold *pwf,
5577 __isl_give isl_pw_qpolynomial_fold *
5578 isl_map_apply_pw_qpolynomial_fold(
5579 __isl_take isl_map *map,
5580 __isl_take isl_pw_qpolynomial_fold *pwf,
5582 __isl_give isl_union_pw_qpolynomial_fold *
5583 isl_union_set_apply_union_pw_qpolynomial_fold(
5584 __isl_take isl_union_set *uset,
5585 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5587 __isl_give isl_union_pw_qpolynomial_fold *
5588 isl_union_map_apply_union_pw_qpolynomial_fold(
5589 __isl_take isl_union_map *umap,
5590 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5593 The functions taking a map
5594 compose the given map with the given piecewise quasipolynomial reduction.
5595 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5596 over all elements in the intersection of the range of the map
5597 and the domain of the piecewise quasipolynomial reduction
5598 as a function of an element in the domain of the map.
5599 The functions taking a set compute a bound over all elements in the
5600 intersection of the set and the domain of the
5601 piecewise quasipolynomial reduction.
5603 =head2 Parametric Vertex Enumeration
5605 The parametric vertex enumeration described in this section
5606 is mainly intended to be used internally and by the C<barvinok>
5609 #include <isl/vertices.h>
5610 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5611 __isl_keep isl_basic_set *bset);
5613 The function C<isl_basic_set_compute_vertices> performs the
5614 actual computation of the parametric vertices and the chamber
5615 decomposition and store the result in an C<isl_vertices> object.
5616 This information can be queried by either iterating over all
5617 the vertices or iterating over all the chambers or cells
5618 and then iterating over all vertices that are active on the chamber.
5620 int isl_vertices_foreach_vertex(
5621 __isl_keep isl_vertices *vertices,
5622 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5625 int isl_vertices_foreach_cell(
5626 __isl_keep isl_vertices *vertices,
5627 int (*fn)(__isl_take isl_cell *cell, void *user),
5629 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5630 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5633 Other operations that can be performed on an C<isl_vertices> object are
5636 isl_ctx *isl_vertices_get_ctx(
5637 __isl_keep isl_vertices *vertices);
5638 int isl_vertices_get_n_vertices(
5639 __isl_keep isl_vertices *vertices);
5640 void isl_vertices_free(__isl_take isl_vertices *vertices);
5642 Vertices can be inspected and destroyed using the following functions.
5644 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5645 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5646 __isl_give isl_basic_set *isl_vertex_get_domain(
5647 __isl_keep isl_vertex *vertex);
5648 __isl_give isl_multi_aff *isl_vertex_get_expr(
5649 __isl_keep isl_vertex *vertex);
5650 void isl_vertex_free(__isl_take isl_vertex *vertex);
5652 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
5653 describing the vertex in terms of the parameters,
5654 while C<isl_vertex_get_domain> returns the activity domain
5657 Chambers can be inspected and destroyed using the following functions.
5659 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5660 __isl_give isl_basic_set *isl_cell_get_domain(
5661 __isl_keep isl_cell *cell);
5662 void isl_cell_free(__isl_take isl_cell *cell);
5664 =head1 Polyhedral Compilation Library
5666 This section collects functionality in C<isl> that has been specifically
5667 designed for use during polyhedral compilation.
5669 =head2 Dependence Analysis
5671 C<isl> contains specialized functionality for performing
5672 array dataflow analysis. That is, given a I<sink> access relation
5673 and a collection of possible I<source> access relations,
5674 C<isl> can compute relations that describe
5675 for each iteration of the sink access, which iteration
5676 of which of the source access relations was the last
5677 to access the same data element before the given iteration
5679 The resulting dependence relations map source iterations
5680 to the corresponding sink iterations.
5681 To compute standard flow dependences, the sink should be
5682 a read, while the sources should be writes.
5683 If any of the source accesses are marked as being I<may>
5684 accesses, then there will be a dependence from the last
5685 I<must> access B<and> from any I<may> access that follows
5686 this last I<must> access.
5687 In particular, if I<all> sources are I<may> accesses,
5688 then memory based dependence analysis is performed.
5689 If, on the other hand, all sources are I<must> accesses,
5690 then value based dependence analysis is performed.
5692 #include <isl/flow.h>
5694 typedef int (*isl_access_level_before)(void *first, void *second);
5696 __isl_give isl_access_info *isl_access_info_alloc(
5697 __isl_take isl_map *sink,
5698 void *sink_user, isl_access_level_before fn,
5700 __isl_give isl_access_info *isl_access_info_add_source(
5701 __isl_take isl_access_info *acc,
5702 __isl_take isl_map *source, int must,
5704 __isl_null isl_access_info *isl_access_info_free(
5705 __isl_take isl_access_info *acc);
5707 __isl_give isl_flow *isl_access_info_compute_flow(
5708 __isl_take isl_access_info *acc);
5710 int isl_flow_foreach(__isl_keep isl_flow *deps,
5711 int (*fn)(__isl_take isl_map *dep, int must,
5712 void *dep_user, void *user),
5714 __isl_give isl_map *isl_flow_get_no_source(
5715 __isl_keep isl_flow *deps, int must);
5716 void isl_flow_free(__isl_take isl_flow *deps);
5718 The function C<isl_access_info_compute_flow> performs the actual
5719 dependence analysis. The other functions are used to construct
5720 the input for this function or to read off the output.
5722 The input is collected in an C<isl_access_info>, which can
5723 be created through a call to C<isl_access_info_alloc>.
5724 The arguments to this functions are the sink access relation
5725 C<sink>, a token C<sink_user> used to identify the sink
5726 access to the user, a callback function for specifying the
5727 relative order of source and sink accesses, and the number
5728 of source access relations that will be added.
5729 The callback function has type C<int (*)(void *first, void *second)>.
5730 The function is called with two user supplied tokens identifying
5731 either a source or the sink and it should return the shared nesting
5732 level and the relative order of the two accesses.
5733 In particular, let I<n> be the number of loops shared by
5734 the two accesses. If C<first> precedes C<second> textually,
5735 then the function should return I<2 * n + 1>; otherwise,
5736 it should return I<2 * n>.
5737 The sources can be added to the C<isl_access_info> by performing
5738 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5739 C<must> indicates whether the source is a I<must> access
5740 or a I<may> access. Note that a multi-valued access relation
5741 should only be marked I<must> if every iteration in the domain
5742 of the relation accesses I<all> elements in its image.
5743 The C<source_user> token is again used to identify
5744 the source access. The range of the source access relation
5745 C<source> should have the same dimension as the range
5746 of the sink access relation.
5747 The C<isl_access_info_free> function should usually not be
5748 called explicitly, because it is called implicitly by
5749 C<isl_access_info_compute_flow>.
5751 The result of the dependence analysis is collected in an
5752 C<isl_flow>. There may be elements of
5753 the sink access for which no preceding source access could be
5754 found or for which all preceding sources are I<may> accesses.
5755 The relations containing these elements can be obtained through
5756 calls to C<isl_flow_get_no_source>, the first with C<must> set
5757 and the second with C<must> unset.
5758 In the case of standard flow dependence analysis,
5759 with the sink a read and the sources I<must> writes,
5760 the first relation corresponds to the reads from uninitialized
5761 array elements and the second relation is empty.
5762 The actual flow dependences can be extracted using
5763 C<isl_flow_foreach>. This function will call the user-specified
5764 callback function C<fn> for each B<non-empty> dependence between
5765 a source and the sink. The callback function is called
5766 with four arguments, the actual flow dependence relation
5767 mapping source iterations to sink iterations, a boolean that
5768 indicates whether it is a I<must> or I<may> dependence, a token
5769 identifying the source and an additional C<void *> with value
5770 equal to the third argument of the C<isl_flow_foreach> call.
5771 A dependence is marked I<must> if it originates from a I<must>
5772 source and if it is not followed by any I<may> sources.
5774 After finishing with an C<isl_flow>, the user should call
5775 C<isl_flow_free> to free all associated memory.
5777 A higher-level interface to dependence analysis is provided
5778 by the following function.
5780 #include <isl/flow.h>
5782 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5783 __isl_take isl_union_map *must_source,
5784 __isl_take isl_union_map *may_source,
5785 __isl_take isl_union_map *schedule,
5786 __isl_give isl_union_map **must_dep,
5787 __isl_give isl_union_map **may_dep,
5788 __isl_give isl_union_map **must_no_source,
5789 __isl_give isl_union_map **may_no_source);
5791 The arrays are identified by the tuple names of the ranges
5792 of the accesses. The iteration domains by the tuple names
5793 of the domains of the accesses and of the schedule.
5794 The relative order of the iteration domains is given by the
5795 schedule. The relations returned through C<must_no_source>
5796 and C<may_no_source> are subsets of C<sink>.
5797 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5798 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5799 any of the other arguments is treated as an error.
5801 =head3 Interaction with Dependence Analysis
5803 During the dependence analysis, we frequently need to perform
5804 the following operation. Given a relation between sink iterations
5805 and potential source iterations from a particular source domain,
5806 what is the last potential source iteration corresponding to each
5807 sink iteration. It can sometimes be convenient to adjust
5808 the set of potential source iterations before or after each such operation.
5809 The prototypical example is fuzzy array dataflow analysis,
5810 where we need to analyze if, based on data-dependent constraints,
5811 the sink iteration can ever be executed without one or more of
5812 the corresponding potential source iterations being executed.
5813 If so, we can introduce extra parameters and select an unknown
5814 but fixed source iteration from the potential source iterations.
5815 To be able to perform such manipulations, C<isl> provides the following
5818 #include <isl/flow.h>
5820 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5821 __isl_keep isl_map *source_map,
5822 __isl_keep isl_set *sink, void *source_user,
5824 __isl_give isl_access_info *isl_access_info_set_restrict(
5825 __isl_take isl_access_info *acc,
5826 isl_access_restrict fn, void *user);
5828 The function C<isl_access_info_set_restrict> should be called
5829 before calling C<isl_access_info_compute_flow> and registers a callback function
5830 that will be called any time C<isl> is about to compute the last
5831 potential source. The first argument is the (reverse) proto-dependence,
5832 mapping sink iterations to potential source iterations.
5833 The second argument represents the sink iterations for which
5834 we want to compute the last source iteration.
5835 The third argument is the token corresponding to the source
5836 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5837 The callback is expected to return a restriction on either the input or
5838 the output of the operation computing the last potential source.
5839 If the input needs to be restricted then restrictions are needed
5840 for both the source and the sink iterations. The sink iterations
5841 and the potential source iterations will be intersected with these sets.
5842 If the output needs to be restricted then only a restriction on the source
5843 iterations is required.
5844 If any error occurs, the callback should return C<NULL>.
5845 An C<isl_restriction> object can be created, freed and inspected
5846 using the following functions.
5848 #include <isl/flow.h>
5850 __isl_give isl_restriction *isl_restriction_input(
5851 __isl_take isl_set *source_restr,
5852 __isl_take isl_set *sink_restr);
5853 __isl_give isl_restriction *isl_restriction_output(
5854 __isl_take isl_set *source_restr);
5855 __isl_give isl_restriction *isl_restriction_none(
5856 __isl_take isl_map *source_map);
5857 __isl_give isl_restriction *isl_restriction_empty(
5858 __isl_take isl_map *source_map);
5859 __isl_null isl_restriction *isl_restriction_free(
5860 __isl_take isl_restriction *restr);
5861 isl_ctx *isl_restriction_get_ctx(
5862 __isl_keep isl_restriction *restr);
5864 C<isl_restriction_none> and C<isl_restriction_empty> are special
5865 cases of C<isl_restriction_input>. C<isl_restriction_none>
5866 is essentially equivalent to
5868 isl_restriction_input(isl_set_universe(
5869 isl_space_range(isl_map_get_space(source_map))),
5871 isl_space_domain(isl_map_get_space(source_map))));
5873 whereas C<isl_restriction_empty> is essentially equivalent to
5875 isl_restriction_input(isl_set_empty(
5876 isl_space_range(isl_map_get_space(source_map))),
5878 isl_space_domain(isl_map_get_space(source_map))));
5882 B<The functionality described in this section is fairly new
5883 and may be subject to change.>
5885 #include <isl/schedule.h>
5886 __isl_give isl_schedule *
5887 isl_schedule_constraints_compute_schedule(
5888 __isl_take isl_schedule_constraints *sc);
5889 __isl_null isl_schedule *isl_schedule_free(
5890 __isl_take isl_schedule *sched);
5892 The function C<isl_schedule_constraints_compute_schedule> can be
5893 used to compute a schedule that satisfy the given schedule constraints.
5894 These schedule constraints include the iteration domain for which
5895 a schedule should be computed and dependences between pairs of
5896 iterations. In particular, these dependences include
5897 I<validity> dependences and I<proximity> dependences.
5898 By default, the algorithm used to construct the schedule is similar
5899 to that of C<Pluto>.
5900 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5902 The generated schedule respects all validity dependences.
5903 That is, all dependence distances over these dependences in the
5904 scheduled space are lexicographically positive.
5905 The default algorithm tries to ensure that the dependence distances
5906 over coincidence constraints are zero and to minimize the
5907 dependence distances over proximity dependences.
5908 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5909 for groups of domains where the dependence distances over validity
5910 dependences have only non-negative values.
5911 When using Feautrier's algorithm, the coincidence and proximity constraints
5912 are only taken into account during the extension to a
5913 full-dimensional schedule.
5915 An C<isl_schedule_constraints> object can be constructed
5916 and manipulated using the following functions.
5918 #include <isl/schedule.h>
5919 __isl_give isl_schedule_constraints *
5920 isl_schedule_constraints_copy(
5921 __isl_keep isl_schedule_constraints *sc);
5922 __isl_give isl_schedule_constraints *
5923 isl_schedule_constraints_on_domain(
5924 __isl_take isl_union_set *domain);
5925 isl_ctx *isl_schedule_constraints_get_ctx(
5926 __isl_keep isl_schedule_constraints *sc);
5927 __isl_give isl_schedule_constraints *
5928 isl_schedule_constraints_set_validity(
5929 __isl_take isl_schedule_constraints *sc,
5930 __isl_take isl_union_map *validity);
5931 __isl_give isl_schedule_constraints *
5932 isl_schedule_constraints_set_coincidence(
5933 __isl_take isl_schedule_constraints *sc,
5934 __isl_take isl_union_map *coincidence);
5935 __isl_give isl_schedule_constraints *
5936 isl_schedule_constraints_set_proximity(
5937 __isl_take isl_schedule_constraints *sc,
5938 __isl_take isl_union_map *proximity);
5939 __isl_give isl_schedule_constraints *
5940 isl_schedule_constraints_set_conditional_validity(
5941 __isl_take isl_schedule_constraints *sc,
5942 __isl_take isl_union_map *condition,
5943 __isl_take isl_union_map *validity);
5944 __isl_null isl_schedule_constraints *
5945 isl_schedule_constraints_free(
5946 __isl_take isl_schedule_constraints *sc);
5948 The initial C<isl_schedule_constraints> object created by
5949 C<isl_schedule_constraints_on_domain> does not impose any constraints.
5950 That is, it has an empty set of dependences.
5951 The function C<isl_schedule_constraints_set_validity> replaces the
5952 validity dependences, mapping domain elements I<i> to domain
5953 elements that should be scheduled after I<i>.
5954 The function C<isl_schedule_constraints_set_coincidence> replaces the
5955 coincidence dependences, mapping domain elements I<i> to domain
5956 elements that should be scheduled together with I<I>, if possible.
5957 The function C<isl_schedule_constraints_set_proximity> replaces the
5958 proximity dependences, mapping domain elements I<i> to domain
5959 elements that should be scheduled either before I<I>
5960 or as early as possible after I<i>.
5962 The function C<isl_schedule_constraints_set_conditional_validity>
5963 replaces the conditional validity constraints.
5964 A conditional validity constraint is only imposed when any of the corresponding
5965 conditions is satisfied, i.e., when any of them is non-zero.
5966 That is, the scheduler ensures that within each band if the dependence
5967 distances over the condition constraints are not all zero
5968 then all corresponding conditional validity constraints are respected.
5969 A conditional validity constraint corresponds to a condition
5970 if the two are adjacent, i.e., if the domain of one relation intersect
5971 the range of the other relation.
5972 The typical use case of conditional validity constraints is
5973 to allow order constraints between live ranges to be violated
5974 as long as the live ranges themselves are local to the band.
5975 To allow more fine-grained control over which conditions correspond
5976 to which conditional validity constraints, the domains and ranges
5977 of these relations may include I<tags>. That is, the domains and
5978 ranges of those relation may themselves be wrapped relations
5979 where the iteration domain appears in the domain of those wrapped relations
5980 and the range of the wrapped relations can be arbitrarily chosen
5981 by the user. Conditions and conditional validity constraints are only
5982 considere adjacent to each other if the entire wrapped relation matches.
5983 In particular, a relation with a tag will never be considered adjacent
5984 to a relation without a tag.
5986 The following function computes a schedule directly from
5987 an iteration domain and validity and proximity dependences
5988 and is implemented in terms of the functions described above.
5989 The use of C<isl_union_set_compute_schedule> is discouraged.
5991 #include <isl/schedule.h>
5992 __isl_give isl_schedule *isl_union_set_compute_schedule(
5993 __isl_take isl_union_set *domain,
5994 __isl_take isl_union_map *validity,
5995 __isl_take isl_union_map *proximity);
5997 A mapping from the domains to the scheduled space can be obtained
5998 from an C<isl_schedule> using the following function.
6000 __isl_give isl_union_map *isl_schedule_get_map(
6001 __isl_keep isl_schedule *sched);
6003 A representation of the schedule can be printed using
6005 __isl_give isl_printer *isl_printer_print_schedule(
6006 __isl_take isl_printer *p,
6007 __isl_keep isl_schedule *schedule);
6009 A representation of the schedule as a forest of bands can be obtained
6010 using the following function.
6012 __isl_give isl_band_list *isl_schedule_get_band_forest(
6013 __isl_keep isl_schedule *schedule);
6015 The individual bands can be visited in depth-first post-order
6016 using the following function.
6018 #include <isl/schedule.h>
6019 int isl_schedule_foreach_band(
6020 __isl_keep isl_schedule *sched,
6021 int (*fn)(__isl_keep isl_band *band, void *user),
6024 The list can be manipulated as explained in L<"Lists">.
6025 The bands inside the list can be copied and freed using the following
6028 #include <isl/band.h>
6029 __isl_give isl_band *isl_band_copy(
6030 __isl_keep isl_band *band);
6031 __isl_null isl_band *isl_band_free(
6032 __isl_take isl_band *band);
6034 Each band contains zero or more scheduling dimensions.
6035 These are referred to as the members of the band.
6036 The section of the schedule that corresponds to the band is
6037 referred to as the partial schedule of the band.
6038 For those nodes that participate in a band, the outer scheduling
6039 dimensions form the prefix schedule, while the inner scheduling
6040 dimensions form the suffix schedule.
6041 That is, if we take a cut of the band forest, then the union of
6042 the concatenations of the prefix, partial and suffix schedules of
6043 each band in the cut is equal to the entire schedule (modulo
6044 some possible padding at the end with zero scheduling dimensions).
6045 The properties of a band can be inspected using the following functions.
6047 #include <isl/band.h>
6048 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
6050 int isl_band_has_children(__isl_keep isl_band *band);
6051 __isl_give isl_band_list *isl_band_get_children(
6052 __isl_keep isl_band *band);
6054 __isl_give isl_union_map *isl_band_get_prefix_schedule(
6055 __isl_keep isl_band *band);
6056 __isl_give isl_union_map *isl_band_get_partial_schedule(
6057 __isl_keep isl_band *band);
6058 __isl_give isl_union_map *isl_band_get_suffix_schedule(
6059 __isl_keep isl_band *band);
6061 int isl_band_n_member(__isl_keep isl_band *band);
6062 int isl_band_member_is_coincident(
6063 __isl_keep isl_band *band, int pos);
6065 int isl_band_list_foreach_band(
6066 __isl_keep isl_band_list *list,
6067 int (*fn)(__isl_keep isl_band *band, void *user),
6070 Note that a scheduling dimension is considered to be ``coincident''
6071 if it satisfies the coincidence constraints within its band.
6072 That is, if the dependence distances of the coincidence
6073 constraints are all zero in that direction (for fixed
6074 iterations of outer bands).
6075 Like C<isl_schedule_foreach_band>,
6076 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
6077 in depth-first post-order.
6079 A band can be tiled using the following function.
6081 #include <isl/band.h>
6082 int isl_band_tile(__isl_keep isl_band *band,
6083 __isl_take isl_vec *sizes);
6085 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
6087 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
6088 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
6090 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
6092 The C<isl_band_tile> function tiles the band using the given tile sizes
6093 inside its schedule.
6094 A new child band is created to represent the point loops and it is
6095 inserted between the modified band and its children.
6096 The C<tile_scale_tile_loops> option specifies whether the tile
6097 loops iterators should be scaled by the tile sizes.
6098 If the C<tile_shift_point_loops> option is set, then the point loops
6099 are shifted to start at zero.
6101 A band can be split into two nested bands using the following function.
6103 int isl_band_split(__isl_keep isl_band *band, int pos);
6105 The resulting outer band contains the first C<pos> dimensions of C<band>
6106 while the inner band contains the remaining dimensions.
6108 A representation of the band can be printed using
6110 #include <isl/band.h>
6111 __isl_give isl_printer *isl_printer_print_band(
6112 __isl_take isl_printer *p,
6113 __isl_keep isl_band *band);
6117 #include <isl/schedule.h>
6118 int isl_options_set_schedule_max_coefficient(
6119 isl_ctx *ctx, int val);
6120 int isl_options_get_schedule_max_coefficient(
6122 int isl_options_set_schedule_max_constant_term(
6123 isl_ctx *ctx, int val);
6124 int isl_options_get_schedule_max_constant_term(
6126 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
6127 int isl_options_get_schedule_fuse(isl_ctx *ctx);
6128 int isl_options_set_schedule_maximize_band_depth(
6129 isl_ctx *ctx, int val);
6130 int isl_options_get_schedule_maximize_band_depth(
6132 int isl_options_set_schedule_outer_coincidence(
6133 isl_ctx *ctx, int val);
6134 int isl_options_get_schedule_outer_coincidence(
6136 int isl_options_set_schedule_split_scaled(
6137 isl_ctx *ctx, int val);
6138 int isl_options_get_schedule_split_scaled(
6140 int isl_options_set_schedule_algorithm(
6141 isl_ctx *ctx, int val);
6142 int isl_options_get_schedule_algorithm(
6144 int isl_options_set_schedule_separate_components(
6145 isl_ctx *ctx, int val);
6146 int isl_options_get_schedule_separate_components(
6151 =item * schedule_max_coefficient
6153 This option enforces that the coefficients for variable and parameter
6154 dimensions in the calculated schedule are not larger than the specified value.
6155 This option can significantly increase the speed of the scheduling calculation
6156 and may also prevent fusing of unrelated dimensions. A value of -1 means that
6157 this option does not introduce bounds on the variable or parameter
6160 =item * schedule_max_constant_term
6162 This option enforces that the constant coefficients in the calculated schedule
6163 are not larger than the maximal constant term. This option can significantly
6164 increase the speed of the scheduling calculation and may also prevent fusing of
6165 unrelated dimensions. A value of -1 means that this option does not introduce
6166 bounds on the constant coefficients.
6168 =item * schedule_fuse
6170 This option controls the level of fusion.
6171 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6172 resulting schedule will be distributed as much as possible.
6173 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6174 try to fuse loops in the resulting schedule.
6176 =item * schedule_maximize_band_depth
6178 If this option is set, we do not split bands at the point
6179 where we detect splitting is necessary. Instead, we
6180 backtrack and split bands as early as possible. This
6181 reduces the number of splits and maximizes the width of
6182 the bands. Wider bands give more possibilities for tiling.
6183 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6184 then bands will be split as early as possible, even if there is no need.
6185 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6187 =item * schedule_outer_coincidence
6189 If this option is set, then we try to construct schedules
6190 where the outermost scheduling dimension in each band
6191 satisfies the coincidence constraints.
6193 =item * schedule_split_scaled
6195 If this option is set, then we try to construct schedules in which the
6196 constant term is split off from the linear part if the linear parts of
6197 the scheduling rows for all nodes in the graphs have a common non-trivial
6199 The constant term is then placed in a separate band and the linear
6202 =item * schedule_algorithm
6204 Selects the scheduling algorithm to be used.
6205 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6206 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6208 =item * schedule_separate_components
6210 If at any point the dependence graph contains any (weakly connected) components,
6211 then these components are scheduled separately.
6212 If this option is not set, then some iterations of the domains
6213 in these components may be scheduled together.
6214 If this option is set, then the components are given consecutive
6219 =head2 AST Generation
6221 This section describes the C<isl> functionality for generating
6222 ASTs that visit all the elements
6223 in a domain in an order specified by a schedule.
6224 In particular, given a C<isl_union_map>, an AST is generated
6225 that visits all the elements in the domain of the C<isl_union_map>
6226 according to the lexicographic order of the corresponding image
6227 element(s). If the range of the C<isl_union_map> consists of
6228 elements in more than one space, then each of these spaces is handled
6229 separately in an arbitrary order.
6230 It should be noted that the image elements only specify the I<order>
6231 in which the corresponding domain elements should be visited.
6232 No direct relation between the image elements and the loop iterators
6233 in the generated AST should be assumed.
6235 Each AST is generated within a build. The initial build
6236 simply specifies the constraints on the parameters (if any)
6237 and can be created, inspected, copied and freed using the following functions.
6239 #include <isl/ast_build.h>
6240 __isl_give isl_ast_build *isl_ast_build_from_context(
6241 __isl_take isl_set *set);
6242 isl_ctx *isl_ast_build_get_ctx(
6243 __isl_keep isl_ast_build *build);
6244 __isl_give isl_ast_build *isl_ast_build_copy(
6245 __isl_keep isl_ast_build *build);
6246 __isl_null isl_ast_build *isl_ast_build_free(
6247 __isl_take isl_ast_build *build);
6249 The C<set> argument is usually a parameter set with zero or more parameters.
6250 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6251 and L</"Fine-grained Control over AST Generation">.
6252 Finally, the AST itself can be constructed using the following
6255 #include <isl/ast_build.h>
6256 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6257 __isl_keep isl_ast_build *build,
6258 __isl_take isl_union_map *schedule);
6260 =head3 Inspecting the AST
6262 The basic properties of an AST node can be obtained as follows.
6264 #include <isl/ast.h>
6265 isl_ctx *isl_ast_node_get_ctx(
6266 __isl_keep isl_ast_node *node);
6267 enum isl_ast_node_type isl_ast_node_get_type(
6268 __isl_keep isl_ast_node *node);
6270 The type of an AST node is one of
6271 C<isl_ast_node_for>,
6273 C<isl_ast_node_block> or
6274 C<isl_ast_node_user>.
6275 An C<isl_ast_node_for> represents a for node.
6276 An C<isl_ast_node_if> represents an if node.
6277 An C<isl_ast_node_block> represents a compound node.
6278 An C<isl_ast_node_user> represents an expression statement.
6279 An expression statement typically corresponds to a domain element, i.e.,
6280 one of the elements that is visited by the AST.
6282 Each type of node has its own additional properties.
6284 #include <isl/ast.h>
6285 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6286 __isl_keep isl_ast_node *node);
6287 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6288 __isl_keep isl_ast_node *node);
6289 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6290 __isl_keep isl_ast_node *node);
6291 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6292 __isl_keep isl_ast_node *node);
6293 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6294 __isl_keep isl_ast_node *node);
6295 int isl_ast_node_for_is_degenerate(
6296 __isl_keep isl_ast_node *node);
6298 An C<isl_ast_for> is considered degenerate if it is known to execute
6301 #include <isl/ast.h>
6302 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6303 __isl_keep isl_ast_node *node);
6304 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6305 __isl_keep isl_ast_node *node);
6306 int isl_ast_node_if_has_else(
6307 __isl_keep isl_ast_node *node);
6308 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6309 __isl_keep isl_ast_node *node);
6311 __isl_give isl_ast_node_list *
6312 isl_ast_node_block_get_children(
6313 __isl_keep isl_ast_node *node);
6315 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6316 __isl_keep isl_ast_node *node);
6318 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6319 the following functions.
6321 #include <isl/ast.h>
6322 isl_ctx *isl_ast_expr_get_ctx(
6323 __isl_keep isl_ast_expr *expr);
6324 enum isl_ast_expr_type isl_ast_expr_get_type(
6325 __isl_keep isl_ast_expr *expr);
6327 The type of an AST expression is one of
6329 C<isl_ast_expr_id> or
6330 C<isl_ast_expr_int>.
6331 An C<isl_ast_expr_op> represents the result of an operation.
6332 An C<isl_ast_expr_id> represents an identifier.
6333 An C<isl_ast_expr_int> represents an integer value.
6335 Each type of expression has its own additional properties.
6337 #include <isl/ast.h>
6338 enum isl_ast_op_type isl_ast_expr_get_op_type(
6339 __isl_keep isl_ast_expr *expr);
6340 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6341 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6342 __isl_keep isl_ast_expr *expr, int pos);
6343 int isl_ast_node_foreach_ast_op_type(
6344 __isl_keep isl_ast_node *node,
6345 int (*fn)(enum isl_ast_op_type type, void *user),
6348 C<isl_ast_expr_get_op_type> returns the type of the operation
6349 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6350 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6352 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6353 C<isl_ast_op_type> that appears in C<node>.
6354 The operation type is one of the following.
6358 =item C<isl_ast_op_and>
6360 Logical I<and> of two arguments.
6361 Both arguments can be evaluated.
6363 =item C<isl_ast_op_and_then>
6365 Logical I<and> of two arguments.
6366 The second argument can only be evaluated if the first evaluates to true.
6368 =item C<isl_ast_op_or>
6370 Logical I<or> of two arguments.
6371 Both arguments can be evaluated.
6373 =item C<isl_ast_op_or_else>
6375 Logical I<or> of two arguments.
6376 The second argument can only be evaluated if the first evaluates to false.
6378 =item C<isl_ast_op_max>
6380 Maximum of two or more arguments.
6382 =item C<isl_ast_op_min>
6384 Minimum of two or more arguments.
6386 =item C<isl_ast_op_minus>
6390 =item C<isl_ast_op_add>
6392 Sum of two arguments.
6394 =item C<isl_ast_op_sub>
6396 Difference of two arguments.
6398 =item C<isl_ast_op_mul>
6400 Product of two arguments.
6402 =item C<isl_ast_op_div>
6404 Exact division. That is, the result is known to be an integer.
6406 =item C<isl_ast_op_fdiv_q>
6408 Result of integer division, rounded towards negative
6411 =item C<isl_ast_op_pdiv_q>
6413 Result of integer division, where dividend is known to be non-negative.
6415 =item C<isl_ast_op_pdiv_r>
6417 Remainder of integer division, where dividend is known to be non-negative.
6419 =item C<isl_ast_op_cond>
6421 Conditional operator defined on three arguments.
6422 If the first argument evaluates to true, then the result
6423 is equal to the second argument. Otherwise, the result
6424 is equal to the third argument.
6425 The second and third argument may only be evaluated if
6426 the first argument evaluates to true and false, respectively.
6427 Corresponds to C<a ? b : c> in C.
6429 =item C<isl_ast_op_select>
6431 Conditional operator defined on three arguments.
6432 If the first argument evaluates to true, then the result
6433 is equal to the second argument. Otherwise, the result
6434 is equal to the third argument.
6435 The second and third argument may be evaluated independently
6436 of the value of the first argument.
6437 Corresponds to C<a * b + (1 - a) * c> in C.
6439 =item C<isl_ast_op_eq>
6443 =item C<isl_ast_op_le>
6445 Less than or equal relation.
6447 =item C<isl_ast_op_lt>
6451 =item C<isl_ast_op_ge>
6453 Greater than or equal relation.
6455 =item C<isl_ast_op_gt>
6457 Greater than relation.
6459 =item C<isl_ast_op_call>
6462 The number of arguments of the C<isl_ast_expr> is one more than
6463 the number of arguments in the function call, the first argument
6464 representing the function being called.
6466 =item C<isl_ast_op_access>
6469 The number of arguments of the C<isl_ast_expr> is one more than
6470 the number of index expressions in the array access, the first argument
6471 representing the array being accessed.
6473 =item C<isl_ast_op_member>
6476 This operation has two arguments, a structure and the name of
6477 the member of the structure being accessed.
6481 #include <isl/ast.h>
6482 __isl_give isl_id *isl_ast_expr_get_id(
6483 __isl_keep isl_ast_expr *expr);
6485 Return the identifier represented by the AST expression.
6487 #include <isl/ast.h>
6488 __isl_give isl_val *isl_ast_expr_get_val(
6489 __isl_keep isl_ast_expr *expr);
6491 Return the integer represented by the AST expression.
6493 =head3 Properties of ASTs
6495 #include <isl/ast.h>
6496 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6497 __isl_keep isl_ast_expr *expr2);
6499 Check if two C<isl_ast_expr>s are equal to each other.
6501 =head3 Manipulating and printing the AST
6503 AST nodes can be copied and freed using the following functions.
6505 #include <isl/ast.h>
6506 __isl_give isl_ast_node *isl_ast_node_copy(
6507 __isl_keep isl_ast_node *node);
6508 __isl_null isl_ast_node *isl_ast_node_free(
6509 __isl_take isl_ast_node *node);
6511 AST expressions can be copied and freed using the following functions.
6513 #include <isl/ast.h>
6514 __isl_give isl_ast_expr *isl_ast_expr_copy(
6515 __isl_keep isl_ast_expr *expr);
6516 __isl_null isl_ast_expr *isl_ast_expr_free(
6517 __isl_take isl_ast_expr *expr);
6519 New AST expressions can be created either directly or within
6520 the context of an C<isl_ast_build>.
6522 #include <isl/ast.h>
6523 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6524 __isl_take isl_val *v);
6525 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6526 __isl_take isl_id *id);
6527 __isl_give isl_ast_expr *isl_ast_expr_neg(
6528 __isl_take isl_ast_expr *expr);
6529 __isl_give isl_ast_expr *isl_ast_expr_add(
6530 __isl_take isl_ast_expr *expr1,
6531 __isl_take isl_ast_expr *expr2);
6532 __isl_give isl_ast_expr *isl_ast_expr_sub(
6533 __isl_take isl_ast_expr *expr1,
6534 __isl_take isl_ast_expr *expr2);
6535 __isl_give isl_ast_expr *isl_ast_expr_mul(
6536 __isl_take isl_ast_expr *expr1,
6537 __isl_take isl_ast_expr *expr2);
6538 __isl_give isl_ast_expr *isl_ast_expr_div(
6539 __isl_take isl_ast_expr *expr1,
6540 __isl_take isl_ast_expr *expr2);
6541 __isl_give isl_ast_expr *isl_ast_expr_and(
6542 __isl_take isl_ast_expr *expr1,
6543 __isl_take isl_ast_expr *expr2)
6544 __isl_give isl_ast_expr *isl_ast_expr_or(
6545 __isl_take isl_ast_expr *expr1,
6546 __isl_take isl_ast_expr *expr2)
6547 __isl_give isl_ast_expr *isl_ast_expr_access(
6548 __isl_take isl_ast_expr *array,
6549 __isl_take isl_ast_expr_list *indices);
6551 #include <isl/ast_build.h>
6552 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6553 __isl_keep isl_ast_build *build,
6554 __isl_take isl_pw_aff *pa);
6555 __isl_give isl_ast_expr *
6556 isl_ast_build_access_from_pw_multi_aff(
6557 __isl_keep isl_ast_build *build,
6558 __isl_take isl_pw_multi_aff *pma);
6559 __isl_give isl_ast_expr *
6560 isl_ast_build_access_from_multi_pw_aff(
6561 __isl_keep isl_ast_build *build,
6562 __isl_take isl_multi_pw_aff *mpa);
6563 __isl_give isl_ast_expr *
6564 isl_ast_build_call_from_pw_multi_aff(
6565 __isl_keep isl_ast_build *build,
6566 __isl_take isl_pw_multi_aff *pma);
6567 __isl_give isl_ast_expr *
6568 isl_ast_build_call_from_multi_pw_aff(
6569 __isl_keep isl_ast_build *build,
6570 __isl_take isl_multi_pw_aff *mpa);
6572 The domains of C<pa>, C<mpa> and C<pma> should correspond
6573 to the schedule space of C<build>.
6574 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6575 the function being called.
6576 If the accessed space is a nested relation, then it is taken
6577 to represent an access of the member specified by the range
6578 of this nested relation of the structure specified by the domain
6579 of the nested relation.
6581 The following functions can be used to modify an C<isl_ast_expr>.
6583 #include <isl/ast.h>
6584 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6585 __isl_take isl_ast_expr *expr, int pos,
6586 __isl_take isl_ast_expr *arg);
6588 Replace the argument of C<expr> at position C<pos> by C<arg>.
6590 #include <isl/ast.h>
6591 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6592 __isl_take isl_ast_expr *expr,
6593 __isl_take isl_id_to_ast_expr *id2expr);
6595 The function C<isl_ast_expr_substitute_ids> replaces the
6596 subexpressions of C<expr> of type C<isl_ast_expr_id>
6597 by the corresponding expression in C<id2expr>, if there is any.
6600 User specified data can be attached to an C<isl_ast_node> and obtained
6601 from the same C<isl_ast_node> using the following functions.
6603 #include <isl/ast.h>
6604 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6605 __isl_take isl_ast_node *node,
6606 __isl_take isl_id *annotation);
6607 __isl_give isl_id *isl_ast_node_get_annotation(
6608 __isl_keep isl_ast_node *node);
6610 Basic printing can be performed using the following functions.
6612 #include <isl/ast.h>
6613 __isl_give isl_printer *isl_printer_print_ast_expr(
6614 __isl_take isl_printer *p,
6615 __isl_keep isl_ast_expr *expr);
6616 __isl_give isl_printer *isl_printer_print_ast_node(
6617 __isl_take isl_printer *p,
6618 __isl_keep isl_ast_node *node);
6620 More advanced printing can be performed using the following functions.
6622 #include <isl/ast.h>
6623 __isl_give isl_printer *isl_ast_op_type_print_macro(
6624 enum isl_ast_op_type type,
6625 __isl_take isl_printer *p);
6626 __isl_give isl_printer *isl_ast_node_print_macros(
6627 __isl_keep isl_ast_node *node,
6628 __isl_take isl_printer *p);
6629 __isl_give isl_printer *isl_ast_node_print(
6630 __isl_keep isl_ast_node *node,
6631 __isl_take isl_printer *p,
6632 __isl_take isl_ast_print_options *options);
6633 __isl_give isl_printer *isl_ast_node_for_print(
6634 __isl_keep isl_ast_node *node,
6635 __isl_take isl_printer *p,
6636 __isl_take isl_ast_print_options *options);
6637 __isl_give isl_printer *isl_ast_node_if_print(
6638 __isl_keep isl_ast_node *node,
6639 __isl_take isl_printer *p,
6640 __isl_take isl_ast_print_options *options);
6642 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6643 C<isl> may print out an AST that makes use of macros such
6644 as C<floord>, C<min> and C<max>.
6645 C<isl_ast_op_type_print_macro> prints out the macro
6646 corresponding to a specific C<isl_ast_op_type>.
6647 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6648 for expressions where these macros would be used and prints
6649 out the required macro definitions.
6650 Essentially, C<isl_ast_node_print_macros> calls
6651 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6652 as function argument.
6653 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6654 C<isl_ast_node_if_print> print an C<isl_ast_node>
6655 in C<ISL_FORMAT_C>, but allow for some extra control
6656 through an C<isl_ast_print_options> object.
6657 This object can be created using the following functions.
6659 #include <isl/ast.h>
6660 __isl_give isl_ast_print_options *
6661 isl_ast_print_options_alloc(isl_ctx *ctx);
6662 __isl_give isl_ast_print_options *
6663 isl_ast_print_options_copy(
6664 __isl_keep isl_ast_print_options *options);
6665 __isl_null isl_ast_print_options *
6666 isl_ast_print_options_free(
6667 __isl_take isl_ast_print_options *options);
6669 __isl_give isl_ast_print_options *
6670 isl_ast_print_options_set_print_user(
6671 __isl_take isl_ast_print_options *options,
6672 __isl_give isl_printer *(*print_user)(
6673 __isl_take isl_printer *p,
6674 __isl_take isl_ast_print_options *options,
6675 __isl_keep isl_ast_node *node, void *user),
6677 __isl_give isl_ast_print_options *
6678 isl_ast_print_options_set_print_for(
6679 __isl_take isl_ast_print_options *options,
6680 __isl_give isl_printer *(*print_for)(
6681 __isl_take isl_printer *p,
6682 __isl_take isl_ast_print_options *options,
6683 __isl_keep isl_ast_node *node, void *user),
6686 The callback set by C<isl_ast_print_options_set_print_user>
6687 is called whenever a node of type C<isl_ast_node_user> needs to
6689 The callback set by C<isl_ast_print_options_set_print_for>
6690 is called whenever a node of type C<isl_ast_node_for> needs to
6692 Note that C<isl_ast_node_for_print> will I<not> call the
6693 callback set by C<isl_ast_print_options_set_print_for> on the node
6694 on which C<isl_ast_node_for_print> is called, but only on nested
6695 nodes of type C<isl_ast_node_for>. It is therefore safe to
6696 call C<isl_ast_node_for_print> from within the callback set by
6697 C<isl_ast_print_options_set_print_for>.
6699 The following option determines the type to be used for iterators
6700 while printing the AST.
6702 int isl_options_set_ast_iterator_type(
6703 isl_ctx *ctx, const char *val);
6704 const char *isl_options_get_ast_iterator_type(
6709 #include <isl/ast_build.h>
6710 int isl_options_set_ast_build_atomic_upper_bound(
6711 isl_ctx *ctx, int val);
6712 int isl_options_get_ast_build_atomic_upper_bound(
6714 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6716 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6717 int isl_options_set_ast_build_exploit_nested_bounds(
6718 isl_ctx *ctx, int val);
6719 int isl_options_get_ast_build_exploit_nested_bounds(
6721 int isl_options_set_ast_build_group_coscheduled(
6722 isl_ctx *ctx, int val);
6723 int isl_options_get_ast_build_group_coscheduled(
6725 int isl_options_set_ast_build_scale_strides(
6726 isl_ctx *ctx, int val);
6727 int isl_options_get_ast_build_scale_strides(
6729 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6731 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6732 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6734 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6738 =item * ast_build_atomic_upper_bound
6740 Generate loop upper bounds that consist of the current loop iterator,
6741 an operator and an expression not involving the iterator.
6742 If this option is not set, then the current loop iterator may appear
6743 several times in the upper bound.
6744 For example, when this option is turned off, AST generation
6747 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6751 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6754 When the option is turned on, the following AST is generated
6756 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6759 =item * ast_build_prefer_pdiv
6761 If this option is turned off, then the AST generation will
6762 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6763 operators, but no C<isl_ast_op_pdiv_q> or
6764 C<isl_ast_op_pdiv_r> operators.
6765 If this options is turned on, then C<isl> will try to convert
6766 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6767 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6769 =item * ast_build_exploit_nested_bounds
6771 Simplify conditions based on bounds of nested for loops.
6772 In particular, remove conditions that are implied by the fact
6773 that one or more nested loops have at least one iteration,
6774 meaning that the upper bound is at least as large as the lower bound.
6775 For example, when this option is turned off, AST generation
6778 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6784 for (int c0 = 0; c0 <= N; c0 += 1)
6785 for (int c1 = 0; c1 <= M; c1 += 1)
6788 When the option is turned on, the following AST is generated
6790 for (int c0 = 0; c0 <= N; c0 += 1)
6791 for (int c1 = 0; c1 <= M; c1 += 1)
6794 =item * ast_build_group_coscheduled
6796 If two domain elements are assigned the same schedule point, then
6797 they may be executed in any order and they may even appear in different
6798 loops. If this options is set, then the AST generator will make
6799 sure that coscheduled domain elements do not appear in separate parts
6800 of the AST. This is useful in case of nested AST generation
6801 if the outer AST generation is given only part of a schedule
6802 and the inner AST generation should handle the domains that are
6803 coscheduled by this initial part of the schedule together.
6804 For example if an AST is generated for a schedule
6806 { A[i] -> [0]; B[i] -> [0] }
6808 then the C<isl_ast_build_set_create_leaf> callback described
6809 below may get called twice, once for each domain.
6810 Setting this option ensures that the callback is only called once
6811 on both domains together.
6813 =item * ast_build_separation_bounds
6815 This option specifies which bounds to use during separation.
6816 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6817 then all (possibly implicit) bounds on the current dimension will
6818 be used during separation.
6819 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6820 then only those bounds that are explicitly available will
6821 be used during separation.
6823 =item * ast_build_scale_strides
6825 This option specifies whether the AST generator is allowed
6826 to scale down iterators of strided loops.
6828 =item * ast_build_allow_else
6830 This option specifies whether the AST generator is allowed
6831 to construct if statements with else branches.
6833 =item * ast_build_allow_or
6835 This option specifies whether the AST generator is allowed
6836 to construct if conditions with disjunctions.
6840 =head3 Fine-grained Control over AST Generation
6842 Besides specifying the constraints on the parameters,
6843 an C<isl_ast_build> object can be used to control
6844 various aspects of the AST generation process.
6845 The most prominent way of control is through ``options'',
6846 which can be set using the following function.
6848 #include <isl/ast_build.h>
6849 __isl_give isl_ast_build *
6850 isl_ast_build_set_options(
6851 __isl_take isl_ast_build *control,
6852 __isl_take isl_union_map *options);
6854 The options are encoded in an <isl_union_map>.
6855 The domain of this union relation refers to the schedule domain,
6856 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6857 In the case of nested AST generation (see L</"Nested AST Generation">),
6858 the domain of C<options> should refer to the extra piece of the schedule.
6859 That is, it should be equal to the range of the wrapped relation in the
6860 range of the schedule.
6861 The range of the options can consist of elements in one or more spaces,
6862 the names of which determine the effect of the option.
6863 The values of the range typically also refer to the schedule dimension
6864 to which the option applies. In case of nested AST generation
6865 (see L</"Nested AST Generation">), these values refer to the position
6866 of the schedule dimension within the innermost AST generation.
6867 The constraints on the domain elements of
6868 the option should only refer to this dimension and earlier dimensions.
6869 We consider the following spaces.
6873 =item C<separation_class>
6875 This space is a wrapped relation between two one dimensional spaces.
6876 The input space represents the schedule dimension to which the option
6877 applies and the output space represents the separation class.
6878 While constructing a loop corresponding to the specified schedule
6879 dimension(s), the AST generator will try to generate separate loops
6880 for domain elements that are assigned different classes.
6881 If only some of the elements are assigned a class, then those elements
6882 that are not assigned any class will be treated as belonging to a class
6883 that is separate from the explicitly assigned classes.
6884 The typical use case for this option is to separate full tiles from
6886 The other options, described below, are applied after the separation
6889 As an example, consider the separation into full and partial tiles
6890 of a tiling of a triangular domain.
6891 Take, for example, the domain
6893 { A[i,j] : 0 <= i,j and i + j <= 100 }
6895 and a tiling into tiles of 10 by 10. The input to the AST generator
6896 is then the schedule
6898 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6901 Without any options, the following AST is generated
6903 for (int c0 = 0; c0 <= 10; c0 += 1)
6904 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6905 for (int c2 = 10 * c0;
6906 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6908 for (int c3 = 10 * c1;
6909 c3 <= min(10 * c1 + 9, -c2 + 100);
6913 Separation into full and partial tiles can be obtained by assigning
6914 a class, say C<0>, to the full tiles. The full tiles are represented by those
6915 values of the first and second schedule dimensions for which there are
6916 values of the third and fourth dimensions to cover an entire tile.
6917 That is, we need to specify the following option
6919 { [a,b,c,d] -> separation_class[[0]->[0]] :
6920 exists b': 0 <= 10a,10b' and
6921 10a+9+10b'+9 <= 100;
6922 [a,b,c,d] -> separation_class[[1]->[0]] :
6923 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6927 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6928 a >= 0 and b >= 0 and b <= 8 - a;
6929 [a, b, c, d] -> separation_class[[0] -> [0]] :
6932 With this option, the generated AST is as follows
6935 for (int c0 = 0; c0 <= 8; c0 += 1) {
6936 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6937 for (int c2 = 10 * c0;
6938 c2 <= 10 * c0 + 9; c2 += 1)
6939 for (int c3 = 10 * c1;
6940 c3 <= 10 * c1 + 9; c3 += 1)
6942 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6943 for (int c2 = 10 * c0;
6944 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6946 for (int c3 = 10 * c1;
6947 c3 <= min(-c2 + 100, 10 * c1 + 9);
6951 for (int c0 = 9; c0 <= 10; c0 += 1)
6952 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6953 for (int c2 = 10 * c0;
6954 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6956 for (int c3 = 10 * c1;
6957 c3 <= min(10 * c1 + 9, -c2 + 100);
6964 This is a single-dimensional space representing the schedule dimension(s)
6965 to which ``separation'' should be applied. Separation tries to split
6966 a loop into several pieces if this can avoid the generation of guards
6968 See also the C<atomic> option.
6972 This is a single-dimensional space representing the schedule dimension(s)
6973 for which the domains should be considered ``atomic''. That is, the
6974 AST generator will make sure that any given domain space will only appear
6975 in a single loop at the specified level.
6977 Consider the following schedule
6979 { a[i] -> [i] : 0 <= i < 10;
6980 b[i] -> [i+1] : 0 <= i < 10 }
6982 If the following option is specified
6984 { [i] -> separate[x] }
6986 then the following AST will be generated
6990 for (int c0 = 1; c0 <= 9; c0 += 1) {
6997 If, on the other hand, the following option is specified
6999 { [i] -> atomic[x] }
7001 then the following AST will be generated
7003 for (int c0 = 0; c0 <= 10; c0 += 1) {
7010 If neither C<atomic> nor C<separate> is specified, then the AST generator
7011 may produce either of these two results or some intermediate form.
7015 This is a single-dimensional space representing the schedule dimension(s)
7016 that should be I<completely> unrolled.
7017 To obtain a partial unrolling, the user should apply an additional
7018 strip-mining to the schedule and fully unroll the inner loop.
7022 Additional control is available through the following functions.
7024 #include <isl/ast_build.h>
7025 __isl_give isl_ast_build *
7026 isl_ast_build_set_iterators(
7027 __isl_take isl_ast_build *control,
7028 __isl_take isl_id_list *iterators);
7030 The function C<isl_ast_build_set_iterators> allows the user to
7031 specify a list of iterator C<isl_id>s to be used as iterators.
7032 If the input schedule is injective, then
7033 the number of elements in this list should be as large as the dimension
7034 of the schedule space, but no direct correspondence should be assumed
7035 between dimensions and elements.
7036 If the input schedule is not injective, then an additional number
7037 of C<isl_id>s equal to the largest dimension of the input domains
7039 If the number of provided C<isl_id>s is insufficient, then additional
7040 names are automatically generated.
7042 #include <isl/ast_build.h>
7043 __isl_give isl_ast_build *
7044 isl_ast_build_set_create_leaf(
7045 __isl_take isl_ast_build *control,
7046 __isl_give isl_ast_node *(*fn)(
7047 __isl_take isl_ast_build *build,
7048 void *user), void *user);
7051 C<isl_ast_build_set_create_leaf> function allows for the
7052 specification of a callback that should be called whenever the AST
7053 generator arrives at an element of the schedule domain.
7054 The callback should return an AST node that should be inserted
7055 at the corresponding position of the AST. The default action (when
7056 the callback is not set) is to continue generating parts of the AST to scan
7057 all the domain elements associated to the schedule domain element
7058 and to insert user nodes, ``calling'' the domain element, for each of them.
7059 The C<build> argument contains the current state of the C<isl_ast_build>.
7060 To ease nested AST generation (see L</"Nested AST Generation">),
7061 all control information that is
7062 specific to the current AST generation such as the options and
7063 the callbacks has been removed from this C<isl_ast_build>.
7064 The callback would typically return the result of a nested
7066 user defined node created using the following function.
7068 #include <isl/ast.h>
7069 __isl_give isl_ast_node *isl_ast_node_alloc_user(
7070 __isl_take isl_ast_expr *expr);
7072 #include <isl/ast_build.h>
7073 __isl_give isl_ast_build *
7074 isl_ast_build_set_at_each_domain(
7075 __isl_take isl_ast_build *build,
7076 __isl_give isl_ast_node *(*fn)(
7077 __isl_take isl_ast_node *node,
7078 __isl_keep isl_ast_build *build,
7079 void *user), void *user);
7080 __isl_give isl_ast_build *
7081 isl_ast_build_set_before_each_for(
7082 __isl_take isl_ast_build *build,
7083 __isl_give isl_id *(*fn)(
7084 __isl_keep isl_ast_build *build,
7085 void *user), void *user);
7086 __isl_give isl_ast_build *
7087 isl_ast_build_set_after_each_for(
7088 __isl_take isl_ast_build *build,
7089 __isl_give isl_ast_node *(*fn)(
7090 __isl_take isl_ast_node *node,
7091 __isl_keep isl_ast_build *build,
7092 void *user), void *user);
7094 The callback set by C<isl_ast_build_set_at_each_domain> will
7095 be called for each domain AST node.
7096 The callbacks set by C<isl_ast_build_set_before_each_for>
7097 and C<isl_ast_build_set_after_each_for> will be called
7098 for each for AST node. The first will be called in depth-first
7099 pre-order, while the second will be called in depth-first post-order.
7100 Since C<isl_ast_build_set_before_each_for> is called before the for
7101 node is actually constructed, it is only passed an C<isl_ast_build>.
7102 The returned C<isl_id> will be added as an annotation (using
7103 C<isl_ast_node_set_annotation>) to the constructed for node.
7104 In particular, if the user has also specified an C<after_each_for>
7105 callback, then the annotation can be retrieved from the node passed to
7106 that callback using C<isl_ast_node_get_annotation>.
7107 All callbacks should C<NULL> on failure.
7108 The given C<isl_ast_build> can be used to create new
7109 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
7110 or C<isl_ast_build_call_from_pw_multi_aff>.
7112 =head3 Nested AST Generation
7114 C<isl> allows the user to create an AST within the context
7115 of another AST. These nested ASTs are created using the
7116 same C<isl_ast_build_ast_from_schedule> function that is used to create the
7117 outer AST. The C<build> argument should be an C<isl_ast_build>
7118 passed to a callback set by
7119 C<isl_ast_build_set_create_leaf>.
7120 The space of the range of the C<schedule> argument should refer
7121 to this build. In particular, the space should be a wrapped
7122 relation and the domain of this wrapped relation should be the
7123 same as that of the range of the schedule returned by
7124 C<isl_ast_build_get_schedule> below.
7125 In practice, the new schedule is typically
7126 created by calling C<isl_union_map_range_product> on the old schedule
7127 and some extra piece of the schedule.
7128 The space of the schedule domain is also available from
7129 the C<isl_ast_build>.
7131 #include <isl/ast_build.h>
7132 __isl_give isl_union_map *isl_ast_build_get_schedule(
7133 __isl_keep isl_ast_build *build);
7134 __isl_give isl_space *isl_ast_build_get_schedule_space(
7135 __isl_keep isl_ast_build *build);
7136 __isl_give isl_ast_build *isl_ast_build_restrict(
7137 __isl_take isl_ast_build *build,
7138 __isl_take isl_set *set);
7140 The C<isl_ast_build_get_schedule> function returns a (partial)
7141 schedule for the domains elements for which part of the AST still needs to
7142 be generated in the current build.
7143 In particular, the domain elements are mapped to those iterations of the loops
7144 enclosing the current point of the AST generation inside which
7145 the domain elements are executed.
7146 No direct correspondence between
7147 the input schedule and this schedule should be assumed.
7148 The space obtained from C<isl_ast_build_get_schedule_space> can be used
7149 to create a set for C<isl_ast_build_restrict> to intersect
7150 with the current build. In particular, the set passed to
7151 C<isl_ast_build_restrict> can have additional parameters.
7152 The ids of the set dimensions in the space returned by
7153 C<isl_ast_build_get_schedule_space> correspond to the
7154 iterators of the already generated loops.
7155 The user should not rely on the ids of the output dimensions
7156 of the relations in the union relation returned by
7157 C<isl_ast_build_get_schedule> having any particular value.
7161 Although C<isl> is mainly meant to be used as a library,
7162 it also contains some basic applications that use some
7163 of the functionality of C<isl>.
7164 The input may be specified in either the L<isl format>
7165 or the L<PolyLib format>.
7167 =head2 C<isl_polyhedron_sample>
7169 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7170 an integer element of the polyhedron, if there is any.
7171 The first column in the output is the denominator and is always
7172 equal to 1. If the polyhedron contains no integer points,
7173 then a vector of length zero is printed.
7177 C<isl_pip> takes the same input as the C<example> program
7178 from the C<piplib> distribution, i.e., a set of constraints
7179 on the parameters, a line containing only -1 and finally a set
7180 of constraints on a parametric polyhedron.
7181 The coefficients of the parameters appear in the last columns
7182 (but before the final constant column).
7183 The output is the lexicographic minimum of the parametric polyhedron.
7184 As C<isl> currently does not have its own output format, the output
7185 is just a dump of the internal state.
7187 =head2 C<isl_polyhedron_minimize>
7189 C<isl_polyhedron_minimize> computes the minimum of some linear
7190 or affine objective function over the integer points in a polyhedron.
7191 If an affine objective function
7192 is given, then the constant should appear in the last column.
7194 =head2 C<isl_polytope_scan>
7196 Given a polytope, C<isl_polytope_scan> prints
7197 all integer points in the polytope.
7199 =head2 C<isl_codegen>
7201 Given a schedule, a context set and an options relation,
7202 C<isl_codegen> prints out an AST that scans the domain elements
7203 of the schedule in the order of their image(s) taking into account
7204 the constraints in the context set.